Axially symmetric LED light bulb

CROSS-REFERENCE TO RELATED APPLICATIONS

This non-provisional application claims priority under 35 U.S.C. §119(a) on Patent Application No(s). 104207617 filed in Taiwan, R.O.C. on May 18, 2015, the entire contents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to the field of LED light bulbs, and more particularly to an axially symmetric LED light bulb with the features of high light uniformity and wide-angle illumination range.

2. Description of the Related Art

LED with the features of high efficiency, high color rendering, environmental friendliness, energy saving and long service life is used generally used as a light source for various illumination lamps.

For example, the conventional light bulb at an early stage uses a tungsten filament as the light source, wherein electricity is passed through the tungsten filament, and the tungsten filament is heated to incandescence to emit light for the illumination purpose due to the resistance of the tungsten filament. The light emission of such light bulb is similar to that of a light source, so that when such light bulb is used for illumination, a luminous efficacy of 360-degree full-circumferential radiation is achieved. A s described above, LEDs are used extensively as a light source for lamps, but most of the light sources in the present LED light bulbs are designed with a light emitting surface facing upward and perpendicular to the light emitting angle. In the meantime, the shape and structure of the light bulb provides a screening effect to the light, so that the light emitting angle of the conventional LED light bulb is usually not too large, and the light is too concentrated and comes with a narrow light emitting angle. With the aforementioned restrictive properties including the light emitting angle and the total light lumen of the LED, the conventional LED light bulb is unable to achieve the full-circumferential uniform illumination effect like the conventional incandescent lamps with the feature of a uniform wide-angle light emission. Therefore, the conventional LED light bulb still requires improvements of the illumination angle and the uniformity of light to achieve a better illumination performance of the LED light bulb.

To improve the luminous efficacy of the LED light bulb, most manufacturers adopt a 3D light source to increase the illumination angle of the LED light bulb, such that the LED light bulb can achieve the effect of a full-circumferential illumination similar to that of the tungsten filament. With reference to FIGS. 1 to 4 for various types of conventional LED light bulbs 1 available in the market, the LED light bulb 1 adopts an LED light source 10 arranged in a vertical direction, such that the light output angle of the light emitted from the LED light bulb 1 may be increased. In FIG. 2, the LED light bulb 1 also adopts a vertically arranged LED light source 10. Compared with the LED light bulb 1 as shown in FIG. 1, the LED light bulb 1 as shown in FIG. 2 uses a greater number of LED light sources 10, so that a 3D light source with more surfaces produces and outputs more lights in different angles. In FIG. 3, the LED light bulb 1 is assembled by using a multi-angle circuit substrate 1, such that the lights of the LED light sources 10 may be emitted to different angles. In FIG. 4, a secondary optical lens 12 is added to the top of the LED light source 10 to achieve the effects of increasing the illumination angle and providing the full-circumferential radiation. However, the aforementioned method is commonly adopted in the LED light bulb with a light emitting surface facing upward, and it is necessary to design and consider the LED light source 10 again or even re-design the area for installing the LED light source 10 whenever the installation direction of the LED light source 10 is adjusted. In the LED light bulb 1 as shown in FIG. 1, there are just two areas for installing the LED light source 10, and thus there still exists an illumination angle unreachable by light. In the LED light bulb 1 as shown in FIGS. 2 and 3, such LED light bulb 1 is the present common 3D light source design. To improve the light output angle of the LED light source 10, it is necessary to increase the quantity of LED light sources 10, so that the quantity of lead frame or circuit substrates 12 for installing the LED light source 10 is increased accordingly, and the manufacturing and assembling costs are increased significantly. Although the light source is a 3D light source, the shape of the aforementioned LED light bulb 1 affects the light emitting angle of the LED light source 10, so that different LED light bulbs 1 require the lead frame or circuit substrates 11 which are designed one by one to comply with the required light output angle. In FIG. 4, some manufacturers adopt the method of installing an additional secondary optical lens 12 outside the LED light source 10, such that the illumination angle of the light is increased by the secondary optical lens 12. However, this method requires the installation of other components to the LED light bulb 1, and thus the manufacturing cost and assembling time are increased.

Therefore, the present methods adopted for improving the light output angle and uniformity of the LED light bulb increase the manufacturing cost, the assembling time and the level of difficulty of the design. Although these methods may overcome the issue of a low luminous efficacy of the LED light bulb, yet they still have the following drawbacks. Therefore, the inventor of the present invention provides an axially symmetric LED light bulb in hope of overcoming the drawbacks of the conventional LED light bulb and improving the illumination angle and light uniformity of the LED light bulb with planar light emission to omit the complicated design of the light source and lower the production cost.

SUMMARY OF THE INVENTION

Therefore, it is a primary objective of the present invention to provide an axially symmetric LED light bulb capable of adjusting the upward LED light output angle with respect to the light emitting surface and homogenizing the overall light uniformity to provide the wide-angle light emitting angle and excellent illumination uniformity similar to those of a full-circumferential radiation.

To achieve the aforementioned and other objectives, the present invention provides an axially symmetric LED light bulb comprising a lamp shade, a substrate and a connecting seat, and the substrate being installed on the connecting seat and having a plurality of LED light sources, and an edge of the lamp shade being coupled to the connecting seat and the substrate being covered inside the lamp shade, characterized in that the lamp shade has an unequal thickness, and the thickness of the top of the lamp shade is greater than the thickness of the lateral side of the lamp shade, such that the LED light source is arranged at a polar coordinate origin position, and when the illumination of LED light source points at a direction towards the polar coordinate 0 degree and after the light of the LED light source passes through the lamp shade, at least 5% of the total flux of the LED light source is obtained at the polar coordinate position from 135 degrees to 180 degrees. The axially symmetric LED light bulb 2 further satisfy a illumination relation (|I−Iavg|/Iavg)<25%, wherein I is an intensity of light of at least 90% of a spatial position between 0 degree to 135 degrees of the polar coordinate positions, and Iavg is an average light intensity situated between the polar coordinate position from 0 degree to 135 degrees.

Wherein, the ratio of the thickness of the lamp shade at the polar coordinates from +30 degrees to −30 degrees to the thickness of the lamp shade at the polar coordinates from +90 degrees to +30 degrees and from −90 degrees to −30 degrees is equal to (1.8−3):1. Within this range, the present invention meets the conditions of the optimal light uniformity and wide-angle illumination angle and achieves the best lighting performance.

In addition, the cross-sectional edge of the inner side of the lamp shade is arc-shaped or is a curve with a plurality of turning points, and the curve is bilaterally symmetrical, and the distance from the top end of the inner side of the lamp shade to the substrate is equal to 50 mm-60 mm, and the maximum width of the external periphery of the lamp shade is equal to 58 mm-70 mm.

In summation of the description above, the axially symmetric LED light bulb of the present invention effectively improves the luminous efficacy of a light bulb that uses LED as a light source, and the lamp shade with unequal thickness reduces a too-strong light of the LED light source generated at specific angles, so that the light of the light bulb at a predetermined light output angle is more uniform and the illumination angle is wider.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a first conventional LED light bulb;

FIG. 2 is a schematic view of a second conventional LED light bulb;

FIG. 3 is a schematic view of a third conventional LED light bulb;

FIG. 4 is a schematic view of a fourth conventional LED light bulb;

FIG. 5 is a perspective view of an axially symmetric LED light bulb of a preferred embodiment of the present invention;

FIG. 6 is a schematic view showing the polar coordinate space of an axially symmetric LED light bulb of a preferred embodiment of the present invention;

FIG. 7 is a cross-sectional view of an axially symmetric LED light bulb of a preferred embodiment of the present invention;

FIG. 8 shows the light pattern of a lamp shade of an axially symmetric LED light bulb of a preferred embodiment of the present invention with a thickness ratio of 1:1;

FIG. 9 shows the light pattern of a lamp shade of an axially symmetric LED light bulb of a preferred embodiment of the present invention with a thickness ratio of 1.7:1;

FIG. 10 shows the light pattern of a lamp shade of an axially symmetric LED light bulb of a preferred embodiment of the present invention with a thickness ratio of 1.8:1;

FIG. 11 shows the light pattern of a lamp shade of an axially symmetric LED light bulb of a preferred embodiment of the present invention with a thickness ratio of 3:1; and

FIG. 12 shows the light pattern of a lamp shade of an axially symmetric LED light bulb of a preferred embodiment of the present invention with a thickness ratio of 3.1:1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The technical content of the present invention will become apparent with the detailed description of preferred embodiments and the illustration of related drawings as follows. It is noteworthy that same numerals are used for representing the same respective elements respectively for simplicity.

With reference to FIGS. 5, 6 and 7 for a perspective view of an axially symmetric LED light bulb, a schematic view showing the polar coordinate space of the axially symmetric LED light bulb, and a cross-sectional view of the axially symmetric LED light bulb in accordance with a preferred embodiment of the present invention respectively, the axially symmetric LED light bulb 1 comprises a lamp shade 20, a substrate 21 and a connecting seat 22, and the substrate 21 is disposed on the connecting seat 22 and includes a plurality of LED light sources 211 used as a light source, and a power supply element 23 is installed in the connecting seat 22 for supplying electric power to the LED light sources 211, and an end of the lamp shade 20 is connected to the connecting seat 22, and the substrate 21 is covered inside the lamp shade 20.

The axially symmetric LED light bulb 2 is characterized in that the lamp shade 20 has an unequal thickness, wherein the thickness of the top of the lamp shade 20 is greater than the thickness of the lateral side of the lamp shade 20, so that the lamp shade 20 comes with an unequal thickness. Please refer to FIG. 6, for purpose of explanation, the LED light sources 211 are arranged at an origin position of a polar coordinate, and the LED light sources 211 are pointing in a direction toward the polar coordinate 0 degree. After the lights of the LED light sources 211 pass through the lamp shade, the flux between the polar coordinate from 135 degrees to 180 degrees is equal to at least 5% of the total flux of the LED light source. The axially symmetric LED light bulb 2 further satisfy a illumination relation (|I−Iavg|/Iavg)<25%, wherein I is an intensity of light of at least 90% of a spatial position between 0 degree to 135 degrees of the polar coordinate positions, and Iavg is an average light intensity situated between the polar coordinate position from 0 degree to 135 degrees, so that the light emission of the axially symmetric LED light bulb 2 has better uniformity and wider illumination range to achieve the 360-degree full-circumferential radiation effect. The greater the thickness of the lamp shade 20, the better is the light reflection effect. In other words, a greater thickness has a better chance to achieve the full-circumferential radiation effect. Meanwhile, the light intensity and brightness of the LED light sources 211 projected onto the lamp shade 20 will become weaker accordingly, so that the light of the LED light sources 211 has an increasingly weaker light intensity and an increasingly wider illumination angle as the thickness of the lamp shade 20 increases. On the hand, the light of the LED light sources 211 has an increasingly stronger light intensity and an increasingly narrower illumination angle as the thickness of the lamp shade 20 decreases. Obviously, the light shows a progressive change of intensity and illumination angle with the thickness of the lamp shade 20. Therefore, the light emitting angle and the light intensity of the LED light sources 211 may be changed by adjusting the thickness of the lamp shade 20. To achieve a better illumination effect of the axially symmetric LED light bulb 2 to meet the aforementioned flux and light intensity requirements, the thickness ratio of the lamp shade 20 may be further defined.

The following data are obtained from optical experiments, and these data relate to the thickness ratios of the lamp shade 20 (hereinafter referred to as “thickness ratio”) at the polar coordinate from +30 degrees to −30 degrees with respect to the polar coordinate +90 degrees to +30 degrees and −90 degrees to −30 degrees. The thickness of the lamp shade 20 at the polar coordinate from +30 degrees to −30 degrees and the thickness of the lamp shade 20 at the polar coordinate from +90 degrees to +30 degrees and from −90 degrees to −30 degrees are obtained after conducting the optical experiments, and if their ratio is equal to (1.8−3):1, the aforementioned restrictive condition of the flux and the light emitting intensity is met, and the axially symmetric LED light bulb 2 achieves the effects of full circumferential luminous efficacy and light uniformity.

Firstly, optical experiments on testing whether or not the light emitting intensity satisfies the relation (|I−Iavg|/Iavg)<25% are conducted repeatedly, and the experiment results are listed in Tables 1-1 to 1-5. Wherein, Tables 1-1 to 1-5 show the numeric values of the measured light intensity at the polar coordinate positions (γ,c) and the measured average light intensity Iavg as shown in FIG. 6.

Table 1-1 lists the experiment data provided that the thickness ratio of the lamp shade 20 is 1:1 and shows the light emitting intensity I at each spatial position within the polar coordinate positions from 0 degree to 135 degrees and the numeric value of (|I−Iavg|/Iavg) of the average light intensity Iavg; Table 1-2 lists the experiment data provided that the thickness ratio of the lamp shade 20 is 1.7:1, and shows the light emitting intensity I at each spatial position within the polar coordinate positions from 0 degree to 135 degrees and the numeric value of (|I−Iavg|/Iavg) of the average light intensity Iavg; Table 1-3 lists the experiment data provided that the thickness ratio of the lamp shade 20 is 1.8:1, and shows the light emitting intensity I at each spatial position within the polar coordinate positions from 0 degree to 135 degrees and the numeric value of (|I−Iavg|/Iavg) of the average light intensity Iavg; Table 1-4 lists the experiment data provided that the thickness ratio of the lamp shade 20 is 3:1, and shows the light emitting intensity I at each spatial position within the polar coordinate positions from 0 degree to 135 degrees and the numeric value of (|I−Iavg|/Iavg) of the average light intensity Iavg; and Table 1-5 lists the experiment data provided that the thickness ratio of the lamp shade 20 is 3.1:1, and shows the light emitting intensity I at each spatial position within the polar coordinate positions from 0 degree to 135 degrees and the numeric value of (|I−Iavg|/Iavg) of the average light intensity Iavg, wherein the numeric values listed in each table is in the unit of %.

TABLE 1-1

c

γ
0
22.5
45
67.5
90
112.5
135
157.5
180
202.5
225
247.5
270
292.5
315
337.5
360

0
17.91
18.03
17.91
17.85
17.91
18.21
18.09
18.26
18.44
18.03
17.91
17.85
17.91
18.21
18.09
18.26
17.91

2.5
18.44
17.91
17.62
17.58
19.31
19.73
19.94
22.65
23.42
25.03
25.72
26.71
24.66
23.53
22.08
19.26
18.44

5
18.38
17.91
17.56
17.64
19.37
19.61
19.88
22.35
23.30
24.78
25.66
26.27
24.60
23.28
22.08
18.96
18.38

7.5
18.32
17.68
17.56
17.70
19.26
19.55
20.06
22.04
23.05
24.60
25.28
26.01
24.22
23.28
21.96
18.96
18.32

10
18.09
17.68
17.39
17.41
19.20
19.43
19.71
21.80
22.87
24.29
24.84
25.70
23.73
22.91
21.65
18.90
18.09

12.5
18.03
17.62
17.09
17.23
18.72
19.25
19.41
21.62
22.62
23.79
24.40
24.82
23.54
22.61
21.41
18.79
18.03

15
17.74
17.33
16.92
17.17
18.66
19.01
19.29
21.07
21.95
23.29
23.96
24.37
23.17
22.11
20.80
18.19
17.74

17.5
17.56
17.03
16.63
16.94
18.24
18.83
18.93
20.77
21.64
22.73
23.65
24.06
22.61
21.74
20.38
17.96
17.56

20
17.32
16.74
16.28
16.70
17.95
18.30
18.57
20.10
21.27
22.05
22.71
23.55
22.11
21.07
19.89
17.72
17.32

22.5
16.86
16.33
16.10
16.06
17.77
17.70
17.85
19.85
20.53
21.67
22.21
22.61
21.49
20.33
19.77
17.31
16.86

25
16.33
16.04
15.87
15.77
17.06
17.34
17.68
19.00
19.98
20.80
21.58
21.79
20.75
20.08
19.16
17.07
16.33

27.5
15.86
15.68
15.05
15.47
16.64
16.93
17.08
18.33
19.00
20.05
20.70
20.97
20.13
19.28
18.86
16.18
15.86

30
15.80
15.39
14.64
15.00
16.04
16.33
16.66
18.09
18.63
18.87
19.70
20.21
19.32
18.91
18.07
15.95
15.80

32.5
15.33
15.04
15.05
14.71
15.69
15.74
15.76
17.23
17.77
18.37
19.01
19.26
18.64
18.30
17.28
15.35
15.33

35
15.15
14.57
14.40
14.13
15.33
14.90
15.59
16.69
17.10
17.69
18.25
18.63
18.27
17.62
17.22
15.24
15.15

37.5
14.80
14.45
14.29
14.07
15.15
14.90
15.11
16.02
16.36
16.82
17.37
18.00
17.34
17.31
16.73
14.88
14.80

40
14.62
14.10
14.11
13.89
14.74
14.31
14.57
15.47
15.75
16.19
16.31
17.31
16.28
16.82
16.12
14.70
14.62

42.5
14.15
13.69
13.64
13.31
14.32
14.43
13.91
14.86
15.20
15.39
15.81
16.55
15.73
15.59
15.27
13.99
14.15

45
13.74
13.57
13.35
12.84
13.73
13.41
13.26
14.13
14.52
14.64
14.87
15.48
15.17
15.22
14.73
13.82
13.74

47.5
13.57
13.04
12.82
12.72
13.61
12.82
12.72
13.52
13.79
13.77
13.99
14.47
14.42
14.60
14.54
13.17
13.57

50
13.16
12.87
12.71
12.43
12.83
12.52
12.18
13.16
12.93
13.15
12.92
13.71
13.62
13.87
13.75
12.81
13.16

52.5
12.51
12.46
12.18
11.84
12.30
11.75
11.71
12.24
12.07
12.21
12.17
12.83
12.75
12.94
13.21
12.22
12.51

55
12.16
12.10
11.83
11.37
12.00
11.33
10.87
11.45
11.39
11.22
11.29
12.01
11.76
12.39
12.48
11.63
12.16

57.5
11.57
10.99
11.01
10.91
10.81
10.20
10.33
10.54
10.47
10.10
10.04
10.74
10.64
11.34
11.57
11.27
11.57

60
10.75
10.64
10.31
10.14
9.92
9.72
9.50
9.81
9.37
9.16
9.16
9.48
9.52
10.11
10.84
10.21
10.75

62.5
10.16
9.93
9.90
9.21
9.21
8.77
8.78
8.77
8.45
8.17
8.28
8.22
8.78
9.25
9.80
9.62
10.16

65
9.22
9.29
8.96
8.50
8.38
8.12
7.82
8.04
7.41
6.92
6.90
7.34
7.23
8.02
8.89
8.55
9.22

67.5
8.16
8.00
7.97
7.39
7.54
7.28
6.69
6.77
6.24
5.80
5.52
5.95
6.36
6.79
7.56
7.78
8.16

70
7.28
7.24
7.03
6.57
6.53
5.97
5.62
5.30
5.14
4.43
4.51
4.37
4.94
5.49
6.46
6.84
7.28

72.5
6.11
6.06
6.03
5.40
5.23
5.20
4.66
4.39
3.85
3.31
3.32
3.11
3.63
4.39
5.49
5.65
6.11

75
4.93
4.95
4.81
4.46
4.15
3.65
3.47
2.99
2.68
1.76
1.63
1.78
2.14
3.09
4.03
4.65
4.93

77.5
3.82
3.60
3.58
3.06
2.97
2.40
2.03
1.83
1.03
0.64
0.25
0.21
0.66
1.37
2.51
3.46
3.82

80
2.35
2.54
2.29
2.06
1.48
1.15
0.78
0.25
0.32
0.92
1.45
1.56
0.71
0.20
1.42
2.34
2.35

82.5
1.06
0.61
1.18
0.72
0.07
0.34
0.83
0.97
1.92
2.66
2.95
3.14
2.57
1.77
0.47
0.74
1.06

85
0.70
0.51
0.69
0.57
1.49
1.83
1.79
2.49
3.45
3.91
4.52
4.91
4.00
3.25
1.98
0.56
0.70

87.5
2.05
2.09
1.92
1.98
3.10
3.14
3.58
4.25
5.29
5.53
6.15
6.61
5.79
5.15
4.17
2.21
2.05

90
3.70
3.62
3.50
3.73
4.52
4.80
4.95
6.14
6.33
7.21
7.84
8.06
7.59
6.63
5.75
4.05
3.70

92.5
5.64
5.32
5.08
5.43
6.31
6.47
6.68
7.72
8.36
9.07
9.91
9.83
9.27
8.23
7.27
5.47
5.64

95
7.22
7.08
6.55
7.07
7.79
8.32
8.41
9.43
10.38
10.82
11.42
12.10
10.94
10.08
9.22
7.72
7.22

97.5
9.04
8.78
8.71
8.65
9.58
9.80
10.09
11.43
12.28
12.56
13.30
13.68
12.80
12.35
11.16
9.14
9.04

100
11.39
10.77
10.35
10.64
11.54
11.71
12.12
13.63
13.88
14.80
15.25
15.89
14.60
13.89
13.35
11.15
11.39

102.5
13.15
12.83
12.57
12.34
13.50
13.79
13.91
15.39
15.90
16.54
16.94
17.53
16.90
16.29
15.29
13.34
13.15

105
15.62
15.00
14.56
14.45
15.88
15.82
15.76
17.52
17.86
18.53
19.39
19.80
18.88
18.39
17.72
15.64
15.62

107.5
17.67
16.99
16.85
16.79
17.84
17.78
17.91
19.53
19.89
20.59
21.14
21.69
20.80
20.54
20.15
17.71
17.67

110
19.55
19.57
18.89
18.61
19.98
19.81
20.00
21.72
21.91
22.70
23.34
23.65
22.79
22.82
22.34
19.96
19.55

112.5
22.31
21.69
21.59
21.07
22.42
22.01
21.85
24.03
24.06
24.94
25.16
26.04
25.33
25.03
24.89
22.56
22.31

115
24.43
24.03
23.69
23.17
24.44
24.21
24.30
26.10
26.33
27.25
27.10
28.32
27.13
27.43
27.08
24.81
24.43

117.5
27.01
26.32
25.97
25.22
26.94
26.59
26.56
28.48
28.72
29.42
29.61
30.84
29.67
29.34
29.82
27.30
27.01

120
29.83
28.78
28.43
27.74
29.02
28.86
28.77
30.67
31.05
31.35
31.81
32.86
31.78
32.05
31.94
29.66
29.83

122.5
32.35
31.48
30.95
30.44
31.63
31.30
31.28
33.10
33.32
33.91
34.07
35.19
34.32
34.82
34.62
32.15
32.35

125
35.00
33.89
33.82
32.95
34.31
33.86
33.55
35.30
35.71
36.02
36.14
37.53
36.62
36.97
37.05
34.69
35.00

127.5
37.23
36.64
35.86
35.41
37.10
36.18
35.88
37.61
38.29
38.39
39.21
39.93
38.97
39.31
39.66
37.35
37.23

130
39.81
39.05
38.91
38.11
39.42
38.80
38.33
40.10
40.32
41.12
41.16
42.20
41.27
41.96
42.21
39.78
39.81

132.5
42.45
41.98
41.01
40.33
41.98
41.18
40.95
42.78
42.59
42.93
43.92
44.66
43.75
44.54
45.07
42.44
42.45

135
45.10
44.56
43.71
43.20
44.65
43.86
42.98
45.34
45.35
45.61
46.17
47.12
46.29
46.88
47.01
45.64
45.10

TABLE 1-2

c

γ
0
22.5
45
67.5
90
112.5
135
157.5
180
202.5
225
247.5
270
292.5
315
337.5
360

0
3.20
3.20
3.45
3.26
3.20
3.26
3.38
3.26
3.51
3.20
3.38
3.26
3.01
3.26
3.38
3.26
3.20

2.5
3.82
2.07
1.18
2.30
4.03
4.66
5.26
5.71
5.07
3.18
3.21
4.84
6.99
8.61
8.31
5.89
3.82

5
3.82
2.49
1.61
2.30
3.91
5.10
5.39
5.59
5.13
3.06
3.15
5.28
7.24
8.48
8.18
6.27
3.82

7.5
3.76
2.62
1.79
2.60
3.91
4.97
5.33
5.71
5.01
3.49
3.27
5.09
7.31
8.61
8.25
6.08
3.76

10
3.88
3.23
2.03
3.16
4.22
5.29
5.39
6.09
5.20
3.37
3.64
4.97
7.18
8.81
8.70
6.15
3.88

12.5
4.38
3.48
2.64
3.46
4.84
5.29
5.64
5.71
5.13
3.24
3.64
5.09
7.31
8.68
8.90
6.59
4.38

15
4.75
4.15
3.25
4.26
5.28
5.54
5.77
6.22
5.45
3.49
3.52
5.09
7.24
9.14
8.77
6.78
4.75

17.5
4.87
4.46
3.73
4.44
5.59
6.35
6.21
6.60
6.01
3.99
3.83
5.41
7.82
9.20
9.29
7.04
4.87

20
5.18
4.82
4.40
5.30
6.09
6.23
6.65
6.73
6.01
4.17
4.01
5.91
7.89
9.14
9.35
7.55
5.18

22.5
5.80
5.38
4.77
5.49
6.40
6.73
6.91
7.04
6.64
4.30
4.57
6.10
8.21
9.53
9.48
7.74
5.80

25
5.99
6.11
5.56
6.10
6.96
6.98
6.97
7.55
6.89
4.67
4.95
6.36
8.40
9.79
9.87
7.99
5.99

27.5
6.67
6.60
6.17
6.71
7.40
7.49
7.09
7.99
7.33
5.10
5.19
6.74
8.73
9.85
10.33
8.05
6.67

30
7.29
7.52
6.96
7.39
7.71
8.12
7.54
8.06
7.78
5.60
5.63
7.05
8.86
10.25
10.33
8.82
7.29

32.5
7.97
8.13
7.56
8.00
8.58
8.74
8.04
8.75
8.34
5.97
6.37
7.43
9.31
10.77
10.72
9.20
7.97

35
8.47
8.69
8.60
9.04
9.20
9.18
8.61
8.94
8.72
6.90
6.69
7.87
9.82
10.83
11.24
9.71
8.47

37.5
9.15
9.61
9.08
9.47
9.64
9.63
9.05
9.58
9.41
7.52
7.55
8.25
10.27
11.29
11.57
10.09
9.15

40
9.77
10.34
9.63
10.15
10.26
10.07
9.37
9.96
9.47
7.77
7.74
8.95
9.95
11.62
11.76
10.47
9.77

42.5
10.27
10.77
10.18
10.58
10.57
10.25
9.75
10.15
10.23
8.45
8.18
9.14
10.73
11.81
12.02
10.98
10.27

45
10.70
11.26
10.91
10.88
11.26
10.63
10.19
10.65
10.48
8.82
8.98
9.77
10.92
11.88
12.15
11.30
10.70

47.5
11.14
11.81
11.57
11.44
11.38
10.76
10.38
11.03
10.92
9.32
9.36
10.02
10.86
11.94
12.22
11.42
11.14

50
11.26
12.43
12.00
11.56
11.57
11.01
10.63
11.03
10.80
9.63
9.73
10.34
11.11
12.01
12.54
11.87
11.26

52.5
11.57
12.43
12.00
12.05
11.82
11.13
11.07
11.10
11.30
10.00
10.10
10.59
11.31
11.94
12.28
11.62
11.57

55
12.00
12.79
12.36
12.11
11.75
11.13
10.69
11.35
11.49
10.00
10.22
10.71
11.31
11.75
12.41
11.55
12.00

57.5
12.19
12.67
12.42
12.29
11.75
11.51
11.07
11.03
11.05
10.50
10.22
10.78
11.05
11.55
11.83
11.68
12.19

60
12.19
12.43
12.49
12.23
11.75
10.95
10.75
10.97
11.05
10.43
10.72
10.65
11.11
11.16
11.76
11.55
12.19

62.5
11.88
12.43
12.49
12.11
11.57
10.76
10.57
10.84
10.98
10.43
10.41
10.53
10.73
10.70
11.44
11.42
11.88

65
11.69
11.93
12.24
11.87
11.32
10.82
10.38
10.34
10.67
10.56
10.47
10.21
10.47
10.18
10.91
10.98
11.69

67.5
11.32
11.57
11.63
11.31
10.76
9.88
9.87
10.02
10.17
10.00
10.10
9.83
9.44
9.72
10.26
10.60
11.32

70
10.89
11.20
11.57
10.76
10.51
9.88
9.43
9.64
9.66
9.69
9.79
9.58
9.18
9.07
9.55
9.90
10.89

72.5
10.14
10.52
10.91
9.96
9.76
9.18
8.80
8.82
9.10
9.26
9.29
9.07
8.53
8.35
8.77
9.14
10.14

75
9.52
9.79
9.99
9.54
8.70
8.43
8.10
7.99
8.34
8.64
8.61
8.38
7.70
7.57
7.92
8.24
9.52

77.5
8.59
8.87
9.26
8.68
8.08
7.49
7.16
7.04
7.59
7.95
7.87
7.62
6.79
6.52
6.88
7.48
8.59

80
7.85
7.89
8.23
7.51
6.84
6.61
6.21
5.84
6.58
7.15
6.87
6.48
5.83
5.48
5.71
6.27
7.85

82.5
6.67
6.54
7.02
6.59
6.09
5.41
5.39
5.08
5.57
6.53
6.06
5.47
4.73
4.37
4.60
5.26
6.67

85
5.31
5.50
6.10
5.61
4.59
4.53
4.25
3.75
4.31
5.10
5.44
4.59
3.44
2.87
2.91
4.30
5.31

87.5
4.07
4.46
4.65
4.38
3.54
3.21
2.99
2.42
3.31
4.23
4.14
3.26
2.34
1.76
1.03
2.71
4.07

90
2.64
3.05
3.19
2.85
2.04
1.51
1.54
1.22
1.67
2.87
2.96
1.68
0.79
0.06
0.21
1.50
2.64

92.5
1.15
1.27
2.15
1.19
0.73
0.38
0.04
0.11
0.29
1.75
1.78
1.05
0.69
1.57
1.71
0.09
1.15

95
0.65
0.33
0.27
0.28
1.13
1.32
1.36
1.57
1.28
0.08
0.29
0.78
2.04
3.33
3.01
1.68
0.65

97.5
2.14
1.98
1.55
1.87
2.75
2.95
2.69
3.15
2.61
1.16
1.33
2.23
3.59
4.77
5.02
3.27
2.14

100
4.06
3.82
3.25
3.83
4.18
4.78
4.45
4.60
4.56
2.46
3.13
3.68
5.59
6.59
6.65
4.98
4.06

102.5
5.86
5.66
4.96
5.86
6.24
6.41
6.10
6.57
6.07
4.32
4.55
5.64
7.59
8.62
8.47
7.21
5.86

105
7.72
7.68
7.14
7.45
7.92
7.92
7.80
8.47
7.83
6.06
6.48
7.22
9.07
10.58
10.68
8.80
7.72

107.5
9.89
9.77
9.09
9.48
10.22
10.06
10.07
10.17
9.90
8.04
8.28
9.37
11.33
12.14
12.57
11.03
9.89

110
11.81
11.91
11.21
11.56
11.97
12.14
11.40
11.95
11.85
9.97
9.96
11.20
13.20
14.30
14.91
13.06
11.81

112.5
14.17
14.36
13.52
13.71
14.46
14.02
13.79
14.23
13.87
11.83
12.01
13.41
15.07
16.84
16.86
15.03
14.17

115
16.28
16.45
15.95
16.04
16.57
16.16
15.75
16.44
16.20
13.93
13.43
15.50
17.39
18.80
19.33
17.64
16.28

117.5
18.69
18.84
18.26
18.55
18.81
18.61
18.21
18.53
18.33
16.04
15.98
17.77
19.39
20.95
21.35
19.74
18.69

120
21.05
21.23
20.94
20.70
21.12
20.63
20.29
21.06
20.79
18.21
17.97
19.92
21.78
23.63
23.95
22.28
21.05

122.5
23.47
23.56
23.07
23.52
23.42
23.02
22.76
23.09
22.68
20.32
20.02
22.06
24.36
25.59
26.30
24.38
23.47

125
26.01
26.32
25.80
25.85
25.91
25.60
25.09
25.62
25.00
22.86
23.00
24.53
26.29
28.46
28.77
27.12
26.01

127.5
28.68
28.89
28.35
28.55
28.46
28.05
27.17
28.15
28.15
24.97
25.30
26.93
28.93
30.68
31.43
29.34
28.68

130
31.41
31.34
30.90
30.64
31.08
30.63
29.76
30.37
30.60
27.51
27.66
29.01
31.38
33.36
33.84
32.01
31.41

132.5
33.64
34.22
33.82
33.52
33.57
32.64
32.16
32.84
33.12
29.99
30.33
31.60
33.71
35.58
36.57
34.37
33.64

135
36.31
36.92
36.13
36.40
36.18
35.60
34.75
35.05
35.32
32.66
32.69
34.51
36.61
38.19
39.05
38.06
36.31

TABLE 1-3

c

γ
0
22.5
45
67.5
90
112.5
135
157.5
180
202.5
225
247.5
270
292.5
315
337.5
360

0
0.60
0.66
0.53
0.27
0.93
0.86
0.79
0.86
1.32
0.66
0.53
0.27
0.93
0.86
0.79
0.86
0.60

2.5
1.06
0.70
1.51
3.20
2.85
2.45
0.51
0.36
0.15
2.22
4.06
5.38
5.70
4.26
1.79
0.19
1.06

5
0.99
0.89
0.99
2.94
3.10
2.71
0.57
0.43
0.05
1.83
3.87
5.13
5.82
3.88
1.73
0.59
0.99

7.5
1.19
0.83
1.06
2.62
2.60
2.64
0.05
0.82
0.21
1.83
3.55
4.57
5.51
3.32
1.73
0.46
1.19

10
1.12
0.83
0.73
2.88
2.41
2.20
0.14
0.82
0.47
1.45
3.05
4.13
5.14
2.87
1.28
0.72
1.12

12.5
1.19
1.42
0.54
2.18
2.21
2.20
0.66
1.21
1.06
1.25
2.61
3.33
4.65
2.12
0.96
1.44
1.19

15
1.72
1.75
0.18
1.99
2.02
1.30
0.99
1.54
1.64
0.74
2.42
2.77
3.85
1.55
0.51
1.05
1.72

17.5
1.92
2.35
0.57
1.29
0.88
0.92
1.83
2.07
2.17
0.04
1.54
2.58
3.60
1.30
0.20
1.90
1.92

20
2.58
2.35
1.02
0.65
0.31
0.09
2.09
2.59
2.69
0.73
0.79
1.34
2.55
0.48
0.58
2.69
2.58

22.5
3.23
3.34
1.67
0.18
0.90
0.10
3.20
3.64
3.53
1.31
0.10
0.66
1.44
0.52
1.35
2.89
3.23

25
3.96
3.74
2.91
0.69
1.41
1.25
3.40
3.97
3.92
2.21
0.53
0.33
0.45
1.78
2.19
3.80
3.96

27.5
4.69
4.80
3.16
1.58
2.36
2.08
4.44
4.42
5.03
2.97
1.73
1.64
0.53
2.66
2.70
4.20
4.69

30
5.21
5.66
4.33
2.60
3.12
2.72
5.35
5.67
5.42
4.13
2.80
2.44
1.40
3.36
3.47
4.92
5.21

32.5
5.74
6.39
4.66
3.88
4.39
3.74
6.19
6.32
6.86
4.64
4.05
3.75
2.57
4.49
4.30
5.91
5.74

35
6.40
7.18
5.57
4.32
5.03
4.88
7.04
7.18
7.44
5.79
4.62
4.74
3.43
5.75
5.33
6.82
6.40

37.5
7.19
7.91
6.61
5.41
6.36
5.52
7.89
7.96
8.49
6.82
5.88
6.10
4.85
6.19
6.04
7.94
7.19

40
8.31
8.63
7.71
6.68
7.57
6.54
8.86
8.95
9.40
7.65
7.26
7.10
5.97
7.26
7.00
8.33
8.31

42.5
9.17
9.36
8.68
7.38
8.14
7.56
9.64
9.60
9.66
8.55
7.64
8.09
6.83
9.02
8.34
9.32
9.17

45
9.70
9.96
9.59
8.78
9.29
8.46
10.23
10.06
10.51
9.38
9.15
8.90
8.00
9.90
8.60
9.65
9.70

47.5
9.77
10.49
10.50
8.97
9.92
9.61
10.81
10.65
10.96
10.22
9.84
10.26
8.99
10.53
9.50
10.50
9.77

50
10.75
11.21
11.15
10.18
10.68
10.12
11.33
11.76
11.29
10.60
10.72
10.94
9.91
11.29
10.53
10.90
10.75

52.5
11.35
11.55
11.54
10.89
11.64
11.01
11.98
12.02
12.07
11.24
11.16
11.81
10.53
12.11
10.78
11.49
11.35

55
11.41
12.21
12.06
11.71
12.15
11.26
12.18
12.29
12.33
11.95
12.04
12.12
11.33
12.67
11.42
11.62
11.41

57.5
12.01
11.94
12.38
12.16
12.21
11.58
12.64
12.22
12.72
12.07
12.16
12.99
11.95
12.67
11.42
12.21
12.01

60
12.01
12.27
12.38
12.54
12.91
12.09
12.90
12.35
12.59
12.65
12.48
13.18
12.51
13.24
12.32
12.08
12.01

62.5
12.01
11.94
12.58
12.42
13.23
12.48
12.83
12.09
12.79
12.39
13.11
13.30
12.94
13.37
12.51
12.41
12.01

65
11.81
12.21
12.97
12.86
13.23
12.35
12.70
12.35
12.26
12.65
12.73
13.24
13.00
13.49
12.45
12.21
11.81

67.5
12.01
12.34
12.38
12.54
13.29
12.60
12.24
12.29
12.20
12.33
12.73
13.30
13.19
13.05
12.39
11.95
12.01

70
11.35
11.74
11.99
12.54
12.91
12.35
12.18
11.76
11.87
12.33
12.67
12.93
13.00
12.99
11.94
11.55
11.35

72.5
11.08
11.41
11.99
12.54
12.15
11.84
11.33
11.24
11.22
11.69
12.04
12.93
12.88
12.48
11.68
11.09
11.08

75
10.36
11.02
11.15
11.78
12.02
11.33
10.88
10.71
10.57
11.24
11.72
12.31
12.57
12.48
11.17
10.90
10.36

77.5
9.50
10.02
10.50
11.40
11.13
11.01
9.64
9.67
9.92
10.66
11.35
11.63
11.83
11.29
10.65
9.98
9.50

80
8.91
9.03
9.59
10.57
10.24
10.18
8.80
8.75
8.75
9.89
10.34
10.94
11.40
10.66
9.82
9.45
8.91

82.5
7.79
7.58
8.62
9.93
9.60
9.10
8.15
7.64
7.83
9.00
9.77
10.20
10.59
9.78
8.79
8.07
7.79

85
7.13
6.78
7.77
8.34
8.71
8.46
7.10
6.52
6.34
7.65
8.77
9.08
9.61
8.90
8.09
7.02
7.13

87.5
5.41
5.52
6.15
7.32
7.19
7.12
5.41
5.28
5.36
6.69
7.39
7.72
8.56
7.39
6.74
5.64
5.41

90
4.42
4.07
5.05
6.42
5.98
5.78
4.63
3.84
3.73
5.22
6.38
6.97
7.26
6.00
5.52
4.33
4.42

92.5
2.38
2.42
3.88
4.77
4.46
4.82
2.87
2.53
2.56
3.94
4.62
5.11
6.03
4.43
4.05
2.82
2.38

95
1.06
1.03
2.26
3.68
2.80
3.10
1.31
0.76
1.19
2.53
3.68
3.68
4.61
2.79
2.51
1.24
1.06

97.5
0.33
0.63
0.44
1.84
1.47
1.38
0.51
0.82
0.83
0.54
2.17
2.13
3.00
1.53
0.97
0.07
0.33

100
1.91
2.55
0.73
0.01
0.44
0.04
2.20
2.65
2.40
0.93
0.22
0.52
1.58
0.08
0.70
1.91
1.91

102.5
3.63
4.07
2.74
1.73
1.90
1.81
4.09
4.09
4.09
2.98
1.98
1.40
0.45
2.62
2.43
4.07
3.63

105
5.87
6.38
5.15
3.52
4.18
3.54
6.17
6.19
6.11
4.33
3.55
3.70
1.93
4.01
4.10
5.91
5.87

107.5
7.91
8.10
6.70
5.87
5.90
5.58
8.12
8.09
8.00
6.77
5.69
5.44
3.97
6.40
6.15
8.08
7.91

110
9.96
10.22
9.11
7.60
8.12
7.94
9.75
10.32
10.15
8.94
7.51
7.49
6.50
8.73
8.59
9.92
9.96

112.5
12.46
12.21
11.64
9.95
10.35
10.17
12.42
12.67
12.36
10.80
9.65
9.59
8.29
10.68
10.58
12.15
12.46

115
13.98
14.98
13.78
12.12
13.08
12.28
14.69
14.51
14.84
13.05
12.04
11.89
10.76
13.39
13.02
14.58
13.98

117.5
16.55
17.37
15.92
14.35
15.24
14.06
16.78
17.00
17.12
15.10
14.37
14.06
13.23
15.09
15.26
16.35
16.55

120
19.33
19.42
18.65
16.45
17.65
16.93
19.51
19.03
19.86
17.79
17.07
16.98
15.57
17.98
17.38
19.31
19.33

122.5
21.50
22.00
20.86
19.19
20.26
19.55
21.66
21.65
22.33
20.22
19.46
18.72
17.92
20.37
19.62
21.67
21.50

125
23.81
24.38
23.45
21.87
22.42
21.72
24.13
24.40
24.81
22.66
22.04
21.76
20.14
23.14
22.89
23.90
23.81

127.5
26.25
26.89
25.86
24.23
25.28
24.59
26.73
26.63
27.22
24.90
24.36
24.36
23.16
25.66
24.88
26.79
26.25

130
29.09
29.67
28.52
27.10
28.01
26.50
29.14
29.71
29.96
27.72
26.63
27.15
25.45
28.37
27.32
29.29
29.09

132.5
31.53
32.12
31.12
29.52
30.74
29.18
31.61
31.67
32.24
30.54
29.21
29.88
28.23
30.70
29.82
31.58
31.53

135
34.37
34.83
33.91
32.51
33.73
31.61
34.67
35.08
34.91
33.36
31.97
32.37
30.94
33.47
32.65
35.06
34.37

TABLE 1-4

c

γ
0
22.5
45
67.5
90
112.5
135
157.5
180
202.5
225
247.5
270
292.5
315
337.5
360

0
4.00
3.71
3.62
3.23
3.04
3.23
2.65
3.42
3.13
3.71
3.62
3.23
3.04
3.23
2.65
3.42
4.00

2.5
3.71
2.51
2.70
2.56
2.69
3.58
3.04
3.19
2.45
2.03
1.09
0.48
0.08
0.45
1.84
2.33
3.71

5
3.04
2.90
3.18
2.17
2.69
3.29
2.56
2.80
2.06
2.42
0.79
0.12
0.02
0.95
1.35
2.23
3.04

7.5
3.52
3.00
2.89
1.69
2.30
2.72
2.37
2.51
2.25
2.32
0.89
0.02
0.22
0.25
1.94
2.43
3.52

10
3.04
2.61
2.60
2.56
1.82
2.81
2.37
2.03
2.15
1.93
0.59
0.62
0.52
0.45
1.94
2.62
3.04

12.5
3.04
2.90
2.21
1.40
1.53
2.91
1.99
2.13
1.57
1.74
0.99
0.62
0.62
0.65
2.14
2.23
3.04

15
3.13
2.41
1.44
1.59
1.04
2.04
1.79
1.26
1.77
1.83
0.79
0.22
0.32
1.25
1.84
2.33
3.13

17.5
2.75
2.22
1.83
1.11
1.24
1.76
1.02
1.06
0.89
1.25
0.40
0.12
0.22
0.65
2.14
2.14
2.75

20
3.04
2.03
1.92
0.14
0.46
0.89
0.44
0.68
0.70
1.15
0.20
0.32
0.92
0.65
1.55
2.04
3.04

22.5
2.07
1.44
1.25
0.04
0.12
0.60
0.13
0.38
0.22
0.56
0.20
0.22
0.32
0.55
1.45
1.75
2.07

25
2.07
0.57
0.96
0.83
1.28
0.74
1.58
0.67
0.95
0.56
0.70
0.22
0.02
0.05
1.84
1.45
2.07

27.5
0.72
0.47
0.11
1.12
1.95
1.60
1.96
1.54
1.43
0.31
0.89
0.58
0.28
0.45
1.25
1.26
0.72

30
1.01
0.69
1.37
1.71
3.30
2.28
3.31
2.70
2.40
0.80
1.79
0.68
0.68
0.45
1.05
1.06
1.01

32.5
0.14
1.47
1.37
2.87
3.21
3.53
4.37
3.76
3.66
1.78
2.58
1.48
1.78
1.54
0.17
0.21
0.14

35
1.12
2.05
3.02
4.42
4.75
4.29
5.43
4.92
4.44
2.66
3.28
2.18
1.58
1.94
0.72
0.89
1.12

37.5
1.21
3.02
3.31
5.00
5.82
5.16
6.58
6.18
5.60
4.12
4.37
2.48
2.48
2.64
1.11
1.87
1.21

40
3.14
3.79
4.47
6.07
6.59
6.60
7.07
7.04
6.09
4.61
5.16
3.37
3.48
3.24
2.29
2.75
3.14

42.5
3.53
5.54
5.34
6.94
7.85
7.27
8.89
7.62
7.35
5.78
5.95
3.97
4.58
4.43
2.98
3.43
3.53

45
5.07
6.02
6.60
7.52
8.43
8.90
9.28
8.78
7.83
6.96
6.85
5.47
5.48
5.43
4.06
4.41
5.07

47.5
5.65
7.09
7.09
8.59
9.30
8.71
9.95
9.36
8.90
7.44
7.54
6.07
5.87
6.13
4.85
5.77
5.65

50
6.52
7.48
8.06
9.08
10.07
9.67
10.63
10.13
9.87
8.23
8.04
6.57
7.17
6.72
5.83
6.56
6.52

52.5
7.97
8.74
8.64
10.14
10.84
10.73
11.40
11.00
10.45
9.50
9.03
7.07
7.57
7.62
6.42
7.14
7.97

55
8.17
9.13
9.61
10.82
10.94
10.92
11.78
11.58
10.84
9.89
9.23
7.96
8.07
8.12
6.91
7.92
8.17

57.5
9.52
9.42
10.19
11.31
11.52
12.26
12.65
11.48
11.32
10.18
9.62
8.46
8.47
8.92
7.90
8.51
9.52

60
8.94
9.81
10.38
11.21
11.52
11.40
12.36
12.16
11.42
10.77
9.72
9.56
8.37
9.02
8.09
9.00
8.94

62.5
10.48
10.10
10.97
11.31
11.33
12.07
12.36
12.06
12.00
10.47
10.72
9.26
9.17
8.82
8.88
9.78
10.48

65
10.00
10.68
10.67
11.79
11.42
11.88
11.98
12.26
11.42
10.86
10.42
9.86
9.47
9.91
9.96
9.49
10.00

67.5
10.48
11.07
10.67
11.40
11.81
11.78
12.36
11.87
11.71
11.35
9.82
10.36
9.17
9.81
9.37
10.46
10.48

70
10.19
11.07
10.48
11.31
11.13
11.59
11.69
11.58
11.32
10.38
10.32
9.56
9.37
9.81
9.77
10.07
10.19

72.5
10.00
10.58
10.09
10.82
11.04
11.30
11.88
11.19
10.74
10.86
9.72
9.46
9.07
9.31
8.88
10.07
10.00

75
10.39
10.10
10.29
10.43
9.88
10.73
10.24
10.52
10.16
9.69
9.53
8.66
8.47
9.41
9.27
9.68
10.39

77.5
9.52
9.81
9.41
9.85
9.49
9.67
9.66
9.94
9.58
9.30
9.13
8.06
8.67
8.92
9.27
8.70
9.52

80
9.23
9.13
8.83
8.78
8.43
9.19
9.28
9.17
9.00
8.81
8.43
7.96
7.67
8.22
8.88
9.10
9.23

82.5
8.55
8.74
8.54
7.62
8.14
9.10
8.22
8.11
8.61
8.52
7.34
7.67
7.77
7.62
8.29
8.41
8.55

85
8.17
7.77
7.48
7.14
6.88
7.46
7.07
6.95
7.35
7.44
7.05
6.47
6.37
7.42
8.09
7.53
8.17

87.5
7.59
6.99
6.60
5.68
5.72
6.21
6.01
5.79
5.99
6.08
6.05
5.47
6.07
6.23
7.01
7.53
7.59

90
6.33
5.83
5.83
4.62
4.66
4.87
4.27
5.40
4.92
5.49
4.66
5.07
4.98
5.43
6.52
6.07
6.33

92.5
5.36
4.86
4.57
3.55
3.30
3.91
3.50
3.47
3.18
4.61
3.47
4.07
4.28
3.73
6.23
4.70
5.36

95
4.69
3.70
2.92
2.39
2.44
2.76
2.15
2.31
2.40
3.54
2.09
3.17
2.68
3.14
3.67
4.02
4.69

97.5
3.43
2.14
1.95
1.32
0.70
1.41
0.33
0.48
1.14
1.58
1.39
1.48
1.48
1.54
3.18
3.14
3.43

100
2.08
0.98
0.60
0.04
1.14
0.32
1.41
0.10
0.60
0.71
0.40
0.58
0.78
0.64
1.50
1.48
2.08

102.5
0.83
0.28
0.86
2.56
2.69
1.85
2.66
2.51
1.96
1.15
1.68
0.52
1.52
1.15
0.23
0.11
0.83

105
1.11
1.74
2.02
3.53
3.85
3.87
4.39
4.15
3.32
2.91
3.27
2.31
2.02
1.95
0.66
1.06
1.11

107.5
2.94
3.87
3.77
5.47
5.59
5.79
6.03
5.89
6.03
3.89
4.76
4.41
3.72
4.14
2.53
2.72
2.94

110
3.91
5.13
5.51
6.73
7.62
7.23
8.05
7.72
7.39
6.03
6.05
5.31
5.22
5.33
4.10
4.48
3.91

112.5
5.84
7.07
7.45
8.96
9.16
8.67
10.27
9.65
9.52
7.99
8.23
6.90
6.82
6.73
5.87
6.24
5.84

115
7.29
8.72
9.39
10.70
11.00
11.55
12.58
11.97
10.88
9.84
10.22
8.80
9.02
9.02
6.95
7.31
7.29

117.5
9.03
10.85
11.23
12.84
13.41
12.99
13.73
13.52
12.72
11.70
11.70
10.79
10.92
11.41
9.12
9.36
9.03

120
11.83
12.31
13.17
14.78
15.06
14.63
15.95
15.54
14.66
13.75
14.09
12.39
12.92
12.61
10.89
11.12
11.83

122.5
13.37
14.73
15.49
17.01
17.86
17.51
18.93
17.96
17.38
15.80
15.87
14.29
14.22
14.40
12.86
13.27
13.37

125
15.11
16.77
16.85
19.04
19.11
19.43
20.76
19.98
19.51
17.66
18.15
17.28
16.02
16.30
15.12
15.03
15.11

127.5
17.23
19.10
19.08
21.08
21.43
21.35
22.88
22.30
21.84
19.51
20.24
19.28
18.72
18.09
16.50
17.27
17.23

130
19.26
21.33
21.21
23.41
24.33
23.94
25.19
24.13
24.26
22.64
23.01
20.67
19.62
20.88
18.86
19.13
19.26

132.5
21.77
23.37
23.15
25.44
26.27
25.67
27.02
27.03
26.40
24.50
24.50
23.27
22.82
23.17
21.61
21.18
21.77

135
24.19
26.18
26.06
27.96
28.59
28.84
30.00
28.86
28.82
26.94
26.98
24.86
25.02
25.36
23.77
24.40
24.19

TABLE 1-5

c

γ
0
22.5
45
67.5
90
112.5
135
157.5
180
202.5
225
247.5
270
292.5
315
337.5
360

0
29.93
29.85
29.85
29.61
29.61
29.29
29.61
29.61
29.21
29.85
29.85
29.61
29.61
29.29
29.61
29.61
29.93

2.5
30.26
28.53
27.92
27.42
27.56
29.83
31.53
33.88
35.57
37.32
37.75
36.69
35.88
34.21
32.70
31.38
30.26

5
30.34
29.36
27.92
27.59
28.31
29.50
31.45
33.05
35.14
36.75
36.40
35.97
34.50
33.83
32.01
30.67
30.34

7.5
29.85
28.95
28.25
28.17
28.39
29.26
31.29
32.60
33.97
35.75
35.26
34.97
33.77
33.08
31.47
30.59
29.85

10
29.53
28.20
28.00
27.75
28.06
28.45
30.43
31.24
32.37
34.53
34.20
33.32
32.23
31.96
30.55
30.20
29.53

12.5
28.97
27.54
27.33
27.42
27.48
27.72
29.02
30.71
31.13
33.03
32.49
31.74
30.48
30.61
29.86
29.17
28.97

15
27.92
26.88
26.66
26.74
26.81
26.67
27.93
28.91
29.24
31.31
30.86
29.37
28.51
29.04
28.40
27.99
27.92

17.5
26.95
26.31
25.82
25.90
25.90
25.46
26.44
27.10
27.35
29.52
28.66
27.58
26.62
27.10
26.71
26.57
26.95

20
25.74
24.66
24.65
24.72
24.65
23.68
24.72
25.37
25.16
27.30
26.88
25.43
24.65
25.60
24.94
24.83
25.74

22.5
24.61
22.84
23.39
23.37
23.32
22.87
22.84
23.18
23.56
25.09
24.75
23.28
22.53
23.58
22.95
23.18
24.61

25
22.67
21.19
21.55
21.94
21.82
20.60
21.20
21.23
21.23
23.08
22.76
20.98
20.34
21.41
20.72
21.36
22.67

27.5
20.65
19.13
19.95
20.26
20.15
19.06
18.85
18.89
18.76
20.65
19.77
18.40
17.94
19.46
18.88
19.23
20.65

30
18.55
17.31
17.86
18.07
18.24
16.64
16.58
16.63
16.21
18.22
17.50
16.47
15.53
16.77
16.49
17.34
18.55

32.5
16.37
14.84
15.43
16.05
16.07
13.40
14.54
13.84
13.08
15.71
14.80
13.88
12.90
14.45
14.11
14.66
16.37

35
13.87
12.11
12.66
13.35
13.32
11.29
11.41
11.06
10.60
12.92
11.67
10.80
10.28
11.53
11.04
12.06
13.87

37.5
10.96
9.39
9.81
10.91
10.74
9.03
8.75
8.42
7.84
9.85
9.18
7.79
7.65
9.28
8.50
9.45
10.96

40
8.38
6.67
7.21
8.13
8.41
6.11
6.41
5.49
5.00
7.34
6.27
5.14
4.81
6.66
6.12
6.77
8.38

42.5
5.23
3.86
5.12
5.78
5.75
3.52
3.51
2.70
1.94
4.27
3.71
2.48
2.04
3.44
3.05
4.01
5.23

45
2.89
1.38
2.52
3.25
3.08
1.10
0.69
0.01
0.46
1.55
0.80
0.17
0.66
0.75
0.28
1.49
2.89

47.5
0.39
1.09
0.25
0.89
0.67
1.74
2.05
2.35
3.52
1.60
2.11
2.68
3.44
1.57
2.10
1.19
0.39

50
2.03
4.06
2.59
2.22
2.08
3.84
4.39
4.76
6.14
4.11
4.74
5.69
5.70
4.27
4.32
3.80
2.03

52.5
4.94
6.12
5.53
4.41
4.33
6.19
6.58
7.32
8.40
6.82
7.23
7.99
8.18
6.59
7.01
6.40
4.94

55
7.28
8.44
7.45
6.43
6.58
8.45
8.78
9.65
10.65
9.04
9.65
10.28
10.15
8.76
8.86
8.14
7.28

57.5
9.22
10.83
9.72
8.62
8.74
10.72
10.81
11.46
13.13
11.69
12.13
12.43
12.19
11.00
10.93
10.34
9.22

60
11.88
13.06
11.73
11.23
11.07
12.50
13.24
13.87
14.58
13.48
13.84
14.58
14.45
13.17
13.24
12.55
11.88

62.5
13.33
14.79
13.66
12.75
13.24
14.28
15.04
15.83
16.11
15.55
15.97
16.16
15.84
14.52
14.85
14.21
13.33

65
15.27
16.19
15.16
14.69
14.40
15.98
16.45
17.11
17.86
17.20
17.53
17.81
17.44
16.47
16.54
15.79
15.27

67.5
16.80
17.68
16.84
16.20
16.23
17.03
17.78
18.31
19.32
18.70
19.17
19.03
18.83
17.96
17.54
17.13
16.80

70
18.34
18.75
17.76
17.21
17.57
18.81
18.87
19.67
20.63
20.13
20.31
20.03
19.85
18.86
18.84
18.31
18.34

72.5
19.31
19.99
19.44
18.47
18.90
19.38
20.28
20.57
21.43
21.28
21.16
21.18
20.65
20.43
19.84
19.65
19.31

75
20.19
20.81
20.19
19.57
19.48
20.43
20.59
21.40
22.37
22.06
22.08
22.25
21.38
20.73
20.61
20.68
20.19

77.5
21.24
21.47
20.78
20.07
20.40
20.76
21.61
21.70
22.30
22.85
22.65
22.54
21.89
21.33
20.99
21.07
21.24

80
21.16
21.31
21.20
20.58
21.06
21.48
21.84
22.00
22.59
23.42
23.29
22.76
22.25
22.16
21.69
21.70
21.16

82.5
22.21
21.64
21.12
21.42
21.23
21.24
21.77
22.15
22.88
23.64
23.50
23.04
22.62
22.38
21.84
21.70
22.21

85
21.89
21.56
21.45
21.42
21.15
21.73
21.92
22.53
22.59
23.85
23.43
23.04
22.47
22.23
21.84
21.78
21.89

87.5
22.21
21.23
21.12
21.34
21.23
21.16
21.61
21.85
22.74
23.35
23.29
22.76
22.18
22.01
21.92
21.47
22.21

90
21.65
21.14
21.12
21.25
20.81
20.59
20.98
21.33
21.94
23.28
23.15
21.90
21.53
21.78
20.99
21.62
21.65

92.5
21.48
19.99
20.53
20.83
20.65
19.79
20.44
20.80
21.14
22.64
22.29
21.39
20.65
21.33
20.38
20.68
21.48

95
20.27
19.58
19.44
20.07
19.90
19.54
19.65
20.04
19.90
21.71
21.51
20.60
20.29
20.58
19.84
19.89
20.27

97.5
19.55
18.50
18.60
19.23
19.48
18.49
18.95
19.29
18.88
20.49
20.31
19.53
18.83
19.16
18.84
18.39
19.55

100
18.90
17.27
17.76
17.80
18.07
16.79
18.01
18.01
17.93
19.63
19.17
18.02
17.95
18.34
17.46
17.76
18.90

102.5
17.69
15.94
16.76
17.13
17.23
15.90
16.13
16.81
16.19
18.42
17.60
16.80
16.05
16.92
16.46
16.50
17.69

105
16.24
14.38
15.08
15.27
15.49
14.61
15.04
14.85
14.73
16.70
16.18
14.65
14.45
15.12
14.85
15.23
16.24

107.5
14.70
12.81
13.74
13.76
13.82
12.82
13.24
13.34
12.84
15.27
14.62
13.36
12.70
13.85
13.16
13.18
14.70

110
12.36
11.08
11.64
12.50
12.49
10.72
10.97
11.38
10.80
13.41
12.56
11.50
10.80
11.98
11.24
11.37
12.36

112.5
10.83
8.68
9.47
10.64
10.66
8.37
9.17
9.20
8.62
11.05
10.43
9.28
8.83
10.10
9.09
9.63
10.83

115
8.65
6.45
7.20
8.20
8.66
6.43
6.98
6.79
6.36
9.11
8.01
7.20
6.06
7.93
6.86
7.35
8.65

117.5
6.07
4.31
5.61
6.10
6.24
3.84
4.55
4.31
3.59
6.61
6.02
4.26
3.80
5.24
5.17
5.06
6.07

120
3.89
1.42
2.59
3.07
3.58
1.57
2.05
1.67
0.75
3.96
2.75
1.60
1.32
3.14
2.10
2.85
3.89

122.5
1.14
1.38
0.26
1.30
1.00
1.02
0.69
1.04
1.36
1.10
0.34
1.12
1.89
0.45
0.21
0.33
1.14

125
1.36
4.11
3.27
1.99
1.83
4.01
3.74
4.13
4.78
1.62
2.79
4.06
4.52
2.77
3.43
2.59
1.36

127.5
4.26
7.16
6.04
4.51
5.08
6.84
6.80
6.54
7.69
4.77
5.56
7.00
7.43
5.31
6.20
5.12
4.26

130
7.09
10.13
9.23
7.88
7.58
10.16
9.85
10.15
11.19
7.84
9.11
9.94
11.01
8.31
9.73
8.51
7.09

132.5
10.40
13.35
12.08
10.91
11.08
13.07
12.82
13.32
14.24
11.21
12.31
13.53
13.93
11.60
12.73
11.58
10.40

135
13.55
16.98
15.43
14.20
14.07
16.80
16.50
16.56
17.81
14.71
15.30
17.11
17.57
15.19
15.27
15.76
13.55

In Tables 1-1 to 1-5, the experiment results of the aforementioned different thickness ratios are combined as shown in Table 2. In Table 2, when the thickness ratio of the lamp shade 20 is 1:1, the number of spatial coordinates not complying with (|I−Iavg|/Iavg)<25% is equal to 156, which is 16.68% of the total number of spatial coordinates, so that it does not meet the requirement of having at least 90% of the coordinates satisfying (|I−Iavg|/Iavg)<25%; when the thickness ratio of the lamp shade 20 is 1.7:1, the number of spatial coordinates not complying with (|I−Iavg|/Iavg)<25% is equal to 96 which is 10.26% of the total number of spatial coordinates, so that it does not meet the requirement of having at least 90% of the coordinates satisfying (|I−Iavg|/Iavg)<25%; when the thickness ratio of the lamp shade 20 is 1.8:1, the number of spatial coordinates not complying with (|I−Iavg|/Iavg)<25% is equal to 62, which is 6.63% of the total number of spatial coordinates, so that it meets the requirement of having at least 90% of the coordinates satisfying (|I−Iavg|/Iavg)<25%; when the thickness ratio of the lamp shade 20 is 3:1, the number of spatial coordinates not complying with (|I−Iavg|/Iavg)<25% is equal to 17, which is 1.81% of the total number of spatial coordinates, so that it meets the requirement of having at least 90% of the coordinates satisfying (|I−Iavg|/Iavg)<25%; and when the thickness ratio of the lamp shade 20 is 3.1:1, the number of spatial coordinates not complying with (|I−Iavg|/Iavg)<25% is equal to 145, which is 15.5% of the total number of spatial coordinates, so that it does not meet the requirement of having at least 90% of the coordinates satisfying (|I−Iavg|/Iavg)<25%.

TABLE 2

Whether or not
Number of Coordinates Not

complies with at least 90% of
Complying with the

Thickness
the coordinate satisfying
Relation/Total number of

Ratio
(|I − Iavg|/Iavg) < 25%
Coordinates

1:1
No
156/935 = 16.68%

1.7:1
No
96/935 = 10.26%

1.8:1
Yes
62/935 = 6.63%

3:1
Yes
17/935 = 1.81%

3.1:1
No
145/935 = 15.5%

In addition to the measurement of the numeric values of the light intensity I at each spatial position within the polar coordinate positions from 0 degree to 135 degrees, and the calculation of the numeric values of the relation of the average light intensity Iavg within the polar coordinate positions from 0 degree to 135 degrees, the present invention also measures the flux of the LED light sources 211 at the polar coordinate positions from 135 degrees to 180 degrees and calculates the total flux of the LED light sources 211 to obtain the numeric value of the cumulative percentage of the total flux at the polar coordinate positions from 135 degrees to 180 degrees. Experiments are performed for different thickness ratios of the lamp shade 20, and the experiment results are listed in Tables 3-1 to 3-5. Table 3-1 lists the experiment results for the thickness ratio of the lamp shade 20 equal to 1:1; Table 3-2 lists the experiment results for the thickness ratio of the lamp shade 20 equal to 1.7:1; Table 3-3 lists the experiment results for the thickness ratio of the lamp shade 20 equal to 1.8:1; Table 3-4 lists the experiment results for the thickness ratio of the lamp shade 20 equal to 3:1; and Table 3-5 lists the experiment results for the thickness ratio of the lamp shade 20 equal to 3.1:1, wherein γ(∘) is the angle at the polar coordinate position; Average 1(cd) is the average light intensity at each angular position which is measured in the unit of candle (cd); Zonal F(lm) is the regional flux at each angular position, which is measured in the unit of lumen (lm); Sum F(lm) is the sequentially cumulative flux at each angular position, which is measured in the unit of lumen (Im); Eff Fiux(%) is the percentage (%) of the flux at each angular position with respect to the total flux; and Eff Sum(%) is the cumulative percentage of the flux at each angular position with respect to the total flux, which is measured in the unit of percent (%).

TABLE 3-1

Sum

Eff

γ (°)
Average I (cd)
Zonal F (lm)
F (lm)
Eff Flux (%)
Sum (%)

0.0
87.230
.000
.000
.000%
.000%

2.5
87.216
.522
.522
.066%
.066%

5.0
87.130
1.563
2.085
.198%
.264%

7.5
87.037
2.599
4.683
.329%
.594%

10.0
86.861
3.626
8.309
.460%
1.053%

12.5
86.655
4.640
12.949
.588%
1.641%

15.0
86.392
5.638
18.587
.715%
2.356%

17.5
86.153
6.618
25.205
.839%
3.195%

20.0
85.825
7.577
32.782
.960%
4.155%

22.5
85.473
8.510
41.292
1.079%
5.234%

25.0
85.109
9.417
50.709
1.194%
6.427%

27.5
84.659
10.292
61.001
1.304%
7.732%

30.0
84.277
11.138
72.138
1.412%
9.143%

32.5
83.873
11.957
84.095
1.515%
10.659%

35.0
83.526
12.747
96.842
1.616%
12.275%

37.5
83.208
13.514
110.356
1.713%
13.987%

40.0
82.840
14.246
124.602
1.806%
15.793%

42.5
82.417
14.935
139.537
1.893%
17.686%

45.0
81.999
15.584
155.121
1.975%
19.661%

47.5
81.603
16.199
171.319
2.053%
21.714%

50.0
81.204
16.778
188.097
2.127%
23.841%

52.5
80.703
17.307
205.404
2.194%
26.035%

55.0
80.253
17.792
223.196
2.255%
28.290%

57.5
79.594
18.217
241.413
2.309%
30.599%

60.0
78.973
18.581
259.994
2.355%
32.954%

62.5
78.376
18.909
278.902
2.397%
35.350%

65.0
77.674
19.183
298.086
2.431%
37.782%

67.5
76.876
19.390
317.475
2.458%
40.239%

70.0
76.068
19.538
337.014
2.476%
42.716%

72.5
75.266
19.642
356.656
2.490%
45.205%

75.0
74.341
19.687
376.343
2.495%
47.701%

77.5
73.365
19.665
396.008
2.493%
50.193%

80.0
72.402
19.596
415.604
2.484%
52.677%

82.5
71.268
19.463
435.067
2.467%
55.144%

85.0
70.224
19.279
454.346
2.444%
57.587%

87.5
69.042
19.048
473.394
2.414%
60.002%

90.0
67.900
18.766
492.160
2.379%
62.380%

92.5
66.661
18.440
510.599
2.337%
64.717%

95.0
65.384
18.060
528.659
2.289%
67.006%

97.5
64.090
17.641
546.301
2.236%
69.242%

100.0
62.672
17.173
563.473
2.177%
71.419%

102.5
61.267
16.662
580.135
2.112%
73.531%

105.0
59.714
16.107
596.242
2.042%
75.572%

107.5
58.227
15.520
611.762
1.967%
77.539%

110.0
56.712
14.918
626.680
1.891%
79.430%

112.5
55.033
14.275
640.955
1.809%
81.240%

115.0
53.468
13.612
654.568
1.725%
82.965%

117.5
51.763
12.936
667.504
1.640%
84.605%

120.0
50.108
12.242
679.746
1.552%
86.156%

122.5
48.297
11.531
691.277
1.462%
87.618%

125.0
46.567
10.811
702.088
1.370%
88.988%

127.5
44.788
10.098
712.187
1.280%
90.268%

130.0
43.012
9.385
721.527
1.190%
91.458%

132.5
41.214
8.680
730.252
1.100%
92.558%

135.0
39.375
7.979
738.231
1.011%
93.569%

137.5
37.648
7.301
745.531
.925%
94.494%

140.0
35.950
6.651
752.183
.843%
95.337%

142.5
34.166
6.015
758.198
.762%
96.100%

145.0
32.490
5.402
763.601
.685%
96.785%

147.5
30.798
4.819
768.420
.611%
97.396%

150.0
29.000
4.252
772.672
.539%
97.934%

152.5
27.237
3.708
776.380
.470%
98.404%

155.0
25.087
3.172
779.552
.402%
98.806%

157.5
22.776
2.642
782.194
.335%
99.141%

160.0
20.135
2.132
784.326
.270%
99.412%

162.5
17.534
1.660
785.985
.210%
99.622%

165.0
14.779
1.239
787.225
.157%
99.779%

167.5
11.544
.858
788.082
.109%
99.888%

170.0
8.035
.524
788.606
.066%
99.954%

172.5
4.195
.255
788.861
.032%
99.986%

175.0
1.220
.081
788.942
.010%
99.997%

177.5
1.047
.020
788.962
.003%
99.999%

180.0
1.052
.006
788.968
.001%
100.000%

TABLE 3-2

Average

γ (°)
I (cd)
Zonal F (lm)
Sum F (lm)
Eff Flux (%)
Eff Sum (%)

0.0
72.256
.000
.000
.000%
.000%

2.5
72.280
.432
.432
.054%
.054%

5.0
72.361
1.297
1.729
.163%
.218%

7.5
72.397
2.160
3.889
.272%
.490%

10.0
72.548
3.022
6.911
.381%
.871%

12.5
72.668
3.883
10.794
.489%
1.361%

15.0
72.871
4.741
15.536
.598%
1.958%

17.5
73.137
5.600
21.136
.706%
2.664%

20.0
73.338
6.453
27.589
.813%
3.477%

22.5
73.582
7.299
34.888
.920%
4.397%

25.0
73.845
8.138
43.027
1.026%
5.423%

27.5
74.119
8.970
51.997
1.131%
6.554%

30.0
74.441
9.794
61.791
1.234%
7.788%

32.5
74.832
10.614
72.405
1.338%
9.126%

35.0
75.206
11.425
83.830
1.440%
10.566%

37.5
75.580
12.221
96.052
1.540%
12.106%

40.0
75.846
12.991
109.043
1.637%
13.744%

42.5
76.139
13.736
122.779
1.731%
15.475%

45.0
76.432
14.461
137.240
1.823%
17.298%

47.5
76.640
15.156
152.396
1.910%
19.208%

50.0
76.811
15.814
168.209
1.993%
21.201%

52.5
76.933
16.435
184.644
2.071%
23.273%

55.0
76.993
17.015
201.659
2.145%
25.417%

57.5
76.993
17.549
219.208
2.212%
27.629%

60.0
76.933
18.037
237.245
2.273%
29.902%

62.5
76.809
18.475
255.720
2.329%
32.231%

65.0
76.627
18.862
274.582
2.377%
34.608%

67.5
76.258
19.181
293.763
2.418%
37.026%

70.0
75.992
19.450
313.213
2.451%
39.477%

72.5
75.531
19.667
332.879
2.479%
41.956%

75.0
75.008
19.810
352.689
2.497%
44.453%

77.5
74.422
19.895
372.584
2.508%
46.961%

80.0
73.709
19.914
392.498
2.510%
49.471%

82.5
73.020
19.878
412.375
2.505%
51.976%

85.0
72.212
19.788
432.164
2.494%
54.470%

87.5
71.344
19.635
451.798
2.475%
56.945%

90.0
70.346
19.417
471.215
2.447%
59.392%

92.5
69.405
19.151
490.366
2.414%
61.806%

95.0
68.296
18.834
509.200
2.374%
64.180%

97.5
67.220
18.464
527.664
2.327%
66.507%

100.0
66.029
18.051
545.716
2.275%
68.782%

102.5
64.757
17.582
563.298
2.216%
70.998%

105.0
63.518
17.078
580.376
2.153%
73.151%

107.5
62.111
16.532
596.908
2.084%
75.234%

110.0
60.774
15.950
612.857
2.010%
77.245%

112.5
59.272
15.335
628.193
1.933%
79.178%

115.0
57.775
14.684
642.877
1.851%
81.028%

117.5
56.210
14.012
656.890
1.766%
82.795%

120.0
54.594
13.315
670.205
1.678%
84.473%

122.5
53.037
12.612
682.817
1.590%
86.063%

125.0
51.283
11.889
694.706
1.498%
87.561%

127.5
49.563
11.147
705.853
1.405%
88.966%

130.0
47.860
10.414
716.268
1.313%
90.279%

132.5
46.125
9.685
725.953
1.221%
91.499%

135.0
44.281
8.951
734.904
1.128%
92.628%

137.5
42.640
8.239
743.143
1.038%
93.666%

140.0
40.861
7.546
750.689
.951%
94.617%

142.5
39.063
6.857
757.546
.864%
95.481%

145.0
37.401
6.197
763.743
.781%
96.262%

147.5
35.587
5.558
769.302
.701%
96.963%

150.0
33.764
4.931
774.233
.622%
97.585%

152.5
31.698
4.316
778.549
.544%
98.129%

155.0
29.436
3.706
782.255
.467%
98.596%

157.5
26.820
3.106
785.360
.391%
98.987%

160.0
23.980
2.524
787.884
.318%
99.305%

162.5
20.897
1.977
789.861
.249%
99.554%

165.0
17.659
1.479
791.340
.186%
99.741%

167.5
13.497
1.015
792.355
.128%
99.869%

170.0
9.787
.623
792.978
.078%
99.947%

172.5
4.629
.301
793.278
.038%
99.985%

175.0
1.391
.090
793.368
.011%
99.996%

177.5
1.082
.022
793.390
.003%
99.999%

180.0
1.047
.006
793.397
.001%
100.000%

TABLE 3-3

Average

γ (°)
I (cd)
Zonal F (lm)
Sum F (lm)
Eff Flux (%)
Eff Sum (%)

0.0
66.257
.000
.000
.000%
.000%

2.5
66.246
.396
.396
.050%
.050%

5.0
66.319
1.188
1.585
.150%
.200%

7.5
66.479
1.982
3.566
.251%
.451%

10.0
66.648
2.776
6.342
.351%
.802%

12.5
66.943
3.572
9.914
.452%
1.254%

15.0
67.231
4.371
14.286
.553%
1.807%

17.5
67.616
5.172
19.458
.654%
2.461%

20.0
68.052
5.977
25.435
.756%
3.217%

22.5
68.584
6.788
32.223
.859%
4.076%

25.0
69.091
7.600
39.823
.961%
5.037%

27.5
69.658
8.411
48.234
1.064%
6.101%

30.0
70.233
9.223
57.457
1.167%
7.268%

32.5
70.881
10.034
67.491
1.269%
8.537%

35.0
71.458
10.839
78.330
1.371%
9.908%

37.5
72.120
11.637
89.967
1.472%
11.381%

40.0
72.801
12.433
102.400
1.573%
12.953%

42.5
73.384
13.211
115.612
1.671%
14.624%

45.0
73.942
13.964
129.576
1.766%
16.391%

47.5
74.425
14.690
144.266
1.858%
18.249%

50.0
74.927
15.391
159.657
1.947%
20.196%

52.5
75.342
16.063
175.720
2.032%
22.228%

55.0
75.664
16.692
192.412
2.111%
24.339%

57.5
75.860
17.269
209.681
2.184%
26.524%

60.0
76.079
17.804
227.485
2.252%
28.776%

62.5
76.160
18.295
245.779
2.314%
31.090%

65.0
76.166
18.726
264.505
2.369%
33.459%

67.5
76.095
19.103
283.608
2.416%
35.875%

70.0
75.897
19.417
303.024
2.456%
38.332%

72.5
75.624
19.666
322.691
2.488%
40.819%

75.0
75.312
19.862
342.552
2.512%
43.332%

77.5
74.805
19.986
362.539
2.528%
45.860%

80.0
74.262
20.040
382.578
2.535%
48.395%

82.5
73.636
20.036
402.614
2.534%
50.929%

85.0
72.952
19.973
422.587
2.527%
53.456%

87.5
72.049
19.832
442.420
2.509%
55.965%

90.0
71.236
19.635
462.055
2.484%
58.448%

92.5
70.224
19.385
481.440
2.452%
60.900%

95.0
69.235
19.074
500.514
2.413%
63.313%

97.5
68.139
18.717
519.231
2.368%
65.681%

100.0
67.030
18.312
537.543
2.316%
67.997%

102.5
65.755
17.851
555.394
2.258%
70.255%

105.0
64.467
17.338
572.732
2.193%
72.448%

107.5
63.109
16.788
589.519
2.124%
74.572%

110.0
61.669
16.195
605.715
2.049%
76.621%

112.5
60.185
15.567
621.281
1.969%
78.590%

115.0
58.621
14.905
636.186
1.885%
80.475%

117.5
57.148
14.232
650.418
1.800%
82.276%

120.0
55.413
13.526
663.945
1.711%
83.987%

122.5
53.805
12.798
676.743
1.619%
85.606%

125.0
52.091
12.069
688.811
1.527%
87.132%

127.5
50.388
11.328
700.139
1.433%
88.565%

130.0
48.622
10.584
710.723
1.339%
89.904%

132.5
46.927
9.847
720.569
1.246%
91.149%

135.0
44.997
9.102
729.671
1.151%
92.301%

137.5
43.394
8.378
738.049
1.060%
93.361%

140.0
41.564
7.678
745.727
.971%
94.332%

142.5
39.730
6.974
752.701
.882%
95.214%

145.0
38.079
6.306
759.008
.798%
96.012%

147.5
36.311
5.665
764.672
.717%
96.728%

150.0
34.488
5.034
769.707
.637%
97.365%

152.5
32.224
4.398
774.105
.556%
97.922%

155.0
29.651
3.751
777.856
.474%
98.396%

157.5
27.571
3.159
781.015
.400%
98.796%

160.0
26.028
2.663
783.677
.337%
99.132%

162.5
24.851
2.242
785.919
.284%
99.416%

165.0
23.085
1.839
787.758
.233%
99.649%

167.5
19.419
1.385
789.142
.175%
99.824%

170.0
12.526
.854
789.997
.108%
99.932%

172.5
5.833
.383
790.380
.048%
99.980%

175.0
1.882
.115
790.495
.015%
99.995%

177.5
1.665
.032
790.526
.004%
99.999%

180.0
1.708
.010
790.536
.001%
100.000%

TABLE 3-4

Average

γ (°)
I (cd)
Zonal F (lm)
Sum F (lm)
Eff Flux (%)
Eff Sum (%)

0.0
47.399
.000
.000
.000%
.000%

2.5
47.535
.284
.284
.039%
.039%

5.0
47.662
.853
1.137
.116%
.155%

7.5
47.885
1.426
2.563
.194%
.349%

10.0
48.289
2.005
4.568
.273%
.623%

12.5
48.793
2.596
7.164
.354%
.977%

15.0
49.384
3.199
10.363
.436%
1.412%

17.5
50.152
3.818
14.181
.520%
1.933%

20.0
50.854
4.450
18.631
.607%
2.539%

22.5
51.608
5.090
23.721
.694%
3.233%

25.0
52.465
5.745
29.466
.783%
4.016%

27.5
53.455
6.421
35.887
.875%
4.892%

30.0
54.393
7.110
42.997
.969%
5.861%

32.5
55.527
7.816
50.813
1.065%
6.926%

35.0
56.788
8.553
59.366
1.166%
8.092%

37.5
57.870
9.293
68.659
1.267%
9.358%

40.0
59.065
10.032
78.691
1.367%
10.726%

42.5
60.242
10.782
89.474
1.470%
12.196%

45.0
61.436
11.533
101.007
1.572%
13.768%

47.5
62.471
12.268
113.275
1.672%
15.440%

50.0
63.507
12.982
126.257
1.770%
17.209%

52.5
64.538
13.688
139.945
1.866%
19.075%

55.0
65.465
14.370
154.315
1.959%
21.034%

57.5
66.363
15.024
169.339
2.048%
23.082%

60.0
67.081
15.637
184.976
2.131%
25.213%

62.5
67.833
16.213
201.189
2.210%
27.423%

65.0
68.486
16.758
217.947
2.284%
29.707%

67.5
68.953
17.243
235.190
2.350%
32.057%

70.0
69.389
17.673
252.863
2.409%
34.466%

72.5
69.704
18.053
270.916
2.461%
36.927%

75.0
69.915
18.373
289.288
2.504%
39.431%

77.5
70.007
18.629
307.918
2.539%
41.970%

80.0
70.005
18.822
326.740
2.566%
44.536%

82.5
69.921
18.956
345.696
2.584%
47.120%

85.0
69.777
19.034
364.730
2.594%
49.714%

87.5
69.473
19.046
383.776
2.596%
52.310%

90.0
68.993
18.975
402.750
2.586%
54.896%

92.5
68.554
18.849
421.599
2.569%
57.465%

95.0
67.911
18.665
440.264
2.544%
60.010%

97.5
67.239
18.414
458.678
2.510%
62.520%

100.0
66.439
18.110
476.788
2.468%
64.988%

102.5
65.566
17.746
494.534
2.419%
67.407%

105.0
64.606
17.331
511.864
2.362%
69.769%

107.5
63.551
16.864
528.729
2.299%
72.068%

110.0
62.393
16.347
545.075
2.228%
74.296%

112.5
61.156
15.783
560.858
2.151%
76.447%

115.0
59.841
15.180
576.039
2.069%
78.516%

117.5
58.379
14.533
590.572
1.981%
80.497%

120.0
56.912
13.855
604.426
1.888%
82.386%

122.5
55.377
13.158
617.584
1.793%
84.179%

125.0
53.745
12.436
630.021
1.695%
85.874%

127.5
51.982
11.687
641.707
1.593%
87.467%

130.0
50.168
10.919
652.627
1.488%
88.955%

132.5
48.405
10.158
662.785
1.385%
90.340%

135.0
46.485
9.395
672.180
1.281%
91.621%

137.5
44.788
8.651
680.832
1.179%
92.800%

140.0
42.768
7.913
688.744
1.079%
93.878%

142.5
40.804
7.170
695.914
.977%
94.856%

145.0
38.895
6.460
702.374
.880%
95.736%

147.5
36.972
5.777
708.151
.787%
96.524%

150.0
35.012
5.119
713.270
.698%
97.221%

152.5
33.138
4.493
717.763
.612%
97.834%

155.0
31.074
3.893
721.656
.531%
95.364%

157.5
29.011
3.317
724.972
.452%
98.816%

160.0
26.361
2.751
727.723
.375%
99.191%

162.5
23.381
2.192
729.915
.299%
99.490%

165.0
19.430
1.642
731.557
.224%
99.714%

167.5
13.971
1.088
732.645
.148%
99.862%

170.0
8.952
.613
733.258
.084%
99.946%

172.5
4.328
.277
733.535
.038%
99.984%

175.0
1.510
.087
733.622
.012%
99.995%

177.5
1.315
.025
733.647
.003%
99.999%

180.0
1.313
.008
733.655
.001%
100.000%

TABLE 3-5

Average

γ (°)
I (cd)
Zonal F (lm)
Sum F (lm)
Eff Flux (%)
Eff Sum (%)

0.0
37.827
.000
.000
.000%
.000%

2.5
37.873
.226
.226
.032%
.032%

5.0
38.087
.681
.907
.096%
.128%

7.5
38.353
1.141
2.048
.161%
.289%

10.0
38.879
1.610
3.658
.227%
.516%

12.5
39.465
2.095
5.753
.296%
.812%

15.0
40.235
2.597
8.350
.366%
1.178%

17.5
41.067
3.118
11.468
.440%
1.618%

20.0
42.025
3.661
15.129
.516%
2.134%

22.5
43.006
4.224
19.353
.596%
2.730%

25.0
44.110
4.809
24.162
.678%
3.409%

27.5
45.317
5.421
29.584
.765%
4.173%

30.0
46.572
6.058
35.642
.855%
5.028%

32.5
47.990
6.724
42.366
.949%
5.976%

35.0
49.544
7.427
49.793
1.048%
7.024%

37.5
51.036
8.152
57.945
1.150%
8.174%

40.0
52.535
8.886
66.831
1.253%
9.428%

42.5
54.103
9.637
76.468
1.360%
10.787%

45.0
55.578
10.396
86.864
1.467%
12.254%

47.5
57.064
11.153
98.017
1.573%
13.827%

50.0
58.504
11.910
109.927
1.680%
15.507%

52.5
59.884
12.655
122.582
1.785%
17.292%

55.0
61.099
13.373
135.955
1.887%
19.179%

57.5
62.344
14.068
150.023
1.985%
21.164%

60.0
63.551
14.752
164.776
2.081%
23.245%

62.5
64.522
15.390
180.166
2.171%
25.416%

65.0
65.427
15.975
196.141
2.254%
27.669%

67.5
66.222
16.517
212.658
2.330%
29.999%

70.0
66.902
17.006
229.664
2.399%
32.398%

72.5
67.532
17.449
247.113
2.461%
34.860%

75.0
67.984
17.833
264.945
2.516%
37.375%

77.5
68.291
18.144
283.089
2.559%
39.935%

80.0
68.532
18.394
301.482
2.595%
42.530%

82.5
68.668
18.587
320.069
2.622%
45.152%

85.0
68.684
18.715
338.784
2.640%
47.792%

87.5
68.562
18.772
357.555
2.648%
50.440%

90.0
68.334
18.760
376.315
2.646%
53.086%

92.5
67.979
18.680
394.994
2.635%
55.721%

95.0
67.551
18.537
413.531
2.615%
58.336%

97.5
66.973
18.329
431.860
2.586%
60.922%

100.0
66.355
18.062
449.922
2.548%
63.470%

102.5
65.633
17.744
467.666
2.503%
65.973%

105.0
64.730
17.356
485.023
2.448%
68.421%

107.5
63.830
16.917
501.940
2.387%
70.808%

110.0
62.759
16.430
518.370
2.318%
73.126%

112.5
61.606
15.887
534.258
2.241%
75.367%

115.0
60.348
15.300
549.558
2.158%
77.525%

117.5
59.027
14.675
564.233
2.070%
79.595%

120.0
57.536
14.007
578.240
1.976%
81.571%

122.5
56.072
13.313
591.553
1.878%
83.449%

125.0
54.396
12.590
604.143
1.776%
85.225%

127.5
52.804
11.850
615.992
1.672%
86.897%

130.0
50.995
11.096
627.088
1.565%
88.462%

132.5
49.222
10.328
637.415
1.457%
89.919%

135.0
47.302
9.557
646.972
1.348%
91.267%

137.5
45.504
8.796
655.769
1.241%
92.508%

140.0
43.589
8.052
663.821
1.136%
93.644%

142.5
41.623
7.311
671.131
1.031%
94.675%

145.0
39.598
6.583
677.714
.929%
95.604%

147.5
37.599
5.879
683.593
.829%
96.433%

150.0
35.481
5.196
688.789
.733%
97.166%

152.5
33.246
4.531
693.320
.639%
97.806%

155.0
30.819
3.884
697.204
.548%
98.353%

157.5
28.064
3.251
700.455
.459%
98.812%

160.0
25.103
2.641
703.096
.373%
99.185%

162.5
22.112
2.080
705.176
.293%
99.478%

165.0
18.554
1.560
706.736
.220%
99.698%

167.5
14.215
1.068
707.803
.151%
99.849%

170.0
9.385
.631
708.434
.089%
99.938%

172.5
5.353
.307
708.742
.043%
99.981%

175.0
1.605
.104
708.846
.015%
99.996%

177.5
1.077
.024
708.870
.003%
99.999%

180.0
1.068
.006
708.876
.001%
100.000%

From the numeric values listed in the cumulative fields of the flux at each angular position with respect to the total flux as shown in Tables 3-1 to 3-5, we know that when the thickness ratio of the lamp shade 20 is 1:1, the flux of the polar coordinate positions from 135 degrees to 180 degrees is approximately equal to 6.431% of the total flux of the LED light sources 211; when the thickness ratio of the lamp shade 20 is 1.7:1, the flux of the polar coordinate positions from 135 degrees to 180 degrees is approximately equal to 7.372% of the total flux of the LED light sources 211; when the thickness ratio of the lamp shade 20 is 1.8:1, the flux of the polar coordinate positions from 135 degrees to 180 degrees is approximately equal to 7.699% of the total flux of the LED light sources 211; when the thickness ratio of the lamp shade 20 is 3:1, the flux of the polar coordinate positions from 135 degrees to 180 degrees is approximately equal to 8.379% of the total flux of the LED light sources 211; and when the thickness ratio of the lamp shade 20 is 3.1:1, the flux of the polar coordinate positions from 135 degrees to 180 degrees is approximately equal to 8.733% of the total flux of the LED light sources 211. Although the flux of the testing items can reach up to 5% of the total flux of the LED light source 21 at the polar coordinate position from 135 degrees to 180 degrees provided that the thickness ratio of the lamp shade 20 is 1:1, 1.7:1, 1.8:1, 3:1 or 3.1:1, yet the present invention is characterized in that the axially symmetric LED light bulb 2 not just achieves a brightness with a flux equal to 5% of the total flux of the LED light sources 211 at the polar coordinate position from 135 degrees to 180 degrees only, but also satisfy the relation (|I−Iavg|/Iavg)<25%, wherein, I is an intensity of light of at least 90% of a spatial position between the polar coordinate positions from 0 degree to 135 degrees, and Iavg is an average light intensity between the polar coordinate positions from 0 degree to 135 degrees. With reference to the aforementioned experiment results, the expected illumination effect of the present invention has not been achieved when the lamp shade 20 has a thickness ratio of 1:1, 1.7:1 or 3.1:1.

With reference to FIGS. 8-12 for different light polar radiation patterns drawn according to the experiment results respectively, these figures show the sectional light intensity distributions at the polar coordinate positions 0 degree and 180 degrees and the polar coordinate position 90 degrees and 270 degrees of the axially symmetric LED light bulb 2 respectively. In FIGS. 8-12, L_Arepresents the light curve formed on a plane composed of the polar coordinate positions 0 degree and 180 degrees, and L_Brepresents the light curve formed on a plane composed of the polar coordinate positions 90 degrees and 270 degrees. FIG. 8 shows a light polar radiation pattern of the lamp shade 20 with a thickness ratio of 1:1, FIG. 9 shows a light polar radiation pattern of the lamp shade 20 with a thickness ratio of 1.7:1, FIG. 10 shows a light polar radiation pattern of the lamp shade 20 with a thickness ratio of 1.8:1, FIG. 11 shows a light polar radiation pattern of the lamp shade 20 with a thickness ratio of 3:1, and FIG. 12 shows a light polar radiation pattern of the lamp shade 20 with a thickness ratio of 3.1:1. The se light polar radiation patterns show that both of the best light illumination range and uniformity will be achieved if the lamp shade 20 has the thickness ratios of 1.8:1 and 3:1, so that the LED light bulb with an LED light source can achieve an illumination effect similar to the full circumferential illumination effect. To achieve the expected full circumferential illumination effect, the present invention maintains a specific light emitting intensity and combines with the aforementioned experiment results to limit the thickness of the lamp shade 20 in a range of the polar coordinate +30 degrees to −30 degrees with respect to the polar coordinate +90 degrees to +30 degrees and −90 degrees to −30 degrees to a ratio of (1.8-3):1, so that the axially symmetric LED light bulb 2 satisfies the aforementioned flux and light emitting intensity conditions and achieves the best light emitting efficiency and uniformity.

Preferably, the edge of a sectional line on an inner side of the lamp shade 20 is an arc, or a curve having a plurality of turning points, wherein the curve is laterally symmetrical. In this preferred embodiment, the edge of the sectional line on the inner side of the lamp shade 20 is an arc. In addition, the distance L from the top of the inner side of the lamp shade 20 to the substrate 21 is 50 mm-60 mm, and the maximum width W of the external periphery of the lamp shade 20 is 58 mm-70 mm.

In summation of the description above, the present invention focuses at the LED light bulbs with a light emitting surface that faces upward, and makes use of the lamp shade 20 of unequal thickness to reduce the light intensity of the LED light sources 211 at specific angles to scatter the light to predetermined light output angle and achieve a uniform light emitting effect and a wide-angle illumination range, so as to overcome the drawbacks of the conventional LED light bulb including non-uniform light emission and too-concentrated light angle effectively.

Number	Name	Date	Kind
4988911	Miller	Jan 1991	A
20110080096	Dudik	Apr 2011	A1
20110080742	Allen	Apr 2011	A1
20140160762	Dudik	Jun 2014	A1

Axially symmetric LED light bulb

Information

Patent Number

Date Filed

Date Issued

Inventors

Original Assignees

Examiners

Agents

CPC

Field of Search

CPC

International Classifications

Term Extension

Abstract

Description

Claims

Priority Claims (1)

US Referenced Citations (4)

Related Publications (1)