An aspheric lens is a lens with a non-spherical surface but a radius of curvature that varies radially from the center of the lens.
One common mathematical representation of aspheric lenses is the conic section, which is defined by the equation:
z = Ax^2 + Bxy + Cy^2 + Dx + Ey + F
where x, y, and z are the coordinates of a point on the lens surface and A, B, C, D, E, and F are the coefficients that determine the shape of the surface. By adjusting the values of the coefficients, the lens surface can be designed to correct for specific aberrations.
Another mathematical representation of aspheric lenses is the aspheric polynomial, which is defined by the equation:
z = C(1 + k) * (r^2/R^2) + Ar^4 + Br^6 + Cr^8 + …
where z is the height of the surface above the optical axis, r is the radial distance from the optical axis, R is the radius of curvature of the surface, C is the conic constant, k is the conic coefficient, and A, B, and C are the polynomial coefficients. The polynomial coefficients can be adjusted to correct for specific aberrations.