Accurate and fast two-step phase shifting algorithm based on principle component analysis and Lissajous ellipse fitting with random phase shift and no pre-filtering

Yu Zhang, Xiaobo Tian, Rongguang Liang

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1 Citation (Scopus)

Abstract

To achieve high measurement accuracy with less computational time-in-phase shifting interferometry, a random phase-shifting algorithm based on principal component analysis and Lissajous ellipse fitting (PCA&LEF) is proposed. It doesn’t need pre-filtering and can obtain relatively accurate phase distribution with only two phase shifted interferograms and less computational time and is suitable for different background intensity, modulation amplitude distributions and noises. Moreover, it can obtain absolutely accurate result when the background intensity and modulation amplitude are perfect and can partly suppress the effect of imperfect background intensity and modulation amplitude. Last but not least, it removes the restriction that PCA needs more than three interferograms with well-distributed phase shifts to subtract relatively accurate mean. The simulations and experiments verify the correctness and feasibility of PCA&LEF.

Original languageEnglish (US)
JournalOptics letters
Volume27
Issue number14
DOIs
StatePublished - Jan 1 2019

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ellipses
interferometry
phase shift
principal components analysis
constrictions
simulation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

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title = "Accurate and fast two-step phase shifting algorithm based on principle component analysis and Lissajous ellipse fitting with random phase shift and no pre-filtering",
abstract = "To achieve high measurement accuracy with less computational time-in-phase shifting interferometry, a random phase-shifting algorithm based on principal component analysis and Lissajous ellipse fitting (PCA&LEF) is proposed. It doesn’t need pre-filtering and can obtain relatively accurate phase distribution with only two phase shifted interferograms and less computational time and is suitable for different background intensity, modulation amplitude distributions and noises. Moreover, it can obtain absolutely accurate result when the background intensity and modulation amplitude are perfect and can partly suppress the effect of imperfect background intensity and modulation amplitude. Last but not least, it removes the restriction that PCA needs more than three interferograms with well-distributed phase shifts to subtract relatively accurate mean. The simulations and experiments verify the correctness and feasibility of PCA&LEF.",
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AB - To achieve high measurement accuracy with less computational time-in-phase shifting interferometry, a random phase-shifting algorithm based on principal component analysis and Lissajous ellipse fitting (PCA&LEF) is proposed. It doesn’t need pre-filtering and can obtain relatively accurate phase distribution with only two phase shifted interferograms and less computational time and is suitable for different background intensity, modulation amplitude distributions and noises. Moreover, it can obtain absolutely accurate result when the background intensity and modulation amplitude are perfect and can partly suppress the effect of imperfect background intensity and modulation amplitude. Last but not least, it removes the restriction that PCA needs more than three interferograms with well-distributed phase shifts to subtract relatively accurate mean. The simulations and experiments verify the correctness and feasibility of PCA&LEF.

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