To improve the accuracy of the point spread function (PSF) extraction of planar grating imaging systems and develop PSF models, a fitting method of edge spread function based on the Boltzmann function is proposed. A hyperbolic PSF model with the incident angle as the independent variable is constructed, and then the PSF distribution rules of the grating imaging systems are obtained. Finally, the Lucy-Richardson algorithm is employed to restore images with different degrees of blur, and the quality of the restored images is evaluated. A grayscale mean gradient (GMG) improvement of above 60.2% and structural similarity (SSIM) improvement of above 66.5% are obtained. In a comparison with the restoration effects of different fitting methods, the proposed method shows better image restoration for large aberrations than other similar methods. The developed PSF model can also accurately represent the characteristics of grating imaging systems.