Image aberrations of optical systems evaluated through an analytical approach

Abstract

An alternative approach to ray tracing is considered to evaluate analytically the imaging properties of optical systems made by any kind of reflecting/diffracting surfaces described by polynomials. The method is based on Fermat's principle and is applied to the case of the concave grating. The description of the image on the focal plane is obtained in polynomial form as a function of the coordinates of the incidence point of the optical element. Substitution of geometrical and physical parameters defines the numerical values of the coefficients to be used to obtain the global image (as in ray tracing) or the images due to different aberrations, allowing a more insightful analysis supported by analytical description. The ranges of validity of the method are discussed in relation to extreme configurations.