Different channels to transmit information in scattering media

A communication channel should be built to transmit information from one place to another. Imaging is 2 or higher dimensional information communication. Conventionally, an imaging channel comprises a lens with free space at its both sides, whose transfer function is usually known and hence the response of the imaging channel can be well defined. Replacing the lens with a thin scattering medium, the image can still be extracted from the detected optical field, suggesting that the scattering medium retains or reconstructs not only energy but also information transmission channels. Aided by deep learning, we find that unlike the lens system, there are different channels in a scattering medium: the same scattering medium can construct different channels to match the manners of source coding. Moreover, it is found that without a valid channel, the convolution law for a spatial shift-invariant system (the output is the convolution of the point spread function and the input object) is broken, and in this scenario, information cannot be transmitted onto the detection plane. Therefore, valid channels are essential to transmit information through even a spatial shift-invariant system. These findings may intrigue new adventures in imaging through scattering media and reevaluation of the known spatial shift-invariance in various areas.