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  1. 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 
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  2. 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 
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  3. Mid-spatial frequency (MSF) errors impact optical performance. Conventional surface specification methods assume isotropy, which gives misleading results for surfaces with anisotropic errors. We propose an alternate surface specification method. © 2019 The Author(s) OCIS codes: (120.0120) Instrumentation, measurement, and metrology; (220.0220) Optical design and fabrication. 
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  4. Sub-aperture manufacturing creates anisotropic surface errors, and modulation transfer functions (MTF) not well represented by 1D cross-sections. We present a 1D ‘non-directional’ MTF for specification and characterization of optical surface errors. © 2019 The Author(s) OCIS codes: (110.4100) Modulation transfer function; (220.0220) Optical design and fabrication. 
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  5. This paper provides a practical connection between the Strehl ratio as an optical performance metric and manufacturing parameters for diamond-machined optics. The choice of fabrication parameters impacts residual midspatial frequency groove structures over the part’s surface, which reduce optical performance. Connections between the Strehl ratio and the fabrication parameters are studied using rigorous Rayleigh–Sommerfeld simulations for a sample optical system. The connections are generalized by incorporating the shape of diamond-machined groove structures and the effects of optical path differences for both transmissive and reflective optics. This work validates the analytical representation of the Strehl ratio as a Fourier transform of a probability density that relates to surface errors. The result is a practical tool that can be used to guide the choice of machining parameters to achieve a targeted optical performance. © 2019 Optical Society of America https://doi.org/10.1364/AO.58.003272 
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