Improved calibration method of a four-quadrant detector based on Bayesian theory in a laser auto-collimation measurement system
Kuan Diao, Xiaojun Liu, Zhenjian Yao, Wenlong Lu, Wenjun Yang
Abstract
Reliable and accurate calibration for a four-quadrant detector (QD) is a prerequisite for high-accuracy laser auto-collimation measurements. However, the calibration accuracy is limited largely by the non-linearity of QD, especially for large-range detection. To address this issue, an improved calibration method of QD based on Bayesian theory in laser auto-collimation measurement is proposed in this paper. First, the non-linearity problem of QD is analyzed, and for accurate calibration of QD, a high-precision identification model based on Bayesian theory is presented. An analytical expression between the output signal of QD and the position of the laser spot is established, and then a calibration system with laser drift compensation to avoid influences from the laser source as a datum is constructed. A series of experiments is conducted to verify the performance of the improved calibration method. The results reveal that the improved method can effectively enhance the calibration accuracy of QD and reduce the residuals in root mean square error by 86% compared to the 15-order polynomial fitting over a detection range of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>±</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mrow> <mml:mspace width="thickmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="normal">m</mml:mi> <mml:mi mathvariant="normal">m</mml:mi> </mml:mrow> </mml:mrow> </mml:math> . The comparison experiments also demonstrate that the proposed calibration method has advantages over the conventional method in terms of accuracy and robustness.