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) Sphere Radius (R) Test Distance (d) LED Position Detector Aperture Aperture Radius (r) 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 AD = r 2 (972) 323-2200 [email protected] 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 = = = Ee, area AD 2 (.035) 15.025 = .015 sr Units(mW/cm2) Ee, area AD Ee, area AD 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 [email protected] 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 [email protected] www.optekinc.com