DATA-DEPENDENT-SYSTEMS AND FOURIER-TRANSFORM METHODS FOR SINGLE-INTERFEROGRAM ANALYSIS

Results of wave-front phase detection obtained from a spatial method b ased on data-dependent-systems (DDS) methodology are compared with tho se obtained from the Fourier-transform method. DDS is a novel approach that extends and improves the way the stochastic autoregressive movin g-average models are obtained and interpreted. The methodology is robu st to noise influence and insensitive to the errors commonly associate d with the Fourier transform. Both the Fourier-transform and the DDS m ethods use one interference pattern, and both offer means for filterin g 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 a pplied to the same interferometric data sets, and the results are pres ented and compared to discuss relative advantages and disadvantages. I n particular, it is shown that the DDS method preserves the detailed s urface 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 de tails. In contrast the Fourier-transform method smooths such details t o an extent that depends on the subjective choice of filters.