Robust linear equation dwell time model compatible with large scale discrete surface error matrix
- 25 March 2015
- journal article
- Published by Optica Publishing Group in Applied Optics
- Vol. 54 (10), 2747-2756
- https://doi.org/10.1364/ao.54.002747
Abstract
The linear equation dwell time model can translate the 2D convolution process of material removal during subaperture polishing into a more intuitional expression, and may provide relatively fast and reliable results. However, the accurate solution of this ill-posed equation is not so easy, and its practicability for a large scale surface error matrix is still limited. This study first solves this ill-posed equation by Tikhonov regularization and the least square QR decomposition (LSQR) method, and automatically determines an optional interval and a typical value for the damped factor of regularization, which are dependent on the peak removal rate of tool influence functions. Then, a constrained LSQR method is presented to increase the robustness of the damped factor, which can provide more consistent dwell time maps than traditional LSQR. Finally, a matrix segmentation and stitching method is used to cope with large scale surface error matrices. Using these proposed methods, the linear equation model becomes more reliable and efficient in practical engineering.Keywords
Funding Information
- National Natural Science Foundation of China (NSFC) (61308075, 61222506)
- Specialized Research Fund for the Doctoral Program of Higher Education (20131101110026)
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