Computational optical sensing and imaging 2021: feature issue introduction.

This Feature Issue includes 2 reviews and 34 research articles that highlight recent works in the field of Computational Optical Sensing and Imaging. Many of the works were presented at the 2021 OSA Topical Meeting on Computational Optical Sensing and Imaging, held virtually from July 19 to July 23, 2021. Articles in the feature issue cover a broad scope of computational imaging topics, such as microscopy, 3D imaging, phase retrieval, non-line-of-sight imaging, imaging through scattering media, ghost imaging, compressed sensing, and applications with new types of sensors. Deep learning approaches for computational imaging and sensing are also a focus of this feature issue.

Computational Optical Sensing and Imaging 2021: introduction to the feature issue.

This feature issue includes two reviews and 34 research papers that highlight recent works in the field of computational optical sensing and imaging. Many of the works were presented at the 2021 Optica (formerly OSA) Topical Meeting on Computational Optical Sensing and Imaging, held virtually from 19 July to 23 July 2021. Papers in the feature issue cover a broad scope of computational imaging topics, such as microscopy, 3D imaging, phase retrieval, non-line-of-sight imaging, imaging through scattering media, ghost imaging, compressed sensing, and applications with new types of sensors. Deep learning approaches for computational imaging and sensing are also a focus of this feature issue.

Efficient computation of 2D point-spread functions for diffractive lenses.

Diffractive lenses, such as Fresnel zone plates, photon sieves, and their modified versions, have been of significant recent interest in high-resolution imaging applications. As the advent of diffractive lens systems with different configurations expands, the fast and accurate simulation of these systems becomes crucial for both the design and image reconstruction tasks. Here we present a fast and accurate method for computing the 2D point-spread function (PSF) of an arbitrary diffractive lens. The method is based on the recently derived closed-form mathematical formula for the PSF and the transfer function of a diffractive lens. In the method, first, the samples of the transfer function are computed using the transmittance function of the diffractive lens, and then the inverse Fourier transform of this transfer function is computed to obtain the PSF. For accurate computation, the selection of the sampling parameters is handled with care, and simple selection rules are provided for this purpose. The developed method requires a single fast Fourier transform, and, therefore, has little computational complexity. Moreover, it is also applicable to any diffractive lens configuration with arbitrary-shaped structures and modulation. As a result, this fast and accurate PSF computation method enables efficient simulation, analysis, and development of diffractive lens systems under both focused and defocused settings.

Compressive spectral imaging with diffractive lenses.

Compressive spectral imaging enables the reconstruction of an entire 3D spectral cube from a few multiplexed images. Here we develop a novel compressive spectral imaging technique using diffractive lenses. Our technique uses a coded aperture to spatially modulate the optical field from the scene and a diffractive lens such as a photon sieve for both dispersion and focusing. Measurement diversity is achieved by changing the focusing behavior of the diffractive lens. The 3D spectral cube is then reconstructed from highly compressed measurements taken with a monochrome detector. A fast sparse recovery method is developed to solve this large-scale inverse problem. The performance is illustrated for various scenarios with different compression ratios through simulations. The results demonstrate that promising reconstruction performance can be achieved at high compression levels. This opens up new possibilities for high-resolution spectral imaging with simpler and low cost designs.

Deep iterative reconstruction for phase retrieval.

The classical phase retrieval problem is the recovery of a constrained image from the magnitude of its Fourier transform. Although there are several well-known phase retrieval algorithms, including the hybrid input-output (HIO) method, the reconstruction performance is generally sensitive to initialization and measurement noise. Recently, deep neural networks (DNNs) have been shown to provide state-of-the-art performance in solving several inverse problems such as denoising, deconvolution, and superresolution. In this work, we develop a phase retrieval algorithm that utilizes two DNNs together with the model-based HIO method. First, a DNN is trained to remove the HIO artifacts, and is used iteratively with the HIO method to improve the reconstructions. After this iterative phase, a second DNN is trained to remove the remaining artifacts. Numerical results demonstrate the effectiveness of our approach, which has little additional computational cost compared to the HIO method. Our approach not only achieves state-of-the-art reconstruction performance but also is more robust to different initialization and noise levels.

Analytical Fresnel imaging models for photon sieves.

Photon sieves are a fairly new class of diffractive lenses that open unprecedented possibilities for high resolution imaging and spectroscopy, especially at short wavelengths such as UV and x-rays. In this paper, we model and analyze the image formation process of photon sieves using Fourier optics. We derive closed-form Fresnel imaging models that relate an input object to the image formed by a photon sieve system, both for coherent and incoherent illumination. These analytical models also provide a closed-form expression for the point-spread function of the system for both in-focus and out-of-focus cases. All the formulas are expressed in terms of Fourier transforms and convolutions, which enable easy interpretation as well as fast computation. The derived analytical models provide a unified framework to effectively develop new imaging modalities enabled by diffractive lenses and analyze their imaging capabilities for different design configurations, prior to physical production. To illustrate their utility and versatility, the derived formulas are applied to several important special cases such as photon sieves with circular holes and pixelated diffractive lenses generated by SLM-type devices. The analytical image formation models presented in this paper provide a generalizable and powerful means for effective analysis and simulation of any imaging system with a diffractive lens, including Fresnel zone plates, Fresnel phase plates, and other modified Fresnel lenses and mask-like patterns such as coded apertures.

A parametric estimation approach to instantaneous spectral imaging.

Spectral imaging, the simultaneous imaging and spectroscopy of a radiating scene, is a fundamental diagnostic technique in the physical sciences with widespread application. Due to the intrinsic limitation of two-dimensional (2D) detectors in capturing inherently three-dimensional (3D) data, spectral imaging techniques conventionally rely on a spatial or spectral scanning process, which renders them unsuitable for dynamic scenes. In this paper, we present a nonscanning (instantaneous) spectral imaging technique that estimates the physical parameters of interest by combining measurements with a parametric model and solving the resultant inverse problem computationally. The associated inverse problem, which can be viewed as a multiframe semiblind deblurring problem (with shift-variant blur), is formulated as a maximum a posteriori (MAP) estimation problem since in many such experiments prior statistical knowledge of the physical parameters can be well estimated. Subsequently, an efficient dynamic programming algorithm is developed to find the global optimum of the nonconvex MAP problem. Finally, the algorithm and the effectiveness of the spectral imaging technique are illustrated for an application in solar spectral imaging. Numerical simulation results indicate that the physical parameters can be estimated with the same order of accuracy as state-of-the-art slit spectroscopy but with the added benefit of an instantaneous, 2D field-of-view. This technique will be particularly useful for studying the spectra of dynamic scenes encountered in space remote sensing.

Phase-space window and degrees of freedom of optical systems with multiple apertures.

We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the space-frequency support of a signal lies completely within this window, the signal passes without information loss. When it does not, the parts that lie within the window pass and the parts that lie outside of the window are blocked, a result that is valid to a good degree of approximation for many systems of practical interest. Also, the maximum number of degrees of freedom that can pass through the system is given by the area of its space-frequency window. These intuitive results provide insight and guidance into the behavior and design of systems involving multiple apertures and can help minimize information loss.

Equivalence of linear canonical transform domains to fractional Fourier domains and the bicanonical width product: a generalization of the space-bandwidth product.

Linear canonical transforms (LCTs) form a three-parameter family of integral transforms with wide application in optics. We show that LCT domains correspond to scaled fractional Fourier domains and thus to scaled oblique axes in the space-frequency plane. This allows LCT domains to be labeled and ordered by the corresponding fractional order parameter and provides insight into the evolution of light through an optical system modeled by LCTs. If a set of signals is highly confined to finite intervals in two arbitrary LCT domains, the space-frequency (phase space) support is a parallelogram. The number of degrees of freedom of this set of signals is given by the area of this parallelogram, which is equal to the bicanonical width product but usually smaller than the conventional space-bandwidth product. The bicanonical width product, which is a generalization of the space-bandwidth product, can provide a tighter measure of the actual number of degrees of freedom, and allows us to represent and process signals with fewer samples.