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Calculation Methods of Luminous Intensity Distributions from Ray Files by using Different Solid Angles

Markus Katona, Ingo Rotscholl, Klaus Trampert, Cornelius Neumann

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

2

Motivation

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

Luminous Intensity DistributionRay file

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

3

Motivation

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

Far field:

Luminous Intensity Distribution

Near field:

Luminance

http://www.ilumetrix.de/de/photometrie

𝐼 𝜑, 𝜗𝐿 𝑥, 𝑦, 𝑧, 𝜑, 𝜗

𝐼/𝐼𝑚𝑎𝑥

𝜗 [°]𝜑 = 𝑐𝑜𝑛𝑠𝑡.

𝜗

𝜑

𝐿 =d2Φ

cos 𝜀′ d𝐴 ∙ dΩ𝐼 =

dΦ

dΩ

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

4

LID calculation of near field data

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

𝜗[°]

𝐿 =d2Φ

cos 𝜀′ d𝐴 ∙ dΩ𝐼 =

dΦ

dΩ

𝐼 𝜑, 𝜗𝐿 𝑥, 𝑦, 𝑧, 𝜑, 𝜗

ϑ

φdA

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

5

LID calculation of near field data

Influence parameters:

Number of rays 𝑀 (stochastic uncertainty)

Shape of the solid angle

Resolution/size of the solid angle

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

𝜗[°]

𝐿 =d2Φ

cos 𝜀′ d𝐴 ∙ dΩ𝐼 =

dΦ

dΩ

𝐼 𝜑, 𝜗𝐿 𝑥, 𝑦, 𝑧, 𝜑, 𝜗

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

6

Cartesian polar coordinates Canonical solid angle Triangulated solid angle

Angle constant Solid angle constant

Cartesian polar coordinates Canonical solid angle Triangulated solid angle

Angle constant

• Resolution (𝑑𝜑, 𝑑𝜗)

• Standard

• dΩ ≠ const

Cartesian polar coordinates Canonical solid angle Triangulated solid angle

Angle constant Solid angle constant

• Resolution (𝑑𝜑, 𝑑𝜗)

• Standard

• dΩ ≠ const

• Number of solid

angles 𝑁

• Almost dΩ = const

Cartesian polar coordinates Canonical solid angle Triangulated solid angle

Angle constant Solid angle constant

• Resolution (𝑑𝜑, 𝑑𝜗)

• Standard

• dΩ ≠ const

• Number of solid

angles 𝑁

• Almost dΩ = const

• Opening angle ω

• Perfect shape

• dΩ = const

• Overlapping/incom-

plete space cover

x

y

zϑ

Cartesian polar coordinates Canonical solid angle Triangulated solid angle

Angle constant Solid angle constant

• Resolution (𝑑𝜑, 𝑑𝜗)

• Standard

• dΩ ≠ const

• Number of solid

angles 𝑁

• Almost dΩ = const

• Opening angle ω

• Perfect shape

• dΩ = const

• Overlapping/incom-

plete space cover

• Number of solid

angles 𝑁

• Dynamic solid angle

LID calculation of near field data

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

Different types of solid angles

𝜔

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

7

Calculation results

Point light source, 𝑀 ≈ 25 million, 𝑁 ≈ 1000

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

x

y

zϑ

Deviation𝐼𝑛𝑢𝑚𝐼𝑎𝑛𝑎 = 𝐼0 cos 𝜗 𝜖 =𝐼𝑎𝑛𝑎 − 𝐼𝑛𝑢𝑚

𝐼𝑎𝑛𝑎

Τ𝐼 𝐼𝑚𝑎𝑥 Τ𝐼 𝐼𝑚𝑎𝑥 𝜖 [%]

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

8

Calculation results

Point light source, 𝑀 ≈ 25 million

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

Τ𝐼 𝐼𝑚𝑎𝑥 𝜖 [%] Τ𝐼 𝐼𝑚𝑎𝑥 𝜖 [%]

𝐼∕𝐼_𝑚𝑎𝑥 𝜖 [%] Τ𝐼 𝐼𝑚𝑎𝑥 𝜖 [%]

x

y

zϑ

𝑁:𝜑 × 𝜗

2=30 × 60

2= 900 𝑁 = 1000

𝑁 = 943𝑁: 𝜔 = 6.36°

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

9

Calculation results

Real lambertian light source, 𝑀 ≈ 25 million

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

𝐼 [𝑐𝑑]

𝐼[𝑐𝑑]

𝜗[°]0°

𝑁𝑎:𝜑 × 𝜗

2=65 × 60

2= 1950

𝑁𝑏 = 2000

𝑁𝑐: 𝜔 = 4.55°

𝑁𝑑 = 2058

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

10

Calculation results

Real narrow beam flash light, 𝑀 ≈ 25 million

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

𝐼[𝑐𝑑]

𝐼[𝑐𝑑]

𝜗[°]

𝑁𝑎:𝜑 × 𝜗

2=50 × 720

2= 18000

𝑁𝑏 = 200 000

𝑁𝑐: 𝜔 = 0.455°

𝑁𝑑 = 2668

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

11

Comparison

a b c D

Calculation speed + + - o

Uniform solid angle size - + + o

Dynamic solid angle disposition o o o +

Unique space cover + + - +

Pseudo-LID calculation + + + -

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

12

Conclusion

LID calculation possible with all types of solid angle

Every solid angle types has their own advantages and limitations

Fastest very unshaped

Fast & good solid angle shape bad for narrow beam LID

Perfect solid angle shape slow & space cover

Dynamic no Pseudo-LID calculation

Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

Light Technology Institute (LTI), Department of

Electrical Engineering and Information Technology

13 Markus Katona - Calculation Methods of Luminous Intensity Distributions from Ray

Files by using Different Solid Angles

27.09.2017

Thank you for your

attention