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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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