Speckle photography fringe analysis by the Walsh transform

Two-dimensional Walsh spectral analysis is presented as a new method of numerically processing the Young's fringes diffraction pattern from a double-exposure speckle photograph. The Walsh spectrum of the fringes is more complex than the Fourier spectrum but can be interpreted reliably by further cross correlation of the fringes with square waves. Compared with Fourier spectral analysis, the new technique gives results of almost identical accuracy but with substantially reduced computational effort. The ideas presented have relevance to the general problem of detecting and accurately determining the frequency components of a 2-D sinusoid in the presence of noise.