Quantum frequency goniometer with common mode noise cancellation

Small-angle measurement technology plays an important role in aerospace, lithography machine chip manufacturing, precision mechanical manufacturing, etc. However, despite decades of development, existing methods still rely on laser interferometers, and the resolution remains at 0.001 arcseconds. As science and technology progress rapidly, high-precision technologies like lithography machines urgently need higher angular resolution. Since frequency is the most precisely measurable physical quantity, converting angle measurement into frequency measurement is expected to achieve order-of-magnitude breakthroughs in the resolution limitation. In this paper, we propose a quantum frequency goniometer (QFG) based on common mode noise-canceling laser frequency measurement designed to achieve ultra-high precision in angle measurement. The QFG integrates a frequency selection element interference filter (IF) with a transparent solid or liquid medium, exploiting the high sensitivity of laser frequency to variations in cavity length and the incident angle of the IF. A beat frequency measurement equipment is used to detect the differential output frequency before and after angle variations, allowing for precise determination of the frequency shift induced by angle changes. By extracting the frequency difference from the beat frequency signal, the system effectively eliminates the common mode frequency noise introduced during free-running operation. Theoretical analysis indicates that the QFG has the potential to enhance angular measurement resolution, achieving a resolution better than 10^-5 arcseconds (10^-9 deg).