Fourier Optics as Approximation of the Kirchhoff Integral - 1.

In Fourier optics Fraunhofer diffraction and coherent imaging are described by Fourier transform and convolution of the object amplitude. This customary formalism results from the angular spectrum of plane waves and from the Kirchhoff integral after approximations with limited validity. Now these ranges of validity are discussed for the 4F path of rays with thin lenses. Spherical surfaces are considered for pupil (Fourier surface) and image.