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

TL;DR

This paper analyzes diffraction microtomography with sample rotation, revealing a missing apple core-shaped region in the frequency space that affects 3D imaging quality, and provides simulations of its impact on reconstructions.

Contribution

It derives the 3D frequency support for sample rotation configuration and identifies a missing apple core-shaped region in the frequency domain.

Findings

The frequency support exhibits a missing apple core-shaped region.

The finite radius of sphere caps limits frequency mapping along the rotation axis.

Simulations show the impact of missing frequency information on object reconstruction.

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 precisely 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. The projection of the diffracted waves in the frequency space onto the set of sphere caps covered by the sample rotation does not allow for a complete mapping of the frequency along the axis of rotation due to the finite radius of the sphere caps. We present simulations of the effects of this missing information on the reconstruction of ideal objects.