Spatiotemporal 3D Fourier transform evaluation of speckle interferogram sequences in double-pulsed TV holography

Abstract

Phase evaluation based on the spatial Fourier transform of speckle interferograms usually assumes that the side lobes corresponding to the interferential terms in the Fourier spectrum of each interferogram do not overlap the terms related to the intensity of the object and reference beams. If this is not the case, a part the autocorrelation of the object beam is taken along with the selected interference term in the subsequent filtering process and induces an error in the resultant phase map. We present a technique for the acquisition and processing of speckle interferogram sequences that separates the interference lobes from the other spectral terms, even if the aforementioned assumption does not apply. A digital camera records a sequence of temporally phase-shifted interferograms with spatial carrier, and a 3D Fourier transform is applied to this set of spatiotemporal data. In the resultant three-dimensional spectrum, the temporal carrier shifts the central temporal frequency of the interferential terms to high frequencies. This minimizes their overlap with the autocorrelation of the object and reference beams, which are essentially located at low temporal frequencies. The spatial carrier prevents a possible overlap of broadband interferential terms along the temporal frequency axis. A filter that rejects the low temporal frequencies is applied to one of the lobes, and a sequence of complex-valued maps containing the optical phases of the interferograms is obtained. The measurement of surface acoustic waves propagating in a metallic plate, obtained with a double-pulsed TV holography setup, is presented to illustrate the method.