Tomographic Diffractive Microscopy (TDM) is a technique, which permits to image transparent living specimens
without staining. For weakly diffractive samples, the three-dimensional distribution of the complex Refractive Index (RI)
can be reconstructed from the knowledge of the measured scattered fields sampled under various viewing and
illumination angles, according to the diffraction tomography theorem. TDM is commonly implemented in two ways, by
either rotating the sample illumination keeping the specimen fixed, or by rotating the sample using fixed illumination.
Both methods present limitations. Under the first-order Born approximation, the varying illumination direction method
presents a strong anisotropic resolution along the optical axis due to the so-called "missing cone" of non captured
frequencies. The sample rotation method presents a better isotropic resolution, but with a reduced extension of the
captured frequencies. In view of overcoming the limitations of each method, we have studied various techniques for
expanding the Optical Transfer Function with a tomographic microscope by combining different configurations of the
sample rotation method with the varying illumination direction method, in order to obtain a high and isotropic resolution.
Using simulations, we investigate the performances of the different configurations we propose.
Diffraction microtomography in coherent light is foreseen as a promising technique to image transparent living samples
in three dimensions without staining. Contrary to conventional microscopy with incoherent light, which gives
morphological information only, diffraction microtomography makes it possible to obtain the complex optical refractive
index of the observed sample by mapping a three-dimensional support in the spatial frequency domain. The technique
can be implemented in two configurations, namely, by varying the sample illumination with a fixed sample or by rotating
the sample using a fixed illumination. In the literature, only the former method was described in detail. In this report, we
derive the three-dimensional frequency support that can be mapped by the sample rotation configuration. We found that,
within the first-order Born approximation, the volume of the frequency domain that can be mapped exhibits a missing
part, the shape of which resembles that of an apple core. A brightfield transmission microscope was modified to form a
Mach-Zehnder interferometer that was used to generate phase-shifted holograms recorded in image plane. We report
preliminary experimental results.
We report first results in the comparison between filtered backprojection reconstruction and Fourier diffraction theorem
reconstruction of transparent spherical samples using a diffractive optical microtomography instrument. A brightfield
transmission microscope was modified to form a Mach-Zehnder interferometer that was used to generate phase-shifted
holograms recorded in image plane. Transparent objects mixed with an index matching medium were inserted into a
microcapillary and holograms of these objects were taken under different view angles by rotating the microcapillary.
Precise rotation of the microcapillary was accomplished by clipping the microcapillary in a precisely machined V-groove,
a system that when combined with software correction of the object centre achieved a precision of object
positioning on the order of a micrometer. Tomography of weakly diffracting objects was performed and the observed
objects were reconstructed by two methods namely, the filtered backprojection method and the Fourier diffraction
method. In the filtered backprojection reconstruction, the 3-D distribution of the refractive index was computed from the
tomography of the object phase. In the Fourier diffraction reconstruction, the 3-D distribution of the scattering potential
was computed by 3-D Fourier transform of the mapping of the object spatial frequencies. It was confirmed that the
Fourier diffraction reconstruction based on the first order Born approximation is limited to small phase changes. In
contrast, the backprojection performed well on large phase changes, but dramatically failed to reconstruct diffractive
objects by generating reconstruction line artifacts that spread from the diffractive object to other nearby objects. Weakly
diffractive polymer beads exhibiting small phase changes were correctly reconstructed by both methods, the Fourier
diffraction method giving sharper edges than the filtered backprojection method.
We report first results in the development of a diffractive optical microtomography instrument for imaging
transparent/semi-transparent biological samples without staining and sectioning. A brightfield transmission microscope
was modified to form a Mach-Zehnder interferometer that was used to generate phase-shifted holograms recorded in
image plane. Transparent/semi-transparent objects mixed with an index matching medium were inserted into a
microcapillary and holograms of these objects were taken under different view angles by rotating the microcapillary.
Precise rotation of the microcapillary was accomplished by clipping the microcapillary in a precisely machined V-groove,
a system that when combined with software correction of the object centre achieved a precision of object
positioning on the order of a micrometer. In this study, the observed objects were considered to be weakly diffracting
and reconstructed by projection tomography of the phases of their measured scattered fields. The three-dimensional
distribution of the refractive index was obtained by backprojecting the phases. Refractive index distributions are shown
for a glass bead and a pollen grain. The measured difference between the refractive index of the glass bead and the
microcapillary was within ±0.01. An isotropic spatial-resolution of the instrument in the micrometer range was obtained
with an objective having a numerical aperture of 0.4.
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