## A fast feedback method to design easy-molding freeform optical system with uniform illuminance and high light control efficiency |

Optics Express, Vol. 21, Issue 1, pp. 1258-1269 (2013)

http://dx.doi.org/10.1364/OE.21.001258

Acrobat PDF (1713 KB)

### 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 *(**equi-*

© 2013 OSA

## 1. Introduction

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

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]

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]

- (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)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.
*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 [8–108. 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]]. 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 [810. 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]**46**(18), 3716–3723 (2007). [CrossRef] [PubMed]**19**(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]

- (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]. 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.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] - (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.

## 2. Feedback method combined with fitting technique

*(*

*(*

*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

*(*

*-(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]

*(*

*equi-*

*equi-*

*equi-*

*i th*stripe (space between the

*i-th equi-*

*i*+ 1)-

*th equi-*

*i-th*stripe, while

*equi-*

*equi-*

**19**(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]

*x or y*on the target plane is fixed during the feedback process. What varies along with the feedback iterations is the prescribed energy assigned into these cells, which corresponds to different

*θ*and

*φ*angle. Let

*f(.)*is needed to assign

*f(.)*can be expressed in the following form:It implies that for

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]

**19**(S5Suppl 5), A1022–A1030 (2011). [CrossRef] [PubMed]

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

*(*

*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]

*(*

*(*

*(*

*(*

*(*

*(*

*x = Fitting(*

*y = Fitting(*

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.

*x = f*

_{1}(*y = f*

_{2}(*(*

*x*values in the

*(*

*(*

*equi-*

*equi-*

**46**(18), 3716–3723 (2007). [CrossRef] [PubMed]

*(*

## 3. Case study – Street Lamp with uniform illuminance

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]

**18**(9), 9055–9063 (2010). [CrossRef] [PubMed]

## 4. Summary

## Acknowledgment

## References and links

1. | A. Zukauskas, M. S. Shur, and R. Caska, |

2. | E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science |

3. | L. Caffarelli and V. Oliker, “Weak solutions of one inverse problem in geometric optics,” J. Math. Sci. |

4. | V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE |

5. | H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A |

6. | W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE |

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. |

8. | L. Wang, K. Y. Qian, and Y. Luo, “Discontinuous free-form lens design for prescribed irradiance,” Appl. Opt. |

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 |

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 |

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 |

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. |

13. | Y. Ding, X. Liu, Z. R. Zheng, and P. F. Gu, “Freeform LED lens for uniform illumination,” Opt. Express |

14. | Z. Zhenrong, H. Xiang, and L. Xu, “Freeform surface lens for LED uniform illumination,” Appl. Opt. |

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 |

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 |

18. | W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE |

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

- A. Zukauskas, M. S. Shur, and R. Caska, Introduction to Solid-state Lighting.(John Wiley & Sons, 2002).
- E. F. Schubert and J. K. Kim, “Solid-state light sources getting smart,” Science308(5726), 1274–1278 (2005). [CrossRef] [PubMed]
- L. Caffarelli and V. Oliker, “Weak solutions of one inverse problem in geometric optics,” J. Math. Sci. 154(1), 37–46 (2008, Preprint, 1994).
- V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE5924, 594207, 594207-12 (2005). [CrossRef]
- H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A19(3), 590–595 (2002). [CrossRef] [PubMed]
- W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998).
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- 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]
- Z. Zhenrong, H. Xiang, and L. Xu, “Freeform surface lens for LED uniform illumination,” Appl. Opt.48(35), 6627–6634 (2009). [CrossRef] [PubMed]
- 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.
- 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]
- 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]
- W. J. Cassarly, “Iterative reflector design using a cumulative flux compensation approach,” Proc. SPIE7652, 76522L, 76522L-9 (2010). [CrossRef]
- 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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