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.

In recent years, there has been a significant transformation in the field of incoherent imaging with new possibilities of compressing three-dimensional (3D) information into a two-dimensional intensity distribution without two-beam interference (TBI). Most incoherent 3D imagers without TBI are based on scattering by a random phase mask exhibiting sharp autocorrelation and low cross-correlation along the depth axis. Consequently, during reconstruction, high lateral and axial resolutions are obtained. Scattering based-Imaging requires a wasteful photon budget and is therefore precluded in many power-sensitive applications. This study develops a proof-of-concept 3D incoherent imaging method using a rotating point spread function termed 3D Incoherent Imaging with Spiral Beams (3DI2SB). The rotation speed of the point spread function (PSF) with displacement and the orbital angular momentum has been theoretically analyzed. The imaging characteristics of 3DI2SB were compared with a direct imaging system using a diffractive lens, and the proposed system exhibited a higher focal depth than the direct imaging system. Different computational reconstruction methods such as the Lucy–Richardson algorithm (LRA), non-linear reconstruction (NLR), and the Lucy–Richardson–Rosen algorithm (LRRA) were compared. While LRRA performed better than both LRA and NLR for an ideal case, NLR performed better than both under real experimental conditions. Both single plane imaging, as well as synthetic 3D imaging, were demonstrated. We believe that the proposed approach might cause a paradigm shift in the current state-of-the-art incoherent imaging, fluorescence microscopy, and astronomical imaging.

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.

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