Equations for designing a dialyte with minimal TSA based on the caustic surfaces.

A method to design a dialyte based on the caustic surfaces is presented, with correction at the third-order spherical aberration. We predefined, a priori, the value for the back focal length of the separated doublet for two different wavelengths to calculate their radii of curvature, which depend on all the parameters involved in the refraction process. Additionally, we approached the caustic surface by applying a Taylor series, which provided the analytical spherical aberration coefficient at the third order. Two alternatives to design achromatic separated doublets are provided. Finally, we extended the method to design achromatic cemented triplets.

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.

Ronchi-Hartmann type null screens for testing a plano-freeform surface with a detection plane inside a caustic surface.

We have implemented an exact ray trace through a plano-freeform surface for an incident plane wavefront. We obtain two caustic surfaces and provide the critical points related to the ray tracing process. Additionally, we study the propagation of the refracted wavefronts through the plane-curved surface. Finally, by using the Ronchi-Hartmann type null screen and placing the detection plane within the caustic region, we have evaluated the shape of a plano-freeform optical surface under test, obtaining an RMS difference in sagitta value of 6.3 µm.