Calibration-free single-shot imaging of an axially moving object beyond the optical memory effect through a scattering medium

Image degradation caused by light scattering makes it challenging to gather information about an object, especially when it extends beyond the region of the optical memory effect (OME), and even more so for a moving object rushing across a wide area. In the latter case, a speckle pattern is synthesized, which is usually regarded as a combination of a series of time-varying speckle patterns. Each of them is a convolution of the object's ideal image and the point spread function (PSF) associated with a corresponding OME region. Specifically, suppose a small object moves axially over a relatively long distance under the illumination of a narrow-banded incoherent light. In this case, the imaging system is composed of a sequence of linear shift-invariant (LSI) systems. Theoretical analysis reveals that discarding the amplitude component of the dynamic system's equivalent optical transfer function (E-OTF) enables calibration-free object retrieval while simultaneously reducing noise. This insight helps us to retrieve the shape of the rapidly moving object (though not its trajectory) from a synthesized speckle captured in a single shot. Note that we also further demonstrate the feasibility of retrieving an axially moving small object even under white light illumination.