This publisher’s note corrects the paper type and title of J. Opt. Soc. Am. A 36, D31 (2019) [CrossRef] .

Editor-in-Chief P. Scott Carney introduces the Journal’s newest Topical Editors, Irina V. Larina and Jonathan Petruccelli.

The OSA Topical Meeting on Digital Holography and 3D Imaging (DH) was held 20–23 May 2019 in Bordeaux, France. Feature issues based on the DH meeting series have been released by Applied Optics (AO) since 2007. This year, AO and the Journal of the Optical Society of America A (JOSA A) jointly decided to have one such feature issue in each journal. This feature issue includes 46 papers in AO and 9 in JOSA A and covers a large range of topics, reflecting the rapidly expanding techniques and applications of digital holography and 3D imaging. The upcoming DH Conference (DH 2020) will be held from 22 to 26 June in Vancouver, Canada, as part of the OSA Imaging and Applied Optics Congress.

We propose a numerical method for phase curvature compensation in digital holographic microscopy, in which the phase curvature is compensated for by subtracting a numerical phase mask from the distorted phase. The parameters of the phase mask are obtained based on phase gradient fitting and optimization, in which the initial mask parameters are obtained by fitting the phase gradient, and then more accurate mask parameters are determined using a spectrum energy search. The compensation can be executed in a hologram without extra devices or any prior knowledge of the setup and specimen. A computer simulation and experimental results demonstrated the feasibility of the proposed method.

Complex object wave recovery from a single-shot interference pattern is an important practical problem in interferometry and digital holography. The most popular single-shot interferogram analysis method involves Fourier filtering of the cross term, but this method suffers from poor resolution. To obtain full pixel resolution, it is necessary to model the object wave recovery as an optimization problem. The optimization approach typically involves minimizing a cost function consisting of a data consistency term and one or more constraint terms. Despite its potential performance advantages, this method is not used widely due to several tedious and difficult tasks such as empirical tuning of free parameters. We introduce a new optimization approach, mean gradient descent (MGD), for single-shot interferogram analysis that is simple to implement. MGD does not have any free parameters whose empirical tuning is critical to the object wave recovery. The MGD iteration does not try to achieve minimization of a cost function but instead aims to reach a solution point where the data consistency and the constraint terms balance each other. This is achieved by iteratively progressing the solution in the direction that bisects the descent directions associated with the error and constraint terms. Numerical illustrations are shown for recovery of a step phase object from its corresponding off-axis as well as on-axis interferograms simulated with multiple noise levels. Our results show full pixel resolution as evident from the recovery of the phase step and excellent rms phase accuracy relative to the ground truth phase map. The concept of MGD as presented here can potentially find applications to a wider class of optimization problems.

In digital holography, the inherited speckle noise degrades imaging quality due to the coherent laser source. To overcome this problem, a hybrid method for speckle noise reduction is presented by combining a novel angular diversity approach with the block-matching and 3D filtering (BM3D) algorithm. A serial of holograms is first captured by the proposed recording approach, and then the image with high signal-to-noise ratio is obtained by averaging multiple reconstructed intensity images. Finally, the residual noise in the averaged image is further eliminated by the BM3D filtering algorithm. The speckle noise is significantly suppressed, and a nearly speckle-free image can be obtained. Experimental results demonstrate the effectiveness of the proposed method.

For this research, we have developed key technologies for a 1.5 µm pixel pitch spatial light modulator (SLM) using ${\rm{Ge}_{2}}{\rm{Sb}_{2}}{\rm{Te}_{5}}$ (GST) phase change material. To uniformly modulate each pixel, we designed a lateral pixel structure in which a heating current flows through a bottom indium tin oxide layer. To check hologram reconstruction both after multilevel fabrication processes and before implementing full source and driver circuits, we fabricated an $8\,\,{\rm{K}} \times 2\,\,{\rm{K}}$ hologram on the topology by changing the GST film’s phase using laser irradiation. To overcome the limitation of SLM size, we tested a physical tiling structure and found that flatness of tiled SLMs was the most important factor in the realization of holographic displays.

This paper provides a tutorial of iterative phase retrieval algorithms based on the Gerchberg–Saxton (GS) algorithm applied in digital holography. In addition, a novel GS-based algorithm that allows reconstruction of 3D samples is demonstrated. The GS-based algorithms recover a complex-valued wavefront using wavefront back-and-forth propagation between two planes with constraints superimposed in these two planes. Iterative phase retrieval allows quantitatively correct and twin-image-free reconstructions of object amplitude and phase distributions from its in-line hologram. The present work derives the quantitative criteria on how many holograms are required to reconstruct a complex-valued object distribution, be it a 2D or 3D sample. It is shown that for a sample that can be approximated as a 2D sample, a single-shot in-line hologram is sufficient to reconstruct the absorption and phase distributions of the sample. Previously, the GS-based algorithms have been successfully employed to reconstruct samples that are limited to a 2D plane. However, realistic physical objects always have some finite thickness and therefore are 3D rather than 2D objects. This study demonstrates that 3D samples, including 3D phase objects, can be reconstructed from two or more holograms. It is shown that in principle, two holograms are sufficient to recover the entire wavefront diffracted by a 3D sample distribution. In this method, the reconstruction is performed by applying iterative phase retrieval between the planes where intensity was measured. The recovered complex-valued wavefront is then propagated back to the sample planes, thus reconstructing the 3D distribution of the sample. This method can be applied for 3D samples such as 3D distribution of particles, thick biological samples, and other 3D phase objects. Examples of reconstructions of 3D objects, including phase objects, are provided. Resolution enhancement obtained by iterative extrapolation of holograms is also discussed.

Coherence properties of light sources are indispensable for optical coherence microscopy/tomography as they greatly influence the signal-to-noise ratio, axial resolution, and penetration depth of the system. In the present paper, we report the investigation of longitudinal spatial coherence properties of a pseudothermal light source (PTS) as a function of the laser spot size at the rotating diffuser plate. The laser spot size is varied by translating a microscope objective lens toward or away from the diffuser plate. The longitudinal spatial coherence length, which governs the axial resolution of the coherence microscope, is found to be minimum for the beam spot size of 3.5 mm at the diffuser plate. The axial resolution of the system is found to be equal to an $\sim{13}\,\,{\rm \unicode{x00B5}{\rm m}}$ at 3.5 mm beam spot size. The change in the axial resolution of the system is confirmed by performing the experiments on standard gauge blocks of a height difference of 15 µm by varying the spot size at the diffuser plate. Thus, by appropriately choosing the beam spot size at the diffuser plane, any monochromatic laser light source can be utilized to obtain high axial resolution irrespective of the source’s temporal coherence length. It can provide speckle-free tomographic images of multilayered biological specimens with large penetration depth. In addition, a PTS avoids the use of any chromatic-aberration-corrected optics and dispersion-compensation mechanism unlike conventional setups.

In remote-sensing applications, digital holography data often includes both phase errors from atmospheric turbulence and fully developed laser speckle from rough objects. When processing single-shot data, i.e., data from a single hologram, the high speckle contrast makes it more difficult to correct for atmospheric phase errors compared to scenarios where multiple speckle realizations are available for processing. A Bayesian phase-error correction algorithm [J. Opt. Soc. Am. A 34, 1659 (2017) [CrossRef] ] was recently developed for use with single-shot data. The features of this approach are discussed and used to implement an alternative algorithm based on image-sharpness maximization. Algorithm performance is tested using simulated data for a range of signal-to-noise ratios (SNRs) and turbulence conditions. Using a combination of appropriate parameterization of the phase-error estimates and spatial binning for speckle-contrast reduction, the image-sharpness algorithm achieves performance comparable (better in the high-SNR regime but worse in the low-SNR regime) to the Bayesian approach. Limited experimental results are also presented.

This paper includes a tutorial on how to reconstruct in-line holograms using an inverse problems approach, starting with modeling the observations, selecting regularizations and constraints, and ending with the design of a reconstruction algorithm. A special focus is placed on the connections between the numerous alternating projections strategies derived from Fienup’s phase retrieval technique and the inverse problems framework. In particular, an interpretation of Fienup’s algorithm as iterates of a proximal gradient descent for a particular cost function is given. Reconstructions from simulated and experimental holograms of micrometric beads illustrate the theoretical developments. The results show that the transition from alternating projections techniques to the inverse problems formulation is straightforward and advantageous.

Multifilter phase imaging with partially coherent light (MFPI-PC) and phase optical transfer function recovery (POTFR) are two viable defocus-based, two-dimensional quantitative phase imaging (QPI) methods. While both methods use transfer function inversion, MFPI-PC is based on the in-focus intensity derivative, while POTFR is based on the intensity difference between symmetrically defocused images. This paper compares and contrasts MFPI-PC and POTFR. Six disadvantages (five in MFPI-PC and one in POTFR) are identified. Improvement strategies to overcome each of the six shortcomings are identified and implemented, and both methods are shown to be clearly improved. The revised MFPI-PC is shown to be more accurate than the original MFPI-PC and generally more accurate than the revised POTFR. The revised POTFR is shown to be inherently faster than the original POTFR and also slightly faster than the revised MFPI-PC.

Signal-to-noise ratio (SNR) of an optical wireless communication (OWC) link that operates in anisotropic oceanic turbulence is evaluated. To find the SNR advantage of the anisotropy in the oceanic turbulent medium, SNR in anisotropic oceanic turbulence is normalized by the SNR in isotropic oceanic turbulence. The dB values of this normalized SNR are examined versus the oceanic turbulence parameters of the ratio of temperature to salinity contributions to the refractive index spectrum, the rate of dissipation of mean-squared temperature, the rate of dissipation of kinetic energy per unit mass of fluid at various oceanic anisotropic factors, the avalanche multiplication factors, the radii of receiver aperture, link lengths, and detector responsivity values. It is found that as the oceanic turbulence becomes more anisotropic, at any link parameter, the SNR of the OWC link becomes advantageous over the isotropic counterpart.

In a stratified or a spherically symmetric atmosphere, we consider some cases where a curved light ray connects two points, $A$ and $S$, on the sea or the ground, at the same height as in some cases of superior mirages or “arctic mirages.” We study the range $D$ of this ray (i.e., the geodesic distance between $A$ and $S$) as a function of ${\alpha _S}$, the ray inclination with respect to the vertical at $A$ or $S$. The fundamental expression of $D$ is an improper integral. We show that a change of variable, also used to calculate the astronomical refraction, usually gives a well-behaved integral. In a spherically symmetric atmosphere, this happens when the refraction coefficient exceeds unity on the entire ray, producing a hillingar effect (alias strong looming for an erect image) or superior mirages. We then find a nice expression of ${{{\rm d}D}/{{\rm d}{\alpha _S}}}$, which is usually negative. Inverted images (i.e., mirages in the strict sense) show up when ${{{\rm d}D}/{{\rm d}{\alpha _S}}}$ is positive; for this, we find a necessary condition in each atmospheric model. The strength of these results comes from not requiring precise knowledge of the ray paths.

An efficient tensor approach is used to simulate the propagation of partially coherent Hermite–sinh–Gaussian (H–ShG) beams through an ABCD optical system in a turbulent atmosphere. Analytical expressions for the average intensity are derived. The properties of the average intensity of the beam are studied numerically. It is found that the average intensity distribution of the beam is almost independent of the structure constant of turbulence when the spatial coherence length is very small and the beam with larger spatial coherence length is less affected by the turbulent atmosphere. Moreover, the transition from an H–ShG beam into a Gaussian beam becomes quicker with smaller beam order and smaller Sh parameters.

The effect of anisotropy on the channel capacity of underwater optical wireless communication (OWC) links operating in strong oceanic turbulence is investigated. We consider a Gaussian beam wave propagating through a turbulent oceanic fading channel whose statistical distribution is modelled by a gamma–gamma function. To numerically calculate the channel capacity of the OWC system, related entities of the propagating beam such as coherence length, received signal intensity, and the scintillation index are formulated. Further, in this way, the received signal-to-noise ratio and fading distribution of the channel are obtained. The channel capacity examinations analyzed in this paper depend on the oceanic turbulence parameters, especially for the anisotropic factor of oceanic turbulence, and also depend on the other system parameters such as wavelength, link distance, noise variance, and the quantum efficiency of the photodetector.

In this paper, based on the extended Rytov theory that combines modified large-scale and small-scale amplitude spatial-frequency filters, we theoretically derive the scintillation index (SI) of the plane and spherical waves by means of the approximate oceanic refractive-index spectrum with the variable eddy diffusivity ratio propagating through moderate-to-strong oceanic turbulence. The mean bit-error rate (BER) of the underwater optical wireless communication systems is analyzed by use of the predicted SI and the gamma–gamma distribution model. Numerical results show that the obtained SI models are in good agreement with the results in weak-fluctuation regions. Also, we find that in weak turbulence, the mean BER drops sharply with the increase in mean signal-to-noise ratio, while in moderate-to-strong turbulence, the situation is opposite. We also note that the mean BER differs between the cases of unity and the variable eddy diffusivity ratio.

A fruitful approach for light–droplet interaction in atmospheric optics, the quantum optical analogy combined with partial wave analysis, is used to characterize (location, width) very sharp tunneling optical resonances (TORs). For this purpose, a fast and flexible technique of computation, the transfer matrix method, has been developed; it is described herein. This paper proposes explicit calculations of TORs, considering isolated droplets and a droplet population, and so goes further than earlier studies. Applied in the context of POLDER observations, from the visible to the near infrared, it is shown that TORs enhance cross sections with respect to Mie’s theory as currently computed in atmospheric optics. Precisely, for a typical warm cloud droplet population, this enhancement can reach almost 30% in the case of absorption. Scattering and extinction cross sections are also higher than those of Mie’s theory, but to a lesser extent. As a conclusion, it is suggested that tunneling should be taken into account more explicitly when addressing light scattering by droplets. No scattering inversion technique is investigated in this paper, but for the time being, the results presented can be used as look-up tables (at least orders of magnitude) for practical computations in atmospheric remote sensing. Finally, the approach presented herein is proposed as a perspective to be used in different situations involving other spherical (or almost spherical) scatterers that otherwise should be addressed approximately.

When light that is spatially partially coherent, such as sunlight, is incident on a sphere, the scattered field exhibits surprising coherence properties. The observed oscillatory behavior with deep minima means that the field in certain pairs of directions is highly correlated, whereas in others, it is essentially uncorrelated, and can even have correlation singularities. Because any subsequent scattering event is strongly affected by the state of coherence, these results are particularly important for multiple scattering in discrete disordered media.

The angle-impact Wigner function (AIWF) is a tool that assigns weights to rays in a way such that ray tracing can be used to exactly model the irradiance and polarization properties of nonparaxial, partially coherent, partially polarized electromagnetic fields. Although the AIWF offers computational advantages over more conventional wave propagation integrals, in practice, the large number of rays that must be traced has proved to be a significant bottleneck. We demonstrate an efficient method to implement AIWF propagation algorithms inspired by a plenoptic field representation. We illustrate the method by computing irradiance and polarization properties of several paraxial and nonparaxial fields.

Peridot’s yellowish-green color is not only produced by ${{\rm Fe}^{2+}}$ but is also influenced by background, observer, illuminance, and color temperature of the light source. In this research, we studied the most effective background for peridot color grading under a 6504K fluorescent lamp. Ninety-five gem-quality peridot samples from China, Pakistan, and Myanmar were studied using electron probe micro-analyzer, spectrophotometer, Munsell neutral gray backgrounds, and standard gold alloy backgrounds. The results provided the color effects of 24K, 22K, 20K, 18K, and 16K gold alloy backgrounds and Munsell neutral gray backgrounds on the peridot’s color. It was found that the Munsell N9 background seems to be the most effective background for peridot color grading. Using the Munsell N9 background, peridot colors were graded into three levels from good to bad: Fancy Intense, Fancy Deep, and Fancy by using K-means clustering analysis and Fisher discriminant analysis methods. The peridot’s color level reverse phenomenon should be considered when the background varies between Munsell N7 and N9 gray.

By using Huygens–Fresnel diffraction integral formula and the transfer matrix method, the analytical expression of radially and azimuthally polarized chirped Airy–Gaussian vortex beams through left-handed materials and right-handed materials can be obtained. We study the effects of the chirp factor and the distribution factor on the radially and azimuthally polarized chirped Airy–Gaussian vortex beams in the propagation process, including the light intensity, the phase distribution, the propagation path, the peak intensity, and the radiation force. The focal position of the beams can be adjusted by the chirp parameter.

To expand the spectral bandwidths with high diffraction efficiency of volume phase (VP) gratings, it is important to know the influence of a variety of refractive index distributions (RIDs) inside the recording material on the bandwidths. The influence of various graded types of RIDs on the full width at half the maximum of the spectral bandwidth (${\lambda _{\rm FWHM}}$) and the angular bandwidth (${\theta _{\rm FWHM}}$) is investigated in the Bragg regime. It becomes clear that various graded types of RIDs influence their bandwidths and the characteristics, and the combination of the RIDs and refractive index modulation (${{ n}_m}$) is the most important factor for obtaining the large bandwidths of VP gratings. Theoretically, the ${\lambda _{\rm FWHM}}$ are obtained as the values of 149.7 nm and 257.6 nm (${{ n}_m} = {0.045}$) for the wavelengths of 900 nm and 1550 nm, respectively. Furthermore, I have succeeded in developing the expression for ${\lambda _{\rm FWHM}}$ and ${\theta _{\rm FWHM}}$, using the proportional characteristics of VP gratings investigated in this work. The correlative coupling-length coefficients “G-factors” devised as a variety of RID functions in the previous paper are introduced into them. It is apparent that the derived equations of the bandwidths can be adapted to any graded type of RID that changes continuously from a triangular type to a rectangular type of VP grating, which has not been reported yet. The equations have made it easy to design ${\lambda _{\rm FWHM}}$ and ${\theta _{\rm FWHM}}$ of VP gratings.

This paper presents a paraxial lens design method for anamorphic zoom lenses with double telecentricity. Four types of such lens systems are provided, which are the Y-X-Y-Y type, the Y-Y-Y-X type, the Y-X-Y-X type, and the Y-X-X-Y type. For each lens type, it can work in two different conditions: (a) the distance between the object and the image is fixed during anamorphic zooming, or (b) the magnifications in the tangential plane and the sagittal plane can be changed independently by changing the interval lens distances. For each condition, given the optical power of each lens component and the design parameters, such as the total length, the magnifications in the tangential plane and the sagittal plane, and the anamorphic ratio, formulas determining the interval distances between lens components, the object position, and the stop position are provided. Eight examples of double-telecentric anamorphic zoom lenses are provided, and all the examples are tested in Zemax, which shows the validity of the proposed design method.

When using freeform surfaces in optical design, the field dependence of the aberrations can become quite complex, and understanding these aberrations facilitates the design process. Here we calculate the field dependence of low-order Zernike astigmatism (Z5/6) up to the eighth order in nodal aberration theory (NAT). Expansion of NAT astigmatism terms to the eighth order facilitates a more accurate fit to the Zernike astigmatism data. We then show how this estimated field dependence can be used to quantitatively analyze a freeform telescope design. This analysis tool adds to the optical designer’s arsenal when up against the challenge of designing with freeform optics.

We present an algorithm for generating high-quality holograms for computer generated holography: holographic predictive search. This approach is presented as an alternative to traditional holographic search algorithms such as direct search (DS) and simulated annealing (SA). We first introduce the current search-based methods and then introduce an analytical model of the underlying Fourier elements. This is used to make prescient judgments regarding the next iteration of the algorithm. This approach is developed for the case of phase-modulating devices with phase-sensitive reconstructions. When compared to conventional iterative approaches such as DS and SA on a multiphase device, holographic predictive search offered a fivefold improvement in quality as well as up to a 10-fold improvement in convergence time. This comes at the cost of an increased iteration overhead.

The standard two-dimensional (2D) image recorded in bright-field fluorescence microscopy is rigorously modeled by a convolution process involving a three-dimensional (3D) sample and a 3D point spread function. We show on synthetic and experimental data that deconvolving the 2D image using the appropriate 3D point spread function reduces the contribution of the out-of-focus fluorescence, resulting in a better image contrast and resolution. This approach is particularly interesting for superresolution speckle microscopy, in which the resolution gain stems directly from the efficiency of the deconvolution of each speckle image.

Linearly polarized Gaussian beams, under the slowly varying envelope approximation, tightly focused by a perfect parabola modeled with the integral formalism of Ignatovsky are found to be well approximated with a generalized Lax series expansion beyond the paraxial approximation. This allows obtaining simple analytic formulas of the electromagnetic field in both the direct and momentum spaces. It significantly reduces computing time, especially when dealing with the problem of simulating direct laser acceleration. The series expansion formulation depends on integration constants that are linked to boundary conditions. They are found to depend significantly on the region of space over which the integral formulation is fit. Consequently, the net acceleration of electrons initially at rest is extremely sensitive to the chosen set of initial parameters due to the extreme focusing investigated here. This suggests avoiding too tight focusing schemes in order to obtain reliable predictions when the process of interest is sensitive mainly to the field and not the intensity.

This paper presents the application of an immersed interface method in efficient modal analysis of dielectric chiral optical fibers. Under the easily implemented finite-difference framework, the second- and fourth-order accuracy formulations are developed, which in principle are applicable for automatically computing various types of modes in dielectric chiral optical fibers with an arbitrary, electromagnetic parameters piecewise constant profile. To validate the developed formulations, numerical examples are given for the guided, leaky, and surface modes in dielectric chiral step-profile and Bragg fibers.

We put forward a robust technique to encode a plethora of arbitrary images as nondiffracting beams by optimizing their respective phase components. This technique works directly under the constraint of a ring of infinitesimal width in Fourier space. The procedure reported is based on a stochastic direct search and global optimization: the differential evolution method. Unlike previous methods reported, the present approach is also able to optimize the spatial frequency of the image used. Remarkably, this technique also demonstrates that it is possible to encode even more arbitrary images on demand into nondiffracting forms by allowing a segmentation of the profile. We provide some codes to generate nondiffracting beams by using this algorithm.

Determining the size and composition of core-shell particles using morphology-dependent resonances (MDRs) is a computationally intensive problem due to the large parameter space that needs to be searched during the fitting process. Very often, it is not even practical to consider a reasonable range of physical parameters due to time constraints, leading to restrictive assumptions concerning the system being studied. The lengthy computational time is so limiting that there has, to date, to the best of our knowledge, been no comprehensive study of fitting measured MDRs for core-shell particles. In this work, we address the issue of fitting speed by developing an algorithm that (i) reduces the multi-dimensional grid search to a one-dimensional search using a least squares method and (ii) implements a new method for calculating MDRs that is much faster than previous methods. With the program presented here, we analyze the best-fits for core-shell MDRs across a large range of physically relevant scenarios using noise levels typical for conventional spectroscopic experiments. For many cases, it has been found that excellent fits can be quickly determined. However, there are also some surprising situations where accurate best-fits are not possible (e.g., if only one mode order is present in the measured MDR set).

This special issue of the Journal of the Optical Society of America A (JOSA A) is devoted to the wide array of French researchers from universities and state research organisms, offering them the opportunity to share and showcase their current research in the fields of optics and imaging sciences to the global community.