Reconstruction of a stable and good quality solution from noisy single-shot Fourier intensity data is a challenging problem for phase retrieval algorithms. We examine behavior of the solution provided by the hybrid input–output (HIO) algorithm for noisy data, from the perspective of the complexity guidance methodology that was introduced by us in an earlier paper [J. Opt. Soc. Am. A 36, 202 (2019)

A refined model of an extreme ultraviolet (EUV) mask stack consisting of the Mo/Si multilayer coated by a Ru protective layer and a TaBN/TaBO absorber layer was developed to facilitate accurate simulations of EUV mask performance for high-NA EUV photo-lithography (EUVL) imaging. The model is derived by combined analysis of the measured EUV and x ray reflectivity of an industry-representative mask blank

In this paper, we concentrate on dense estimation of disparities between fish-eye images without corrections. Because of the distortions, fish-eye images cannot be processed directly utilizing the classical adaptive support weight (ASW) method for perspective images. To address this problem, we propose a modified hemispherical ASW method in a hemispherical framework. First, 3D epipolar curves are calculated

In this work, the theoretical study of the interaction of terahertz (THz) waves with graphene embedded into two different semi-infinite metamaterials was carried out. To model the graphene, the effective surface conductivity approach based on the Kubo formalism was used. In addition, two types of metamaterials, i.e., double-positive (DPS) and double-negative (DNG), were studied in the THz regime. The

The aim of this paper is to describe and demonstrate what should be done to the measured Zernike coefficients when conjugating the pupil and wavefront sensor planes with a ${4}f$ system. I provide theoretical and experimental evidence. The experimental setup consisted of two ${4}f$ systems of magnifications 1 and 1/3 with their corresponding wavefront sensors at their ends. Spherical and cylindrical

Based on the polarization property of fluorescent dipoles, fluorescence super-resolution microscopy recently has been proposed by modulating the polarization of the excitation light. In this technique, the super-resolution image is reconstructed by processing the polarization-modulated fluorescence image stack with an iteration algorithm. However, the mechanism of resolution improvement by polarization

This paper addresses a number of approximate, analytically invertible solutions of the scalar Helmholtz equation. Primary attention is devoted to the Glauber approximation (GA) derived for the far-field pattern. It is shown that the GA has the form of a nonlinear Radon-to-Helmholtz (RtH) mapping, which transforms a sinogram of the scattering potential into an approximate solution of the Helmholtz equation

A systematic and formal study of the global and elemental properties of the propagating-order scattering matrix of conically mounted and crossed gratings is presented. The most general formulation of the scattering matrix is established. Expressions of the global properties (reciprocity and unitarity) of the scattering matrix ($S$ matrix) in the general form previously not available in the literature

Given an arbitrary input wavefront, we derive the analytical refractive surface that refracts the wavefront into a single image point. The derivation of the surface is fully analytical without paraxial or numerical approximations. We evaluate the performance of the surface with several cases, and the results were as expected.

From a geometric perspective, the caustic is the most classical description of a wave function since its evolution is governed by the Hamilton–Jacobi equation. On the other hand, according to the Madelung–de Broglie–Bohm equations, the most classical description of a solution to the Schrödinger equation is given by the zeros of the Madelung–Bohm potential. In this work, we compare these descriptions

The present paper describes a novel implementation of the continuous phase shifting method (PSM), named heterodyne holography, in a scanning probe microscope configuration, able to retrieve the complex scattered field in on-axis configuration. This can be achieved by acquiring a continuous sequence of holograms at different wavelengths in just a single scan through the combination of scanning interference

A theoretical analysis of properties of an objective composed of three thin lenses is described in this paper. The formulas for the calculation of parameters of the three-lens objective are derived and the procedure for calculation of the shape of individual lenses of the objective is described using the third-order aberration theory. The application of the described analysis is presented in an example

An upper bound is derived for a figure of merit that quantifies the error in reconstructed pixel or voxel values induced by the presence of null functions for any list-mode system. It is shown that this upper bound decreases as the region in attribute space occupied by the allowable attribute vectors expands. This upper bound allows quantification of the reduction in this error when this type of expansion

In dual-wavelength interferometry, the key issue is how to efficiently retrieve the phases at each wavelength using the minimum number of wavelength-multiplexed interferograms. To address this problem, a new dual-wavelength interferogram decoupling method with the help of deep learning is proposed in this study. This method requires only three randomly phase-shifted dual-wavelength interferograms.

At present, the application of machine vision methods for roughness measurement in production sites is limited by its adaptability to illumination variations during the measurement. In this study, a machine vision method for roughness measurement with robustness to illumination is proposed so as to explore the functions of its color image indices in improving the mathematical expression of the vector

An iterative wavefront reconstruction method using Shack–Hartmann wavefront sensor (SHWFS) measurements is presented in this paper. A new cost function for the wavefront reconstruction problem is derived and the solution is obtained iteratively using the gradient descent method. The proposed method aims to effectively handle the scintillated SHWFS measurements and to provide simpler and accurate ways

Many LED lighting applications involve the design of multiple optical surfaces. A prime example is a single lens with two refractive surfaces. In this paper, we consider an LED light source approximated as a point and a far-field target intensity. Using Hamilton’s characteristic functions, the design problem is converted into two generalized Monge–Ampère equations by deriving a generating function

An improved algorithm for numerical evaluation of the Hankel transform is developed. The algorithm originally proposed by Yu et al. [Opt. Lett. 23, 409 (1998) [CrossRef] ] uses the quadrature in which the nodes are zeros of the Bessel function. In this work, it is shown that the accuracy of the algorithm can be significantly improved, with virtually no increase in computation time, via two steps. One

Light beams with multiple phase singularities, namely, optical vortex arrays (OVAs), can be generated via coherent superpositions of symmetric laser modes, e.g., the combination of a circular vortex beam and a Gaussian beam. Further, a non-trivial evolution of the singularity structure can be obtained when the system’s symmetry is broken. In this paper, we propose an asymmetric OVA (AOVA) with a highly

A hybrid optoelectronic bistability is realized with the assistance of an ultrahigh-order mode (UHM) excited in a symmetrical metal-cladding waveguide (SMCW). PMN-PT ceramics is selected as the guiding layer, which possesses the voltage modulated refractive index and thickness by means of an electro-optical effect and converse-piezoelectric effect. An amplified voltage signal translated from the intensity

In this paper, a tunable plasmon-induced transparency (PIT) structure based on a monolayer black phosphorus metamaterial is designed. In the structure, destructive interference between the bright and dark modes produces a significant PIT in the midinfrared band. Numerical simulation and theoretical calculation methods are utilized to analyze the tunable PIT effect of black phosphorus (BP). Finite-

A structured optical field with controllable three-dimensional intensity and multiple polarization singularities is demonstrated by utilizing a combination of a radially polarized (RP) beam, a designed phase mask, and a high numerical aperture lens. Owing to the tight focusing property of RP beams as well as the interference of multiple linearly polarized non-coplanar plane waves, various lattice-like

Based on the interferometric particle imaging (IPI) technology, we present a method for comparison of aspect ratios of ellipsoidal particles. By simulating the interference in-focus and out-of-focus images of transparent ellipsoidal particles with different aspect ratios, we find that, under the same orientation angle, the larger the particle aspect ratio is, the higher the spatial frequency of the

In this paper, some explicit analytical solutions for single-scattered radiance in a half-space medium under consideration of a reflecting boundary are derived. We consider both a unidirectional beam source as well as an isotropic point source. In addition to direct applications within optical tomography and computer graphics, the obtained solutions are also needed when solving the radiative transport

We validate a physically based and spectral rendering framework with improved color reproduction. With a recently developed model, we take into account both the colorimetric specifications of the rendering display as well as the spectral and angular characteristics of lighting and also the spectral reflectance of the objects. Therefore, it should provide much better color reproduction than those based

Higher-order spatial correlations contribute strongly to visual structure and salience, and are common in the natural environment. One method for studying this structure has been through the use of highly controlled texture patterns whose obvious structure is defined entirely by third- and higher-order correlations. Here we examine the effects that longer-term training has on discrimination of 17 such

Editor-in-Chief P. Scott Carney introduces the Journal’s newest Topical Editor, Angela Dudley.

This feature issue of JOSA A and Applied Optics is dedicated to the fourteenth OSA Topical Meeting “Digital Holography and 3D Imaging” held 22–26 June 2020 in a virtual meeting. The conference, taking place every year, is a focal point for global technical interchange in the field of digital holography and 3D imaging, providing premier opportunities for people working in the field to present their

Surface topography measuring interference microscopy is a three-dimensional (3D) imaging technique that provides quantitative analysis of industrial and biomedical specimens. Many different instrument modalities and configurations exist, but they all share the same theoretical foundation. In this paper, we discuss a unified theoretical framework for 3D image (interferogram) formation in interference

In this paper, a compact waveguide eyeglass integrating freeform surfaces and volume holographic gratings (VHGs) is proposed for full-color display with high energy utilization. The in-coupler with four freeform surfaces collimates the light emitting from the micro image source (MIS) and couples them into the waveguide. The six-layer VHGs as an outcoupler are designed to modulate the light propagating

The self-focusing effect on the beam quality of Hermite–Gaussian beams propagating upwards through the inhomogeneous atmosphere is studied. The analytical formula of the beam width is derived, and its validity is confirmed. Furthermore, the analytical formulas of the actual focal length and ${M^2}$-factor are also derived. It is found that the self-focusing effect in the inhomogeneous atmosphere results

To compare neuroimaging data between subjects, images from individual sessions need to be aligned to a common reference or “atlas.” Atlas registration of optical intrinsic signal imaging of mice, for example, is commonly performed using affine transforms with parameters determined by manual selection of canonical skull landmarks. Errors introduced by such procedures have not previously been investigated

We investigate the use of plenoptic data for locating non-line-of-sight (NLOS) objects from a scattered light signature. Using Fourier analysis, the resolution limits of the depth and transversal location estimates are derived from fundamental considerations on scattering physics and measurement noise. Based on the refocusing algorithm developed in the computer vision field, we derive an alternative

The modified rigorous coupled-wave analysis technique is developed to describe the optical characteristics of the plasmonic structures with the grating-gated delta-thin conductive channel in the far- and near-field zones of electromagnetic waves. The technique was applied for analysis of the resonant properties of AlGaN/GaN heterostructures combined with a deeply subwavelength metallic grating, which

Fluorescent molecular tomography (FMT) is an important molecular imaging technique for medical diagnosis and treatment. In FMT, a typical forward model is the diffusion approximation. However, this approximation is not valid in biological tissues with low-scattering regions. To overcome this problem, a Bayesian method in combination with the model error is proposed. Further, an iteration method of

The poor visibility of underwater images is caused not only by scattering and absorption effects but is also related to light conditions. To improve robustness, a novel underwater image enhancement method based on natural light and reflectivity is proposed. Aiming at the scattering effects of reflectivity, a dehazing process based on the non-correlation of a foreground scene and background light is

We developed a general theory about the performance of a rotational shearing interferometer. We apply the aberration theory to the detection of planets outside our planet system. We considered cases when the mutual coherence functions of the on-axis and the off-axis system are 0 and 1.

Precisely measuring the three-dimensional position and orientation of individual fluorophores is challenging due to the substantial photon shot noise in single-molecule experiments. Facing this limited photon budget, numerous techniques have been developed to encode 2D and 3D position and 2D and 3D orientation information into fluorescence images. In this work, we adapt classical and quantum estimation

Various techniques have been developed to measure the 2D and 3D positions and 2D and 3D orientations of fluorescent molecules with improved precision over standard epifluorescence microscopes. Due to the challenging signal-to-background ratio in typical single-molecule experiments, it is essential to choose an imaging system optimized for the specific target sample. In this work, we compare the performance

Interaction of light and matter can be controlled and manipulated by exploiting the properties of the isofrequency contours (IFCs) of a material. IFC in metamaterial/artificial anisotropic materials can be open and/or closed. The class of metamaterials with open IFC are known as hyperbolic metamaterials (HMMs)/indefinite media. HMMs support large wavevectors, which can lead to some important consequences

A tunable dual-ring microstructure fiber that can support stable transmission for different orbital angular momentum (OAM) states and possess ultrahigh dispersion coefficients and low confinement losses is proposed and theoretically investigated. The proposed fiber is composed of two high-refractive-index rings and a double-cladding structure. Owing to the central air core and outer cladding, the dual-ring

We establish the concept of cross-spectral purity for nonstationary electromagnetic fields having any degree of coherence or polarization. The conditions of cross-spectral purity in all Stokes parameters are derived for both space–time and space–frequency domains, which demonstrate that the normalized two-point coherence properties of such fields can be expressed as products of a spatial and a time

A three-dimensional printed beam-steering reflector surface with dielectric fluids as the tuning agent is presented. The reflector is made using ECO-ABS with six rows of 19 parallel channels of square cross-sections. The permittivity of the ECO-ABS was measured at 2.55 with a loss tangent of 0.053. A conductor is placed at the back of the dielectric. The squared channels are filled with either distilled

We study the scattering of a linearly polarized electromagnetic plane wave by a two-dimensional random slightly rough surface separating the vacuum from a chiral medium. We implement the first-order small perturbation method (SPM) and the first-order small slope approximation (SSA) and determine the analytical expressions of the coherent and incoherent intensities. The effects of chirality on the polarization

When two visual patterns moving in opposite directions are superimposed on the same depth plane, they appear to have two transparent surfaces moving independently (transparent motion). Additionally, the direction of the slow phase of optokinetic nystagmus (OKN) corresponds to the direction of motion that dominates the perceptual appearance. This study examines whether pupil changes correspond to the

While much attention has been given to understanding biases in gloss perception (e.g., changes in perceived reflectance as a function of lighting, shape, viewpoint, and other factors), here we investigated sensitivity to changes in surface reflectance. We tested how visual sensitivity to differences in specular reflectance varies as a function of the magnitude of specular reflectance. Stimuli consisted

This paper presents a computationally efficient framework in which a single focal-plane image is used to obtain a high-resolution reconstruction of dynamic aberrations. Assuming small-phase aberrations, a non-linear Kalman filter implementation is developed whose computational complexity scales close to linearly with the number of pixels of the focal-plane camera. The performance of the method is tested

We employ non-diffractive Bessel–Gaussian beams to investigate the effect of oceanic turbulence on quantum communication protocols via behaviors of quantum-channel capacity and trace distance, based on the analytical expression of the phase structure function of an orbital-angular-momentum (OAM) beam in underwater wireless optical communication. Our results show that turbulence conditions with a larger

Laser beams can carry multi-scale properties in space and time that ultimately impact their quality. The study of their evolution along complex optical sequences is of crucial interest, especially in high-intensity laser chains. For such analysis, results obtained with standard numerical methods strongly depend on the sampling. In this paper, we develop an analytic model for a sinusoidal phase modulation

Gamut mapping is an important part of the color reproduction pipeline. A color’s appearance depends on the gamut achievable by the reproduction device (e.g., display, printer, etc.) or the reproduction material (e.g., plastics, paints, textiles, etc.). In the surface color industry, often a single color is managed such that, if it lies outside of the reproduction gamut, it would be mapped to a visually

X-ray phase contrast imaging (PCI) combined with phase retrieval has the potential to improve soft-material visibility and discrimination. This work examined the accuracy, image quality gains, and robustness of a spectral phase retrieval method proposed by our group. Spectroscopic PCI measurements of a physical phantom were obtained using state-of-the-art photon-counting detectors in combination with

We report on the derivation of a spectral element method whose originality comes from the use of a hierarchical basis built with modified Legendre polynomials. We restrict our work to TM polarization, which is the most challenging. The validation and convergence are carefully checked for metallic dielectric gratings. The method is shown to be highly efficient and remains stable for huge truncation

Any general first-order optical system can be represented using ${\textbf{S}} \in Sp(4,\mathbb{R})$, where $Sp(4,\mathbb{R})$ is the symplectic group with real entries in four dimensions. We prove that any ${\textbf{S}} \in Sp(4,\mathbb{R})$ can be realized using not more than 18 thin lenses of arbitrary focal length and seven unit distance. New identities that realize ${\textbf{S}} = {S_1} \oplus

The aberrations of reflective optical systems with one plane of symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this first paper in a series of two, we establish generalized ray-tracing equations including transverse aberrations up to the third order in ray coordinates. The ray-tracing treatment

The aberrations of reflective optical systems with planar symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this second and last paper, closed-form expressions are derived for the aberrations created by an individual mirror. We study two-mirror off-axis telescopes and establish a new family

The paper presents a methodology of calculation of the inner structure of two- and three-component hybrid liquid-membrane lenses with variable focal length that have corrected spherical aberration and coma. Specifically, the formulas for calculation of initial-design inner parameters (radii of curvatures of individual surfaces, axial thickness, and refractive indices of a material of the lens) of a

We report on the quality assessment of an optical coherence tomography (OCT) image. A set of recent digital filters are used for denoising the interferometric signals. It is found that when a combination of continuous wavelet transform (WT) decomposition and the WT denoising techniques is imposed on raw signals, the highest signal-to-noise ratio of 17.8 can be reached. The structural similarity (SSIM)

In light-sheet fluorescence microscopy (LSFM), using Gaussian beams for light-sheet generation results in a trade-off between the thickness and the field of view (FOV). Here we present a theoretical analysis of using spherical aberration to enlarge the FOV while keeping the light-sheet thickness small. Such spherical aberration can arise when focusing beams through an interface between materials of

The detection of the optic disc (OD) and fovea is essential to many automatic diagnosis systems for retinal diseases. The single shot multibox detector (SSD) can generate predictions from feature maps of various resolutions, which has not been introduced into the OD and fovea detection. To enhance the detection performance, we propose an improved SSD network, which has strengthened information flow

Efficient and quick extraction of unknown objects in cluttered 3D scenes plays a significant role in robotics tasks such as object search, grasping, and manipulation. This paper describes a geometric-based unsupervised approach for the segmentation of cluttered scenes into objects. The proposed method first over-segments the raw point clouds into supervoxels to provide a more natural representation