# IR LED - Help me convert 'Maximum radiant power' to irradiance (Watts per meter squared)

I am not an electrical engineer or physicist. I am trying to understand if the light emitted by an LED poses an eye hazard.

A manufacturer has a device that has LEDs in it. They are infrared LEDs. They emit light at 950 nm and their 'maximum radiant power' is listed as 3000 mW/steradian. It is my understanding that W/steradian is called 'radiant intensity' by physicists.

To determine if the LED is a hazard, I need to calculate its irradiance, E, (Watts per meter squared). This is the equation I wish to use: E (W/m^2) = Sigma(from 770 nm to 3000 nm) E_lambda x delta_lambda. E_lambda is the spectral irradiance (W m^-2 nm^-1) and delta_lambda is source spectral bandwidth in nanometers (nm).

I cannot figure out how to use the given information (950 nm, 3 W/sr) to calculate the spectral irradiance or the source spectral bandwidth. Can someone help?

Thanks!

(Note added January 16, 2016) It took awhile but I think I found the datasheet for the LED. I know I wrote 3000 mW/sr in my original post, but when I spoke with the manufacturer I discovered that the LED in question is actually only 1000 mW/sr.

http://www.vishay.com/docs/81009/tsal6100.pdf

Thanks!

• the irradiance will depend on the distance away from the source. the area subtended by one steradian is equal to the squared distance from the source (see here ) – costrom Jan 4 '16 at 18:27
• "How do I convert from W/sr to W/m^2?" You can't unless you know more about the optical layout. And also the beam profile of the LED... (how many steradians does it emit into?) A link to the led would be nice. – George Herold Jan 4 '16 at 18:40
• @GeorgeHerold - I suspect beam profile is irrelevant, since the maximum radiant power is 3 W/steradian, which I would interpret as a peak value. At 1 meter the radiant power is 1 watt/$m^2$ peak. – WhatRoughBeast Jan 4 '16 at 22:35
• @WhatRoughBeast, If the led is emitting into 180 degrees (2*pi steradians) that will be a lot different than 15 degrees. There also could be a lens after the LED which could focus the light and give a much higher intensity. 3W/steradian sounds like a lot of power to me. And the IR nature of the light makes it more dangerous because the blink reflex of the eye will not be activated. – George Herold Jan 5 '16 at 14:58
• @GeorgeHerold - It's only a lot of power if the LED is a wide-beam device, but the OP does not state that. It only specifies peak power. Assuming a pupil diameter of 8 mm and a LED/eye distance of 1 meter, intercepted power is about 150 microwatts, which should not be a problem. – WhatRoughBeast Jan 5 '16 at 16:47

If you can provide a link to the data sheet, that would be a very good thing. In its absence, you can try interpreting "maximum" as "peak". Since a steradian produces 1 square meter area at 1 meter, a "maximum radiant power" of 3 W/sr should produce a peak of 3 watts/ $m^2$ at 1 meter, 1.5 watts/ $m^2$ at 2 meters, etc.