The autocorrelation function calculations have been carried out on photon-limited computer-simulated images of binary stars that recorded through kolmogorov atmospheric turbulence. The effect of the parameters of photon limited binary star on the variation of signal to noise, signal to background ratios, number of images that processed and the magnitude of binary stars are studied and mathematic equations are given to investigate this effect. The result indicates that signal to background ratio of photon limited images of a binary star is independent of the total number of recorded photons.