Diffractive efficiency of diffractive lenses and its effects on MTF

A weighted sum equation,which describes the relation between the diffractive efficiency and modulation transfer function of diffractive lenses,is derived.According to diffractive efficiency and optical transfer function,the total optical transfer function can be expressed with weighted sum of the series of order optical transfer functions of diffractive lights.The weighted factors are the diffractive efficiency.We employed the results to calculate MTF of various diffractive lens singlets and got consistent results with the literature 1.