The Zernike polynomials are a complete set of continuous functions orthogonal over a unit circle. Since first developed by Zernike in 1934, they have been in widespread use in many fields ranging from optics, vision sciences, to image processing. However, due to the lack of a unified definition, many confusing indices have been used in the past decades and mathematical properties are scattered in the literature. This review provides a comprehensive account of Zernike circle polynomials and their noncircular derivatives, including history, definitions, mathematical properties, roles in wavefront fitting, relationships with optical aberrations, and connections with other polynomials. We also survey state-of-the-art applications of Zernike polynomials in a range of fields, including the diffraction theory of aberrations, optical design, optical testing, ophthalmic optics, adaptive optics, and image analysis. Owing to their elegant and rigorous mathematical properties, the range of scientific and industrial applications of Zernike polynomials is likely to expand. This review is expected to clear up the confusion of different indices, provide a self-contained reference guide for beginners as well as specialists, and facilitate further developments and applications of the Zernike polynomials.

Electronic digital convolutions could extract key features of objects for data processing and information identification in artificial intelligence, but they are time-cost and energy consumption due to the low response of electrons. Although massless photons enable high-speed and low-loss analog convolutions, two existing all-optical approaches including Fourier filtering and Green’s function have either limited functionality or bulky volume, thus restricting their applications in smart systems. Here, we report all-optical convolutional computing with a metasurface-singlet or -doublet imager, considered as the third approach, where its point spread function is modified arbitrarily via a complex-amplitude meta-modulator that enables functionality-unlimited kernels. Beyond one- and two-dimensional spatial differentiation, we demonstrate real-time, parallel, and analog convolutional processing of optical and biological specimens with challenging pepper-salt denoising and edge enhancement, which significantly enrich the toolkit of all-optical computing. Such meta-imager approach bridges multi-functionality and high-integration in all-optical convolutions, meanwhile possessing good architecture compatibility with digital convolutional neural networks.

Photoacoustic computed tomography (PACT) is a novel biomedical imaging modality and has experienced fast developments in the past two decades. Spatial resolution is an important criterion to measure the imaging performance of a PACT system. Here we survey state-of-the-art literature on the spatial resolution of PACT and analyze resolution degradation models from signal generation, propagation, reception, to image reconstruction. Particularly, the impacts of laser pulse duration, acoustic attenuation, acoustic heterogeneity, detector bandwidth, detector aperture, detector view angle, signal sampling, and image reconstruction algorithms are reviewed and discussed. Analytical expressions of point spread functions related to these impacting factors are summarized based on rigorous mathematical formulas. State-of-the-art approaches devoted to enhancing spatial resolution are also reviewed. This work is expected to elucidate the concept of spatial resolution in PACT and inspire novel image quality enhancement techniques.

High-performance imaging is essential for widespread applications of photoacoustic tomography (PAT) in biomedicine. So far, no comprehensive studies are reported on the impact of system factors on imaging performance, in spite of their importance. Based on a prototype PAT scanner, we study eight factors associated with the acoustic reception process in PAT, namely, detector view angle, element number, center frequency, bandwidth, aperture size, focusing, orientation error, and scan step angle error, and investigated how they impact on the image quality. Simulations and experiments are both presented to support the findings in this study. This work is expected to provide a practical guide for advanced PAT scanner design with enhanced imaging performance.

Based on the energy conversion of light into sound, photoacoustic computed tomography (PACT) is an emerging biomedical imaging modality and has unique applications in a range of biomedical fields. In PACT, image formation relies on a process called acoustic inversion from received photoacoustic signals. While most PACT systems perform this inversion with a basic assumption that biological tissues are acoustically homogeneous, the community gradually realizes that the intrinsic acoustic heterogeneity of tissues could pose distortions and artifacts to finally formed images. This paper surveys the most recent research progress on acoustic heterogeneity correction in PACT. Four major strategies are reviewed in detail, including half-time or partial-time reconstruction, autofocus reconstruction by optimizing sound speed maps, joint reconstruction of optical absorption and sound speed maps, and ultrasound computed tomography (USCT) enhanced reconstruction. The correction of acoustic heterogeneity helps improve the imaging performance of PACT.

Photoacoustic (PA) imaging has been widely used in biomedical research and preclinical studies during the past two decades. It has also been explored for nondestructive testing and evaluation (NDT/E) and for industrial applications. This paper describes the basic principles of PA technology for NDT/E and its applications in recent years. PA technology for NDT/E includes the use of a modulated continuous-wave laser and a pulsed laser for PA wave excitation, PA-generated ultrasonic waves, and all-optical PA wave excitation and detection. PA technology for NDT/E has demonstrated broad applications, including the imaging of railway cracks and defects, the imaging of Li metal batteries, the measurements of the porosity and Young’s modulus, the detection of defects and damage in silicon wafers, and a visualization of underdrawings in paintings.