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.

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.

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. One such method 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 a 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 a smaller area. The diffractive sub-apertures were manufactured using photolithography. The fabricated diffractive element was implemented in indirect imaging mode using non-linear reconstruction and the Lucy–Richardson–Rosen algorithm with synthesized point spread functions. The computational optical experiments revealed improved optical and computational imaging resolutions compared to previous studies.

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.

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.

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.

Computational imaging techniques are indirect ones consisting of two steps: optical recording and computational reconstruction. In this study, deterministic optical fields such as Bessel, Airy, Gaussian and Laguerre-Gaussian were studied in this indirect imaging framework.

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.