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A recently reported vision ray metrology technique [Opt. Express29,43480(2021)OPEXFF1094-408710.1364/OE.443550] measures geometric wavefronts with high precision. This paper introduces a method to convert these wavefront data into height information, focusing on the impact of back surface flatness and telecentricity errors on measurement accuracy. Systematic errors from these factors significantly affect height measurements. Using ray trace simulations, we estimate reconstruction errors with various plano-concave and plano-convex elements. We also developed a calibration technique to mitigate telecentricity errors, achieving submicron accuracy in surface reconstruction. This study provides practical insights into vision ray metrology systems, highlighting validity limits, emphasizing the importance of calibration for larger samples, and establishing system alignment tolerances. The reported technique for the conversion of geometric wavefronts to surface topography employs a direct non-iterative ray-tracing-free method. It is ideally suited for reference-free metrology with application to freeform optics manufacturing. 

We report the experimental demonstration of an optical differentiation wavefront sensor (ODWS) based on binary pixelated linear and nonlinear amplitude filtering in the far-field. We trained and tested a convolutional neural network that reconstructs the spatial phase map from nonlinear-filter-based ODWS data for which an analytic reconstruction algorithm is not available. It shows accurate zonal retrieval over different magnitudes of wavefronts and on randomly shaped wavefronts. This work paves the way for the implementation of simultaneously sensitive, high dynamic range, and high-resolution wavefront sensing. 

Reimaging telescopes have an accessible exit pupil that facilitates stray light mitigation and matching to auxiliary optical systems. Freeform surfaces present the opportunity for unobscured reflective systems to be folded into geometries that are otherwise impracticable with conventional surface types. It is critical, however, to understand the limitations of the enabled folding geometries and choose the one that best balances the optical performance and mechanical requirements. Here, we used the aberration theory of freeform surfaces to determine the aberration correction potential for using freeform surfaces in reimaging three-mirror telescopes and established a hierarchy for the different folding geometries without using optimization. We found that when using freeform optics, the ideal folding geometry had 9× better wavefront performance compared to the next best geometry. Within that ideal geometry, the system using freeform optics had 39% better wavefront performance compared to a system using off-axis asphere surfaces, thus quantifying one of the advantages of freeform optics in this design space. 

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. 

Afocal telescopes are often used as foreoptics to existing imaging systems. Here, we discuss some unique aspects of designing afocal systems and detail various afocal design studies we performed using freeform optics. 

We developed, tested, and applied a software tool that automatically generates high-accuracy CAD models of freeform elements with datums and fiducials, facilitating the efficient transition from freeform design to fabrication and measurement. 

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. 

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. 

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. 

Traditional optical manufacturing techniques such as abrasive polishing and diamond turning create precise surfaces by removing material from the optical surface of a mirror. Such techniques often require many cycles of removal and metrology and can leave surface roughness or tool marks that negatively affect the straylight properties of an optical system. These residual artifacts often necessitate expensive postprocessing such as ion beam finishing. Limiting straylight is particularly crucial in the design of reflecting coronagraphs or optical systems that are sensitive to scattered light, for example for exoplanet detection, where even low-level scattering can degrade contrast ratios below the sensitivity needed to detect exoplanets. We introduce a non-contact method for shaping thin front-surface mirrors to avoid tool artifacts. Using laser techniques to alter local surface stresses, we deterministically introduce ≥ 8 waves (632.8 nm) of shape to 2 mm thick substrates. A deterministic method for creating arbitrary surface figures is under development and calibration.