The imaging through optical systems may have distortions called aberrations. It can be chromatic aberrations, an effect resulting from dispersion due to the impossibility to focus all colors to the same point or monochromatic aberrations, where the rays emerging from one object point will not all meet at a single image point. Thanks to an analogy between the quantum and classical intensity light correlations, the previous studies explored the ghost imaging under both viewpoint. Although, the first approach was the use of correlated-photon imaging for the cancellation of phase aberrations, some authors have suggested theoretical models for the cancellation of phase aberrations using classical light in the ghost-imaging scheme. However, a detailed experimental study of the cancelation of phase aberrations using classical light intensity correlation is still missing in the literature. In this work, we show that exploring correlations of fluctuations in speckle intensity it is possible to cancel out aberrations that may exist in the Fraunhofer plane of an optical system. The aberrations cancelation occurs independently of its shape and it does not need coordinate inversion. We use high-order intensity correlations to obtain high visibility. Therefore, we extended the quantum-classical analogy to the study of cancelation of phase aberrations showing an interesting and useful distinction from the quantum case. It is possible to embed images into speckle patterns, and to recover it though the spatial correlation function. Therefore, this effect can be useful in imaging through random media and microscopy, canceling inherent aberrations than can cause distortions in the image.
We obtain a well-defined topological charge signature from the intensity correlation of two spatially incoherent Laguerre-Gauss beams of differing orders when each beam is diffracted by a triangle. We show that the value of the obtained topological charge follows a correlation rule such that its value is related to the topological charges associated to both incoherent beams. This paper suggests a way to measure an effective topological charge of the coherence function, and opens a new window for studies of correlation between different orders of optical vortex beams.