Modeling microsphere axial displacement in optical projection tomographic microscopy to analyze effects on filtered backprojection reconstruction

A computationally efficient method of simulating illumination in Optical Projection Tomographic Microscopy (OPTM) is presented to analyze the effect of microsphere axial displacement on image reconstruction using the filtered backprojection. OPTM reconstructs three-dimensional images of single cells from two-dimensional projection images in a fashion similar to Computed Tomography (CT). Projection images are acquired from circumferential positions around the cell by scanning the objective focal plane through the cell, while the condenser focal plane remains stationary. Unlike CT, the cell rotates between the source and detector in a microcapillary where it is not necessarily positioned at the optical axis. As the cell rotates, its axial position changes relative to the condenser focal plane for every projection. These differences in illumination have an impact on the overall reconstruction that cannot be understood experimentally. The computational model presented in this work relies on an alternative method of calculating illumination using a matrix formalism with near-field Mie theory. This method provides the ability to calculate the response of a microsphere illuminated with plane waves propagating from different directions. The response from each plane wave is subsequently summed to determine the total response. The power of this method is provided by the ability to arbitrarily choose the microsphere position after calculating the plane wave response, meaning illumination for all axial displacements can be computed in approximately the same time as a single position. Projection images are computed for microspheres at intervals away from the optical axis to understand how the axial displacement degrades the reconstructed image.