Imaging through motional scattering layers via PSF reshaping and deconvolution

Speckle deconvolution is a forcefully effective technique for imaging through scattering layers. However, this technique is not suitable for imaging through motional scattering layers, since the motion of the scattering layer after the point-spread-function (PSF) measurement makes the recovered image become blurred. To recover the image, the motion of the scattering layer is analyzed in four dimensions: rotation around the optical axis, translation along the optical axis, rotation around the cross-axis, and translation along the cross-axis. As a result, the speckles output from the scattering layer are distorted in four ways: speckle rotation, speckle scaling, speckle stretch, and speckle shift. According to these speckle distortions, the object image can be sharply recovered again by numerically reshaping the premeasured PSF. Moreover, the motion of the scattering layer can be roughly determined during the PSF reshaping process. This method effectively breaks the limitation of the deconvolution technique and has its meanings.