A refractive lens is one of the simplest, most cost-effective and easily available imaging elements. Given a spatially incoherent illumination, a refractive lens can faithfully map every object point to an image point in the sensor plane, when the object and image distances satisfy the imaging conditions. However, static imaging is limited to the depth of focus, beyond which the point-to-point mapping can only be obtained by changing either the location of the lens, object or the imaging sensor. In this study, the depth of focus of a refractive lens in static mode has been expanded using a recently developed computational reconstruction method, Lucy-Richardson-Rosen algorithm (LRRA). The imaging process consists of three steps. In the first step, point spread functions (PSFs) were recorded along different depths and stored in the computer as PSF library. In the next step, the object intensity distribution was recorded. The LRRA was then applied to deconvolve the object information from the recorded intensity distributions during the final step. The results of LRRA were compared with two well-known reconstruction methods, namely the Lucy-Richardson algorithm and non-linear reconstruction.

We present the autofocusing and self-healing properties of aberration laser beams (ALBs) in a turbulent media. The ALB is generated by a diffractive optical element (DOE) whose phase profile consists of radial and periodic angular dependence, and then propagated through a turbulent media under weak, moderate, and strong turbulence conditions. The theoretical calculations, numerical simulations, and experimental results are presented. The results show that the presence of turbulence leads to distortion in the spatial structure of ALBs, as well as causes beam wandering. However, the autofocusing properties of ALBs remain invariant. Further, ALBs also possess self-healing abilities in free space as well as in a turbulent media. The self-healing sustains reasonably well even when a large portion of ALB (approximately $60\mathrm{\%}$) is truncated. The distance requires for the self-healing of truncated ALBs remains the same for various percentage of truncation. Particularly, for any amount of truncation up to approximately $60\mathrm{\%}$, ALB self-heals by propagating up to autofocusing distance corresponding to a nontruncated beam.

Indirect-imaging methods involve at least two steps, namely optical recording and computational reconstruction. The optical-recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object’s image corresponding to different spatial and spectral dimensions. There have been numerous optical-modulation functions and reconstruction methods developed in the past few years for different applications. In most cases, a compatible pair of the optical-modulation function and reconstruction method gives optimal performance. A new reconstruction method, termed nonlinear reconstruction (NLR), was developed in 2017 to reconstruct the object image in the case of optical-scattering modulators. Over the years, it has been revealed that the NLR can reconstruct an object’s image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR isinvestigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

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.