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How Accurate is NURBS?
- By Mark Nicholson
- Published 7 April 2008
- CAD Exchange
- Unrated
How Accurate is NURBS?
When sequential surfaces, or non-sequential objects, are exported to CAD programs, ZEMAX describes them as NURBS (Non-Uniform Rational B-Splines). A useful overview is given here.
A very useful property of the rational b-spline is that conic aspheres are represented exactly by the NURBS formalism. Therefore spheres, ellipses, parabolas and hyperbolas can be represented exactly by the NURBS surface form. This is great news for optical engineers, of course, because these shapes are so commonly used in optical design.
Higher-order aspheres, like polynomial aspheres, are approximated by using multiple segmented splines, which is in general a piece-wise fit over the whole optical surface using multiple lower-order polynomials. Typically, multiple third or fourth order polynomials are used to approximate the surface. This is adequate for mechanical design, but should be carefully tested for optical precision ray tracing, where surfaces may be needed to be known to fractions of the wavelength of light.
This problem often arises when a high optical precision surface is modeled in ZEMAX, then exported as a CAD file to have mechanical sections added, and then imported as a CAD file for subsequent ray tracing. The optical precision of non-conic-asphere parts is reduced upon exporting the native ZEMAX asphere as a NURBS surface form. For non-imaging optics, the precision of the CAD representation is usually adequate, but for imaging systems, care must be taken to verify that the imported CAD part is a suitably accurate description of the desired shape. Note ZEMAX uses a relative internal optical precision of about 10-12 for ray tracing. Most CAD representations of objects are many orders of magnitude more coarse.
A very useful property of the rational b-spline is that conic aspheres are represented exactly by the NURBS formalism. Therefore spheres, ellipses, parabolas and hyperbolas can be represented exactly by the NURBS surface form. This is great news for optical engineers, of course, because these shapes are so commonly used in optical design.
Higher-order aspheres, like polynomial aspheres, are approximated by using multiple segmented splines, which is in general a piece-wise fit over the whole optical surface using multiple lower-order polynomials. Typically, multiple third or fourth order polynomials are used to approximate the surface. This is adequate for mechanical design, but should be carefully tested for optical precision ray tracing, where surfaces may be needed to be known to fractions of the wavelength of light.
This problem often arises when a high optical precision surface is modeled in ZEMAX, then exported as a CAD file to have mechanical sections added, and then imported as a CAD file for subsequent ray tracing. The optical precision of non-conic-asphere parts is reduced upon exporting the native ZEMAX asphere as a NURBS surface form. For non-imaging optics, the precision of the CAD representation is usually adequate, but for imaging systems, care must be taken to verify that the imported CAD part is a suitably accurate description of the desired shape. Note ZEMAX uses a relative internal optical precision of about 10-12 for ray tracing. Most CAD representations of objects are many orders of magnitude more coarse.