Tomographic observation of transparent objects under coherent illumination and reconstruction by filtered backprojection and Fourier diffraction theorem

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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.