Phase tomography with axial structured illumination

Holographic Tomography (HT) or Optical Diffraction Tomography (ODT) provides slice-by-slice information about the refractive index (RI) of three-dimensional (3D) samples and is emerging as an important label-free imaging modality for Life sciences. HT systems go beyond the digital holographic microscopy (DHM) systems that provide a two-dimensional (2D) representation of the total accumulated phase acquired by a plane beam on transmission through a 3D sample. While the early HT systems used a direct reconstruction methodology based on the Fourier diffraction theorem, in recent years, there has been an increasing shift towards using iterative optimization frameworks for solving the 3D RI reconstruction problem. Despite this algorithmic framework shift, the HT system hardware still largely uses the multi-angle illumination geometries that were suitable for reconstructions based on the Fourier diffraction theorem. The present work examines the possibility of HT reconstruction through the use of on-axis structured illumination(s) that nominally illuminates the 3D sample along the axial direction. Through a simulation study, it is shown that a cross-talk free slice-by-slice 3D RI reconstruction of the sample is possible in this case via the use of sparsity penalties if the slice-to-slice distance obeys a design curve based on the notion of effective depth of focus. The simulation results for two-, three- and four-slice 3D objects with laterally overlapping features clearly outline the separate roles played by the slice-to-slice de-correlation of the field propagating through the 3D sample and that of the sparsity penalty used to guide the iterative solution. Our results suggest the possibility of realizing an Axial Structured Illumination Tomography (ASIT) system configuration that avoids the use of hardware-intensive multi-angle illumination geometry.