An analytic expression have been obtained by using asymptotic approximations to the type of integral expression that frequently occurs in near field optics.By using the expression,the image degradation and some factors repressurized by imaging system of the near field optics are interpreted respectively.Furthermore,an expression of the degrees of freedom of scanning near field optical microscopy is given.Also the relation between the resolution and the degrees of freedom in the scanning image system of near field optics is analyzed.