Data-dependent-systems and Fourier-transform methods for single-interferogram analysis

Results of wave-front phase detection obtained from a spatial method based on data-dependent-systems (DDS) methodology are compared with those obtained from the Fourier-transform method. DDS is a novel approach that extends and improves the way the stochastic autoregressive moving-average models are obtained and interpreted. The methodology is robust to noise influence and insensitive to the errors commonly associated with the Fourier transform. Both the Fourier-transform and the DDS methods use one interference pattern, and both offer means for filtering out disturbances such as noise and background variations. We present a brief review of the two methods to compare them theoretically, and then we describe their experimental implementation. The methods were applied to the same interferometric data sets, and the results are presented and compared to discuss relative advantages and disadvantages. In particular, it is shown that the DDS method preserves the detailed surface texture because a convolution of the component that represents the surface dynamic aspect with the component that corresponds to the independent and dynamic-free aspect is able to recover the original details. In contrast the Fourier-transform method smooths such details to an extent that depends on the subjective choice of filters.