Representation of freeform surfaces suitable for optimization

Yabe, Akira

doi:10.1364/ao.51.003054

Cited by 20 publications

(8 citation statements)

References 9 publications

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“…To fit the final free-form refractive surface, one point was chosen from each faceted refractor. Many smooth surface description methods have been proposed and developed to fit an optical surface, such as Zernike polynomials [30], nonuniform rational basis spline (NURBS) [31,32], and Forbes polynomials [33,34]. Each model may have merit in different aspects, such as designing or manufacturing, which has been discussed in detail in previous works.…”

Section: Design Example and Simulation Resultsmentioning

confidence: 99%

Free-form illumination of a refractive surface using multiple-faceted refractors

et al. 2015

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We report a design method based on multiple-faceted refractors for free-form illumination of a refractive surface. The free-form surface is constructed as a set of primitive surface elements, which provide flexibility to satisfy the requirements of practical design problems. An extended light source can be considered, and a smooth free-form refractive surface can be established by adding feedback to the design process for a point source. Moreover, the performance can be improved by iterating this feedback process. Illumination systems with a point source and an extended source are designed and analyzed, resulting in uniform illuminance distribution, which demonstrates the validity of the method.

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Section: Design Example and Simulation Resultsmentioning

confidence: 99%

Free-form illumination of a refractive surface using multiple-faceted refractors

et al. 2015

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“…For the sake of completeness and in accordance with (16) and ISO 10110 Part 12, the computation of the Q con -polynomials up to the order of m = 5 results in con…”

Section: Surface Descriptions By Conic Part and Q Con -Polynomialsmentioning

confidence: 99%

“…More complex surfaces up to freeform surfaces are not considered within the ISO standard 10110 Part 12 [1] but can be found in ISO 10110 Part 19 [3] as generalized surfaces. Furthermore, more complex description forms based on (58) but using mixed terms for x and y can be found in [14][15][16] and other publications.…”

Section: Aspheric Description Functions For Surfaces Of Less Symmetrymentioning

confidence: 99%

Description of aspheric surfaces

Schuhmann¹

2019

Advanced Optical Technologies

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Aspheric surfaces, in particular rotationally invariant surfaces, can be described according to the ISO standard 10110 Part 12 as sagitta functions of the surface coordinates. Usually, such functions are standardized as a combination of conic terms and power series or orthogonal polynomials. Similar functions are applied for surface forms, which are not rotationally invariant as cylindric and toric surfaces. In the following, different forms of describing aspheric surfaces as given in the standard as well as other forms will be presented and compared in an overview, and their special features will be discussed.

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“…Figure 9 shows the base functions of the surface irregularity for the control of the sensitivity to the surface irregularity [ 6 ]. These base functions are included in the base functions for the representation of the freeform surfaces [ 10 ]. These functions are axially symmetric.…”

Section: Examplementioning

confidence: 99%

“…The author proposed a representation of freeform surfaces suitable for optimization in 2012 [ 10 ]. This representation consists of the rotationally asymmetric quadric and orthogonal polynomials with terms of more than the second order of the coordinate variables.…”

Section: Introductionmentioning

confidence: 99%