Abstract: Based on the sea bottom is modeled as a thin layer which scatters the sound wave, obtained the formula of sonar array space-time correlation function of bathymetric sidescan sonar (BSSS). Two important results are given. The first is the formula of mean and variance of differential phase estimation of BSSS. The second is, except kd sin(θ-θ_m), there is a phase error term ξ in the phase of space-time correlation function, it is named as phase error factor, and causes large sounding error in the vicinity of nadir. Based on the results mentioned above, the standard how to select the parameter of differential phase estimation is given, then ξ may be reduced, so the performance of BSSS in a wide angle range is improved. Under the direction of the theory mentioned above, we designed a BSSS. The experimental results obtained in a deep lake are consistent well with the theory results, and proves that our theory is correct.