On-machine self-calibration of rotary encoders in the normal vector tracing method.

We developed a nano-profiler to determine the shape from slope distribution data for highly accurate free-form surface shape measurement; for example, high-precision optical systems are required in the x-ray and semiconductor fields. An accuracy of ±0.2 µrad is required to achieve a shape measurement accuracy of 30 nm. The angle of the rotary stage is controlled by the rotary encoder, and the calibration curve of the rotary encoder is guaranteed by the national standard machine. However, the error associated with assembling the rotary encoder to the device is not included in the national standard machine's calibration data. Therefore, we propose a method that combines self-calibration with six encoder heads and calibration with a national standard machine. Using this method reduces the extent of calibration by the national standard machine and minimizes the influence of the assembly error. Furthermore, to verify whether the calibration in the proposed method is appropriate, a new encoder for evaluation was installed and evaluated. The results revealed that the influence of the assembly error was reduced to the minimum, and the difference in the calibration between the encoder for evaluation and the national standard machine was 0.027 µrad.