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Express"],"published-print":{"date-parts":[[2026,7,13]]},"abstract":"<jats:p>Conventional incoherent holography approximates the hologram\u2013object 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. 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