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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. 

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. 

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. 

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. 

Tolerancing is a critical step in creating successful commercial products. We explore recent advances in tolerancing illumination optics with particular emphasis on surface perturbations and extended sources. 

We consider the requirements for first-order pupil location control using the matrix method for both finite-conjugate systems and afocal systems at infinite imaging conjugates. We show that two-element systems allow for only limited pupil location control, while with three elements or more the first-order pupil locations can be freely and independently controlled. 

A spatial light modulator is deployed as the nulling element in the interferometric measurement of a freeform optic. Form measurement of a 65 mm aperture concave freeform with 91 μm peak-valley freeform sag is reported. 

This work demonstrates the utility of a design, fabrication, and testing loop on 10 mm diameter metalenses to accelerate large-scale production of flat optics. By enabling rapid measurement and analysis of metalenses, it is possible to identify differences between designed performance and as-built performance quickly and correlate those to process characteristics. This accelerated feedback between the design, fabrication, and testing is expected to enable higher yields of better-performing metalenses. 

Metaforms are novel optical components formed by conforming a metasurface to a freeform substrate. Metaforms can be a powerful solution when designing compact imaging systems such as augmented reality displays. Given the rotationally variant nature of the metaform substrate and the difficulty of metasurface fabrication on curved substrates, the proper alignment of the metasurface nanofeatures to the freeform substrate is essential. Thus, to seamlessly bridge the metaform design, manufacturing, and metrology, we developed a software tool that automatically generates ISO standard highaccuracy CAD models for the designed metaform components.