Laguerre-Gaussian-Domain Rotational Image Restoration beyond the Camera Response

It is a crucial task to capture clearpictures of fast-rotatingobjects for both scientific research and industrial manufacture. However,when the rotational speed exceeds the camera response, the recordedimage generally suffers from motion blur. Particularly, the rotation-inducedblur becomes severer along with the increasing radius. It still lacksan effective way to break the camera limitation and restore the imagefrom rotational motion blur. Here, we propose and experimentally demonstratea novel Laguerre-Gaussian (LG) domain rotational image restorationtechnique. In LG domain, the rotation introduces an additional phaseinto each azimuthal LG component of the image, resulting in motionblur. The blur factor of LG spectrum is related to the rotationalspeed, which can be precisely measured according to the rotationalDoppler effect. After correcting the LG spectrum, we successfullyrecover the image of an object rotating at a constant or time-varyingspeed beyond the camera response. Our results provide a useful approachto record high-quality images of astronomical targets, biologicalmolecules, and industrial centrifuges rotating at an ultrahigh speed.