The authors are with the Center for Energy and Environmental Physics, Jacob Blaustein Institute for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus 84993, Israel and the Department of Mechanical Engineering, The Pearlstone Center for Aeronautical Engineering Studies, Ben-Gurion University of the Negev, Beersheva, Israel.
Olivier Georlette and J. M. Gordon, "Generalized nonimaging compound elliptical and compound hyperbolic luminaire designs for pair-overlap illumination applications," Appl. Opt. 33, 4171-4178 (1994)
Generalized nonimaging compound elliptical luminaires (CEL’s) and compound hyperbolic luminaires (CHL’s) are developed for pair-overlap illumination applications. A comprehensive analysis of CEL’s and CHL’s is presented. This includes the possibility of reflector truncation, as well as the extreme direction that spans the full range from positive to negative. Negative extreme direction devices have been overlooked in earlier studies and are shown to be well suited to illumination problems for which large cutoff angles are required. Flux maps can be calculated analytically without the need for computer ray tracing. It is demonstrated that, for a broad range of cutoff angles, adjacent pairs of CEL’s and CHL’s can generate highly uniform far-field illuminance while maintaining maximal lighting efficiency and excellent glare control. The trade-off between luminaire compactness and flux homogeneity is also illustrated. For V troughs, being a special case of CHL’s and being well suited to simple, inexpensive fabrication, we identify geometries that closely approach the performance characteristics of the optimized CEL’s and CHL’s.
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S, (flat) source width; A, exit aperture width; D, depth; H, height, which is the vertical source-to-caustic distance for a CEL; d, distance between caustics (interfocus distance); θr, θs, θt, see Section 2.
Summary of Emin/Emax Ratios and Luminaire Dimensionsa for Optimized CEL’s/CHL’s (Pair-Overlap Flux Maps)b
θmax = θt
30
35
40
45
50
55
60
65
70
θr, CHL
14
19
21
23
28
44
− 48
− 52
− 52
θs, CEL optimal
θs CHL
24
26
27
33
49
55
14
− 19
− 35
θr, CEL optimal
Emin/Emax design position
0.95
0.96
0.97
0.95
0.97
0.96
0.97
0.90
0.60
Emin/Emax placement error
0.84
0.79
0.78
0.82
0.88
0.91
0.91
0.83
0.53
A/S
2.89
2.44
2.22
1.95
1.57
1.31
6.78
6.75
5.01
D/S
3.37
2.45
1.92
1.47
1.08
0.81
2.24
1.81
1.09
Optimal x0
0.83
0.85
0.94
0.96
0.93
0.93
0.98
1.00
1.00
Luminaire dimensions (A/S and D/S) are the same for the CEL and CHL (for each θmax value); only reflector curvature is different.
Sensitivity to 5% error in luminaire placement is also listed; angles are in degrees.
Table 4
Best Achievable Pair-Overlap Emin/Emax Values for Luminaires with Pure Positive Versus Pure Negative Extreme Direction at Large Cutoff Angles
θmax (degrees)
Best Emin/Emax Pure Positive Extreme Direction CEL/CHL
Best Emin/Emax Pure Negative Extreme Direction CEL/CHL
Trade-off between flux uniformity and luminaire size. Figures are for a CHL with θmax = θt = 60°. Angles are in degrees.
Table 6
Summary of Emin/Emax Ratios and Luminaire Dimensions for Optimized V Troughs (Pair-Overlap Flux Maps)a
θmax = θt
35
40
45
50
55
60
65
70
θr optimal
− 20
− 20
− 25
− 35
− 40
− 42
− 44
− 52
θs optimal
35
30
20
5
− 5
− 12
− 19
− 32
Emin/Emax design position
0.89
0.91
0.92
0.90
0.92
0.93
0.90
0.60
Emin/Emax 5% placement error
0.77
0.85
0.88
0.76
0.78
0.80
0.80
0.51
A/S
6.8
5.41
5.67
7.65
7.48
5.97
4.78
4.82
D/S
5.57
3.82
3.34
3.63
2.97
2.01
1.35
1.06
Optimal x0
0.71
0.83
0.93
0.70
0.74
0.83
1.00
1.00
Angles are in degrees.
Table 7
Comparison of CHL Dimensions for the Optical Design of a Tubular Source (Fig. 5) Versus Creating a Flat Virtual Source from the Tube by Use of an Involute and Designing for the Flat Source (Fig. 6)a
Characteristic Angles
Virtual Source
Flat Design
Design Directly for Tube
θmax = θt
θr
θs
A/S
D/S
A/S
D/S
30
14
24
2.89
4.18
3.04
2.91
35
19
26
2.44
3.27
2.47
2.29
40
21
27
2.22
2.74
2.27
1.85
45
23
33
1.95
2.29
1.98
1.47
50
28
49
1.57
1.90
1.57
1.12
55
44
55
1.31
1.63
1.30
0.90
60
−48
14
6.78
3.06
10.49
3.46
65
−19
−52
6.75
2.63
15.60
4.08
70
−35
−52
5.01
1.91
14.83
3.18
CHL configurations cited are those that maximize flux uniformity. All the angles are in degrees.
S, (flat) source width; A, exit aperture width; D, depth; H, height, which is the vertical source-to-caustic distance for a CEL; d, distance between caustics (interfocus distance); θr, θs, θt, see Section 2.
Summary of Emin/Emax Ratios and Luminaire Dimensionsa for Optimized CEL’s/CHL’s (Pair-Overlap Flux Maps)b
θmax = θt
30
35
40
45
50
55
60
65
70
θr, CHL
14
19
21
23
28
44
− 48
− 52
− 52
θs, CEL optimal
θs CHL
24
26
27
33
49
55
14
− 19
− 35
θr, CEL optimal
Emin/Emax design position
0.95
0.96
0.97
0.95
0.97
0.96
0.97
0.90
0.60
Emin/Emax placement error
0.84
0.79
0.78
0.82
0.88
0.91
0.91
0.83
0.53
A/S
2.89
2.44
2.22
1.95
1.57
1.31
6.78
6.75
5.01
D/S
3.37
2.45
1.92
1.47
1.08
0.81
2.24
1.81
1.09
Optimal x0
0.83
0.85
0.94
0.96
0.93
0.93
0.98
1.00
1.00
Luminaire dimensions (A/S and D/S) are the same for the CEL and CHL (for each θmax value); only reflector curvature is different.
Sensitivity to 5% error in luminaire placement is also listed; angles are in degrees.
Table 4
Best Achievable Pair-Overlap Emin/Emax Values for Luminaires with Pure Positive Versus Pure Negative Extreme Direction at Large Cutoff Angles
θmax (degrees)
Best Emin/Emax Pure Positive Extreme Direction CEL/CHL
Best Emin/Emax Pure Negative Extreme Direction CEL/CHL
Trade-off between flux uniformity and luminaire size. Figures are for a CHL with θmax = θt = 60°. Angles are in degrees.
Table 6
Summary of Emin/Emax Ratios and Luminaire Dimensions for Optimized V Troughs (Pair-Overlap Flux Maps)a
θmax = θt
35
40
45
50
55
60
65
70
θr optimal
− 20
− 20
− 25
− 35
− 40
− 42
− 44
− 52
θs optimal
35
30
20
5
− 5
− 12
− 19
− 32
Emin/Emax design position
0.89
0.91
0.92
0.90
0.92
0.93
0.90
0.60
Emin/Emax 5% placement error
0.77
0.85
0.88
0.76
0.78
0.80
0.80
0.51
A/S
6.8
5.41
5.67
7.65
7.48
5.97
4.78
4.82
D/S
5.57
3.82
3.34
3.63
2.97
2.01
1.35
1.06
Optimal x0
0.71
0.83
0.93
0.70
0.74
0.83
1.00
1.00
Angles are in degrees.
Table 7
Comparison of CHL Dimensions for the Optical Design of a Tubular Source (Fig. 5) Versus Creating a Flat Virtual Source from the Tube by Use of an Involute and Designing for the Flat Source (Fig. 6)a
Characteristic Angles
Virtual Source
Flat Design
Design Directly for Tube
θmax = θt
θr
θs
A/S
D/S
A/S
D/S
30
14
24
2.89
4.18
3.04
2.91
35
19
26
2.44
3.27
2.47
2.29
40
21
27
2.22
2.74
2.27
1.85
45
23
33
1.95
2.29
1.98
1.47
50
28
49
1.57
1.90
1.57
1.12
55
44
55
1.31
1.63
1.30
0.90
60
−48
14
6.78
3.06
10.49
3.46
65
−19
−52
6.75
2.63
15.60
4.08
70
−35
−52
5.01
1.91
14.83
3.18
CHL configurations cited are those that maximize flux uniformity. All the angles are in degrees.
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