Post on 12-Oct-2015
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
1 Optronic Laboratories
Radiance to Irradiance Conversion
Training Level: Intermediate
Dr. Richard Young
Optronic Laboratories, Inc.
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
2 Optronic Laboratories
Geometry
Source Detector
Let us start off with a source of radiance, e.g. a
sphere source, and a detector
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
3 Optronic Laboratories
Geometry
Source Detector
Each point on the detector is illuminated by
light within the solid angle (cone) to the source
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
4 Optronic Laboratories
Geometry
Source Detector
A large distance between source and detector
is required for even illumination.
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
5 Optronic Laboratories
Geometry
Source Detector
The solid angle is calculated byA/d when
d>>A
Area=
A
Distance = d
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
6 Optronic Laboratories
Geometry
Error in A/d for Calculation of steradians
0.001%
0.01%
0.1%
1.0%
10.0%
100.0%
1000.0%
10000.0%
0 5 10 15 20 25 30 35 40 45 50
Distance to 1 cm aperture [cm]
RelativeErrorinsteradian
value[%]
Although it is a simple
formula, it works well atd>10 x source diameter
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
7 Optronic Laboratories
Geometry
Source Detector
If the source is uniform, then the light in the
solid angle to the source
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
8 Optronic Laboratories
Geometry
Source Detector
is equal to the light in the same solid angle
from the source.
5/21/2018 1224787085p23 Radiance to Irradiance Conversion
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Radiance to Irradiance Conversion
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Geometry
Source Detector
Irradiance from Radiance: E = L * A/d
Radiance from Irradiance: L = E * d/A
L [W/(cm sr)] E [W/(cm)]x sr