The two-dimensional Fourier transform algorithm had been previously as
sessed to out-perform other existing algorithms in the aspect of analy
tical efficacy but not in the area of computing speed when used to num
erically process Young's fringe diffraction patterns from double expos
ure speckle photographs. In this paper, a two-dimensional Hartley tran
sform algorithm is outlined and demonstrated to provide the same level
of analytical capability as the Fourier transform algorithm but with
improvements in processing speed.