# How to calculate the total power of a LED using solid angle?

I have a LED with the max power of 130mW/sr and an opening angle of +-10° (so approx. around 20°). I conducted an experiment using this LED, the LED shines light to an un-doped silicon semiconductor from a distance of 2.5cm.

I have a setup where there are 3 identical LEDs with enough space between them so there is minimal overlap. The silicon bar is around 2cm x 1cm.

I want to calculate how much mW/cm2 intensity is shined onto my silicon bar?

(I already calculated the solid angle : Ω = 0.1sr)

Link to the datasheet of the used LED : https://www.vishay.com/ir-emitting-diodes/list/product-81009/

• Pls. show links to both datasheets. path loss is d² but might not be uniform over half power angles or centred. Use a good light sensor or PD with 0.5 mA/mW Commented May 11, 2022 at 16:00
• How much light is lost using that geometry? Commented May 11, 2022 at 16:19
• You can measure it, if you know the specs for mA/mW or estimate using 0.5 with reverse bias measuring current to ground. Otherwise use raytrace software. Commented May 11, 2022 at 18:24
• @TonyStewartEE75 atm I can't physically measure it, an estimated calculation by hand would work in this case. Commented May 11, 2022 at 18:32
• It's not possible to compute without a lot of work and more specs on tolerances. Let's say you get 50% of the emitted nominal power. What is the purpose? to get max distance? or max power or the knee of the sensitivity curve of both. Commented May 11, 2022 at 19:32

Vishay has published how to measure light density and intensity at a conical distance in a document from the datasheet page you posted. "General Information Measurement Techniques"

## Other info

Beamwidth Standard

• IR LEDs are always specified in half-angle from peak-centre (due to reflector centre error in the early days)

• Visible LEDs are in full angle for any colour and angle.

• Sharp Japan was the chief developer of IR 5mm LEDs and PD's and that business was sold to Vishay.

Silicon detectors are wide-viewing angles and follow Lambertian Cosine response much like PV power arrays.

• Vishay/Sharp Si Photo Diodes (PD) 5mm types are very accurate cheap sensors with consistent 5 mA/mW. More expensive detectors may be slightly higher. Yours might be less.

To convert the optical power to electrical power you need to match the impedance due to the Maximum Power Transfer (MPT) Theorem. This can be easily measured as Zmpt=Voc/Isc for open-circuit Voltage over Short Circuit current. In both of these states, the power is 0 but the ratio happens at the MPT operating point. This is critical to understand in any solar power design. The Vmpt is about 82% of Voc and then drops slowly with solar power to ~ 70%Voc for low power.

The LED should not exceed suggested values in the datasheet for DC and pulse-operation otherwise self-heating can degrade the results. You can run yours in series with a good active current limiter circuit and then controlled without worries. This can be done using an LM317 and a single resistor with a low-side switch.