Nanoradian angle sensor and in situ self-calibration

We describe a high-precision angle sensor and a new calibration system for calibrating the linearity error of an angle sensor under in situ conditions without the need for accurate reference instruments. To achieve accuracy in the nanoradian (nrad) order, we elongated the critical-angle prism to increase the sensitivity, and we added a thermal controller to the angle sensor. This served to suppress thermal drift of the light source to improve stability. The proposed angle sensor demonstrated a stability of 3 nrad over 1 min, and the maximum repeatability error of the calibration curve determined by the in situ self-calibration method was approximately 35 nrad with a measurement range of 500 murad.