A denoising framework for 3D and 2D imaging techniques based on photon detection statistics.

A method to capture three-dimensional (3D) objects image data under extremely low light level conditions, also known as Photon Counting Imaging (PCI), was reported. It is demonstrated that by combining a PCI system with computational integral imaging algorithms, a 3D scene reconstruction and recognition is possible. The resulting reconstructed 3D images often look degraded (due to the limited number of photons detected in a scene) and they, therefore, require the application of superior image restoration techniques to improve object recognition. Recently, Deep Learning (DL) frameworks have been shown to perform well when used for denoising processes. In this paper, for the first time, a fully unsupervised network (i.e., U-Net) is proposed to denoise the photon counted 3D sectional images. In conjunction with classical U-Net architecture, a skip block is used to extract meaningful patterns from the photons counted 3D images. The encoder and decoder blocks in the U-Net are connected with skip blocks in a symmetric manner. It is demonstrated that the proposed DL network performs better, in terms of peak signal-to-noise ratio, in comparison with the classical TV denoising algorithm.

Optical Trajectory Manipulations Using the Self-Written Waveguide Technique.

This study is novel for several reasons: We used a thin drop cast layer of dry photosensitive materials to study the behaviors of wet photopolymer media using microscopic distances during the Self-Written Waveguide (SWW) process; then, we examined the self-trajectories formed inside the solid material. The results provide a framework for theoretical and experimental examinations by handling the effects of manipulating the alignment of fibers. The other main advantage of these techniques is their lightweight, easy to process, highly flexible, and ultimately low-cost nature. First, the SWW process in wet photopolymer media (liquid solutions) was examined under three cases: single-, counter-, and co-fiber exposure. Then, the SWWs formed inside the solid material were examined along with the effects of manipulating the alignment of the fibers. In all cases, high precision measurements were used to position the fiber optic cables (FOCs) before exposure using a microscope. The self-writing process was indirectly monitored by observing (imaging) the light emerging from the side of the material sample during SWW formation. In this way, we examined the optical waveguide trajectories formed in Acrylamide/Polyvinyl Alcohol (AA/PVA), a photopolymer material (sensitized at 532 nm). First, the transmission of light by this material is characterized. Then, the bending and merging of the waveguides that occur are investigated. The predictions of our model are shown to qualitatively agree with the observed trajectories. The largest index changes taking place at any time during exposure, i.e., during SWW formation, are shown to take place at the positions where the largest exposure light intensity is present. Typically, such maxima exist close to the input face. The first maximum is referred to as the location of the Primary Eye. Other local maxima also appear further along the SWW and are referred to as Secondary Eyes, i.e., eyes deeper within the material.

Orthographic projection images-based photon-counted integral Fourier holography.

Unlike coherent imaging techniques, light field imaging uses incoherent (white light) illumination to generate a digital hologram of three-dimensional (3D) objects in real time. Multiple projections (or elemental images) of a 3D object are captured using a microlens array attached to a digital camera. Orthographic projection images (OPIs) can be synthesized from the recorded elemental images. The synthesized intensity-based OPIs are then multiplied by the corresponding phase functions and combined to form a digital hologram (also known as an integral hologram) of a 3D object under illumination. In this study, we analyze the performance of a synthesized integral hologram under low light imaging (photon-counting) conditions. The feasibility of this technique is verified experimentally by capturing the elemental images and subsequently generating orthographic projection images and by varying photon counts to reconstruct the digital holograms.

Improving the uniformity of holographic recording using multilayer photopolymer. Part I. Theoretical analysis.

An experimental and theoretical investigation of the preparation and exposure of multilayer photosensitive materials is presented. It is shown how the recorded change in the refractive index in each layer depends on the dye (photosensitizer) concentrations in each layer. It is also shown how the photosensitive material properties in each layer can be controlled to optimize some recording characteristics for particular applications. To do so, a set of equations, predicting the amplitude of higher harmonics refractive index amplitudes induced in the material layers with depth during exposure, is derived. This results in a technique for varying the dye concentration in each layer of a multilayer, so as to optimize volume diffraction grating performance. In part I of this paper, the 3D nonlocal photopolymerization-driven diffusion (NPDD) model is applied to calculate the resulting combined multilayer absorption and polymerization processes. The NPDD describes the time-varying behaviors taking place during exposure in such photopolymer materials. Simulations are performed for an acrylamide/polyvinyl alcohol-based photopolymer containing erythrosine-B dye. It is predicted that, in general, non-uniform gratings are formed, with the resulting refractive index being distorted both from the ideal sinusoidal cross-sectional spatial distribution and also with depth. This agrees with previous results indicating that increasing the thickness of a single photopolymer layer does not in practice lead to ever-increasing angular selectivity. In part II of this paper, it is confirmed experimentally that a suitably modified multilayer can be used to increase grating angular selectivity, i.e., reduce the width of the off-Bragg replay curve.

Improving the uniformity of holographic recording using multi-layer photopolymer: Part II. Experimental results.

In the first part of this study, a 3D nonlocal photopolymerization driven diffusion model was developed and applied to simulate the absorption and polymerization taking place during holographic exposures of a multi-layer. The Beer-Lambert law was used to choose appropriate dye concentrations for each layer, with the objective of improving the resulting volume grating uniformity and thus diffraction characteristics. The predictions made, using previously estimated physical parameter values, indicated that improvements in the uniformity of the recorded modulation were possible. In this paper the results of experiments carried out to explore the validity of these predictions are presented. Improvements in material response are demonstrated experimentally, with improved grating diffraction (narrower angular selectivity) being observed for appropriately sensitized multi-layers.

Self-written waveguides in photopolymer.

Self-written waveguide (SWW) trajectories fabricated inside a dry photopolymer bulk material, acrylamide/polyvinyl alcohol (AA/PVA), are studied. Their production using both Gaussian and Laguerre-Gauss exposing (writing) light beams, output from optical fibers, is explored. The formation of the primary and secondary eyes is also discussed. Furthermore, the interactions that take place when two counterpropagating beams pass through the photopolymer material (both Gaussian and Laguerre-Gauss) are examined. In all cases experimental and theoretical results are presented. Good agreement between the predictions of the proposed model and experimental observations are demonstrated.

Low photon count based digital holography for quadratic phase cryptography.

Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

Volumetric Light-field Encryption at the Microscopic Scale.

We report a light-field based method that allows the optical encryption of three-dimensional (3D) volumetric information at the microscopic scale in a single 2D light-field image. The system consists of a microlens array and an array of random phase/amplitude masks. The method utilizes a wave optics model to account for the dominant diffraction effect at this new scale, and the system point-spread function (PSF) serves as the key for encryption and decryption. We successfully developed and demonstrated a deconvolution algorithm to retrieve both spatially multiplexed discrete data and continuous volumetric data from 2D light-field images. Showing that the method is practical for data transmission and storage, we obtained a faithful reconstruction of the 3D volumetric information from a digital copy of the encrypted light-field image. The method represents a new level of optical encryption, paving the way for broad industrial and biomedical applications in processing and securing 3D data at the microscopic scale.

Phase-retrieval-based attacks on linear-canonical-transform-based DRPE systems.

The hybrid input-output algorithm, error reduction algorithm, and combinations of both phase retrieval algorithms are applied to perform ciphertext-only attacks on linear canonical transform (LCT)-based amplitude encoding double-random-phase encryption (DRPE) systems. Special cases of LCT-based DRPE systems, i.e., Fourier-transform-based, fractional-Fourier-transform-based, and Fresnel-transform-based DRPE, can also be successfully attacked using the method proposed. Numerical simulations are performed to demonstrate the efficacy of the proposed attacking method.

Interferometry based multispectral photon-limited 2D and 3D integral image encryption employing the Hartley transform.

We present a method of securing multispectral 3D photon-counted integral imaging (PCII) using classical Hartley Transform (HT) based encryption by employing optical interferometry. This method has the simultaneous advantages of minimizing complexity by eliminating the need for holography recording and addresses the phase sensitivity problem encountered when using digital cameras. These together with single-channel multispectral 3D data compactness, the inherent properties of the classical photon counting detection model, i.e. sparse sensing and the capability for nonlinear transformation, permits better authentication of the retrieved 3D scene at various depth cues. Furthermore, the proposed technique works for both spatially and temporally incoherent illumination. To validate the proposed technique simulations were carried out for both the 2D and 3D cases. Experimental data is processed and the results support the feasibility of the encryption method.

Encryption and volumetric 3D object reconstruction using multispectral computational integral imaging.

This paper presents a new method for three-dimensional (3D) scene acquisition via reconstruction with multispectral information and its Fourier-based encryption using computational integral imaging, by which the field of view, resolution, and information security are increased, respectively. The color imaging sensors covered with a Bayer color filter array captures elemental images (EI) at different spectral bands (400 and 700 nm intervals in the visible spectrum). Subsequently, double random phase encryption (DRPE) in the Fourier domain is employed on Bayer formatted EI to encrypt the captured 3D scene. Proper 3D object reconstruction only can be achieved by applying inverse decryption and a geometric ray backpropagation algorithm on the encrypted EI. Further, the high-resolution multispectral 3D scene can be visualized by using various adaptive interpolation algorithms. To objectively evaluate our proposed method, we carried out computational experiments for 3D object sensing, reconstruction, and digital simulations for DRPE. Experiment results validate the feasibility and robustness of our proposed approach, even under severe degradation.