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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.
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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-
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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.
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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
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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
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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
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11. Russian patent No. 2140661. Confocal scanning
3D microscopy and confocal scanning tomographic
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12. Vishnyakov G.N., Levin G.G. Optical tomography of living
cells using phase-shifting Linnik microscope. Proc. SPIE.
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Microobjects: Numerical Simulation and Experimental
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14. Herman G.T. Image Reconstruction from Projections: The
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©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
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