Abstract: Based on the normative fractional Fourier transform and the concept of the optical transfer function, using the linear system theory, the mathematic expressions of fractional transfer function in Fresnel diffraction system and Fraunhofer diffraction system are given respectively. It is proved that the fractional Fourier transform has the cascade feature, and the optical transfer function is the special case of fractional transfer function. The result can be used to support the application of fractional Fourier transform in information processing and image quality assessment.