Diffraction microtomography with sample rotation: primary result on the influence of a missing apple core in the recorded frequency space

Abstract

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.

Problems and Solutions in 3-D Analysis of Phase Biological Objects by Optical Diffraction Tomography

“…Because the Radon domain is associated with the Fourier domain both in an x-ray tomography [34] and diffraction tomography, [11] that lack of data is also present in the spectrum of the reconstruction. [35] These constraints impose the necessity to implement different algorithms than FBPJ or FBPP. Iterative methods, like iterative constraint algorithm [36] or Simultaneous Algebraic Reconstruction Technique (SART), [37] may be applied to improve quality of the reconstruction.…”

Tomographic diffractive microscopy: basics, techniques and perspectives

“…Figure 8 describes the object frequency support in the case of transmission TDM with a complete specimen rotation about the x-axis and a plane wave illumination along the z-axis [40][41][42].…”

Improved and isotropic resolution in tomographic diffractive microscopy combining sample and illumination rotation

“…The resulting optical transfer function is depicted on Fig. 3, and takes the shape of a "ball", but because of the curvature of the successive caps of sphere, a small subset of uncaptured frequencies does remain along the rotation axis (here the -axis), which takes a characteristic shape of an apple-core [18,19]. The resolution is therefore almost isotropic, but is lower than in the previous configuration for two reasons.…”

“…However, for transmission or reflection tomographic set-ups with fixed specimen, it is always anisotropic. With a rotating specimen, the resolution is almost isotropic [18,19], but is lower than what is achievable with tomographic diffractive microscopy with illumination rotation.…”