It is believed that combining the techniques of smoothing by spectral dispersion (SSD) in the time domain and diffractive optical elements (DOE) in the space domain can improve beam uniform illumination. Adding another SSD unit to the combined system in different grating direction can disturb the incidence wave front more confused, thus the number of speckle patterns in the target plane is increased. The intensity in the target plane becomes smoother after a period of accumulation. However, the wave front distortion is limited by the dimension number of grating directions and the intensity distribution in each direction. In this paper we introduce the air turbulence and study its influence on the wavefront. The disturbance on wave front acts as an infinite aggregate in the number of direction dimension and intensity dimension because of the property of turbulence. The numerical calculation indicates that introducing disturbance by air turbulence on amplitude and phase of the light beam that incident to DOE can smooth the distribution on target plane after a period of accumulation.