Polar transformation-based phase-scanning method for centering a non-diffracting fringe image

Abstract

A polar transformation-based phase-scanning method for centering a concentric circle fringe image is proposed. The basic principle is that the amplitude of phase-fluctuation, along with the polar angle, is proportional to the deviation from the center of the non-diffracting spot. The minimum of such amplitude appears in the position of the ideal center. The image of a non-diffracting beam, the cross section of which is a concentric circle fringe, is first recorded by a matrix array image sensor, downloaded to a computer, and then expanded into polar grayscale in the initial position. We contrast the phase of a standard sine pattern produced by a computer with the polar grayscale along with the polar angle through the principle of phase-scanning to obtain the phase fluctuation for the non-diffracting beam along with the polar angle. The common center of the non-diffracting image is then calculated by searching for the position of the phase amplitude minimum. The effect of background noise and non-circular fringe on centering is significantly reduced, and the center position resolution can still reach the order of a charge-coupled device in a complex background because all the intact data on the non-diffracting image are used in the calculation.