Approach for designing thick cemented doublet lenses based on the caustic surface

A new, to the best of our knowledge, method for designing a thick-lens achromatic doublet based on the concept of a caustic surface to correct both third- and fifth-order spherical aberration is presented. We consider two different wavelengths brought into coincidence at the back focal length instead of the effective focal length as it is usually done, to calculate the radii of curvature assuming predefined values for axial thicknesses and their indices of refraction for both lenses. Alternatively, we apply Taylor's series around the optical axis, and to vanish the approximate caustic surface, we obtain the values for the conic constants, which reduce at third- and fifth-order spherical aberration. Two designs for cemented doublets are provided assuming that the lenses are cemented. Finally, we propose a method to qualitatively test doublet lenses by using null screens, considering to place the detection plane at arbitrary positions.