We present an optical surface in closed form that can be used to design lenses for controlling relative illumination on a target surface. The optical surface is constructed by rotation of the pedal curve to the ellipse about its minor axis. Three renditions of the surface are provided, namely as an expansion of a base surface, and as combinations of several base surfaces. Examples of the performance of the surfaces are presented for the case of a point light source. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

We discuss the behavior of air lenses in lens design. The structural aberration coefficients of a thin air lens are derived and compared with their glass thin lens counterpart. Examples are provided for a telephoto lens and the Monochromatic Quartet where air lenses or aspheric surfaces are used.

Aspheric and freeform surfaces are becoming more common as optical designs become more sophisticated and new generations of fabrication tools reduce cost. Unlike spherical surfaces, these surfaces are fabricated with processes that leave a signature or "structure" that is primarily in the mid-spatial frequency region. Tolerancing aspheric and freeform surfaces requires attention to both surface form and structured mid-spatial frequency fabrication errors. These structured surface errors are shown to create image artifacts such as ghosts, and ripples in the MTF profile. Spatial frequencies beyond "form" errors are often ignored or are modeled with statistical descriptors, which do not account for structured errors.This work explores and develops the theory to describe these errors without statistical assumptions. The analytic source of these artifacts in the image Point Spread Function and the Modulation Transfer Function are compared with computational models. The magnitudes of the image artifacts arising from structured surface errors are shown to be non-linear with surface height. It is also shown that multiple structured surface frequencies mix to create sum and difference diffraction orders that are not present in statistical models.An algorithm is developed that enables an optical designer to determine the important spatial frequencies and magnitudes of allowable errors given an MTF performance budget.