Bringing metasurfaces to analytical lens design: stigmatism and specific ray mapping.

We propose a method to design the exact phase profile of at least one metasurface in a stigmatic singlet that can be made to implement a desired ray mapping. Following the generalized vector law of refraction and Fermat's principle, we can obtain exact solutions for the required lens shape and phase profile of a phase gradient metasurface to respect particular ray conditions (e.g., Abbe sine) as if it were a freeform refractive element. To do so, the method requires solving an implicit ordinary differential equation. We present comparisons with Zemax simulations of illustrative designed lenses to confirm the anticipated optical behaviour.

Orthoscopic elemental image synthesis for 3D light field display using lens design software and real-world captured neural radiance field.

The elemental images (EIs) generation of complex real-world scenes can be challenging for conventional integral imaging (InIm) capture techniques since the pseudoscopic effect, characterized by a depth inversion of the reconstructed 3D scene, occurs in this process. To address this problem, we present in this paper a new approach using a custom neural radiance field (NeRF) model to form real and/or virtual 3D image reconstruction from a complex real-world scene while avoiding distortion and depth inversion. One of the advantages of using a NeRF is that the 3D information of a complex scene (including transparency and reflection) is not stored by meshes or voxel grid but by a neural network that can be queried to extract desired data. The Nerfstudio API was used to generate a custom NeRF-related model while avoiding the need for a bulky acquisition system. A general workflow that includes the use of ray-tracing-based lens design software is proposed to facilitate the different processing steps involved in managing NeRF data. Through this workflow, we introduced a new mapping method for extracting desired data from the custom-trained NeRF-related model, enabling the generation of undistorted orthoscopic EIs. An experimental 3D reconstruction was conducted using an InIm-based 3D light field display (LFD) prototype to validate the effectiveness of the proposed method. A qualitative comparison with the actual real-world scene showed that the 3D reconstructed scene is accurately rendered. The proposed work can be used to manage and render undistorted orthoscopic 3D images from custom-trained NeRF-related models for various InIm applications.

Focus Issue Introduction: 3D Image Acquisition and Display: Technology, Perception and Applications.

This Feature Issue of Optics Express is organized in conjunction with the 2022 Optica conference on 3D Image Acquisition and Display: Technology, Perception and Applications which was held in hybrid format from 11 to 15, July 2022 as part of the Imaging and Applied Optics Congress and Optical Sensors and Sensing Congress 2022 in Vancouver, Canada. This Feature Issue presents 31 articles which cover the topics and scope of the 2022 3D Image Acquisition and Display conference. This Introduction provides a summary of these published articles that appear in this Feature Issue.

Wavefront control capability in a modal lens with segmented circular peripheral electrodes.

We report the detailed investigation of the capability of an electrically tunable liquid crystal lens (TLCL) to dynamically generate various wavefront shapes. The TLCL operates in the modal-control mode with a peripheral circular electrode divided into eight individually controlled segments. This segmentation allows producing a rather rich set of influence functions. We characterize these functions and the crosstalk between them by adjusting the voltage and the frequency of electrical signals applied to different electrode segments. Various wavefronts are produced in a closed-loop control mode and described using Zernike polynomials. The dynamical response of the lens is also briefly investigated. Obtained results may be used to design different adaptive optical systems where a dynamic wavefront control is required.

Exact vectorial model for nonparaxial focusing of freeform wavefronts.

We present a new formalism, based on Richards-Wolf theory, to rigorously model nonparaxial focusing of radially polarized electromagnetic beams with freeform wavefront. The beams can be expressed in terms of Zernike polynomials. Our approach is validated by comparing known results obtained by Richards-Wolf theory. Our integral representation is compliant with diffraction theory, is thoroughly discussed and solved for various freeform wavefront that, so far, have not been treated analytically. The extension of the method to other polarization states is straightforward.

Inferring the solution space of microscope objective lenses using deep learning.

Lens design extrapolation (LDE) is a data-driven approach to optical design that aims to generate new optical systems inspired by reference designs. Here, we build on a deep learning-enabled LDE framework with the aim of generating a significant variety of microscope objective lenses (MOLs) that are similar in structure to the reference MOLs, but with varied sequences-defined as a particular arrangement of glass elements, air gaps, and aperture stop placement. We first formulate LDE as a one-to-many problem-specifically, generating varied lenses for any set of specifications and lens sequence. Next, by quantifying the structure of a MOL from the slopes of its marginal ray, we improve the training objective to capture the structures of the reference MOLs (e.g., Double-Gauss, Lister, retrofocus, etc.). From only 34 reference MOLs, we generate designs across 7432 lens sequences and show that the inferred designs accurately capture the structural diversity and performance of the dataset. Our contribution answers two current challenges of the LDE framework: incorporating a meaningful one-to-many mapping, and successfully extrapolating to lens sequences unseen in the dataset-a problem much harder than the one of extrapolating to new specifications.

Impact of wavefront aberrations on the duration of few-cycle laser pulses.

It is generally difficult to define the duration of few-cycle laser pulses in the presence of spatiotemporal coupling. The pulse temporal width can indeed vary locally across the pulse front and spatially varying delays can complicate the definition of the temporal pulse length over the whole pulse front. However, the simple formalism of the global pulse length can be used to define the duration of such pulses. The variation of the rms temporal pulse width and the maximum instantaneous intensity of this global pulse is used here to investigate the impact of various aberrations. This is done for a collimated Gaussian few-cycle pulse propagating in a vacuum with no dispersion as a perfect plane wave of uniform, Gaussian, and super-Gaussian spatial profiles and for various local temporal pulse widths. It is shown that the temporal global profile of an aberrated pulse front can lose its Gaussian profile even for low amplitudes of aberration. This results in an increase of the rms temporal width and a decrease of the maximum instantaneous intensity of the global pulse, depending on the type of aberration. This is generally associated with a decrease in the performance for optical systems using few-cycle pulses.

Study of the impact of wavefront aberrations on the characterization of ultrashort laser pulses with GRENOUILLE.

In recent years, GRENOUILLE has emerged as a relatively simple technique to fully characterize the electric field of an ultrashort laser pulse in a single shot. It does so by spatially mapping the delays on the transverse spatial coordinate and by mapping the frequencies on the angular coordinate of the orthogonal direction. Because of this spatial mapping, an aberrated wavefront could distort and affect the measurement of the pulse. It is shown here experimentally how these aberrations can affect the measurement using a deformable mirror to induce various aberrations in the wavefront. This can result in distortions of the spectral or temporal profile of the retrieved pulse, and a decrease of the intensity of the second-harmonic signal generated by the nonlinear crystal. Additionally, the signatures of some of the distortions of the trace resemble those previously identified as being caused by pulse-front tilt or spatial chirp and could be interpreted as such while being in fact caused by aberrations. This can complicate the identification of the real source of the distortions, since a purely spatial effect can cause distortions similar to those created by dispersion-based phenomena or other types of spatiotemporal couplings.

The Underwater Vision Profiler 6: an imaging sensor of particle size spectra and plankton, for autonomous and cabled platforms.

Autonomous and cabled platforms are revolutionizing our understanding of ocean systems by providing 4D monitoring of the water column, thus going beyond the reach of ship-based surveys and increasing the depth of remotely sensed observations. However, very few commercially available sensors for such platforms are capable of monitoring large particulate matter (100-2000 µm) and plankton despite their important roles in the biological carbon pump and as trophic links from phytoplankton to fish. Here, we provide details of a new, commercially available scientific camera-based particle counter, specifically designed to be deployed on autonomous and cabled platforms: the Underwater Vision Profiler 6 (UVP6). Indeed, the UVP6 camera-and-lighting and processing system, while small in size and requiring low power, provides data of quality comparable to that of previous much larger UVPs deployed from ships. We detail the UVP6 camera settings, its performance when acquiring data on aquatic particles and plankton, their quality control, analysis of its recordings, and streaming from in situ acquisition to users. In addition, we explain how the UVP6 has already been integrated into platforms such as BGC-Argo floats, gliders and long-term mooring systems (autonomous platforms). Finally, we use results from actual deployments to illustrate how UVP6 data can contribute to addressing longstanding questions in marine science, and also suggest new avenues that can be explored using UVP6-equipped autonomous platforms.

Freeform wide-angle camera lens enabling mitigable distortion.

Allowing natural scenes as well as maximizing field of view (FoV) can benefit from the minimization of distortion for the wide-angle camera. The wide-angle camera utilizing freeform surfaces for mitigating distortions, either barrel distortion or pincushion distortion, is therefore of interest. In this paper, the designs of using all-aspherical surfaces and aspherical surfaces combined with freeform surfaces are investigated. To minimize the deviation before and after converting from aspherical surfaces to freeform surfaces, a mathematical conversion scheme is derived. By applying it to the design example, the methodology is shown to be effective in the case of an optical system with a large number of aspherical/freeform surfaces. Additionally, custom freeform analysis tools are developed for quantitative analysis and visualization of the critical characteristics of optical performance, namely, a 2D lateral color field map, 2D relative illumination field map, 2D spot radius field map, and 2D average modulation transfer function (MTF) field map. Compared to classical all-aspherical design, simulation results show that freeform design has the capability to reduce distortion, and other performances such as relative illumination, spot size, and MTF can also be improved, even though there are some compromises on the peripheral FoV. The design approach will have potential important research and application values for lens systems utilized in miniature camera lenses, especially the wide FoV capability.

Higher Na+-Ca2+ Exchanger Function and Triggered Activity Contribute to Male Predisposition to Atrial Fibrillation.

Male sex is one of the most important risk factors of atrial fibrillation (AF), with the incidence in men being almost double that in women. However, the reasons for this sex difference are unknown. Accordingly, in this study, we sought to determine whether there are sex differences in intracellular Ca2+ homeostasis in mouse atrial myocytes that might help explain male predisposition to AF. AF susceptibility was assessed in male (M) and female (F) mice (4-5 months old) using programmed electrical stimulation (EPS) protocols. Males were 50% more likely to develop AF. The Ca2+ transient amplitude was 28% higher in male atrial myocytes. Spontaneous systolic and diastolic Ca2+ releases, which are known sources of triggered activity, were significantly more frequent in males than females. The time to 90% decay of Ca2+ transient was faster in males. Males had 54% higher Na+-Ca2+ exchanger (NCX1) current density, and its expression was also more abundant. L-type Ca2+ current (ICaL) was recorded with and without BAPTA, a Ca2+ chelator. ICaL density was lower in males only in the absence of BAPTA, suggesting stronger Ca2+-dependent inactivation in males. CaV1.2 expression was similar between sexes. This study reports major sex differences in Ca2+ homeostasis in mouse atria, with larger Ca2+ transients and enhanced NCX1 function and expression in males resulting in more spontaneous Ca2+ releases. These sex differences may contribute to male susceptibility to AF by promoting triggered activity.

Connexin Lateralization Contributes to Male Susceptibility to Atrial Fibrillation.

Men have a higher risk of developing atrial fibrillation (AF) than women, though the reason for this is unknown. Here, we compared atrial electrical and structural properties in male and female mice and explored the contribution of sex hormones. Cellular electrophysiological studies revealed that action potential configuration, Na+ and K+ currents were similar in atrial myocytes from male and female mice (4-5 months). Immunofluorescence showed that male atrial myocytes had more lateralization of connexins 40 (63 ± 4%) and 43 (66 ± 4%) than females (Cx40: 45 ± 4%, p = 0.006; Cx43: 44 ± 4%, p = 0.002), with no difference in mRNA expression. Atrial mass was significantly higher in males. Atrial myocyte dimensions were also larger in males. Atrial fibrosis was low and similar between sexes. Orchiectomy (ORC) abolished sex differences in AF susceptibility (M: 65%; ORC: 38%, p = 0.050) by reducing connexin lateralization and myocyte dimensions. Ovariectomy (OVX) did not influence AF susceptibility (F: 42%; OVX: 33%). This study shows that prior to the development of age-related remodeling, male mice have more connexin lateralization and larger atria and atrial myocyte than females. Orchiectomy reduced AF susceptibility in males by decreasing connexin lateralization and atrial myocyte size, supporting a role for androgens. These sex differences in AF substrates may contribute to male predisposition to AF.

Deep learning-enabled framework for automatic lens design starting point generation.

We present a simple, highly modular deep neural network (DNN) framework to address the problem of automatically inferring lens design starting points tailored to the desired specifications. In contrast to previous work, our model can handle various and complex lens structures suitable for real-world problems such as Cooke Triplets or Double Gauss lenses. Our successfully trained dynamic model can infer lens designs with realistic glass materials whose optical performance compares favorably to reference designs from the literature on 80 different lens structures. Using our trained model as a backbone, we make available to the community a web application that outputs a selection of varied, high-quality starting points directly from the desired specifications, which we believe will complement any lens designer's toolbox.

MCVD-based GRIN-axicon for the generation of scalable Bessel-Gauss beams.

In this Letter, we introduce a graded-index (GRIN)-lens combination named GRIN-axicon, which is a versatile component capable of generating high-quality scalable Bessel-Gauss beams. To the best of our knowledge, the GRIN-axicon is the only optical component that can be introduced in both larger-scale laboratory setups and miniaturized all-fiber optical setups, while having an easy control of the dimensioning of the generated focal line. We show that a GRIN lens with a hyperbolic secant refractive index profile with a sharp central dip and no ripples generates a Bessel-Gauss beam with a high-intensity central lobe when coupled to a simple lens. Such fabrication characteristics are very suitable for the modified chemical vapor deposition (MCVD) process and enable easy manufacturing of an adaptable component that can fit in any optical setup.

On the diffraction of a high-NA aplanatic and stigmatic singlet.

We present a study of the diffraction pattern according to Richards-Wolf for an aplanatic and stigmatic singlet based on an exact analytical equation. We are able to put emphasis on the maximum diameter and illumination pattern, which are the two parameters that influence the diffraction pattern and how to compute it. Designs of low- and high-NA aplanatic and stigmatic lenses are implemented to display these effects.

The Surprising Creativity of Digital Evolution: A Collection of Anecdotes from the Evolutionary Computation and Artificial Life Research Communities.

Evolution provides a creative fount of complex and subtle adaptations that often surprise the scientists who discover them. However, the creativity of evolution is not limited to the natural world: Artificial organisms evolving in computational environments have also elicited surprise and wonder from the researchers studying them. The process of evolution is an algorithmic process that transcends the substrate in which it occurs. Indeed, many researchers in the field of digital evolution can provide examples of how their evolving algorithms and organisms have creatively subverted their expectations or intentions, exposed unrecognized bugs in their code, produced unexpectedly adaptations, or engaged in behaviors and outcomes, uncannily convergent with ones found in nature. Such stories routinely reveal surprise and creativity by evolution in these digital worlds, but they rarely fit into the standard scientific narrative. Instead they are often treated as mere obstacles to be overcome, rather than results that warrant study in their own right. Bugs are fixed, experiments are refocused, and one-off surprises are collapsed into a single data point. The stories themselves are traded among researchers through oral tradition, but that mode of information transmission is inefficient and prone to error and outright loss. Moreover, the fact that these stories tend to be shared only among practitioners means that many natural scientists do not realize how interesting and lifelike digital organisms are and how natural their evolution can be. To our knowledge, no collection of such anecdotes has been published before. This article is the crowd-sourced product of researchers in the fields of artificial life and evolutionary computation who have provided first-hand accounts of such cases. It thus serves as a written, fact-checked collection of scientifically important and even entertaining stories. In doing so we also present here substantial evidence that the existence and importance of evolutionary surprises extends beyond the natural world, and may indeed be a universal property of all complex evolving systems.

Toric lens analysis as a focal ring and Bessel beam generator.

We propose an analytical solution of the focal ring generated at the focus of a toric lens. The analytical field of the focal ring is used with a Fourier transform lens to generate a Bessel beam. A comparative analysis between the use of an illuminated annular aperture, an axicon, and a toric lens to generate a Bessel beam is performed, and the benefits and drawbacks of each are discussed. This highlights the advantages of using a toric lens with a Gaussian beam to produce a focal line of increasing intensity, which is advantageous for applications such as high depth-of-field microscopy.

Geometrical-based quasi-aspheric surface description and design method for miniature, low-distortion, wide-angle camera lens.

In addition to utilizing traditional aspheric surfaces, complicated geometric curves for meeting stringent design requirements can also be adopted in optical systems. In this paper, we investigate two geometric shape modeling schemes, namely, pedal and cosine curves, which allow for representation of an S-shaped profile for the optical design of a camera lens. To obtain a powerful tool for representing a quasi-aspheric surface (QAS) to resemble the designed form surface, we linearly combine the pedal/cosine function with a base conic section. The detailed parameterization process of representation is discussed in this paper. Subsequently, an existing starting point that has similar specifications to that of the design requirements is selected. During the optimization process, a least-squares fitting algorithm is implemented to obtain the optimal coefficient values of the proposed QAS representation, and then the parameters (radii, air thickness, lens thickness, coefficients, materials, etc.) of the optical system are set to optimize the optical performance, gradually aiming to minimize the predefined merit function. We demonstrate the applicability of the proposed geometric modeling schemes via two design examples. In comparison to a conventional aspheric camera lens of the same specifications, the optical performance with respect to field of view and distortion has been improved due to higher degrees of design freedom. We believe that the proposed technology of geometric modeling schemes promises to improve optical performance due to these higher degrees of freedom and appears to be applicable to many different camera lenses.

Extrapolating from lens design databases using deep learning.

We propose for the first time a deep learning approach in assisting lens designers to find a lens design starting point. Using machine learning, lens design databases can be expanded in a continuous way to produce high-quality starting points from various optical specifications. A deep neural network (DNN) is trained to reproduce known forms of design (supervised training) and to jointly optimize the optical performance (unsupervised training) for generalization. In this work, the DNN infers high-performance cemented and air-spaced doublets that are tailored to diverse desired specifications after being fed with reference designs from the literature. The framework can be extended to lens systems with more optical surfaces.