Caustics and wavefronts produced by multiple refraction-reflections through plane-parallel plates.

We study the formation of caustics and wavefronts produced by multiple refraction-reflections through a plane-parallel transparent plate, assuming a point source placed at an arbitrary position along the optical axis. The caustic surfaces are obtained by using the envelope's method. Subsequently, the wavefronts are directly related to the involutes, which are associated with the envelopes for all the rays.

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.

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.

Sagittal and tangential foci produced by tilted plane wavefronts refracted through simple lenses.

We study the formation of caustic and wavefront surfaces produced by a tilted plane wavefront propagating through spherical positive lenses. The shape of the caustic surface is a function of the indices of refraction, the geometrical parameters of the lens involved in the process of refraction, and the obliquity angle with respect to the optical axis, as we expect. We provide exact and approximate analytic equations for tangential and sagittal focal surfaces and also for Petzval field curvature considering arbitrary lenses.

Design of Hartmann type null screens for testing a plano-convex aspheric lens with a CCD sensor inside the caustic.

A new method to design Hartmann type null screens to test either qualitatively or quantitatively fast plano-convex aspherical lenses is presented. We design both radial and square null screens that produce arrays of circular spots uniformly distributed at predefined planes, considering that the CCD sensor is solely placed inside the caustic region. The designs of these null screens are based on knowledge of the caustic by refraction and on exact ray tracing.

Analytic aspheric coefficients to reduce the spherical aberration of lens elements used in collimated light.

We provide closed-form formulas for aspheric terms for either plano-convex or convex-plano aspheric lenses as functions of the paraxial parameters involved in the process of refraction. These formulas are obtained through an expansion in Taylor's series from the exact caustic equation produced by aspheric lenses considering a plane wavefront propagating parallel to the optical axis and impinging on the refracting surface. A comparison of the aspheric coefficients obtained through our analytic formulas and commercial optical design software is presented, showing good agreement.