A Virtual-Movement Scheme for Eliminating Spot-Positioning Errors Applicable to Quadrant Detectors

Abstract

Traditionally, spot-positioning algorithms applied in quadrant detector (QD) face some dilemmas, such as blind area between each quadrant, spot shape shift with Gaussian distribution distortion, and also restricted measurement range. In this article, a virtual-movement scheme, which is to build a mapping relationship between spot position and captured luminous energy of photodetectors, based on equations in mathematical physics, is proposed to resolve the above three problems. On the grounds of the proposed scheme, with establishment of spot-trail functions, the actual position of the spot can be obtained by solving the coordinates of intersection point formed by more than one spot virtual-movement trails. Furthermore, a series of novel algorithms capable of theoretically eliminating the errors caused by blind area and Gaussian distribution distortion and maximumly enlarging detecting range is devised. Significantly, the devised algorithms do not have problems of nonlinearity compensation since we do not depend on any fitting method but to solve the exact position of spot centroid. By modifying integral boundaries, the devised algorithms can be applied in any shape of existing 4-QD or promising $n$ -QD. Taking circular and square 4-QDs as two typical examples in this work, the devised algorithms have excellent performances in both types, whether spots near or far away from 4-QD’s center. With an energy-distribution model and the utilization of tolerance zones, wide measurement range and superhigh accuracy are verified both qualitatively and quantitatively. The devised algorithms have also been experimentally demonstrated to work effectively. The proposed scheme is believed to be capable of eliminating the spot-positioning errors in diverse $n$ -QD and provide wide application prospects for different types of quadrant photodetectors used in many cutting-edge areas, including optical manipulation, laser guidance, as well as quantum communication.