A research on the geometric fitting method to design aberration-corrected flat-field holographic concave gratings

A geometric fitting method for optimal design of the aberration-corrected flat-field holographic concave gratings is described. That is to make the minimum area between the defocus focusing curve and the astigmatic focusing curve over the entire spectral range as the condition of optimal design, and search for the minimum area by computer scanning of different parameters in separated proper numerical range according to the area formula. Then calculate the location parameters of the two recording sources which determined the designed concave gratings on the basis of the obtained parameters corresponding to the minimum area. The proposed geometric fitting method can be shown by figure, thus very intuitive to readers. Besides, its physical meaning is clear and accurate. In this paper, the aberrations under different incident angles, different effective grating grooves and different radii are discussed. The results indicate that the incident angle has the biggest influence on the defocus; radius has little influence on the optimal incident angle; the bigger the radius is, the smaller the defocus becomes. In certain conditions, there is an optimal range for effective grating grooves, so an optimal choice can be made according to the spectrometer needs of detector pixel size and spectral resolution ability.