### Application Bulletin 222.pub

```Converting Radiant
Intensity in Units of
mW/cm2 to mW/sr.
Application Bulletin 222
Radiant intensity is commonly measured in units of
power per steradian and power per area. The SI
standard is power per steradian. Optek’s standard is
power per area. Many customers will design their
application around power per steradian so there is a
need for a conversion between both standards.
To derive the conversion, an understanding of solid
angles and how it relates to the SI intensity measurement needs to be presented. Imagine the LED and a
detector placed in front of it with circular aperture.
Place an imaginary sphere around the LED with the
radius defined by the distance from the LED to the
detector aperture. Place a cone in the sphere and
locate it with respect to the LED and the detector aperture. The portion of the sphere bounded by the
aperture is a spherical zone. Refer to the exploded
view of the measurement diagram below.
of a sphere is calculated by the following formula.
AS = 4
R2
A sphere contains 4 steradians. This is analogous
to a circle containing 2 radians. The solid angle is
calculated by multiplying 4 by the ratio of the zone’s
area to the sphere’s area.
With this information, the conversion of mW/cm2 to
mW/sr can be derived .
R = ¥d2+(D/2)2
(D=Diameter of aperture)
Test Distance (d)
LED Position
Detector Aperture
Zone Height (h)
The area of the sphere (AS) is
AS = 4
R2
The area of the zone (AZ) is
Spherical Zone
AZ = 2
The cone represents the measurement solid angle
( ). The SI unit for solid angles is the steradian (sr).
A steradian is defined as the solid angle for which the
spherical area bounded by the solid angle is equal to
the square of the sphere’s radius. The surface area
Optek Technology, Inc.
Carrollton, Texas 75006
Rh
(h = R-d)
The area of the detector (AD) is
(972) 323-2200
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May 2003
Issue 1.0
www.optekinc.com
Application Bulletin 222
The solid angle of the cone (w) is calculated by the following:
=
4
AZ
4
=
AS
(2
4
R h)
R2
=
2
h
R
Optek measures the radiant intensity of the OP265
and OP266 with a 2.06 mm apertured detector
placed 14.99 mm away from the LED. The apertured
area of the detector is 3.333 mm2 or .03333 cm2.
The distance from the LED to the detector’s aperture
edge is 15.025 mm. The height of the zone is .035
mm. The solid angle formed by the LED and detector is calculated below.
The conversion of mW/cm2 to mW/sr is derived below.
Ee, sr
Units mW/sr)
=
=
Ee, sr
Ee, sr
Power
=
=
=
2
(.035)
15.025
=
.015 sr
Units(mW/cm2)
For this measurement set up, the conversion is 2.255
(mW/sr)/(mW/cm2).
Many customers will measure the intensity using different aperture sizes and test distances. Because
the detector will capture only a portion of the nonuniform image projected from the LED, the power
measured will not be proportional to the aperture
size. This will cause the intensity measurement to
vary. Therefore it is very important to consider the
measurement setup when comparing intensities.
May 2003
Issue 1.0
Optek Technology, Inc.
Carrollton, Texas 75006
(972) 323-2200
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www.optekinc.com
Application Bulletin 222
Conversion Table for Optek LEDs.
Test Distance
Aperture Diameter
Solid Angle
Conversion Factor
cm
cm
sr
Cm2/sr
OP123
1.270
0.079
0.003
1.614
OP124
1.270
0.079
0.003
1.614
OP140
1.660
0.457
0.059
2.795
OP145
1.660
0.457
0.059
2.795
OP165
1.499
0.206
0.015
2.255
OP166
1.499
0.206
0.015
2.255
OP168
1.016
0.206
0.032
1.040
OP169
1.660
0.457
0.059
2.795
OP223
1.270
0.079
0.003
1.614
OP224
1.270
0.079
0.003
1.614
OP231
3.630
0.635
0.024
13.252
OP232
3.630
0.635
0.024
13.252
OP233
3.630
0.635
0.024
13.252
OP231W
1.184
0.635
0.214
1.477
OP232W
1.184
0.635
0.214
1.477
OP233W
1.184
0.635
0.214
1.477
OP240
1.660
0.457
0.059
2.795
OP245
1.660
0.457
0.059
2.795
OP265
1.499
0.206
0.015
2.255
OP266
1.499
0.206
0.015
2.255
OP268
1.016
0.206
0.032
1.040
OP269
1.660
0.457
0.059
2.795
OP290
1.270
0.635
0.188
1.688
OP291
1.270
0.635
0.188
1.688
OP292
1.270
0.635
0.188
1.688
OP293
1.070
0.635
0.260
1.220
OP298
1.070
0.635
0.260
1.220
OP294
1.270
0.635
0.188
1.688
OP299
1.270
0.635
0.188
1.688
OP295
3.630
0.635
0.024
13.252
OP296
3.630
0.635
0.024
13.252
OP297
3.630
0.635
0.024
13.252
Product
May 2003
Issue 1.0
Optek Technology, Inc.
Carrollton, Texas 75006
(972) 323-2200
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```