Self-healing of the statistical properties of exact non-Rayleigh nondiffracting speckle fields

We investigate the capacity of the exact non-Rayleigh nondiffracting (ENRND) speckle field to reconstruct its statistical properties along the propagation. It is unclear in the literature how the statistical properties of such a speckle field can affect the reconstruction of the statistics itself after encountering an obstruction. Therefore, we have conducted this study using the first-order and second-order intensity statistics, revealing a remarkable superior robustness of the super-Rayleigh speckles. This study has the potential to be beneficial for future applications of speckles with controlled statistics in microscopic systems and quantum imaging.