Zernike mapping of optimum dwell time in deterministic fabrication of freeform optics

Abstract

In optics fabrication technologies such as computer controlled optical surfacing (CCOS), accurate computation of the dwell time map plays an essential role in the deterministic performance of the fabrication process. However, it is still difficult for existing methods to derive smooth dwell time maps that reduce dynamic stressing on the machine especially at the aperture edge region, while retaining fine correction capability on freeform optics. To answer these challenges, we propose a new method based on Zernike decomposition and improved differential evolution optimization of the dwell time map, which can be applied to time-dependent optics fabrication processes such as fluid jet machining. Simulations and experiments based on a bisinusoidal freeform design were carried out to assess the feasibility of the proposed methodology. With appropriate fluid jet pressure, a bi-sinusoidal optical surface with demanding form error target of sub-100 nm in peak-to-valley was achieved, showing a remarkable improvement on the state-of-the-art, while keeping a good average surface roughness of 2.6 nm Ra on the optical glass.

A comprehensive review of dwell time optimization methods in computer-controlled optical surfacing

“…Additionally, parameterizing the surface error with Zernike polynomials [61] or B-spline surfaces [62] before dwell time optimization helps improve the smoothness of dwell time solutions, owing to the inherently smooth and continuous properties of these parametric modeling methods. The smoothness of the dwell time solution can be controlled by the order of Zernike polynomials or the number of knots of the B-spline surface, which also determines the number of total dwell points and computational efficiency.…”

“…For matrix-form methods seeking further smoothness, post-processing steps such as Zernike mapping [61] or B-spline fitting [62] can be applied to the calculated dwell time.…”

“…The matrix-form methods comprise the matrixform iterative method (MIM) [49], Tikhonov-regularized methods [11,16,17,29,30,31,50,51,52,53,54,55,56,57,58], constrained linear least-squares methods (CLLS) [30,59,60], and universal dwell time optimization method (UDO) [32]. Based on these matrix-form methods, modeling the surface error using Zernike polynomials [61] or B-splines [62] before dwell time optimization help obtain smoother dwell time solutions while maintaining a relatively sparser and more computationally efficient dwell time solver. Although these methods were developed independently and prioritized different objectives illustrated in Fig.…”

Fabrication of a 4 m SiC Aspheric Mirror Using an Optimized Strategy of Dividing an Error Map

“…Several methods can be used to divide an error map into low-order errors and middlehigh-order errors, including the average method, the 2Sigma formula, and the Fast Fourier Transform (FFT) algorithm. The use of Zernike polynomials is an effective method to fit the surface shape of an optical aspheric mirror [26]. The advantage of using Zernike polynomials for fitting low-order surface errors lies in its capability to effectively eliminate errors induced by misalignment.…”

Study on Design and Diamond Turning of Optical Freeform Surface for Progressive Addition Lenses

“…At present, the main methods of fabricating optical freeform surfaces include injection molded [5,6], grinding and polishing [7], raster milling [8,9], and diamond turning (or tool servo turning) [10][11][12][13]. In practical applications, appropriate processing methods are selected according to the comprehensive factors such as the material and size of the workpiece.…”