5/21/2018 1224787085p23 Radiance to Irradiance Conversion

1/9

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

2/9

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

3/9

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

4/9

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

5/9

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

6/9

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

7/9

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

8/9

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

9/9

Radiance to Irradiance Conversion

9 Optronic Laboratories

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