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A min-norm approach for estimating phase distribution in an interferogram

Phase distribution in an interferogram is usually computed from several phase shifted intensity images acquired temporally by means of a CCD camera. These phase shifts are commonly accomplished by translation of a mirror with a piezoelectric transducer (PZT). In reality the PZT motion is not exact. Thus the aim of this paper is to present a novel approach for estimating the phase steps that are imparted to the PZT in the presence of nonsinusoidal waveforms and random noise. The method functions by designing an autocovariance matrix from the intensity registered on the CCD for N data frames. The eigendecomposition of an autocovariance matrix yields the signal and noise subspaces. The phase step values are estimated pixelwise from the noise subspace. This approach provides the flexibility of using arbitrary phase steps, a feature most commonly attributed to generalized phase shifting algorithms. Once the phase steps are estimated the Vandermonde system of equations is applied to estimate the phase distribution.