Displacement compensation algorithm for high-precision absolute six-degree-of-freedom grating encoder

The accuracy of the absolute position and orientation of sub-mirrors in large-aperture optical systems significantly impacts system performance. The precision of sub-mirror alignment directly affects the surface shape error of the main mirror, which, in turn, affects imaging quality and overall system performance. Two main methods for position and orientation measurement are electromagnetic displacement measurement and optical displacement measurement. While electromagnetic methods achieve high precision, their complex structures and susceptibility to environmental factors pose challenges. Optical displacement measurement using grating encoders, which rely on grating pitch as a reference, offers high stability and broad applicability. <br/><br/> To address sub-mirror alignment accuracy in large-aperture telescopes, we propose an absolute six-degree-of-freedom grating encoder based on spot position monitoring. This encoder achieves four degrees of freedom (θX, θY, θZ, Z) absolute position and orientation detection using gratings. Additionally, we employ right-angle prisms for absolute position and orientation detection in the X and Y directions, enabling six-degree-of-freedom absolute position and orientation monitoring for sub-mirrors. The monitoring results serve as feedback for sub-mirror pose correction. To mitigate the impact of grating motion on X and Y displacement calculations, we introduce a displacement calculation algorithm based on ray tracing for error compensation, enhancing the accuracy of X and Y displacement calculations and achieving high-precision six-degree-of-freedom measurement and computation.