An investigation of the robustness of the nonlinear least-squares sphere fitting method to small segment angle surfaces
An investigation of the robustness of the nonlinear least-squares sphere fitting method to small segment angle surfaces
This paper presents an investigation of the nonlinear least-squares sphere fitting algorithm (TLSA). The work concentrates on investigating the reliability of the TLSA algorithm when applied to a small segment angle of a sphere. The definition of small segment angle is discussed in the paper and taken to be below 1° (in both x and y directions) of the spherical surface. This application of the TLSA method is important when it is used on data from optical scanning systems where the measurements are limited by the gauge range and the angular tolerance of the sensor. The TLSA algorithm has been first compared with the TLSD algorithm suggested by Forbes for this application. The results show that the TLSA algorithm can be used in small surface segment angles. The main study is focused on testing the algorithm on a sphere superimposed with surface irregularities (sensor/measurement noise or roughness). Two properties of the TLSA algorithm are covered: the bias and the uncertainty of the estimated radius. Both simulation and theoretical approaches have been attempted. A new algorithm to estimate the bias of the TLSA algorithm has been derived in this paper based on Box's method. Together with uncertainty estimation, which can be produced by using either a conventional method or Zhang's error propagation function (EPF), a comprehensive understanding of the TLSA algorithm in this application is thus achieved, and used to develop a number of recommendations for the precision metrology of spherical and near spherical surfaces.
nonlinear least-squares, sphere fitting, small segment angle, bias, uncertainty
55-62
Sun, Wenjuan
85a2b297-f55f-48a7-9059-a769aade3b89
Hill, Martyn
0cda65c8-a70f-476f-b126-d2c4460a253e
McBride, John W.
d9429c29-9361-4747-9ba3-376297cb8770
January 2008
Sun, Wenjuan
85a2b297-f55f-48a7-9059-a769aade3b89
Hill, Martyn
0cda65c8-a70f-476f-b126-d2c4460a253e
McBride, John W.
d9429c29-9361-4747-9ba3-376297cb8770
Sun, Wenjuan, Hill, Martyn and McBride, John W.
(2008)
An investigation of the robustness of the nonlinear least-squares sphere fitting method to small segment angle surfaces.
Precision Engineering, 32 (1), .
(doi:10.1016/j.precisioneng.2007.04.008).
Abstract
This paper presents an investigation of the nonlinear least-squares sphere fitting algorithm (TLSA). The work concentrates on investigating the reliability of the TLSA algorithm when applied to a small segment angle of a sphere. The definition of small segment angle is discussed in the paper and taken to be below 1° (in both x and y directions) of the spherical surface. This application of the TLSA method is important when it is used on data from optical scanning systems where the measurements are limited by the gauge range and the angular tolerance of the sensor. The TLSA algorithm has been first compared with the TLSD algorithm suggested by Forbes for this application. The results show that the TLSA algorithm can be used in small surface segment angles. The main study is focused on testing the algorithm on a sphere superimposed with surface irregularities (sensor/measurement noise or roughness). Two properties of the TLSA algorithm are covered: the bias and the uncertainty of the estimated radius. Both simulation and theoretical approaches have been attempted. A new algorithm to estimate the bias of the TLSA algorithm has been derived in this paper based on Box's method. Together with uncertainty estimation, which can be produced by using either a conventional method or Zhang's error propagation function (EPF), a comprehensive understanding of the TLSA algorithm in this application is thus achieved, and used to develop a number of recommendations for the precision metrology of spherical and near spherical surfaces.
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Published date: January 2008
Keywords:
nonlinear least-squares, sphere fitting, small segment angle, bias, uncertainty
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Local EPrints ID: 48987
URI: http://eprints.soton.ac.uk/id/eprint/48987
ISSN: 0141-6359
PURE UUID: d05dbae1-17e5-49a2-aa00-2fac5c36a40d
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Date deposited: 25 Oct 2007
Last modified: 16 Mar 2024 02:41
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Author:
Wenjuan Sun
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