Imaging through scattering media via speckle autocorrelation is a popular method based on the optical memory effect. However, it fails if the amount of valid information acquired is insufficient due to a limited sensor size. In this Letter, we reveal a relationship between the detector and object sizes for the minimum requirement to ensure image reconstruction by defining a sampling ratio R, and propose a method to enhance the image quality at a small R by capturing multiple frames of speckle patterns and piecing them together. This method will be helpful in expanding applications of speckle autocorrelation to remote sensing, underwater probing, and so on.

The resolution of a conventional imaging system based on first-order field correlation can be directly obtained from the optical transfer function. However, it is challenging to determine the resolution of an imaging system through random media, including imaging through scattering media and imaging through randomly inhomogeneous media, since the point-to-point correspondence between the object and the image plane in these systems cannot be established by the first-order field correlation anymore. In this Letter, from the perspective of ghost imaging, we demonstrate for the first time, to the best of our knowledge, that the point-to-point correspondence in these imaging systems can be quantitatively recovered from the second-order correlation of light fields, and the imaging capability, such as resolution, of such imaging schemes can thus be derived by analyzing second-order autocorrelation of the optical transfer function. Based on this theoretical analysis, we propose a lensless Wiener–Khinchin telescope based on second-order spatial autocorrelation of thermal light, which can acquire the image of an object by a snapshot via using a spatial random phase modulator. As an incoherent imaging approach illuminated by thermal light, the lensless Wiener–Khinchin telescope can be applied in many fields such as X-ray astronomical observations.