Description and reimplementation of real freeform surfaces

Abstract

Freeform surfaces are becoming an increasingly exciting opportunity in optical design, in particular when correcting systems with off-axis geometries. Nevertheless, especially when coming to commercial use, the challenges for manufacturing are difficult to handle. The optical quality of a system is perturbed by typical deformations, such as localized figure errors and regular mid-spatial-frequency ripples, that come from the diamond-turning process. In this proposal, we investigated a workflow for analyzing the impact of real optical surfaces on the optical performance for even complex systems. Based on a simple and robust description, the surface is implemented back into the design. While the more localized deviations are analytically described by radial basis functions, the residual ripple structures are covered by a new approach based on the power spectral density. The reimport of optical surfaces back into the design software allows simple estimations for the requirements on manufacturing and the analysis of the realistic impact on system performance.

Design, additive manufacturing, processing, and characterization of metal mirror made of aluminum silicon alloy for space applications

“…Analyzing and correcting those parts of the surface deviation are under current investigation. [27][28][29][30][31] The measurement is done using a Zygo interferometer, piston and tilt have been removed from the data, and the aperture was set to 72 mm (therefore removing some edge effects from polishing).…”

Analysis of freeform mirror systems based on the decomposition of the total wave aberration into Zernike surface contributions

“…Thus, to describe the real surface typically a large number of coefficients is necessary if a globally valid polynomial set is used [45]. Alternatively, the deviation from the ideal shape can be described using local descriptions such as lateral shifted radial basis functions (RBFs) [20]:…”

“…After the design stage, it is necessary to assess the performance of the "as-built" freeform system. In this case local representations such as radial basis functions (RBF) appeared to be appropriate to reproduce the manufacturing artifacts [20].…”

“…The geometry for deriving the OPD resulting from refraction on the surface of an ideal incoming wavefront.Thus, OPD accumulated along the real ray (RR) as a result of refraction is obtained as the deviation from the spherical wavefront:=´̅ ̅̅̅̅ −´̅ ̅̅̅̅ = ´̅ ̅̅̅̅ − ̅̅̅̅ (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). …”