Frequency-domain analysis of computer-controlled optical surfacing processes

Abstract

Mid-high spatial frequency errors are often induced on optical surfaces polished by computer-controlled optical surfacing (CCOS) processes. In order to efficiently remove these errors, which would degrade the performances of optical systems, the ability of a CCOS process to correct the errors have been investigated based on the convolution integral model in view of the availability of material removal. To quantify the ability, some conceptions, such as figure correcting ability and material removal availability (MRA), have been proposed. The research result reveals that the MRA of the CCOS process to correct a single spatial frequency error is determined by its tool removal function (TRF), and it equals the normalized amplitude spectrum of the Fourier transform of its TRF. Finally, three sine surfaces were etched using ion beam figuring (IBF), which is a typical CCOS process. The experimental results have verified the theoretical analysis. The employed method and the conclusions of this work provide a useful mathematical basis to analyze and optimize CCOS processes.

Obliquely incident ion beam figuring

“…10 But this effect is very low because the change in the size of the removal function is not significant. The calculations in the Sec.…”

Combined figuring technology for high-precision optical surfaces using a deterministic ion beam material adding and removal method

“…Based on this model, we have defined a figure of merit, named material removal availability r, to evaluate the correcting capability of the removal function, 3,8 given as follows:…”

Extracting of removal function in CCOS based on edge detection algorithm

“…Compared with theoretical modeling method，experiment modeling method is a kind of more accuracy approach to obtain removal function. The basic process of this method could be described like this: (1) Polishing a removal spot on the sample surface at first; (2) Measuring the full surface figure data by interferometry technology; (3) Extracting the removal area data based on the figure measuring result. In the process mentioned above we can obtain the removal function.…”

“…Computer controlled optical surfacing (CCOS) technology, which was proposed by Itek company (in American) in 1970s, is a kind of small tool polishing method [1][2] . This technology points out that target material removal quantity ( ) , F x y equal to the two-dimensional convolution of dwell time matrix ( ) , T x y and removal function ( )…”