Abstract
Standard mid-spatial frequency tooling mark errors were parameterized into a series of characteristic features and systematically investigated. Diffraction encircled and ensquared energy radii at the 90% levels from an unpowered optical surface were determined as a function of the root-mean-square surface irregularity, characteristic tooling mark parameters, fold mirror rotation angle, and incident beam f-number. Tooling mark frequencies on the order of 20 cycles per aperture or less were considered. This subset encompasses small footprints on single-point diamond turned optics or large footprints on sub-aperture tool polished optics. Of the characteristic features, off-axis fabrication distance held the highest impact to encircled and ensquared energy radii. The transverse oscillation of a tooling path was found to be the second highest contributor. Both impacts increased with radial tooling mark frequency.
Highlights
The nature of standard fabrication techniques such as single-point diamond turning (SPDT) and sub-aperture tool polishing (SATP) leads to a meaningful subset of these marks being periodic with well-defined forms [1]
Tooling marks (TM) are thoroughly described through a variety of analytical techniques, including but not limited to Fourier decomposition of the surface profile [2,3,4,5], analysis of power spectral density (PSD) based on the tool influence function and path [6,7], anisotropic error representation via polar root-mean-square (RMS) surface figure plotting [8], and surface fitting of mid-spatial frequency (MSF) errors via Q-polynomials [9]
To describe the anticipated surface errors imposed by various forms of TMs, the contributions are decomposed into a pair of terms as shown in Equation (1)
Summary
Tooling marks (TM) refer to unwanted errors in the surface figure of an optic, which are a byproduct of the means of fabrication. There exist standards to quantify the uncertainty between the measured and modelled data [10,11,12]. These approaches allow for thresholds to be determined for allowable deviation of a tooling shape from a specific TM form assumed for these rigorous models. These inputs are simulated to achieve a parametric optical model to describe diffraction encircled and ensquared spot radii. From this point, standard uncertainty definitions could be applied
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