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A vibration-insensitive, single-shot phase-calibration method for phase-only spatial light modulators (SLM) is reported. The proposed technique uses a geometric phase lens to forma phase-shifting radial shearing interferometer to enable common-path measurements. This configuration has several advantages: (a) unlike diffraction-based SLM calibration techniques, this technique is robust against intensity errors due to misalignment; (b) unlike twobeam interferometers, this technique offers a high environmental stability; and (c) unlike intensity-based methods, the phase-shifting capability provides a phase uncertainty routinely in the order of 2=100. The experimental results show a significantly higher accuracy when compared to the diffraction-based approaches. © 2020 Optical Society of America https://doi.org/10.1364/AO.383610 

Freeform optics can reduce the cost, weight, and size of advanced imaging systems, but it is challenging to manufacture the complex rotationally asymmetric surfaces to optical tolerances. To address the need for disruptive, high-precision sub-aperture forming and finishing techniques for freeform optics, we investigate an alternative, non-contact polishing methodology using femtosecond lasers, combining modeling, experiments, and demonstrations. Femtosecondlaser- based polishing of germanium was investigated using an experimentally-validated twotemperature model of laser/germanium interaction to guide the understanding and selection of laser parameters to achieve near-nonthermal ablation for polishing and figuring. For the first time to our knowledge, model-guided femtosecond laser polishing of germanium was successfully demonstrated, achieving precision material removal while maintaining single-digit nanometer optical surface quality. The demonstrated femtosecond-laser-based polishing technique lays the foundation for semiconductor optics polishing/fabrication using femtosecond lasers and opens a viable path for high-precision, complex sub-aperture optical polishing tasks on various materials. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 

Specification and tolerancing of surfaces with mid-spatial frequency (MSF) errors are challenging and require new tools to augment simple surface statistics to better represent the structured characteristics of these errors. A novel surface specification method is developed by considering the structured and anisotropic nature of MSF errors and their impact on the modulation transfer function (MTF). The result is an intuitive plot of bandlimited RMS error values in polar coordinates which contains the surface error anisotropy information and enables an easy to understand acceptance criterion. Methods, application examples, and the connection of this surface specification approach to the MTF are discussed. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 

There are a variety of common situations in which specification of a onedimensional modulation transfer function (MTF) or two orthogonal profiles of the 2D MTF are not adequate descriptions of the image quality performance of an optical system. These include systems with an asymmetric on-axis impulse response, systems with off-axis aberrations, systems with surfaces that include mid-spatial frequency errors, and freeform systems. In this paper, we develop the concept of the Minimum Modulation Curve (MMC). Starting with the two-dimensional MTF in polar form, the minimum MTF for any azimuth angle is plotted as a function of the radial spatial frequency. This can be presented in a familiar form similar to an MTF curve and is useful in the context of guaranteeing that a given MTF specification is met for any possible orientation of spatial frequencies in the image. In this way, an MMC may be of value in specifying the required performance of an optical system. We illustrate application of the MMC using profile data for surfaces with midspatial frequency errors. © 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement 

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map that transforms the reflector’s shape into a curve that describes light’s direction after reflection. Both segmented reflectors and continuous reflectors are discussed, illustrating how certain reflector characteristics become apparent under this transformation. This method can also be used to study extended sources via translations. © 2019 Optical Society of America https://doi.org/10.1364/OL.44.003809