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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. 

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. 

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. 

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. 

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. 

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. 

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. 

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. 

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.