Ultrahigh-resolution angle sensing based on a laser-frequency measurement

Precision measurement of small angles is essential in both industrial applications and high-precision scientific research. Although a traditional angle interferometer is widely employed, its resolution is fundamentally constrained. In this paper, we introduce an innovative method for ultrahigh-resolution angle measurement based on the laser frequency measurement, directly converting angle measurement into frequency measurement, which can be traced to the most accurate frequency standards. The proposed scheme integrates a frequency selection element interference filter (IF) with a transparent solid or liquid medium, forming a highly sensitive measurement system. This system capitalizes on the sensitivity of laser frequency to changes in cavity length and the incidence angle of the IF. As a result, even minute angular rotations of the sensor induce detectable shifts in the laser's frequency. The angular displacement is inferred directly by analyzing the frequency difference between a test signal and a reference, with this difference arising from variations in the incident angle at the IF and the corresponding changes in cavity length due to medium rotation. Theoretical analysis suggests that this method can achieve a resolution better than ${10}^{\ensuremath{-}4}$ arcsecond (${10}^{\ensuremath{-}8}\phantom{\rule{0.16em}{0ex}}\mathrm{deg}$), representing an order of magnitude improvement over existing techniques.