Fast Zernike fitting of freeform surfaces using the Gauss-Legendre quadrature.

Zernike polynomial orthogonality, an established mathematical principle, is leveraged with the Gauss-Legendre quadrature rule in a rapid novel approach to fitting data over a circular domain. This approach provides significantly faster fitting speeds, in the order of thousands of times, while maintaining comparable error rates achieved with conventional least-square fitting techniques. We demonstrate the technique for fitting mid-spatial-frequencies (MSF) prevalent in small-tool-manufacturing typical of aspheric and freeform optics that are poised to soon permeate a wide range of optical technologies.

Estimating the irradiance of a perturbed surface under an extended source.

This paper presents a method for evaluating the irradiance of a single freeform surface deviation under extended source illumination. The method takes advantage of a well-known concept, the pinhole image. First, the irradiance of the perturbed freeform surface under point source illumination is computed. Second, a pinhole image of the extended source is obtained by placing a small aperture (pinhole) on the freeform surface. Then, the extended source irradiance pattern change can be quickly calculated by convolving the pinhole image with the perturbed point source irradiance change. The method was experimentally verified, demonstrating the efficacy of the underlying concept. The proposed method alleviates the computational demands during extended source tolerancing, expediting the process.

High refresh rate display for natural monocular viewing in AOSLO psychophysics experiments.

By combining an external display operating at 360 frames per second with an Adaptive Optics Scanning Laser Ophthalmoscope (AOSLO) for human foveal imaging, we demonstrate color stimulus delivery at high spatial and temporal resolution in AOSLO psychophysics experiments. A custom pupil relay enables viewing of the stimulus through a 3-mm effective pupil diameter and provides refractive error correction from -8 to +4 diopters. Performance of the assembled and aligned pupil relay was validated by measuring the wavefront error across the field of view and correction range, and the as-built Strehl ratio was 0.64 or better. High-acuity stimuli were rendered on the external display and imaged through the pupil relay to demonstrate that spatial frequencies up to 54 cycles per degree, corresponding to 20/11 visual acuity, are resolved. The completed external display was then used to render fixation markers across the field of view of the monitor, and a continuous retinal montage spanning 9.4 by 5.4 degrees of visual angle was acquired with the AOSLO. We conducted eye-tracking experiments during free-viewing and high-acuity tasks with polychromatic images presented on the external display. Sub-arcminute eye position uncertainty was achieved, enabling precise localization of the line of sight on the monitor while simultaneously imaging the fine structure of the human central fovea. This high refresh rate display overcomes the temporal, spectral, and field of view limitations of AOSLO-based stimulus presentation, enabling natural monocular viewing of stimuli in psychophysics experiments conducted with AOSLO.

Mouse brain elastography changes with sleep/wake cycles, aging, and Alzheimer's disease.

Understanding the physiological processes in aging and how neurodegenerative disorders affect cognitive function is a high priority for advancing human health. One specific area of recently enabled research is the in vivo biomechanical state of the brain. This study utilized reverberant optical coherence elastography, a high-resolution elasticity imaging method, to investigate stiffness changes during the sleep/wake cycle, aging, and Alzheimer's disease in murine models. Four-dimensional scans of 44 wildtype mice, 13 mice with deletion of aquaporin-4 water channel, and 12 mice with Alzheimer-related pathology (APP/PS1) demonstrated that (1) cortical tissue became softer (on the order of a 10% decrease in shear wave speed) when young wildtype mice transitioned from wake to anesthetized, yet this effect was lost in aging and with mice overexpressing amyloid-ß or lacking the water channel AQP4. (2) Cortical stiffness increased with age in all mice lines, but wildtype mice exhibited the most prominent changes as a function of aging. The study provides novel insight into the brain's biomechanics, the constraints of fluid flow, and how the state of brain activity affects basic properties of cortical tissues.

Framework for optimizing AR waveguide in-coupler architectures.

Waveguide displays have been shown to exhibit multiple interactions of light at the in-coupler diffractive surface, leading to light loss. Any losses at the in-coupler set a fundamental upper limit on the full-system efficiency. Furthermore, these losses vary spatially across the beam for each field, significantly decreasing the displayed image quality. We present a framework for alleviating the losses based on irradiance, efficiency, and MTF maps. We then derive and quantify the innate tradeoff between the in-coupling efficiency and the achievable modulation transfer function (MTF) characterizing image quality. Applying the framework, we show a new in-coupler architecture that mitigates the efficiency vs image quality tradeoff. In the example architecture, we demonstrate a computation speed that is 2,000 times faster than that of a commercial non-sequential ray tracer, enabling faster optimization and more thorough exploration of the parameter space. Results show that with this architecture, the in-coupling efficiency still meets the fundamental limit, while the MTF achieves the diffraction limit up to and including 30 cycles/deg, equivalent to 20/20 vision.

Multiconfiguration afocal freeform telescopes.

An approach to designing multiconfiguration afocal telescopes is developed and demonstrated. Freeform surfaces are used to maximize the achievable diffraction-limited zoom ratio while staying in a compact volume for a two-position multiconfiguration afocal optical system. The limitations of these systems with three-mirror beam paths are discussed and subsequently overcome by introducing an additional degree of freedom. In a four-mirror beam path system, the goal of a 5x zoom ratio is achieved with a compensated exit pupil and diffraction-limited performance. A significant benefit in optical performance when using freeform surfaces is shown compared to more conventional surface types.

Workflow for modeling of generalized mid-spatial frequency errors in optical systems.

We propose a workflow for modeling generalized mid-spatial frequency (MSF) errors in optical imaging systems. This workflow enables the classification of MSF distributions, filtering of bandlimited signatures, propagation of MSF errors to the exit pupil, and performance predictions that differentiate performance impacts due to the MSF distributions. We demonstrate the workflow by modeling the performance impacts of MSF errors for both transmissive and reflective imaging systems with near-diffraction-limited performance.

Alignment, calibration, and validation of an adaptive optics scanning laser ophthalmoscope for high-resolution human foveal imaging.

In prior art, advances in adaptive optics scanning laser ophthalmoscope (AOSLO) technology have enabled cones in the human fovea to be resolved in healthy eyes with normal vision and low to moderate refractive errors, providing new insight into human foveal anatomy, visual perception, and retinal degenerative diseases. These high-resolution ophthalmoscopes require careful alignment of each optical subsystem to ensure diffraction-limited imaging performance, which is necessary for resolving the smallest foveal cones. This paper presents a systematic and rigorous methodology for building, aligning, calibrating, and testing an AOSLO designed for imaging the cone mosaic of the central fovea in humans with cellular resolution. This methodology uses a two-stage alignment procedure and thorough system testing to achieve diffraction-limited performance. Results from retinal imaging of healthy human subjects under 30 years of age with refractive errors of less than 3.5 diopters using either 680 nm or 840 nm light show that the system can resolve cones at the very center of the fovea, the region where the cones are smallest and most densely packed.

Waveguide-based augmented reality displays: a highlight.

Augmented reality (AR), which emerged in the 1960s, remains a focal point of interest given its capacity to overlay the real world with digitally presented information through optical combiners. The prevalent combiner, commonly known as the waveguide in the AR literature, is prized for its compact design and generous eyebox-essential elements in human-centric technology. Nonetheless, these combiners encounter unique challenges in meeting various other requirements of the human visual system. This paper highlights a recent review of technological advancements and presents a forward-looking perspective on the future of AR technology.

Sigma vector calculations in nodal aberration theory and experimental validation using a Cassegrain telescope.

Nodal Aberration Theory (NAT) was developed to explain the field dependency of aberration field centers in the image plane of nominally rotationally symmetric optical systems that have lost their symmetry through misalignments. A new insight into the theory led to calculating the sigma vectors, which locate the aberration field centers, using the angle between a real-ray trace of the optical axis ray (OAR) and the normal of the local surface where "local" refers to the object and image optical spaces of that surface. Here, we detail the sigma vector calculations for general optical systems and provide an experimental investigation of a misaligned system with a high-precision customized Cassegrain telescope. In the simulations, a Newtonian telescope, a Cassegrain telescope, and a three-mirror anastigmat telescope were misaligned intentionally in ray-tracing software. The sigma vectors were calculated analytically for the third-order aberrations of astigmatism and coma. Experimentally, the same perturbations were implemented for the Cassegrain telescope system, and the aberrations were quantified through interferometric measurements on a grid of field points in the image plane that verified the analytical derivation and simulations.

Exit pupil quality analysis and optimization in freeform afocal telescope systems.

Afocal telescopes are often used as foreoptics to existing imaging systems to allow for application flexibility. To properly combine an afocal telescope with an existing imaging system, the exit pupil of the afocal telescope and the entrance pupil of the imaging system must be coincident. Additionally, the exit pupil of the afocal telescope must be well-formed; that is, it must be the correct size and shape to mitigate pupil-matching challenges. This work introduces processes for designing freeform afocal telescopes with an emphasis on understanding how to analyze and control the exit pupil quality of such systems. The included 3-mirror design examples demonstrate the advantages of using freeform surfaces in afocal systems and quantify the tradeoffs required to improve the exit pupil quality.

Fluid compartments influence elastography of the aging mouse brain.

Objective. Elastography of the brain has the potential to reveal subtle but clinically important changes in the structure and composition as a function of age, disease, and injury.Approach. In order to quantify the specific effects of aging on mouse brain elastography, and to determine the key factors influencing observed changes, we applied optical coherence tomography reverberant shear wave elastography at 2000 Hz to a group of wild-type healthy mice ranging from young to old age.Main results. We found a strong trend towards increasing stiffness with age, with an approximately 30% increase in shear wave speed from 2 months to 30 months within this sampled group. Furthermore, this appears to be strongly correlated with decreasing measures of whole brain fluid content, so older brains have less water and are stiffer. Rheological models are applied, and the strong effect is captured by specific assignment of changes to the glymphatic compartment of the brain fluid structures along with a correlated change in the parenchymal stiffness.Significance. Short-term and longer-term changes in elastography measures may provide a sensitive biomarker of progressive and fine-scale changes in the glymphatic fluid channels and parenchymal components of the brain.

Metagrating meets the geometry-based efficiency limit for AR waveguide in-couplers.

Recently, augmented reality (AR) displays have attracted considerable attention due to the highly immersive and realistic viewer experience they can provide. One key challenge of AR displays is the fundamental trade-off between the extent of the field-of-view (FOV) and the size of the eyebox, set by the conservation of etendue sets this trade-off. Exit-pupil expansion (EPE) is one possible solution to this problem. However, it comes at the cost of distributing light over a larger area, decreasing the overall system's brightness. In this work, we show that the geometry of the waveguide and the in-coupler sets a fundamental limit on how efficient the combiner can be for a given FOV. This limit can be used as a tool for waveguide designers to benchmark the in-coupling efficiency of their in-coupler gratings. We design a metasurface-based grating (metagrating) and a commonly used SRG as in-couplers using the derived limit to guide optimization. We then compare the diffractive efficiencies of the two types of in-couplers to the theoretical efficiency limit. For our chosen waveguide geometry, the metagrating's 28% efficiency surpasses the SRG's 20% efficiency and nearly matches the geometry-based limit of 29% due to the superior angular response control of metasurfaces compared to SRGs. This work provides new insight into the efficiency limit of waveguide-based combiners and paves a novel path toward implementing metasurfaces in efficient waveguide AR displays.

Intrinsic aberration coefficients for plane-symmetric optical systems consisting of spherical surfaces.

This paper presents the analytical form of the intrinsic aberration coefficients for spherical plane-symmetric optical systems expressed as a function of first-order system parameters and the paraxial chief and marginal ray angles and heights. The derived aberration coefficients are in the third and fourth groups with the multiplication of two or three vector products of pupil and field vectors.

100 years of Emil Wolf: introduction.

The groundbreaking research and ideas introduced by Emil Wolf continue to inspire researchers and motivate ongoing research in the wave properties of light. This special issue commemorates the legacy of Emil Wolf with research in physical optics, with specific focus on those areas where Wolf was active, such as optical coherence theory, inverse problems, singular optics, imaging, and polarization, and the intersection of these fields of study. Here we discuss the life of Emil Wolf and his influence on optical science and the optics community.

Implementation of a null test for freeform optics using a high-definition spatial light modulator.

We report the implementation of an interferometric null test using a high-definition spatial light modulator (SLM) as a reconfigurable alternative to a computer-generated hologram. We detail the alignment process chain, including novel techniques using the SLM to project alignment fiducials on the test part. To validate the alignment protocol, we measure a mild off-axis conic with the SLM-based system and cross-validate with conventional interferometry within 30 nm root-mean-square (RMS) surface figure. Finally, we report the null test of a 65 mm clear aperture concave freeform with 91 µm peak-valley sag departure from the base sphere. The measured surface figure of the freeform is within 40 nm RMS compared to the measurement with a commercial metrology instrument.

Theory of sleep/wake cycles affecting brain elastography.

As elastography of the brain finds increasing clinical applications, fundamental questions remain about baseline viscoelastic properties of the brainin vivo. Furthermore, the underlying mechanisms of how and why elastographic measures can change over time are still not well understood. To study these issues, reverberant shear wave elastography using an optical coherence tomography scanner is implemented on a mouse model, both under awake conditions and in a sleep state where there are known changes in the glymphatic fluid flow system in the brain. We find that shear wave speed, a measure of stiffness, changes by approximately 12% between the two states, sleep versus awake, in the entire cortical brain imaging volume. Our microchannel flow model of biphasic (fluid plus solid) tissue provides a plausible rheological model based on the fractal branching vascular and perivascular system, plus a second parallel system representing the finer scale glymphatic fluid microchannels. By adjusting the glymphatic system fluid volume proportional to the known sleep/wake changes, we are able to approximately predict the measured shear wave speeds and their change with the state of the glymphatic system. The advantages of this model are that its main parameters are derived from anatomical measures and are linked to other major derivations of branching fluid structures including Murray's Law. The implications for clinical studies are that elastography of the brain is strongly influenced by the regulation or dysregulation of the vascular, perivascular, and glymphatic systems.

Method for minimizing lens breathing with one moving group.

Lens breathing in movie cameras is the change in the overall content of a scene while bringing subjects located at different depths into focus. This paper presents a method for minimizing lens breathing or changing angular field-of-view while maintaining perspective by moving only one lens group. To maintain perspective, the stop is placed in a fixed position where no elements between the scene and the stop can move, thus fixing the entrance pupil in one location relative to the object fields. The result is perspective invariance while refocusing the lens. Using paraxial optics, we solve for the moving group's position to focus on every object position and eliminate breathing between the minimum and maximum object distances. We investigate the solution space for optical systems with two positive groups or a positive and a negative group (i.e., retrofocus and telephoto systems). We explain how to apply this paraxial solution to existing systems to minimize breathing. The results for two systems altered using this method are presented. Breathing improved by two orders of magnitude in both cases, and performance specifications were still met when compared to the initial systems.

Local Burr distribution estimator for speckle statistics.

Speckle statistics in ultrasound and optical coherence tomography have been studied using various distributions, including the Rayleigh, the K, and the more recently proposed Burr distribution. In this paper, we expand on the utility of the Burr distribution by first validating its theoretical framework with numerical simulations and then introducing a new local estimator to characterize sample tissues of liver, brain, and skin using optical coherence tomography. The spatially local estimates of the Burr distribution's power-law or exponent parameter enable a new type of parametric image. The simulation and experimental results confirm the potential for various applications of the Burr distribution in both basic science and clinical realms.