Ray Marching Aspheric Surfaces: Robust Ray Intersection Calculation for Design of Optical Sensors

When designing lens systems for optical sensors, a fundamental operation is finding the intersection of a ray and the lens surface. We propose a robust method for finding the intersection of a ray with highly aspherical rotationally symmetric surfaces. Our method provides reliable results for ray incident at large angles relative to the optical axis and successfully calculates intersection points for a significantly larger number of rays than existing methods, improving the reliability of optical modeling and design. The core idea of our method is to calculate an initial approximation of the intersection point for the Newton method using a ray marching procedure with a step size estimated form of analytical derivatives on the surface function. The proposed method does not require maintaining additional complex data structures and is suitable for use in the iterative optimization of optical systems where the surface geometry frequently changes.