The convex reflective diffraction grating is an essential optical component that lends itself to various applications. In this work, we first outline the design principles of convex diffraction gratings from wavefront quality and efficiency perspectives. We then describe a unique fabrication method that allows for the machining of convex diffraction gratings with variable groove structure, which is extendable to rotationally non-symmetric convex diffraction grating substrates. Finally, we demonstrate two quantitative wavefront measurement methods and respective experimental validation.

Surface metrology instruments normally require thermal, seismic and acoustic isolation. Shop-floor metrology solutions offer reduced cost and process time. If they operate on the same principles as laboratory devices, an inherent sensitivity to vibration remains. This paper describes a methodology for evaluating 'environmental tolerance' and applying it to characterize a recently introduced 'environmentally tolerant' scanning white light interferometer (SWLI). Previously published measurements of replicated nickel reference standards on the new instrument and on a stylus profilometer showed good correlation. Surface topography repeatabilities (per ISO 25178-604:2013) were insignificantly different when evaluated on the SWLI instrument in a metrology laboratory and in a manufacturing area. Measurements of reference standards under forced vibration of the entire instrument show maximum ripple error and data dropout in regions of structural resonance. Measurements were performed with large forced horizontal and vertical sample oscillation beneath the objective, exhibiting maximum ripple error near odd integer multiples of half the instrument detector frequency. Error due to data dropout was also investigated.

This paper introduces a new discrete time continuous wavelet transform (DTCWT)-based algorithm, which can be implemented in real time to quantify and compensate periodic error for constant and non-constant velocity motion in heterodyne displacement measuring interferometry. It identifies the periodic error by measuring the phase and amplitude information at different orders (the periodic error is modeled as a summation of pure sine signals), reconstructs the periodic error by combining the magnitudes for all orders, and compensates the periodic error by subtracting the reconstructed error from the displacement signal measured by the interferometer. The algorithm is validated by comparing the compensated results with a traditional frequency domain approach for constant velocity motion. The algorithm demonstrates successful reduction of the first order periodic error amplitude from 4 nm to 0.24 nm (a 94% decrease) and a reduction of the second order * Corresponding author. Tel.: +1 803 777 8236; fax: +1 803 777 0106. E-mail address: JAT@sc.edu (J.A. Tarbutton). 2 periodic error from 2.5 nm to 0.3 nm (an 88% decrease). The algorithm also reduces periodic errors for non-constant velocity motion overcoming limitations of existing methods.

Freeform germanium optics produced by single crystal diamond milling are important for infrared (IR) imaging applications.However the mechanics of interrupted cutting of germaniumis not fully understood. This paper presents new findings from cutting experiments including: (1) uninterrupted orthogonal cutting and (2) interruptedflycutting of germanium. Forces are measured and the cutting mechanics are correlated with surface and subsurface measurements performed with: (1) atomic force microscopy, (2) confocal Raman spectroscopy, and (3) channeling Rutherford backscattering spectrometry. These fundamental results guide parameter choice for more complex freeform ball milling of optics for IR applications ranging from surveillance to medical imaging. Ultra-precision milling, Optical materials, Subsurface damage Figure 1.(a) Orthogonal turning setup and (b) schematic.

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