A task specific uncertainty analysis method for least-squares-based form characterization of ultra-precision freeform surfaces

M. J. Ren, Chi Fai Cheung, L. B. Kong

Research output: Journal article publicationJournal articleAcademic researchpeer-review

21 Citations (Scopus)

Abstract

In the measurement of ultra-precision freeform surfaces, least-squares-based form characterization methods are widely used to evaluate the form error of the measured surfaces. Although many methodologies have been proposed in recent years to improve the efficiency of the characterization process, relatively little research has been conducted on the analysis of associated uncertainty in the characterization results which may result from those characterization methods being used. As a result, this paper presents a task specific uncertainty analysis method with application in the least-squares-based form characterization of ultra-precision freeform surfaces. That is, the associated uncertainty in the form characterization results is estimated when the measured data are extracted from a specific surface with specific sampling strategy. Three factors are considered in this study which include measurement error, surface form error and sample size. The task specific uncertainty analysis method has been evaluated through a series of experiments. The results show that the task specific uncertainty analysis method can effectively estimate the uncertainty of the form characterization results for a specific freeform surface measurement.
Original languageEnglish
Article number054005
JournalMeasurement Science and Technology
Volume23
Issue number5
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • form characterization
  • freeform surface
  • least-squares method
  • precision metrology
  • uncertainty analysis

ASJC Scopus subject areas

  • Instrumentation
  • Applied Mathematics

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