Considering the analytical equations of groove parameters to fourth order and using two spherical mirrors to generate aspherical wavefronts and a spherical blank as a grating blank

we have analyzed the error of groove function and indicated that when the radius of grating blank or the radii of auxiliary mirrors are comparatively small

the series expansion in derivation procedure will introduce comparatively large error. A numerical method based on ray tracing was adopted and the practical groove pattern was calculated. Design example of holographic grating shows that it is necessary to validate the design result of recording parameters through numerical method.