## Overlapping-based optical freeform surface construction for extended lighting source |

Optics Express, Vol. 21, Issue 17, pp. 19750-19761 (2013)

http://dx.doi.org/10.1364/OE.21.019750

Acrobat PDF (1436 KB)

### Abstract

The freeform optical system for an extended source was constructed by partially overlapping a few numbers of point-source freeform surfaces (PFSs) and extracting their contour. Each PFS redistributed the Lambertian emission of a point source into the prescribed light distribution or more frequently into a modified distribution. By adjusting the relative positions of the PFSs and the pattern of the modified light distribution, the optimized freeform surface could be obtained. As an example, an optical system with a height only four times the source radius is designed for achieving a uniform-illuminance distribution on the target. The optimized freeform surface was formed by two PFSs. The virtue-point-sources of the PFSs were located symmetrically on the extended source with a distance of a quarter of the source diameter from each other. Each PFS achieved an increasing-illuminance distribution. The illumination uniformity of this model can be improved by 55.4%, while the optical efficiency within the target area is maintained above 80%.

© 2013 OSA

## 1. Introduction

1. T. Kari, J. Gadegaard, T. Søndergaard, T. G. Pedersen, and K. Pedersen, “Reliability of point source approximations in compact LED lens designs,” Opt. Express **19**(S6Suppl 6), A1190–A1195 (2011). [CrossRef] [PubMed]

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

6. 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]

7. Y. Luo, Z. X. Feng, Y. J. Han, and H. T. 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]

8. P. Benítez, 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]

10. F. Muñoz, P. Beníteza, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. **43**(7), 1522–1530 (2004). [CrossRef]

11. P. A. Davies, “Edge-ray principle of nonimaging optics,” J. Opt. Soc. Am. A **11**(4), 1256–1259 (1994). [CrossRef]

7. Y. Luo, Z. X. Feng, Y. J. Han, and H. T. 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]

13. W. C. Situ, Y. J. Han, H. T. 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]

^{2}extended sources, and the ratio of the optical system height to the source radius (

7. Y. Luo, Z. X. Feng, Y. J. Han, and H. T. 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]

9. O. Dross, R. Mohedano, P. Beníteza, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS Design Methods and Real World Applications,” Proc. SPIE **5529**, 35–47 (2004). [CrossRef]

10. F. Muñoz, P. Beníteza, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. **43**(7), 1522–1530 (2004). [CrossRef]

13. W. C. Situ, Y. J. Han, H. T. 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]

14. K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific Light-Emitting Diode packaging,” Opt. Express **18**(2), 413–425 (2010). [CrossRef] [PubMed]

15. V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE **5942**, 594207 (2005). [CrossRef]

16. V. Oliker, “Designing Freeform Lenses for Intensity and Phase Control of Coherent Light with Help from Geometry and Mass Transport,” Arch. Ration. Mech. Anal. **201**(3), 1013–1045 (2011). [CrossRef]

15. V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE **5942**, 594207 (2005). [CrossRef]

16. V. Oliker, “Designing Freeform Lenses for Intensity and Phase Control of Coherent Light with Help from Geometry and Mass Transport,” Arch. Ration. Mech. Anal. **201**(3), 1013–1045 (2011). [CrossRef]

## 2. Ideal point-source’s freeform surfaces overlapping method

### 2.1 Principle of ideal point-source’s freeform surfaces overlapping method

*A*is the light distribution on the screen from a point source, and

*B*is the light distribution achieved on the screen from an extended source. The light distribution of

*A*can be modified differently from the prescribed light distribution

*G*, so as to make the light distribution of

*B*as closely as possible to

*G*. The pretreatments of the light distribution of the virtual point sources include the following: decreasing the radius of light distribution

*A*according to the prescribed light distribution

*G*; changing the light distribution pattern while maintaining the radius of

*A*; and integrating the two techniques mentioned above.

6. 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]

6. 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]

### 2.2 The design process of the ideal point source’s freeform surfaces overlapping method

*G*on the target plane, the dimensional parameters of the optical system and the material refractive index, etc are determined. Then the pattern of the light distribution

*A*for the point source is set (the prescribed light distribution

*G*can be used as the initial distribution for

*A*), and one of the existent freeform surface construction methods for point source is applied to get the freeform surface

*C*1 which can form the light distribution

*A*on the target. Then the number of the virtual point sources on the extended source is selected, and

*C*1 is emplaced above each selected point sources to precisely control their emission fields individually. The multiple

*C*1’s are joined into a new freeform surface

*C*2 by a combination approach (e. g. by extracting external or internal contour). The light distribution

*B*on the target plane is acquired by simulating the optical field from the extended source through

*C*2. Then

*B*is compared with the prescribed light distribution

*G*. If

*B*does not meet the requirements, it is necessary to use the light distribution pretreatment for modifying the light distribution

*A*, and re-start the process. Otherwise, the optimized freeform surface

*C*2 for the extended source is obtained.

## 3. Design of an optical system and discussions

*G*is the uniform illumination distribution with 1000mm radius on the screen, which is 1000mm from the extended source.

*N*is the number of meshes in the target area,

*C*1

*was the PFS designed by the freeform designing method [6*

_{ps freeform design}**46**(18), 3716–3723 (2007). [CrossRef] [PubMed]

*G*from an ideal point source accurately. When

*C*1

*was used to directly control the optical field from the 5mm radius circular Lambertian source, the optical efficiency within the target area is 84.87%, and the RSD value is 0.4132.*

_{ps freeform design}*C*1’s, respectively

*(C*1 is same as

*C*1

*when light distribution pretreatment is not used). Due to the rotational symmetry of the system, the virtual-point-sources were selected symmetrically on the same diameter of the extended source. The horizontal ordinates in Fig. 5 represent the overlapping modes of the PFSs. For instance, 5F(0,?2.5,?5mm) represents that five*

_{ps freeform design}*C*1’s are located above five uniformly-spaced virtual-point-sources, and one of the point source is in the center of the extended source, two are 2.5mm off the source center and the last two are 5mm off the center. In Fig. 5(a), the outmost point source positions are all 5mm off the extended-source center, and the optical efficiency of the three cases are in the vicinity of 55%, while the RSD values have small fluctuations around 0.04. In Fig. 5(b), the outmost positions are all 2.5mm off the center, and the optical efficiency of the systems are all in the vicinity of 75%, while the RSD values are close to 0.135.

*C*2 was mainly affected by the positions of the outermost point sources, and when the external contour was extracted, varying the number of the PFSs only influences the center region of

*C*2, which accounts for a very small proportion of the entire

*C*2. Therefore, in the following calculations only two virtual-point-sources are considered so as to simplify the optimization procedure.

*S,*respectively.

*S*stands for the distance that the two symmetrical point source positions deviate from the center of the extended source. If

*S*= 0, it means that the proposed overlapping method is not used, and the freeform surface

*C*2 coincides with the PFS

*C*1. According to Fig. 6, as

*S*increasing, no matter the external or the internal contour is extracted, the efficiency of the optical system declines and the value is lower than that of the case

*S*= 0. However, the light distribution uniformity is significantly improved with the increase of

*S*when the external contour is used; but the uniformity deteriorated in the internal contour case. Consequently, to obtain better light distribution uniformity, extracting external contour is adopted as the combination approach of the freeform surfaces

*C*1’s.

*S*varying from 0 to 5mm, assuming the external contour condition. It reveals that an increased efficiency of the optical system is often accompanied by a reduction of the uniformity (RSD value gets larger) when

*S*varies, and vice versa. In addition, it is noticed that when

*S*= 1.25 mm, the efficiency is 81.95% and the uniformity of the light distribution is increased by 36.8% compared with the situation for

*S*= 0. Therefore, the following optimizations would be based on a pair of symmetrical point source positions with

*S*= 1.25 mm firstly, and the light distribution pretreatment was then employed to continue reducing the RSD value while maintaining the efficiency above 80%.

*A*and part of the light distribution pretreatments. The line marked with circles portrays the original light distribution

*A*which is the 1000mm radius uniform illumination distribution (the same as the prescribed distribution

*G*). Considering the scope within [0mm, 1000mm], the solid line and the dotted line portray the linear-decreasing (LD) illuminance distribution (Eq. (6)) and the cosine-decreasing (CD) illuminance distribution (Eq. (7)) respectively; the dash-dot line is the linear-increasing illuminance distribution (Eq. (6)); the dashed line is the hollow illumination distribution (Eq. (8)) in which the minimum illuminance is at the midpoint of the radius; the line marked with dots is the light distribution with a shortened radius. In addition, simultaneously reducing the radius and changing the light distribution are included in light distribution pretreatments. All the axial cross-sectional lines in Fig. 7 are represented with the same total luminous flux on the screen.

*R*is the radius of the prescribed light distribution;

*t*in Eq. (6) and Eq. (7) is the ratio of the illuminance at the edge of the light distribution to the illuminance at the center of the light distribution;

*h*in Eq. (8) is the ratio of the minimum illuminance to the illuminance at the center (or the edge) of the light distribution.

*S*= 1.25 mm, the effect of decreasing illuminance distribution pretreatment on the results was first studied. Linear-decreasing (LD) illuminance distribution and cosine-decreasing (CD) illuminance distribution were analyzed and compared. Figure 8 shows the variations of the efficiency and RSD values of the systems with

*t*varying from 0.5 to 1.0. It indicates that the efficiency of these optical systems is higher than that of the uniform distribution case (

*t*= 1.0), where the decreasing illuminance distribution is used. However, the uniformity suffers significant deterioration. Therefore, the decreasing illuminance distribution pretreatment was improper when the prescribed light distribution for extended source was uniform illuminance.

*t*values. The radius of the light distribution

*A*remained 1000mm. In Fig. 9,

*t*= 1.0 represents the condition in which the light distribution pretreatment is not used. As the value of

*t*increases from 1.0 to 2.3, the optical efficiency drops slightly, but the RSD value decreases discernibly, indicating significant improvement of the light distribution uniformity.

*h*values. The radius of the light distribution

*A*was still 1000mm. In Fig. 10,

*h*= 1.0 represents the condition when the light distribution pretreatment is not used. As

*h*decreases from 1.0 to 0.5, the optical efficiency declines a little faster than that of the systems using the linear-increasing illuminance distribution, and the RSD declines slowly.

*S*= 1.25mm. The criteria for the optimized models are that the efficiency be higher than 80% and the RSD has the minimized value. Compared with the Model Reference2 in which the light distribution pretreatment was not used, the efficiency of the optimized Model OPT1 declines slightly (2.3%), but the uniformity improves significantly by 29.5%. The improvement in uniformity is about 55.4% when compared with Model Reference1. Consequently, OPT1 was selected as the optimized model in the condition that

*S*= 1.25mm.

*S*= 1.875, 2.5, and 3.125 mm, respectively. Table 3 shows the optimized models and results of the four conditions.

*S*= 1.25 mm), OPT3 (

*S*= 1.875 mm), OPT4 (

*S*= 2.5 mm) and OPT5 (

*S*= 3.125 mm).

## 4. Conclusions

## Acknowledgments

## References and links

1. | T. Kari, J. Gadegaard, T. Søndergaard, T. G. Pedersen, and K. Pedersen, “Reliability of point source approximations in compact LED lens designs,” Opt. Express |

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

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

4. | J. Bortz and N. Shatz, “Generalized functional method of nonimaging optical design,” Proc. SPIE |

5. | C. Canavesi, W. J. Cassarly, and J. P. Rolland, “Observations on the linear programming formulation of the single reflector design problem,” Opt. Express |

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

7. | Y. Luo, Z. X. Feng, Y. J. Han, and H. T. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express |

8. | P. Benítez, 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. |

9. | O. Dross, R. Mohedano, P. Beníteza, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS Design Methods and Real World Applications,” Proc. SPIE |

10. | F. Muñoz, P. Beníteza, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng. |

11. | P. A. Davies, “Edge-ray principle of nonimaging optics,” J. Opt. Soc. Am. A |

12. | W. J. Cassarly, “Iterative Reflector Design Using a Cumulative Flux Compensation Approach ,” Proc. SPIE |

13. | W. C. Situ, Y. J. Han, H. T. 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 |

14. | K. Wang, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific Light-Emitting Diode packaging,” Opt. Express |

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

16. | V. Oliker, “Designing Freeform Lenses for Intensity and Phase Control of Coherent Light with Help from Geometry and Mass Transport,” Arch. Ration. Mech. Anal. |

**OCIS Codes**

(230.3670) Optical devices : Light-emitting diodes

(220.2945) Optical design and fabrication : Illumination design

(080.4298) Geometric optics : Nonimaging optics

**ToC Category:**

Geometric Optics

**History**

Original Manuscript: April 29, 2013

Revised Manuscript: August 2, 2013

Manuscript Accepted: August 2, 2013

Published: August 15, 2013

**Citation**

Kun Wang, Yanjun Han, Hongtao Li, and Yi Luo, "Overlapping-based optical freeform surface construction for extended lighting source," Opt. Express **21**, 19750-19761 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-19750

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### References

- T. Kari, J. Gadegaard, T. Søndergaard, T. G. Pedersen, and K. Pedersen, “Reliability of point source approximations in compact LED lens designs,” Opt. Express19(S6Suppl 6), A1190–A1195 (2011). [CrossRef] [PubMed]
- W. A. Parkyn, “Design of illumination lenses via extrinsic differential geometry,” Proc. SPIE3428, 154–162 (1998). [CrossRef]
- H. Ries and J. A. Muschaweck, “Tailored freeform optical surfaces,” J. Opt. Soc. Am. A19(3), 590–595 (2002). [CrossRef] [PubMed]
- J. Bortz and N. Shatz, “Generalized functional method of nonimaging optical design,” Proc. SPIE6338, 633805, 633805-16 (2006). [CrossRef]
- C. Canavesi, W. J. Cassarly, and J. P. Rolland, “Observations on the linear programming formulation of the single reflector design problem,” Opt. Express20(4), 4050–4055 (2012). [CrossRef] [PubMed]
- 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. X. Feng, Y. J. Han, and H. T. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express18(9), 9055–9063 (2010). [CrossRef] [PubMed]
- P. Benítez, 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]
- O. Dross, R. Mohedano, P. Beníteza, J. C. Miñano, J. Chaves, J. Blen, M. Hernández, and F. Muñoz, “Review of SMS Design Methods and Real World Applications,” Proc. SPIE5529, 35–47 (2004). [CrossRef]
- F. Muñoz, P. Beníteza, O. Dross, J. C. Miñano, and B. Parkyn, “Simultaneous multiple surface design of compact air-gap collimators for light-emitting diodes,” Opt. Eng.43(7), 1522–1530 (2004). [CrossRef]
- P. A. Davies, “Edge-ray principle of nonimaging optics,” J. Opt. Soc. Am. A11(4), 1256–1259 (1994). [CrossRef]
- W. J. Cassarly, “Iterative Reflector Design Using a Cumulative Flux Compensation Approach,” Proc. SPIE 7652, 76522L 1–9 (2010).
- W. C. Situ, Y. J. Han, H. T. 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, F. Chen, Z. Y. Liu, X. B. Luo, and S. Liu, “Design of compact freeform lens for application specific Light-Emitting Diode packaging,” Opt. Express18(2), 413–425 (2010). [CrossRef] [PubMed]
- V. Oliker, “Geometric and variational methods in optical design of reflecting surfaces with prescribed irradiance properties,” Proc. SPIE5942, 594207 (2005). [CrossRef]
- V. Oliker, “Designing Freeform Lenses for Intensity and Phase Control of Coherent Light with Help from Geometry and Mass Transport,” Arch. Ration. Mech. Anal.201(3), 1013–1045 (2011). [CrossRef]

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