Complex amplitude reconstruction via the Collins formula and its universality in incoherent holography

Conventional incoherent holography approximates the hologram-object relationship via free-space diffraction, inaccurately describing their correspondence and introducing phase distortions in reconstruction. We establish a unified framework showing that this relationship is rigorously governed by the Collins diffraction formula across diverse incoherent systems. Based on this model, we propose Collins-based incoherent digital holography (CIDH) for complex amplitude reconstruction with adjustable magnification and non-rotationally symmetric optics compatibility. Experiments using CIDH confirm complex amplitude recovery at adjustable magnifications and demonstrate its application to angular alignment of optical elements. This work advances incoherent holography theory and provides a foundation for computational optical imaging and metrology.