Abstract

A compensation process has been developed to design rotational three-dimensional (3D) nonimaging devices. By compensating the desired light distribution during a two-dimensional (2D) design process for an extended Lambertian source using a compensation coefficient, the meridian plane of a 3D device with good performance can be obtained. This method is suitable in many cases with fast calculation speed. Solutions to two kinds of optical design problems have been proposed, and the limitation of this compensated 2D design method is discussed.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Winston and H. Ries, "Nonimaging reflectors as functionals of the desired irradiance," J. Opt. Soc. Am. A 10, 1902-1908 (1993).
    [CrossRef]
  2. H. Ries and R. Winston, "Tailored edge-ray reflectors for illumination," J. Opt. Soc. Am. A 11, 1260-1264 (1994).
    [CrossRef]
  3. R. Winston, J. C. Minano, and P. Benitez, N. Shatz, and J. C. Bortz, "Concentrators for prescribed irradiance," in Nonimaging Optics (Elsevier, 2005), pp. 159-180.
  4. A. Rabl, P. T. Ong, J. M. Gordon, and W. Cai, "Iterative algorithm for reflector design for non-isotropic sources," in Maximum Efficiency Light Transfer III, R.Winston, eds., Proc. SPIE 2538,16-23 (1995).
  5. J. M. Gordon and A. Rabl, "Reflectors for uniform far-field irradiance: fundamental limits and example of an axisymmetric solution," Appl. Opt. , 37, 44-47 (1998).
    [CrossRef]
  6. P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).
  7. W. Tai and R. Schwarte, "Design of an aspherical lens to generate a homogenous irradiance for three-dimensional sensors with a light-emitting-diode source," Appl. Opt. 39, 5801-5805 (2000).
    [CrossRef]
  8. W. B. Elmer, "Curves generation," in The Optical Design of Reflectors, 2nd. ed. (Wiley, 1980), pp. 54-75.

2000 (1)

1998 (1)

1994 (1)

1993 (1)

Benitez, P.

R. Winston, J. C. Minano, and P. Benitez, N. Shatz, and J. C. Bortz, "Concentrators for prescribed irradiance," in Nonimaging Optics (Elsevier, 2005), pp. 159-180.

P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).

Bortz, J. C.

R. Winston, J. C. Minano, and P. Benitez, N. Shatz, and J. C. Bortz, "Concentrators for prescribed irradiance," in Nonimaging Optics (Elsevier, 2005), pp. 159-180.

Cai, W.

A. Rabl, P. T. Ong, J. M. Gordon, and W. Cai, "Iterative algorithm for reflector design for non-isotropic sources," in Maximum Efficiency Light Transfer III, R.Winston, eds., Proc. SPIE 2538,16-23 (1995).

Elmer, W. B.

W. B. Elmer, "Curves generation," in The Optical Design of Reflectors, 2nd. ed. (Wiley, 1980), pp. 54-75.

Gordon, J. M.

J. M. Gordon and A. Rabl, "Reflectors for uniform far-field irradiance: fundamental limits and example of an axisymmetric solution," Appl. Opt. , 37, 44-47 (1998).
[CrossRef]

A. Rabl, P. T. Ong, J. M. Gordon, and W. Cai, "Iterative algorithm for reflector design for non-isotropic sources," in Maximum Efficiency Light Transfer III, R.Winston, eds., Proc. SPIE 2538,16-23 (1995).

Hernandez, M.

P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).

Hirohashi, K.

P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).

Minano, J. C.

P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).

R. Winston, J. C. Minano, and P. Benitez, N. Shatz, and J. C. Bortz, "Concentrators for prescribed irradiance," in Nonimaging Optics (Elsevier, 2005), pp. 159-180.

Ong, P. T.

A. Rabl, P. T. Ong, J. M. Gordon, and W. Cai, "Iterative algorithm for reflector design for non-isotropic sources," in Maximum Efficiency Light Transfer III, R.Winston, eds., Proc. SPIE 2538,16-23 (1995).

Rabl, A.

J. M. Gordon and A. Rabl, "Reflectors for uniform far-field irradiance: fundamental limits and example of an axisymmetric solution," Appl. Opt. , 37, 44-47 (1998).
[CrossRef]

A. Rabl, P. T. Ong, J. M. Gordon, and W. Cai, "Iterative algorithm for reflector design for non-isotropic sources," in Maximum Efficiency Light Transfer III, R.Winston, eds., Proc. SPIE 2538,16-23 (1995).

Ries, H.

Sakai, M.

P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).

Schwarte, R.

Shatz, N.

R. Winston, J. C. Minano, and P. Benitez, N. Shatz, and J. C. Bortz, "Concentrators for prescribed irradiance," in Nonimaging Optics (Elsevier, 2005), pp. 159-180.

Tai, W.

Toguchi, S.

P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).

Winston, R.

Appl. Opt. (2)

J. Opt. Soc. Am. A (2)

Other (4)

R. Winston, J. C. Minano, and P. Benitez, N. Shatz, and J. C. Bortz, "Concentrators for prescribed irradiance," in Nonimaging Optics (Elsevier, 2005), pp. 159-180.

A. Rabl, P. T. Ong, J. M. Gordon, and W. Cai, "Iterative algorithm for reflector design for non-isotropic sources," in Maximum Efficiency Light Transfer III, R.Winston, eds., Proc. SPIE 2538,16-23 (1995).

P. Benitez, J. C. Minano, M. Hernandez, K. Hirohashi, S. Toguchi, and M. Sakai, "Novel nonimaging lens for photodiode receivers with a prescribed angular response and maximum integrated sensitivity," in Optical Wireless Communications III, J.Korevaar, ed., Proc. SPIE 4214,94-103 (2001).

W. B. Elmer, "Curves generation," in The Optical Design of Reflectors, 2nd. ed. (Wiley, 1980), pp. 54-75.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Systems of prescribed illuminance problem:(a) rotational 3D system, (b) 2D system.

Fig. 2
Fig. 2

Solution example:generating uniform illuminance by a reflector.

Fig. 3
Fig. 3

Ray-tracing illuminance distribution of the optical system aiming at uniform illuminance:(a) obtained by model generated from C2D ; (b) obtained by compensated model generated from C2D ′.

Fig. 4
Fig. 4

Solution example:generating linear luminous intensity by a lens.

Fig. 5
Fig. 5

Ray-tracing luminous intensity distribution. The dash-dot curve describes the performance of a rotational 3D device generated directly from C2D , and the solid curve is that from C2D ′. A is the area of the source.

Fig. 6
Fig. 6

Aggravation comparison of the devices generated by two methods when the relative sizes of the sources increase:(a) from the design method with point source, and (b) generated by the compensated method with a disk source with an x axis of θ and a y axis of A(θ)∕A.

Tables (1)

Tables Icon

Table 1 Illustration of Compensation Process and Steps

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

Φ 3 D = 2 π ϕ 1 ϕ 2 I 0 , 3 D cos ϕ sin ϕ d ϕ ,
Φ 3 D = 2 π r 1 r 2 P 3 D ( r ) r d r ,
d Φ 3 D d ϕ 2 = 2 π I 0 , 3 D sin ϕ 2 cos ϕ 2 ,
d Φ 3 D d r 2 = 2 π r 2 P 3 D ( r 2 ) .
d r 3 D = I 0 , 3 D P 3 D ( r ) sin ϕ cos ϕ r d ϕ .
d r 2 D = I 0 , 2 D P 2 D ( r ) cos ϕ d ϕ .
d r 3 D = I 0 , 3 D P 3 D ( r ) P 2 D ( r ) I 0 , 2 D sin ϕ r d r 2 D = ζ ( r , ϕ ) d r 2 D ,
ζ ( r , ϕ ) = I 0 , 3 D P 3 D ( r ) P 2 D ( r ) I 0 , 2 D sin ϕ r .
P 2 D ( r ) = f [ P 2 D ( r ) ] = P 2 D ( r ) / ζ ( r ) .
P 2 D ( r ) = cos 2 θ h L ( θ ) ,
P 3 D ( r ) = sin θ cos 2 θ h r A ( θ ) ,
ζ ( θ , ϕ ) = I 0 , 3 D A ( θ ) L ( θ ) I 0 , 2 D sin ϕ sin θ .
L 2 D ( θ ) = f [ L 2 D ( θ ) ] = L 2 D ( θ ) / ζ ( θ ) .
3 D: I 0,3 D / P 3 D ( r ) = R 2 ,
2 D: P 2 D ( r ) / I 0 , 2 D = R 1 .
ζ ( r ) = R r sin ϕ .
A ( θ ) = A 0 ( 1 + θ θ max ) , 0 < θ < θ max ,
A ( θ ) = 0 , θ > θ max .
2 π 0 π / 2 A ( θ ) sin θ d θ = 2 π 0 π / 2 I 0 , 3 D cos ϕ sin ϕ d ϕ .
I 0 , 3 D / A 0 = 2 ( sin θ max θ max 2 cos θ max + 1 ) .
L ( θ ) = L 0 ( 1 + θ θ max ) , 0 < θ < θ max ,
L ( θ ) = 0 , θ > θ max .
L 0 I 0 , 2 D = 2 3 θ max .
ζ ( θ ) = 4 3 θ max + sin θ max 2 θ max cos θ max θ max 2 sin ϕ sin θ .
A ( θ ) = A 0 ( 1 + θ 60 ° ) ( 0 < θ < 60 ° ) .

Metrics