* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Super-Resolution Fluorescence Microscopy by Structured Light
Silicon photonics wikipedia , lookup
Nonimaging optics wikipedia , lookup
Thomas Young (scientist) wikipedia , lookup
Night vision device wikipedia , lookup
Fourier optics wikipedia , lookup
Gaseous detection device wikipedia , lookup
X-ray fluorescence wikipedia , lookup
Diffraction topography wikipedia , lookup
Ellipsometry wikipedia , lookup
Retroreflector wikipedia , lookup
Preclinical imaging wikipedia , lookup
Surface plasmon resonance microscopy wikipedia , lookup
Ultraviolet–visible spectroscopy wikipedia , lookup
Phase-contrast X-ray imaging wikipedia , lookup
Vibrational analysis with scanning probe microscopy wikipedia , lookup
Ultrafast laser spectroscopy wikipedia , lookup
3D optical data storage wikipedia , lookup
Optical aberration wikipedia , lookup
Magnetic circular dichroism wikipedia , lookup
Fluorescence correlation spectroscopy wikipedia , lookup
Chemical imaging wikipedia , lookup
Photon scanning microscopy wikipedia , lookup
Optical tweezers wikipedia , lookup
Nonlinear optics wikipedia , lookup
Optical coherence tomography wikipedia , lookup
Harold Hopkins (physicist) wikipedia , lookup
DISS. ETH No. 13916 Super-Resolution Fluorescence Microscopy by Structured Light Illumination Dissertation submitted to the SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH for the of degree Doctor of Technical Sciences presented by Jan Tillman Frohn Dipl. Phys. born February 28, citizen of accepted 1971 Germany recommendation of on Prof. Dr. A. Prof. Dr. H. J. Stemmer, Tiziani, Zurich, 2000 examiner co-examiner Acknowledgments The research work period presented from fall 1997 to fall 2000 in the Institute of Robotics. It at the in this thesis has been carried out in the I wish to thank my advisor Prof. who introduced croscopy Nanotechnology Group embedded in the by me to the idea of structured of his young and at the poly project NANO-II Technische Hochschule Zürich". "Eidgenössische Firstly was light dynamic increasing illumination. group Dr. Andreas Stemmer the resolution of The mi¬ inspiring atmosphere essential for the was light success of my work. Furthermore, taking I am very grateful to Prof. Dr. the role of co-advisor of my thesis and for H. J. Tiziani for enlightening discus¬ sions. Special thanks are due to Jakob Zbaeren who showed thetic aspect of fluorescence scientific me beyond an es¬ the pure one. I very much me microscopy which goes appreciate the support of Helmut Knapp who thousands of useful hints and Last but not least, Nanotechnology Group I want to thank my likeable for gave tips. sharing joys Ill and colleagues struggles with me. in the IV Contents Abstract IX Kurzfassung XI Definition of terms 1 XIII Mathematical conventions XIII Abbreviations XVI Introduction 1.1 Historical outline 1 Resolution enhancement 1.1.1 2 Summary 3 Theory by harmonic excitation of the method 4 7 13 3.1 The 3.2 Fluorescence 3.3 1 microscope as linear shift invariant (LSI) system 13 17 3.2.1 Fluorescence 3.2.2 Dye-saturation Harmonic excitation 3.3.1 Interference 3.3.2 Image 3.3.3 OTF polarization 21 23 light microscopy (HELM) generating apparatus reconstruction design ... 24 24 32 36 V VI 4 5 CONTENTS The HELM setup 41 4.1 General considerations 41 4.2 The beam 43 splitting unit 4.2.1 Illumination spot size 45 4.2.2 The piezo 46 4.2.3 The coupling actuator unit 48 4.3 The overall system 50 4.4 System stability 52 Results 5.1 5.1.1 5.2 55 Achievable resolution by HELM 55 Discussion 56 Measuring biological samples 61 5.2.1 Materials and Methods 61 5.2.2 Discussion 62 the OTF 5.3 Measuring 5.4 Determination of 70 geometric parameters of illumination mesh 5.5 6 72 Influence of defocus on HELM 77 Three-dimensional HELM 6.1 The limitation of 6.2 Approaches 79 optical sectioning microscopy ... enhancement 6.2.1 6.2.2 82 The confocal Image Computational 6.2.4 Standing wave microscopy 84 84 excitation methods 85 harmonic excitation 85 3D-OTF extension 6.4 A three-dimensional HELM setup by (I2M) methods 6.3 6.5 82 microscope interference 6.2.3 6.4.1 80 for axial resolution 87 Two-beam interference 88 the incident beam vectors 6.4.2 Choosing 6.4.3 A setup with minimal number of DOF Simulation results 89 .... 90 92 CONTENTS 6.6 7 VII Conclusion 95 Conclusion 101 APPENDIX A Optical trapping 105 in interference fields 105 A.l Physical background 107 A.2 The setup for 109 A.3 Results 113 References 117 Curriculum Vitae 127 optical trapping VIII CONTENTS Abstract Optical many far-field microscopes disciplines with sample preparation of lying physics derstood. image essential tools for are in science and engineering. They high imaging speed. Furthermore, formation in light microscopes Therefore, image interpretation particularly in additionally takes investigations is much scanning probe techniques. advantage of very deeply are more the under¬ applications Unfortunately, ited by Fluorescence microscopy specifically staining individual imately During distinguished 240 nm the last in case decade, hance the resolution of the confocal a optical far-field instruments is lim¬ criterion. It of green light predicts that two points and oil-immersion objectives. various efforts have been undertaken to optical microscopes. The most is the confocal diffraction limited microscope large if their lateral distance falls below approx¬ light microscopy vancement in By scanning biology Rayleigh a and medicine. the resolution of the well known cannot be in un¬ evident than components of the object. Today, fluorescence microscopy has number of in combine convenient and, in en¬ ad¬ scanning microscope. light spot through the increases the lateral resolution 1.5 under ideal conditions common addition, drastically by specimen, a factor of enhances the optical sectioning capability. In this copy thesis, (HELM) a method called harmonic excitation is described which allows lateral resolution in fluorescence one to more light micros¬ than double the microscopy by illuminating the IX spec- ABSTRACT X imen with cessing mesh-like interference pattern and electronic postpro¬ a of the images. The employed interference pattern full field of view and recorded are by a camera. images for different positions of the From these five images, additional information not accessible in conventional fluorescence be extracted by A setup plane of alized. a an fore, a HELM factor of harmonic of artificial patterns in the object as biological samples resolution of approx. optical than 1.5 excitation well as outperforms even more true a can interference of laser beams has been microscope by Images microscopy algebraic approach. producing HELM achieves the covers be shifted in two dimensions relative to the actuators. Five specimen by piezo pattern can the lateral resolving and, additionally, 100 re¬ show that nm. There¬ power of CFM avoids by disadvantages of scanning methods. A further part of the thesis deals with tension of HELM. a three-dimensional three-dimensional ex¬ Basically, possible by imaging stepping the focus through the object and acquiring a stack of twodimensional tional as numeric achieve axially. are well as confocal simulations, an a the axial microscopes resolving power of is far below the lateral conven¬ one. By three-dimensional HELM device is shown to unrivaled resolution of approx. 100 Since the system nm laterally as well as requirements for three-dimensional HELM similar to those of confocal tems could become a However, images. is commercial point a superior of view. devices, it is expected that such sys¬ alternative to confocal ones, even from Kurzfassung sind unerlässliche Optische Fernfeldmikroskope in vielen Gebieten suchungen von für Unter¬ Werkzeuge und Technik. Forschung Sie kom¬ Abbildungsgeschwin¬ Probenpräparation digkeit. Außerdem sind die physikalischen Grundlagen der Bildent¬ binieren einfache mit hoher in Fernfeldmikroskopen gut verstanden. Das macht die Bild¬ interpretation wesentlich einfacher als beispielsweise bei Rasterson¬ stehung denverfahren. Darüberhinaus einzelne Komponenten Auf Grund dieser trum in Biologie Eigenschaft von grünem te nicht unterschieden kleiner als sind viele vermögen ungefähr werden 240 von nm können, wird. unternommen optischen Mikroskopen abgerastert wird, von maximal Fernfeldmikro¬ Es besagt, zwei Punk¬ ihr seitlicher Abstand worden, zu die Probe mit einem Mikroskop optischen wenn ist das konfokale auflösung Anwendungsspek¬ Während des letzten Jahrzehnts fokalen einen Faktor anzufärben. Olimmersionsobjektiven Weiterentwicklung Lichtfleck Spezifität Rayleighkriterium begrenzt. Licht und Anstrengungen von Fluoreszenzmikroskopie, besitzt sie ein breites Auflösungsvermögen durch das bekannte daß im Fall die und Medizin. Leider ist das skopen ermöglicht der Probe mit hoher um erhöhen. Mikroskop. das Auflösungs¬ Die bekannteste Indem beim kon¬ beugungsbegrenzt kann einerseits die seitliche kleinen Auflösung um 1.5 erhöht und andererseits die Tiefen¬ drastisch verbessert werden. In dieser Arbeit wird eine Methode, genannt XI "harmonie excita- KURZFASSUNG XII light microscopy" (HELM), beschrieben, tion seitliche peln, Auflösung indem die Probe mit einem leuchtet wird und die Bilder anschließend Piezostellgliedern zweidimensional verschoben werden. mit einem Fluoreszenzmikroskopie algebraischen Ansatz beweisen, daß HELM eine erreicht. von aufgenom¬ welches System aufgebaut, optische Auflösung immer noch von von um Laser¬ biologischen ungefähr Auflösungs¬ übertrifft HELM das seitliche Folglich vermögen des konfokalen Mikroskops nm Probe zugänglich wären, sowohl künstlichen als auch von zur Objektinformationen, nicht mittels Interferenz Beleuchtungsmuster strahlen erzeugt. Bilder 100 wei¬ rekonstruiert werden. Im Rahmen dieser Arbeit wurde ein Proben relativ des Musters werden mit einer CCD-Kamera ortsharmonische digital Fünf Bilder für verschiedene Aus diesen Bildern können zusätzliche welche mit normaler die zu Das Interferenzmuster deckt das volle Ge¬ sichtsfeld ab und kann mittels Stellungen ermöglicht, es mehr als verdop¬ gitterartigen Interferenzmuster be¬ aufgenommenen terverarbeitet werden. men. die Fluoreszenzmikroskopen von einen Faktor mehr als 1.5 und vermeidet außerdem die Nachteile von rastern- den Verfahren. Ein weiterer Teil der Arbeit sionalen ale Erweiterung Mikroskopie möglich, sionalen Bildern indem aufnimmt, Probe wandern lässt. beschäftigt man während Allerdings einen man daß das Auflösung anforderungen skope ähneln, eine von bleibt die axiale Auflösung Mikroskops ungefähr 100 nm beträgt. denjenigen überlegene zeigen, zum konfokalen Gesichtspunkten. Da die System¬ für konfokale Mikro¬ wird erwartet, daß ein dreidimensionales auch unter kommerziellen sowohl deutlich hin¬ eines dreidimensionalen HELM-Aufbaus für ein solches Gerät Alternative zweidimen¬ zurück. Numerische Simulationen Auflösungsvermögen sowohl seitlich als auch axial Stapel den Fokus axial durch die des konventionellen als auch des konfokalen ter der seitlichen sich mit einer dreidimen¬ HELM. Grundsätzlich ist dreidimension¬ von HELM-System Mikroskop sein könnte, Definition of terms Mathematical conventions A boldface variable scalar product r denotes a rs The modulus of strokes and is n-dimensional vector of two vectors is defined a = (!) y rt s. J2r*s*- (generally complex) = vector is denoted by vertical £>,<, \.= where the asterix denotes the the fraktur letter 3(/)(k)= The inverse transform is ÎTV)(r) = (2) i complex conjugate. The n-dimensional Fourier transform of by The given by |v| denoted (ri,... ,rn). by $ a and is defined function / : Rn —> C is by ff(r)e^dr1...drn. (3) given by (2^T / /(k) XIII e-rk *i • • • <**»• (4) XIV DEFINITION OF TERMS The two- and three-dimensional space is of particular context of this work. The letters x, y coordinates in two- three-dimensional real space, letters kx,ky dimensional or or kx,ky,kz reciprocal or x, y, interest in the denote the Cartesian z respectively. denote the coordinates in two- respectively space, two- and three-dimensional Fourier . transform, As a or The three- notation for the the tilde ~ is used as well: oo oo f f f(kx,ky):=d(f)(kx,ky)= The n-dimensional convolution defined f(x,y)e«k*x+kyyîdxdy. (denoted by the (5) symbol <C^) is by < /, 9 > (r) / /(s) g{r -a)dsx... dsn. = The n-dimensional correlation (denoted by the symbol <>) (6) is defined by <f,g>(r)= With these definitions, ff(a)g*(a-T)dSl...dsn. the following basic Fourier theorems (7) are obtained: Convolution theorem: 3(«/, 2 »)=£(/)£(</) (8) Autocorrelation theorem: 3(//*)=(2^<3(/), 3(/)>- ^ MATHEMATICAL CONVENTIONS Scaling For XV Theorem: g(r) = /(or) the following $(g)W = relation holds: -$(/)(-) a \a J (10) Translation theorem: For g(jc) = /(r — a) the following relation holds: 3(«7)(k)=3(/)(k)e»k Dirac's delta distribution (H) representation: *(r"z):=(2^/e'k(r"')dfcl"A (12) fulfills /(r)= [ f(s)S(r-s)dSl...dsn for any continuous function /. (13) XVI DEFINITION OF TERMS Abbreviations 2D two-dimensional 3D three-dimensional AFM ASWFM Atomic force Axial microscope standing wave fluorescence CFM Confocal fluorescence DNA Deoxyribonucleic DOF Degree Electron FM Fluorescence HRP acid of freedom EM HELM microscope microscope microscope microscopy Harmonic excitation Horseradish light microscopy peroxidase I2M Image interference microscopy I5 M Image interference microscopy with incoherent interference illumination LSI LSWFM NA Linear shift invariant Lateral standing wave fluorescence OSM Optical sectioning microscopy OTF Optical PSF SNOM SNR TIR microscope Numerical aperture Point transfer function spread Scanning function near-field Signal-to-noise optical microscope ratio Total internal reflection Chapter 1 Introduction 1.1 Historical outline Today's human by employing One knowledge in natural sciences could important class of such the word microscope was instruments used for a length scale not directly a ufacturing microscopes was underlying physical principles understanding man¬ microscopes were Ernst Abbe were not investigated wave image formation development, however, imaging satisfactorily out of scope of Gauß's framework of of in op¬ by Carl Friedrich Gauß who geometric optics. These geometric optics formed the basis for instrument effects and achieved in 1840 established fundamentals of erties of The his¬ close interweavement between progresses. A first milestone for the tical a it variety of physical properties accessible to the human eye. tory of microscopy is characterized by scientific advancements in the perceptivity. microscopes. Originally optical magnifiers but, today, denotes instruments which visualize on are be achieved only technical instruments to extend the human the ray-optical imaging description of light 1 understood process in and found as treatment. a a prop¬ diffraction In microscope 1872, in the simple relationship CHAPTER 1 2 between achievable resolution and His investigations whose resolution approximates the limit employed light lens in the realization of glass manufacturing permitted of of the wavelength with advancements together INTRODUCTION grinding optical the imposed by microscopes nature wave light In 1924, De Broglie studied the properties of electron beams and found out that these (EM) 1986) 1936, be described can Prom that point, the idea of length evident was and M F In fact, eight microscopes with very short as waves building wave¬ electron microscope an years later E Ruska (Nobel Price Knoll realized the first EM using magnetic lenses Krause could demonstrate ter than 100 nm EM with an the and, thus, outperform Technical advancements in power of resolving EM gle deoxyribonucleic design made it optical possible (T Komoda, 1966) and to observe (DNA) molecules (J Dubochet, 1970) acid the sixties, the scanning electron microscope became sible and could extend the three-dimensional Optical applicability microscopes, incompatible ration is however, new with living were specimens dehydrated Secondly, required and, thirdly, the specimen technically sin¬ In fea¬ of EMs to surface imaging of objects still essential due to several herent drawbacks of electron microscopy must be In resolution of bet¬ a to achieve atomic resolution is and as First, the object under observation relatively complicated sample a the radiation dose sometimes The first restriction, however, in¬ the majority of EMs can be prepa¬ destroys overcome by the environmental scanning electron microscopes at the expense of a lower resolution In the eighties, actions between one was neling [10] a a variety of scanning the scanning tunneling current between In the following a In 1984, and the The first sample emerged microscope which measures the tun¬ metallic tip and the surface of the specimen years, measured using scanning microscopes using short range inter¬ probe the probe the scanning near-field physical properties microscopes optical were that could be strongly microscope extended (SNOM) was in- HISTORICAL OUTLINE 1 1 3 vented which enables measurement of restricted by the force microscope (AFM) light [66] developed was without optical properties propagation of wave which In 1986, the force measures teraction between tip and sample [9] Scanning probe based interactions (e on physical various [46], surements [59]) lateral force measurements it could be demonstrated that the scanning in aqueous environments However, probe scanning more, the the local into object as approach least, to images influenced are the scanning overcome some electron microscopy are today applicability tions of light specimens with have become specific a probe microscopes, Many problems systems to image microscopy high 1For an [60, 75, 13] overview was By article were to further extend the found in for investiga¬ biological (FM) is capable specimens as localizing DNA living scanning [82] can techniques1 sequences [25] or cells and have successfully [16] optical the invention of the confocal scanning see re¬ of selec¬ dyes An important improvement concerning the resolution of croscope [79] Advanced fluorescence standard tool for far-field microscopes A resolution with sufficient components of the molecules capability are microscopy particularly perform immunological investigations [58, 72] proven their microscopes cannot light attempts Fluorescence microscopy imaging individual be bound to variety of phys¬ [80] of far-field chemical contrast a Further¬ complicated restricted to surfaces is probe techniques incitements for several biological often by disad¬ comparison to of these limitations search require microscopes that combine tively common in is probe The drawbacks of electron and scanning and some very slow are its imaging process which combine scanning or [76] interactions Last but not an promising tip-sample and function probe techniques microscopes share interpretation of scanning probe ical effects mea¬ developed were in¬ microscopes potential far-field microscopes due to the mechanical scanning optical see well One is, that these methods vantages as as surface g being the atomic a focused laser beam through mi¬ the CHAPTER 1. 4 overcame Abbe's century old significantly increase the three- specimen, these types of microscopes limit by factor of 1.5 and could a dimensional become an The imaging capabilities. Today essential tool for high INTRODUCTION the confocal in cell investigations microscope has biology. intensities of the focused laser beam in the confocal microscope enabled the development of methods for resolution hancement based [22, 41] or on non-linear effects such stimulated-emission number of suitable as two-photon absorption depletion [50]. dyes, however, en¬ Due to the restricted non-linear methods are not yet rou¬ tinely employed. Another approach to increase the resolution does not affect the image formation but the image interpretation. By electronic post¬ processing of images produced by conventional a croscopes, knowledge prion methods a significantly are problem about the sensitive sample mi¬ a these images, specifically posing microscopy. Resolution enhancement 1.1.1 light be achieved if can [19, 21]. However, present noise in the against in fluorescence is confocal or enhanced resolution by harmonic exci¬ tation Since Ernst Abbe's works, produce Airy patterns common as points what made. the amounts to A frequency sively more as 27%. The the contrast dip is the well known This radius is de¬ for two universal definition for resolution spectral just resolved Rayleigh criterion, however, assumptions about the observable domain. From the transfers The most two self-luminous ring of the Airy pattern. Rayleigh distance; arbitrary light microscopes known to are (see Fig. 1.1). to radius of the first dark as light microscopes sources According Rayleigh, points just resolved if their lateral separation equals the criterion. considered noted point definition for resolution of Rayleigh are far-field from object spectrum, components within a can the is contrast some¬ dip are be obtained in microscope exclu¬ bounded region, called HISTORICAL OUTLINE 1 1 Figure Image produced by 1 1 the separated by the passband reasonable a Rayleigh the extent of the HELM is (l fact that The disciplines heterodyne conversion signals can are is more In (HELM), brought described in this by employing The patterns is 2 key idea of communications engineering and principle in passband microscopes than doubled excitation in light is known Basically, frequency be shifted with harmonic functions object spectrum the extent of the microscopy widespread practice a many other or light passband sinusoidal) e Thus, for the resolution of measure sources (incoherent imaging) of the microscope space harmonic microscope for two point light a distance In harmonic excitation thesis, 5 domain frequency mixing by modulation additional components of the HELM, into the frequency as mixing describes the passband of the microscope by this shift The idea of croscopy described copy nized 2 as it more required one in From the a the image scaling was not by in the for optical mi¬ The method resolution object plane theorem for Fourier transforms to high to and a micros¬ synchro¬ plane frequency representation corresponds applied [57, 56] Lukosz practical moving mask spatial representation microscope mixing has first been than 30 years ago then, however, width of the the frequency of a For this reason, a function an narrowing of the (Eq 10) is it follows that the reciprocal extension of the point response to the width of passband of the CHAPTER 1 6 In relation to Lukosz's [30, 31] realized a laser shows two by illuminating Secondly, by This source structures ted key in the the is the method microscopes can a of mask way to even in described an this thesis produce high fine illumination resolution microscopes postprocessing of the on is interference pattern of the image easily implemented in the harmonic excitation First, practical object plane be one the specimen with synchronized using electronic the method, differences INTRODUCTION plane has been omit¬ images As a result, conventional fluorescence Chapter 2 Summary of The objective thod without sential for chapters of this chapter the method briefly is to it with details. overloading the HELM understanding summarize the HELM Aspects principle are In the two-dimensional HELM setup four laser plane as croscope under a waves, interfere in the be written can I(x, y) u = angle common Neglecting scaling factors, where the me¬ not es¬ discussed later in to the optical 47msin(a)/A is the + Ax) + cos(uy wavelength of excitation and sample a the fluorescence density of in x- </> which can of mi¬ a (see Fig. 2.1). I of the elec¬ glass, (2.1) Ay), of the harmonic A is the vacuum Ax, Ay describe the shift of the pattern and y-direction, respectively (see subsec¬ derivation of is + spatial frequency n=1.52 is the refractive index of tion 3.3.1 for axis resulting intensity pattern cos(wx relative to the beams, object plane as 2 + = a excitation, the are 3 and 4. be considered tric field which Eq. 2.1). proportional dye-molecules tp, For the illuminated to the excitation the latter called 7 sample, intensity I times original image in the CHAPTER 2 Figure Optical 2 1 train for SUMMARY OF THE METHOD generation of two-dimensional interference a (a) pattern in the object plane of the microscope laser beam is sity that cross polarization and not are split by at E is the orthogonally (only 2 shown) phase and the image plane, to slip and inten¬ only antiparallel beams Piezo-actuated mirrors P axis object by angle to 70° equal The electrical y-interference patterns optical The beam's glass block, corresponding cover x- the the microscope so interfere ones of the through coupled oil-immersed to the slide in the to A collimated top view BS into four beams of axis OA of the oriented cut view are splitters optical parallel used to vary the pendently (b) beam a to glass the inde¬ The four laser beams block GB which is optical in the water layer axis is a=55° between slide 9 following (see text section 3.2): 4>(x, y) ~ With denoting ip{x, y)I(x, y) = (2.2) the two-dimensional Fourier transform of obtains for the spectrum of the illuminated Eq. 2.1 into 2.2 and Eq. A = 4>(K, ky) 4 = = 4>{kx, ky) +elAx i}(kx The spectrum <f> is + u, ky) +e~lAx i}(kx positive and negative reciprocal frequency domain, described in two with an tion (OTF, the nents of the dimensions, section sample, 3.1). a in as In passband cut-off radius (about emission kc = 540 is a of the this are well occurrence spatially shift, the can three, by in called the frequency reconstructed, irrecoverably compo¬ while outside lost. For fluorescence mi¬ region centered where A is the at the origin with vacuum-wavelength for the fiuorescein-like dyes) of and NA is the objective. high frequency regions passband of the Eq. of the 2.3 as to extract the individual high by a Through 2.2 shows the the current setup. must be postprocessed components A..E and resolution image. result optical spectrum microscope. Fig. images acquired for HELM, however, arrange these to the final In be transfer func¬ optical the passband, be can multiplication a harmonic excitation is the basis of HELM. into the electronically kx- and fc^-axis where the OTF is non-zero, enhanced support of the OTF that is achieved The the along direction, respectively. of the shifted spectra B..E in additional brought is as regions circular 47rNA/A, nm numerical aperture of the The or principle, region the information croscopy, the + (2.3) u) - imaging property of the microscope called the support of the OTF this space instrument-specific function, see ky) u, superposition of the original spectrum A plus four spectra B..E that have been shifted in - E u) +e-lAy 4>(kx, ky + C = = $(kx, ky a B D = elAy variable, a sample (by inserting using the convolution theorem Eq. 8): one This is to re¬ possible by CHAPTER 2 10 Figure The enhancement of the support of the OTF 2 2 standing copies nents to the of the circular The four circular spatial frequency five from passband B,C,D,E from Eq citation shows the circular passband (b) microscopy with cut-off frequency kc OTF of HELM recording (a) excitation wave fluorescence shaped SUMMARY OF THE METHOD 2 3, (a) correspond The respectively relocated are to the compo¬ displacement u is equal images for which the nodes and antinodes of the pattern are of of the harmonic excitation at different In the setup, the positions. (Ax, Ay) are sequentially adjusted to (tt/2,0), (tt,0), (0, 7t/2), (0, 7t) by piezo actuators. y-phase means for standard is the cloverleaf- regions 1,2,3,4 and by offsets x- the values ex¬ and (0,0), For the Fourier transforms of the five holds with the 5 x five is 5 set of linear spectral performed obtained of the on the measured Numerically, images and the pixel. By doing which, additionally, so, the a can be solved for the fast Fourier transform set of linear equations is spectral components A... E have been attenuated microscope. The remaining computational task components back them is obtained which equations components A..E. solved for every are acquired images, Eq. 2.3 appropriate coefficients e±îAx and e±îA». Thus, a taking to their personal computer together require only for a the OTF is to shift the original position and, finally, superimpose into account the attenuation All calculation steps by 512 x 512 image. by a the microscope's few seconds on a OTF. standard 11 Fluorescent beads with Figure 2 3 HELM (left) The 1 pm a diameter of 200 and standard fluorescence wavelength microscopy (right) of emission is 540 nm of the objective beads approximates the Rayleigh limit which tions The almost invisible contrast the is 1 4 right image is a one nm tightly packed for these condi¬ between the individual beads in are not point has to take into account that, for water im¬ mersed beads, the effective NA of the smaller is 240 consequence of the fact that the beads Furthermore, sources with Scale bar is and the numerical aperture The center-to-center distance of the dip imaged nm objective (nominal 4) becomes which approxi¬ 1 [44] Fig. 2.3 shows beads with mately equals the The HELM Rayleigh a diameter of 200 nm limit for standard fluorescence microscopy. image (left) demonstrates that such beads clearly distinguished, dard fluorescence even when they are closely packed. microscopy image (right), in can be In the stan¬ contrast, the individual beads remain blurred. In relation to the confocal fluorescence micro¬ scope, there • are several advantages of HELM: The resolution enhancement relativ to conventional FM amounts to more confocal than a factor of 2 scanning compared to 1.5 which is achieved under ideal conditions [78]. by CHAPTER 2 12 • In all HELM, photons entering image formation path In CFM, HELM is mental reasons well as based on confocal contrast, can devices, As a exploited in vs for the imaging the fraction of the signal- CFM, funda¬ result, deteriorated high speed imaging imposed by In subsection 5 11) mechanical scanning limit speed and principle tive to confocal ones be pinhole a imposed by dye-saturation (see practical reasons the is well suited for the imaging For these the lenses which contribute to the image to-noise level of CFM as in makes it necessary to trade off resolution photons • SUMMARY OF THE METHOD as the system requirements for microscopes of harmonic excitation HELM systems could become ones are a similar to those of commercial alterna¬ Chapter 3 Theory The 3.1 a general perspective, very waves within gether with the ent media, time a e.g. microscope boundary the by the propriate directly by to write the the Maxwell or equations [45]. interfaces at the lens surfaces disturbance at any be described by point to¬ it is equations using the electric field as as The in three- E(r, t) the electric field important optical effects such well as more this ap¬ one is photon absorption molecules. The considerations nochromatic) are restricted to the excitation. As a and, therefore, can case of time harmonic consequence of the harmonic the electric field vector E at any harmonic by magnetic induction B(r, t). For this thesis, related to atoms propagation of electromagnetic conditions for the transitions between differ¬ air-glass can the is described dependent electromagnetic dimensional space as linear shift invari¬ as (LSI) system ant From microscope point r be written 13 e I3 (mo¬ excitation, in space is also time by using the complex time- CHAPTER 3 14 microscope k ,-' \/ object plane Figure independent The 3 1 G R3 and E(r) In the context of this notation E(r) notation, to C3. the complex time-independent implicit dependence time 3.1. can describe linear a microscope according imaging to Fig. between imaging property of the microscope work of linear system plane (3.1) as well elliptical as po¬ light. Now, is denoted mapping 6. by theory. 3.1 is considered which per¬ object plane can and image plane. be described in the frame¬ The electrical disturbance in the the Greek letter <f> and that one object in the image notation, the microscope's imaging process is mapping of functions <f> : R2 —> C3 to functions 8 : R2 —> C3. This plane by a G work, Eq. one forms two-dimensional The Re(E(r)erat), = is used with the given according larized image plane notation: E(r,t) With this axis optical ; microscope system studied E(r,t) where THEORY Using this is characterized Linearity by the The response of the turbances in the following two basic microscope object plane to is the a properties: superposition of dis¬ superposition of the re¬ sponses to the individual disturbances: 0{\4>1 + ii4>2) = \0{4>1) + ii0{4>2). (3.2) 3 1 THE MICROSCOPE AS LSI SYSTEM This property is consequence of the a 15 of the Maxwell linearity equations Shift invariance The response to a shifted disturbance is the shifted response to the unshifted disturbance 0(#u with u, v, G a microscope optical approximation completely disturbance, 0(#u))(v + The shift a), axis invariance is aberrations increase Nevertheless, the shift as (3 3) mirroring of the not strictly good invariance is a described (LSI) systems, by the imaging property the response of the system to the so-called point spread function (PSF) a point (3 4) where ö denotes the two-dimensional Dirac's delta-distribution a LSI system to arbitrary an can 1 9(6(u))= PSF(u), response of true for points far away to the real situation For linear shift invariant be = M2 and where magnification and neglected is for real microscopes from the a))(v) + disturbance can be The seen to be the convolution of the disturbance with the PSF of the system 0(</>(u)) E=13 0 Linearity 1 / 4>{w)5{vL-w)dvldv2 9 Linearity ((j>(v)S(u 4>{v)6 (ö(u — — v)) dv\dv2 v)) dv\dv2 (3 5) 1Henceforth, only problems, scalar fields the PSF-formahsm can are be considered for easily simplicity For non-scalar extended to vector fields as well CHAPTER 3. 16 Shift / invariance THEORY 4>(v)PSF(u-v)dv1dv2 R2 Eq_6 For optical systems, is called the of the one 6 According generally, scribed to the Fourier transform of the (OTF). obtains the convolution theorem Eq. 3.7, the a = 4> PSF x 4>x = imaging property of a a microscope microscope a theory [33, 12]. Except for (3.7) microscope (or, system) LSI can pupil scalar by the coherent scaling factors, turns out to be the more be de¬ in Fourier space. be calculated can (Eq. 8): OTF simple multiplicative filtering operation The coherent OTF of diffraction a > For the Fourier transform the transmission characteristic of by OTF of by using </vPSF < = point spread function transfer function optical image 9 (3.6) <</>,PSF> function of the objec¬ tive. In case of incoherent illumination not be described is a fixed no adequately by emission incoherent emitters coherent OTF is object is the a are linear in the object amplitude object points. as can¬ there Instead, intensity. The derivation of the straightforward: squared amplitude scalar system with circular For high NA objectives, Calculations taking and include the theory is complex field intensity is appropriate since systems of The intensity response to (autocorrelation theorem, Eq. 9). [77] fluorescence, a response to point object. a There¬ is used for employed by OTF covers components. are shown in theory high NA optics. qualitative descriptions the high pupil the scalar of image reconstruction NA effects as one The coherent and incoherent OTF is not Fig. well as 3.2. strictly applicable. into account the vector nature of case in¬ point the incoherent OTF is the autocorrelation of the coherent fore, for or relation between different phase description by a In this light thesis, also exist the scalar while the measured OTF algorithm. imperfections The measured in the optical FLUORESCENCE 3 2 17 1 08 06 04 02 0 -4-2024 spatial frequency [1/|am] Figure 540 (dashed line) Coherent 3 2 transfer functions for an objective The rotational and incoherent with (solid line) optical NA of 1 4 and wavelength of two-dimensional OTF is obtained by a a symmetric rotating the graphs around the ordinate nm 3.2 In this Fluorescence section, the basic properties of fluorescence and fluorescence microscopy will be discussed. fied energy level scheme for excited states is orders of electromagnetic This is coherently. as by it allows the one theory excitation then the a and emit —to very important to describe the of incoherent a impact for and, hence, about six exciting oscillation. As ns of the coherence of the very simpli¬ a The lifetime of the exciting good approximation— in¬ property of fluorescence emission image formation of the microscope imaging regardless of the coherence of light. Because the transition from an period fluorophores destroy wave Fig. typical fluorophore. in the order of 1 typically magnitude larger consequence, the a a its 3.3 shows electrical dipole transition, ground level so to the exited state si is the fluorescence absorption rate (FAR) CHAPTER 3 18 Figure 3 3 Simplified representation phore Higher vibrational sublevels the absorption, excited state si from which it possible by fluorescence are quickly shown) or energetic indicated is excited into fluorophore brational relaxation, not of the a is proportional to the parallel absorption dipole depending an on cence absorption modulus of the state. for photon energy fluorophores fluorophore strength oriented moment: c|Endm|2, absorption dipole one isotropically would (3.8) moment electric field polarized light, arbitrary polarization states, distributed probably expect rate of the ensemble is complex For linear = is by and c is a particular fluorophore [71, chapter 2]. ensemble of N considered. In this case, (vi¬ state so The energy of the efficiency to the square of the electrical field where ridm is the normalized Now (not shown) The fraction of the exited FAR constant By photon ground energy and emission is called the quantum the fluoro- relaxes to the lowest sublevel Relaxation to the absorption photon radiatively thin lines a non-radiative conversion both followed by is the well known Stokes shift that relax of states vibrational sublevel of the vibrational relaxation to the lowest sublevel of so difference between by THEORY proportional independent this is in fact fluorophores is that the fluores¬ to the of the squared polarization quite obvious, but, it is not evident. As the interference 3.2. FLUORESCENCE 19 generating apparatus of the setup produces complicated polarization lations are required (see states to validate the excitation patterns with 3.3.1), further calcu¬ subsection expectation for such polarization states. For isotropically distributed fiuorophores, phores dN oriented per solid angle dil is dN the number of fiuoro- N (3.9) _ ~dQ The normalized of fiuorophores polar angles Ç ~ 4tt' absorption dipole oriented in and rj, a moment ridm direction respectively, / ridm absorption fiuorophores. affecting Thus, ellipsis the number exciting the electrical field vector (3.10) . rate of the To general applicability, of the a cos(C) cos(ry) \ =1 sin(C) cos(ry) V sin(?7) / To obtain the fluorescence larization to the azimuthal and is has to be summed up for all without belonging specified by ensemble, Eq. simplify it is assumed that the po¬ electric field is within the can 3.8 the calculations be written x-y-plane. as ExelP* E= where the real field account for an I Eye*Pv amplitudes Ex, Ey arbitrary amplitude the fluorescence absorption rate I and the and FARj- (3.11) , eVx, ev» polarization. For phase ellipticity of factors of the ensemble one obtains CHAPTER 3. 20 FARE \Vndm\zdN c = THEORY all fluorophores cN |Endmrdfi A-k all orientations 2tt it/2 ExelPœ \ cN I cos(C) cos(ry) sin(C) cos(ry) sin(ry) \ EyetPy A-k 0 0 -tt/2 / tt/2 cos(ry) cfoy d£ 2tt cN (77) dr] cos A-k ^cos^(C) x -tt/2 £2 cos2(^ - px) sin2(C) + El sin2(py 2tt cN A 4^" E2X 3 - px) sin2(C) d( 2tt cos2 (C)dC + sin2(Ç)dÇ E2y f(E2x+E2y)^f\n2. For spatially N within a distributed fluorophores, tp denoting the number of fluorophores volume element dV is N where (3.12) is the density the quantum the fluorescence </> ,M of = fluorophores efficiency (3.13) dVip, of the in the specimen. ffuorophore, one With QE obtains for emitted per volume = QE^>=^,WIEWr<. (3.14) FLUORESCENCE 3.2. Eq. of 21 3.14 is the basic relation distributed isotropically the exciting what In the light. form simpler describing the fluorescence emission rate fiuorophores literature, Eq. for any 3.14 polarization state be found in a some¬ can of using the intensity instead of the electric field and omitting scaling factors: </>(r) Eq. 3.15 is specialization is setting it proportional (i.e. J(r) excitation Eq. oc of Eq. If the to the V>(r)i"(r). (3.15) 3.14 for excitation with to the energy flux proportional [26, chapter 20]. wave field a |E|2 for which oc generalized intensity squared |E(r)|2), Eq. or modulus of the plane waves intensity of the I is defined complex 3.15 is also valid for the by electric complicated patterns used in HELM. 3.15 is very fundamental for HELM. It states that the of dyes in the specimen tp is modulated by the exci¬ intensity I before being imaged by the microscope. density tation Fluorescence 3.2.1 In this light The subsection, will be briefly degree of polarization the effect of discussed. polarization polarization Fig. of emitted fluorescence 3.4 shows the p is defined <p\\ + geometry considered. by <p± where and <f>\\ and </>j_ is the fluorescence emission polarized along the yx-axis, respectively. In general, the degree of polarization is de¬ pendent sion the on dipole rotational angle between moment, the mobility. fiuorophores are absorption dipole angular For many isotropically distribution of situations, it can moment and emis¬ fiuorophores and its be assumed that the distributed and that their orientations CHAPTER 3 22 THEORY iy J! Figure Geometry 3 4 electrical observed (</>_!_) of excitation is polarization circle represents the the first for observation of the along one parallel to labeling are fixed. y-axis [7]. ß is the of polarization and the second one is reduced are 3cos2(/3) cos2(/3) - occurs by important for dye molecules fluorophores dyes bound to specific are </> is discriminated, one perpendicular used later to describe (3.17) ' and emission for coincident ones (/? = free to rotate, the lifetime of the excited state embedded in Fluorescence 1 + 3 absorption the orientation of the as The grey y-axis po becomes perpendicular fluorophores The polarization = between the maximum the minimum for If the is the to The minimum and maximum value for po respectively, 0), angle (</>||) polarization Po where degrees is consistent to the microscope geometry the Two the the Then, parallel region containing fluorophores the z-axis The axis of degree are dipole +1/2 dipole moment and —1/3, (/? moments = 90°). degree of polarization fluorophores changes during thermal motion [73, 71]. the This effect in aqueous environment but not for solids, e.g. fluorescent molecules in polymer biological specimens, beads. For the situation FLUORESCENCE 3 2 be can more vanishing complicated number of As mentioned before rophores have a restricted but not dye lifetime of about 1 effect which [70] saturation" fiuorophores the imaging the in rate cannot exceed on fraction of the non-negligible an As a speed a fiuorophores "ground consequence of the the fluores¬ ground state, This imposes a of fluorescence microscopy, steady state conditions, the fluorescence rate FER emission becomes FER=^—, (3 18) Q.Tp + 1 where Tp is the lifetime of the excited state and is the excitation intensity, is the absorbed emission rate photon not is hmC(_>00(FER) = — a the is [70] energy linear even in absorption One half of its upper limit For one h isat i^- = with I section and hv that the fluorescence it as for infinite excitation intensity Jsat, equals sees a cross excitation power For the so-called saturating intensity rate fiuo- sufficient named is upper limit an typical For ns for confocal scanning particularly Under a "dye or number of emission fundamental limit of a this section, the excited states of in the excited state, in decreasing cence have of rotational freedom relatively long a depletion" [7] state dyes potentially degrees excitation power, reside can as Dye-saturation 3.2.2 high 23 limited is (see Fig the fluorescence Jsat this leads by 5) 3 emission to 1/ (3 19) = (TTp typical fiuorophore (Rhodamm B, absorption For a 1 10~20 x m2, Tp = cross section Ins, [70]), the saturating intensity Jsat is a = approx 10iow It should be sity of dyes at a noted, that dye saturation certain location is independent Consequently, dye of the den¬ saturation does CHAPTER 3 24 1 <u , r -*-1 ,L ro 2! <u £ o c =! o M- (0 05 ro - <u E i- ü c o <u c o 0 * excitation Figure Dependence 3 5 THEORY intensity of fluorescence emission rate on excitation in¬ The fluorescence emission rate is normalized to its maximum tensity value not decrease the contrast of duces the number of results in a fluorescence a photons darker and noisier emitted the re¬ specimen and, thus, image. Harmonic excitation 3.3 microscope image but by light microscopy (HELM) Interference 3.3.1 In this subsection, which is 2.1) an generating apparatus expression for the electrical field distribution the interference produced by will be derived. Fig. generating apparatus (see Fig. 3.6 shows the geometry for one pair of (oriented in the x-z-plane and referred to herein pair (not shown, oriented in the y-z-plane and as y-pair) is polarized perpendicular to the ones incident laser beams as x-pair). The other referred to herein shown and can Due to the partial glass boundary, of four plane be considered independently the electric field is waves later. reflection of the two incident beams at the water- with wave effectively generated by interference vectors ku, ^in kir, &2r- 3.3. HELM Figure 3 6 tern at the and k2i) 25 Plane electromagnetic water-glass boundary are waves For producing the interference pat¬ the two incident beams clarity, It turns out, that the reflected beams lead to z-dependence excitation the electrical field E\, E2 of the intensity Because all beams where are strength = ElT = E2l = E2r = the field 2The negative signs an the y-axis, a scalar notation for is used: E1e-t(-k*x+k*z\ (3.20) -E1Re-<k'x-k-z\ E2etAe-<-k*x+k*z^ (3.21) (3.22) and -E2elARe-l<--k*x-k*z\ amplitudes sin(«j sin(«j of the incident — + denser medium. (3.23) beams,2 at) where (3.24) at) of E\T and E21 describe the 180° optically unwanted plane. polarized along Eu are intensity an distribution which reduces the in the focal R reflection at (ki! horizontally displaced phase shift induced by CHAPTER 3 26 is the coefficient of reflection with aj the incident beam's 3.6) according angle to the Fresnel THEORY formulae [12] (Fig. to the interface normal vector and with at = ( arcsin wa \ the transmitted beam's er to the angle sin(at) «glass (3.25) I / interface normal vector «water and ngiass the refractive indices of water and (with glass, respectively) and where are kx = 27rnwater sin(aJ/A kz = 27rnwater cos(«j)/A the x-and z-component of the beam (with and where incident A the e*A waves. accounts for The resulting vector of the left incident plane wave) arbitrary phase an By using Eq. calculations, Eres one = £ii = 2E\e% (E2 For the + - 3.23 and Eq. Eles is the sum plus the two reflected performing tedious but basic obtains Elr 2 3.20 to shift between the two electric interference field of the two incident electric field distributions ones. (3.27) of the incident wave wavelength vacuum (3.26) and + cos E2l ( + kxx E2t f(l , Exy^ék*x (1 - - R)e-lk*z -R2ism{kzz) R)e-tk'z -R2isin(kzz) . (3.28) intensity distribution / (more strictly the squared modulus of the electrical field, intensity definition) see section 3.2 for motivation of this one obtains generalized 3.3. HELM 27 = *i *?F I F {El+Ei)[l+ E2' *2coS(2kxx + A] \Eies\ — M„ (1 2R ^)1 + l + R2 As can be from seen the Eq. 3.29, and F\\ (3.29) Mi = consists of two factors cos(2A;z,^ of the spatial dependence which F± depend only on intensity the and x- z-coordinate, respectively. F\\ provides cosinusoidal x-modulation of the which is the basis of the HELM method. the ratio of the field M|| depends on beams. equivalent 1), a For pure obtained. M|| standing plus a propagating of the F± leads to an glass boundary. at the interface (z unity increasing = 0) is enhanced cover slip, first to by 1 + object specimen results in cover as a = an a depth standing additional node at the water- by a factor of 1 R, — the intensity M± while the M± for the antinodal planes at z = Table 3.1 shows the relative attenuation different incident beam's angles has to be located in direct ensure objectives and, secondly, onto the the modulation coefficient of reflection is reduced — In most cases, the the one M\\ to electrical field is the field consists of as The latter one. E2 leading vanishing depth of the incident intensity distribution. (n/kz)(l+l/2) with / G N+. (1 Mj_)/(1 + M±) for ratio = unwanted z-modulation with For intensity amplitudes (E\ amplitudes E\ ^ E2, For different DC-component amplitudes E\, Ei with nodes of becomes smaller than wave — field wave intensity distribution The x-modulation best imaging fidelity standard slip. Then, a,. proximity to of oil-immersion sample preparations deposit the first antinodal plane the of the CHAPTER 3 28 Table 3 1 M_i (1-Mj_)/(1 0 14 0 27 0 57 0 20 0 38 0 45 55 3° 0 31 0 57 0 28 80° 59 5° 0 54 0 84 0 08 85° 60 7° 0 73 0 95 0 02 at at R 50° 42 1° 60° 49 3° 70° and 1 52 for 3 24 and glass antmodal by are based on calculated is at M_l equals the factor jr^r by Eq according which the intensity is Eq to calculated is by Eq The last column shows decreased for nodal planes relative to ones plane of the microscope enhanced relative to the m-focus components is strongly for incident beam's increases it has to be taken into account subsection 3 3 3 The and, as paragraphs, electrical field in the pair of incident beams 6) is 3One possibility 90°) in is at approximating 90°, discussing the optimal expression in at was derived for the y-polanzed interference of the x-pair of incident laser x-z-plane (oriented Now, in the the situation when the y- y-z-plane, The not shown on the cover advantageous For an Fig of a dielectric slip of mesh-like interference patterns for appendix A in resulting polarization to reduce the unwanted ^-modulation would be coating 4The application discussed fa an also present will be considered anti reflection angles of the interference field produced by beams oriented when As this effect 3 4 polarization In the last «j 3 25, R 3 29 consequence, the out-of-focus blur for images of three-dimensional objects 3 refractive index of 1 33 for water a z-modulation coincides with the focal a Mj_) Calculated values for the intensity attenuation rate of the nodal The calculations planes + THEORY optical trap, working optical trapping near flat incidence are (1 e 3.3. HELM 29 the electrical field distribution will be discussed and its fluorescence will be studied. following impact on made under the are two constraints: 1. equal amplitudes 2. points Then, Eq. (i.e. z = 0) 3.28 becomes The electric field beams is of all four incident beams at the interface Eles For the The considerations = 2(1- R)Eie1^ and y-polarized (kxx+ — interference of the produced by with completely analogous x- cos exchanged electric field j (3.30) . y-pair of incident and x- y-coordinates. Ex and Ey, respectively, one obtains where Ax — scaling Ay and factors polarization the on electrical field can states Assuming Ey = Ex = are = see section = shown (3.31) (kyy (3.32) + ^Y or on the phase elliptically polarized. schematically angle to the in Fig. optical of incident beams and oc |E|2 (which 3.2) 2 + one difference cos(wx + = fluorophores, Two possible 3.7. axis at using the are equi¬ generalized is consistent with fluorescence obtains sin(aj)/A and identity cos2 (a) distributed (kxx + ^ J neglected. Depending 47T «.glass and where the cally cos that the beam's I(y) u e^ linearly are pairs intensity definition I with cos position within the interference pattern, the total be valent for both absorption, e1^ Ax) + where cos(uy scaling ^(1 +cos(2a)) + (3.33) Ay), factors are neglected is used. For the fluorescence is isotropi- proportional to the CHAPTER 3. 30 THEORY A» t S 4X4* X •- 4X4* X QtQt0 4X4* X 4 Î -At Figure Two 3.7: possible polarization x- and y-direction, respectively, maximum crosses intensity. The polarization panel at every illustrates the in the position circular to let the of the interference field. vanishing polarization point is pure linear polarization object plane, (indicated by circles) for the or Ax bright zones, electrical field. for vectors (—Ay/2ky) and origin coincide with grey bars illustrate the indicate the nodes with shows the electrical states displaced by (— Ax/2kx) The coordinate system is phase point of the diagonal The left offsets Ax in a = panel Ay. The (indicated by arrows). The right Ay + n. Depending on the = polarization can elliptical (between be pure linear, pure the two extremes, not shown). generalized intensity Eq. 3.33 gives the interference distributed not as A second the situation is different and describe the fluorescence modulation point worth mentioning ization of the fluorescence if Thus, for this case, modulation of fluorescence introduced spatial by generating apparatus. However, for non-isotropically fluorophores, necessarily defined in section 3.2. the light. is the This Eq. resulting degree polarization 3.33 does adequately. can be of polar¬ neglected 3.3. HELM • the 31 ffuorophores destroy 3.2.1) section • the the polarization by (see thermal motion or imaging properties of the microscope are not affected by the polarization. Both conditions may not be true and, in those cases, the effective mod¬ ulation function may be different from distributed Eq. 3.33 even for isotropically ffuorophores. Generalization for non-ideal interference geometry Now, the 3.33) will be of description intensity distribution generalized in the to account for non-ideal object plane (Eq. condi¬ experimental tions. The equations describing the 3.32 and Eq. 3.31, respectively) x- and are y-polarized based on the electric field (Eq. idealiza¬ following tions: 1. The and x- y-pair of incident beams x-z-plane Minor out-off-plane components of the tors lead to and are in the slight a assumed to be oriented y-z-plane, respectively. rotation of the incident beam's x- and wave vec¬ electric y-polarized field distribution.5 2. The beam's angles at to the optical axis are equivalent for all incident beams. Different angles of tial frequency of electnc BBy and this field the the incident beams lead to dommantly x- and a different spa¬ dommantly y-polarized distribution. rotation, the polarizations «-axis, respectively. dommantly «-polarized are To indicate this not fact, longer exactly parallel the to the naming dommantly electric field distribution is used. x- x- and CHAPTER 3 32 The field 3 Differences the in the electric of of all four incident beams amplitudes (Eq field 3 32 and Eq intensity distribution sulting be modified I{y) in = the 2 + a equivalent reduced modulation depth distribution the above described Considering distributions lead to amplitudes are THEORY following Mx cos(Ua;r generalizations for the electric field 3 31 under ideal conditions), the re¬ conditions) has to (Eq 3 33 under ideal form + Ax) My cos(u„r + + (3 34) A„), where fcos(jx)\ _ (3 35) Vsin(7x)/ u with ux, 7X and the the Mx, My ux, uy, 7-r, 7y, sity distribution Eq is a very 3 34 with the an¬ generated by and with uy, ^y and values for the y-pair 6 the in Image 3.3.2 (3 36) J beams, respectively, corresponding graphical illustration) a V œshy) of the intensity distribution depth pair of incident x- denoting (-smbvA V Mx denoting the spatial frequency rotational and modulation gle =u V (see Fig 3 8 My for appropriate values for good approximation to the real inten¬ experimental setup reconstruction In this subsection the influence of the non-uniform excitation pattern the image on 6In Eq of the field 34, it was implicitly moduli of the distributions, holds for a 3 squared the microscope will be studied and produced by le it was assumed that the total intensity dominantly assumed \EX + Ey\2 equals dominantly y-polarized by minor imperfections in the only, l e = \EX\2 for jx + \Ey\2 the sum electric This relation jy It remains, however, good approximation for the small rotational angles jy < 1° and jy < 1° caused orthogonally polarized fields ic-and an experimental setup = 3 3 HELM Figure 33 Schematic 3 8 produced by algebraic approach an extended With ~ representation of the non-ideal intensity pattern the interference for reconstruction of the passband denoting J(k) = Eq. specimen spectrum within will be derived. the Fourier transform of the spectrum I of the transform of generating apparatus a variable, one obtains intensity pattern by calculating the Fourier 3.34: 87r2(5(k)+27r2Ma; ,iAa (5(k + ux e-*A*<5(k-< 2tt2M„ „«A, (5(k + uy e-lAyö(k-Uy) (3.37) where ö is Dirac's delta function cos(a) To are = 7}(ela + simplify introduced: e~*a) further (Eq. 12) and where the identity is used. calculations, the following scale-shift operators CHAPTER 3. 34 si(F(v = -F(v) is the identical s2(F(v = MxF(v + s3(F(v = MxF(v s4(F(v = MyF(v ss(F(v = MyF(v-uy). - + The inverse scale-shift operators «i l = THEORY (3.38) mapping, (3.39) ux), (3.40) ux), Uy), are (3.41) and (3.42) given by (3.43) «l, ^1(f(v)):=Ü4F(v"Ul) (3.44) S3"1(f(v)):=if(v (3.45) Ul) + *yj> M„ (3.46) and ^(f(v)):=77nv + U: (3.47) M„ In optical Thus, the frequency domain, described as a multiplication transfer function one imaging property of the microscope of the fluorescence spectrum (OTF) T of the microscope (see obtains for the spectrum 6 of the <f> is with the section 3.1). image produced by the microscope e = 3q= 15 E^8 = (3.48) T4> T T{$I) (3.49) T«V>,/» 4si(^) + eîA-S2(V>) + e-îA*s30/0 eîA» sS) + e"*A" ss(^) + ? (3.50) HELM 3 3 35 where <C^ denotes the convolution tors are neglected. five Experimentally, y-phase operation and where scaling fac¬ offsets images d3 are recorded for which the set to different values are (Ax, Ay) (0, tt). Eq. by piezo-actuators. is (0, 7t/2) 3.48 holds for each of the with the 5 x and set to appropriate coefficients e±îAx and 5 set of linear and In the (0,0), (tt/2,0), (tt,0), setup, the pair sequentially x- e±îA», acquired images thus resulting in a equations: M s (h\ /4 1 1 1 1\ 4 1 —1 1 1 4 -1 -1 1 1 4 1 1 1 —1 \4 1 1 -1 02 03 = T 04 W The components Sj(V0 can -V be calculated (*S)\ «2(V') S3(i>) s4(V>) (3.51) \S5$)J by inversion of matrix M: /0~i\ /si(V>)\ «2(^) S3(V0 s4(V>) 02 1 = ^M"1 W^V 03 04 w / 0 0 1 4 -1-H 1 4 l—1 2 1 4 -1-î = T 4 2 4 ±±i 0 0 0 0 w In each row of from components Eq. 3.52, the 0 1 \ (h\ 0 0 02 0 0 03 —* -i+» 2 4 _1"V 2 4 / original spectrum tp Sj(tp) by shifting it in the (3.52) 04 \hj can opposite be calculated direction (i.e. CHAPTER 3 36 with the multiplication with the shift operator inverse ) s and THEORY by rescalmg OTF inverse M-le ^ where 6 is = CM \ 3 | 3 m y notation for the vector a and where the subscript j of These five equations for indices j reconstruct the For points original spectrum certain index j, a of definition of main Eq 1 = 5 3 53 the basic relations to are be evaluated can For an for those only (T(kx, ky)) ^ 0, 3 53 for index j Eq 6$ j-th component from the measured images domain where s~ frequency in consisting of components d\ vector denotes its a (3 53) 1<J<5, called the do¬ ideal fluorescence microscope, the radius support of the OTF, T, is a circular region with a kc where kc 47rNA/A, NA is the numerical aperture of the = emission wavelength (see section 3 1) Recalling 47, the domains of definition for the particular in¬ microscope and A the Eq Eq 3 43 to dices j 1 = 5 of definition microscopy trast, for j the is can be determined equals as in the circular For instance, for j passband the shift operator 2 = kx-8xis 3 s^1 is a The obtained is as s^ resulting passband the total of the domains of definition for the indices j resulting clover leaf 3.3.3 OTF In the trum overlap can 3 53 for shaped passband is shown regions of the circles 1 than one index j for different indices should be level As con¬ along for HELM The 9, the original spec¬ = 1 3 9 design 5 m Fig To achieve ratio of the final image, the results obtained noise In shifts 5 Fig in 3 be calculated from the measured images more 1 the domain the identical mapping different circular region positive direction = of conventional fluorescence noise is a high signal-to-noise by evaluating Eq weighted according amplified by the by evaluating Eq inverse to their 3 53 respective of the denominator HELM 3 3 Figure 37 The 3 9 the circular (b) frequency kc information are pattern (see Fig equal Eq. 3.53, i.e. Wj = s~ to 3 the the index j of HELM The The object 1...5 by displacements ux regions of the harmonic excitation spatial frequencies weights w3 are set to the value of the to estimate of the 53 w3s3 -l = shows 8) these original weights w0, denominator, the following spectrum within the clover for HELM is obtained: shaped passband V'est (a) HELM by microscopy with cut-off passband corresponding (T(kx,ky)). By using expression -i/>est leaf shows the extended 3 53 with the and Uj, enhancement achieved for standard fluorescence be reconstructed within the five circular can applying Eq in passband passband I v M-le\ h 3=1 V (3.54) T j=i To calculate the spectrum of the final tional modifications to noise amplification Eq. 3.54 are image introduced. when the denominator in HELM, First, 5^,=i s71(r^) two addi¬ the maximum tends to zero CHAPTER 3 38 (1 at the e Secondly, are boundary of the to reduce the apodized by of the spectrum ripple modifications, ?/>h of the HELM image *y) chosen is is current noise, noise of the the The influence of the spread of the passband = noticeable rections It 20 is studied is Th As is on 10) for setting acquired dark dependent and frame analog-to-digital quantization) function grabber For converter values between samples Except 7-limitation Th numerically simple can case be reduced of a for the Tr sets in, on the Fig resulting point 3 10a and constant OTF in the Fig Th lobes, = 1 most diagonal di¬ originating constructively, this level by smoothly reducing frequency Fig used for the HELM images page 55 well known from basic Fourier transform towards the cut-off 7The equation 2 2 in camera could interfere sources properties, the side lobes finally level of the into account the fact that such overshoots hardly acceptable value of (3 be seen, that the PSF has strong side from different point is noise the negative overshoot of about 26% Taking ) M"** where the apodisation (PSF) can ac¬ transfer function for HELM 3 10b show the situation for the and 7 circuits camera, 8-bit resulting optical function into 1 results for the measured outermost region of the equals = shot noise, temperature noise (uncooled yield good by analog and, finally, quantization 20 and 50 Taking obtained to the total according influenced the system used is E-71 7 0 images which Tn(kx,ky) 5 Ta(kx,k. The limiter 7 has to be limited \ mm = HELM) the final equation for reconstruction / -i/>H for the final image, the Fourier spectra in appropriate function an count the above passband THEORY 7 With the 3 10c shows the OTF Th chosen that way, the Th within the clover leaf shaped passband (see Fig is ,. T^kx'ky) T . , = , (M l-\K- Jk|2 + |kp\2 ^-bK-) ' (356) HELM 3 3 39 negative overshoot PSF As can be a non could Fig 3 largely be avoided of 60° is not isotropic trum is sample approach experimental could amsotropy without some missing into account computational within the missing regions main to reduce the a application [2, 19] in parts of the object priori knowledge potentially yield reconstruction of the the object directions diagonal an more of band With such al¬ in spec¬ about the Applied non-negativity of the intensity distribution as the laser beams oriented to the HELM images possible by taking such eight six or add-ons would be the the reconstruction of HELM, leading this amsotropy Experimentally by employing extrapolation algorithms gorithms, OTF This 45°, respectively or Another interesting the need for to 9, the PSF for HELM circularly-symmetric multiples in seen in consequence of the amsotropy of the interference pattern is a to reduced to about 13% while the width of the is largely preserved is information frequency isotropic point spread do¬ function where km is the maximum cut-off frequency = u (3 57) + kc and where fc2+«2_2„ I 1 \l - — -q I (3 58) with 2u(ky/kX)2 i + (3 59) and with (ky/kxy «<%fcl)2fcc2 is the cut-off frequency quadrant only, do not fulfill this and at the kx « — for l e « direction of k > condition, diagonal kx, ky in ky — axes ky 0 and the mirror must be and kx « kx > 3 59 and 3 60 Eq ky For reciprocal symmetry of Th employed, ky (360) must be l e apply space at the to one half points which kx- and fcy-axis the appropriate transformations performed befor applying Eq 3 56 CHAPTER 3 40 Figure Optical 3 10 transfer functions for HELM point spread functions (right) for (a) and and 7 = (b) show the situation for 20, and also 7 = (c) 20 and (d) for a two a different and corresponding functions Th 1 apodisation Tn(kx, ky) function 3 apodisation (Eq 56) constant smoother (left) apodisation THEORY = Chapter 4 The HELM setup In this chapter, the setup which is used to achieve resolution enhance¬ ment in HELM is described. The basic goal of the setup is the generation of mesh-like interference pattern in the As has already been mentioned result of interference of four cross in the object plane object plane (see chapter 2), mutually of the coherent laser beams which requirement for the HELM setup preparations should be usable. Standard slip slide (size typically which form the exist to 1. microscope. this pattern is the microscope. One essential a two-dimensional General considerations 4.1 of a of the couple same x mm specimen 25 are optics sample preparations consist mm x imaging 1 mm) and thin cover elegant two the as it objective (see Fig. partly employs and for illumination. No 41 a Basically, possibilities specimen chamber: coupled through This arrangement is rather for sample chamber. the laser beams to the The laser beams 4.1). 75 is that standard problems the arise CHAPTER 4 42 Figure fluorescence plane filter Simplified optical 4 1 shown spot in objective The collimated beams the back focal plane coupling interference pat¬ an simplicity only focused by a or unit would be microscope as optical parameters as objective (infinity two lens to form beams a focal with the condenser used for trans¬ A drawback of this arrangement illumination type of are For of the microscope with the translation stage the for generation of tram the by illuminating through tern are back focal THE HELM SETUP strongly the unit's connected to design or the fact that one particular would be influenced focal distance of the corrected is not) and, by objective, type last but not least, of the available ports of the microscope 2 The laser beams backside an the through arrangement same are coupled the slide is direction the fact that the direct laser as the fluorescence to record the interference filter from the imaging vantageous ily as to the specimen chamber from the One fundamental difference of such pattern by path light light This allows obtained from these non-fluorescence images hand, could potentially light in one removing the fluorescence of the microscope This geometric parameters of the pattern the residual laser travels can is be ad¬ eas¬ On the other which passes the fluorescence filter deteriorate the fluorescence image This draw- THE BEAM SPLITTING UNIT 4 2 turned out to be back, however, monochromatic laser reason for that splitting unit that is Last but not light backside-arrangement be realized can a to one Advantageous particular microscope (the and equal unit in light A rotatable ratio of 1 1 mutually exceeds a Three produce path lengths the with can with an upright 4 2 few millimeters is resolution achievable with long one tied inverted (with an of the microscope and as to the beam a polarizer are splitting beam serve orientation with equal intensity length an a split¬ Because least to a few the crossing beams length of the laser of the used ylr-ion only and, hence, distance condensers poses by couplers for setting the splitters the coherence (Om- serves as unit fiber equivalent (at The coherence rough mW) 488 nm, power 120 non-polanzmg used for closely an An ylr-ion laser integrated pigtail-style long on con¬ unit four laser beams of as distance not be used by production imperfections), coherent still usable and is is a de¬ elegant an long a object plane Fig in of the four beams 1Trans-illumination By generate four coherent laser beams coupled A/2-wave-plate millimeters caused are is fiber with incident laser power the shown is It source It even 543-AP-A01, wavelength coherent made that the setup splitting to optical single-mode was possible fact, serves mchrome ting the intensity that interfere The arrangement used a still case) and stage) normal splitting for the beam of the two arrangements, cons type of microscope The beam The beam of are is appropriate translation 4.2 One remarkably simpler stage with little modifications trans-illummation images 1 strictly using the setup a plane parallel arrangement into account the pros sign, the translation least, be used can decision for the backside arrangement denser due to the negligible, probably attenuation ratio of the fluorescence filter for the high Taking 43 no problem the lower CHAPTER 4 44 OT ® fiber - 1 polarization maintaining single mode fiber fiber coupler X/2 THE HELM SETUP coupler waveplate <8> polarizing Ar-laser beam splitter lens 4J beam 4fc splitter beam shutter A splitter ÎJ» I 1 piezo shutter £"" *<F-#-^-#-Jft I shutter I coupling ^j unit (f M shutter beam 1 Figure 4 2 to X Optical and ® denote the paper splitter piezo:o\ •# train of the beam translatory degrees plane, respectively rotational degrees the paper plane, respectively splitting The unit symbols of freedom within and The of freedom around symbols axes T parallel and and -.—». perpendicular c=> denote perpendicular to 4 2 THE BEAM SPLITTING UNIT laser is to be specified acceptable The for two beams to mirrors move Four shutters imen These shutters optical axis in During are the for one or piezo- laser beams more the four beams to aligning cross at the an optical interference trap are appendix A in spot size (focal length / weak lens a of sub-micrometer sized optical trapping First results of such The beam diameter at the output of the 1 5 mm, by object plane Illumination 4.2.1 varied the work with the HELM setup, the idea of using the mesh- arose presented slightly to block provided are helpful be can the excitation pattern relative to the spec¬ like interference pattern for particles well within the and, consequently, mm range path length actuated 300 45 focus the laser beam = fiber colhmatmg 300 Gaussian beam optics mm) [68] predict is coupler used to a is slightly beam waist diameter wj of wf where A the is wavelength 2 of the incident beam Fig 4 3) is uniform extent of the field of image x 2Eq is a 4 1 The (4 1) 125/xm, light and wq experimental sample view is the beam waist diameter value x 512 strictly holds good approximation plane pixels only However, employed on 63 x CCD-chip NA 1 4 140 /xm, of 2 5 25/xm x or 1 see large spot view The objective, and for the amounts to 25 /xm magnification for processed or 40 /xm 6, respectively if the primary beam waist coincides with the focal for the as (roughly This rather illumination within the field of for the intermediate an of the lens and focal of distance of 8 3 /xm of 512 40 /xm for plane it pixel size = TIWq close to the theoretical expectation size ensures the given =A^— long does not exceed a large as primary beam waist diameter (15 mm) the distance between primary beam waist few meters CHAPTER 4 46 Figure 4 3 Image beams are of the illumination by shutters) polystyrene beads with tributed blocked lOx NA 0 2 It can a be shown negligible a that, beam one (three scattering sample of statistically dis¬ diameter of 200 2) 4 nm is is set to a imaged with an position where Scale bar is 100 pm for this geometry, the curvature of the in the field of view few centimeters between the waist. ellipsis produced by (see Fig The lens objective the spot diameter is minimal fronts is A THE HELM SETUP even when there is object plane Therefore, displacements of the lens and the can wave- distance of a secondary beam be used to extend the spot size. 4.2.2 In set The HELM, to five the piezo phase offset of the interference pattern is different values. crucial that the known actuator During acquisition offset is constant. phase creeping of common piezoelectric of one sequentially image it is For this reason, the wellactuators causes problems. THE BEAM SPLITTING UNIT 4 2 An alternative to physical piezoelectric 47 actuators difference between the two is electrostrictive are that piezoelectric remanently polarized during manufacturing (and, consequently, be operated below the Curie temperature to maintain while electrostrictive ated slightly view, there remanently polarized not ones are above the Curie temperature four are linear for actuation are relation to in strongly is a is approximately quadratic applied voltage an is factor between five and ten a This potentially amplifiers, as function these are in relation to problem a poses with designed not more tem¬ actuators The electrical capacity of electrostrictive actuators by of one perature dependent for electrostrictive 4 oper¬ reduced for electrostrictive piezoelectric The mechanical extension for 3 are ones and creep Hysteresis polarization) and practical point a applied voltage an actuators while it piezoelectric for electrostrictive 2 are must differences key The mechanical response to 1 From The ones actuators is increased piezoelectric common ones high voltage for such strong capacitive loads As the dence are is linearity of minor of the actuator impact for (XIRE 0710L, They are for the (Fig The 4 operated high capacitive 4) a , self-made load (approx as the temperature indepen¬ electrostrictive piezo actuators Finally, XINETICS Inc with well HELM, well suited for the demands tors as electrostrictive stack actua¬ Devens MA, USA) were chosen high voltage amplifier designed 9,2 /xF) The measured curve confirms the expectation about the actuator characteristic hysteresis piezoelectric is 1% which actuators is about one tenth of a typical value for CHAPTER 4 48 Ë 350 | 300 THE HELM SETUP TO g 250 £Z | 200 150 - £ ioo 50 « > 0 2*0 5 10 15 piezo Figure 4 4 25 plotted against shown is the response to The a triangular coupling 30 voltage [V] The measured actuator characteristic interference pattern is 4.2.3 20 the The applied voltage control position of the The trajectory voltage unit As has been mentioned in the beams are the slide. coupled to the To achieve duced by the beam (TIR) at the beginning of this chapter, the laser specimen chamber from the backside through this, hypotenuses oil-immersed to the slide termines the beam's nodal the four splitting unit plane parallel undergo of four custom-made ( Fig. 4.5). angle a to the The spacing of the interference pattern, setup allowing one NA oil-immersion choice). to directly a glass prisms design optical axis of these and, as a which are prisms de¬ result, the is set to 55° in the current observe of the laser objective (see laser beams pro¬ total internal reflection section 5.1.1 for light through a a high discussion of this 4.2. THE BEAM SPLITTING UNIT 49 TIR \ / TIR TIR / i TIR epoxy resin i i aluminum frame optical axis a" objective Figure 4.5: prisms are TIR at the The hypotenuses plane parallel (approx. 0.2°, caused coupling glued together to the shown unit, to (a) couple of the by laser light which (b) for cut view. the laser beams to the prisms, the beams object plane. exagerated top view, The prism clarity) to are block is Four glass sample. By "bent" out of slightly a rotated avoid power fluctuations is back-reflected into the laser cavity. CHAPTER 4. 50 Figure 4.6: Cut view is moved between the the along optical THE HELM SETUP showing axis how the sample microscope desk and the interference generating apparatus. The assembly of the four coupling unit) together ence splitting verted to fit unit microscopes) on as or shown in it can x-y-translation stage can Fig. be replaced. Fig. edge of the interference by can Fig. an the to herein as unit form the interfer¬ be attached to the 4.6 (for 180° around using used; only inverted clamp use with in¬ lateral axis a microscope, mechanism for 4.6 illustrates how the slide is moved in the air gap between the upper lower unit 4.5 and When (referred 4.5 splitting be rotated upright microscopes. the slide must be 4 Fig. in generating apparatus. The coupling beam the prisms with the beam of the edge specimen stage and the generating apparatus (the gap is approx. mm). 4.3 The overall The interference croscope (Zeiss system generating apparatus Axiovert 100, see is mounted Fig. 4.7). on an inverted mi¬ The used camera is THE OVERALL SYSTEM 4 3 Figure an on an uncooled industrial the microscope to acquisition with with a required (Pic-Port, one apparatus (LV-8500, Leutron Vision, connected to the bottom port of image deterioration caused paths data, by imper¬ A standard control the image calculations mea¬ The computer grabber allowing pixel-synchronous Leutron image Vision, Glattbrugg, Switzerland) card (ADIODA-12, MESSCOMP the computer runs and GmbH, A dedicated real-time operating system for measurement control DOWS NT 4 0 generating the standard folded perform frame analog input-output an that in is used to read out image is Wasserburg, Germany) as which minimize surement sequence and equipped interference CCD-camera grade optical components personal computer is the inverted Zeiss Axiovert 100 microscope Glattbrugg, Switzerland) fect of Photography 4 7 mounted 51 is not under MS WIN¬ (the one for measurement control as well reconstruction) is programmed in C++ using the The software for image BORLAND C++-Builder 4 0 The choice of C++ as programming CHAPTER 4 52 THE HELM SETUP PC (WINDOWS NT) acquisition control and postprocessing software interference generating apparatus laser high-voltage amplifier Figure language 4 8 Schematic of the HELM system and the realization of the command line program ensure image easy An overview of the system is shown in Fig. to different 4.8. The measured interference pattern is shown in practical avoid interest is the stability Fig. 4.9. One point of the interference pattern. To expensive materials like INVAR, the interference generating paratus mainly consists of aluminum parts which have thermal coefficient of extension. into as platforms. System stability 4.4 of algorithm reconstruction portability an acceptable interference range, a very To nevertheless compact design bring was rather ap¬ large thermal drift chosen for the generating apparatus. Experimentally, the thermal drift of the pattern has been determined to be system a in thermal equilibrium typically 20 nm/min with the environment. As phase for a offset 4 4 SYSTEM STABILITY errors of one 53 tenth of the nodal tolerable, thermal spacing (20 nm) turned drift limits the onds. For the uncooled acquisition CCD-camera, this since the dark current does not allow ever, for cooled cameras the limitation could be set during INVAR. a long overcome term measurement or imposes longer it could become easily time to a a no out to be just few tens of sec¬ additional limit exposure times. restriction. by recalibrating In this the How¬ case phase off¬ using advanced materials like 54 CHAPTER 4 THE HELM SETUP Chapter 5 Results Achievable resolution 5.1 As test 100 nm available fluorescent were distance is used below that For far below the (240 croscopy nm one for a closely packed beads, Rayleigh NA=1 4 with slip com¬ diameter of the center-to-center and green objective Inc device, a limit for standard fluorescence , light) mi¬ and also To stabilize the structures, the surface of the beads microspheres, Polysciences cover beads with polystyrene of confocal devices carboxylate-modified late HELM for the achieved resolution of the HELM objects mercially by (Fluoresbnte Warrington PA) YG polylysme (poly-L-lysme hydrobromide, carboxy- linked to the was MW 36 kDa, Sigma, Buchs, Switzerland) To compare the region of H2O resolving standard illumination 1A short images comply in power of different immersed beads note to this thesis (Fig pixelation The pixel 5 band-limited imaged using HELM and confocal scanning and printing resolution of all distance of the with the Shannon criterion generated by was lb), acquired (Fig (Fig light images to 55 one same 5 5 la), 1 lc) microscopic was The quasi-continuous images interpolation the techniques, chosen to printed quarter of the original pixel were size CHAPTER 5 56 As reference for the actual locations of the individual a atomic force microscope image acquired (Fig also given is Id) 5 The resolution of the HELM image individual beads is HELM, although limit not possible for HELM the latter in the even when In the standard fluorescence microscopy image remain Choosing the (see blurred axis (Fig 4 5) 3 9 on page in HELM is also 2 3 3 1 on 195 nm) 37) vs trading of 28) page is a contrast, page 11) amsotropy and most noticeable The are an in subsequent bicubic interpolation procedure for the granular opti¬ to interpolation smoothes the structure of e is to the pixel g near the in observation mesh spacing of allows the one to directly objectives edges diagonal in good 5 lc of the of the directions beads, in Fig agreement with the required printing noise Fig a vs Tab the images of the beads show passband, zones plane (see the focal (55° leading overshooting the dark experimental at to the frequency (see cut-off maximum and, additionally, compromise Due to the non-isotropic reason in amsotropy of the resulting passband and The chosen value good angle observe the interference pattern with oil-immersion with on spatial frequency of excitation unwanted decrease of excitation intensity 5 la 3b, 5 can closely packed are Fig Fig the beam's which determines the The choice of at requires some micros¬ of excitation spatial frequency One important parameter Fig which approx¬ Discussion 5.1.1 cal Fourier space in nm they in close to the 5 3a demonstrates that such beads Fig clearly distinguished by HELM, the individual beads possible is is limit for standard fluorescence Rayleigh The HELM image diameter of 200 a Distinguishing but ones 100-nm beads resolving 5 3 shows beads with imately equals copy an was superior to that of clearly is 5 2 illustrates the achieved resolution gam Fig Fig beads, which in air the standard and also to that of the confocal image be RESULTS original resolution images and This is the 5 1 ACHIEVABLE RESOLUTION BY HELM Figure Identical 5 1 polystyrene 1 /xm Plan (a) Apo beads was of area imaged imaged using 63x NAl 4 diameter using was a set to an on a (b) Apo nm diameter fluorescent techniques Zeiss Axiovert was Scale-bar image (c) lOOx NAl 4 length microscope imaged through The confocal Leica Plan was with is a identical lenses recorded objective The on a pinhole 67% of the inner Airy-disk diameter, the resolution deterioration due to this finite recorded with of 100 sample HELM objective using standard illumination Leica NTSP a with different 57 atomic force pinhole size is about 15% microscope (Topometrix [69] (d) was MS) Accurex II CHAPTER 5 58 Figure The Fourier transforms of the HELM 5 2 of the standard image Fig Fourier transform in 5 lb logarithmic a RESULTS 5 la and image Fig Shown is the modulus of the complex scale function theoretically predicted point spread given in Fig. 3.10d on page 40. A more isotropic resolution together with is achievable by employing This has been shown various orientations. recent work citation a for patterns rotatable almost [35] at more a isotropic a 0°, 120° and 240° are at the expense of higher acquisition one men leading chamber approach to TIR at the [20]. However, to thin cut-off frequency experimentally Here, in along a very harmonic ex¬ produced sequentially by the point spread function additional mechanical is degree time. A further resolution enhancement is values high somewhat different setup. phase grating. As expected, of freedom and a than four laser beams oriented possible by increasing glass-water boundary around the at to speci¬ the evanescent illumination restricts the specimens and does not allow one three-dimensional ACHIEVABLE RESOLUTION BY HELM 5.1. Figure 5.3: Fluorescent beads with HELM (a) and standard fluorescence 2 /xm. The microscope system identical to the ones imaging which is HELM devices expected In 5.1a and to be as with the specimen preparation is are area of application for future ratio and imaging speed in relation to confo- microscopy scanning confocal fluorescence microscopy (CFM), ited light spot light emitted By imaged 5.1b, respectively. crucial a nm microscopy (b). Scale-bar length (see chapter 6). Signal-to-noise cal Fig. in diameter of 200 a well as 59 means of a is scanned by the of CFM is increased hole across specimen pinhole in by a a vs. the lenses can Regarding be collected this Conversely, by the a using the an diffraction lim¬ and the fluorescence secondary image plane, factor of 1.5 for resolution. the specimen is collected [69, 85, 78]. Unfortunately, noise level the the objective. same resolving infinitesimally pinhole necessitates in HELM all power small pin¬ trading off photons entering camera. experimental data, it is striking that the signal-to- CHAPTER 5 60 (SNR) ratio noise of the HELM image of the confocal image laser power Fig 5 lc 5 la for the reduced SNR of the confocal image photon-blockmg pinhole the and noise (see the 2) roughly pattern at applies half of the rate of the only to million for a in orders of for the magnitude parallel to one one of HELM A in spot Jspot 2 is Fig to or tt Fig in speed Fig lOOnm 5 1 HELM, CFM this one per is several are of CFM than to the proportional a higher photon acquisition up image dye polarizing field of view beam size 0 12 mWs measurement actually saturation The intensity flux (or a lOOnm x (see 5 lc size in for the though X splitter, acquisition 140 (im X 140 /im X Assuming 25% security 0 16 mWs 5 1 above the saturating 2) Therefore, dye striking SNR difference the saturating intensity 5 mW 25 (im W nr subsection 3 2 object plane 25 /im occurs the focal 16xlOn^r magnitude even in roughly is ,, one reason Laser power time 6 5 s, geometric spot size by sequential operation two orders of 5 la and 25 /im, spot In the interference limited to values that = assumed to be Confocal image 4 mW out of limited 5mW area one tion), acquisition saturation consequence, the total a acquired photons, or intensity of typical fiuorophores between As = spot saturation dye single-point Since the SNR laser power = is reason both) of the CFM used This value is fiuorophores (approx for moderate laser powers even /Spot is is illuminated common estimation illustrates that rough CFM SNR increase combination of the smaller for the square root of the number of allows are pixel image) flux from the specimen photon integrated One the above described CFM in fiuorophores tiny fraction of the 1024x1024 a speed fiuorophores time, whereas one is one Due to the finite lifetime of the excited state, maximum emission one superior to that Another very fundamental effect increasing the imaging limiting subsection 3 2 is the total time mWs, respectively2 0 16 mWs and 32 was Fig though even RESULTS (manufacturer specifica¬ HELM image time 16 s, image l/cos(55°) Laser power size 25 /im => Laser energy factor to account for errors X in in MEASURING BIOLOGICAL SAMPLES 5 2 of the particular fiuorophore embedded the beads in Concerning high speed are performed contrast to in dye culties of CFM, however, the advantages experimental required required is the by multi-point newer Fig in Fig grade speed can also be seen in 5 la 16s was Taking 5 lc compared into account the CCD camera, this is a is to 6 5 s for the higher signal-to- achieved with uncooled an clear difference Measuring biological samples 5.2 HELM was used with 5 7 show different various polymer preparation methods tubulin filaments portant role in 5 8 and Fig propriate stammg are for employed routinely are 3 biological samples embedded rat tissues presence and localization of cells per image The total acquisition time for the five images ratio of the HELM image which industrial as the field of imaging in data for HELM confocal image noise per line one scan problems scans and the mechanical scanning diffi¬ be reduced can five only as [47, 86] scanners The where CFM, problem saturation not known is imaging, HELM also reduces the linked to mechanical scanning mechanisms Both the 61 e hormones g 5 4 to Fig diagnostic can purposes be studied by ap¬ 5 9 show cell cultures where the Fig immunostained spatial organization Fig Similar specimen Tubulin filaments play an im¬ and transport mechanisms within [3, chapter 16] 5.2.1 Materials and Methods The tissue Histological samples (2-hydroxyethyl methacrylate) 3I gratefully samples (Fig thank Jakob 5 4 to Fig 5 sample (Fig 5 9) resin and, using and a microtubule Ueh in GMA microtome, semi- embedded were Zbaren, Inselspital, Bern, 7) thank Rosemarie Sutterhn and Prof microtubule samples a for supplying histological sample (Fig 5 8) Aebi, Biozentrum, Basel, Likewise, I for the other CHAPTER 5 62 (approx thm sections from the 750 of different use the four tissue sections nm) were Fig 5 4 to Due to the very weak penetration of the 7) 5 was section surface attached to oxidase a In the next step, suitable dextran (HRP) chain with polymer (EnVision, sites Dako bound onto the primary antibodies HRP-antibodies were available, sites thus antibodies horseradish per¬ fluorochrome used to visualize the reaction sites providing added were secondary Diagnostics, Zug, Switzerland) Finally, eral hundred fluorochrome conjugates for same restricted to the is numerous the molecules into primary antibodies Firstly, appropriate to the tissue section procedure basically large antibody the GMA resin, the immunohistochemical reaction Apart knives glass the lmmunostammg antibodies, (Fig cut with RESULTS can bind to the conjugated whereby sev¬ HRP numerous strong fluorescence signal despite the a limited antigen epitopes present in the surface of the layer resin sec¬ tions Tubulin filaments (Fig. 5.8) cells After fixation by suitable a was a Human endothelial cells primary conjugated Tubulin sample Human fibroblasts mary mouse binding numerous seven cultured Finally (a few slides on followed applied was visualization hundred) fluo¬ anti-biotm antibodies to the reaction sites of human were grown anti-mouse ftuorophore-to-protem therefore, of on gingiva a cover anti-/3-tubulm antibody rophore conjugated The were anti-/3-tubulm antibody secondary biotmylated antibody achieved with the rochrome immunostained in human endothelial ratio fluorophores was antibody was per 7 0 fibroblasts applied was (Fig. 5.9) After fixation slip Finally a a pri¬ fluo- used for visualization (manufacturer specification), antigen epitope is the maximum achievable 5.2.2 Discussion Concerning the histological samples Fig that the HELM images show a granularity 5 4 to Fig 5 7, it is of the fluorescence striking emission MEASURING BIOLOGICAL SAMPLES 5 2 which visible hardly is probably does not the standard FM images in is cannot to be expected to real correspond of the vesicles amounts to and, hence, partially the observation a result of the stammg procedure employed binds is required biological This a that, the as multiplication size [3, chapter 13] The granularity The fluorophores of fluorescence to one emission compensate for the relatively low number of antigens to as a granularity sample preparation few hundred available for immunochemical reactions is This structures few hundred nanometers a fully explain specific antigen epitope 63 result of the beled antigen epitopes high (with a The presumption polymer in resolution of few hundred the individual la¬ HELM, fluorophores attached) resolved and lead to the granular power of HELM shows stammg artifacts which the Hence, structure are are high resolving hardly visible in the standard FM images For cell culture procedures of were samples sample (Fig lium cell sample (Fig lium cell sample to the fibroblast expected in 5 8 and Fig subsection 5 2 Fig 1) 5 As a 9, different stammg was 5 5 is a brightness factor of approx a Since this for the seven few hundred for the endothe¬ The observed higher by sample as a 9) 8) while it the number result, per labeled antigen epitope amounts to fluorophores fibroblast than (see used brightness of the endothe¬ four difference result of the different stammg in is relation much less procedures, it is as¬ sumed that the number of antigen epitopes available for stammg higher in the fibroblast image along Fig the filaments 5 8c fluorescence sample is confirmed observation that the fluorescence distribution experimental uniform This assumption even emission is of available antigens, in Fig 5 9 than shows little gaps observed however, is The along reason not clear in Fig 5 8 was by is the more The HELM the filaments where no for the different number CHAPTER 5. 64 Figure 5.4: secreted by Rat pancreas semi-thin the /3-cells plastic of the islets of section. RESULTS The hormone insulin Langerhans is immunostained. Prior to release from the cells, insulin is contained in secretory vesicles granules by cytoplasma. (a) FM, respectively. Scale within the standard small detail of (a) and and (b) are imaged by bar is 10 pm. (b), respectively. (c) and Scale bar is 1 pm. or HELM and (d) show a 5.2. MEASURING BIOLOGICAL SAMPLES Figure 5.5: glucagon Rat secreted pancreas by semi-thin or HELM and (d) show a granules by section. the a-cells of the islets of tained. Prior to release from the cells, vesicles plastic within the standard FM, small detail of (a) glucagon cytoplasma. respectively. and 65 (a) The Langerhans hormone is immunos- is contained in secretory and (b) are imaged by Scale bar is 10 pm. (b), respectively. (c) and Scale bar is 1 pm. CHAPTER 5 66 Figure 5 6 matotropin Rat hypophysis (pituitary gland) is immunostained hormone, sematotropin, which ules within the imaged by (c) and 1 pm (d) The show a by sematotroph plastic section cells secret the is contained in secretory vesicles cytoplasma prior HELM and semi-thin RESULTS to release from the cells standard FM, small detail of (a) respectively and (a) growth or and Se- gran¬ (b) are Scale bar is 10 pm (b), respectively Scale bar is 5.2. MEASURING BIOLOGICAL SAMPLES Figure 5.7: tained. Rat kidney Laminin and semi-thin collagen basement membranes which (b) are imaged by bar is 10 pm. (c) and Scale bar is 1 pm. show Laminin is immunos- structural support for epithelial HELM and (d) section. fibrils compose the basal lamina provide build selective barriers between and plastic 67 a by layer of epithelia and cells and connective tissue, (a) standard FM, small detail of (a) respectively. and Scale (b), respectively. CHAPTER 5 68 Figure 5 8 Microtubules in human endothelial cells of the tubulin filaments is about 25 imaged by (c) and 1 pm (d) HELM and show a by nm standard FM, small detail of (a) The actual diameter [3, chapter 16] (a) respectively and RESULTS and (b) are Scale bar is 10 pm (b), respectively Scale bar is 5.2. MEASURING BIOLOGICAL SAMPLES Figure 5.9: Microtubules in a 69 cell culture of human gingiva fibroblasts. nm. [3, chapter 16]. (a) and (b) are imaged by HELM and by standard FM, respectively, (c) and (d) show a small detail of (a) and (b), respectively. Scale bar The actual diameter of the tubulin filaments is about 25 is 1 pm. contrast low The structured of the luminosity relation to the camera of the images background had to be set to sample. in Fig. is a a result of the fact that the very high value for the relative Therefore, the noise level is increased in 5.4 to Fig. 5.8. CHAPTER 5. 70 the OTF Measuring 5.3 RESULTS reconstruction in HELM by applying Eq. 3.55 requires at least approximate knowledge of the optical transfer function of the mi¬ Image an The OTF croscope. predicted cut-off the measured To and were modeled were the the calculations. was on a point Secondly, light over an area acts as which effective on a cover Additionally (Zeiss wavelength x the [55]. filter ideal which is computed was an of 540 nm. assumed to be free from First, by easily 53 pixel in the finite pixel a Fig. or the , this, in conjunction termines the of the of shape bandwidth, the with the passband DIC) itself is not were ad¬ thickness of 170±5 /jm. a calculated curve communication Dr. The manufacturer's of the objective and the tube lens for both components material a were imperfections. spatial frequency for HELM. As spatial frequency incoming the beads Most crucial for HELM is the usable bandwidth of the since x size and finite bead frequency 5.10. calculations, geometric /jm object plane) the CCD-camera optical system consisting In the con¬ The attenuation at the theo¬ selected for 1.4 Oil to the be introduced into size Göttingen (personal 63x the beads CCD-pixels (8.3 nm The cut-off in nm Two sources. opposed optical conditions, presented for Apochromat Plan as to the measured and scalar curves, Faulstich, 1999) was the as diameter of 100 point CCD-pixels integrate introduced assure slip [33], can nm approximates low-pass obtained from Carl Zeiss in A. to 53 28%, respectively. affected at all. To curve well different from In this case, the spec¬ the finite size of the As the frequency size is 10% and sorbed source, and chip corresponding retical cut-off a as circles. besmc-function taken into account. an served nm uniformly emitting spectrum of 8.3 /jm of 540 introduced in the OTF calculations: as trum is the well-known stant as noticeably beads with OTF, polystyrene wavelength emission corrections theory [33] from scalar turned out to be ones. measure an expected frequency a of microscope excitation, de¬ practical measure for which the value of the OTF MEASURING THE OTF 5 3 71 measured scalar 08 - 06 - 04 - 02 - theory computation manufacturer's j_ 0 12 3 4 5 [1/u.m] Figure 5 10 Measured and calculated spatial frequency factor of 2n from the theory is a is 4.9//xm imposes an transfer function The per pm which is different by a used elsewhere in the text The 1%-bandwidth whereas the measured difference of 20%. tween and optical pairs angular frequency below 1% is used. drops in line specified is one expected The manufacturer's value upper limit for what from scalar 3.95//xm (4.45//xm) is is about can which in be¬ be achieved with the microscope. Various possible reasons manufacturer's cut-off tolerances of the objective ditional components filter) exist for the 10% difference between the frequency and the measured and tube lens as well (OPTOVAR magnification will deteriorate the one. as For example, imperfect image. Furthermore, the fluorescence sion of the beads is not monochromatic as ad¬ system, fluorescence emis¬ assumed in the calculations. CHAPTER 5 RESULTS characteristic of fluorophores 72 Last but not at the least, glass-water the embedded rophores Measurements Eclipse E800 with Again, the angular interface in complicated also performed for than that a cut-off frequency (NIKON objective) NIKON system NIKON Plan Fluor 100x 13 Oil DIC experimental of fluo¬ one [5] media homogeneous were a emission is more was about 25% less than expected Measurements performed by other groups also report noticeable differences between measured and 25% approx ditions, fer by were the OTF performed was theory conditions instead of edge-object under were are Cut-off reported quite different broadened reported are frequencies by The con¬ which dif¬ [74] and [83] but the (non-fluorescence mode, in point-object) For the image reconstruction OTF of the microscope is HELM, the measured geometric parame¬ algorithm of used Determination of 5.4 properties of the are comparable experimental not considered about 50% from experimental imaging functions which relation to theoretical expectation in measurements predicted [51], point spread In microscope ters of illumination mesh To determine the orientation and pattern, one bright-field from the imaging orescence filter, light is alternatively, of light of the interference is acquired 4 from the laser beams several orders of magnitude Without the flu¬ is dominant weaker the correlation between the measured image and term for the interference cence image of the microscope the direct the fluorescence ically, path spatial frequency I\> with the fluorescence filter removed images [35] pattern with the mesh parameters Using bright working independently can an since Numer¬ analytical varying orientation and spatial also be determined from the fluores¬ field images for that purpose has the of the SNR of the fluorescence images advantage DETERMINATION OF MESH PARAMETERS 5 4 frequency maximized is to the according following 73 expression max cos where / and is the pixel m ( m dux the are Ax Ay and ) mj distances x- and the in ( ) ^y) tional due to filter fore, there or in not a the image, Fortunately, for all images easily Assuming be Ax,Ay (ex + TT, ey), (ex, acquired ey + that, by applying Eq the the absolute is reconstructed 1, el£x, e~l£x, ely vr/2) images become and (ex, ey + and mechanical offset ex and ey There¬ bright-field phase n) offset and common offset pairs phase (ex,ey), (ex It be can additional = e~*e», respectively adjustment can 5 + n/2,ey), easily 3 53 with the given coefficients of matrix For the indices j and to addi¬ slightly wedge- optical path the phase offsets, original spectrum tp multiplied by tors a rise determined from the fluorescence images additional constant for the five corrected gives coincidence between spatial fluorescence image can probably ideally infinity absolute is no and d the removal Unfortunately, path displacements (5 2) , 2, the phase off¬ expression 5 in of the fluorescence filter from the imaging shaped ) Ay y-pixel coordinates, respectively, also determined are ( object plane the maximization By performing sets ) ( + l dwy Uy +cos U-œ +Ax ^y +AX+cosdUy+ ^cc M_1, complex phase 5 these 1 shown phase Depending on factors fac¬ are temperature of the HELM setup, the constant phase have any value between 0 and 2n To determine ex and ey from the measured fluorescence images, the reconstructed spectra for different indices j 5) 1 5 to a are compared in the appropriate Since the fluorescence filter lateral displacement is affect the lateral image position systems However wavelength the if the system parallel tilted of the beams beam in is by 45° (denoted overlap relative to the This lateral beam case not of parallel displacement leads to a optical V'j=fcj in k = More foraxis infinity corrected for it leads does not displacement beams ideally infinity as regions corrected a lateral image shift certain CHAPTER 5. 74 mally ex and calculated are ey RESULTS by u-xe ex = arg -f— ^=1 arg = (5.3) and — M-le M-le arg -^— = = (5.4) arg M-le %=i where Eq. 3.53 is inserted and where the fact that the OTF T is real number is used. are averaged for a few account for the real tp:J=k,k = 1...5 1, e~lx, elx, an points phase are precise results, Eq. in the 5.3 and a Eq. 5.4 appropriate overlap region. To offsets ex and ey, the reconstructed spectra with the inverse phase factors (i.e. e*e», respectively) before Eq. 3.55 is employed multiplied e~*e» and to calculate the influence of To achieve spectrum of the final image. Fig. 5.11 illustrates the intentionally introduced phase offset error of n on the resulting images. Fig. 5.12 shows the resulting images introduced mesh parameter errors. with various intentionally The conclusion is that errors of 0.1% and 0.25° in spatial frequency and orientation angle, respectively, do not significantly surpassed by deteriorate the the correlation images. procedure. This accuracy is easily DETERMINATION OF MESH PARAMETERS 5 4 Figure in 5 11 HELM The influence of absolute Scale bar 1 pm (a) shows modulus of the Fourier transform of phase by n offset ex determined This looks like an in the overlap echo image region Fig For images by applying Eq for image reconstruction errors on detail of a (a) shifted components of the spectrum the cancellation phase 5 3 was effectively As a In 75 image formation 5 4a (b) (c) and shows the (d) the x- intentionally changed the inverts horizontally (d) clearly (b) the result image spatial domain shows image CHAPTER 5. 76 Figure 5.12: The influence of mesh parameter in HELM. Scale bar 1 pm. A detail of with standard fluorescence microscopy, (b) image. was In (d) the x-angle intentionally changed by struction. ux (c) and was In (e) and (f), changed by 0.1% Fig. 0.25° and 1°, image formation 5.4 is shown, is the jx determined (a) is corresponding imaged HELM by applying Eq. for 5.2 respectively, image recon¬ spatial frequency of excitation 0.5%, respectively. the determined and errors on RESULTS INFLUENCE OF DEFOCUS ON HELM 5 5 Influence of defocus 5.5 For defocused rithm OTF in is also altered increasing one [33, 12, 24] HELM used by As consequence, the effective HELM- a the image reconstruction Because the width of the OTF the HELM-OTF defocus, HELM on the effective OTF of the microscope lenses be¬ objects, different from the comes 77 frequencies Experimentally, shows basically reduced for gap at medium a the influence of defocus is algo¬ shown is Fig in 5 13 For increasing noticeable is scaling procedure most nm îmmersion for various a objectives [44] defocus z z In to nm depth to scalar most result of the a defocus of about high NA is oil- calculated The calculations theory the value of the OTF at half the cut¬ are in 6 Therefore, good agreement the with predictions 6The parameter numerical aperture nm a the OTF 55% of the m-focus value results about focus sensitivity of HELM 240 side-lobes, is of focus of [12, chapter 9], according 240 = frequency drops theoretical This of visible image deterioration for result of the very low show that for off level which sets the most negative value to black and the occurrence is background to white positive The 200 the images show stronger defocus, the increased for NA=1 m used as m = 4, A=540 in the calculations ^r—z nm Therefore, and ra=l 52 in m [12] = 1 can be rewritten using the corresponds to a defocus of CHAPTER 5. 78 Figure 5.13: Influence of fluorescent beads of the with HELM (bottom) The are slip In images which (d) a same obtained cover to show four different 100 by an a slip imaged grey-scale range. and 200 nm, of 0.6° relative to the same (top) of all plane left at the images are and on a cover object plane. size located approx. with the focal brightness diameter respectively. preparation of beads dried angle embedded bead of the is nm in HELM. nm with standard FM sample imaged by using interface. Contrast and the full (c) image formation errors on for defocus of 0, 105 inclinated gelatine behind the water was focusing Images (a) Scale bar 1 pm. RESULTS 1-2 pm cover slip- scaled to span Chapter 6 Three-dimensional HELM In the previous the HELM method chapters, framework of two-dimensional imaging For tions, investigating the three-dimensional is of major interest ping the focus the specimen index of this requires vestigations in structural Unfortunately, show 1In 200 potential OSM has become is artifacts has been interference reported in the applica¬ possible by step¬ acquiring a stack an with low refractive belong to this class important tool for in¬ biology strongly (see contrast to fluorescence nm specimens the axial resolution achievable standard microscopes is and, thus, weakly absorbing objects heterogeneity Typical biological objects and, therefore, of ("optical sectioning microscopy", OSM) of two-dimensional images Evidently, large area structure of the specimen Three-dimensional imaging through discussed was a for limited section 6 imaging, phase a 1) 79 1 very sensitive contrast) [43] and, in even fluorescence with worse, the images Several attempts have been high axial resolution of approx imaging modes (e g differential CHAPTER 6 80 THREE-DIMENSIONAL HELM made to enhance the axial resolution common being ferent known methods for HELM, high referred to herein In this dif¬ chapter, micros¬ the three-dimensional extension 3D-HELM, as The limitation of 6.1 microscopy, the most resolution three-dimensional Afterwards, copy will be discussed of optical in the confocal scanning microscope will be studied mi¬ optical sectioning croscopy In the following, the considerations will be restricted to the fluorescence microscopy, l e incoherent imaging two-dimensional case, the microscope can be described completely by their (denoted three-dimensional OTF which can be calculated (shown schematically by degrees 6 1) is a of can linear torus-like The be derived defocus2 [29, 24] theory [33] scalar diffraction Fig in various a 1, LSI systems 3 3D-OTF) as as of to the transfer function optical herein from the two-dimensional OTF for section in case analogy be described can As mentioned shift invariant system In The 3D-OTF object with two key properties 1 The support of the OTF cone-shaped (generally very low known as frequency parallel "missing cone") The spectrum of to the x-y-plane, are hardly resolved 2With OTFZ0(kx,ky) denoting OTF(fcj;, ky,kz) can be easily shown with respect to the zo-coordinate by averaging the values along As the [54] the a at consequence, region not ori¬ consists of Consequently, such The fact that the resolution for 2D-OTF for defocus z0, to be the Fourier transform of The 2D-OTF fcz-axis even are slice-shaped objects mainly a the origin object spectrum for instance, components within the cone-shaped objects does not include A;z-axis centered components of the transferred at all ented (the passband) region around the can the 3D-OTF OTFZ0(fcj;, ky) be obtained from the 3D-OTF THE LIMITATION OF OSM 6 1 Figure The support of the three-dimensional OTF of 6 1 Shown microscope The OTF tion is is a kx-kz exactly particular objects to as cut-view within can break down conical region around the A;z-axis completely often referred is image corresponds is singular at the origin independent highly-resolved This property of to the fact that the average of the defocus of the consequence, the contrast of thick the fluorescence artifactual imaging the OTF an a a of the rotational symmetric func¬ zero The 3D-OTF becomes 2 81 objects m-focus information is is intensity of 3 object strongly overlaid As reduced by a a as strong out-off-focus blur Due to these unfavorable properties of orescence high ied microscopes, resolution in in in with standard flu¬ three-dimensional space have been the last three decades discussed 3D-imagmg alternative methods to achieve The most relevant ones an uniformly intensely will be stud¬ shortly the next section Conservation of average intensity is a consequence of the fact that all photons entering the lenses contribute to the image produced by the microscope CHAPTER 6 82 for axial resolution Approaches 6.2 THREE-DIMENSIONAL HELM enhancement The confocal 6.2.1 microscope In confocal fluorescence microscopy out-off-focus planes a secondary microscope image can are partially (CFM), photons originating blocked by of the microscope plane a small 6 2a) be shown to be the autocorrelation of the standard The extent of the doubled passband direction is However, the achievable resolution gam in of the OTF towards is lateral nm pinhole, consequently 1 are as well less due to the [14] and, thus, photon efficiency The a high peak result, by the newer an is minimum noise less 4For speed These photon illuminating number of pinhole, practical rea¬ difficulties, however, [47, 86] CFM in 2) subsection 3 2 As flux emitted from the specimen magnitude the whole specimen photons is required the fundamental imaging wavelength the scanners fluorophores (see fluorescence microscopy, this relation account the small [49, 23, 85, 78] by intensities of the focused laser beam saturate the the total level, objectives mfimtesimally caused multi-point limited to values several orders of methods decline rapid drawbacks be reduced potentially axial in still inferior to the The scanning data acquisition limits—at least for can (see cones as The lateral resolution achieved for sons—the achievable imaging 2 is the real resolution gam In addition to the limited mam missing at best for NA 1 4 oil-immersion about 0 8 /xm one is CFM has two nor lateral relation to standard fluorescence microscopy These ideal values one in high spatial frequencies of the order of 150 and the axial in The OTF of the confocal OTF4 [75, 54] and has neither singularities Fig from located pinhole is an in for speed a parallel Since certain signal-to- limitation approximation difference between excitation and is lower than for not emission is much taking light a into AXIAL RESOLUTION ENHANCEMENT Figure 83 Qualitative illustration of passband enhancements achieved 6 2 (a) different approaches by confocal microscopy, l2M, l5M, ASWFM and LSWFM, respectively (f) is the Panels (e) by resulting passband to show the passbands obtained in 3D-HELM for one combination of excitation patterns with various orientations cal was particular Only confo¬ and 3D-HELM allow simultaneous enhancement of lateral microscopy well as achieved axial resolution lower for CFM than for parallel methods (see also subsection 5.1.1). A derivative of the CFM is the so-called a second objective such By using about 120 pared nm an is used for one and for imaging purposes. arrangement, the axial resolution is improved while the lateral resolution remains to the CFM. The ments of 4n-microscope [39, 40]. Here, illuminating objective 4n-arrangement unchanged is very sensitive to relative to the other and it to com¬ displace¬ requires digital CHAPTER 6 84 image processing to remove THREE-DIMENSIONAL HELM artifacts originating from the extremely non-uniform OTF As the 47T-microscope does, employs second a method image interference microscopy objective The images superimposed on a But, in an increased axial resolution A further making of the development As a the is focal plane is inating from device is selectively an incoherent 120 nm Just as approx (see Fig 2c) 6 to relative illuminated displacements processing of the images and I5 M light still a high resulting missing (see Fig cone 6 2b) interference with "image (I5M) [38] Here, in¬ the interference of two beams orig¬ The axial resolution of this source outperforms the lateral one 4n-microscopy, I2M and I5M are sensitive and, thus, of the even objectives Furthermore, not increased at all is by is also coherently additional transferred are coherent interference illumination" microscopy (I2M) non-scanning are artifactual potentially I2 M a result, there However, is objectives of the specimen the images it contrast, the two CCD-chip [36, 37] frequency components the OTF in produced by axial in microscopy (I2M) interference Image 6.2.2 in and require digital post¬ the lateral resolution of I2M relation to standard fluorescence microscopy Computational 6.2.3 Another approach for lateral itself but one) employs digital such struction of OTF to is noise for increased axial resolution microscopy image processing sometimes also in algorithms [8, 2, 1, 42, 53, 18, 19] Taking as some possible in (and does not address the image formation tional information knowledge methods the microscope to extract addi¬ into account non-negativity of the intensity distribution, a priori recon¬ parts of the spectrum outside the support of the In practice, the images, however, particularly such methods posing a problem are in susceptible fluorescence 3D-0TF EXTENSION BY HARMONIC EXCITATION 6 3 excitation methods 6.2.4 Standing Different approaches addressing nodal and antmodal ployed selectively to standing thm are wave excitation have been wave ing wave For Another wave 400 ASWFM) tenth of the cone in based in For which objects an axial wavelength emission the imaging the OTF em¬ (axial [52] was is still remains (see interference fields with their nodal on to the parallel optical LSWFM) demonstrated [64, 65], has been be 3) is planes missing axis (lateral standing An axial resolution of about fluorescence microscope, nm can of the excitation pattern, period one as a approach and antmodal object plane arbitrary objects, however, artifactual 6 2d and section 6 Fig Interference fields with their to the fluorescence microscope, [6, 28, 54] potentially proposed stand¬ by excite individual sections of the specimen resolution of the order of found axial resolution enhancement planes parallel relation to the in 85 which is an improvement to standard fluorescence microscopy but still inferior to the lateral resolution wave (see Fig patterns on Another related Here, a topographic jection of the depth tern a 2e) The effect of technique fringe pattern Digital arbitrarily is is onto the encoded image processing is oriented formally standing section 6 3 in topometry by fringe projection map of the specimen information information 6.3 6 the 3D-OTF will be studied object in the is obtained surface phase By by oblique [88] pro¬ this projection, shift of the used to reconstruct the fringe pat¬ topographic [87] 3D-OTF extension harmonic exci¬ by tation The effect of excitation with on the 3D-OTF dimensional can case a three-dimensional interference pattern be described (see in far-reaching analogy section 3 3 1 and 3 3 2) to the two- An excitation pattern CHAPTER 6. 86 generated by interference of two laser J(r) according distribution intensity J(r) 1 + M = where M is the modulation tion, A are accounts for = an depth, beams5 cos(ur u 87r3(5(k) + + is the arbitrary phase 4tt3M can be described by an to A)), (6.1) spatial frequency of excita¬ offset and where The Fourier transform I of the neglected. J(k) THREE-DIMENSIONAL HELM [elAö(k + u) + where ö denotes Dirac's delta function. scaling factors intensity distribution is e~îAc5(k - Introducing u)] (6.2) , the following scale-shift operators one si(F(v)) = F(v), s2(F(v)) = MF(v S3(F(V)) = MF{w (6.3) + - u) (6.4) and u) (6.5) obtains for the spectrum 6 of the three-dimensional duced by the T = where tp scaling #i,#2 2si(V>) is the fluorescence factors an(i following 3 ^3 x image pro¬ microscope: are f°r „«A ,-»A S2W S3W spectrum and T is the 3D-OTF and where neglected. By sequential acquisition phase (6.6) offsets of 3 set of linear Ai,A2 equations and of three images A3, respectively, the is obtained: (6.7) 5 Section 6.4 explains why ference for 3D-HELM. the considerations are restricted to two beam inter¬ A THREE-DIMENSIONAL HELM SETUP 6.4. The object spectrum can be reconstructed ((M-^e) V> in S2 and S3 shift \ 1 < j < T ^ 0 for at least the vector ±u in becomes the total of the plus j < two shifted copies. in desired di¬ reciprocal be obtained by employing space can reciprocal to patterns with appropriate orientations. lateral Thus, space. as a well passband regions cut-off high section, analyzed. possible ployed. a be su¬ axial resolution enhancement as time in 3D-HELM. one practical In section can frequency throughout A three-dimensional HELM In this three with passband a be achieved at 6.4 As 3. the effective copies of the 3D-passband shifted perimposed 1. one space, Additional 6.2f illustrates how such additional Fig. index 1 < one reciprocal original (6.8) 3, rections in excitation can s;1 by by /J s^1^) regions where passband is = 87 6.3, realization of a setup 3D-HELM device will be it is shown that extension of the 3D-passband if interference patterns with various orientations In relation to the 2D-setup described in are em¬ there chapter 4, are major differences: In 2D-HELM, two overlaid in the patterns with orthogonal orientation object space at one Urne. This enables were one to enhance the resolution in two dimensions without the need for deflection units. cal as one In 3D-HELM, would have to various orientations. patterns oriented Therefore, along propriate deflection this method becomes overlay more a practical setup selected orientations units. unpracti¬ than two patterns with will produce sequentially by ap¬ CHAPTER 6 88 Figure Superposition 6 3 vectors pi and p2 For of two THREE-DIMENSIONAL HELM mutually coherent beams with pi is assumed to be simplicity, parallel wave the to x-axis 2. In the 2D-HELM, propagation vectors of the incident reside within the lower half space the from the backside specimen the 3D-HELM, as the beams the slide through vectors of the two propagation (see reside in the lower and upper half space This 3. In requires a 2D-HELM, parallel second the objective mechanical plates. coupled (Fig. 4.5). degrees in a beams subsection 6.4.1). linearly polarized are would 3D-setup of freedom (DOF) depth (see with Ensur¬ depth. require additional for rotatable half-wave Using circularly polarized light duced modulation to In interfering orientation for maximum modulation ing parallel polarization beams for illumination. beams interfering are subsection instead leads to 6.4.1) a re¬ but makes the setup remarkably simpler. The following HELM setup in 6.4.1 subsections will discuss the realization of more with 3D- Two-beam interference We consider the interference of two coherent Fig. a detail. 6.3. The two opposite plane sense waves are of rotation. plane assumed to be The complex waves according to circularly polarized electric fields of these 64 A THREE-DIMENSIONAL HELM SETUP be described waves can 89 by (6 9) (6 10) where |pi| |pi| = K with K = of excitation and J(r) intensity distribution 7(r) Except to Eq the |Ei = for E2|2 + = one (l 4 1 C0°S(a) ~ + 6 1 with the modulation a is (pi — cos([Pl - phase offset, Eq depth of excitation spatial frequency the difference vector where A the wavelength For the obtains factors and scaling ^p = the refractive index of the medium is n u p2) only, a M pi = (1 = — — p2]r)) 6 11 corresponds cos(a))/2 As p2 (6 11) u and with depends on rotation of both incident beam vectors around the dashed horizontal line m Fig 6 3 leaves the pattern unaffected |pi identity cos(2a) By using rewritten p2| — = 2 According Eq to the shift vector As shown 2K sm(a/2) — 1, and by using the the modulation trigonometric M depth can be as M 6.4.2 = cos2 (a) u 6 ^f^=(M)2 12, M a proportional desired zero for u to the = (612) modulus of squared 0 the incident beam vectors subsection 6 4 Pi and p2 for is and becomes Choosing m = 1, the choice of the incident beam spatial frequency of excitation u is vectors ambiguous CHAPTER 6 90 In this subsection, P2 reside in Given a particular choice will be derived for which pi and the lower and upper half space, desired 0,6 and uz > a THREE-DIMENSIONAL HELM the incident beam vectors Pl2 respectively of excitation spatial frequency are < 'IK set to (6 13) (6 14) 2 K2 P2a |u| " uy\ 2 with 2 P22 Pia u 1 VLt (6 15) 4' Uf, (6 16) Pia if2 P2y This choice fulfills u = pi — - p2 (6 18) Plj , |pi| = |p»21 makes the z-components of pi and P2 the A 6.4.3 A possible 6uz not > 0 change = K inverse and, additionally, of each other setup with minimal number of DOF realization for setup makes (6 17) and lœ-\ Pli use implies a 3D-HELM setup of the fact no the pattern that, for the essential restriction (Eq 6 1) as is shown particular in Fig 6 4 The choice of incident the transformation u -u does A THREE-DIMENSIONAL HELM SETUP 64 91 laser [circularly polarized) ^ CCD M1V Figure Proposed setup 6 4 for 3D-HELM minimum number of DOF beam into two beams of through two objectives A beam This arrangement splitter equal intensity 01 and 02 mirror M3 located in the focal serves for plane setting the A dichromatic mirror Ml allows with a optical on specimen [63] A focal common Abbe-Konig prisms axis a An actuated respectively off- Rl and piezo actuated phase offset of the interference pattern acquisition of the fluorescence image CCD-camera beam vectors described in subsection P2 collimated laser of LI and L2 sets the Rotatable one a Two lenses LI and L2 form R2 rotate the focal spots around the mirror M2 splits which illuminate the spot in the back aperture of 01 and 02, axis distance of the focal spots BS requires the the object plane have 6.4.2, the projections of equivalent length. This pi and corresponds to the fact that the off-axis distances of the focal spots formed in the back apertures of the two If the DOFs for CFM 3D-HELM, objectives required are in equivalent. practice it turns out that 3D-HELM are requires related to those of one additional DOF: CHAPTER 6 92 THREE-DIMENSIONAL HELM 3D-HELM CFM Pattern orientation 2 Lateral scanning 2 Pattern spacing 1 Pinhole radius 1 z-Translation stage 1 z-Translation stage 1 Phase offset 1 E 5 E 4 The drawback of the additional DOF pensated by In CFM, the lower the fastest DOF requires piezo actuated stage per require mirror one scan 3D-image only, lower it is should not cost one scan m than that a per line The other DOFs require drastically simplify practical simulations 540 are excitation nm m based on a wavelength realization of 3D-HELM m nm and an is calculations, 3D-HELM, be employed particular an approximation simulations, is object this approx¬ For the 3D-HELM computationally apodized withm cosine-bell a variety of possible combinations of shift directions for passband extension The simulations combinations of shift vectors given sulting passband 4, of 15 /jm object spectrum a of 1 wavelength objective valid if the thickness of the used without any modifications the passband by In can is is The presented emission the calculations This approximation For the standard fluorescence microscope imative OTF are numerical aperture of the of 488 The 3D-OTF used [24] does not exceed approx the the actu¬ for CFM one In this section, simulation results for 3D-HELM given one scan Since these Simulation results 6.5 an In 3D-HELM the offset and the z-translation several tens of seconds for 3D-HELM expected more phase 2D-image per is com¬ for the 3D-HELM actuators one scan for setting the speed requirements design, ator l e 3D-HELM, however, m speed requirements is shown schematically m m Fig Tab 6 5 cover three 6 1 The Case (b) re¬ is a SIMULATION RESULTS 6 5 case normalized number of minimal shift vectors required modulation [kx, ky, kz) images depth a (0 5,0,0) (0,0,0 65) (0 5,0,0 325) (0,-0 5,0 325) (-0 5,0,0 325) (0,0 5,0 325) (0,0,0 65) (0 5,0,0 325) (0,-0 5,0 325) (-0 5,0,0 325) (0,0 5,0 325) (0 5,0,0 975) (0,-0 5,0 975) (-0 5,0,0 975) (0,0 5,0 975) c d are The performed particular for images very is simple used 7The the The minimum one since Therefore, first employed object spectrum regions known 3 0 23 11 0 31 19 0 31 combinations of shift vectors the simulations is modulation only one the OTF are normalized with respect to 471"^A depth The number of is calculated shift direction (as well shift vector requires For each additional is 2N + 1 with N the number of within the Therefore, only which frequency (per 2D-section) 7 — The shift vectors given the incoherent cut-off vectors 1 — b Table 6 1 93 a as the PSF) to the not shift 6 12 A^-axis symmetric total of three images to reconstruct original passband plus shift vector, is employed by Eq parallel required the the two shifted unshifted component two additional images per further shift vector passband is are already required CHAPTER 6 94 Figure Schematic 6 5 by using THREE-DIMENSIONAL HELM representation of the passband regions obtained the combinations of shift vectors given in Tab 6 1 The panels (a) (e) correspond to the cases (a) to (e) from Tab 6 1 Shown is a projection on the kx-kz-p\ar\e (top row) and on the kx-ky-p\ar\e (bottom to row) with respect to the kx- and A^-coordinate. Case (c) employs five shift directions. The OTF respect to the well by using metry corresponds diagonal to that one of direction in the fluorescence microscopy (case (a)). each For each of these cases, the is calculated. First, the 3D-PSF of 3D-HELM. a objects clearly figure are microscope's parallel case are a total of symmetric with increases the (c) also and The sym¬ (d), data in Fig. given shows calculations for standard response to two different point-like object Secondly, diameter of 2 /im oriented Such slice (c). kx-ky-plajie For case Additionally, a the PSF four additional shift directions. 6.8 and 6.9. objects as kx- and fey-coordinate. Case (d) further axial resolution for the as a infinitesimally to the illustrate the is simulated to obtain x-y-plane imaging thin slice with is considered. artifacts present in CONCLUSION 6 6 case Table 6 2 to point in Fig 95 FWHM FWHM FWHM lateral axial axial point point a 200 nm 480 nm 2270 125 nm 470 nm 410 nm c 125 nm 180 nm 220 nm d 125 nm 115 nm 120 nm objects Fig are of the responses extracted from the are graphs shown 6 9 optical sectioning microscopy (see Fig. 6.7a). the simulations The results of summarized in Tab. 6.2. Conclusion 6.6 The simulation results in the 100 excitation well as demands nm range by choosing size which is an especially practical can useful be the lateral feature, adjusted for 3D-HELM to the given frequency the spécifie vectors. in Tab. 6.1 eight is images same higher times in 3D-HELM number of realization of as well in CFM is twice that microscopy. Therefore, the original images times faster to obtain the a isotropic resolution it must be related to the maximum voxel the cut-off Consequently, almost the Shannon criterion. In lateral imposed by volume of the For an required images of standard fluorescence an appropriate combination of shift high. However, direction, in CFM. show that be achieved in three-dimensional harmonic axial resolution in 3D-HELM rather in axial clearly can light microscopy. As The number of seems The data nm (FWHM) The full widths at half maximum 6 8 and 2 /xm0 b and slice standard as slice, can some maximum voxel in 3D-HELM than photons 3D-HELM, as one be acquired eight per voxel. aspects have to be CHAPTER 6. 96 Figure 6.6: Calculated THREE-DIMENSIONAL HELM point spread functions for for 3D-HELM. Panels (a) to (d) correspond to to the respective cases in Tab. 6.1. Shown is a kx-kz-sect\or\ of the three-dimensional PSF. To enhance the visibility of the side lobes, a non-linear grey scale with 7 1.2 = was used. Scale bar is 1 pm. considered come a time. It is an more serious carefully problem than in 2D-HELM. Thermal drift could be¬ due to the expected, however, strongly that drift problems optimized design and/or computational image reconstruction algorithm. regions but not of the different least, the as well as required. in three passband copies efficiency drift Furthermore, for pattern parameter estimation is sible in two dimensions extended data of the a different Basically, by analyzing in 3D-HELM algorithm acquisition be handled by compensation by the can is of approach this is pos¬ the overlap [35]. And, major concern last due 6 6 CONCLUSION Figure HELM Calculated responses to 6 7 Panels Shown is visibility a (a) to (d) correspond a slice to to object (diameter the respective kx-kz-sect\or\ of the three-dimensional image of the side lobes, a 2 cases non-linear grey scale with 7 pm) in 3D- in Tab 6 1 To enhance the = used 1.2 was an unrivaled Scale bar is 1 /jm to the To high volume of data. conclude, 3D-HELM has the potential resolution in three dimensional space. inherent advantages compared ing pinhole relevant. one is required The cost of the of CFM. case a imposed by dye experimental setup are HELM has to CFM since neither limitations The additional the two-dimensional solvable. nor to achieve Furthermore, problems technical is photon some block¬ saturation comparable are to that of 3D-HELM in relation to ones and are expected to be CHAPTER 6 98 THREE-DIMENSIONAL HELM lateral PSF lateral PSF lateral PSF axial PSF -0 5 0 axial PSF 05 -08-06-04-02 [um] 0 lateral PSF (diagonal) lateral PSF (x) axial PSF 0 02 04 Figure (d) 6 8 06 -04-03-02-01 the different case 0 01020304 [um] Calculated point refer to (diagonal) lateral PSF (x) axial PSF [um] to 02040608 [um] lateral PSF 16-04-02 (x) (y) (a) scalmgs on to spread (d) functions of Tab the abscissae 6 1 m 3D-HELM Graphs (a) paid to Attention should be 6 6 CONCLUSION 99 1 p^^^ ^ y 08 1 06 S 04 - 02 U 0 -2-15-1-050051 152 I I [|xm] x I -2-15-1-050 L 05 1 15 2 [um] diagonal diagonal x ~ -2-15-1-050051 152 "«' I Figure 6 9 to (d) of Tab 'W ~ 152 [|xm] Calculated lateral responses to parallel I -2-15-1-050051 [um] oriented I to 6 1 the a thin slice of 2 pm diameter fe^-A^-plane Graphs (a) to (d) refer to cases (a) CHAPTER 6 100 THREE-DIMENSIONAL HELM 1 - 08 >. - <7> - 06 - 04 "s. - 02 - -"l 3 I -2 -1 I I 0 1 i^-> 2 I I 0 3 I -1 -0 5 z[|xm] I 0 05 1 z[|xm] 1 08 ë h 06h 04 02 0 -06-04-02 0 02 04 06 -04-03-02-01 z[|xm] Figure to (d) parallel of Tab the abscissae to 6 1 01020304 z[|xm] Calculated axial responses to 6 10 oriented 0 the a thin slice of 2 pm diameter fe^-A^-plane Graphs (a) Attention should be paid to to (d) refer to the different cases scalings (a) on Chapter 7 Conclusion This thesis concentrates cence A on resolution enhancement in far-field fluores¬ microscopy by illuminating the specimen with structured light. method, called "harmonic excitation been introduced and realized which light microscopy" (HELM), has employs space-harmonic intensity patterns generated by interference of laser beams to than double more the resolution. The first part of the thesis is field distribution in the pattern on the a theoretical object plane image formation. study of the electrical and of the influence of the Frequency domain analysis that additional information not accessible in conventional can be extracted. For that purpose, shifts of the pattern must be images acquired and for different light shows microscopy translatory postprocessed electroni¬ cally. In a next step, a was planed and realized. The main compo¬ generating apparatus which produces a two- setup nent is the interference dimensional mesh-like interference pattern in the a mesh-like pattern allows one sions without mechanical actuators to rotate the design issue was the stability object plane. Using to enhance the resolution in two dimen¬ pattern. of the pattern for the 101 A critical relatively long CHAPTER 7 102 Sufficient time acquisition design reducing could be achieved stability thermal drift and CONCLUSION by by compact a using electrostrictive actuators Since the interference generating apparatus illuminates the specimen from the backside path were The no modifications is in of difficulties The paraxial theory not restricted to any optical transfer function calculated transfer function under of samples a sample verify an was can Compared speed was well as the enhancement, imaged acquir¬ histological samples was limitations widely achieved same is not of HELM has subject of res¬ practical an even no photon to fundamental imag¬ the small illumination spot imposed by ad¬ Images showed that the objects area and, used confocal microscope, Furthermore, and biolog¬ as with HELM also be achieved with to the efficiency reducing pinhole ing tested with artificial the resolution various olution enhancement better resolution by atomic force microscope for reference microtubules and of interest conditions and images with the fluorescence filter removed of fluorescent beads with ditionally, pre¬ path The HELM-method To sub-pixel measuring the by carefully comparable optical brightfield from the imaging ical by turned out to be too inaccurate and the orientation These hurdles could be mastered ing additional showed algorithm image reconstruction an of the interference pattern had to be determined with cision the imaging of microscope implementation mam slide, For this reason, the setup required particular type two the through size in confocal microscopy A further topic of the thesis dimensional imaging to generate entation setup is in the extension of the method to three- A modified setup space harmonic interference three-dimensional space comparable with that resolution gam of this device provides is an the need for one was The proposed which allows complexity any desired of the of confocal devices analyzed by almost isotropic resolution a is patterns with in lateral scanning mechanism numeric the 100 nm one ori¬ proposed The achievable simulations It range without These properties are not 103 achieved by any other method. The next step would be the realization of HELM setup and the algorithm. construction HELM are an It is employing complications efficiency provide and long image acqui¬ by that these issues the can high by add-ons to three-dimensional unrivaled resolution combined with high speed imaging capability. volume be solved algorithms and, probably, experimental an re¬ in three-dimensional limitations caused expected, however, three-dimensional appropriate image object and/or pattern position. Then, HELM would ton computational smart calibrate the Possible a increased mechanical drift due to the sition time and of data. implementation of the high pho¬ 104 CHAPTER 7 CONCLUSION A Appendix in Optical trapping interference fields This thesis is part of the NANO-II project at the "Eidgenössische Technische Hochschule Zürich" where NANO stands for "Non-contact Assembly jects". and of and Non-contact Nano-Objects The goal of the project manipulating objects is to study Analysis of Nano-Ob- methods for in the sub-micrometer range. visualizing The HELM setup described in this thesis produces interference patterns which expected to be applicable to optical trapping obvious to also consider the first results for are well. as manipulation aspect. optical trapping Therefore, In this it are was appendix, with HELM-like interference patterns presented. Generally, vorable since nipulating methods light are used for non-contact methods for problems tool are are avoided. One optical traps. Here, employed particle handling with adhesive forces between important class of such forces exerted to control their motion. optical trapping works with 105 on and ma¬ non-contact particles by The most strongly very fa¬ are object intense common setup focused laser beams. APPENDIX A 106 Under suitable the laser focus forms conditions, [4, 11, 34] dielectric well as erate laser powers metallic as of Manipulation [61] illumination time-multiplexed OPTICAL TRAPPING a [81] particles even few is by or particles for mod¬ possible by methods holographic using well for potential a [67] In practice, ten essential which make ped parallel handling Parallel bright force which denoted Till as less than one particle in crystals, non-contact are trap¬ result of the dominant form a regular array matter To meet the requirements must be reduced to notice¬ sizes Potential micrometer traps he of¬ is interference traps have been realized for rela¬ micrometer) objects only few of the NANO-II project, the ably as a optical or objects by optical traps Basically, particles Suspended particles optical crystal today, however, tively large (a be achieved of such patterns [15, 84, 17] gradient is zones number of large a can of interference patterns use within the of manipulation applications particle transport and of such [27] the field of writing diffractive structures controlling or optical photonic the crystal¬ by electron lization of macromolecules for structural investigations microscopy The connection to HELM lies patterns used for harmonic trapping very small particles the interference field in the as setup wells zones are However, an this observation gives 1A transport demonstrated by by Therefore, [32, 62] Using extent probability and, together rise to the using a of slightly larger D Hafliger in a beads (200 nm a source one in potential the bright predictions, complete trapping 1 diameter) beam TIR setup similar 100 mW ylr-ion with theoretical assumption that a which allows of presence stronger laser a one of HELM system turned out to be trapping forces greater increased could be observed could be achieved a capable the intensity of beads could still escape from the polystyrene 100-nm to be expected Unfortunately, built within two semester theses to focus the laser beams to laser, well presented too small to achieve sufficient was the fact that the interference in excitation could be recently A 1 PHYSICAL BACKGROUND A.l 107 Physical background In this section, the basic forces exerted fields will be discussed to be consistent with To on particles in electromagnetic the mathematical simplify the Gaussian system of units literature, and description used is [45, appendix] The of size wavelength act a Rayleigh as Rayleigh known employed light dipole As scatterers scatterer is a polarized [45] characteristic time harmonic ( 100 of interest particles of the electromagnetic is given 128 the Therefore, result of A Rayleigh is scatterer For ir5nm f m? the refractive index of the R energy flux [84] is - gradient pwhere E is the = complex t sphere force is lx Rb S, 2There A and S is is, however, for the a more is m the the time one is the vacuum averaged by l^rijRS V(|E|2)' electric field to be the dominant zero a (A 1) (A2) strength [84] since studied, the gradient force is the lateral energy flux of the field distribution vanishes due to the lateral symmetry almost to the scat¬ spherical particles, medium, given For the two-beam interference setup expected exposed forces, embedding medium, and particle the radius of the The field, to the well by ratio of refractive indices of wavelength, particles basically field experiences two fgrad well below the according 3cA4 where nm is external electric an and radiates tering force Fscat and the gradient force the scattering force less) nm or small axial force component relevant setup described in 2 This axial force becomes section A 2 APPENDIX A 108 Since the defined force gradient For one,3 conservative is a this spherical particle, a OPTICAL TRAPPING potential can be be calculated by potential a can integrating Eq A 2 r W(r) J -Fgrad(r) = dr -cm = R3 |E(r)|2, (A 3) oo where the potential Eq A duced this 3 allows to calculate the one the electric field end, pattern has flux S of a strength |S| where c medium is (1 the velocity of light (see Fig {E\ and E<i 140 /jm calculated by using £i Eq A = 3) 4 in 4 = the two 3The curl of the the definition of a gradient potential = in¬ To of the illumi¬ by is (A4) the refractive index of the a the In HELM, beam diameter of amplitudes 22, respectively) /ERG 101 = is \ used of the can be /a n 2Ei beams cos is is (1 ERG according ( kxx + zero (A 5) —r, 10~7 J) [45, = of the interference pattern amplitude Eles force field is given 3 20 and 3 Eq y-polanzed Eres zones 0) as i— The electric field generated by bright Therefore, where the Gaussian energy unit ERG appendix] spherical particles focused to /87r|S| £2 well potential particles) [45, chapter 7] are = The modulus of the energy wave is and nm 33 for water immersed incident beams the W(oo) e ^|E|2, = four laser beams of 25 mW each approx small to be calculated first plane electromagnetic of the depth on m infinity (l at zero the HELM interference field by nation set to is energy — J for Eq 3 28 (A 6) , due to V unambiguous except to X an (VF) = 0 Therefore, additive constant A.2. THE SETUP FOR OPTICAL TRAPPING where the reflection at the partial In the antinodal zones, the slip cover neglected (i.e. Since the Eles equals 2E\. the maximum field x-polarized field, is 109 amplitude Emax R = 0). is true for same of the two- dimensional pattern becomes Emax a/2 where the factor mersed = 1.59 the J 2.86 results from the orthogonality beads cm is 0.147. potential a W0 well = is obtained for 100 = depth 1.5 nm 1.33, refractive (nm Inserting Eq. A.7 and two to three orders of x 10-16ERG = 1.5 calculations, prediction strongly The the HELM setup is not is in complete agreement increased A.2 The was a few ence, the In the key (A.8) 4 x temperature, the 10~21 J and, hence, Wq (k Kelvin). expected to is the Boltzmann According to these trap particles. This with the observations. one For this to achieve a intensity. setup for optical trapping significant is similar to the HELM differences exist. trapping setup provides only interference pattern to reduce A polystyrene the value of cm into built which enables optical trap setup (Fig. A.l) ever, and y- room = than magnitude larger different setup index of 10~23J x At diameter beads. and T is the temperature in a x- of average kinetic energy is of the order of kT reason, of the well depth Wq can be calculated by applying appropriate material constant cm. For water im¬ polystyrene [48]), constant (A.7) cmJr, V potential with the Eq. A.3 = field components. polarized Now, Eq. A.3 V2x2E1 = a one-dimensional complexity a focal (fringe-like) and costs. difference is the reduced diameter of the trapping setup, lenses with setup. How¬ As the most obvious differ¬ length illuminating spot. of 18.4 mm are placed APPENDIX A 110 L1 Figure A 1 used for Setup laser beam is P1 split by beam Two lenses LI and L2 PI and P2 form slip A collimated BS into two beams of equal intensity 18 4 mm A vertical translation of the beams the position of the focal spot angle L2 optical trapping experiments splitters (focal length changes for P2 focal spot in the water a OPTICAL TRAPPING of incidence by air) in and two (illustrated by cover the dashed maximum ±2.5° without An inverted glass prisms between slide and layer line) affecting microscope (not shown) the serves observing in direct proximity of the prisms resulting diameter of 7.6 /jm for the used laser waist diameter wq = 1.5 HELM, of 200. a theoretical beam waist (Eq. 4.1, primary beam mm). The measured value is plained by in source aberrations and roughly by 10 /xm; the difference measurement the reduced spot size leads to an errors intensity [62]. can be ex¬ In relation to increase by a factor A 2 THE SETUP FOR OPTICAL TRAPPING 2 111 - £15o a= 3 "q. 05 ra - 0 - 0 10 20 30 40 incident Figure A 2 Amplitude one layer 60 70 80 in direct 90 coefficient of the transmitted beam for Shown is the ratio of the electric field water transition water 50 angle [degree] proximity to a glass- amplitude in the the interface relative to the incident The dashed line indicates the critical angle (61°) for TIR the criterions for choosing the angle of incidence a.% quite different for optical trapping than for HELM. The reasons Furthermore, are for choosing 5.1.1) do not propagating at smaller than the critical apply waves to amplitude for TIR trapping experiments. Trapping [15] well as the achievable electrical field one angle as with evanescent strength is of (see is subsection possible ones [48]. with Since major importance, the coefficient of the transmitted beam relative to the incident (Fresnel formulae, [12]) illustrates that working enhances the electric field four times increased should be taken into account. near strength by intensity. incidence is approx. 184 the critical The a angle Fig. A.2 is favorable factor of two fringe spacing as resulting for these this in angles a of nm. As in the HELM setup, a piezo actuator is provided to shift the APPENDIX A 112 Figure A 3 ZEISS microscope of the Photography OPTICAL TRAPPING trapping setup mounted The two visible adjustment knobs on serve an inverted for aligning the illumination spots relative to each other interference a sawtooth perpendicular and relative to the immersion medium. fringes voltage Fig. A.4 to the to the show actuator, fringes an expected is photographs of the glass-water interface, intensity 800 in relation to the HELM tions leading of 1.2 (4 x x to Eq. A.3, 10~20 J which one is obtains slightly Fig. A.3 to be achievable. amplitude amplification is enhanced setup. By applying particle transport trapping setup. Due to the reduced spot size and the the effective by a By re-performing an the calcula¬ expected potential well the setup described makes probability of presence for observable. Such an a sense depth above the average kinetic energy 10~21 J). Though the estimated potential well depth of ?>kT may not be sufficient for at the factor of approx. approx. complete (i.e. long term) trapping, for two particles reasons: within the an increased zones should be First, bright observation would validate the theoretical calcu- A 3 RESULTS Figure A 4 Visible are Bottom view of the lations. the Secondly, by employing A.3 power is expected the beam splitter) to be achievable and/or increasing the viscosity medium to reduce thermal motion. Results To test the beads with As complete trapping a stronger laser a embedding optical trapping setup with removed base plate optical components (prisms, mirrors and flexible joints for aligning the optical paths and two of the 113 trapping behavior of the setup fluorescent polystyrene a diameter of 100 axis at expected, escape from was the beads one fringe statistical method presence was set to was nm were slightly were and not cross used. The beam's below the critical completely trapped, over to another i.e. one. needed to find out whether the nonuniform. angle angle to the for TIR. they could Therefore, a probability of APPENDIX A 114 slip cover A 5 Figure of the interference Geometry OPTICAL TRAPPING zone In contrast to the HELM setup, the interference in the optical trap setup zone is at the slide-water interface Due to the small spot size and the flat the water layer, ones even for a angle of the beams in the reflected beams do not interfere with the incident very thin water A statistical with analysis is of layer few micrometer a possible by measuring CCD-camera and the scattered light it to the scattered a relating intensity intensity without interference.4 For this analysis, the total light intensity on the CCD-chip for an ensemble of scatterers is assumed to be the the intensities of the individual wave of one individual ones. The Rayleigh particle is proportional particle position [45, chapter 25]. Therefore, on the CCD-chip It can be calculated J Ij=C field of where p is the C is a constant. (Eq. 3.28) Now, the incident beam £„» 4The = light to |E|2 at the light intensity p(r)|E(r)|2, (A.9) dr object plane and where the field distribution of the interference field a glass-water R = 0, see 2Eie-tk'z cos(kxx) fluorescence due to the (i.e. the total view has to be rewritten in beam reflected at the of by of the scatterers in the density sum intensity of the scattered + somewhat different form. Since the transition does not interfere with Fig. A.5), Eq. (E2 - 3.28 becomes Ex)etk'xe-tk'z, (A.10) turned out to be useless for quantitative measurements rapid photo-bleaching A.3. RESULTS where the 115 shift A is set to phase applicability. Taking \Eres\A cos(2x)) view, are one E( = Ei + sin2(x) where the identities used. zero the modulus of + ^-(1 = without Eq. — {El cos(2x)) + interference pattern. For the first second El) + 2E1E2 image For the acquired cos2(x) ^(1 = + \ J ^ caa(2kxx) the first beam was (A.12) dv view sample with total intensities was blocked both beams could interfere. intensities particle distribution and of immersed and 11^2 blocked (i.e. E\ According beads, three It, respectively. (i.e. E2 =0), for the 0) and for the last = to Eq. A.12, the total are For the ratio h = CNEf, h = CNEl Il = CN{E\+El) It/(Ii +12) i, _ h +h intensity ratio one (A.14) and + = l + (A.16) K, E\ approximately equals E2. By evaluating Eq. A.16, For 100 (A.15) 2CE1E2K. obtains the correlation K between bution and interference pattern total intensities. (A.13) E21+El+2E1E2K E\+ El where it is assumed that the same image the second beam image and Eq. A.9 into where K describes the correlation between were general (A.ll) =K field of images the obtains With N the number of scatter ers in the field of ( IJ=CN affecting one 2E1E2 œs(2kxx), by inserting Eq. A.ll obtains A.10 nm can particle distri¬ be calculated from the measured diameter beads immersed in a mixture APPENDIX A 116 of 50% glycerin To validate the prepared, an method, here the zero of approx to nm the setup is well depth to be sufficient for by J increased was of the was near particles, of presence probability constructed to function with the is a in the as well laboratory, factor of ln5nw 100 ^ mw 2 By the = using a in the 6 25 common 5 W laser of well potential depth Therefore, ' would be of the order of 80 kT which is the expected complete trapping estimation of 3fcT optical paths correlation of 0 15 for mobile found slip certainly independent is the measured value for K of Nd-YAQ lasers available would be increased potential slightly a was cover agreement with the estimated potential well depth wavelength this type which BThe expected, 0 15 = 5 ?>kT Fortunately, 1064 a is in zones, correlation K of beads fixed to the distribution (0 02) Furthermore, corresponding bright As a sample a particle interference pattern to 50% water, OPTICAL TRAPPING Therefore, is based on infinitesimal small the value should be particles interpreted carefully and lossless as "of the order of kT" 6The are factor = isa result of the fact that the inversely proportional to the wavelength gradients of the in an interference field employed light Bibliography [1] D. A. Agard, croscopy: Y. Hiraoka, and J. W. Sedat. Three-dimensional mi¬ image processing for high resolution subcellular imag¬ ing. Proceedings of the SPIE, 1161:24-30, [2] D. A. Agard, microscopy cence Y. Alberts, [4] A. Cells in and Spectroscopy, Biology. Academic Press, 1989. D. Cell Bray, J. Lewis, Biology of M. Raff, K. Roberts, the Cell. Garland Ashkin, J. M. Dziedzic, J. E. single-beam gradient Bjorkholm, force volume 30 and J. D. Publishing, third and S. Chu. Ob¬ optical trap particles. Optics Letters, ll(5):288-290, for dielectric 1994. D. Axelrod and E. H. Hellen. Emission of fluorescence at face. In D. L. Cells in Imaging Fluores¬ Quantitative 1994. servation of [5] Taylor, editor, Culture Part B. Microscopy—Imaging in Watson. Molecular edition, and J. W. Sedat. Fluorescence Shaw, in three dimensions. In D. L. Fluorescence B. P. Microscopy of Living of Methods [3] Hiraoka, 1989. Taylor, editor, Culture Part B. and Academic Quantitative Spectroscopy, Press, Fluorescence Fluorescence volume 30 of Methods 1989. 117 an inter¬ Microscopy of Living in Microscopy— Cell Biology. BIBLIOGRAPHY 118 [6] B. Bailey, D. L. Farkas, D. L. Nature, 366:44-48, excitation. [7] P. L. X. F. Becker. Wang microscopy by standing-wave 1993. fluorescence Quantitative and B. and F. Lanni. Enhancement Taylor, of axial resolution in fluorescence Herman, editors, measurements. Fluorescence In Imaging Spec¬ troscopy and Microscopy, volume 137 of Chemical Analysis. Wi¬ ley, [8] 1996. M. Bertero and P. Boccaci. light microscopy. [9] Scientific, G. Binnig G. and C. F. Binnig, H. C. Gerber, microscope. Physical and E. Weibel. work with Making light edition, Brakenhoff, Brakenhoff, Nanninga. copy. In D. L. Cells in Imaging P. Blom, with and P. Barends. high aperture Academic Letters, Nature, tweezers. Pergamon Press, E. A. van Confocal scanning immersion lenses. Journal 1979. Spronsen, H. T. M. van der Voort, and Three-dimensional confocal fluorescence micros¬ Taylor, editor, Culture Part B. and optical Principles of Optics. of Microscopy, 117(2):219-232, G. J. Surface stud¬ Review 1980. light microscopy N. force 1986. 1992. M. Born and E. Wolf. G. J. Torresani, Detection and 1982. S. M. Block. sixth [14] Scattering: by scanning tunneling microscopy. Physical 360:493-495, [13] Rohrer, and B. 1988. Quate. Atomic Letters, 56(9):930-933, in confocal problems Chiapetta, Inverse Problems. World 49(1):57-61, [12] P. and Acoustic ies [11] Linear inverse Bourrely, editors, Electromagnetic Review [10] In C. Quantitative Spectroscopy, Press, 1989. Fluorescence Microscopy of Living Fluorescence volume 30 of Methods in Microscopy— Cell Biology. BIBLIOGRAPHY [15] M. M. Burns, [16] M. J.-M. Y. Chalfie, Chiou, W. Interferometric 10, [18] G. Tu, protein 263(5148) :802-805, A. E. and and J. A. Golovchenko. binding in intense optical Optical fields. Sci¬ 1990. 249:749-754, fluorescent [17] Fournier, Crystallization matter: ence, 119 and W. W. Ward. Euskirchen, as a marker for gene expression. Green Science, 1994. Wang, optical G. J. Sonek, tweezers. J. Hong, and M. W. Berns. Optics Communications, 133:7- 1997. J.-A. Conchello. Superresolution and point spread function sen¬ sitivity analysis of the expectation-maximization algorithm for computational optical sectioning microscopy. Proceedings of SPIE, 2302:369-378, [19] J.-A. Conchello. the Superresolution and convergence properties of expectation-maximization algorithm for maximum-likelihood deconvolution of incoherent ety of [20] G. E. America Cragg standing [21] 76, Optics Letters, 25(l):46-48, Observing deformations of 20 2000. nanome¬ microscope. Proceedings of the 1996. J. H. Strickler, and W. W. Webb. Two-photon scanning fluorescence microscope. Science, 248(4951):73- Denk, laser [23] waves. low numerical aperture SPIE, 2782:180-191, W. 1998. and P. T. C. So. Lateral resolution enhancement with evanescent a images. Journal of the Optical Soci¬ A, 15:2609-2618, G. Danuser and E. Mazza. ter with [22] the 1994. 1990. V. Drazic. Three-dimensional transfer function focal fluorescence tector. Journal of microscope Modern with a analysis finite-sized Optics, 40(5):879-887, source 1993. of a con- and de¬ BIBLIOGRAPHY 120 [24] A. G. Erhardt, ing Zinser, D. Komitowski, plied Optics, 24(2):194-200, [25] Y.-S. L. M. Fan, sequences by metaphase of [26] [27] fluorescence in situ edition, R. Fournier, Freimann, wave [29] J. T. tion the Frohn, beyond M. M. F. Optical H. F. the transfer of the three-dimensional Knapp, Rayleigh and A. Stemmer. True limit achieved the National optical by standing Academy of object. 1967. wave resolu¬ illumi¬ Sciences USA, 2000. Füglistaler. Optical Resolution enhancement for fluo¬ matter. Hochschule, Zürich, J. W. Goodman. second 1997. microscopy by standing-wave illumination. EOS Topical Technische [33] the and H. Horler. Development of a standingmicroscope with high nodal plane flatness. Meetings Digest Series, 25:58-59, [32] Writ¬ by optical trapping. Proceedings of J. T. Frohn and A. Stemmer. rescence and J. A. Golovchenko. Optical Society of America, 57(l):56-66, 97(13):7232-7236, [31] Burns, 1995. Proceedings of nation. 1990. of Microscopy, 187(3): 193-200, of banded Academy Pentz, B. R. Frieden. Journal [30] S. fluorescence Journal the National 1997. SPIE, 2406:101-111, [28] small DNA Elektrodynamik. Spektrum Akademischer Verlag, diffractive structures ing Mapping hybridization directly on Proceedings of USA, 87:6223-6227, T. Fliessbach. J.-M. R. 1985. and T. B. Shows. Davis, chromosomes. Sciences second and J. Bille. Reconstruct¬ light-microscopic images by digital image processing. Ap¬ 3-D edition, 2000. Semesterarbeit, Eidgenössische 1999. Introduction to Fourier 1996. Optics. McGraw-Hill, BIBLIOGRAPHY [34] [35] K. O. 121 Greulich. Micromanipulation by Light Mediane. Birkhäuser Verlag, Basel, M. G. L. Gustafsson. Surpassing factor of two using [36] M. G. L. Gustafsson, D. A. two objective lenses. microscopy. by a Journal 2000. Agard, improvement of axial resolution ing the lateral resolution limit structured illumination of Microscopy, 198(2):82-87, and Biology in 1999. and J. W. Sedat. in 3D widefield Proceedings of the Sevenfold microscopy us¬ SPIE, 2412:147-156, 1995. [37] M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat. 3D widefield microscopy with with two objective lenses: experimental verifi¬ cation of enhanced axial resolution. 2655:62-66, [38] M. G. L. widefield tion. [39] Gustafsson, light microscopy S. W. 100 [41] Hell, nm P. D. Journal microscope. fluorescence [42] Y. and J. W. Sedat. Properties of the of nm I5M: 3D axial resolu¬ 1999. a 4n confocal fluores¬ Optical Society of America A, Schrader, and H. T. M. van der Voort. Far-field microscopy with three-dimensional resolution in the Higdon, Journal P. Journal of Microscopy, 187(2):l-7, Török, and T. Wilson. fluorescence J. W. Sedat, and D. A. Imaging properties imaging properties Partial confocal behavior in Biophysical Journal, 57:325-333, Agard. of 1997. scanning optical of Microscopy, 193(2):127-141, three-dimensional tem: SPIE, M. range. Hiraoka, the 1992. high aperture multiphoton scopes. Agard, with better than 100 of Microscopy, 195(1) :10—16, Journal 9:2159-2166, [40] D. A. S. Hell and E. H. K. Stelzer. cence Proceedings of 1996. a of micro¬ 1999. Determination of light microscope sys¬ epifiuorescence microscopy. 1990. BIBLIOGRAPHY 122 [43] S. Inoué. precision D. L. Taylor, editor, Culture Part B. and Press, [45] and objects, superresolution, In microscopy. Microscopy of Living Fluorescence volume 30 of Methods Cells in Microscopy—Imaging in Cell Biology. Aca¬ 1989. S. Inoué and K. R. Plenum Fluorescence Quantitative Spectroscopy, demic [44] of unresolved Imaging of distance measurement with video Press, J. D. Jackson. Video Spring. Microscopy: The Fundamentals. 1997. Classical Electrodynamics. Wiley, second edition, 1975. [46] H. O. face Jacobs, H. F. Knapp, potential mapping: A R. Juskaitis, T. [48] M. A. A. Neil, and M. Kozubek. Efficient microscopy with white light soureces. Nature, 1996. S. Kawata and T. 17(ll):772-774, Sugiura. Movement of micrometer-sized par¬ on a laser beam. the pinhole Dependence of 3-D T. A. Klar and S. W. Hell. fluorescence [51] N. S. an 1996. microscopy. 1999. computed point indirect water immersion three-dimensional fluorescence SPIE, 2655:34-42, optical Subdiffraction resolution in far-field and F. Lanni. Measured and functions for transfer 1990. microscopy. Optics Letters, 24(14):954-956, Kontoyannis spread optical radius in fluorescent confocal microscope. Applied Optics, 29(20):3007-3011, [50] Optics Letters, 1992. S. Kimura and C. Munakata. functions Sur¬ 1997. ticles in the evanescent field of [49] and A. Stemmer. material contrast in SPM. Wilson, real-time confocal 383:804-806, Müller, qualitative Ultramicroscopy, 69:39-49, [47] S. objective Proceedings of in the BIBLIOGRAPHY [52] V. 123 B. Krishnamurtlii, 3-D standing-wave SPIE, 2655:18-25, [53] V. and F. Lanni. Bailey, fluorescence Image processing microscopy. in the Proceedings of 1996. Y.-H. Krishnamurtlii, T. Liu, J. Holmes, B. Roysam, and J.N. Turner. Blind deconvolution of 2D and 3D fluorescent mi¬ the crographs. Proceedings of [54] F. Lanni, field B. as a means in fluorescence [55] data. 56(11):1463-1472, W. Lukosz and Überschreitung tica [58] of theorem for SPIE, 1660:140-147, with of the Excitation Taylor. enhanced axial resolution resolving 1993. square-pixel 1992. powers exceeding Optical Society of America, 1966. M. der Mclntyre, specifity [59] Journal Optische Abbildung Marchand. J. F. adoptive and R. M. Welsh. Bukowski, Exquisite immunization in arenavirus-infected mice. Antiviral Research, 5(5):299-305, G. and N. M. Amer. Simultaneous measurement of lateral Meyer an 1985. optical-beam-defiection atomic force microscope. Applied Physics Letters, 57(20):2089-2091, M. Minsky. scope. [61] Op¬ 1963. and normal forces with [60] unter beugungsbedingten Auflösungsgrenze. Acta, 10:241-255, K. W. Sampling the Optical systems the classical limit. [57] obtaining 1992. microscopes. Bioimagmg, 1:187-196, Proceedings of W. Lukosz. and D. L. Farkas, for F. Lanni and G. J. Baxter. image [56] D. L. Bailey, synthesis SPIE, 1660:95-102, C. Memoir on inventing the confocal scanning Scanning, 10:128-138, Mio, scanning T. Gong, A. Terray, laser optical 1990. trap for micro¬ 1988. and D. W. M. Marr. Design multiparticle manipulation. of Scientific Instruments, 71(5):2196-2200, 2000. of a Review BIBLIOGRAPHY 124 [62] M. Münchinger. mesterarbeit, Transportieren mit dem Lichtförderband. Technische Eidgenössische Hochschule, Se¬ Zürich, 2000. [63] H. Naumann and G. Schröder. Hauser [64] sixth Verlag, München, Bauelemente der edition, M. A. A. Neil, R. Juskaitis, and T. Wilson. Method of obtain¬ ing optical sectioning by using structured light in a conventional microscope. Optics Letters, 22(24):1905-1907, [65] M. A. A. Neil, R. two beam interference illumination. Communications, 153:1-4, D. W. Pohl, recording W. Optics 1998. and M. Lanz. Denk, A/20. with 1997. and T. Wilson. Real time 3D fluores¬ Juskaitis, microscopy by cence [66] Carl Opük. 1992. Optical stethoscopy: Image Applied Physics Letters, 44(7):651-653, 1984. [67] M. Reicherter, tical ten [68] Haist, particle trapping on E. U. with D. R. Op¬ computer-generated holograms liquid-crystal display. Optics Letters, 24(9):608-610, 1999. Fundamentals of Photonics. 1991. Sandison, D. W. ratio, and resolution croscopes. D. R. and H. J. Tiziani. writ¬ Piston, Quantitative comparison [70] Wagemann, B. E. A. Saleh and M. C. Teich. Wiley, [69] T. of R. M. in confocal and full-field laser Applied Optics, 34(19):3576-3588, Sandison, and W. W. Webb. Williams, background rejection, signal-to-noise R. M. Williams, K. S. scanning mi¬ 1985. Wells, J. Strickler, W. W. Webb. fluorescence confocal laser logical Confocal Microscopy. Plenum and Quantitative scanning microscopy (CSLM). In J. B. Pawley, editor, Handbook of Bio¬ Press, second edition, 1995. BIBLIOGRAPHY [71] 125 S. G. Schulman. Fluorescence and and Physicochemical Principles [72] Chemistry. Pergamon Press, L. Syrjänen, M. Seveus, R. S. Väisälä, J. Harju, Salo, I. Time-resolved fluorescence immunohistochemistry 13(4):329-338, Z. Shen and H. H. C. J. R. Sandberg, A. Annals Hemmilä, Kojola, imaging of europium chelate label and in situ hybridization. of contact Cytometry, enhancement of the in vivo Biomedical and A. using optical sectioning zone Engineering, 25:521-535, Choudhury. Image Science, 232(4747):211-213, [77] J. J. Stamnes. [78] E. H. K. Stelzer. in Focal 1997. 1977. microscopy 1986. Regions. Adam Hilger, 1986. Contrast, resolution, pixelation, dynamic signal-to-noise fluorescence [79] Waves ratio: mi¬ formation in the R. Sonnenfeld and P. K. Hansma. Atomic resolution and in Introduction to Fluorescence Lipowski. Image Sheppard in water. Kuu- and E. Soini. scanning microscope. Optica Acta, 24(10):1051-1073, [76] Analytical 1999. leukocyte-endothelium [75] M. H. A. Sharma and S. G. Schulman. croscopy. volume 59 of 1992. Spectroscopy. Wiley, [74] Practice, 1977. sisto, [73] Phosphorescence Spectroscopy: range Fundamental limits to resolution in microscopy. Journal of Microscopy, 189:15-24, 1997. A. Stemmer. surface A hybrid scanning force and light microscope for imaging and three-dimensional optical sectioning in differ¬ ential interference contrast. Journal of Microscopy, 178(l):28-36, 1995. [80] A. Stemmer, structures R. Reichelt, imaged croscope and 35:255-264, in a R. Wyss, and A. hybrid scanning scanning tunneling microscope. 1991. Engel. Biological transmission electron mi¬ Ultramicro s copy, BIBLIOGRAPHY 126 [81] K. Svoboda and S. M. Block. Optical trapping Rayleigh particles. Optics Letters, 19(13):930-932, [82] D. L. new M. Taylor, vision ol F. Nederlof, Lanni, and A. S. American light microscopy. ol metallic 1994. Waggoner. The Scientist, 80:322-335, 1992. [83] den Doel, A. L. R. van F. R. Boddeke, evaluation ol L. J. D. van Klein, light microscopes based niques. Bioimagmg, 6:138-149, [84] K. Visscher and G. induced forces cally I: [85] Rayleigh T. Press, Wilson, R. Juskaitis, microscopy by 1881, [87] pinhole edition, Theoretical in in confocal a study single ol opti¬ beam trap 1992. imaging systems. In of Biological Confocal Microscopy. 1995. M. A. A. Neil, aperture correlation. and M. Kozubek. Confocal Optics Letters, 21(23):1879- 1996. R. Windecker and H. J. Tiziani. phase Netten, image processing tech¬ spherical particles Handbook second on H. Young. Quantitative Optik, 89(4):174-180, scatterers. Pawley, editor, Plenum [86] on Ellenberger, 1998. J. Brakenhoff. T. Wilson. The role olthe J. B. S. L. and I. T. Vliet, evaluation algorithm. Semispatial, robust, and accurate Applied Optics, 34(31):7321-7326, 1995. [88] R. Windecker and H. J. Tiziani. Topometry ol technical and bio¬ logical objects by fringe projection. Applied Optics, 34(19):36443650, 1995. Curriculum Vitae Personal data: Name: Jan Tillman Prolin Date ol birth: 28nd ol Place ol Bonn, Germany origin: Nationality: February, 1971 German Education: 1977-1981 Primary school, Bonn, Germany 1981-1990 Secondary (Gymnasium), Bonn, Germany school Degree: Abitur 1990-1992 University Degree: 1992-1996 University Diploma 1997-2000 ol Bonn, Germany Intermediate ol diploma in physics Freiburg, Germany thesis on selective emitters lor thermophotovoltaic energy conversion Degree: Diploma physics in Nanotechnology Group, Institute ol Swiss Federal Institute ol Robotics, Technology (ETH) Ph.D. research and supervision ol student projects in the field ol science nano (ETH Zurich) Stuttgart) Thesis advisors: Prol. A. Stemmer Prol. H. J. Tiziani (University ol and Collateral engagement: 1989-1992 Development telescopic 1992-1997 ol power and analog electronics for camera cranes Development ol electronics and software for second generation telescopic camera cranes 127