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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 1 — Jan. 14, 2013
  • pp: 1258–1269
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A fast feedback method to design easy-molding freeform optical system with uniform illuminance and high light control efficiency

Li Hongtao, Chen Shichao, Han Yanjun, and Luo Yi  »View Author Affiliations


Optics Express, Vol. 21, Issue 1, pp. 1258-1269 (2013)
http://dx.doi.org/10.1364/OE.21.001258


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Abstract

A feedback method combined with fitting technique based on variable separation mapping is proposed to design freeform optical systems for an extended LED source with prescribed illumination patterns, especially with uniform illuminance distribution. Feedback process performs well with extended sources, while fitting technique contributes not only to the decrease of pieces of sub-surfaces in discontinuous freeform lenses which may cause loss in manufacture, but also the reduction in the number of feedback iterations. It is proved that light control efficiency can be improved by 5%, while keeping a high uniformity of 82%, with only two feedback iterations and one fitting operation can improve. Furthermore, the polar angle θ and azimuthal angle φ is used to specify the light direction from the light source, and the ( θ,φ )-(x,y) based mapping and feedback strategy makes sure that even few discontinuous sections along the equi- φ plane exist in the system, they are perpendicular to the base plane, making it eligible for manufacturing the surfaces using injection molding.

© 2013 OSA

1. Introduction

Light-emitting diodes(LEDs), distinguished for its long life, high reliability, environmental friendly working process and energy saving potential, are used more and more widely not only in areas of special lighting, such as architectural lighting, stage lighting, traffic lighting and sign display, but also in areas of general indoor and outdoor lighting [1

1. A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-state Lighting.(John Wiley & Sons, 2002).

, 2

2. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]

]. However, traditional encapsulated LED devices have a Lambertian light distribution, which could not meet various practical requirements of lighting applications. Therefore freeform nonimaging optical systems are developed to redistribute the light rays emitted for LED devices to form prescribed illuminance or luminance distribution on the target area. Research on design method for freeform nonimaging optical systems has been an active field during the last two decades [3

3. L. Caffarelli and V. Oliker, “Weak solutions of one inverse problem in geometric optics,” J. Math. Sci. 154(1), 37–46 (2008, Preprint, 1994).

16

16. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation usingsource-target maps,” Opt. Express 18(5), 5295–5304 (2010). [CrossRef] [PubMed]

]. Amongst them the variable separation mapping method is widely used to design freeform optical systems with point sources [8

8. L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007). [CrossRef] [PubMed]

]. Based on energy conservation and Snell’s law, it uses numerical techniques to establish separately the correspondence between variables on the light source and the target plane, ensuring that the optical surfaces could redirect the incident light rays to their corresponding target points. Recently feedback design methods based on variable separation mapping are developed for extended LED sources with complicated illumination patterns [9

9. Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18(9), 9055–9063 (2010). [CrossRef] [PubMed]

, 10

10. W. Situ, Y. Han, H. Li, and Y. Luo, “Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source,” Opt. Express 19(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]

]. These are simple but super effective method to design freeform optical systems for point or extended LED sources. Nonetheless, there still remain some problems calling for a better solution, including:

  • (1) Tradeoff between accuracy and speed. Accuracy in light control adds to the difficulty in the design process. Typically, the freeform surfaces are made with many facets, whether smooth or unsmooth, with each little facet controlling only a proportion of the energy emitted from the source. Hence, calculating the large amount of points on the surfaces in order to obtain a satisfying result becomes challenging, even with the help of advanced softwares. For example, the previous iterative illuminance compensation approach, using the (simulated illuminance)/(desired illuminance) ratio to compensate the distribution, requires several to dozons of feedback iterations for a lens or reflector surface to reach the final desired distribution. Researchers have to figure out the solution to a quick design and overcome the error in freeform surface construction process.
  • (2) Difficulty of manufacturing the surfaces using injection molding. In the variable separation mapping method and the feedback modification methods based on it, (u, v)-(x, y) mapping is commonly used wherein the (x, y) Cartesian coordinates is used to specify the position on the irradiance plane, while (u, v) coordinates is used to specify the light direction from the light source, with u being the angle between the light ray and the y axis parallel to the emitting plane of the LED chip, and v the angle that the plane containing the light ray and the y axis forms with the z axis perpendicular to the emitting plane [8

    8. L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007). [CrossRef] [PubMed]

    10

    10. W. Situ, Y. Han, H. Li, and Y. Luo, “Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source,” Opt. Express 19(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]

    ]. In order to limit the deviation produced in the surface construction process, a normal vector correction mechanism is employed, and as a result discontinuities are introduced onto the lens surface. As the discontinuous section is not perpendicular to the base plane [8

    8. L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007). [CrossRef] [PubMed]

    , 10

    10. W. Situ, Y. Han, H. Li, and Y. Luo, “Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source,” Opt. Express 19(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]

    ], it can prevent the mould from escaping the lens during injection molding process, as shown in Fig. 1(a)
    Fig. 1 Discontinuous section direction and injection molding difficulty (a) discontinuous sections are not perpendicular to the base plane (b) discontinuous sections are perpendicular to the base plane.
    .
    Fig. 1Discontinuous section direction and injection molding difficulty (a) discontinuous sections are not perpendicular to the base plane (b) discontinuous sections are perpendicular to the base plane.
  • (3) Manufacturing defects. Even if the discontinuous section is perpendicular to the base plane, as shown in Fig. 1(b), manufacturing defects such as surface roughness and obtuse transition between two discrete sub-surfaces exist in discontinuous freeform lenses, which often leads to loss on light control ability, sometimes with up to 30% decrease in uniformity [11

    11. K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufacturing defects on optical performance of discontinuous freeform lenses,” Opt. Express 17(7), 5457–5465 (2009). [CrossRef] [PubMed]

    ]. Though some work has been done to obtain a quite uniform result using sub-surfaces mechanism method with hundreds of pieces of discrete sub-surfaces, it is not a good option for mass production.
  • (4) Actual light control efficiency. We define light control efficiency (LCE) as the ratio between the energy projected to the target zone and the total energy emitted from the source. It is different from light output efficiency, which includes rays hitting outside the target zone, which ought to be a waste of energy. However, most of the previous reports didn’t provide the LCE value. Their efficiency, sometimes reaching above 90%, is actually light output efficiency.

In this paper, a feedback method combined with fitting technique is proposed to effectively address the problems mentioned above. It reduces the feedback iterations from a dozen to a few while achieving higher LCE as well as light distribution accuracy. Besides, it keeps the number of discrete sub-surfaces at a reasonable level and ensures the discontinuous sections perpendicular to the base plane, which is eligible for the injection molding process.

2. Feedback method combined with fitting technique

These modifications and the fitting technique are illustrated below:

(1) (θ,φ)-(x, y) mapping strategy is employed.

In the proposed method, the (θ,φ) coordinates is used to specify the light direction from the light source, with θ to be the polar angle between the light ray and the symmetry axis of the light source, and φ to be the azimuthal angle between the light ray and x axis parallel to the emitting plane of the LED chip. Traditional (θ,φ) -(x, y) mapping strategy mostly deals with rotational illuminance requirement [17

17. R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express 20(13), 13727–13737 (2012). [CrossRef] [PubMed]

]. In the proposed method, the target plane could have complicated illumination patterns rather than only a rotational one. In the following, a rectangular region with uniform illuminance distribution is taken as an example, and this region is sampled into cells as shown in Fig. 3
Fig. 3 Divide the target plane into cells (Only two equi-φlines and equi-θlines are drawn. Points are equally spaced on either axis).
. Take the first quadrant for example, points are equally spaced along x direction below the diagonal line (correspondingly, equally spaced along y direction above the diagonal line), since this scheme can minimize the statistical error of the simulation software through our experiment. (θ,φ) division is employed to construct the lens surface with equi-θ curves on lens corresponding to horizontal lines and vertical lines in Fig. 3 (green dashed lines), and equi-φ curves on lens corresponding to oblique lines with different slope in Fig. 3 (red dashed lines).

After dividing the target plane into cells with specified energy (defined as prescribed energy in later paragraphs), the target-to-source mapping is calculated with two steps, both of which are based on the energy proportion.

Firstly, equi-φ curves are determined. Let Eprescribed(i,j) be the prescribed energy of the jth cell on the i th stripe (space between the i-th equi-φ line and the (i + 1)- th equi-φ line on target plane, shown in Fig. 3), Estripe(i) the sum of all the cell energy along the i-th stripe, while φ(i,j)and φ(i+1,j)stand for the φ value of the two edges of equi-φ stripe on target plane (red dashed lines in Fig. 3), respectively. Then φ(i,j) is obtained according to the following equation:

φ(i,j)=π2m=1i1Estripe(m)Estripe
(1)

Secondly, θ values in each equi-φstripe are determined. θdivision is more complicated than φdivision, since the energy integration of specified solid angle is a quadratic term of cosθ, expressed as:

E=φφ+dφθθ+dθI0cos2θsinφdθdφ
(2)

(2) A new feedback strategy is employed.

Eprescribed= Eprescribed_pre(EsimuEinitialEsimuEsource)0.5 
(6)

(3) A fitting technique is employed.

The advantage of (θ,φ)-(x, y) mapping compared with (u, v)- (x, y) mapping is that even if discontinuous facet exists, it will be perpendicular to the base plane and hence to be easy-molding. However, according to the work done in [11

11. K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufacturing defects on optical performance of discontinuous freeform lenses,” Opt. Express 17(7), 5457–5465 (2009). [CrossRef] [PubMed]

], discontinuous sections will cause the problem of losing uniformity and efficiency. For lens shape whose corresponding target distribution reaches the requirement, we use fitting method to reestablish the (θ,φ)-(x, y) mappings to smoothen the lens surface and to decrease the number of truncation surfaces.

It is necessary to state that our fitting method is to act not on the three dimensional spatial points but on the (θ,φ)-(x, y) mapping [15

15. Florian Fournier, “Freeform reflector design with extended sources”, A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in CREOL, the College of Optics and Photonics at the University of Central Florida Orlando, Florida, 2010.

]. After obtaining the mapping between (θ,φ)-(x, y), we actually have a data sets containing limited amount of sample points. Taking x or y as dependent variable and (θ,φ) as two dimensional independent variables, then fitting process is implemented for the (θ,φ) -x or (θ,φ) –y data sets, expressed as x = Fitting(θ,φ) and y = Fitting(θ,φ). The algorithm can be referred to [19

19. J. D’Errico, “Surface Fitting using gridfit,” (MATLAB CENTRAL File Exchange, 11 Nov 2005, Updated 29 Jul 2010). http://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit.

]. After fitting, a surface x = f1(θ,φ) and y = f2(θ,φ) is obtained. The results before and after fitting technique are shown in Fig. 4
Fig. 4 (θ,φ)-x coordinate system before(black solid dots) and after(colored surface) fitting technique.
.

It is worth noting that the lens surface assumes the role of transforming the light distribution of the LED source to the desired distribution on the target plane. However, the lens surface is constructed using the discrete points created by the mapping [8

8. L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007). [CrossRef] [PubMed]

].Therefore, more points there are in the mapping, higher accuracy of the lens surface and more efficient to achieve the distribution transform. Certainly we can divide the target plane into more cells at the beginning, but it would be time-consuming to construct so many points in every feedback iteration. As an alternative, interpolation at more grid points of (θ,φ) in the fitting after completing the feedback process, can be employed to obtain similar effect. In our work, we inserted 3 times of points along θ and 4 times along φ direction.

3. Case study – Street Lamp with uniform illuminance

In order to specify the proposed method, a street LED lamp is designed for uniform illuminance distribution over a rectangular target. The sketch of the setting is shown in Fig. 6
Fig. 6 LED is 1mm*1mm in size. The lens is restricted to 10 mm in height.Target plane is a rectangular zone of 30*10m on the road [9].
and the detailed description can be found in Ref [9

9. Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18(9), 9055–9063 (2010). [CrossRef] [PubMed]

], except that lens height (the distance from center apex to the LED source) is restricted to 10 mm. The possibility of Fresnel loss is not taken into account in the calculation of efficiency.

Obviously, the source and target distribution has mirror symmetry for each neighborhood quadrant pairs. Thus we can simply construct the lens surface in first quadrant and use mirror technique to complement it into the whole lens. The freeform lens model is obtained using a fitting technique after two feedback iterations. The freeform lens models before and after fitting are shown in Fig. 7
Fig. 7 The freeform lens models with LEDs before and after fitting. (a)Before fitting, there are 22*4 truncation surfaces. (b)After fitting the number reduces to 7*4.
. It is clearly shown that the discontinuous sections are perpendicular to the base plane, and the number of discontinuous sections is reduced from 88 to 28 after fitting, indicating the high performance of fitting technique in reducing discontinuous sections.

4. Summary

Acknowledgment

This work was supported by the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2011BAE01B07, and 2012BAE01B03), Science and Technology Planning Project of Guangdong Province (Grant No. 2011A081301003), the National Basic Research Program of China (Grant Nos. 2011CB301902, and 2011CB301903), the High Technology Research and Development Program of China (Grant Nos. 2011AA03A112, 2011AA03A106, and 2011AA03A105), the National Natural Science Foundation of China (Grant Nos. 61176015, 60723002, 61176059, 60977022, and 51002085). Thanks to Synopsys for providing a temporary license of the illumination design software LightTools.

References and links

1.

A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-state Lighting.(John Wiley & Sons, 2002).

2.

E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science 308(5726), 1274–1278 (2005). [CrossRef] [PubMed]

3.

L. Caffarelli and V. Oliker, “Weak solutions of one inverse problem in geometric optics,” J. Math. Sci. 154(1), 37–46 (2008, Preprint, 1994).

4.

V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE 5924, 594207, 594207-12 (2005). [CrossRef]

5.

H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A 19(3), 590–595 (2002). [CrossRef] [PubMed]

6.

W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE 3428, 154–162 (1998).

7.

P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng. 43(7), 1489–1502 (2004). [CrossRef]

8.

L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. 46(18), 3716–3723 (2007). [CrossRef] [PubMed]

9.

Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18(9), 9055–9063 (2010). [CrossRef] [PubMed]

10.

W. Situ, Y. Han, H. Li, and Y. Luo, “Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source,” Opt. Express 19(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]

11.

K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufacturing defects on optical performance of discontinuous freeform lenses,” Opt. Express 17(7), 5457–5465 (2009). [CrossRef] [PubMed]

12.

K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt. 11(10), 105501 (2009). [CrossRef]

13.

Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express 16(17), 12958–12966 (2008). [CrossRef] [PubMed]

14.

Z. Zhenrong, H. Xiang, and L. Xu, “Freeform surface lens for LED uniform illumination,” Appl. Opt. 48(35), 6627–6634 (2009). [CrossRef] [PubMed]

15.

Florian Fournier, “Freeform reflector design with extended sources”, A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in CREOL, the College of Optics and Photonics at the University of Central Florida Orlando, Florida, 2010.

16.

F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation usingsource-target maps,” Opt. Express 18(5), 5295–5304 (2010). [CrossRef] [PubMed]

17.

R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express 20(13), 13727–13737 (2012). [CrossRef] [PubMed]

18.

W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE 7652, 76522L, 76522L-9 (2010). [CrossRef]

19.

J. D’Errico, “Surface Fitting using gridfit,” (MATLAB CENTRAL File Exchange, 11 Nov 2005, Updated 29 Jul 2010). http://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit.

OCIS Codes
(220.2740) Optical design and fabrication : Geometric optical design
(220.3620) Optical design and fabrication : Lens system design
(230.3670) Optical devices : Light-emitting diodes
(220.2945) Optical design and fabrication : Illumination design
(080.4225) Geometric optics : Nonspherical lens design
(080.4298) Geometric optics : Nonimaging optics

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: October 24, 2012
Revised Manuscript: December 6, 2012
Manuscript Accepted: January 2, 2013
Published: January 11, 2013

Citation
Li Hongtao, Chen Shichao, Han Yanjun, and Luo Yi, "A fast feedback method to design easy-molding freeform optical system with uniform illuminance and high light control efficiency," Opt. Express 21, 1258-1269 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-1-1258


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References

  1. A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-state Lighting.(John Wiley & Sons, 2002).
  2. E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science308(5726), 1274–1278 (2005). [CrossRef] [PubMed]
  3. L. Caffarelli and V. Oliker, “Weak solutions of one inverse problem in geometric optics,” J. Math. Sci. 154(1), 37–46 (2008, Preprint, 1994).
  4. V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE5924, 594207, 594207-12 (2005). [CrossRef]
  5. H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A19(3), 590–595 (2002). [CrossRef] [PubMed]
  6. W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).
  7. P. Benitez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, and W. Falicoff, “Simultaneous multiple surface optical design method in three dimensions,” Opt. Eng.43(7), 1489–1502 (2004). [CrossRef]
  8. L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt.46(18), 3716–3723 (2007). [CrossRef] [PubMed]
  9. Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010). [CrossRef] [PubMed]
  10. W. Situ, Y. Han, H. Li, and Y. Luo, “Combined feedback method for designing a free-form optical system with complicated illumination patterns for an extended LED source,” Opt. Express19(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]
  11. K. Wang, S. Liu, F. Chen, Z. Y. Liu, and X. Luo, “Effect of manufacturing defects on optical performance of discontinuous freeform lenses,” Opt. Express17(7), 5457–5465 (2009). [CrossRef] [PubMed]
  12. K. Wang, S. Liu, F. Chen, Z. Qin, Z. Y. Liu, and X. B. Luo, “Freeform LED lens for rectangularly prescribed illumination,” J. Opt. A, Pure Appl. Opt.11(10), 105501 (2009). [CrossRef]
  13. Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express16(17), 12958–12966 (2008). [CrossRef] [PubMed]
  14. Z. Zhenrong, H. Xiang, and L. Xu, “Freeform surface lens for LED uniform illumination,” Appl. Opt.48(35), 6627–6634 (2009). [CrossRef] [PubMed]
  15. Florian Fournier, “Freeform reflector design with extended sources”, A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in CREOL, the College of Optics and Photonics at the University of Central Florida Orlando, Florida, 2010.
  16. F. R. Fournier, W. J. Cassarly, and J. P. Rolland, “Fast freeform reflector generation usingsource-target maps,” Opt. Express18(5), 5295–5304 (2010). [CrossRef] [PubMed]
  17. R. Hu, X. Luo, H. Zheng, Z. Qin, Z. Gan, B. Wu, and S. Liu, “Design of a novel freeform lens for LED uniform illumination and conformal phosphor coating,” Opt. Express20(13), 13727–13737 (2012). [CrossRef] [PubMed]
  18. W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE7652, 76522L, 76522L-9 (2010). [CrossRef]
  19. J. D’Errico, “Surface Fitting using gridfit,” (MATLAB CENTRAL File Exchange, 11 Nov 2005, Updated 29 Jul 2010). http://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit .

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