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Structured light illumination for extended resolution in fluorescence microscopy
ARTICLE IN PRESS
Optics and Lasers in Engineering 43 (2005) 403–414
Structured light illumination for extended resolution in fluorescence microscopy R. Fedosseev, Y. Belyaev, J. Frohn, A. Stemmer* Nanotechnology Group, Swiss Federal Institute of Technology, Tannenstrasse 3, CH-8092 Zurich, Switzerland Received 8 December 2003; received in revised form 26 April 2004; accepted 30 April 2004 Available online 28 July 2004
Abstract During the last two decades fluorescence microscopy has become a powerful experimental tool in modern biology. Resolution of optical microscopes is limited by the diffraction nature of light and amounts to approximately 200 nm for point objects imaged with green light and high-NA objectives. Recently, several successful attempts have been made to break the resolution limit of microscopes. One of them is the so-called harmonic excitation light microscopy. 2D structured illumination produced by four interfering laser beams improves the lateral resolution by a factor of 2 to reach 100 nm. Structured illumination extends optical resolution since spatial frequencies beyond the classical cut-off frequency are brought into the passband of the optical microscope by frequency mixing. The extended passband is reconstructed computationally from several images acquired with shifted illumination patterns. Here we discuss an extension towards high resolution imaging of thick specimens by combining 2D structured illumination with deconvolution techniques. r 2004 Elsevier Ltd. All rights reserved. Keywords: Laser interference; Extended resolution; Fluorescence microscopy; Structured illumination; Deconvolution
1. Introduction Since Ernst Abbe (1873) and Lord Rayleigh (1896) laid the foundation to modern light microscopy by linking the imaging process to diffraction theory and, as a result *Corresponding author. Tel.: +41-1-632-4572; fax: +41-1-632-1278. E-mail address: [email protected] (A. Stemmer). 0143-8166/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2004.04.008
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of this, diffraction-limited objectives became available, resolution in light microscopy did not change for almost 70 years. The invention of the confocal microscope in the middle of last century extended lateral resolution slightly (theoretically by a factor of 1.4—in practice, however, much less) and primarily led to an improvement of the resolving power along the microscope axis. Despite the limited resolution of light microscopes, a strong demand of biologists for imaging their transparent samples resulted in developments of new imaging techniques such as dark-field, phase contrast, differential interference contrast, to name just the most prominent ones. Later, dramatic progress in the development of new fluorescent dyes and staining techniques converted fluorescence microscopy into a standard and irreplaceable tool for biological research. This progress gave a powerful impetus for a serious challenge of the resolution limits set by diffraction theory. Surprisingly, however, in practice the physical limits of microscopy resolution have been broken successfully only during the last decade. The problem of extending resolution in optical microscopy has been recently discussed in several comprehensive reviews [1–3]. New imaging techniques with resolution extension over the classical limit take advantage of three main concepts: (i) gathering light over a possibly larger set of angles around the sample, (ii) using a fluorescence process involving two or more photons nonlinearly, (iii) using excitation light varying with position. In the following we present a brief overview of the most interesting methods that increase the resolution along one or several microscope axes. Image interference (InM) microscopy invented by Gustafsson et al. [4,5] requires a second objective lens mounted opposite to the ‘‘normal’’ one. This group of methods recombines fluorescence light emitted in the directions of both objectives for interference on the camera chip. A significant resolution improvement in axial direction was observed. Combination with structured illumination along the z-axis further improves resolution. However, these methods do not extend the lateral resolution. 4Pi confocal microscopy developed by Scharder and Hell [6] and Bahlmann et al. [7], like InM, requires a second objective lens and is based on the same principles of recombination with possible interference of fluorescence light emitted by the sample in different directions. The important difference is that 4Pi is a confocal system and, therefore, has a pinhole reducing the emitted light intensity and requires raster scanning to acquire the full image while InM is a wide-field system. 4Pi confocal microscopy significantly improves axial resolution, but suffers from the strong side lobes in axial direction. Combining 4Pi confocal microscopy with two-photon excitation and deconvolution has allowed Schrader et al. [8] to decrease the side lobes. Such a system allows one to image relatively thick fixed biological specimens even though the overall resolution is slightly reduced when compared with standard 4Pi confocal microscopy. Another technique making use of several objectives is the multiple imaging axis microscope developed by Swoger et al. [9]. This system is based on four high-NA water immersion objectives arranged in tetrahedral geometry. The fluorescence images for each objective are recorded simultaneously. By mechanically scanning the
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sample four raw 3D image stacks are acquired. Finally, a single high-resolution image is reconstructed computationally from the raw data stacks. The system increases the volumetric resolution by a factor of 3.5 compared with an equivalent one-lens system and has essentially isotropic resolution in all directions. A further advantage of this technique is the possibility to image fluorescent samples that are at least 300-mm thick. Multiphoton excitation microscopy takes advantage of multiple (two [10] or three [11]) photon absorption in confocal systems. Multiphoton fluorescence occurs due to a nonlinear absorption process at extremely high illumination intensities. The intensity of fluorescence then depends on the illuminating light intensity as a power of two or three leading to a narrowing of the absorption focal spot. Advantages of this method are a decreased rate of photo bleaching and the possibility of imaging through thicker samples, as light absorption and scattering for longer excitation wavelengths are normally lower. Drawbacks are the decrease in resolution due to the application of a longer illumination wavelength and the significantly higher system price compared with standard confocal microscopy. A technically even more involved method is stimulated emission depletion [12] which can be applied to ‘‘carve’’ away some of the fluorescence emission volume. All the above methods result in extended resolution in axial and, to a certain extent, lateral direction depending on the realization of the system. Axial standing wave fluorescence microscopy was developed by Bailey et al. [13]. In this method the interference pattern generated by two coherent light beams, counter-propagating along the microscope axis, is used to illuminate a specimen. Fluorescence from the sample encoded by the interference pattern carries additional information about the sample structure. This additional information leading to increased axial resolution can be decoded from three images acquired for specific relative shifts of the interference pattern. Moving the spatially structured illumination along the microscope axis allows one to obtain optical sections of the sample [14]. However, the sample thickness is limited by the period of the standing wave field. A further development of this method, called excitation field synthesis [15], improves the sectioning capability by utilizing a superposition of different interference patterns giving one sharp interference maximum. Structured illumination microscopy, a generalization of the above technique, uses excitation light with periodic variations of intensity along specified directions. Actually, the idea of applying frequency mixing via non-uniform illumination to obtain extended resolution was put forward more than 30 years ago by Lukosz [16]. 2D or 3D structures (e.g. masks, gratings or interference patterns) are used in this method to create suitable variations of excitation light intensity in the studied specimen. If fine lateral structures are used for specimen illumination, resolution can be improved in the direction specified by the structure. Applied in several directions structured illumination has been shown to increase lateral resolution [17]. Cole et al. demonstrated that laterally structured illumination also enables optical sectioning [18]. Application of 3D structures for specimen illumination is expected to result in extended resolution in both lateral and axial directions [3].
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Harmonic excitation light microscopy (HELM) developed by our group [19] illuminates the fluorescent sample with a 2D mesh-like pattern that is generated by interference of four mutually coherent laser beams. Lateral resolution reaches 100 nm for green emission light, which exceeds the resolution of standard confocal microscopes by a factor of 1.5 and a factor of 2 compared with standard wide-field systems. Here we present applications of HELM to biological samples and discuss an extension towards high resolution optical sectioning by combining the 2D structured illumination with deconvolution algorithms.
2. HELM image formation 2.1. Setup The optical train of our HELM setup is shown in Fig. 1a. A 2D interference pattern is generated within the object plane of a microscope by interference of four laser beams. An Ar-ion laser (Omnichrome 543-AP-A01, wavelength 488 nm, power 120 mW) serves as a coherent light source. It is coupled to the interference generating apparatus by an optical fiber with integrated pigtail-style collimators. The beam diameter at the output of the collimator is 1.5 mm, a weak lens L (focal length 300 mm) is used to slightly focus the laser beam resulting in a beam diameter of 120 mm in the object plane. With this configuration, the curvature of the wavefronts is negligible in the small field of view, which is about 25 mm 25 mm. A rotatable l/2-wave-plate and a polarizer serve for setting the incident laser power. Three non-polarizing beam splitters BS with a splitting ratio of 1:1 produce four laser beams of equal intensity. Since the electrical polarization is parallel to the object plane only anti-parallel beams interfere. Piezo-actuated mirrors vary the path lengths of two beams in order to shift the excitation pattern relative to the specimen. The beams undergo total internal reflection at the hypotenuses of four custom-made glass prisms (Fig. 1b). The design of these prisms determines the angle a between the intersecting beams and the optical axis and, as a result, the nodal spacing of the interference pattern. In our current setup a is set to 55 , allowing direct observation of the laser light through a high-NA oil immersion objective. The prisms are oil immersed to the slide to couple the laser beams to the specimen chamber. The interference-generating apparatus is mounted on an inverted microscope (Zeiss Axiovert 100) and images are recorded with an uncooled industrial grade CCD camera (LV-8500, Leutron Vision, Glattbrugg, Switzerland). A standard personal computer with a frame grabber (Pic-Port, Leutron Vision, Glattbrugg, Switzerland) reads out image data, controls the measurement sequence and performs image calculations. All images were recorded with a Zeiss Plan Apo 63 /1.4 oilimmersion objective with 2.5 Optovar.
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Fig. 1. Optical train of HELM setup: (a) top view, and (b) cut view along the optical axis.
2.2. HELM theory Here we present a short description of the theoretical basis of HELM, for more detailed explanations the reader is referred to [19]. In light microscopy, image formation is described by a convolution of the specimen’s geometry with the point spread function of the microscope, i.e. the image of a point source of light [20]. In Fourier space this convolution corresponds to a multiplication of the specimen’s spectrum with the optical transfer function (OTF) where the latter is the Fourier transform of the microscope’s point spread function. Denoting with B a 2D Fourier transform, and with y being the resulting image of
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the specimen, f the specimen signal, and T the OTF of the microscope we obtain the following equation: * x ; ky Þ: * x ; ky Þ ¼ Tðkx ; ky Þfðk yðk
ð1Þ
In regions where the OTF is non-zero, called the support of the OTF or the passband, the spatial frequency components of the sample signal are transmitted to the image. Outside the passband the frequency information is irrecoverably lost. In case of fluorescence microscopy, the passband is a circular region (Fig. 2a) centered at the origin. The passband radius r corresponds to the cutoff frequency 4pNA/l, where l is the vacuum wavelength of the emission and NA is the numerical aperture of the objective. In fluorescence microscopy, the specimen signal f is proportional to the product of excitation intensity I times the density of fluorophore molecules c fðx; yÞ ¼ cðx; yÞIðx; yÞ:
ð2Þ
In our experimental setup the excitation intensity I is produced by four interfering laser beams. With x and y denoting the orthogonal spatial coordinates within the object plane and neglecting scaling factors, the resulting intensity distribution I of the electric field can be written as Iðx; yÞ ¼ 2 þ cos ðux þ Dx Þ þ cos ðuy þ Dy Þ;
ð3Þ
where u = (4pn) sin (a)/l is the spatial frequency of the harmonic excitation, n = 1.52 is the refractive index of glass, l is the vacuum wavelength of excitation, a is the beam’s angle to the optical axis according to Fig. 1b, and Dx and Dy describe the shift of the pattern relative to the sample in x and y directions, respectively. Combining Eqs. (1)–(3) we obtain the following formula for the Fourier transform of the image in case of HELM: y* ¼ Tð4A þ eiDx Bþ þ eiDx B þ eiDy C þ þ eiDy C Þ; * x ; ky Þ; B with A ¼ cðk
7
* x 7u; ky Þ and C ¼ cðk
7
ð4Þ
* x ; ky 7uÞ: ¼ cðk
Fig. 2. The OTF support of: (a) conventional fluorescence microscopy, and (b) the enhanced support of the OTF achieved by the HELM setup.
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As a result of the structured illumination four shifted spectra B7 and C7 occur in the Fourier spectrum of the image. Shifted by u along the kx and ky axes in positive and negative directions with respect to the original spectrum A, these additional spectra lead to the enhanced support of the OTF (Fig. 2b) that brings higher frequency components into the passband and, therefore, extends the resolution beyond standard fluorescence microscopy. Reconstruction of a high resolution HELM image requires acquisition of five wide-field images with different phase offsets of the illumination pattern. The five spectra A, B7 and C7 are extracted by solving a 5 5 set of linear equations (Eq. (4)) for the Fourier transforms of the acquired images. In our setup, the x and y phase offsets ( Dx and Dy) are adjusted sequentially to the values (0, 0) (p/2, 0), (p, 0), (0, p/2), and (0, p) by piezo-actuators (Fig. 1a). After calculating the five spectral components they are shifted to their required position and, finally, superimposed, taking into account the attenuation by the microscope’s OTF. The final HELM image is obtained by an inverse Fourier transform of the extended spectrum. 2.3. Deconvolution algorithms A no-neighbor deconvolution algorithm [21] was used in order to decrease the blur effect of thicker specimens. The deconvolution was performed according to the following formula: * y* d ¼ ½y* 2cT1 y G; ð5Þ where G is the Wiener filter [22], y* is the Fourier transform of the observed image, T1 is the out-of-focus OTF, y* d is the deconvolved image spectrum, and c is an empirical constant. The Wiener filter of the form G ¼ T0 =ðT02 þ aÞ with an empirical constant a was used. T0 stands for the in-focus OTF. The OTF T0,1 were calculated according the formulas given by Agard [23] for different values of defocusing. Values for numerical aperture of the objective, wavelength of light, media index of refraction and index of refraction of the immersion oil were chosen according to experimental conditions. Above algorithm was shown to be very effective for deblurring images [21]. The algorithm does not require neighboring images and uses only a single in-focus image. The out-of-focus contribution is simulated by the scaled product of optical transfer function times Fourier spectrum of the observed image. This makes the no-neighbor algorithm easily applicable and also very effective from a computational point of view. The algorithm further allows one to perform a Wiener inverse filtering when parameter c in Eq. (5) is set to 0. Deconvolution parameters a and c were optimized to achieve the best deblurring of the fluorescence image or inverse filtering.
3. Results and discussion Fig. 3 demonstrates the resolution achievable with HELM when imaging 100-nm diameter fluorescent polystyrene beads fixed to the surface of a glass cover slip.
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Fig. 3. Fluorescent latex beads, 100 nm dia., imaged with: (a) HELM, (b) inverse filtering deconvolution, and (c) conventional wide-field fluorescence microscopy. Scale bar is 1 mm.
Fig. 4. Rat pancreas semi-thin plastic section imaged with: (a) HELM, and (b) conventional fluorescence microscopy. Scale bar is 1 mm.
Shown are the reconstructed HELM image (Fig. 3a), the wide-field fluorescence image corrected for the microscope’s OTF using inverse filtering (Fig. 3b), and the standard wide-field fluorescence image (Fig. 3c). Clearly, the HELM image reveals much better resolution, reaching about 100 nm. It is possible to distinguish individual beads in the HELM image whereas for wide-field microscopy the bead size is two times smaller than the resolution of the image (about 200 nm). The OTF deconvolution improves the resolution slightly but nevertheless cannot reach the one obtained by HELM. The HELM OTF support is slightly narrower in diagonal than in axial directions (Fig. 2b), resulting in some resolution anisotropy that can be discerned on HELM images. This effect can be avoided by using illumination structured in more than 2 directions simultaneously. Figs. 4 and 5 present a rat pancreas semi-thin plastic section and microtubules in human endothelial cells, respectively. Both pictures demonstrate the high resolution of HELM images. The HELM image of rat pancreas (Fig. 4a) shows significantly finer details than the standard wide-field image (Fig. 4b). Similarly, closely spaced microtubules can be distinguished in HELM (Fig. 5a) but remain blurred when imaged conventionally (Fig. 5b). It is striking that the HELM images in Figs. 4 and 5 show a granularity of fluorescence emission, which is hardly visible in the conventional fluorescence images. This granularity probably does not correspond
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Fig. 5. Microtubules in human endothelial cells imaged with: (a) HELM, and (b) conventional fluorescence microscopy. Scale bar is 1 mm.
to real biological structures since, in case of microtubules, the antigen epitopes are expected to be distributed uniformly along the filaments and, in case of rat pancreas tissue, the typical size of the vesicles amounts to a few hundred nanometers. We suppose that the observed granularity is a result of the staining procedure, which binds several fluorochromes to one antigen epitope to achieve a strong fluorescence signal. The capability to resolve such ‘‘speckle’’ structures by HELM, in contrast to standard wide-field microscopy, may further extend the application range of fluorescent speckle microscopy (for a recent overview see e.g. [24]) in the analysis of dynamic events in living cells. The specimens presented in Figs. 3–5 all consist of a single very thin layer (100 nm or less) of fluorescent material. The HELM setup combined with a simple 2D image reconstruction algorithm evidently results in much improved resolution. However, the situation changes when the specimen contains much thicker fluorescing layers, as demonstrated in Fig. 6. The specimen, a 0.5-mm thick section of beech wood stained with acridine orange, exhibits a variable thickness and the intensity of staining varies considerably. In this case, the HELM image (Fig. 6a) does not show any resolution improvement compared with standard fluorescence (Fig. 6b). On the contrary, in the reconstructed HELM image a mesh-like artificial structure is evident that is particularly pronounced in zones of high fluorescence signal. Significant out-of-focus contributions in the initial images and local variations of refractive index in the sample are likely causes of these artifacts. We found experimentally that 200–300 nm is the maximum thickness of fluorescent samples for which 2D image reconstruction without correction for out-of-focus contributions leads to increased resolution. However, many biological objects are considerably thicker than this value. This problem motivated simulations of a 3D-HELM setup with increased resolution both laterally and axially [25]. This system requires a second objective to produce interference patterns in three dimensions. We expect that such a system combined with optical sectioning techniques will allow one to obtain images with extended resolution in thick specimens. However, since for each optical section the specimen needs to be illuminated with structured light along 5 or more directions and, correspondingly, 11 or more images need to be acquired [25], time resolution of such a 3D-HELM setup will be rather low.
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Fig. 6. Section of 0.5-mm thick beech wood stained with acridine orange imaged with: (a) HELM, (b) conventional fluorescence microscopy, (c) no-neighbor deconvolution applied before reconstructing the HELM image, (d) no-neighbor deconvolution of conventional fluorescence microscopy. Arrows mark identical features to compare resolution. Scale bar is 2 mm.
Combining the HELM technique with deconvolution methods offers a simpler and faster approach for imaging thick specimens. To test this idea we applied the noneighbor deconvolution algorithm as described above to each of the individual fluorescence images before reconstructing the final image with the 2D HELM algorithm. Fig. 6c demonstrates the suitability of this approach with clearly improved resolution for the beech wood section. Furthermore, the mesh-like artifacts observed in Fig. 6a are reduced to a great extent. No-neighbor deconvolution applied to the standard wide-field fluorescence image (Fig. 6d) also reduces the out-of-focus blur, but the finer features marked by arrows in Figs. 6c and d remain unresolved. The unprocessed wide-field fluorescence image (Fig. 6b) suffers both from strong blur and low resolution. Thus, the combination of deconvolution algorithms and HELM offers significant potential for imaging thicker specimens. A large variety of deconvolution algorithms have been developed and many are even available commercially. Each algorithm has its own characteristic advantages and disadvantages as detailed in [26]. Simple debluring methods such as no-neighbor or nearest-neighbor algorithms are very fast computationally, but produce images of lower intensity since they simply subtract the blur. More complicated deconvolution procedures apply a model of the microscope’s imaging process to reassign out-offocus blur. They are more economical from the point of view of preserving light intensity after deconvolution, but require bigger calculation efforts. We expect that combining such sophisticated deconvolution techniques, for example an iteration
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algorithm [27], with HELM will allow us to further increase the imaging quality of thicker specimens both with respect to resolution and quantification of fluorescence intensity.
4. Conclusion Harmonic excitation light microscopy combines structured illumination with digital image processing to increase the resolution of wide-field fluorescence microscopes. Employing a mesh-like 2D interference pattern as described in this paper, a true optical resolution of about 100 nm is achieved. The linear, algebraic and non-iterative 2D image reconstruction algorithm requires only moderate computational power. On specimens thicker than 200–300 nm, out-of-focus contributions need to be taken into account before reconstructing the HELM image. We have demonstrated here that preprocessing the set of five images required for reconstructing the final HELM image with a simple no-neighbor deconvolution algorithm preserves much of the resolving power associated with the 2D HELM technique. We expect that applying more complex deconvolution methods could increase the optical sectioning capabilities of our setup even further.
Acknowledgements This work was supported by the ETH Zurich NANO II polyproject. We gratefully thank Jakob Zb.aren, Inselspital, Bern, for supplying the microtubule and rat pancreas samples and for helpful discussions. We also like to thank Tanja Zimmermann, EMPA, Dubendorf, . for supplying the beech wood samples.
References [1] Jonkman JEN, Swoger J, Kress H, Rohrbach A, Stelzer EHK. Resolution in optical microscopy. Methods Enzymol 2003;360:416–46. [2] Weiss S. Shattering the diffraction limit of light: a revolution in fluorescence microscopy? Proc Natl Acad Sci USA 2000;97(16):8747–9. [3] Gustafsson MGL. Extended resolution fluorescence microscopy. Curr Opin Struct Biol 1999;9(5):627–34. [4] Gustafsson MG, Agard DA, Sedat JW. Sevenfold improvement of axial resolution in 3D wide-field microscopy using two objective-lenses. Proc SPIE 1995;2412:147–56. [5] Gustafsson MGL, Agard DA, Sedat JW. (IM)-M-5: 3D widefield light microscopy with better than 100 nm axial resolution. J Microsc-Oxford 1999;195:10–6. [6] Schrader M, Hell SW. 4Pi-confocal images with axial superresolution. J Microsc-Oxford 1996;183:189–93. [7] Bahlmann K, Jakobs S, Hell SW. 4Pi-confocal microscopy of live cells. Ultramicroscopy 2001;87(3):155–64.
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[8] Schrader M, Bahlmann K, Giese G, Hell SW. 4Pi-confocal imaging in fixed biological specimens. Biophys J 1998;75(4):1659–68. [9] Swoger J, Huisken J, Stelzer EHK. Multiple imaging axis microscopy improves resolution for thicksample applications. Opt Lett 2003;28(18):1654–6. [10] Denk W, Strickler JH, Webb WW. 2-Photon laser scanning fluorescence microscopy. Science 1990;248(4951):73–6. [11] Schrader M, Bahlmann K, Hell SW. Three-photon-excitation microscopy: theory, experiment and applications. Optik 1997;104(3):116–24. [12] Klar TA, Engel E, Hell SW. Breaking Abbe’s diffraction resolution limit in fluorescence microscopy with stimulated emission depletion beams of various shapes. Phys Rev E 2001;6406(6):art. no.-066613. [13] Bailey B, Farkas DL, Taylor DL, Lanni F. Enhancement of axial resolution in fluorescence microscopy by standing-wave excitation. Nature 1993;366(6450):44–8. [14] Bailey B, Lanni F, Farkas DL, Taylor DL. High-resolution direct 3-D fluorescence microscopy of cells and organelles by standing-wave excitation-based optical subsectioning. Biophys J 1994;66(2):A275. [15] Lanni F, Bailey B, Farkas DL, Taylor DL. Excitation field synthesis as a means for obtaining enhanced axial resolution in fluorescence microscopes. Bioimaging 1993;1:187–96. [16] Lukosz W. Optical systems with resolving powers exceeding classical limit. J Opt Soc Am 1966;56(11):1463–72. [17] Gustafsson MGL. Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy. J Microsc-Oxford 2000;198:82–7. [18] Cole MJ, Siegel J, Webb SED, Jones R, Dowling K, French PMW, Lever MJ, Sucharov LOD, Neil MAA, Juskaitis R, Wilson T. Whole-field optically sectioned fluorescence lifetime imaging. Opt Lett 2000;25(18):1361–3. [19] Frohn JT, Knapp HF, Stemmer A. True optical resolution beyond the Rayleigh limit achieved by standing wave illumination. Proc Natl Acad Sci USA 2000;97(13):7232–6. [20] Goodman JW. Introduction to Fourier optics, 2nd ed. New York: McGraw-Hill; 1996. [21] Monck JR, Oberhauser AF, Keating TJ, Fernandez JM. Thin-section ratiometric Ca2+ images obtained by optical sectioning of Fura-2 loaded mast-cells. J Cell Biol 1992;116(3):745–59. [22] Russ JC. The image processing handbook, 4th ed. Boca Raton: CRC Press; 2002. [23] Agard DA. Optical sectioning microscopy—cellular architecture in 3 dimensions. Annu Rev Biophys Bioeng 1984;13:191–219. [24] Danuser G, Waterman-Storer CM. Quantitative fluorescent speckle microscopy: where it came from and where it is going. J Microsc-Oxford 2003;211:191–207. [25] Frohn JT, Knapp HF, Stemmer A. Three-dimensional resolution enhancement in fluorescence microscopy by harmonic excitation. Opt Lett 2001;26(11):828–30. [26] Wallace W, Schaefer LH, Swedlow JR. A workingperson’s guide to deconvolution in light microscopy. Biotechniques 2001;31(5):1076–97. [27] Verveer PJ, Gemkow MJ, Jovin TM. A comparison of image restoration approaches applied to threedimensional confocal and wide-field fluorescence microscopy. J Microsc-Oxford 1999;193:50–61.
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Structured light illumination for extended resolution in fluorescence microscopy R. Fedosseev, Y. Belyaev, J. Frohn, A. Stemmer* Nanotechnology Group, Swiss Federal Institute of Technology, Tannenstrasse 3, CH-8092 Zurich, Switzerland Received 8 December 2003; received in revised form 26 April 2004; accepted 30 April 2004 Available online 28 July 2004
Abstract During the last two decades fluorescence microscopy has become a powerful experimental tool in modern biology. Resolution of optical microscopes is limited by the diffraction nature of light and amounts to approximately 200 nm for point objects imaged with green light and high-NA objectives. Recently, several successful attempts have been made to break the resolution limit of microscopes. One of them is the so-called harmonic excitation light microscopy. 2D structured illumination produced by four interfering laser beams improves the lateral resolution by a factor of 2 to reach 100 nm. Structured illumination extends optical resolution since spatial frequencies beyond the classical cut-off frequency are brought into the passband of the optical microscope by frequency mixing. The extended passband is reconstructed computationally from several images acquired with shifted illumination patterns. Here we discuss an extension towards high resolution imaging of thick specimens by combining 2D structured illumination with deconvolution techniques. r 2004 Elsevier Ltd. All rights reserved. Keywords: Laser interference; Extended resolution; Fluorescence microscopy; Structured illumination; Deconvolution
1. Introduction Since Ernst Abbe (1873) and Lord Rayleigh (1896) laid the foundation to modern light microscopy by linking the imaging process to diffraction theory and, as a result *Corresponding author. Tel.: +41-1-632-4572; fax: +41-1-632-1278. E-mail address: [email protected] (A. Stemmer). 0143-8166/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlaseng.2004.04.008
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of this, diffraction-limited objectives became available, resolution in light microscopy did not change for almost 70 years. The invention of the confocal microscope in the middle of last century extended lateral resolution slightly (theoretically by a factor of 1.4—in practice, however, much less) and primarily led to an improvement of the resolving power along the microscope axis. Despite the limited resolution of light microscopes, a strong demand of biologists for imaging their transparent samples resulted in developments of new imaging techniques such as dark-field, phase contrast, differential interference contrast, to name just the most prominent ones. Later, dramatic progress in the development of new fluorescent dyes and staining techniques converted fluorescence microscopy into a standard and irreplaceable tool for biological research. This progress gave a powerful impetus for a serious challenge of the resolution limits set by diffraction theory. Surprisingly, however, in practice the physical limits of microscopy resolution have been broken successfully only during the last decade. The problem of extending resolution in optical microscopy has been recently discussed in several comprehensive reviews [1–3]. New imaging techniques with resolution extension over the classical limit take advantage of three main concepts: (i) gathering light over a possibly larger set of angles around the sample, (ii) using a fluorescence process involving two or more photons nonlinearly, (iii) using excitation light varying with position. In the following we present a brief overview of the most interesting methods that increase the resolution along one or several microscope axes. Image interference (InM) microscopy invented by Gustafsson et al. [4,5] requires a second objective lens mounted opposite to the ‘‘normal’’ one. This group of methods recombines fluorescence light emitted in the directions of both objectives for interference on the camera chip. A significant resolution improvement in axial direction was observed. Combination with structured illumination along the z-axis further improves resolution. However, these methods do not extend the lateral resolution. 4Pi confocal microscopy developed by Scharder and Hell [6] and Bahlmann et al. [7], like InM, requires a second objective lens and is based on the same principles of recombination with possible interference of fluorescence light emitted by the sample in different directions. The important difference is that 4Pi is a confocal system and, therefore, has a pinhole reducing the emitted light intensity and requires raster scanning to acquire the full image while InM is a wide-field system. 4Pi confocal microscopy significantly improves axial resolution, but suffers from the strong side lobes in axial direction. Combining 4Pi confocal microscopy with two-photon excitation and deconvolution has allowed Schrader et al. [8] to decrease the side lobes. Such a system allows one to image relatively thick fixed biological specimens even though the overall resolution is slightly reduced when compared with standard 4Pi confocal microscopy. Another technique making use of several objectives is the multiple imaging axis microscope developed by Swoger et al. [9]. This system is based on four high-NA water immersion objectives arranged in tetrahedral geometry. The fluorescence images for each objective are recorded simultaneously. By mechanically scanning the
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sample four raw 3D image stacks are acquired. Finally, a single high-resolution image is reconstructed computationally from the raw data stacks. The system increases the volumetric resolution by a factor of 3.5 compared with an equivalent one-lens system and has essentially isotropic resolution in all directions. A further advantage of this technique is the possibility to image fluorescent samples that are at least 300-mm thick. Multiphoton excitation microscopy takes advantage of multiple (two [10] or three [11]) photon absorption in confocal systems. Multiphoton fluorescence occurs due to a nonlinear absorption process at extremely high illumination intensities. The intensity of fluorescence then depends on the illuminating light intensity as a power of two or three leading to a narrowing of the absorption focal spot. Advantages of this method are a decreased rate of photo bleaching and the possibility of imaging through thicker samples, as light absorption and scattering for longer excitation wavelengths are normally lower. Drawbacks are the decrease in resolution due to the application of a longer illumination wavelength and the significantly higher system price compared with standard confocal microscopy. A technically even more involved method is stimulated emission depletion [12] which can be applied to ‘‘carve’’ away some of the fluorescence emission volume. All the above methods result in extended resolution in axial and, to a certain extent, lateral direction depending on the realization of the system. Axial standing wave fluorescence microscopy was developed by Bailey et al. [13]. In this method the interference pattern generated by two coherent light beams, counter-propagating along the microscope axis, is used to illuminate a specimen. Fluorescence from the sample encoded by the interference pattern carries additional information about the sample structure. This additional information leading to increased axial resolution can be decoded from three images acquired for specific relative shifts of the interference pattern. Moving the spatially structured illumination along the microscope axis allows one to obtain optical sections of the sample [14]. However, the sample thickness is limited by the period of the standing wave field. A further development of this method, called excitation field synthesis [15], improves the sectioning capability by utilizing a superposition of different interference patterns giving one sharp interference maximum. Structured illumination microscopy, a generalization of the above technique, uses excitation light with periodic variations of intensity along specified directions. Actually, the idea of applying frequency mixing via non-uniform illumination to obtain extended resolution was put forward more than 30 years ago by Lukosz [16]. 2D or 3D structures (e.g. masks, gratings or interference patterns) are used in this method to create suitable variations of excitation light intensity in the studied specimen. If fine lateral structures are used for specimen illumination, resolution can be improved in the direction specified by the structure. Applied in several directions structured illumination has been shown to increase lateral resolution [17]. Cole et al. demonstrated that laterally structured illumination also enables optical sectioning [18]. Application of 3D structures for specimen illumination is expected to result in extended resolution in both lateral and axial directions [3].
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Harmonic excitation light microscopy (HELM) developed by our group [19] illuminates the fluorescent sample with a 2D mesh-like pattern that is generated by interference of four mutually coherent laser beams. Lateral resolution reaches 100 nm for green emission light, which exceeds the resolution of standard confocal microscopes by a factor of 1.5 and a factor of 2 compared with standard wide-field systems. Here we present applications of HELM to biological samples and discuss an extension towards high resolution optical sectioning by combining the 2D structured illumination with deconvolution algorithms.
2. HELM image formation 2.1. Setup The optical train of our HELM setup is shown in Fig. 1a. A 2D interference pattern is generated within the object plane of a microscope by interference of four laser beams. An Ar-ion laser (Omnichrome 543-AP-A01, wavelength 488 nm, power 120 mW) serves as a coherent light source. It is coupled to the interference generating apparatus by an optical fiber with integrated pigtail-style collimators. The beam diameter at the output of the collimator is 1.5 mm, a weak lens L (focal length 300 mm) is used to slightly focus the laser beam resulting in a beam diameter of 120 mm in the object plane. With this configuration, the curvature of the wavefronts is negligible in the small field of view, which is about 25 mm 25 mm. A rotatable l/2-wave-plate and a polarizer serve for setting the incident laser power. Three non-polarizing beam splitters BS with a splitting ratio of 1:1 produce four laser beams of equal intensity. Since the electrical polarization is parallel to the object plane only anti-parallel beams interfere. Piezo-actuated mirrors vary the path lengths of two beams in order to shift the excitation pattern relative to the specimen. The beams undergo total internal reflection at the hypotenuses of four custom-made glass prisms (Fig. 1b). The design of these prisms determines the angle a between the intersecting beams and the optical axis and, as a result, the nodal spacing of the interference pattern. In our current setup a is set to 55 , allowing direct observation of the laser light through a high-NA oil immersion objective. The prisms are oil immersed to the slide to couple the laser beams to the specimen chamber. The interference-generating apparatus is mounted on an inverted microscope (Zeiss Axiovert 100) and images are recorded with an uncooled industrial grade CCD camera (LV-8500, Leutron Vision, Glattbrugg, Switzerland). A standard personal computer with a frame grabber (Pic-Port, Leutron Vision, Glattbrugg, Switzerland) reads out image data, controls the measurement sequence and performs image calculations. All images were recorded with a Zeiss Plan Apo 63 /1.4 oilimmersion objective with 2.5 Optovar.
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Fig. 1. Optical train of HELM setup: (a) top view, and (b) cut view along the optical axis.
2.2. HELM theory Here we present a short description of the theoretical basis of HELM, for more detailed explanations the reader is referred to [19]. In light microscopy, image formation is described by a convolution of the specimen’s geometry with the point spread function of the microscope, i.e. the image of a point source of light [20]. In Fourier space this convolution corresponds to a multiplication of the specimen’s spectrum with the optical transfer function (OTF) where the latter is the Fourier transform of the microscope’s point spread function. Denoting with B a 2D Fourier transform, and with y being the resulting image of
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the specimen, f the specimen signal, and T the OTF of the microscope we obtain the following equation: * x ; ky Þ: * x ; ky Þ ¼ Tðkx ; ky Þfðk yðk
ð1Þ
In regions where the OTF is non-zero, called the support of the OTF or the passband, the spatial frequency components of the sample signal are transmitted to the image. Outside the passband the frequency information is irrecoverably lost. In case of fluorescence microscopy, the passband is a circular region (Fig. 2a) centered at the origin. The passband radius r corresponds to the cutoff frequency 4pNA/l, where l is the vacuum wavelength of the emission and NA is the numerical aperture of the objective. In fluorescence microscopy, the specimen signal f is proportional to the product of excitation intensity I times the density of fluorophore molecules c fðx; yÞ ¼ cðx; yÞIðx; yÞ:
ð2Þ
In our experimental setup the excitation intensity I is produced by four interfering laser beams. With x and y denoting the orthogonal spatial coordinates within the object plane and neglecting scaling factors, the resulting intensity distribution I of the electric field can be written as Iðx; yÞ ¼ 2 þ cos ðux þ Dx Þ þ cos ðuy þ Dy Þ;
ð3Þ
where u = (4pn) sin (a)/l is the spatial frequency of the harmonic excitation, n = 1.52 is the refractive index of glass, l is the vacuum wavelength of excitation, a is the beam’s angle to the optical axis according to Fig. 1b, and Dx and Dy describe the shift of the pattern relative to the sample in x and y directions, respectively. Combining Eqs. (1)–(3) we obtain the following formula for the Fourier transform of the image in case of HELM: y* ¼ Tð4A þ eiDx Bþ þ eiDx B þ eiDy C þ þ eiDy C Þ; * x ; ky Þ; B with A ¼ cðk
7
* x 7u; ky Þ and C ¼ cðk
7
ð4Þ
* x ; ky 7uÞ: ¼ cðk
Fig. 2. The OTF support of: (a) conventional fluorescence microscopy, and (b) the enhanced support of the OTF achieved by the HELM setup.
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As a result of the structured illumination four shifted spectra B7 and C7 occur in the Fourier spectrum of the image. Shifted by u along the kx and ky axes in positive and negative directions with respect to the original spectrum A, these additional spectra lead to the enhanced support of the OTF (Fig. 2b) that brings higher frequency components into the passband and, therefore, extends the resolution beyond standard fluorescence microscopy. Reconstruction of a high resolution HELM image requires acquisition of five wide-field images with different phase offsets of the illumination pattern. The five spectra A, B7 and C7 are extracted by solving a 5 5 set of linear equations (Eq. (4)) for the Fourier transforms of the acquired images. In our setup, the x and y phase offsets ( Dx and Dy) are adjusted sequentially to the values (0, 0) (p/2, 0), (p, 0), (0, p/2), and (0, p) by piezo-actuators (Fig. 1a). After calculating the five spectral components they are shifted to their required position and, finally, superimposed, taking into account the attenuation by the microscope’s OTF. The final HELM image is obtained by an inverse Fourier transform of the extended spectrum. 2.3. Deconvolution algorithms A no-neighbor deconvolution algorithm [21] was used in order to decrease the blur effect of thicker specimens. The deconvolution was performed according to the following formula: * y* d ¼ ½y* 2cT1 y G; ð5Þ where G is the Wiener filter [22], y* is the Fourier transform of the observed image, T1 is the out-of-focus OTF, y* d is the deconvolved image spectrum, and c is an empirical constant. The Wiener filter of the form G ¼ T0 =ðT02 þ aÞ with an empirical constant a was used. T0 stands for the in-focus OTF. The OTF T0,1 were calculated according the formulas given by Agard [23] for different values of defocusing. Values for numerical aperture of the objective, wavelength of light, media index of refraction and index of refraction of the immersion oil were chosen according to experimental conditions. Above algorithm was shown to be very effective for deblurring images [21]. The algorithm does not require neighboring images and uses only a single in-focus image. The out-of-focus contribution is simulated by the scaled product of optical transfer function times Fourier spectrum of the observed image. This makes the no-neighbor algorithm easily applicable and also very effective from a computational point of view. The algorithm further allows one to perform a Wiener inverse filtering when parameter c in Eq. (5) is set to 0. Deconvolution parameters a and c were optimized to achieve the best deblurring of the fluorescence image or inverse filtering.
3. Results and discussion Fig. 3 demonstrates the resolution achievable with HELM when imaging 100-nm diameter fluorescent polystyrene beads fixed to the surface of a glass cover slip.
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Fig. 3. Fluorescent latex beads, 100 nm dia., imaged with: (a) HELM, (b) inverse filtering deconvolution, and (c) conventional wide-field fluorescence microscopy. Scale bar is 1 mm.
Fig. 4. Rat pancreas semi-thin plastic section imaged with: (a) HELM, and (b) conventional fluorescence microscopy. Scale bar is 1 mm.
Shown are the reconstructed HELM image (Fig. 3a), the wide-field fluorescence image corrected for the microscope’s OTF using inverse filtering (Fig. 3b), and the standard wide-field fluorescence image (Fig. 3c). Clearly, the HELM image reveals much better resolution, reaching about 100 nm. It is possible to distinguish individual beads in the HELM image whereas for wide-field microscopy the bead size is two times smaller than the resolution of the image (about 200 nm). The OTF deconvolution improves the resolution slightly but nevertheless cannot reach the one obtained by HELM. The HELM OTF support is slightly narrower in diagonal than in axial directions (Fig. 2b), resulting in some resolution anisotropy that can be discerned on HELM images. This effect can be avoided by using illumination structured in more than 2 directions simultaneously. Figs. 4 and 5 present a rat pancreas semi-thin plastic section and microtubules in human endothelial cells, respectively. Both pictures demonstrate the high resolution of HELM images. The HELM image of rat pancreas (Fig. 4a) shows significantly finer details than the standard wide-field image (Fig. 4b). Similarly, closely spaced microtubules can be distinguished in HELM (Fig. 5a) but remain blurred when imaged conventionally (Fig. 5b). It is striking that the HELM images in Figs. 4 and 5 show a granularity of fluorescence emission, which is hardly visible in the conventional fluorescence images. This granularity probably does not correspond
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Fig. 5. Microtubules in human endothelial cells imaged with: (a) HELM, and (b) conventional fluorescence microscopy. Scale bar is 1 mm.
to real biological structures since, in case of microtubules, the antigen epitopes are expected to be distributed uniformly along the filaments and, in case of rat pancreas tissue, the typical size of the vesicles amounts to a few hundred nanometers. We suppose that the observed granularity is a result of the staining procedure, which binds several fluorochromes to one antigen epitope to achieve a strong fluorescence signal. The capability to resolve such ‘‘speckle’’ structures by HELM, in contrast to standard wide-field microscopy, may further extend the application range of fluorescent speckle microscopy (for a recent overview see e.g. [24]) in the analysis of dynamic events in living cells. The specimens presented in Figs. 3–5 all consist of a single very thin layer (100 nm or less) of fluorescent material. The HELM setup combined with a simple 2D image reconstruction algorithm evidently results in much improved resolution. However, the situation changes when the specimen contains much thicker fluorescing layers, as demonstrated in Fig. 6. The specimen, a 0.5-mm thick section of beech wood stained with acridine orange, exhibits a variable thickness and the intensity of staining varies considerably. In this case, the HELM image (Fig. 6a) does not show any resolution improvement compared with standard fluorescence (Fig. 6b). On the contrary, in the reconstructed HELM image a mesh-like artificial structure is evident that is particularly pronounced in zones of high fluorescence signal. Significant out-of-focus contributions in the initial images and local variations of refractive index in the sample are likely causes of these artifacts. We found experimentally that 200–300 nm is the maximum thickness of fluorescent samples for which 2D image reconstruction without correction for out-of-focus contributions leads to increased resolution. However, many biological objects are considerably thicker than this value. This problem motivated simulations of a 3D-HELM setup with increased resolution both laterally and axially [25]. This system requires a second objective to produce interference patterns in three dimensions. We expect that such a system combined with optical sectioning techniques will allow one to obtain images with extended resolution in thick specimens. However, since for each optical section the specimen needs to be illuminated with structured light along 5 or more directions and, correspondingly, 11 or more images need to be acquired [25], time resolution of such a 3D-HELM setup will be rather low.
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Fig. 6. Section of 0.5-mm thick beech wood stained with acridine orange imaged with: (a) HELM, (b) conventional fluorescence microscopy, (c) no-neighbor deconvolution applied before reconstructing the HELM image, (d) no-neighbor deconvolution of conventional fluorescence microscopy. Arrows mark identical features to compare resolution. Scale bar is 2 mm.
Combining the HELM technique with deconvolution methods offers a simpler and faster approach for imaging thick specimens. To test this idea we applied the noneighbor deconvolution algorithm as described above to each of the individual fluorescence images before reconstructing the final image with the 2D HELM algorithm. Fig. 6c demonstrates the suitability of this approach with clearly improved resolution for the beech wood section. Furthermore, the mesh-like artifacts observed in Fig. 6a are reduced to a great extent. No-neighbor deconvolution applied to the standard wide-field fluorescence image (Fig. 6d) also reduces the out-of-focus blur, but the finer features marked by arrows in Figs. 6c and d remain unresolved. The unprocessed wide-field fluorescence image (Fig. 6b) suffers both from strong blur and low resolution. Thus, the combination of deconvolution algorithms and HELM offers significant potential for imaging thicker specimens. A large variety of deconvolution algorithms have been developed and many are even available commercially. Each algorithm has its own characteristic advantages and disadvantages as detailed in [26]. Simple debluring methods such as no-neighbor or nearest-neighbor algorithms are very fast computationally, but produce images of lower intensity since they simply subtract the blur. More complicated deconvolution procedures apply a model of the microscope’s imaging process to reassign out-offocus blur. They are more economical from the point of view of preserving light intensity after deconvolution, but require bigger calculation efforts. We expect that combining such sophisticated deconvolution techniques, for example an iteration
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algorithm [27], with HELM will allow us to further increase the imaging quality of thicker specimens both with respect to resolution and quantification of fluorescence intensity.
4. Conclusion Harmonic excitation light microscopy combines structured illumination with digital image processing to increase the resolution of wide-field fluorescence microscopes. Employing a mesh-like 2D interference pattern as described in this paper, a true optical resolution of about 100 nm is achieved. The linear, algebraic and non-iterative 2D image reconstruction algorithm requires only moderate computational power. On specimens thicker than 200–300 nm, out-of-focus contributions need to be taken into account before reconstructing the HELM image. We have demonstrated here that preprocessing the set of five images required for reconstructing the final HELM image with a simple no-neighbor deconvolution algorithm preserves much of the resolving power associated with the 2D HELM technique. We expect that applying more complex deconvolution methods could increase the optical sectioning capabilities of our setup even further.
Acknowledgements This work was supported by the ETH Zurich NANO II polyproject. We gratefully thank Jakob Zb.aren, Inselspital, Bern, for supplying the microtubule and rat pancreas samples and for helpful discussions. We also like to thank Tanja Zimmermann, EMPA, Dubendorf, . for supplying the beech wood samples.
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