On the relation between Abbe's theory and Rayleigh diffraction in coherent imaging through the use of Collins' Integral

Diffraction effect resulting from the entrance pupil of the optical imaging system was proposed by Abbe. An equivalent view regarding diffraction effect from the exit pupil was considered by Rayleigh. In the present work, the relation of the two effects is first established using Collins' integral and the Fresnel diffraction formula. For a general optical system including multiple optical elements and an aperture stop, we develop an approach in that the elements of the matrix for Collins' integral are derived. Subsequently, we perform optical experiments to verify our developed approach.