Coded aperture 3D imaging techniques have been rapidly evolving in recent years. The two main directions of evolution are in aperture engineering to generate the optimal optical field and in the development of a computational reconstruction method to reconstruct the object’s image from the intensity distribution with minimal noise. The goal is to find the ideal aperture–reconstruction method pair, and if not that, to optimize one to match the other for designing an imaging system with the required 3D imaging characteristics. The Lucy–Richardson–Rosen algorithm (LR²A), a recently developed computational reconstruction method, was found to perform better than its predecessors, such as matched filter, inverse 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 when the PSF is known along with MATLAB codes for reconstruction. The common problems and pitfalls in using LR²A have 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 is 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 case of aberrations, if the PSF is known, then the blurred object image can be deblurred by scanning the PSF over the recorded object intensity pattern and looking for pattern matching conditions through a mathematical process called correlation. Deep learning-based image classification for computer vision applications gained attention in recent years. The classification probability is highly dependent on the quality of images as even a minor blur can significantly alter the image classification results. In this study, a recently developed deblurring method, the Lucy-Richardson-Rosen algorithm (LR²A), was implemented to computationally refocus images recorded in the presence of spatio-spectral aberrations. The performance of LR²A was compared against the parent techniques: Lucy-Richardson algorithm and non-linear reconstruction. LR²A exhibited a superior deblurring capability even in extreme cases of spatio-spectral aberrations. Experimental results of deblurring a picture recorded 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 a barium fluoride substrate close to the sample. Preliminary results of imaging the thick and sparse silk fibers showed an improved focal depth with a slight decrease in lateral resolution and an increase in background noise.

Coded aperture imaging (CAI) is a powerful imaging technology that has rapidly developed during the past decade. CAI technology and its integration with incoherent holography have led to the development of several cutting-edge imaging tools, devices, and techniques with widespread interdisciplinary applications, such as in astronomy, biomedical sciences, and computational imaging. In this review, we provide a comprehensive overview of the recently developed CAI techniques in the framework of incoherent digital holography. The review starts with an overview of the milestones in modern CAI technology, such as interferenceless coded aperture correlation holography, followed by a detailed survey of recently developed CAI techniques and system designs in subsequent sections. Each section provides a general description, principles, potential applications, and associated challenges. We believe that this review will act as a reference point for further advancements in CAI technologies.

Coded aperture imaging (CAI) is a well-established computational imaging technique consisting of two steps, namely the optical recording of an object using a coded mask, followed by a computational reconstruction using a computational algorithm using a pre-recorded point spread function (PSF). In this tutorial, we introduce a simple yet elegant technique called spatial ensemble mapping (SEM) for CAI that allows us to tune the axial resolution post-recording from a single camera shot recorded using an image sensor. The theory, simulation studies, and proof-of-concept experimental studies of SEM-CAI are presented. We believe that the developed approach will benefit microscopy, holography, and smartphone imaging systems.

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.