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

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.Comment: 7 pages, 11 figures, presented at Focus On Microscopy 200

Three-dimensional computed tomography from interferometric measurements within a narrow cone of views

A theory to determine the properties of a fluid from measurements of its projections was developed and tested. Viewing cones as small as 10 degrees were evaluated, with the only assumption being that the property was space limited. The results of applying the theory to numerical and actual interferograms of a spherical discontinuity of refractive index are presented. The theory was developed to test the practicality and limits of using three-dimensional computer tomography in internal fluid dynamics