Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise

Rajesh Langoju; Abhijit Patil; Pramod Rastogi

doi:10.1364/OL.31.001058

Optics Letters
Vol. 31,
Issue 8,
pp. 1058-1060
(2006)
•https://doi.org/10.1364/OL.31.001058

Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise

Rajesh Langoju, Abhijit Patil, and Pramod Rastogi

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Rajesh Langoju, Abhijit Patil, and Pramod Rastogi, "Phase-shifting interferometry in the presence of nonlinear phase steps, harmonics, and noise," Opt. Lett. 31, 1058-1060 (2006)

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Abstract

A phase-shifting piezo device commonly employed in phase-shifting interferometry exhibits a nonlinear response to applied voltage. Hence, a method for estimation of phase distribution in the presence of nonlinear phase steps is presented. The proposed method compensates for the harmonics present in the intensity fringe, allows the use of arbitrary phase-step values between 0 and $π rad$ , and does not impose constraints on the selection of particular phase-step values for minimizing nonlinearity and compensating for the harmonics. The comparison of the proposed method with other well-known benchmarking algorithms shows that our method is highly efficient and also works well in the presence of noise.

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$ϵ_{1}$	$ϵ_{2}$	$N = 6$ , $K = 1$		$ϵ_{1}$	$ϵ_{2}$	$N = 9$ , $K = 2$
$ϵ_{1}$	$ϵ_{2}$	Our Method	Hibino Algorithm	$ϵ_{1}$	$ϵ_{2}$	Our Method	Hibino Algorithm
0.1	0.00	$7.49 \times 10^{- 8}$	$3.48 \times 10^{- 4}$	0.1	0.01	$2.12 \times 10^{- 4}$	$2.17 \times 10^{- 2}$
0.0	0.20	$6.58 \times 10^{- 8}$	$9.62 \times 10^{- 3}$	0.0	0.05	$1.32 \times 10^{- 4}$	$3.16 \times 10^{- 2}$
0.1	0.20	$1.26 \times 10^{- 8}$	$1.43 \times 10^{- 2}$	0.1	0.05	$2.94 \times 10^{- 6}$	$1.33 \times 10^{- 1}$
0.0	0.40	$3.35 \times 10^{- 8}$	$3.72 \times 10^{- 2}$	0.0	0.10	$9.97 \times 10^{- 6}$	$1.97 \times 10^{- 1}$
0.1	0.40	$3.34 \times 10^{- 8}$	$3.20 \times 10^{- 2}$	0.1	0.10	$1.46 \times 10^{- 5}$	$4.05 \times 10^{- 1}$

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Optics Letters