Defocusing effects of lensless ghost imaging and ghost diffraction with partially coherent sources

The defocusing effect is inevitable and degrades the image quality in the conventional optical imaging process significantly due to the close confinement of the imaging lens. Based on classical optical coherent theory and linear algebra, we develop a unified formula to describe the defocusing effects of both lensless ghost imaging (LGI) and lensless ghost diffraction (LGD) systems with a partially coherent source. Numerical examples are given to illustrate the influence of defocusing length on the quality of LGI and LGD. We find that the defocusing effects of the test and reference paths in the LGI or LGD systems are entirely different, while the LGD system is more robust against defocusing than the LGI system. Specifically, we find that the imaging process for LGD systems can be viewed as pinhole imaging, which may find applications in ultra-short-wave band imaging without imaging lenses, e.g. x-ray diffraction and γ-ray imaging. (letter)