Spherical aberration correction using refractive-diffractive lenses with an analytic-numerical method

We propose an alternative method to design diffractive lenses free of spherical aberration for monochromatic light. Our method allows us to design diffractive lenses with the diffraction structure recorded on the last surface; this surface can be flat or curved with rotation symmetry. The equations that we propose calculate the diffraction profiles for any substratum, for any f-number, and for any position of the object. We use the lens phase coefficients to compensate the spherical aberration. To calculate these coefficients, we use an analytic-numerical method. The calculations are exact, and the optimization process is not required.