A fast Gabor wavelet transform for high-precision phase retrieval in spectral interferometry

A fast implementation of the Gabor wavelet transform for phase retrieval in spectral interferometry is discussed. This algorithm is experimentally demonstrated for the characterization of a supercontinuum, using spectral phase interferometry for direct electric-field reconstruction (SPIDER). The performance of wavelet based ridge tracking for frequency demodulation is evaluated and compared to traditional Fourier filtering techniques. It is found that the wavelet based strategy is significantly less susceptible toward experimental noise and does not exhibit cycle slip artifacts. Optimum performance of the Gabor transform is observed for a Heisenberg box with unity aspect ratio. As a result, the phase jitter of 60 individual measurements is reduced by about a factor 2 compared to Fourier filtering, and the detection window increases by 20%. With an optimized implementation, retrieval rates of several 10 Hz can be reached, which makes the fast Gabor transform a superior one-to-one replacement even in applications that require video-rate update, such as a real-time SPIDER apparatus. (C) 2007 Optical Society of America.