Abstract

Two complementary methods have now been proposed for deriving phase-shifting algorithms that correct for both nonlinear and spatially nonuniform phase shifts. Some advantages of symmetrical algorithms are outlined, and a simple method for ensuring algorithmic symmetry is presented. Noise susceptibility of the algorithms and the phase-shifter calibration are also discussed briefly.

© 1998 Optical Society of America

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References

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  1. Y. Surrel, “Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts: comment,” J. Opt. Soc. Am. A 15, 1227–1233 (1998).
    [CrossRef]
  2. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35, 51–60 (1996).
    [CrossRef] [PubMed]
  3. K. Hibino, B. F. Oreb, D. I. Farrant, K. G. Larkin, “Phase-shifting algorithms for nonlinear and spatially nonuniform phase shifts,” J. Opt. Soc. Am. A 14, 918–930 (1997).
    [CrossRef]
  4. K. Hibino, “Susceptibility of systematic error-compensating algorithms to random noise in phase-shifting interferometry,” Appl. Opt. 36, 2084–2093 (1997).
    [CrossRef] [PubMed]

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Equations (6)

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tan[ϕ(x, y)]=n=-NNsnI(x, y, α-nδ)n=-NNcnI(x, y, α-nδ).
tan[ϕ(x, y)+θ]=n=-NNsnI(x, y, α-nδ)n=-NNcnI(x, y, α-nδ).
sn2+cn2=s-n2+c-n2,
tan θ=-sn+s-ncn+c-n=cn-c-nsn-s-n.
sn={cn-c-n}cn+{sn-s-n}sn
cn={sn-s-n}cn-{cn-c-n}sn.

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