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Sheppard CJR (2004) Microscopy overview, Encyclopedia of Modern Optics, RD Guenther, DG Steel, L Bayvel, eds, Elsevier, Oxford, ISBN 0-12-227600-0, 3, pp. 61-68 Microscopy Overview CJR Sheppard Division of Bioengineering National University of Singapore 9 Engineering Drive 1 Singapore 117576 Synopsis The basic construction and imaging properties of the optical microscope, one of the most important optical instruments, are described. But the restrictive meaning of a microscope as a device that the user looks down to see a magnified image is far from the present terminology that includes scanning systems (where the image is stored in a computer), non-visible radiation such as electrons or X-rays, and a variety of different contrast mechanisms. Key words Optical microscope, light microscope, electron microscope, probe microscope, nearfield microscope, acoustic microscope, scanning microscope, confocal microscope, microscope objective, resolution, Köhler illumination, Abbe theory, Rayleigh criterion. Published as: Sheppard CJR (2004) Microscopy overview, Encyclopedia of Modern Optics, RD Guenther, DG Steel, L Bayvel, eds, Elsevier, Oxford, ISBN 0-12-2276000, 3, pp. 61-68 According to the Oxford English Dictionary a microscope is "an instrument magnifying objects by means of lenses so as to reveal details invisible to the naked eye". Thus basically a microscope forms a magnified image of an object. The first microscopes used visible light and formed an image showing variations in the intensity of light scattered by the object. This intensity is in general related to the optical properties of the object in a complicated way. But in transmitted light microscopy, the intensity of the image of a weak object is proportional to the transmittance of the object. Nowadays there are many different types of microscope. Our understanding of a microscope must therefore be generalized in the following ways. • The microscope may not be a conventional imaging system using lenses or mirrors. For example, it may be a scanning imaging system. A confocal system is a combination of a conventional and a scanning system. Another important category of microscopes is that of probe microscopes, including near-field optical microscopes. Some probe microscopes, for example the atomic force microscope (AFM) do not even seem at first glance to rely on the direct use of radiation. • The microscope may not use visible light, but other electromagnetic radiation, or even other forms of radiation. • The image can be formed using a variety of different contrast mechanisms. Some of these, such as phase contrast, are designed to image particular optical properties of the sample. Others image the generation of a form of radiation when the object is stimulated by another form of radiation. In particular, in principle virtually any form of spectroscopy can be the basis of building up an image by measuring the spatial variations in the signal. 1 Different form of microscope 1.1 The conventional microscope In a simple microscope, an objective lens forms a real, magnified and inverted image of an object. In a compound microscope, an eyepiece is added, forming a virtual image that is viewed by eye to give real image on the retina. The eye can be replaced by CCD camera to record moving or still images. In early microscopes, the objective lens and eyepiece are mounted in the two ends of a brass tube. The objective screws into the tube using an RMS thread, until its mounting face is flush with the end of the tube. The length of the tube is the mechanical tube length. The distance from the mounting face of the objective to the plane of the real image is the optical tube length, which varied according to different manufacturers in the range 160-210 mm. Now most objectives have infinity tube length, so that they collimate the light from the object. The collimated light is brought to a focus by an additional tube lens. An objective of correct tube length should always be used as otherwise spherical aberration is introduced. As the objective, tube lens and eyepiece are designed together as a system, great care should be exercised when mixing components from different manufacturers. Abbe showed that in order to form a perfect lateral image the objective must satisfy the sine condition. Otherwise the image of an off-axis point will suffer from coma. An aberration-free system satisfying the sine condition is called an aplanatic system. A microscope produces a three-dimensional (3-D) image of a 3-D object. A point of the object closer to the lens appears further from the lens in the image. If the lateral magnification is M, the longitudinal magnification is approximately equal to M2. However, it can be shown that it is impossible to devise an instrument that can produce a perfect 3-D image of a 3-D object, because to have a perfect transverse image the system must satisfy Abbe's sine condition, but to have a perfect axial image the system must satisfy the Herschel condition. These two conditions are not mutually compatible. Actually we find that the longitudinal magnification is not exactly equal to M2, and is not even constant in space. Different depths of the object are imaged differently: the microscope objective only produces a good image for one plane of focus, and other planes will exhibit spherical aberration. However, all of these problems can be overcome by bringing the part of the object under observation into focus, without refocusing the eye or other detector. A 3-D image can thus be generated by scanning the object stage in the axial direction, and recording a stack of images from different depths in a computer. For modern objectives of infinite tube length, focusing can be alternatively achieved by piezoelectric scanning of the objective lens. 1.1.1 Resolution For an object consisting of a single bright point object in a dark background, the image produced by a perfect microscope, according to paraxial diffraction theory, is the so-called Airy disk, consisting of a bright central spot, surrounded by a series of rings. The intensity in a meridional cross-section through the Airy disc is the same for any aperture of objective, or wavelength of light, but its width varies. The intensity of the first bright ring is 1.75% of that at the peak. The radius of the first dark ring of the Airy disk is r0 = 0.61λ , nsin α [1] where λ is the wavelength, n is the refractive index of the immersion medium and α is the angle subtended at the edge of the objective aperture. The radius depends on n sinα , which is called the numerical aperture and should be as large as possible for good resolution. Thus high magnification lenses often use an immersion fluid, usually oil with a refractive index of 1.518 (ISO 8036/1). The optical coordinate v is defined as v= 2π r nsin α , λ [2] so that the dark ring of the Airy disc occurs at a value of v of 2π ×0.61 = 3.83. Resolution is sometimes expressed in terms of the FWHM (full width at half maximum) of the image of a point object, which is 3.232 in optical coordinates. A full non-paraxial theory does not give a very different figure. Resolution of a microscope is often specified by two-point resolution, which describes whether the image of two points can be distinguished from that of a single point. According to the Rayleigh criterion of two-point resolution, two points are just resolved if the second point is placed on the first dark ring of the first. The separation is then 0.61 λ /(n sin a). A cross-section through the image in an incoherent optical system of two bright point objects of equal strength and different separations is shown in Fig. 1. The intensity in the image between the points decreases as the separation is increased. The ratio of the intensity midway between the points to that at the points for the Rayleigh criterion to be satisfied is then found to be 0.735. The concept of resolution should be distinguished from sensitivity or precision. An object much smaller than the resolution limit can still be detected, perhaps weakly, in a microscope: this detection of weak contrast depends on the sensitivity of the microscope rather than its resolution. The size of an object can also be measured with a precision much greater than the resolution of the microscope. Fig. 1 A cross-section through the image of two equal point objects in an incoherent microscope. The separation of the points is that for the Rayleigh criterion to be satisfied, and for changes of ±10,20% of the Rayleigh separation. 1.1.2 Illumination If the object is not self-luminous, in order to be imaged in a microscope it must be illuminated. A semitransparent object, such as a biological slice, is illuminated in transmission. For observation of bulk objects, or surfaces, we use illumination in the reflection geometry, called epi-illumination. Either a tungsten halogen lamp or an arc source is usually used. In critical illumination, the source is focused on to the object by a condenser lens. The disadvantage of this approach is that variations in emission of the source are imaged directly into the image. Cheaper microscopes avoid this problem by using a diffuser. Better microscopes use instead the Köhler illumination system, where the source is placed in the front focal plane of the condenser lens. Fig. 2 shows a Köhler illumination system in which the source is imaged into the front focal plane of the condenser lens by another, projector, lens. The system incorporates a separate field stop and aperture stop. In practice, the size of the field stop should be reduced to illuminate as small a region of the object as necessary in order to minimize stray light. An important part of setting up a microscope to operate properly consists in centring the aperture stop of the condenser. This is often done using a Bertrand lens to image the aperture stop. Fig. 2 Geometry of the Köhler illumination system. In practice an arrangement with a smaller number of lenses is usually used. 1.1.3 Image formation The Rayleigh criterion was originally specified for an incoherent optical system. It is thus applicable in fluorescence microscopy, as fluorescence is an incoherent process as two fluorescent point objects fluoresce independently. But for the image of a transilluminated object, the resolution depends on the coherence of the illumination. This is controlled by the numerical aperture of the condenser lens as compared with that of the objective. The ratio of these numerical apertures is called the coherence parameter, S, so that S= nc sin α c . nsin α [3] For S = 0 the illumination is purely coherent, while for S → ∞ imaging becomes purely incoherent, thus corresponding to the Rayleigh criterion. (So S should really be called an incoherence parameter.) An important in-between case is when S = 1, when the apertures of objective and condenser are equal. This is termed matched, full or complete illumination. According to the generalized Rayleigh criterion the points are just resolved when the ratio of the intensity midway between the points to that at the points is 0.735, which is called the generalized Rayleigh criterion. We require that the distance between the points is as small as possible when this occurs. The generalized Rayleigh separation is the same for incoherent illumination and for S = 1, and corresponds to a distance of 2v 0 = 3.83 in optical coordinates. Note, however that for other separations of the points the ratio is different for these two cases: it is not true, but often erroneously stated, that S = 1 corresponds to incoherent imaging. Resolution improves as the aperture of the condenser is increased ( 2v 0 = 5.15 in optical coordinates for coherent illumination) reaching a maximum when S = 1.46, when resolution is 9% better than for incoherent imaging ( 2v 0 = 3.58 ). This maximum in resolution is achieved when the numerical aperture of the condenser is larger than that of the objective, which is not physically achievable if the objective has the highest possible numerical aperture. Similarly, it is impossible to achieve incoherent illumination with very large objective numerical apertures. The effect of coherence on the resolution of an image depends on the form of the object, and on the particular resolution criterion employed. In practice contrast also depends on the aperture of the condenser. Usually, opening the condenser improves resolution, but reduces contrast, so there will be an optimum condenser aperture size. 1.1.4 Abbe theory of microscope imaging Abbe argued that for coherent illumination of a grating, the grating spectra can be observed in the back focal plane of the objective. The tube lens then forms an image from the grating components. This is thus an early description of Fourier optics. The strength of the grating components can be altered in the back focal plane to give various optical effects, such as phase contrast. Abbe’s theory was not properly appreciated at the time because it was known that in practice resolution could be improved by using a larger condenser aperture, which does not give coherent illumination. There was much controversy about the merits of Köhler versus critical illumination, and different sizes of condenser aperture. We now know that Köhler and critical illumination are in principle equivalent. The aberrations of the condenser lens are not important, so that the source and condenser together behave simply as a partially coherent effective source. Imaging can still be described by Fourier optics within the framework of partially coherent imaging theory. Although Köhler and critical illumination are equivalent in principle, Köhler illumination is in practice better because of its improved illumination uniformity. 1.1.5 Depth of focus The longitudinal image of a point object is found to be approximately invariant when expressed in terms of an optical coordinate u defined as u= 8π α z nsin 2 . λ 2 [4] The axial resolution, and thus also the depth of focus, varies strongly with aperture. The FWHM for longitudinal imaging is 11.13 in optical coordinates. 1.1.6 Microscope objectives Because microscope objectives often have large apertures, aberrations will be very strong unless the objective is designed correctly. The basic design principle for a high aperture lens is the aplanatic front element (Fig.3). It is found that all rays from a point A in a sphere of refractive index n, where A is a distance r/n from its centre, appear to come from a point B, distant rn, without any aberration. This principle is used by employing a front element that has one surface of the same radius of curvature as the sphere. The front surface is a sphere centred on A (Fig. 3(b)), so that the rays are not deviated on crossing it. Fig. 3 The principle of the aplanatic front: (a) an aplanatic surface, (b) a meniscus lens that acts as an aplanatic system. A low-power achromat uses just two components with different optical dispersion to cancel chromatic aberration and correct for other aberrations (an achromatic doublet). For higher powers, two separated doublets are necessary. For the highest apertures, an aplanatic front is used. However, this can never converge the light, but only makes it less divergent. It is thus used together with an achromatic doublet. For oil immersion the interface between the oil and the front element is not very important, so it is made planar to simplify manufacture. In practice it is usually made planar even for a dry lens, and the resulting aberrations cancelled out elsewhere in the objective. Apochromats, corrected for three colours, use more elements, which may include two or more stages of aplanatic front. The final objective thus consists of a number of elements that must be accurately aligned relative to one another. The objective is adjusted by the manufacturer to give a good star image (image of a point object). First a spacer is selected to optimise spherical aberration. Then a sleeve is adjusted to make the objective parfocal with others. Finally a screw is used to centre the assembly to remove coma. 1.2 Conventional and scanning microscopes 1.2.1 Conventional microscope Various different types of transmission microscope are illustrated in Fig. 4. We consider image formation in a conventional microscope as illustrated schematically in Fig. 4(a), showing a microscope with critical illumination. A large area incoherent source is focused by the condenser lens on to the specimen, illuminating a comparatively large area of the specimen, corresponding to the whole field of view of the objective. Information from each illuminated point in the specimen is simultaneously transmitted by the objective lens to form the primary image. The objective is responsible for forming the image, with the condenser playing only a secondary role in determining the resolution of the system, through control of the coherence of the illumination. Fig. 4(b) shows a conventional microscope in which the image is measured point by point by a detector. In practice this could be achieved by using a CCD detector. Fig. 4 Different geometries of transmission microscope: (a) a conventional microscope, (b) a conventional microscope with a point detector, (c) a scanning microscope, (d) a confocal microscope. 1.2.2 Scanning microscope An image can be generated by a scanning system, as illustrated in Fig. 4(c). A probe of light is formed by demagnification of a source, and is scanned over the object in a raster. The transmitted (or reflected) light is detected by a photo-detector and thus builds up an image. The size of the probe of light limits the resolution of the system, that is, the smallest detail in the object that can be seen in the image. It should be noted that the magnification of the image is given simply by the ratio of the distance scanned in the image to the distance scanned by the probe. It is thus unrelated to the demagnification of the source. The image magnification can be altered without changing the lens and is not in any way related to the resolution. It has been shown that the imaging properties of scanning and conventional microscopes are identical under analogous conditions, this being known as the principle of equivalence. This property is based on the principle of reciprocity, which is a very general physical law that holds even with diffraction, absorption, multiple scattering and stray light. The principle of equivalence is generally valid except if there are non-reciprocal magnetic or polarization effects, or energy losses involved (such as in fluorescence microscopy, and with inelastic scattering in electron microscopy). Scanning systems exhibit a number of important advantages over conventional systems. Broadly, these are based on two classes of property. First, in a scanning system the image is in the form of an electronic signal. As a result, this is advantageous for quantitative measurements, as well as for image processing, including image enhancement, image restoration and image analysis. Second, in a scanning system the object is illuminated by a focused spot, which extends the range of imaging modes available. 1.2.3 Confocal microscope Finally in Fig. 4(d), we combine the arrangements of Figs. 4(b) and (c) to give a confocal scanning optical microscope, in which a point source illuminates just a small region of the object, and a confocal point detector detects light from this illuminated region. If the point source and detector are scanned in unison, a two-dimensional image is generated. However, this system now behaves very differently from the previous ones. The confocal microscope is thus not a special case of the general partially coherent conventional imaging system. From the symmetry of Fig. 4(d) it is clear that the two lenses play an equal part in the imaging process. This results in an improvement in resolution. In fact, the confocal system behaves as a coherent imaging system, but with a sharper effective point spread function than in a conventional coherent microscope. Although Fig. 4 is drawn for the transmission geometry, in practice most confocal systems operate in the reflection or epi-illumination mode, in which the same objective lens is used both for illumination and detection. For a specimen placed in the focal plane, the properties of confocal transmission and reflection systems are identical. However, once the object is moved from the focal plane certain differences arise: in particular in confocal reflection a strong optical sectioning effect occurs that allows a single section through a thick object to be imaged. This is the major advantage of the confocal microscope arrangement. Fig. 4 also applies equally well to fluorescence imaging. However, in this case, because of the incoherent nature of fluorescence emissions after excitation by coherent light, imaging is then incoherent. Confocal microscopes can be achieved by using either a point detector, in practice performed by placing a pinhole in front of a photo-detector, or by using a coherent detector. Such a coherent detector, sensitive to the amplitude of the incident radiation, is not directly available for light, but is available for acoustic radiation, as in a scanning acoustic microscope. For light, a confocal effect can also be achieved by using an interferometric method to synthesize a coherent detector. Thus in interference microscopes using the high aperture condenser and objective lenses, an optical sectioning effect arises similar to that in the confocal microscope. Another way of producing a coherent detector is to use a single-mode optical fibre. 1.3 Probe microscopes 1.3.1 Scanning tunnelling microscope The scanning tunnelling microscope was the first of the family of probe microscopes, relying on a fundamentally different principle from the usual forms of microscope. A physical tip in the nanometre range is brought close, also in the nanometre range, to a conducting sample. If an electric potential is applied, electrons can tunnel across between the sample and the tip. By scanning the tip mechanically across the sample, an image can be generated with a resolution in the sub-nanometre range. The surface topography can also be measured with sub-nanometre sensitivity. While interference microscopy can measure surface topography with sub-nanometre sensitivity, in this case the profile is averaged over the lateral resolution of the microscope, of the order of the wavelength in dimensions. The scanning tunnelling microscope can image individual atoms. The signal is related to the work function of the material. Altering the bias voltage allows the band structure of the material to be investigated. 1.3.2 Atomic force microscope In the atomic force microscope, the force between the surface and the tip is measured using a cantilever beam and used to build up an image. Atomic force microscopy can be performed in either a contact or non-contact mode. It can be used with insulating specimens. Optical methods, often using a position sensitive detector, are used to measure displacements of the cantilever. 1.3.3 Near-field scanning optical microscope (NSOM) In a near-field scanning optical microscope, a very small tip or aperture is scanned relative to the specimen to attain resolution greater than the classical limit set by the wavelength of the radiation. As Fig. 5 shows, various different designs of near-field microscope have been proposed. It is evident that these again form into the conventional/scanning categories described earlier. The sample can be illuminated using the near-field probe as in Fig. 5(a). This is called the illumination-mode NSOM. Or the sample can be uniformly illuminated, and a signal detected using a near-field probe as in Fig. 5(b), giving a collection-mode NSOM. Or a confocal arrangement can be used, with a near-field probe used for both illumination and collection (c). In this case, an uncoated tip can be used. Finally, Fig. 5(d) shows the photon tunnelling microscope (PSTM), in which the sample is illuminated with evanescent waves produced by total internal reflection and an uncoated tip used to probe the evanescent field in the presence of the sample. Fig. 5 Different forms of near-field microscope: (a) illumination-mode NSOM, (b) collection-mode NSOM, (c) a near-field probe used for both illumination and collection in a confocal arrangement, (d) photon tunnelling microscope (PSTM). 2 Different types of radiation 2.1 Electromagnetic radiation 2.1.1 UV radiation and X rays The first microscopes used visible light, but in fact we do not need to use visible light, but can use any electromagnetic radiation, over a broad range of different available wavelengths. In Fig. 6 we show the wavelength of the electromagnetic spectrum, illustrating how the wavelength in air varies with frequency. Instead of using visible light, shorter wavelengths allow greater resolution to be achieved. Ultra-violet light is commonly used to excite fluorescence. X rays have also successfully been used to image biological samples. Fig. 6 The wavelength of different forms of electromagnetic radiation and acoustic radiation. 2.1.2 IR and microwave radiation In the longer wavelength region, infra-red radiation is used for observation of semiconductors or for molecular spectroscopic imaging. Imaging of emitted midinfra-red radiation can show up variations in temperature, such as hot spots in semiconductors. Microwaves have also been used, but resolution is limited by the long wavelength. For this reason microwaves (and mid-IR) have also been used for near-field microscopy. 2.2 Other radiation 2.2.1 Electron microscope The other important class of radiation that can be used for illumination is matter waves. The most common of these, of course, are electrons, the wavelength of which, as a function of acceleration voltage, is shown in Fig. 7. The bend in the curve at very high voltages is caused by relativistic effects. The wavelength of the electrons is very small: even for 100V electrons the wavelength is only 0.1 nm. But aberrations caused by the electron lenses limit resolution so that at present atomic resolution is only just achievable, even with much higher voltages. Fig. 7 The wavelength of matter waves (electrons and protons) as a function of accelerating voltage. In a transmission electron microscope (TEM), a beam of electrons is produced by an electron gun. The specimen is illuminated via a condenser lens (or lenses). Usually these are magnetic lenses in which a current in a coil produces a magnetic field that focuses the electrons. The electrons that are transmitted through the specimen are then focused by a series of lenses to form a final image that can be viewed directly on a phosphor screen. An X ray detector can be used to characterize the elements in the specimen. An electron-energy-loss spectrometer, together with a detector, can measure the energy of the electrons in a particular region of the image 2.2.2 Other matter radiation Instead of electrons, other particle beams can be used for illumination. Fig. 7 shows the wavelength of a beam of protons, as function of the accelerating voltage. Because of the larger mass of protons, relativistic effects are not apparent for protons in the curve in Fig. 7. Microscope images have also been formed using ions, and even neutral particles such as neutrons. Neutral atom microscopes are also under development. 2.2.3 Acoustic radiation Or instead of electromagnetic waves, acoustic radiation can be used to form a scanning acoustic microscope (SAM). Ultrasonic waves are focused into a water immersion medium. Mechanical scanning is again used to build up an image. Fig. 6 shows the wavelength of the acoustic wave as a function of frequency. By using microwave frequencies, wavelengths, and therefore resolution, in the sub-micron range can be generated. The SAM acts as a confocal microscope because the detector is sensitive to the amplitude of the acoustic wave. The acoustic microscope provides information on variations in the elastic properties (viscosity and elasticity) of the sample. 3 Different contrast mechanisms The bright field microscope detects the intensity of the light transmitted through the object. A microscope with a condenser aperture of appreciable size behaves as a partially coherent system, and the image will in general depend on the phase of the light coming from the object as well as its intensity. Many objects are weakly scattering, so the contrast of this phase information is weak. In this case the microscope effectively images variations in the transmittance or reflectance of the sample. Different designs of microscope can be used to image various properties of the object, thus providing new and complementary information. Phase contrast microscopy provides but one example of a different contrast mechanism. In fact in general any physical or chemical interaction of the illuminating radiation with the sample can in principle be used as the basis for a contrast mechanism. These different contrast mechanisms can be performed in either a conventional or scanning arrangement, or in a confocal system. 3.1.1 Phase contrast microscopy Phase contrast is a widely used technique in both biological microscopy (in transmission) and materials microscopy (in reflection). Its importance in biological microscopy stems, firstly, from the fact that contrast may otherwise be too weak to be visible, but secondly because the phase variations are caused by changes in optical thickness, related to physical density. In reflection microscopy, phase is related to surface height variations, but also depends on the optical material properties of the sample. 3.1.2 Polarization microscopy The polarization state of light transmitted through or reflected from a sample can also be changed. This change is detected in polarization microscopy, for example by placing the sample between crossed polarizers. The birefringence detected can be either material birefringence, or form birefringence (caused by the shape of the microstructure). Polarization microscopy is widely used in biological microscopy, and in mineralogy. 3.1.3 Fluorescence microscopy In fluorescence microscopy, electrons excited by illumination decay to the ground state and emit photons of light. Autofluorescence is natural fluorescence of the sample. Fluorescent dyes can be used as labels for particular biological or chemical constituents. Fluorescence microscopy is usually performed in the epi-illumination geometry to assist rejection of light from the source. Often it is performed in a confocal microscope, allowing 3-D localization of the fluorescent labels. 3.1.4 Raman microscopy Raman spectroscopy can be performed on a microscopic scale to produce images of presence of particular molecular bonds. It is usually performed in a scanning system, often of the confocal type. This is one example of the wider class of spectroscopic microscopies: in principle any form of spectroscopy can be used as the basis for a microscope contrast mode. 3.1.5 Non-linear microscopy Another class of contrast mechanisms is based on non-linear optical interactions. Again any non-linear mechanism can be used as the basis for a contrast mechanism. These include two- (or multi-photon) fluorescence, second (or higher order) harmonic generation, sum or difference frequency generation, and CARS. Probably other nonlinear optical mechanisms will be exploited in microscopy in the future. 3.1.6 Other contrast mechanisms The contrast mechanisms described above all rely on illumination and detection of light. But in many other modes radiation of one form can be converted into another. These include cathodoluminescence microscopy (electrons to light), X-ray microanalysis (electrons to X-rays), photoemission microscopy (light, usually UV, to electrons), photo-acoustic microscopy (light to ultrasonics), photo-thermal microscopy (light to thermal waves), optical or electron beam induced current (OBIC/EBIC). Again, in many of these, the illuminating or emitted radiation can be focused, or a combination can be used in a confocal arrangement. Bibliography Born M, Wolf E (1999) Principles of Optics, 7th edn, Cambridge University Press, Cambridge. Bradbury S, Bracegirdle B (1997) Introduction to the optical microscope, Bios Scientific Publishers, Oxford. 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Wilson T, Sheppard CJR (1984) Theory and Practice of Scanning Optical Microscopy, Academic Press, London.