An improved differential-grating plane-mirror heterodyne interferometer for small roll angle measurement of a linear motion

In the previous studies on roll angle (ROLL) measurements which are based on the concept of the combination of a diffraction grating displacement technique and a laser heterodyne interferometry, there is always a lack of ideally functional retro-reflectors and corresponding optical configurations resulting in misalignment and unconfident monitoring. To overcome this problem, a differential-grating plane-mirror heterodyne interferometer is proposed in this paper, in which the grating displacement sensing method is utilized to promote angular interferometry as a reliable ROLL measurement. The working mechanism is thoroughly demonstrated through the theoretical derivation and performance analysis. In particular, the exploited configuration here including a differential grating with excellent robustness and a plane mirror with doubled resolution enables improved performance compared with the existing methods. Furthermore, a corresponding prototype is also developed to validate the proposed method successfully. So, it features merits such as an ultra-high resolution up to 1 nrad, a high sampling rate of kHz and easy practicability, which is significant for high-accuracy and real-time ROLL monitoring and compensation for advanced manufacturing and scientific instruments.