An improved two dimensional micro-/nanoradian angle generator (2D-MNAG) with single rotation center located on the tilting plane and error compensation of capacitive sensors is presented in this study. The 2D-MNAG is structured on an optimized flexure hinge with single rotation center in orthogonal axes. The rotation center is located on the center of tilting plane of 2D-MNAG so that there is no linear displacement coupled in the angular output of the tilting plane. Three capacitive sensors are used in the 2D-MNAG to monitor the angular output for feedback control. The principle error of capacitive sensor while used in angle measurement is compensated using an established model, thus to improve the accuracy and repeatability of the angular output. A synthetic output error of 0.212 arcsec of 2D-MNAG is obtained using Monte Carlo simulation while the distance from rotation center to each driving and angle monitoring point is 40 mm with manufacturing and mounting errors in the range of [-0.01, 0.01] mm in rectangular distribution. The performance of the angular output monitoring unit and the strategy for closed-loop control are the key for improving the 2D-MNAG while the mechanical structure and driving unit are optimized.
A rigid geometric-optics autocollimation model is established using ray-tracing method to overcome the limitations of conventional autocollimation model due to its lack of necessary parameters. The established model describes the transmission process of the light rays that are emitted from the illuminated target plane and transmit through the autocollimation system and return back to the receiving plane. Simulation results of the model indicate that the cross-talk of 2D micro-angle measurement in autocollimation can be 0.035 arcsec in a measurement range of ±1000 arcsec. The coordinate deviation of ±3 mm from the optical axis of the points on the target plane could result to a variation of -0.045 to 0.246 arcsec in autocollimation. The defocus of ±50 μm of the target plane and the receiving plane could result to an error of 0.278 arcsec. The variation of measurement distance from 200 to 2000 mm could result to a maximum error of 0.500 arcsec in autocollimation while the defocus of receiving plane is 50 μm. The established model can be used for further analysis and improvement of autocollimation.
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