Download Superresolution size determination in fluorescence microscopy: A

JOURNAL OF APPLIED PHYSICS
VOLUME 95, NUMBER 12
15 JUNE 2004
Superresolution size determination in fluorescence microscopy:
A comparison between spatially modulated illumination and confocal
laser scanning microscopy
Udo Spöri
Applied Optics and Information Processing, Kirchhoff Institute for Physics (KIP), Im Neuenheimer Feld
227, D-69120 Heidelberg, Germany
Antonio Virgilio Faillaa)
Applied Optics and Information Processing, Kirchhoff Institute for Physics (KIP), Im Neuenheimer Feld
227, D-69120 Heidelberg, Germany
Christoph Cremerb)
Applied Optics and Information Processing, Kirchhoff Institute for Physics (KIP), Im Neuenheimer Feld
227, D-69120 Heidelberg, Germanyand Interdisciplinary Center for Scientific Computing (IWR),
University of Heidelberg, D-69120 Heidelberg, Germany
共Received 8 January 2004; accepted 25 March 2004兲
Recently developed far field light optical methods are a powerful tool to analyze biological
nanostructures and their dynamics, in particular including the interior of three-dimensionally
conserved cells. In this article, the recently described method of spatially modulated illumination
共SMI兲 microscopy has been further extended to the online determination of the extension of small,
subwavelength sized, fluorescent objects 共nanosizing兲. Using fluorescence excitation with 488 nm,
the determination of fluorescent labeled object diameters down to 40 nm corresponding to about
1/12th of the wavelength used for one-photon excitation could be shown. The results of the SMI
nanosizing procedure for a detailed, systematic variation of the object diameter are presented
together with a fast algorithm for online size evaluation. In addition, we show a direct comparison
of the diameter of ‘‘colocalization volumes’’ between SMI nanosizing and conventional confocal
laser scanning microscopy. © 2004 American Institute of Physics. 关DOI: 10.1063/1.1751633兴
silencers, 共complexes兲 for transcription, replication, activation, and chromatin remodeling.
From the light optical point of view, cells can be considered as thick, transparent objects, which can be analyzed in
the three-dimensionally 共3D兲 preserved or even living state
by means of far field light microscopy. However, far field
light microscopical images experience a lack of structural
information given by the resolution limit. In recent years, the
methods of 4Pi fluorescence confocal scanning
microscopy11–13 together with stimulated emission
depletion14,15 have been developed to narrow substantially
the full-width-at-half-maximum 共FWHM兲 of the microscopic
point spread function 共PSF兲, thus breaking the conventional
‘‘Rayleigh limit of diffraction.’’
In addition to the approaches based on narrowing the
FWHM of the PSF, the desired topological information may
also be obtained by other far field light microscopical methods. These unique methods are applicable under certain geometrical constraints; however, these apply in a large variety
of biologically relevant cases. In the recently introduced approach of spectral precision distance microscopy
共SPDM兲,16 –21 the subwavelength sized objects to be measured are labeled with fluorescent markers using different
‘‘spectral signatures’’22 which allow the simultaneous identification of many objects due to their excitation/emission
spectra or fluorescence life time.23 The positions of the objects will be derived from their diffraction intensity distribu-
I. INTRODUCTION
Numerous efforts are being made to elucidate the functional architecture of cells of higher organisms. Typically,
such analyses have been performed using ultrastructural imaging techniques like electron microscopy 共EM兲 or x-ray microscopy. Optical resolution down to the subnanometer range
共for EM兲 or of few tens of nanometers 共x-ray microscopy兲1
can be achieved. However, these methods require high, lethal
doses of radiation. In the case of EM, physical sectioning of
thick objects is mandatory.
For many nanostructural analyses, it may be sufficient to
measure the relative positions and small mutual distances
between, as well as the sizes of specifically labeled fluorescent intracellular nanostructures. A special focus of interest
are specific chromatin regions which may form elaborate
structures the knowledge of which will be necessary for an
improved understanding of the functional architecture of the
genome.2– 8 For example, genetically active chromatin regions are regarded to be somewhat decondensed, taking up
larger volumes in the cell nucleus, compared to their inactive
state.9,10 In addition, even a specific chromatin folding pattern might exist, e.g., to regulate the accessibility of protein
a兲
Present address: Institut für Physik, Universität Potsdam, Postfach 601553,
D-14415 Potsdam, Germany.
b兲
Electronic mail: [email protected] and [email protected]
0021-8979/2004/95(12)/8436/8/$22.00
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© 2004 American Institute of Physics
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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004
tion in the image data file. Distances between such objects
down to about 15 nm have been measured with a precision
共95% confidence limit兲 as good as 10 nm using optically
‘‘conventional’’ fluorescence microscopes.19,24 In this article,
results from a different far field light microscopical approach, spatially modulated illumination 共SMI兲 microscopy,
are described, making use of ‘‘point spread function engineering’’ methods.25–27 It has been shown that using this
technique, distances in the few nanometer range, and object
size evaluations considerably below 100 nm,28 under conditions of low fluorescence photon detection, as it is typical for
many biological nanostructures marked with fluorochromes,16 can be measured with high precision. This ‘‘superresolution’’ information can be extracted from the axial
intensity distribution 共AID兲28 of a fluorescent object recorded
in SMI microscopical 3D images.25–27,29–31
Since the AID is highly sensitive to the size32,33 and the
position31 of small fluorescent objects 共with a size of about
and below the 100 nm range兲, it is possible to obtain quantitative, reliable information about sizes and mutual distances
of the fluorescent labeled objects by digital image analysis
and ‘‘virtual microscopy’’ procedures.32 In the following, we
introduce the term ‘‘size resolution.’’ By ‘‘size resolution,’’
in analogy to the conventional term resolution, is meant that
any two small objects with a size difference of ⌬S can be
identified as different in size, when the size resolution is
better than ⌬S 共‘‘the smallest size that can be resolved’’兲.
Here, the object’s extensions are defined by the fluorochrome
distribution.
In this article, we summarize the theory of SMInanosizing developed previously and report the results of
‘‘nanosizing’’ measurements of spherical fluorescent objects
with known diameters according to a fast size determination
algorithm. In the measurements shown, object sizes down to
40 nm have been measured using fluorescence excitation
with 488 nm. In addition, we compare the axial extensions
共corresponding to the object diameters兲 with the results obtained by confocal laser scanning microscopy 共CLSM兲. For
this comparison, the same objective lens was used in both
microscope systems.
Spori, Failla, and Cremer
8437
FIG. 1. Axial intensity distribution 共AID兲 for a fluorescent object with diameter d⫽58 nm, as obtained by SMI-virtual microscopy 共SMI-VIM兲. The
fluorescence intensity distribution to be observed is given by the AID-curve.
From this, an enveloping ‘‘outer’’ adaptation curve 共dashed line兲 and an
‘‘inner’’ adaptation curve 共dotted line兲 may be calculated. The axial coordinate 共z兲 is given in absolute units 共␮m兲 of the object space.
tured in axial direction 共cf. Fig. 1兲. The full-width-at-halfmaximum 共FWHM兲 of the PSF can be calculated on the
basis of the ‘‘hardware’’ parameters of the system, i.e., the
numerical aperture, the wavelength of the laser light 共excitation兲, and the refractive index in the object space. Along the
optical axis, the intensity distribution of ‘‘point-like’’ objects
is represented by a 关 sin(z兲/z兴 2 -function 共modulated by a cos2
term兲, thus differing from the intensity distribution in the
x-y-plane, represented by a 关 BesselJ1 (x兲/x兴 2 -function.
Given physical objects, the term ‘‘axial intensity distribution’’ 共AID兲 is used to describe the fluorescence intensity
distribution of the SMI microscope image along the z-axis.
As the objects become small with respect to the wavelength
of the standing electromagnetic field, the AID becomes identical to the PSF. By reference to Fig. 1, the maximum object
size for real objects which can be considered to behave
‘‘pointlike’’ may be defined, e.g., to be 20% of the fullwidth-at-half-maximum (FWHMmod) of the oscillating
fringes within the SMI-PSF. Typical theoretical values for
the FWHM of the SMI-PSF under the conditions used are
about 650 nm; and about 80 nm for the FWHMmod 共cf. Figs.
1 and 2兲.
II. THEORY OF SMI-NANOSCOPY
A. Theoretical limits for SMI size measurements
In the following, a short introduction to the concept of
SMI microscopy is given, 共for details, see Failla et al.兲.32 In
the SMI microscope, the limits imposed by the PSF on the
determination of structural details is partly overcome by
modulating the illumination light pattern. This allows 共a兲 a
structural improvement in ‘‘topological resolution’’ 共positions, mutual distances兲 and 共b兲 a determination of object
sizes far below the limit imposed by the illumination light
共the corresponding conventional optical resolution limit is
given by about half the excitation wavelength兲. The basic
principle of the SMI microscope setup is as follows: two
counterpropagating beams of coherent excitation light are
allowed to interfere in the object space, yielding a cos2
shaped spatially modulated illumination intensity pattern. In
the present setup, the SMI uses a standing wave field along
the optical axis25 to generate a PSF which is highly struc-
As the PSF of the SMI may be described by the product
of the microscope detection PSF and the illumination PSF,34
the FWHMs of both, the objective lens used for detection,
and the cos2 modulation still impose limits on the application
of SMI microscopy. The latter results in a lower limit for
object sizes to be determined, and depends linearly on the
excitation wavelength. The PSF of the detection objective
lens imposes basic restrictions on the optical resolution for
this microscope setup. As it has been shown, the size resolution and the topological resolution 共positions, distances兲
can be increased substantially, as long as certain criteria can
be fulfilled. 共In the SMI-measurements described here by
‘‘size’’ the extension/diameter of the object in direction of
the optical axis is meant兲. In particular, to measure the sizes
and the topology of multiple objects 共e.g., protein complexes
or chromatin domains兲, sites labeled with the same spectral
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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004
Spori, Failla, and Cremer
FIG. 2. SMI-VIM calculation of
modulation contrast calibration curve.
共a兲 Two objects represented by Gaussian fluorescence distributions 共axial direction兲 with half widths S⫽50 nm
and S⫽100 nm, respectively. 共b兲 SMIVIM calculated axial or z intensity distributions 共AID兲 of the SMIdiffraction image. In both 共a兲 and 共b兲,
the abscissa is given in absolute units
共␮m兲 of z in the object space. OF: oscillating fringes. 共c兲 SMI-VIM calculated modulation contrast function
f (S)⫽R⫽M i /M o 共c.f. Fig. 1兲 for
various values of S. Here, the size S
was defined as the axial half width of
the object fluoresce intensity distribution as displayed in 共a兲.
signature have to fulfil the Rayleigh criterion for the SMI
setup described: Apart from the cos2 modulated illumination,
the detection is the same as in a standard epifluorescence
microscope. For example, in the x-y-plane, the minimal distance 共lateral optical resolution兲 for two objects labeled with
the same spectral signature to be allowed for size measurements is given by d⫽0.61⫻␭/NA, where ␭ is the emission
wavelength and NA is the numerical aperture of the objective lens.35,36 In the direction of the optical axis, the minimal
distance may be approximated by d⫽2⫻n␭/NA 2 . The ellipsoidal volume given by this formalism in all three dimensions of space may be called the ‘‘exclusive volume,’’ or
‘‘observation volume of the PSF.’’ ‘‘Exclusive volume’’
means that it is not possible to distinguish this object from a
second one of the same spectral signature being located
within this exclusive volume of the first object. Using digital
image restoration, this limit can be reduced only
marginally.16
A practical consequence of this criterion to SMI/SPDM
microscopy is that two sites of the same spectral signature
must be ‘‘optically isolated’’ to allow the determination of
size and topology. Either the lateral distance has to be equal
to or greater than the lateral optical resolution, or the axial
distance has to be equal to or greater than the axial optical
resolution. These optical resolution limits are obtained by the
values of the corresponding FWHMs either in lateral or in
axial direction, where for the axial FWHM only the outer
enveloping function of the SMI-PSF is considered. 共cf. Figs.
1 and 2兲.
III. METHODS
A. Virtual microscopy to calculate size dependency
of the AID
Topological and size information is extracted from the
AID using the mathematical formalism determined by SMIvirtual microscopy 共SMI-VIM兲.32 For clarity, these considerations are briefly summarized: The basic concept behind
SMI-VIM is to compare experimentally measured AIDs to
computer generated AIDs. If noise is neglected, the theoretically generated AIDs can be obtained by the convolution of
the fluorescence distribution with the theoretically computed
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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004
Spori, Failla, and Cremer
PSF. When noise is considered too, according to e.g., fluorescence efficiency, photon shot noise or charge-coupled device 共CCD兲 read-out noise, the procedure is more complex.32
In order to compare the theoretical and the experimental
AID, the empirical multiparameter fit function
冉 冊 冉 冊
冉 冊
AID共 z 兲 ⫽ 共 M o ⫺M i 兲 sinc2
⫹M i sinc2
z⫺z o
z⫺z 2
cos2
Bo
C
z⫺z i
,
Bi
共1兲
may be used, with each parameter corresponding to a physically detectable value:
The subscripts i and o are used for the inner and outer
enveloping AID profiles 共cf. Fig. 1兲. M i,o are the maximum
intensities of the enveloping functions; B i,o are constants
proportional to the FWHM of the enveloping AID profiles
共e.g., 650 nm兲; z i,o are the positions of the maximum of the
enveloping AID profiles; C is proportional to the FWHMmod
of the cos2 shaped standing wave field present between the
two objective lenses; and z 2 is the position of one maximum
共arbitrarily chosen and then fixed兲 of the previously mentioned standing wave field, (z 2 ⫺z o )/C represents the phase
of the standing wave field at the object position.
Although with the algorithms presented, the determination of the object positions becomes obvious, the dependence
of the AID on the object size needs further investigation.
Figure 2 shows that for extended objects, the AID presents
an nonmodulated inner part. This is based on the SMI-PSF
being the product of the illumination PSF and the detection
PSF. Objects which are not ‘‘pointlike’’ with respect to the
modulation of the illumination light, will not result in an AID
having the same form as the PSF, but will present a nonvanishing fluorescence intensity when moved through the
minima of the illumination PSF. As the objects are extended,
part of the fluorochromes will get excited, no matter where
the objects are situated with respect to the standing wave
field. SMI-VIM employs this fact to calculate the relationship between changes of the form of the AID and given
object sizes.
In order to do so, the modulation contrast ratio R
⫽M i /M o is calculated for different object sizes 共here: extension of the object in axial direction, axial diameter兲 using
only hardware parameters and the SMI-VIM algorithms.
Starting from so-called ‘‘pointlike’’ objects, which are supposed to have a diameter much smaller than the FWHMmod
of the illumination modulation, the unmodulated inner part
of the AID increases with augmenting object size. This results in an increase of the modulation contrast R. By increasing the objects size beyond the FWHMmod, the modulation of
the AID becomes more and more insignificant, as the unmodulated inner part of the AID dominates, and the modulation contrast becomes R⫽1. From SMI-VIM calibrations,
the upper limit for object size dependent modulation can be
determined to be at 160 nm or somewhat higher values using
an excitation wavelength of ␭ ex⫽488 nm and a Gaussian distribution of the fluorophores along the optical axis. The functional relationship of the modulation contrast to the object
8439
size R⫽R(S) is dependent on the excitation wavelength
used, therefore R⫽R(S,␭ exc). 32
B. SMI size measurements
A fast algorithm allows online size determination with
minimal numerical computation power. An adaptation curve
to the measured AID can be used to calculate the corresponding contrast ratio R⫽M i /M o from the fit parameters M i and
M o . Thus, it is possible to extract the object diameter using
the R(S) function curves for the corresponding excitation
wavelength 共see also online supplementary material37兲.
First, the ‘‘effective’’ modulation wavelength is defined
as ␭ mod⬅␭ exc /(2n). Using SMI-VIM with the refractive index n fixed to n⫽1.44, the R-S curve is calculated by determination of the modulation contrast R for a set of different
object sizes and a set of different excitation wavelengths ␭ exc
共360, 488, 568, and 647 nm兲. For each wavelength, the discrete value pairs (R,S) are then fitted to a parametrical adaptation function
S 共 R,␭ mod兲 ⫽ ␣ 共 ␭ mod兲 ⫹ ␤ 共 ␭ mod兲 R⫹ ␥ 共 ␭ mod兲 ln共 1⫺R 兲
⫹ ␦ 共 ␭ mod兲 冑R,
共2兲
which for a given wavelength ␭ mod depends on four parameters ␣, ␤, ␥, and ␦. The last two terms 共proportional to ␥ and
␦, respectively兲 are the major contribution to the S(R) function, and represent the general behavior of the curve,
whereas the first two parameters ␣ and ␤ are small corrections. The parameters ␣, ␤, ␥, and ␦ itself are dependent on
the wavelength ␭ mod only. As a result, a general expression
for the inverse of the R-S curve was found under the assumption of Gaussian fluorochrome distribution, and with
the ‘‘hardware’’ parameters of the present microscope setup.
The errors in size made by this approach turned out to be less
than 1 nm for the wavelength and size ranges used here 共see
online supplementary material37兲. Considering that the effective wavelength of the standing wavefield ␭ mod⬅␭/(2n) is a
function of the local refractive index n, the S-R curve is also
affected by small fluctuations ⌬n of the refractive index,
even though the excitation wavelength obtained from a frequency stabilized laser can be considered to be fixed. Using
the previously defined effective wavelength obtained from
the adaptation function parameter C, these fluctuations of the
refractive index are taken into account. A comparison between this evaluation method and the algorithms described in
Failla et al.32 is shown in the online supplementary
materials.37
C. Preparation of the specimen
As specimens, fluorescence standard particles 共beads兲
were used with known diameters as provided by the manufacturers. In the following, these diameters are referred to as
the ‘‘actual’’ diameters, assumed to be the ‘‘true’’ sizes. Since
in most cases the manufacturers did not reveal the methods
used to determine the diameters, these diameters had to be
taken by face value. Before preparing the object slide, the
beads were sonificated to decompose nanoclusters which
were found after long storage. The beads were spread out on
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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004
FIG. 3. SMI microscope principle. 共a兲 Two laser beams in a Mach–Zehnder
interferometer are focused into the back focal plane of two opposite objective lenses to obtain spatial modulation of the fluorescence excitation. 共b兲
Detection is performed as in a conventional epifluorescence microscope.
The object slide is moved in steps of ⌬z 共e.g., 20 nm兲 along the optical
axis 共z兲.
a standard microscope object slide. Then, an antifade mounting medium 共VectaShield, refractive index n⫽1.440) was
applied to minimize photobleaching. A standard cover slip
was used to cover the specimen. The cover slip was then
fixed with nail polish. This preparation allowed the easy
transport from one microscope to another, and is one of the
major advantages of SMI microscopy. After preparation, a
standard fluorescence microscope was used to check the
quality of the object slide, and to scan for objects of interest.
D. Experimental setup
Two microscopes were used to perform the measurements and to compare the results obtained, a standard confocal laser scanning microscope 共Leica TCS NT兲 and a SMI
microscope which has been designed and built at the Kirchhoff Institute as described in Albrecht et al.30 and Albrecht
et al.31
The basic principle of the SMI microscope and the image acquisition process are shown in Fig. 3. The setup represents a far field fluorescence microscope mounted on an
optical breadboard. As light source, a frequency stabilized
Argon ion laser is operated in polarized TEM00 mode, and
emits at 488 nm. The laser beam is collimated to a beam
diameter of 25 mm. The laser light entering the microscope
is split in two beams of equal intensity and polarization and
then focused into the back focal plane of two opposing 100⫻
oil objective lenses 共Leica Mikrosysteme Vertrieb GmbH兲
with a numerical aperture of 1.4. Thus, a standing wavefield
is generated which produces the cos2 modulation of the excitation light of wavelength ␭ exc . This is referred to as the
illumination PSF. The whole setup represents a Mach–
Zehnder interferometer, where the phase of the standing
wavefield can be controlled separately by a piezomovable
Spori, Failla, and Cremer
mirror. On the detection side, a dichroic mirror between detection objective lens and focusing lens is used to separate
the fluorescence light from the excitation light. The fluorescence light is transmitted through this beam splitter, and focused via a tube lens 共magnification⫽1.25⫻兲 onto the chip
of a cooled CCD camera, after passing a blocking filter to
reduce background intensity related to the excitation light.
The total field of view with the magnification used here is
about 73⫻55 ␮m2.
After placing the object slides with the fluorescent objects between the objective lenses, immersion oil 共Zeiss, refractive index n⫽1.515) is applied on both sides 共a兲 between
the cover slip and the detection objective lens and 共b兲 between the second objective lens and the object slide. After
having brought the objects into the focus of the detection
lens, a second nanoprecision piezostage is used for moving
the object stage with steps of 20 nm 共with an error less than
1 nm兲 along the optical axis, providing axial optical sectioning. The object stage itself is assembled according to the
thermally induced shift compensation.27
IV. MEASUREMENTS
A. Fluorescent objects
Experiments were performed on fluorescent nanospheres
共beads兲 with actual diameters of 40, 44, 57, 71, 88, 100, and
140 nm, according to the manufacturers Duke Scientific
共Palo Alto, California兲 and Molecular Probes 共Leiden, The
Netherlands兲. Additional information obtained from the
manufacturers stated that the fluorochromes were randomly
distributed throughout the beads during polymerization, and
that the diameters of the beads were subject to fluctuations
共5%–15%兲 due to the manufacturing process. The maximum
absorption for the fluorochromes were at ␭ abs,max⫽468 nm,
and the maximum emission at ␭ em⫽508 nm. In this SMI
microscope, the Argon ion laser was used operating the 488
nm laser line to excite the fluorochromes, whereas in the
CLSM, an Ar:Kr mixed gas laser together with an acousto
optical tunable filter 共AOTF兲 was used to excite at ␭ ex
⫽488 nm.
B. Size measurements in SMI
In the SMI-microscope the objects were scanned along
the axial direction 共z兲 by moving them with the piezoelectric
object stage through the focus of the detection objective lens
as described above, acquiring a two-dimensional image at
every axial position 共optical sectioning兲.38 The recording
time for a single image was adjusted to obtain a good signalto-noise ratio and to avoid photobleaching effects of the fluorochromes. Typical acquisition times for a single 2D image
ranged from 0.1 to 3 s. To avoid the evaluation of clusters of
beads 共with unknown spatial configuration兲, objects with
very high fluorescence intensity 共more than 1.5 of the average object intensity兲 were neglected during the evaluation
process. From the adaptation function 共see above兲, the parameters M o and M i were used to calculate the modulation
contrast R. This experimentally determined modulation contrast was inserted into the inverse calibration function
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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004
S⫽ f̄ (R,␭ mod) obtained by numerical approximation to SMIVIM computer simulated curves. From the fit function in Eq.
共1兲, the fit parameter C can be used to calculate directly the
effective wavelength ␭ mod of the standing wavefield at the
position of the object. For the present experiments, this entire
evaluation process was automated, thus allowing online
SMI-nanosizing.
The asymmetry in the present SMI setup has been analyzed for systematic effects on the AID 共results not shown兲,
particularly resulting from the difference in the optical paths
through object slide versus cover slip. It was found that the
asymmetry of the AID was neither systematically toward one
direction, nor significantly dependent on the size, as one
would expect from internal reflections on the boundary of the
different media 共object slide glass-mounting media or
mounting media-cover slip glass兲. The experimental results
indicate that such an asymmetrical outcome, if present, induces only minor effects on the size determination. This result fits well with the fact that the differences in the refraction indices are small 共in the order of a few percent兲.
Presently, virtual SMI-microscopy simulations are planned to
study the influence of materials with different refractive indices in the optical path in detail.
C. Comparison with size measurements in confocal
laser scanning microscopy
Confocal laser scanning microscopy 共CLSM兲 was used
to compare the results obtained from SMI measurements
with those of ‘‘conventional’’ high resolution microscopy.
For this comparison, the 100⫻ oil immersion detection objective lens taken from the SMI microscope was used also in
the CLSM. The objects were prepared as described above
and placed into the confocal microscope. Excitation was performed at 488 nm. After visually searching for the focus
plane, the object slide was scanned for an area suitable for
size evaluation. The objects need to be separated spatially as
defined by the Rayleigh criteria, and again, the very bright
spots were neglected during evaluations to avoid measuring
clusters of beads. During the confocal scanning procedure, a
pinhole size of 0.5 optical units,39 i.e., half the airy disk
diameter, was used to minimize photon detection from out of
focus regions, at the state of acceptable signal-to-noise ratio,
at least for objects with a diameter of more than 50 nm.
Mechanical instabilities and optical aberrations of the
system resulted in a drift of the images in the lateral direction
throughout the optical sectioning. The mechanical shift was
composed of the shift of the scanning table and the shifting
position of the scanning mirrors. Focusing on one lateral
direction in a single z section, the total shift may result in
both positive or negative displacement during image acquisition. Averaging over multiple images in the same z position
was applied to correct for the error made herewith and to
increase the number of detected photons. This procedure resulted in a broadening of the measured PSF with respect to
the theoretically expected values. To reduce the effect of mechanical instabilities of the microscope system, an additional
scan was performed with the laser beam deflected using the
Spori, Failla, and Cremer
8441
FIG. 4. Comparison between sizes as measured by SMI microscopy and by
confocal microscopy 共CLSM兲. Ordinate: relative size⫽experimentally detected size divided by ‘‘true’’ size. In this case, the ‘‘true’’ size was assumed
to be the actual bead diameter 共abscissa兲 as given by the manufacturers.
Whereas size measurements by SMI 共cross marker兲 yielded results close to
the ‘‘true’’ sizes 共relative size estimates close to unity兲, the sizes obtained
from measurements by CLSM showed substantial deviations below the conventional resolution limit, i.e., about 200 nm in lateral 共triangles兲 and 600
nm in axial 共diamonds兲 direction. For CLSM, beads with a ‘‘true’’ diameter
below 44 nm were not measurable due to bleaching.
microscope’s acousto optical tunable filter 共AOTF兲 before
each acquisition.
The FWHM values of the CLSM measurements of the
different bead classes were extracted by fitting theoretical
curves to the measured intensity distribution, in lateral as
well as in axial directions. The adaptation function in both
cases was a Gaussian intensity distribution 共see online
supplementary material37兲. For the lateral case, only the values in x direction are extracted. For all the single 3D data
stacks, the mean of the FWHM for all objects 共beads兲 measured were evaluated and considered as the estimate of the
size 共diameter兲 of the beads. The standard deviation of the
mean was considered as the estimate of the accuracy.
Figure 4 shows the comparison for size determination
using SMI nanosizing and CLSM determination of the
FWHM. The ratio between the expectation values 共object
sizes as specified by the manufacturer兲 and the measured
values are plotted. The SMI size determination yielded good
agreement with the expected object sizes. The sizes as determined with the confocal microscope show significant, large
deviations for objects smaller than the FWHM of the PSF.
For objects with 44 nm diameter, e.g., the ratio of the detected axial size to the ‘‘actual size’’ 共expectation value兲 became as large as 13 resulting in an overestimation of the
object size of 1200%.
V. CONCLUSIONS
In this article, we improved the SMI-nanosizing approach described previously by features of online evaluation;
furthermore, a systematic variation of the diameter of optically isolated fluorescent, subwavelength sized objects confirmed the applicability of ‘‘nanosizing’’ by spatially modulated illumination 共SMI兲 microscopy to reliably discriminate
between classes of individual small fluorescent objects with
diameters of about and considerably below 100 nm using
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8442
J. Appl. Phys., Vol. 95, No. 12, 15 June 2004
visible light excitation. In addition, we performed a direct
comparison of size determination by SMI and confocal microscopy 共CLSM兲. The actual diameters of the objects used
in these experiments varied between 40 and 140 nm. These
nominal sizes provided by the manufacturers were comparable with the sizes obtained by SMI microscopy using onephoton excitation at 488 nm. Although such ‘‘nanosizing’’
results critically depend on optimum optical conditions, it is
expected that even under conditions less ideal like that of
fluorescent nanostructures in thick transparent biological objects, size measurements considerably below the size resolution of any ‘‘conventional’’ epifluorescence or confocal fluorescence microscope will still be achieved. Preliminary
results on SMI-nanosizing of individual, fluorescence labeled
gene regions in intact cell nuclei40 support this expectation.
The results of size measurements of transcription factories
inside of cryosections of cells also confirm the general applicability of SMI nanosizing to biological cell preparations.41
The advantage of SMI microscopy for the determination
of subwavelength object sizes was documented by a direct
comparison with confocal laser scanning microscopy. In this
comparison with an advanced method of conventional far
field light microscopy under good optical conditions, an increase by a factor of 4.2 in size was obtained in the directions where the best results were expected, i.e., the axial
direction in SMI microscopy, and the lateral direction in confocal microscopy.
In summary, results from the SMI nanosizing methods
were far beyond the limits of CLSM, the most advanced
‘‘conventional’’ high resolution far field fluorescence microscopy: By SMI nanosizing at 488 nm excitation wavelength,
the actual object diameters were correctly or almost correctly
estimated for all the bead sizes investigated 共here down to 40
nm兲. That means that sizes larger than that can be discriminated and thus be ‘‘resolved.’’ In terms of colocalization volumes, this means a difference in colocalization volume resolution of almost two orders of magnitude. In contrast to that,
the experimental CLSM lateral FWHM using the same objective lens for fluorescence detection and the same excitation wavelength indicated a ‘‘best’’ size resolution in the order of 200 nm, using the lateral resolution as criterion. If
only the axial size resolutions are considered 共biologically
relevant, e.g., to estimate the thickness of membrane bound
complexes兲, the experimentally estimated difference in colocalization volume resolution increases even to three orders of
magnitude.
Theoretical considerations32 indicated that under ideal
optical conditions, the SMI size resolution, using visible or
near UV light one-photon excitation is in the range of about
10 to 20 nm, corresponding to about 1/30 of the exciting
wavelength. In contrast to that, the theoretical ‘‘best size
resolution’’ estimates for CLSM using volume conserving
deconvolution were about 100 nm diameter.16
The results shown here indicate that SMI size measurements of individual biological nanostructures in their natural
environment such as in 3D intact cells present a complementary alternative to other high resolution microscopical investigations as obtainable, e.g., from electron microscopy or
x-ray microscopy, which require high doses of ionizing ra-
Spori, Failla, and Cremer
diation 共x-ray兲; in addition, these methods do not allow the
large range of multispectral, combinatorial molecular labeling schemes possible with light microscopy. It is envisaged
that a combination of both approaches to study the same
structures in the same cells will provide synergistic benefits
to understand the functional architecture of the cell on a level
of resolution until now thought to be impractical.
In general applications of SMI nanosizing, the object
shape will not be spherical; the fluorochrome distribution
will not correspond to a simple Gaussian function. Therefore,
different calibration functions would have to be applied.
However, even without an a priori knowledge of the dye
distribution inside the objects, an approximate size information can be obtained assuming spherical objects. For two
objects of similar shape, due to the monotonics dependence
of the modulation contrast on the axial extension 共at least in
the ⭐100 nm range investigated here兲, a qualitative difference in size can be detected even without this approximation.
Recently, SMI-VIM computer simulations are in progress to
analyze the effect of shape and fluorochrome distribution on
SMI nanosizing.
Limits to the SMI nanosizing are the requirements of
‘‘optical isolation’’ given by the ‘‘exclusive volume’’ 共see
above兲 for given sites labeled with a specific fluorochrome:
All fluorochromes of the same spectral signature within the
conventional optical resolution limit 共as given, e.g., by the
FWHM of the PSF兲 are ascribed to the diffraction image of a
single object, resulting in the size determination for the
whole cluster. This limit can be overcome with multispectral
labeling. Using different ‘‘colors’’, size determination is possible even when the objects are within the exclusive volume,
even if their surfaces are separated only by a few nanometers. Together with SMI topology analysis obtained by SMISPDM, nanostructure analysis for, e.g., protein–protein interactions, chromosome condensation, and others become
feasible.28
Beyond the analysis of biological nanostructures, SMI
microscopy might find interesting applications also in other
fields of nanostructure research. For example, the thickness
of any transparent fluorescence labeled structure, even in the
interior of a transparent medium, could be measured by SMI
nanosizing down to the 20 nm range 共assuming best optical
conditions兲, without the necessity of refractive index differences; a distribution of single, laterally ‘‘optically isolated’’
fluorescent objects on a surface or in the interior of a transparent medium could be measured by SMI distance determination down to a few nanometers distance, with a precision
in the 1.0 nm range, without needing refractive index
differences.31 The general advantage would be again the possibility of relatively fast, far field light optical measurements
under ‘‘normal’’ conditions of pressure, temperature, ionic
conditions, etc.
ACKNOWLEDGMENTS
This work was supported by the Bundesministerium für
Bildung und Forschung 共BMBF兲 and the Deutsche Forschungsgemeinschaft 共DFG兲. Many thanks to Susanne Fenz
for her work with the confocal microscope. We also thank
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J. Appl. Phys., Vol. 95, No. 12, 15 June 2004
Dorothee Schroth from Leica Bensheim for her help with the
CLSM measurements. For stimulating discussions, we thank
Dr. Ana Pombo 共MRC, London兲, Christian Wagner, and Andreas Schweitzer.
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