## High-efficiency free-form condenser overcoming rotational symmetry limitations

Optics Express, Vol. 16, Issue 25, pp. 20193-20205 (2008)

http://dx.doi.org/10.1364/OE.16.020193

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### Abstract

Conventional condensers using rotational symmetric devices perform far from their theoretical limits when transferring optical power from sources such as arc lamps or halogen bulbs to the rectangular entrance of homogenizing prisms (target). We present a free-form condenser design (calculated with the SMS method) that overcomes the limitations inherent to rotational devices and can send to the target 1.8 times the power sent by an equivalent elliptical condenser for a 4:1 target aspect ratio and 1.5 times for 16:9 target and for practical values of target etendue.

© 2008 Optical Society of America

## 1. Introduction

1. J. C. Miñano and J. C. González, “New method of design of nonimaging concentrators,” Appl. Opt. **31**, 3051–3060 (1992). http://www.opticsinfobase.org/abstract.cfm?URI=ao-31-16-3051 [CrossRef] [PubMed]

7. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff. “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE **5185**, 18–29 (2003). [CrossRef]

8. J. Chaves, *Introduction to Nonimaging Optics*, (CRC Press, Boca Ratón, 2008). [CrossRef]

4. P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A **14**, 1988–1997 (1997). http://www.opticsinfobase.org/abstract.cfm?URI=josaa-14-8-1988 [CrossRef]

^{2}srad etendue range have collection efficiencies about 40–50% for the best condensers, although theory allows about 100% (collection efficiency defined as the ratio of power sent to the target to total source power).

*i.e.*, coma).

## 2. Design of the XX condenser

_{1}and c

_{2}are constants that define the mapping of the center of the source to the center of the target. This mapping implies that to a first-order approximation (valid for a small source) the SMS method provides an image-forming design whereby the light source is placed on the object plane and the target on the image plane. In Fig. 3, points A, B, C and D are object points while A’, B’, C’ and D’ are their corresponding image points. The diagonal of the matrix in the previous equation defines the magnifications of the optical system. Constants M and N, are defined as: magnification M: ratio between the segment of the target C’D’, and the segment CD of the source; magnification N: ratio between the segment of the target A’B’, and the segment AB of the source. Parameters M and N can be either positive or negative, so four families of XX can be considered.

*i.e.*, the SMS seed rib, [7

7. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff. “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE **5185**, 18–29 (2003). [CrossRef]

7. P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff. “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE **5185**, 18–29 (2003). [CrossRef]

8. J. Chaves, *Introduction to Nonimaging Optics*, (CRC Press, Boca Ratón, 2008). [CrossRef]

## 2.1 The XX design for a cylindrical source

*β*

_{MIN}with the cylinder’s axis. The rays accepted by the target are those reaching a rectangle forming an angle smaller than

*ϕ*

_{MAX}with the normal to the rectangle. The condenser has to maximize the power transferred from the source to the target.

_{ox}are spherical and centered at the midpoints of the sides of the rectangular target. Two of the wavefront couples WF

_{i3}-WF

_{o3}and WF

_{i4}-WF

_{o4}are used for the calculations of the SMS chains while the other two couples WF

_{i1}-WF

_{o1}and WF

_{i2}-WF

_{o2}are only used only for initial curve calculation. This is why there is only a partial control of one dimension of the source images. WF

_{i3}and WF

_{i4}are orthonormal rays issuing form the cylinder edges. WF

_{i1}and WF

_{i2}are formed by tangent rays to the cylinder.

## 3. Ray tracing results.

*β*

_{MIN}=45°.

*ϕ*

_{MAX}=19°.

*E*

_{target}=

*A*

_{target}π sin

^{2}(

*ϕ*

_{MAX}), where

*A*

_{target}is the target area and

*ϕ*

_{MAX}=±19° is the target acceptance angle. The etendue of the target was varied by varying the target area

*A*

_{target}while freezing the target aspect ratio (4:1) and its circular field of view

*ϕ*

_{MAX}.

*ϕ*

_{MAX}=±30° (which is also the standard value in the market). The third curve in Fig. 13 corresponds to the theoretical limit, which is imposed by etendue constraints: an ideal condenser achieving it (which may not exist) would transfer all the source power to the target if the target etendue is greater than the source etendue (i.e., it will have a 100% collection efficiency in this case), and would fully fill the target etendue with light from the source if the source etendue is larger than the target etendue. Then the ideal condenser will have a collection efficiency equal to the ratio of target to source etendue when the target etendue is smaller than the source etendue.

_{source}=3.13 mm

^{2}. Fig. 13 shows that the XX performs much better than the elliptical reflector (for all mirrors, specular reflectivity has been set equal to 1), getting close to the theoretical limit. There are three factors, however, that prevent the XX from reaching the theoretical limit:

^{2}) and keeping the rest of parameters unchanged, will produce a 16:9 irradiance distribution on the target plane. Fig. 16 shows the ray tracing results. The XX with target’s circular field of view of

*ϕ*

_{MAX}=19° still performs better than elliptical reflector, although the gain is reduced to 1.5, due to the lower aspect ratio of the target (again, for all mirrors, specular reflectivity has been set equal to 1). The theoretical limit is also reduced to 2.

## 4. Demonstrator prototype

## 6. Conclusions

## Acknowledgment

## References and Links

1. | J. C. Miñano and J. C. González, “New method of design of nonimaging concentrators,” Appl. Opt. |

2. | J. C. Miñano, P. Benítez, and J. C. González, “RX: a nonimaging concentrator,” Appl. Opt. |

3. | J. C. Miñano, J. C. Gonźlez, and P. Benítez, “A high-gain, compact, nonimaging concentrator: RXI,” Appl. Opt. |

4. | P. Benítez and J. C. Miñano, “Ultrahigh-numerical-aperture imaging concentrator,” J. Opt. Soc. Am. A |

5. | R. Winston, J. C. Miñano, and P. Benítez, |

6. | W. Cassarly, “Nonimaging Optics,” in |

7. | P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, and W. Falicoff. “SMS Design Method in 3D Geometry: Examples and Applications,” Proc. SPIE |

8. | J. Chaves, |

9. | H. Moench and A. Ritz. “Higher Output, More Compact UHP Lamp Systems,” |

10. | K. Strobl, “Efficient light engine systems, components and methods of manufacture,” US Patent6,356,700 (2002). |

11. | K. K. Li, “Condensing and collecting optical system using parabolic reflectors or a corresponding ellipsoid/hyperboloid pair of reflectors,” US Patent6,672,740 (2004). |

12. | N. Tadaaki, “Illuminator and projection type display device,” JP Patent7,174,974 (1995). |

13. | J. A. Shimizu, “Method and light collection system for producing uniform arc image size,” US Patent5,966,250 (1999). |

14. | D. S. Dewald, S. M. Penn, and M. Davis, “Sequential Color Recapture and Dynamic Filtering: A Method of Scrolling Color,” |

15. | J. A. Shimizu, “Scrolling Color LCOS for HDTV Rear projection,” |

16. | M. Duelli and A. T. Taylor, “Novel polarization conversion and integration system for projection displays,” |

17. | |

18. | |

19. | |

20. | N. Shatz, J. C. Bortz, R. Winston, J. C. Miñano, and P. Benítez, (Academic Press, New York, 2005) Chap. 10. |

**OCIS Codes**

(080.2740) Geometric optics : Geometric optical design

(080.2175) Geometric optics : Etendue

(220.2945) Optical design and fabrication : Illumination design

(080.4035) Geometric optics : Mirror system design

(220.4298) Optical design and fabrication : Nonimaging optics

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: August 4, 2008

Revised Manuscript: November 13, 2008

Manuscript Accepted: November 18, 2008

Published: November 24, 2008

**Citation**

Juan C. Miñano, Pablo Benítez, José Blen, and Asunción Santamaría, "High-efficiency free-form condenser overcoming rotational symmetry limitations," Opt. Express **16**, 20193-20205 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20193

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### References

- J. C. Miñano and J. C. González, "New method of design of nonimaging concentrators," Appl. Opt. 31, 3051-3060 (1992), http://www.opticsinfobase.org/abstract.cfm?URI=ao-31-16-3051 [CrossRef] [PubMed]
- J. C. Miñano, P. Benítez, and J. C. González, "RX: a nonimaging concentrator," Appl. Opt. 34, 2226-2235 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-13-2226. [CrossRef] [PubMed]
- J. C. Miñano, J. C. Gonźlez, and P. Benítez, "A high-gain, compact, nonimaging concentrator: RXI," Appl. Opt. 34, 7850-7856 (1995), http://www.opticsinfobase.org/abstract.cfm?URI=ao-34-34-7850. [CrossRef] [PubMed]
- P. Benítez and J. C. Miñano, "Ultrahigh-numerical-aperture imaging concentrator," J. Opt. Soc. Am. A 14, 1988-1997 (1997), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-14-8-1988. [CrossRef]
- R. Winston, J. C. Miñano, and P. Benítez, Nonimaging Optics, (Academic Press, New York, 2005)
- W. Cassarly, "Nonimaging Optics," in Handbook of Optics, 2nd ed., (McGraw-Hill, NewYork, 2001) pp. 2.23-2.42.
- P. Benítez, J. C. Miñano, J. Blen, R. Mohedano, J. Chaves, O. Dross, M. Hernández, J. Alvarez, W. Falicoff. "SMS Design Method in 3D Geometry: Examples and Applications," Proc. SPIE 5185, 18-29 (2003). [CrossRef]
- J. Chaves, Introduction to Nonimaging Optics, (CRC Press, Boca Ratón, 2008). [CrossRef]
- H. Moench and A. Ritz. "Higher Output, More Compact UHP Lamp Systems," SID Int. Symp. Digest Tech. Papers (33) 1, (2002), pp. 1160-1163.
- K. Strobl, "Efficient light engine systems, components and methods of manufacture," US Patent 6,356,700 (2002).
- K. K. Li, "Condensing and collecting optical system using parabolic reflectors or a corresponding ellipsoid/ hyperboloid pair of reflectors," US Patent 6,672,740 (2004).
- N. Tadaaki, "Illuminator and projection type display device," JP Patent 7,174,974 (1995).
- J. A. Shimizu, "Method and light collection system for producing uniform arc image size," US Patent 5,966,250 (1999).
- D. S. Dewald, S. M. Penn, and M. Davis, "Sequential Color Recapture and Dynamic Filtering: A Method of Scrolling Color," SID Int. Symp. Digest Tech. Papers (32) 1, (2001), pp. 1076-1079.
- J. A. Shimizu, "Scrolling Color LCOS for HDTV Rear projection," SID Int. Symp. Digest Tech. Papers, (32) 1, (2001), pp. 1072-1075.
- M. Duelli and A. T. Taylor, "Novel polarization conversion and integration system for projection displays," SID Int. Symp. Digest Tech. Papers (34) 1, (2003), pp. 766-769.
- http://www.opticalres.com/lt/ltprodds_f.html
- http://www.rhino3d.com/
- http://www.lpi-llc.com/
- N. Shatz and J. C. Bortz, "Consequences of Symmetry," in Nonimaging Optics, R. Winston, J. C. Miñano, and P. Benítez, (Academic Press, New York, 2005) Chap. 10.

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