Diffraction transfer function and its calculation of classic diffraction formula

In scalar diffraction theory, Kirchhoff formula, Rayleigh–Sommerfeld formula, and angular spectrum transmission formula are classic formulas that express diffraction correctly. But as complex calculation, Fresnel diffraction integral, which is the paraxial approximate solution to these formulas, is used widely. This paper presents diffraction transfer function corresponding to each classic diffraction formula, gives discussion on methods when using fast Fourier transform to calculate these formulas, derives conditions each formula must meet when it is calculated correctly based on sampling theorem, and finally real examples are finished to certify the results.