In this study, we investigated, for the first time, the effects of the spatially varying effective mass, asymmetry parameter, and well width on the electronic and optical properties of the quantum well which has an improved Rosen-Morse potential. Calculations are made within the framework of the effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal functions to find eigenvalues and eigenfunctions of the electron confined within the improved Rosen-Morse potential. Our results show that the position-dependence mass, asymmetry, and confinement parameters cause significant changes in the electronic and optical properties of the structure we focus on since these effects create a significant increase in electron energies and a blue shift in the absorption spectrum. The increase in energy levels enables the development of optoelectronic devices that can operate at wider wavelengths and absorb higher energy photons. This offers potential advancements in fields such as optical communication, imaging technology, and solar cells.

The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.

Direct imaging systems that create an image of an object directly on the sensor in a single step are prone to many constraints as a perfect image is required to be recorded within this step. In designing high resolution direct imaging systems with a diffractive lens, the outermost zone width either reaches the lithography limit or the diffraction limit itself imposing challenges in fabrication. However, if the imaging mode is switched to an indirect one consisting of multiple steps to complete imaging, then different possibilities open up. One such methods is the widely used indirect imaging method with Golay configuration telescopes. In this study, a Golay-like configuration has been adapted to realize a large area diffractive lens with three sub-aperture diffractive lenses. The sub-aperture diffractive lenses are not required to collect light and focus them to a single point as in a direct imaging system but to focus independently on different points within the sensor area. This approach of Large Area Diffractive lens with Integrated Sub-Apertures (LADISA) relaxes the fabrication constraints and allows the sub-aperture diffractive elements to have a larger outermost zone width and smaller area. The diffractive sub-apertures were manufactured using photolithography. The fabricated diffractive element has been implemented in indirect imaging mode using non-linear reconstruction and Lucy-Richardson-Rosen algorithm with synthesized point spread functions. The computational optical experiments revealed an improved optical and computational imaging resolutions compared to previous studies.

The Einstein’s Boxes paradox was developed by Einstein, de Broglie, Heisenberg, and others to demonstrate the incompleteness of the Copenhagen Formulation of quantum mechanics. I explain the paradox using the Copenhagen Formulation. I then show how a Time-Symmetric Formulation of quantum mechanics resolves the paradox in the way envisioned by Einstein and de Broglie. Finally, I describe an experiment that can distinguish between these two formulations.

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.

A refractive lens is one of the simplest, cost-effective and easily available imaging elements. With 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 be only obtained by changing either the location of the lens 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 technique consists of three steps. In this first step, the 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 in the final step. The results of LRRA were compared against two well-known reconstruction methods namely Lucy-Richardson algorithm and non-linear reconstruction.

If we assume that: a. The four fundamental forces of nature are independent waves without rest masses, and their speeds are constant in a vacuum, just like light. b. Light or electromagnetic waves and gravity are comparable in structures. Weak and strong interactions are similar in structures. c. Light and weak interaction have the same speed c_L with spin number +1 or –1. d. Gravity and strong interaction have the same speed c_G without spin. e. The primary particles, namely electrons, electron neutrinos, and dark neutrinos in this paper, are made by the above four waves. We can find and describe some fundamental characteristics of the primary particles (e.g., their sizes, energies, and interactions) and introduce new attractive results from them (e.g., the source of the Pauli exclusion principle, the solution to the Einstein-Podolsky-Rosen paradox, and c_G slightly faster than c_L).