Varied line spacing plane holographic grating recorded by using uniform line spacing plane gratings

Uniform line spacing plane gratings are introduced into a recording system to generate aspherical wavefronts for recording varied line spacing plane holographic gratings. Analytical expressions of groove parameters are derived to the fourth order. A ray-tracing validation algorithm is provided based on Fermat's principle and a local search method. The recording parameters are optimized to record a varied line spacing plane holographic grating with the aid of derived analytical expressions. A design example demonstrates the exactness of the analytical expressions and the superiority of recording optics with auxiliary gratings.