Coded aperture 3D imaging techniques have been rapidly evolving in the recent years. The two main directions of evolution are in aperture engineering to generate the optimal optical field and in development of computational reconstruction to reconstruct the object’s image from the intensity distribution with a minimal noise. The goal is to find the ideal aperture-reconstruction method pair and if not, to optimize one to match the other for designing an imaging system with required 3D imaging characteristics. Lucy-Richardson-Rosen algorithm (LR²A), a recently developed computational reconstruction method was found to perform better than its predecessors such as matched filter, Weiner filter, phase-only filter, Lucy-Richardson algorithm and non-linear reconstruction (NLR) for certain apertures when the point spread function (PSF) is a real and symmetric function. For other cases of PSF, NLR performed better than the rest of the methods. In this tutorial, LR²A has been presented as a generalized approach for any optical field along with MATLAB codes for reconstruction of any image when the PSF is known. The common problems and pitfalls in using LR²A has been discussed. Simulation and experimental studies for common optical fields such as spherical, Bessel, vortex beams and exotic optical fields such as Airy, scattered and self-rotating beams have been presented. From this study, it can be seen that it is possible to transfer the 3D imaging characteristics from non-imaging type exotic fields to indirect imaging systems faithfully using LR²A. The application of LR²A to medical images such as colonoscopy images and cone beam computed tomography images with synthetic PSF has been demonstrated. We believe that the tutorial will provide a deeper understanding of computational reconstruction using LR²A.

Pattern recognition techniques form the heart of most, if not all, incoherent linear shift-invariant systems. When an object is recorded using a camera, the object information gets sampled by the point spread function (PSF) of the system, replacing every object point with the PSF in the sensor. The PSF is a sharp Kronecker Delta-like function when the numerical aperture (NA) is large with no aberrations. When the NA is small, and the system has aberrations, the PSF appears blurred. In the above case, if the PSF is known, then the object information can be obtained by scanning the PSF over the recorded object intensity pattern and looking for pattern matching conditions through a mathematical process called correlation. In this study, a recently developed deconvolution method, the Lucy-Richardson-Rosen algorithm (LR2A), has been implemented to computationally refocus images recorded in the presence of spatio-spectral aberrations. The performance of LR2A was compared against the Lucy-Richardson algorithm and non-linear reconstruction. LR2A exhibits a superior deconvolution capability even in extreme cases of spatio-spectral aberrations and blur. Experimental results of deblurring a picture captured using high-resolution smartphone cameras are presented. LR2A was implemented to significantly improve the performances of the widely used deep convolutional neural networks for image classification.

Axial resolution is one of the most important characteristics of a microscope. In all microscopes, a high axial resolution is desired in order to discriminate information efficiently along the longitudinal direction. However, when studying thick samples that do not contain laterally overlapping information, a low axial resolution is desirable as information from multiple planes can be recorded simultaneously from a single camera shot instead of plane-by-plane mechanical refocusing. In this study, we increased the focal depth of an infrared microscope non-invasively by introducing a binary axicon fabricated on barium fluoride substrate close to the sample. Preliminary results of imaging thick and sparse silk fibers showed an improved focal depth with a slight decrease in lateral resolution and increase in background noise.