Analysis and correction of the phase error caused by application of the Hilbert transform to demodulation of fringe patterns with linear and radial carrier frequencies

摘要

Abstract: Filtering some types of fringe patterns in the spatialfrequency domain enables to reconstruct a complexnumber distribution containing full information aboutthe phase of the analyzed pattern. It is shown that byregistering two images mutually shifted in phase by $piit is possible to reduce errors introduced by thefiltering process mentioned above. The technique offurther correction of the intrinsic phase error causedby filtering using the Hilbert transform has beenrecently proposed for patterns with spatial carrierfrequencies in Cartesian coordinates. In this work weshow that the same approach can be applied to analyzefringe patterns with radial carrier frequency (in polarcoordinates). The method of efficient filtering of suchpatterns and the technique for correcting the intrinsicerror caused by the Hilbert transform are given. Thefinal accuracy of the presented HT-based method is veryclose to the one which can be obtained by applying thephase stepping method.!4