Feasible Resolution of Angular Displacement Measurement by an Optical Angle Sensor Based on Laser Autocollimation

Abstract

The feasible resolution of angular displacement measurement by an optical angle sensor based on laser autocollimation is investigated. Improving the sensor sensitivity while maintaining the noise level of the sensor signal as low as possible is necessary to achieve high-resolution angular displacement measurement. In this paper, the contribution of each component, such as a photodiode, a trans-impedance amplifier, and an analog-to-digital converter in the optical angle sensor, to the noise level of the sensor signal is first estimated on the basis of theoretical equations. The feasible sensitivity of the optical angle sensor is also estimated in numerical calculations. The sensitivity of a photodiode element at the edge of its photosensitive area is evaluated in experiments to realize the estimation of the angle sensor sensitivity. Experimental results are applied to the numerical calculations. The influences of the measurement laser beam diameter, the spot diameter of the focused laser beam on the photosensitive area, and the focal length of the collimator objective of the optical angle sensor are also considered in the numerical calculations. Finally, a prototype optical setup is developed. Experiments are performed to demonstrate that a compact optical angle sensor based on laser autocollimation with a collimator objective having a focal length shorter than 100 mm can achieve a resolution beyond 0.001 arc-second with a bandwidth of 1 kHz. This resolution is better than those achieved by commercial autocollimators employing an image sensor or a position-sensitive detector. The industrial contribution of this paper lies in the detailed breakdown of noise components in the readout signal of an angle sensor in a practical condition and the systematic estimation of its feasible resolution as well as its sensitivity.