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 optical memory effect is an interesting phenomenon that has attracted considerable attention in recent decades. Here, we present a new physical picture of the optical memory effect, in which the memory effect and the conventional spatial shift invariance are united. Based on this picture we depict the role of thickness, scattering times, and anisotropy factor and derive equations to calculate the ranges of the angular memory effect (AME) of different scattering components (ballistic light, singly scattered, doubly scattered, etc.), and hence a more accurate equation for the real AME ranges of volumetric turbid media. A conventional random phase mask model is modified according to the new picture. The self-consistency of the simulation model and its agreement with the experiment demonstrate the rationality of the model and the physical picture, which provide powerful tools for more sophisticated studies of the memory-effect-related phenomena and wavefront-sensitive techniques, such as wavefront shaping, optical phase conjugation, and optical trapping in/through scattering media.