Geometrical effects of the source size in correlation imaging

Correlation imaging (CI) is an emerging approach to imaging aimed at overcoming the limitations of conventional, intensity-based imaging modalities. In this paper, we focus on a peculiarity of chaotic-light-based CI: the strict link between image properties, and source size and geometry. We will show that the light source acts as a limiting aperture, whose geometrical properties significantly affect image formation, hence, the defocused resolution and depth of field. In ghost imaging, the image quality is typically associated with the speckle size, namely, with wave-optics effects; here, we evaluate the second-order correlation function of an out-of-focus CI system and demonstrate that the out-of-focus point-spread function is governed by a geometrical circle of confusion determined by the illumination numerical aperture. Both analytical results and numerical simulations indicate that this geometrical effect dominates the optical response of CI systems both in out-of-focus conditions and when large sources are employed. Even more, in correlation plenoptic imaging, the axial resolution is found to be directly linked to the illumination geometry, as the source size is found to constrain both the quality of the refocused images and the axial sectioning capability. The presented analysis applies to all CI architectures, thus providing a comprehensive framework for understanding and optimizing source-dependent effects in CI.