Most of optical systems are axially symmetric. But axially asymmetric systems are necessary in some cases, for example,
to avoid the vignetting of a mirror surface, or to eliminate the keystone distortion of the tilted object surface. The
freeform surface is a surface without the axis of the symmetry. The surface profile is expressed as a function on a 2
dimensional coordinate system. The subject of this paper is a construction method of axially asymmetric lenses, which
consist of freeform surfaces and spherical surfaces. The fabrication and the alignment of the freeform surface are much
more difficult than those of the spherical surface. To minimize the fabrication cost, the total number of freeform surfaces
should be as few as possible. Freeform surfaces should be used at the most efficient position. The question arises, how
the optimal position of the freeform surfaces can be found. One way to find the optimal position of freeform surfaces is
to include the surface numbers of freeform surfaces in the independent variables of the optimization. The surface number
is the integer. If the surface number is extended to the real number, in other words, if the optical system with the realnumber
surface numbers is consistently defined, the real-number surface numbers can be treated as ordinary independent
variables of the optimization.
© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Method to allocate freeform surfaces in axially asymmetric optical systems
", Proc. SPIE 8167, Optical Design and Engineering IV, 816703 (September 20, 2011); doi:10.1117/12.897352; http://dx.doi.org/10.1117/12.897352