Astigmatic Characteristics of Diffractive Optical Elements with Aspherical Phase Term

Analytical expression for the two principal foci of the astigmatic image generated by the diffractive optical elements with aspheric phase term were derived using the ray tracing technique. The relation is given between the principal foci and the coefficients of the aspherical phase term expanded by polynomials. Numerical examples are discussed and compared with the experimental results previously reported. The formulas given here include the equations derived by considering the propagations of an astigmatic wavefront through a hologram.