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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 19 — Jul. 1, 2014
  • pp: 4266–4274

Mathematical modeling and application of removal functions during deterministic ion beam figuring of optical surfaces. Part 1: Mathematical modeling

Wenlin Liao, Yifan Dai, Xuhui Xie, and Lin Zhou  »View Author Affiliations

Applied Optics, Vol. 53, Issue 19, pp. 4266-4274 (2014)

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Ion beam figuring (IBF) is established for the final precision figuring of high-performance optical components, where the figuring accuracy is guaranteed by the stability of the removal function and the solution accuracy of the dwell time. In this deterministic method, the figuring process can be represented by a two-dimensional (2D) convolution operation of a constant removal function and the dwell time. However, we have found that the current 2D convolution operation cannot factually describe the IBF process of curved surfaces, which neglects the influences of the projection distortion and the workpiece geometry on the removal function. Consequently, the current 2D convolution algorithm would influence the solution accuracy for the dwell time and reduce the convergence of the figuring process. In this part, based on the material removal characteristics of IBF, a mathematical model of the removal function is developed theoretically and verified experimentally. Research results show that the removal function during IBF of a curved surface is actually a dynamic function in the 2D convolution algorithm. The mathematical modeling of the dynamic removal function provides theoretical foundations for our proposed new algorithm in the next part, and final verification experiments indicate that this algorithm can effectively improve the accuracy of the dwell time solution for the IBF of curved surfaces.

© 2014 Optical Society of America

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.4610) Optical design and fabrication : Optical fabrication
(220.5450) Optical design and fabrication : Polishing

ToC Category:
Optical Design and Fabrication

Original Manuscript: March 6, 2014
Revised Manuscript: May 27, 2014
Manuscript Accepted: May 27, 2014
Published: June 30, 2014

Wenlin Liao, Yifan Dai, Xuhui Xie, and Lin Zhou, "Mathematical modeling and application of removal functions during deterministic ion beam figuring of optical surfaces. Part 1: Mathematical modeling," Appl. Opt. 53, 4266-4274 (2014)

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