Abstract

A planar optical array is presented that provides a selective concentration of the light incident upon the system onto a given area. Several alternative designs are analyzed and explained geometrically. The photometric calculation is presented for three different levels of approximation. A prototype of the proposed system is tested, showing good accordance with the theoretical predictions.

© 1999 Optical Society of America

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References

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  1. S. Wang, L. Ronchi, “Principles and design of optical arrays,” Prog. Opt. XXV, 279–348 (1988).
  2. J. Alda, H. Kamal, E. Bernabeu, “Optimum design of optical arrays with spatial integration feature,” Opt. Eng. 36, 2872–2877 (1997).
    [CrossRef]
  3. H. Kamal, “Design and properties of optical arrays,” PhD. dissertation (Universidad Complutense de Madrid, Spain, 1998).
  4. D. Vázquez, E. Bernabeu, “Array optical device for natural lighting,” Light. Res. Technol. 29, 33–39 (1997).
    [CrossRef]
  5. J. A. Quiroga, A. González, E. Bernabeu, “Fast method to measure the irradiance response of an image processing system,” Meas. Sci. Technol. 6, 181–187 (1995).
    [CrossRef]

1997

J. Alda, H. Kamal, E. Bernabeu, “Optimum design of optical arrays with spatial integration feature,” Opt. Eng. 36, 2872–2877 (1997).
[CrossRef]

D. Vázquez, E. Bernabeu, “Array optical device for natural lighting,” Light. Res. Technol. 29, 33–39 (1997).
[CrossRef]

1995

J. A. Quiroga, A. González, E. Bernabeu, “Fast method to measure the irradiance response of an image processing system,” Meas. Sci. Technol. 6, 181–187 (1995).
[CrossRef]

1988

S. Wang, L. Ronchi, “Principles and design of optical arrays,” Prog. Opt. XXV, 279–348 (1988).

Alda, J.

J. Alda, H. Kamal, E. Bernabeu, “Optimum design of optical arrays with spatial integration feature,” Opt. Eng. 36, 2872–2877 (1997).
[CrossRef]

Bernabeu, E.

J. Alda, H. Kamal, E. Bernabeu, “Optimum design of optical arrays with spatial integration feature,” Opt. Eng. 36, 2872–2877 (1997).
[CrossRef]

D. Vázquez, E. Bernabeu, “Array optical device for natural lighting,” Light. Res. Technol. 29, 33–39 (1997).
[CrossRef]

J. A. Quiroga, A. González, E. Bernabeu, “Fast method to measure the irradiance response of an image processing system,” Meas. Sci. Technol. 6, 181–187 (1995).
[CrossRef]

González, A.

J. A. Quiroga, A. González, E. Bernabeu, “Fast method to measure the irradiance response of an image processing system,” Meas. Sci. Technol. 6, 181–187 (1995).
[CrossRef]

Kamal, H.

J. Alda, H. Kamal, E. Bernabeu, “Optimum design of optical arrays with spatial integration feature,” Opt. Eng. 36, 2872–2877 (1997).
[CrossRef]

H. Kamal, “Design and properties of optical arrays,” PhD. dissertation (Universidad Complutense de Madrid, Spain, 1998).

Quiroga, J. A.

J. A. Quiroga, A. González, E. Bernabeu, “Fast method to measure the irradiance response of an image processing system,” Meas. Sci. Technol. 6, 181–187 (1995).
[CrossRef]

Ronchi, L.

S. Wang, L. Ronchi, “Principles and design of optical arrays,” Prog. Opt. XXV, 279–348 (1988).

Vázquez, D.

D. Vázquez, E. Bernabeu, “Array optical device for natural lighting,” Light. Res. Technol. 29, 33–39 (1997).
[CrossRef]

Wang, S.

S. Wang, L. Ronchi, “Principles and design of optical arrays,” Prog. Opt. XXV, 279–348 (1988).

Light. Res. Technol.

D. Vázquez, E. Bernabeu, “Array optical device for natural lighting,” Light. Res. Technol. 29, 33–39 (1997).
[CrossRef]

Meas. Sci. Technol.

J. A. Quiroga, A. González, E. Bernabeu, “Fast method to measure the irradiance response of an image processing system,” Meas. Sci. Technol. 6, 181–187 (1995).
[CrossRef]

Opt. Eng.

J. Alda, H. Kamal, E. Bernabeu, “Optimum design of optical arrays with spatial integration feature,” Opt. Eng. 36, 2872–2877 (1997).
[CrossRef]

Prog. Opt.

S. Wang, L. Ronchi, “Principles and design of optical arrays,” Prog. Opt. XXV, 279–348 (1988).

Other

H. Kamal, “Design and properties of optical arrays,” PhD. dissertation (Universidad Complutense de Madrid, Spain, 1998).

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Figures (8)

Fig. 1
Fig. 1

Paraxial arrangement of the input planes for optical arrays, showing the equivalence of the systems: (a) Spheric dome solution; (b) lateral displacement of the second element (prismatic effect array); (c) lateral displacement of the aperture position (inclined array); (d) effect of a negative lens at the input plane.

Fig. 2
Fig. 2

Geometry for the calculation of the solid angle subtended by each element of the array.

Fig. 3
Fig. 3

Simulated illuminance distribution on the synthetic image plane for a 4 × 4 spatial integrator (X and Y axes are in meters). The parameters of the array are r 1 = 0.029 m, 1/f′ = 7.25 m-1, and R - l = 1 m. (a) Constant luminance conditions; (b) clear sky conditions with the Sun located at 45° of elevation.

Fig. 4
Fig. 4

Dependence of the illuminance distribution with respect to the number of elements in the array. The dashed curve corresponds to an individual unit, the solid curve is for a 5 × 5 arrangement, and the dotted curve is for 10 × 10 array. Note that the illuminance range is normalized to the maximum of the distribution for each case. Therefore this graph shows how the homogeneity of the illuminance distribution increases with the number of elements.

Fig. 5
Fig. 5

Prototype configuration of a planar spatial-integrator array: (a) frontal view of the system, showing the input and output planes and apertures for every unit (numbers in millimeters); (b) photograph of the back side of the prototype, showing the circular apertures that contain the lenses.

Fig. 6
Fig. 6

Scheme of the experimental setup used to measure the synthetic image.

Fig. 7
Fig. 7

Synthetic image distribution: (a) photograph of the synthetic image seen from the outside of the experimental setup; (b) three-dimensional illuminance distribution seen by the CCD from the position indicated in Fig. 6.

Fig. 8
Fig. 8

Plot of the experimental illuminance distribution (solid curve) on the synthetic image plane along one of the diameters of the image, compared with the simulated results (dashed curve).

Equations (14)

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

R=l-b/d,
εlocal=εlocall,
ε=ε/R,
ε1j=jp1,  ε2j=jp2,
εj=j p1-p2l,
ε2localj=-jp1l/R,
ε(j)=j p1-p2l=j p1R=j p2R-l.
α=p1-p2l=p1R=p2R-l.
Em=ωmL,
Φu=ωmLπr12,
E=ΦTA=NΦuA=NωmLπr12A,
Ei=4NLωmr2d2,
ωp=ω cos ϕ=ω ll2+ρ21/2.
Φu=0r202π Lω ll2+ρ2 ρdρdα=2πLωll2+r221/2-l.

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