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Please contact us - for 'hyper-aspherical'
optical design software - that may enhance your specific
project.
Hyper-aspherical surfaces are independent of
a conic constant and aspheric coefficients. Hyper-aspheres
generate according to optical path. Hyper-aspheres may control and steer
non-spherical wave-fronts, as desired.
See reference Stavroudis, O.N. 1987, Tracing Wavefronts:
Can it be
done? SPIE Vol.766 'Recent trends in optical design' pp
18-26
Hyper-aspherical surfaces and
associated applications are the subject of on-going
research by Bentec Services Limited.
The following is a 'standard' industry formulation
for aspherical surfaces - which implies knowing all
relevant coefficients C, k, A1, A2, ...etc:
Xray optics:
Reference: Nino
Pereira's Lithium lens - Lithium metal for x-ray
refractive optics. Download
PDF file
(360Kb) N. R. Pereira, Ecopulse, Inc, PO Box 528
Springfield, VA 22150; D. A. Arms, R. Clarke, S. B.
Dierker, and E. M. Dufresne; Department of Physics,
University of Michigan, Ann Arbor, MI, 48109.1120; and
D. Foster, Army Research Laboratory, Adelphi, MD 20873.
Reference: Bruno
Lengeler's hard x-ray lens - Imaging by parabolic
refractive lenses in the hard X-ray range. Download
PDF file
(635Kb) Bruno Lengeler; Christian Schroer; Johannes TuČ
mmler; Boris Benner; Matthias Richwin; Anatoly Snigirev;
Irina Snigireva and Michael Drakopoulos
Design and Fabrication of Compound
Refractive X-ray Lenses for CHESS: Abstract:
It has long
been thought that focusing x-rays with refractive optics
was inefficient, if not impossible. Recent developments,
however, indicate this is not so. In this paper, we
present our work which consisted of designing, building,
and testing several compound refractive x-ray lenses for
the Cornell High Energy Synchrotron Source (CHESS). We
have achieved a gain of 2.5 with one such lens, while
focusing a 12 keV beam to a width of approximately 10
microns. Such a beam could be used in various
experiments due to its extremely small width and high
intensity. Scott
Forth PDF file
Note: Standard aspheric formulations
incorporate a conic constant which, in addition to the
conic base radius, defines the conic - which may be
further modified by employing an extended polynomial
(sometimes 20 terms) with aspheric coefficients. A
comprehensive article by Scott A. Lerner and Prof.
Sassian of the University of Arizona concerning 'Optical
design with parametrically defined aspheric surfaces',
addresses the general difficulties associated with the
standard formulation for aspherical surfaces. This
article was published in revised form on 12th June 2000,
by Applied Optics and in association with the Optical
Society of America.
Regarding fabrication, a good source for research is
Moore Tool Company in Connecticut.
Regarding 'less expensive' fabrication techniques,
much depends on volume of production. Clearly, polymer
optics is cost effective in large volume as the major
cost is associated with mould tool insert manufacture
and set-up cost prior to injection moulding or
replication by other means. On the other hand. It may be
that an existing glass lens, for example, might simply
require its surface modified to aspherical form in order
to better its performance - achieved either by the
removal of surface material or adding surface material
using an optical resin.
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