High-frequency small angle measurement using a dynamic autocollimator based on an improved k-means algorithm

An improved k-means algorithm is proposed to enhance the stability and dynamic measurement accuracy of high-frequency small angle measurement using a dynamic autocollimator. The improved algorithm incorporating an optimized initialization scheme is used to determine the accurate position of the light spot for angle calculation. Simulations executed on different datasets demonstrate the effectiveness of the algorithm. Experimental results indicate that the 30-min stability of 0.58 and 0.69 arc sec at the measurement frequencies of 5 and 10 kHz can be achieved by the improved algorithm, respectively. Also, the dynamic measurement accuracy of 0.99 and 1.25 arc sec under the rotation speeds of 1 and 20 deg/s, respectively, at the measurement frequency of 10 kHz can be obtained. It is confirmed that the improved algorithm is necessary and effective for the autocollimator.