In the satellite-to-ground laser communication, atmospheric turbulence influences the wave-front and increases bit error rate. The data information is got by an unequal arm-length interferometer based on differential phase shift key (DPSK), with the interference between the former code and the latter code of signal light. Generally, atmospheric turbulence makes the same influence on the wave-fronts of the front and rear codes in high speed rate communication, so differential information is obtained by the subtraction of the two successive wave-front phases when interference occurs. On the basis of theoretical foundation above, the diffraction propagation of incident signal light in the structure of the free-space differential interference is analyzed with Fresnel diffraction theory. In numerical simulation, the impact of detected optical wave aberrations on the performance of differential interference system is discussed. It is proved that free-space differential interference structure can overcome the disturbance of optical phase information of atmospheric turbulence effects. In addition, the applications and conclusions of optical signal demodulation with free-space differential interference structures are given.