An integral approach to phase shifting interferometry using a super-resolution frequency estimation method

Abstract

Abstract:The objective of this paper is to describe an integral approachbased on the use of a super-resolution frequency estimation method -to phase shifting interferometry, starting from phase step estimation to phase evaluation at each point on the object surface. Denoising is also taken into consideration for the case of a signal contaminated with white Gaussian noise. The other significant features of the proposal are that it caters to the presence of multiple PZTs in an optical configuration, is capable of determining the harmonic content in the signal and effectively eliminating their influence on measurement, is insensitive to errors arising from PZT miscalibration, is applicable to spherical beams, and is a robust performer even in the presence of white Gaussian intensity noise.

Estimation Techniques in Phase Shifting Interferometry

“…The intensity equation for holographic moiré is assumed to be buried in white Gaussian noise and can be written as [7]   is assumed to depend only on the lag between the two averaged samples. The covariance matrix can thus be written as …”

“…These phase increments are generally applied using a piezoelectric device (PZT). Hence, there is a need to design a generalized phase shifting technique which at a time caters to the presence of multiple PZTs in an optical configuration (for instance, in holographic moiré the use of two PZTs has been suggested), is insensitive to errors due to nonsinusoidal waveforms, to PZT miscalibration and to additive white Gaussian intensity noise, and has the ability to work with diverging as well as converging beams [7]. Several phase shifting algorithms have been designed which minimize the systematic and random sources of errors.…”

“…Multiple phase steps can be extracted using these high-resolution methods either by directly designing a filter which has zeroes at the frequencies that are associated with the polynomial for the intensity fringes [7] or by first formulating a covariance matrix from the intensity signal [8][9][10][11]. Multiple phase steps can be extracted using these high-resolution methods either by directly designing a filter which has zeroes at the frequencies that are associated with the polynomial for the intensity fringes [7] or by first formulating a covariance matrix from the intensity signal [8][9][10][11].…”

Moving ahead with phase

“…Recently, several high-resolution methods have been applied to phase shifting interferometry [85][86][87]. These novel methods have been shown to exhibit the capacity of measuring multiple phase information in a holographic moire´configuration [88][89][90][91][92].…”

Phase-shifting interferometry with genetic algorithm-based twin image noise elimination

“…To compensate these randomly distributed noises, integral methods averaging out whole phases in each interferogram are proposed. One integral method using a polynomial expansion in interferograms detects harmonic contents and deletes white Gaussian noise [10]. Other methods computing the averaged difference of phases among interferograms estimate arbitrary unknown phase shifts [11][12][13].…”