Abstract

The rubric tailored edge-ray designs (TED’s) refers to the procedure for tailoring lighting reflectors to produce a prescribed flux distribution for an extended Lambertian source while ensuring maximum radiative efficiency (no radiation being returned to the source). Most TED studies to date have been restricted to the case in which the two edges of the image of the source in the reflectors are bound by a source edge ray and a reflector edge. The extension to the more general, and challenging, solution in which both edges of the image can be bound by rays from opposite edges of the source was recently begun by Ries and Winston [J. Opt. Soc. Am. A 11, 1260–1264 (1994)] but was described in detail only for one particular design. We show that there are four topologically distinct classes of such reflectors; we derive the governing differential equations and obtain the solution in analytical form. Our results are illustrated for the case of uniform far-field illuminance production with symmetric configurations in two dimensions. Relative to earlier TED’s, these new devices can offer increased uniform core regions and superior glare control, although they are somewhat less compact. We offer a comprehensive analysis of the geometric properties, flux-map characteristics, and limitations of these new TED’s.

© 1996 Optical Society of America

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References

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  1. H. Ries, R. Winston, “Tailored edge-ray reflectors for illumination,” J. Opt. Soc. Am. A 11, 1260–1264 (1994).
    [CrossRef]
  2. R. Winston, H. Ries, “Nonimaging reflectors as functional of the desired irradiance,” J. Opt. Soc. Am. A 10, 1902–1908 (1993).
    [CrossRef]
  3. A. Rabl, J. M. Gordon, “Reflector designs for illumination with extended sources: the basic solutions,” Appl. Opt. 33, 6012–6021 (1994).
    [CrossRef] [PubMed]
  4. W. B. Elmer, The Optical Design of Reflectors (TLA Lighting Consultants, Salem, Mass., Wiley, New York, 1989); see also 1980 edition.
  5. W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).
  6. H. Ries, A. Rabl, “The edge-ray principle of nonimaging optics,” J. Opt. Soc. Am. A 11, 2627–2632 (1994).
    [CrossRef]
  7. A. Rabl, “Edge-ray method for analysis of radiation transfer among specular reflectors,” Appl. Opt. 33, 1248–1259 (1994).
    [CrossRef] [PubMed]
  8. P. T. Ong, J. M. Gordon, A. Rabl, W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 34, 1726–1737 (1995).
    [CrossRef]
  9. P. T. Ong, J. M. Gordon, A. Rabl, “Tailoring lighting reflectors to prescribed illuminance distributions: compact partial-involute designs,” Appl. Opt. 34, 7877–7887 (1995).
    [CrossRef] [PubMed]
  10. J. M. Gordon, A. Rabl, “Nonimaging CPC-type reflectors with variable extreme direction,” Appl. Opt. 31, 7332–7338 (1992).
    [CrossRef] [PubMed]
  11. IES Lighting Handbook: Reference Volume (Illuminating Engineering Society of North America, New York, 1984); IES Recommended Practice RP-24-89: Lighting Offices Containing Computer Visual Display Terminals (Illuminating Engineering Society of North America, New York, 1989).
  12. DIN Standard 66234: Bildschirmarbeitsplätze (Work Places with Video Display Terminals), Part 7, “Ergonomische Gestaltung des Arbeitsraumes: Beleuchtung und Anordnung” (Ergonomic Organization of the Place of Work: Illumination and Arrangement) (Union Technique de l’Electricité, UTE Cedex 64, 92052 Paris, 1990).
  13. C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987).

1995 (2)

P. T. Ong, J. M. Gordon, A. Rabl, W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 34, 1726–1737 (1995).
[CrossRef]

P. T. Ong, J. M. Gordon, A. Rabl, “Tailoring lighting reflectors to prescribed illuminance distributions: compact partial-involute designs,” Appl. Opt. 34, 7877–7887 (1995).
[CrossRef] [PubMed]

1994 (4)

1993 (1)

1992 (1)

Cai, W.

P. T. Ong, J. M. Gordon, A. Rabl, W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 34, 1726–1737 (1995).
[CrossRef]

Elmer, W. B.

W. B. Elmer, The Optical Design of Reflectors (TLA Lighting Consultants, Salem, Mass., Wiley, New York, 1989); see also 1980 edition.

Gordon, J. M.

Ong, P. T.

P. T. Ong, J. M. Gordon, A. Rabl, “Tailoring lighting reflectors to prescribed illuminance distributions: compact partial-involute designs,” Appl. Opt. 34, 7877–7887 (1995).
[CrossRef] [PubMed]

P. T. Ong, J. M. Gordon, A. Rabl, W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 34, 1726–1737 (1995).
[CrossRef]

Rabl, A.

Ries, H.

Welford, W. T.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

Winston, R.

Wyatt, C. L.

C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987).

Appl. Opt. (4)

J. Opt. Soc. Am. A (3)

Opt. Eng. (1)

P. T. Ong, J. M. Gordon, A. Rabl, W. Cai, “Tailored edge-ray designs for uniform illumination of distant targets,” Opt. Eng. 34, 1726–1737 (1995).
[CrossRef]

Other (5)

IES Lighting Handbook: Reference Volume (Illuminating Engineering Society of North America, New York, 1984); IES Recommended Practice RP-24-89: Lighting Offices Containing Computer Visual Display Terminals (Illuminating Engineering Society of North America, New York, 1989).

DIN Standard 66234: Bildschirmarbeitsplätze (Work Places with Video Display Terminals), Part 7, “Ergonomische Gestaltung des Arbeitsraumes: Beleuchtung und Anordnung” (Ergonomic Organization of the Place of Work: Illumination and Arrangement) (Union Technique de l’Electricité, UTE Cedex 64, 92052 Paris, 1990).

C. L. Wyatt, Radiometric System Design (Macmillan, New York, 1987).

W. B. Elmer, The Optical Design of Reflectors (TLA Lighting Consultants, Salem, Mass., Wiley, New York, 1989); see also 1980 edition.

W. T. Welford, R. Winston, High Collection Nonimaging Optics (Academic, San Diego, Calif., 1989).

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Figures (20)

Fig. 1
Fig. 1

Illustration of the far-edge (a) and near-edge (b) TED design procedure. The illuminance at each target point has contributions from both the source and its reflected image the contour of which extends from R T to R. Both boundaries of the image correspond to edge rays of the source. Ries and Winston [1994] used the labels “leading” for “basis”, and “trailing” for “nonbasis”.

Fig. 2
Fig. 2

The 4 classes of TEDs designed directly for cylindrical sources. The devices shown produce uniform far-field illuminance over a uniform core region of half-angle θ c as indicated. The reflector profile consists of an inner modified involute portion (I d to I e ) and an outer TED portion from R b to R e . Arrow along reflector indicates direction in which R moves as |θ| increases.

Fig. 3
Fig. 3

Modified involute designed from the cusp point I d to its truncation (termination) point I e . I d depends on gap size g. I e is defined by the involute truncation angle μ. The edge of the image corresponds to angle β. The rays labeled A, B, C, and F denote the relevant edge rays of the involute (see text).

Fig. 4
Fig. 4

Principal edge rays for the four TED’s of Fig. 2, all drawn for the same tube size. The flux distribution is uniform up to the angle denoted by rays D. For the near-edge designs (b) and (d), eclipsing of the source by the TED reflectors occurs beyond the angles denoted by rays E.

Fig. 5
Fig. 5

Coordinate system for the source and reflector.

Fig. 6
Fig. 6

Luminance contributions of source and images from the inner involute portion.

Fig. 7
Fig. 7

Luminance contribution of the reflected image of the source for the far-edge diverging TED.

Fig. 8
Fig. 8

Luminance contribution of the reflected image of the source for the near-edge diverging TED.

Fig. 9
Fig. 9

Projected image width in involute as seen at θ = 0 for μ < 0 (pertinent to near-edge TED’s).

Fig. 10
Fig. 10

Projected image width in involute as seen at θ = 0 for μ ≥ 0. The drawing corresponds to the maximum allowable involute truncation for a given gap size when we are designing for the maximum attainable uniform core region (pertinent to far-edge TED’s).

Fig. 11
Fig. 11

Normalized far-field flux map of the far-edge diverging TED in Fig. 2(a). For this TED class the spillover region stems strictly from direct emissions of the source. We define Normalized illuminance as E(θ)/E max.

Fig. 12
Fig. 12

Normalized far-field illuminance E(θ)/E max of the near-edge diverging TED in Fig. 2(b).

Fig. 13
Fig. 13

Uniform core region and glare-control angle of far-edge diverging TED’s as a function of involute truncation angle μ for g/t = 1.75.

Fig. 14
Fig. 14

Luminaire dimensions of the far-edge diverging TED’s in Fig. 13.

Fig. 15
Fig. 15

Uniform core region and glare-control angle of far-edge converging TED’s as a function of involute truncation angle μ for g/t = 2.

Fig. 16
Fig. 16

Luminaire dimensions of the far-edge converging TED’s in Fig. 15.

Fig. 17
Fig. 17

Uniform core region and glare-control angle of the near-edge diverging TED’s as functions of gap size.

Fig. 18
Fig. 18

Luminaire dimensions of the near-edge diverging TED’s in Fig. 17.

Fig. 19
Fig. 19

Uniform core region and glare-control angle of the near-edge converging TED’s as functions of gap size.

Fig. 20
Fig. 20

Luminaire dimensions of the near-edge converging TED’s in Fig. 19.

Equations (18)

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d ln ( r ) d ϕ = tan ( α ) ± t r ,
2 α = ϕ θ,
L ( θ ) = E ( θ ) cos 2 ( θ ) .
L ( θ ) = L ( 0 ) cos 2 ( θ ) .
L ( θ ) = L source ( θ ) + L involute ( θ ) + L TED ( θ ) .
L source ( θ ) + L involute ( θ ) = 2 t + 2 t sin ( β L + θ ) + 2 t sin ( β R θ ) | θ | θ d ,
sin ( θ d ) = 1 1 + g t .
L TED ( θ ) = [ r + t tan ( α ) ] sin ( 2 α ) [ r b + t tan ( α b ) ] sin ( 2 α b ) ,
L TED ( θ ) = [ r b + t tan ( α b ) ] sin ( 2 α b ) [ r + t tan ( α ) ] sin ( 2 α ) .
p ( θ ) = { r + t [ tan ( α ) ] ± 1 } sin ( 2 α ) ,
{ 1 for far-edge designs + 1 for near-edge designs } .
[ 1 ± 2 t cos 2 α p ( θ ) ] = sin ( α ) cos ( α ) d [ ln { p ( θ ) } ] sin 2 α + i 2 t p ( θ ) ( + sin 2 α ) ,
tan ( u ) = cot ( α ) ,
tan ( u ) [ p ( θ ) ( 1 i ) ( 2 t ) ] ± ( 2 t ) u i ( 2 t ) θ = P ( θ ) P ( θ m ) ,
P ( θ ) = θ p ( θ ) d θ
A o = [ sin ( β o ) r o t cos ( β o ) ] ( 2 t ) ,
r o t = r d t + ( β o β d ) .
f = [ 0 θ c 1 cos 2 ( θ ) d ( θ ) ] [ A o area of source ] = tan ( θ c ) ( { sin ( β o ) [ r d t + ( β o β d ) ] cos ( β o ) } π ) .

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