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Nodal aberration theory (NAT) is a vectorized aberration theory that was developed to describe systems without rotational symmetry. NAT predicts non-rotationally symmetric aberration field dependences for third-order astigmatism and in particular a “binodal” behavior in which there are two points in the field of view where astigmatism vanishes. This study serves to demonstrate an alignment technique based on an understanding of this binodal behavior using a custom Ritchey-Chretien telescope. A method involving a commercial Shack-Hartmann compact-format wavefront sensor was developed to rapidly measure densely sampled full-field displays of the telescope, which has its secondary mirror mounted on a precision hexapod to allow for repeatable control of the telescope alignment. Real ray-based simulations were carried out on a model of the telescope and were consistent with the observed experimental results for both aligned and misaligned states of the telescope. We then provide guidelines on how to interpret Fringe Zernike astigmatism full-field displays for use during optical system alignment. This method is particularly relevant for freeform systems, which often have asymmetric field dependencies for multiple aberration types including astigmatism. 

Conventional refractive microscope objective lenses have limited applicability to a range of imaging modalities due to the dispersive nature of their optical elements. Designing a conventional refractive microscope objective that provides well-corrected imaging over a broad spectral range can be challenging, if not impossible. In contrast, reflective optics are inherently achromatic, so a system composed entirely of reflective elements is free from chromatic aberrations and, as a result, can image over an ultra-wide spectral range with perfect color correction. This study explores the design space of unobscured high numerical aperture, all-reflective microscope objectives. In particular, using freeform optical elements we obviate the need for a center obscuration, rendering the objective’s modulation transfer function comparable to that of refractive lens systems of similar numerical aperture. We detail the design process of the reflective objective, from determining the design specifications to the system optimization and sensitivity analysis. The outcome is an all-reflective freeform microscope objective lens with a 0.65 numerical aperture that provides diffraction-limited imaging and is compatible with the geometric constraints of commercial microscope systems. 

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 demonstrate nano-structuring and the reduction of mid-spatial-frequency errors using femtosecond laser figuring and finishing. For the first time, to the best of our knowledge, we have corrected mid-spatial-frequency errors from 17 nm to one nanometer in magnitude. We established a method for creating and predicting periodic nanostructures. This demonstration opens the path of using femtosecond lasers to correct surface errors that inherently result from sub-aperture manufacturing techniques.