State-space modeling approach for fringe pattern demodulation

Shikha Sharma; Rishikesh Kulkarni

doi:10.1364/AO.496722

Applied Optics
Vol. 62,
Issue 27,
pp. 7330-7337
(2023)
•https://doi.org/10.1364/AO.496722

State-space modeling approach for fringe pattern demodulation

Shikha Sharma and Rishikesh Kulkarni

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Shikha Sharma and Rishikesh Kulkarni, "State-space modeling approach for fringe pattern demodulation," Appl. Opt. 62, 7330-7337 (2023)

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Abstract

A spatial carrier fringe demodulation technique is proposed based on a state-space modeling approach for phase estimation. The fringe background intensity, carrier frequency, and phase quadrature components are considered to be the elements of the state vector, which are estimated simultaneously. The state estimation is performed using the extended Kalman filter. The simulation and experimental results are provided to demonstrate the performance comparison of the proposed method with popular and state-of-the-art methods in terms of noise robustness and phase estimation accuracy.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Methods	Algorithm Parameters
FT [9]	Half plane filtering of Fourier spectrum of fringe pattern
WFT [17]	$σ = 10$ , [ $ω x l, ω y l] = [- 0.5, 0.2]$ , [ $ω x h, ω y h] = [0.5, 1.8]$ , $ω x i = 0.1$ , $ω y i = 0.1$ , $T h r = 1$ .
ECKF [28]	${\hat{μ}}_{0}^{+} = [\exp [j (π / 5)]; \exp [j (π / 5)]; \exp [- j (π / 5)]], P_{0}^{+} = d i a g ([1; 10^{2}; 10^{2}])$ , $Q_{x} = d i a g ([0.01; 10^{2}; 10^{2}]), R_{x} = 10$ .
EKF	$P_{0}^{+} = d i a g ([10^{- 2}; 10^{- 2}; 10^{2}; 10^{2}]), Q_{x} = d i a g ([10; 10^{- 4}; 10^{3}; 10^{3}]), R_{0} = 1; β = 0.5$ ,
	$b = (max (I) - min (I)) / 2$ , ${\hat{α}}_{0}^{+} = [m e a n (I); π / 5; b \cos (π / 6 + π / 5); b \sin (π / 6 + π / 5)]$ .

Methods
	Computational Time (in Seconds)
Size (in Pixels)	FT	WFT	ECKF	EKF
$400 \times 400$	0.011	2.28	3.51	1.314
$576 \times 768$	0.0202	7.89	9.15	2.84
$651 \times 621$	0.0186	9.06	8.76	3.09

Methods	Algorithm Parameters
FT [9]	Half plane filtering of Fourier spectrum of fringe pattern
WFT [17]	$σ = 10$ , [ $ω x l, ω y l] = [- 0.5, 0.2]$ , [ $ω x h, ω y h] = [0.5, 1.8]$ , $ω x i = 0.1$ , $ω y i = 0.1$ , $T h r = 1$ .
ECKF [28]	${\hat{μ}}_{0}^{+} = [\exp [j (π / 5)]; \exp [j (π / 5)]; \exp [- j (π / 5)]], P_{0}^{+} = d i a g ([1; 10^{2}; 10^{2}])$ , $Q_{x} = d i a g ([0.01; 10^{2}; 10^{2}]), R_{x} = 10$ .
EKF	$P_{0}^{+} = d i a g ([10^{- 2}; 10^{- 2}; 10^{2}; 10^{2}]), Q_{x} = d i a g ([10; 10^{- 4}; 10^{3}; 10^{3}]), R_{0} = 1; β = 0.5$ ,
	$b = (max (I) - min (I)) / 2$ , ${\hat{α}}_{0}^{+} = [m e a n (I); π / 5; b \cos (π / 6 + π / 5); b \sin (π / 6 + π / 5)]$ .

Methods
	Computational Time (in Seconds)
Size (in Pixels)	FT	WFT	ECKF	EKF
$400 \times 400$	0.011	2.28	3.51	1.314
$576 \times 768$	0.0202	7.89	9.15	2.84
$651 \times 621$	0.0186	9.06	8.76	3.09

Abstract

Data availability

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Tables (2)

Equations (34)

Applied Optics