Abstract: The model of laser spectrum used in the method of smoothing by spectral dispersion （SSD） affecting the beam smoothing was theoretically discussed based on the analysis of spatial frequency spectrum, and the response function to the spatial frequency modulation was put forward to describe the effects. With theoretical derivation and numerical simulation, it is concluded that the spatial frequency response function by SSD has periodical property and is determined by dispersion angle and spectrum shape. More generally, spectrum shape was related with the shape of response function, the dispersion angle affects the lowest spatial frequency, and color cycle number can modify the distribution of low and high spatial frequency to change the smoothing effect. Applied to multidimensional SSD, the response function characters can give the guiding principle for optimization.

Keywords: 
• smoothing by spectral dispersion /
• spatial frequency /
• focal spot /
• response function