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TO M O G R A P H I C M I C RO S C O P Y Tomographic Interference Microscopy of Living Cells Gennady N. Vishnyakov 1, Gennady G. Levin 1, Vladimir L. Minaev 1, Valery V. Pickalov 2, Alexey V. Likhachev 2 1. Institute for Optical and Physical Measurements, Moscow, Russia 2. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia INTRODUCTION BIOGRAPHY Gennady Vishnyakov received his engineering physics degree from Moscow Engineering Physics Institute in 1978. Since that time he has worked in the Russian Research Institute For Optical and Physical Measurements (VNIIOFI). Gennady received his PhD in 1985 for the thesis 'Tomographic methods in holographic interferometry' and his DSc in 2000 for the thesis 'Optical tomography of multidimensional objects'. His interests include optical tomography and 3D microscopy, optical data and image processing, holography, optical profilometry and interferometry. He is the author of more than 60 scientific papers and the book "Optical Tomography" (1989), in Russian. ABSTRACT Research on the internal structure of living cells has great interest for biology. For an optically transparent cell (phase sample) this problem can be solved only by tomographic methods. The methods of projection acquisition and tomogram reconstruction are analyzed. The tomographic interference microscopy for 3D refractive index spatial distribution measurements has been proposed. The experimental setup is based on a Linnik interference microscope. Experimental work on lymphocyte reconstruction is described here. Research on the internal structure of living cells gives important information about morphology, spatial distribution of proteins and concentration of chemical drugs inside the cell. In microscopy three types of samples are usually investigated: fluorescent or emissive samples; stained or amplitude samples; and transparent or phase samples. For each type of sample a different method of image acquisition is required. There are various approaches to microscopy of 3D fluorescent samples. In the first approach widefield microscopy and digital image processing are used [1-3]. The second approach is confocal scanning microscopy. The next approach was suggested in [4] in which the optical microscope is used as tomographic device for projection acquisition of fluorescent samples. Earlier in [5] we have offered a tomographic approach to the description 3D imaging properties of optical systems (see [5]). Another wide class of samples in microscopy is phase and absorbing samples. The living cell is a phase object because it is transparent to optical radiation. For 3D absorbing or phase samples it is necessary to use the methods of computed tomography (CT). In this case the microscope is an optical setup for projection acquisition at various probing angles. The authors of [6] were one of the first who proposed to connect CT and microscopy. They used cone-beam microtomography for the reconstruction of absorption coefficient distribution of stratified mediums. For the first time in [7] a microscope with oblique illumination for tomography of phase samples was suggested. Phase contrast was used for visualization of projections. Therefore this method is suitable to study phase objects with small gradients of refractive index. We have developed a new type of optical microscope called a tomographic microscope [8]. As an optical device, this microscope is related to interference microscopes. According to its functional characteristics, it can be classified as a computerized optical tomographic system for optically transparent (phase) or absorptive (amplitude) samples. Its basic advantage consists in that it can measure spatial distribution of refractive index and/or absorption coefficient. M AT E R I A L S A N D M E T H O D S Technique description The tomography includes two stages — projections acquisition and tomogram reconstruction from projections. The second stage is universal for all applications of tomography, but methods of projection acquisition differ from each other. In tomography, projections are obtained by probing the sample at various angles. In optical microscopy the situation is complicated because for illumination and imaging the samples it is necessary to use the special arrangement — a microscope. There are two problems: 1. Providing of angular probing system builds in a microscope; 2. Visualization of probing radiation and evalFigure 1: Possible sample probing geometry in tomographic microscopy. (a-c) Scanning of probing beam around stationary sample. (d, e) Rotation or scanning sample through stationary probing beam. 1, front focal plane of objective. 2, optical axes of probing beam. 3, 5, objectives. 4, sample. 6, back focal plane of objective. 7, sample holder. KEYWORDS 3D microscopy, 3D tomography, 2D projection, reconstruction algorithm, tomogram, 3D refractive index distribution ACKNOWLEDGEMENTS Thanks to E. Streletskaya of National Hematology Research Center (Russia) for help. A U T H O R D E TA I L S Gennady G. Vishnyakov DSc, Russian Research Institute for Optophysical Measurements (VNIIOFI), 46 Ozernaya St., 119361 Moscow, Russia. Tel: + 007 095 437 3401 Email: [email protected] Microscopy and Analysis, 18 (1): 15-17 (UK), 2004. MICROSCOPY AND A N A LY S I S • J A N U A R Y 2 0 0 4 15 Figure 2: The optical setup of tomographic microscope based on Linnik microinterferometer. 1, wide light source. 2, 11, lenses. 3, beam splitter. 4, 8, front focal planes of objectives. 5, 9, objectives. 6, sample. 7, mirror; 10, mirror on PZT (piezoelectric transducer). 12, input plane (CCD camera). uation of the projection data. Angular probing in tomography can be realized in two ways: angular scanning of the probing beam around a stationary sample; and rotation or scanning the sample through the stationary probing beam. The basic requirement of tomography is the necessity to collect as many as possible projections in the maximal angle of view, which should achieve 180 degrees. In practice it is difficult to satisfy this requirement. As is usual in microscopy the number of projections and the angle of view are limited. Possible techniques of angular probing in microscopy are shown in Fig 1. The numerical apertures of objectives 3 and 5 restrict the maximal viewing angle. The principle of angular probing shown in Fig 1a has been realized in our papers [8], and then in [9]. The technique in Fig 1b has been suggested in [10]. A scanner based on a digital micromirror device (DMD) placed in aperture diaphragm plane of a microscope is used. This technique is suitable only for small samples. The size of sample must be smaller than the diameter of the beam waist near the focal plane of the objective. For large objects it is necessary to use the technique represented in Fig 1e. The original procedure of the collected data processing, patented by us [11], allows us to obtain parallel projections. As mentioned above, an optically transparent sample is described by a 3D spatial distribution of refraction index. Therefore such a sample basically causes a phase shift of a probing light wave. In microscopy phase contrast and interference methods are used for its visualization. Phase contrast (proposed by Zernike) does not give the quantitative information about the phase of the optical wave. There are two interference methods: DIC (differential interference contrast or Nomarski method) and interference contrast. DIC is a method of shearing interferometry. It allows the measuring of a wave phase gra- 16 MICROSCOPY AND Figure 3: Schemes of sample probing. (a) The real probing scheme. Sample is placed on the surface of flat mirror. Three positions, A’, B’, C’ of probing beam are shown. (b) The equivalent probing scheme in transmitted light. dient in a direction of shift. However interference fringes code the information about the phase gradient and it requires an operation of decoding. It is more preferable to use the interference method. Special objectives are available for the Michelson and Mirau methods. However these objectives have a small numerical aperture and a small angle of view. The Linnik microinterferometer has the largest numerical aperture. Therefore in the present work we have used it with the technique of angular probing as shown in Fig 1a. Projection acquisition For projection acquisition we used a Linnik interference microscope (Fig 2). Tilted illumination of the sample was achieved by displacement of a point light source [12]. For automatic interferogram decoding a method of 4th phase steps (Carre algorithm) was used. In the Linnik microscope the sample was placed on a mirror, and therefore the probing light beam passes through the sample under different angles twice (Fig 3a). To reduce this problem to usual transmission tomography it is necessary to sum the sample and its own reflected image (Fig 3b). After decoding an interference pattern, one obtains the system of equations: Ci ⌬Ni = 2 (n(s) – n0 )ds (1) Bi where ⌬Ni is the phase difference for ith ray; Bi Ci are points of its input and output in the sample; n(s) is the refractive index of sample along this ray; n0 is the refractive index of the environment medium, which is assumed to be constant; and is the wavelength of a light. The set of these integrals along the parallel rays at a fixed angle is called a two-dimensional parallel projection. The 2D projection is characterized by polar angle and the azimuthally angle which determine the probing vector direction in 3D space. A N A LY S I S • J A N U A R Y 2 0 0 4 Tomogram reconstruction algorithms and projection preprocessing After discretization the tomographic problem is reduced to the system of linear algebraic equations [14]: Ag = f (2) J Here g ⑀ R is a required vector, it represents the difference between the refraction indexes of sample and medium, J is the number of voxels (elementary volumes) where refraction index is reconstructed; f ⑀ RI is a vector of the projection data, I is the number of integrals measured according to (1); and A is a matrix of dimension I x J (projecting matrix). The element of a projecting matrix aij is usually defined as length of crossing ith ray with jth voxel. For solving the system of equations (2) in [15] the combined algebraic algorithm cART with the a-priori information has been used: g (n+1) –1 –1 (n) –1 = ⌽s F ⌽f HG FA g(n) (3) where A is the realization the iteration of ART algorithm, HG(n) is an operator in Fourier space, which changes the 3D Fourier transform according to the central slice theorem [14]; ⌽s and ⌽f are operators for a-priori information in spatial and frequency domain; and F is an operator for 3D Fourier transform. In our case the operator ⌽f has been replaced to 1 (i.e. the a-priori information in frequency domain was not used). In the structure of the operator ⌽ in various combinations could be included: (a) averaging with window 3 x 3 x 3; (b) median filtering with the same window; (c) zeroing outside of two spheres; and (d) procedure of mirror reflection. The first problem of projection preprocessing was the alignment of projection co-ordinates with co-ordinates of the cell. This alignment has been carried out using the relationship between the first geometrical moment of 3D object and the first moments of its 2D pro- TO M O G R A P H I C M I C RO S C O P Y plane Z = 0. After each iteration, negative values of reconstructed function were replaced by zero. The area of reconstructed function was two spheres of radius 0.5. The centers of spheres were located on axis Z, a distance 0.5 from a mirror. Outside these spheres the reconstructed functions were replaced by zero. In Fig 5 a 3D reconstruction of lymphocyte internal structure as some density surfaces is demonstrated. The 3D tomogram resolution was 128 x 128 x 128 voxels. CONCLUSIONS Tomographic microscopy is a new approach to the 3D microscopy of phase or amplitude samples. A spatially incoherent tomographic microscope based on the Linnik phase-shifting interference microscope is proposed. In order to achieve the tomographic mode of the Linnik microscope, oblique illumination of the sample is used. The iterative algorithms for limited-angle tomographic reconstruction were used. 3D images of single human blood cells (lymphocytes) are presented. REFERENCES 1. Komitowski D., Bille J. Reconstructing 3-D light-microscopic images by digital image processing. Appl. Opt. 24, 194-200, 1985. 2. Cogswell C.J. et al. Fluorescence microtomography: multi-angle image acquisition and 3D digital reconstruction. Proc. SPIE 2655, 109-115, 1996. 3. Agard D.A. et al. Fluorescence microscopy in three dimensions. Meth. Cell Biol. 30, 44-48, 1989. 4. Kawata S. et al. Optical microscope tomography. I. Support constraint. JOSA A4, 292-297, 1987. 5. Levin G.G., Vishnyakov G.N., Optical Tomography (in Russian) Moscow, 1989. 6. Tikhonov A.N. et al. Microtomography of stratified mediums in conical beams. DAN 296, 1095-1097, 1987. 7. Noda T. et al. Three-dimensional phase-contrast imaging by a computed-tomography microscope. Appl. Optics. 31, 670-674, 1992. 8. Vishnjakov G.N., Levin G.G. Optical microtomography of phase objects. Opt. Spectrosc. 85, 73-77, 1998. 9. Lauer V. Observation of biological objects using an optical diffraction tomographic microscope. Proc. SPIE 4164, 122-133, 2000. 10. Dlugan A. et al. P. Microscopic optical tomography. 7th Congress of the European Society for Analytical Cellular Pathology, 1-5 April 2001, report Z003. 11. Russian patent No. 2140661. Confocal scanning 3D microscopy and confocal scanning tomographic microscope. Levin G.G. et al. 1999. 12. Vishnyakov G.N., Levin G.G. Optical tomography of living cells using phase-shifting Linnik microscope. Proc. SPIE. 3568, 197-200, 1998. 13. Vishnyakov G.N. et al. Phase tomography of 3D Biological Microobjects: Numerical Simulation and Experimental Results. Opt. Spectrosc. 87, 413-419, 1999. 14. Herman G.T. Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. New-York: Academic Press, 1980. 15. Likhachev A.V., Pickalov V.V. Frequency filtration in algebraic algorithms of a three-dimensional tomography. Optoelectronics, Instrumentation and Data Processing 4, 80-86, 1995. ©2004 Rolston Gordon Communications. Figure 5: 3D reconstructed tomographic images of a human lymphocyte. Figure 4: A set of experimental projections with position of a mirror. jections. The zero 2D moments of all projections should be equal. Therefore it is necessary for the multiplicative calibration of the projections. During the projection preprocessing the elimination of background was also done. R E S U LT S Living lymphocytes were chosen as the phase samples. Cells were placed between a thin cover glass and a flat mirror in a physiological solution with refractive index 1.334. According to the conclusions of work [13] the 'square'scanning trajectory was used for projection acquisition. In this case the geometrical place of points of a probing vector angular coordinates on rectangular plane (, ) coincides with points of a square grid. The angular range of probing for a 100x, 1.25 NA oil immersion objective was 90 degrees. The total number of 2D projections was 43. The projection resolution was 256 x 256 pixels and the real size of the projections was 23 x 23 µm. All projections are shown in Fig 4. For tomogram reconstruction the combined iterative algorithm cART was used. The reconstruction volume was a cube with length of the side equal to 2. All distances are given in dimensionless units. The mirror was placed in MICROSCOPY AND A N A LY S I S • J A N U A R Y 2 0 0 4 17