Abstract

In the stage illumination industry, LED technology is promising both in terms of energy use and novel features, but it also has inherent issues. This paper presents a solution to the poor color homogeneity arising when multiple rectangular images formed from LED dies are combined into a circular spot profile. Using ray tracing, a nonrotationally symmetric collimating lens was optimized to round off such die images. The result is a high-output lens with an almost perfectly circular spot. In a simulated red green blue color mixing projector with seven LEDs, the lens reduced measurable color inhomogeneity by 24.1%, with a 5.3% luminous gain, compared to the best rotationally symmetric benchmark lens.

© 2011 Optical Society of America

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References

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  1. “Summary of the ENERGY STAR solid-state lighting (SSL) criteria v. 1.1,” http://www.energystar.gov/ia/partners/product_specs/program_reqs/SSL_Key_Product_Criteria.pdf(2008).
  2. “ENERGY STAR Program requirements for cfls partner commitments,” http://www.energystar.gov/ia/partners/prod_development/revisions/downloads/cfls/Criteria_Version4_122105.pdf (2005).
  3. J.-Q. Chen, “LED flood light,” China patent CN 200820045569 (2008).
  4. MAC 350 Entour, Martin Professional A/S, http://www.martin.com/product/product.asp?product=mac350entour.
  5. CBT-90 series LED, Luminus Devices, Inc., http://www.luminus.com.
  6. J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001(2010).
    [CrossRef]
  7. J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik (Jena) 121, 1761–1765 (2010).
    [CrossRef]
  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, 1489–1502 (2004).
    [CrossRef]
  9. L. Harris, “Unitary lens system,” U.S. patent 2,254,961(2 September 1941); the relevant figure is Fig. 15.
  10. L. A. Piegl, “On NURBS: a survey,” IEEE Comp. Grap. Appl. 11, 55–71 (1991).
    [CrossRef]
  11. D. Solomon, Curves and Surfaces for Computer Graphics (Springer Verlag, 2005).
  12. T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
    [CrossRef]
  13. G. Sharma, Digital Color Imaging Handbook (CRC, 2003).
  14. G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations” (2004), http://www.ece.rochester.edu/gsharma/ciede2000/ciede2000noteCRNA.pdf.

2010 (2)

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001(2010).
[CrossRef]

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik (Jena) 121, 1761–1765 (2010).
[CrossRef]

2004 (1)

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, 1489–1502 (2004).
[CrossRef]

1991 (1)

L. A. Piegl, “On NURBS: a survey,” IEEE Comp. Grap. Appl. 11, 55–71 (1991).
[CrossRef]

1931 (1)

T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
[CrossRef]

Benítez, P.

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, 1489–1502 (2004).
[CrossRef]

Blen, J.

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, 1489–1502 (2004).
[CrossRef]

Chaves, J.

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, 1489–1502 (2004).
[CrossRef]

Chen, J.-J.

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001(2010).
[CrossRef]

Chen, J.-Q.

J.-Q. Chen, “LED flood light,” China patent CN 200820045569 (2008).

Cheung, B.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik (Jena) 121, 1761–1765 (2010).
[CrossRef]

Dalal, E. N.

G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations” (2004), http://www.ece.rochester.edu/gsharma/ciede2000/ciede2000noteCRNA.pdf.

Dross, O.

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, 1489–1502 (2004).
[CrossRef]

Falicoff, W.

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, 1489–1502 (2004).
[CrossRef]

Guild, J.

T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
[CrossRef]

Harris, L.

L. Harris, “Unitary lens system,” U.S. patent 2,254,961(2 September 1941); the relevant figure is Fig. 15.

Hernández, M.

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, 1489–1502 (2004).
[CrossRef]

Jiang, J.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik (Jena) 121, 1761–1765 (2010).
[CrossRef]

Lee, W. B.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik (Jena) 121, 1761–1765 (2010).
[CrossRef]

Lin, C.-T.

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001(2010).
[CrossRef]

Miñano, J. C.

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, 1489–1502 (2004).
[CrossRef]

Mohedano, R.

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, 1489–1502 (2004).
[CrossRef]

Piegl, L. A.

L. A. Piegl, “On NURBS: a survey,” IEEE Comp. Grap. Appl. 11, 55–71 (1991).
[CrossRef]

Sharma, G.

G. Sharma, Digital Color Imaging Handbook (CRC, 2003).

G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations” (2004), http://www.ece.rochester.edu/gsharma/ciede2000/ciede2000noteCRNA.pdf.

Smith, T.

T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
[CrossRef]

Solomon, D.

D. Solomon, Curves and Surfaces for Computer Graphics (Springer Verlag, 2005).

To, S.

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik (Jena) 121, 1761–1765 (2010).
[CrossRef]

Wu, W.

G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations” (2004), http://www.ece.rochester.edu/gsharma/ciede2000/ciede2000noteCRNA.pdf.

IEEE Comp. Grap. Appl. (1)

L. A. Piegl, “On NURBS: a survey,” IEEE Comp. Grap. Appl. 11, 55–71 (1991).
[CrossRef]

Opt. Eng. (2)

J.-J. Chen and C.-T. Lin, “Freeform surface design for a light-emitting diode-based collimating lens,” Opt. Eng. 49, 093001(2010).
[CrossRef]

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, 1489–1502 (2004).
[CrossRef]

Optik (Jena) (1)

J. Jiang, S. To, W. B. Lee, and B. Cheung, “Optical design of a freeform TIR lens for LED streetlight,” Optik (Jena) 121, 1761–1765 (2010).
[CrossRef]

Trans. Opt. Soc. (1)

T. Smith and J. Guild, “The C.I.E. colorimetric standards and their use,” Trans. Opt. Soc. 33, 73–134 (1931).
[CrossRef]

Other (9)

G. Sharma, Digital Color Imaging Handbook (CRC, 2003).

G. Sharma, W. Wu, and E. N. Dalal, “The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations” (2004), http://www.ece.rochester.edu/gsharma/ciede2000/ciede2000noteCRNA.pdf.

D. Solomon, Curves and Surfaces for Computer Graphics (Springer Verlag, 2005).

L. Harris, “Unitary lens system,” U.S. patent 2,254,961(2 September 1941); the relevant figure is Fig. 15.

“Summary of the ENERGY STAR solid-state lighting (SSL) criteria v. 1.1,” http://www.energystar.gov/ia/partners/product_specs/program_reqs/SSL_Key_Product_Criteria.pdf(2008).

“ENERGY STAR Program requirements for cfls partner commitments,” http://www.energystar.gov/ia/partners/prod_development/revisions/downloads/cfls/Criteria_Version4_122105.pdf (2005).

J.-Q. Chen, “LED flood light,” China patent CN 200820045569 (2008).

MAC 350 Entour, Martin Professional A/S, http://www.martin.com/product/product.asp?product=mac350entour.

CBT-90 series LED, Luminus Devices, Inc., http://www.luminus.com.

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Figures (9)

Fig. 1
Fig. 1

Arrangement of LEDs and TIR lenses in a color mixing projector from Martin Professional. Light from seven LEDs are focused into a gate by seven identical TIR lenses. TIR contributions are not shown. Left: Simulated version. Right: Prototype of the device.

Fig. 2
Fig. 2

(a) Graphical illustration of seven LED die images overlapping at an angle in an attempt to fit to a round spot. (b) Optical calculation of the spot of a 7-LED color mixing projector in the same configuration as in (a). The LED configuration in both images is: two red, two green, one blue, and two white.

Fig. 3
Fig. 3

(a) Cross section of the basic TIR lens design, being rotationally symmetric around the Z axis and working through both Fresnel refraction and TIR. (b) The lens is optimized using ray data collected in a circular optical gate.

Fig. 4
Fig. 4

(a) NURBS modification is added to the TIR lens. The shape can be controlled by k. (b) Modification peak intersects with the diagonals of the LED die. The effects of r and Z modification are shown along a diagonal plane. (c) Examples of Z modification of a TIR lens at two k values, and r modification at k = 0.25 . (d) Side view of an NRS lens. Sections where modification is applied are shown as broken lines.

Fig. 5
Fig. 5

Roundness is measured through the deviation of the intensity-weighted RMS contour (dotted lines) from a reference contour (solid line) along a fan of measuring lines on a ray detector. The RMS of a spot with square features will deviate from a circular reference.

Fig. 6
Fig. 6

Intensity profiles as measured in the gate. Darker shades signify higher intensity. (a) O lens; (b) D lens; (c) NRS lens.

Fig. 7
Fig. 7

Horizontal and diagonal (subscripted with an x) cross sections at the center of the gate detector for each lens type. The vertical lines show the distance at which the horizontal and diagonal profiles of a lens start to diverge significantly. The cross sections of the D and O lenses diverge at almost the exact same radius, while the NRS lens diverges 2 mm further out.

Fig. 8
Fig. 8

Mean CIEDE2000 color distances of the spot of the 7-LED red green blue color projector, as calculated on an array of concentric rings on the detector. ϵ is the noise level and ϵ + JND is the noise level plus the JND. The radius on the detector is proportional to the ring number. The edge ring is not represented since it is mostly noise.

Fig. 9
Fig. 9

Top: Spot of the 7-LED red green blue color projector for (a) the O lens and (b) the NRS lens. Bottom: Mean CIEDE2000 color distances of the spot, calculated in concentric rings: (c) the O lens Δ E 00 max = 17.7 ; (d) the NRS lens Δ E 00 max = 7.3 .

Tables (2)

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Table 1 Roundness Optimization Data a

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Table 2 Color Mixing Data a

Equations (10)

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S ( s , t ) = ( r ( s ) cos ( t π / 2 ) r ( s ) sin ( t π / 2 ) Z ( s ) ) , s , t = 0 1 ,
S ( s , t , k ) = ( ( r ( s ) + r ( s ) N ( t , k ) ) cos ( t π / 2 ) ( r ( s ) + r ( s ) N ( t , k ) ) sin ( t π / 2 ) Z ( s ) + Z ( s ) N ( t , k ) ) , s , t = 0 1 , k [ 0.05 0.45 ] ,
rms ( θ ) = [ j = 1 m I ( r j , θ ) r j 2 j = 1 m I ( r j , θ ) ] 1 / 2 ,
RMSD = [ i = 1 n ( rms ( θ i ) / rms 1 ) 2 n ] 1 / 2 ,
L * = 116 f ( Y / Y n ) 16 ,
a * = 500 [ f ( X / X n ) f ( Y / Y n ) ] ,
b * = 200 [ f ( Y / Y n ) f ( Z / Z n ) ] ,
f ( t ) = { t 1 / 3 , t > ( 6 29 ) 3 1 3 ( 29 6 ) 2 t + 4 / 29 , otherwise ,
ring i { p P r i 1 p x 2 + p y 2 < r i } , i 1 , 2 , , n , r i = r s i / n ,
Δ E 00 , i , m = Δ E 00 ( C Lab ( p ) , C Lab ( p m ) ) , p ring i ,

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