Differentiable ray tracing optimization of freeform spectacle lenses for astigmatism correction.

Refractive error is a global public health challenge, with astigmatism correction being one of the key issues. While spherocylindrical lenses compensate for static astigmatism, they fail to address optical axis shifts during eye movement. To address this problem, we propose a single vision lens design method with freeform surfaces based on differentiable ray tracing. Our method integrates the rotation model of the human eye into the optical design framework. Besides, it leverages the high design freedom of the freeform surface to realize effective correction of optical focus errors across different fields of view. To verify the effectiveness of the method, we develop spectacle lens designs to correct astigmatism in the human eye through systematic comparison of traditional spherocylindrical and aspheric lenses with various freeform designs, including deformed XY polynomials and both single- and double-Zernike surfaces. Results show that our method achieves superior off-axis aberration correction at equivalent optimization orders, demonstrating its technical advantage for vision correction.