High-Precision Angle Measurement Method Based on Annular Light Spot

In angular measurement systems based on four-quadrant detectors, the traditional method requires an extended spot to be formed through the defocusing plane in order to excite the effective differential signal due to the stringent spot diameter requirement of the device. However, this approach introduces a critical limitation: the centroid displacement of the defocused spot exhibits nonlinear dependence on both the incident beam angle and transverse displacement. This coupling effect results in superimposed positional deviations in angular solutions, severely limiting system applicability in dynamic displacement scenarios. To surmount this challenge, we propose a high-precision angle measurement method based on an annular spot. Through the design of an axicon-based optical system, the incident Gaussian beam is transformed into an annular intensity profile, which forms an annular focal spot after lens convergence. By analyzing the energy distribution characteristics of the annular spot, a mathematical mapping model is constructed between the signal output of the four-quadrant detector and the location of the center of mass of the spot. This enables the direct acquisition of high-precision angular values. Experimental findings reveal that the root-mean-square error of the angular solution of this system is as low as 9.8822×10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> rad, signifying a substantial enhancement compared to the traditional method.