Analytic design of hybrid diffractive-refractive achromats

An analytic design of hybrid achromats that combine refractive and diffractive elements is presented. The design procedure does not rely on paraxial approximations and involves two separate stages. In the first stage the chromatic aberrations are corrected for the paraxial rays, and in the second stage the spherical aberrations are corrected by addition of an aspherical phase function to the diffractive element. The residual spherochromatic aberrations of the achromat are evaluated both analytically and numerically, with good agreement between the results. Finally, we illustrate the design procedure by designing a plano-convex achromat for IR radiation with little chromatic dispersion.