Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research

Nonlinear edge enhancement imaging based on Laguerre-Gaussian superimposed vortex filters

Nonlinear reconstruction, which is based on the principle of cross correlation, is a commonly employed reconstruction technique in incoherent correlated digital holography systems. However, the modulation of phase masks in these systems is suppressed during the reconstruction process, resulting in an inability to express the characteristics of the phase masks. Consequently, achieving edge enhancement within these systems is constrained. We propose a nonlinear reconstruction method utilizing Laguerre-Gaussian superimposed vortex filters, which modulates the spectrum of the target during the reconstruction process. Experimental results demonstrate that this method performs well in reconstructing image edges for various phase-masked incoherent imaging systems and effectively suppresses noise. Additionally, this method enables directional edge enhancement.

Incoherent nonlinear deconvolution using an iterative algorithm for recovering limited-support images from blurred digital photographs

Recovering original images from blurred images is a challenging task. We propose a new deconvolution method termed incoherent nonlinear deconvolution using an iterative algorithm (INDIA). Two inputs are introduced into the algorithm: one is a random or engineered point spread function of the scattering system, and the other is a blurred or distorted image of some object produced from this system. The two functions are Fourier transformed, and their phase distributions are processed independently of their magnitude. The algorithm yields the image of the original object with reduced blurring effects. The results of the new method are compared to two linear and two nonlinear algorithms under various types of blurs. The root mean square error and structural similarity between the original and recovered images are chosen as the comparison criteria between the five different algorithms. The simulation and experimental results confirm the superior performance of INDIA compared to the other tested deblurring methods.

3D incoherent imaging using an ensemble of sparse self-rotating beams

Interferenceless coded aperture correlation holography (I-COACH) is one of the simplest incoherent holography techniques. In I-COACH, the light from an object is modulated by a coded mask, and the resulting intensity distribution is recorded. The 3D image of the object is reconstructed by processing the object intensity distribution with the pre-recorded 3D point spread intensity distributions. The first version of I-COACH was implemented using a scattering phase mask, which makes its implementation challenging in light-sensitive experiments. The I-COACH technique gradually evolved with the advancement in the engineering of coded phase masks that retain randomness but improve the concentration of light in smaller areas in the image sensor. In this direction, I-COACH was demonstrated using weakly scattered intensity patterns, dot patterns and recently using accelerating Airy patterns, and the case with accelerating Airy patterns exhibited the highest SNR. In this study, we propose and demonstrate I-COACH with an ensemble of self-rotating beams. Unlike accelerating Airy beams, self-rotating beams exhibit a better energy concentration. In the case of self-rotating beams, the uniqueness of the intensity distributions with depth is attributed to the rotation of the intensity pattern as opposed to the shifts of the Airy patterns, making the intensity distribution stable along depths. A significant improvement in SNR was observed in optical experiments.

3D single shot lensless incoherent optical imaging using coded phase aperture system with point response of scattered airy beams

Interferenceless coded aperture correlation holography (I-COACH) techniques have revolutionized the field of incoherent imaging, offering multidimensional imaging capabilities with a high temporal resolution in a simple optical configuration and at a low cost. The I-COACH method uses phase modulators (PMs) between the object and the image sensor, which encode the 3D location information of a point into a unique spatial intensity distribution. The system usually requires a one-time calibration procedure in which the point spread functions (PSFs) at different depths and/or wavelengths are recorded. When an object is recorded under identical conditions as the PSF, the multidimensional image of the object is reconstructed by processing the object intensity with the PSFs. In the previous versions of I-COACH, the PM mapped every object point to a scattered intensity distribution or random dot array pattern. The scattered intensity distribution results in a low SNR compared to a direct imaging system due to optical power dilution. Due to the limited focal depth, the dot pattern reduces the imaging resolution beyond the depth of focus if further multiplexing of phase masks is not performed. In this study, I-COACH has been realized using a PM that maps every object point into a sparse random array of Airy beams. Airy beams during propagation exhibit a relatively high focal depth with sharp intensity maxima that shift laterally following a curved path in 3D space. Therefore, sparse, randomly distributed diverse Airy beams exhibit random shifts with respect to one another during propagation, generating unique intensity distributions at different distances while retaining optical power concentrations in small areas on the detector. The phase-only mask displayed on the modulator was designed by random phase multiplexing of Airy beam generators. The simulation and experimental results obtained for the proposed method are significantly better in SNR than in the previous versions of I-COACH.