Two-dimensional Fourier transform analysis is presented as an advanced method for numerically processing the Young's fringes diffraction pattern from a double-exposure speckle photograph. The fringe spacing and orientation are determined using only one Young's fringes pattern without any other diffraction halo patterns. This algorithm is based on the 2-D FFT of the fringe pattern with 256×256 pixels. Therefore, it has enabled automatic analysis to be performed with noisy and poor fringe patterns. The measurement of deformation field by the laser speckle method can be carried out with higher accuracy, reliability and speed.