A basic relation in the diffraction theory of the image of a point source is that the distribution of complex amplitude in the PSF is given by the Fourier transform of the distribution of complex amplitude over a reference (or pupil) sphere at the exit pupil. For this relationship to be valid it is essential to express the complex amplitude over the reference sphere as a function of the rectangular coordinates of points on the exit pupil sphere, and not those of points in the exit pupil plane. I describe in what follows the advantages of using, also in geometrical optics, the reference spheres in the object and image spaces respectively as the surfaces of the entrance and exit pupils, rather than the pupil planes.
Harold H. Hopkins,
"Geometrical and physical theory of image formation: a synthesis", Proc. SPIE 1781, Specification and Measurement of Optical Systems, (1 January 1993); doi: 10.1117/12.140994; https://doi.org/10.1117/12.140994