Statistical study of generalized nonlinear phase step estimation methods in phase-shifting interferometry
Applied Computing and Mechanics Laboratory, Ecole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. Applied Optics
(Impact Factor: 1.78).
12/2007; 46(33):8007-14. DOI: 10.1364/AO.46.008007
Signal processing methods based on maximum-likelihood theory, discrete chirp Fourier transform, and spectral estimation methods have enabled accurate measurement of phase in phase-shifting interferometry in the presence of nonlinear response of the piezoelectric transducer to the applied voltage. We present the statistical study of these generalized nonlinear phase step estimation methods to identify the best method by deriving the Cramér-Rao bound. We also address important aspects of these methods for implementation in practical applications and compare the performance of the best-identified method with other bench marking algorithms in the presence of harmonics and noise.
Available from: imacwww.epfl.ch
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ABSTRACT: In this paper we present a novel approach to obtain interference phase measurements using sinusoidal modulation in order to obtain high resolution data at high temporal bandwidths. The use of classical phase stepping techniques generates ringing in PZT-based phase modulators and hence limits the temporal bandwidth at which reliable phase data can be obtained. Signal processing techniques are introduced to extract intensity measurements at any required phase step and hence offer compatibility with existing linear phase shifting interferometry algorithms. It was found that, under high frequency and/or high amplitude sinusoidal excitation, the PZT phase modulator could exhibit a nonlinear response. Strategies are introduced to mitigate these effects on the calculated interference phase. Experimental data is presented demonstrating a phase resolution of 1/600th of a fringe at a temporal bandwidth of 8150 Hz when using the Carré phase stepping algorithm. Data from a multi-wavelength fibre interferometer with sinusoidal modulation to obtain the wrapped phase measurements are also presented where a dynamic range of 1 part in 2 × 10 6 was achieved.
Available from: uwa.edu.au
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ABSTRACT: We present an unscented Kalman filter to identify the phase step imparted to a piezoelectric transducer in phase shifting interferometry in the presence of Gaussian noise. The advantage of the proposed algorithm lies in its ability to determine the phase step values between -pi and pi rad without any prior calibration of the piezoelectric device. The algorithm is tested rigorously by using the simulated data in the presence of Gaussian distributed noise. Experimental validations are also performed in a holographic interferometry optical setup to verify the proposed approach. Once the phase step is identified, the interference phase can be estimated by using the least-squares fitting approach.
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