# Procedure to express radiantion intensity of a LED in watts/cm^2 , given luminous intensity or total radiant power [closed]

I am calculating Responsivity of a PN junction photodiode by irradiating radiation from LED sources. For this purpose, I have two LEDs, one UV and another green LED. Note that LEDs are placed close to the target.

UV LED: Manufacturer has given total radiant power to be 20 mW. Given that LED is placed close to the target, how can I calculate radiant intensity? should I just divide by the total area of the target since all radiation from UV LED is reaching the target (given that LED is placed close to the target)?

Green LED: Luminous intensity is given in mcd (as"x" mcd). I have converted mcd into lumens then finally to watts as follows:

Firstly, I find total solid angle using the expression: Ω (solid angle)= 2(pi)(1-cos(θ)). here, θ is half the apex angle of the light cone. Apex angle is also equal to viewing angle of the LED mentioned in the datasheet.

Now, Lumens = Ω*(x) mcd. After this, I use the luminosity efficiency function to convert lumens into watts.

Now, given that I have placed the LED near the target, how to find the radiant intensity in watts/cm^2 ? Should I just divide the power by area of the target? Or, should I divide the power of the LED by the area of the circle projected onto the target by the light cone?

• I'm confused. What exactly is the situation. Show a crafted diagram of your optical arrangement. This should include the emitter and details about it and the receiving photodiode and details about it, as well. In addition, a crafted diagram showing the optical arrangement would be necessary.
– jonk
May 29, 2022 at 7:42
• "For Green LED, luminous intensity is given (in mcd)" - by itself this data is useless, because the candela is weighted to the response of the human eye. Does the LED datasheet include spectral response? May 29, 2022 at 8:14

It sounds like you're trying to use the LEDs as a reference to calibrate or characterise your system. This may work but it will be imprecise: the LEDs are probably not that precisely specified in the first place, and you will be making multiple approximations in your conversion from mcd to W/cm2. Treat any results you get from this with a healthy dose of suspicion.

For the green LED:

• start with the luminous intensity in candela = lumen per steradian.

• use the LED spectrum and luminous efficiency function to convert lumens to watts. For a green LED, because the LED spectrum is well aligned with the luminous efficiency function, you may be able to take a shortcut and assume 683 lm/W. For other colours this shortcut would not work.

• you now have the radiant intensity in Watt per steradian. Now bring in the distance between the LED and the target, compute the area covered by 1 steradian at that distance, and you have the irradiance in W/cm2.

Note that this is only valid for a small area in the center of the beam, because the illumination pattern of a LED is typically not uniform. So don't put the LED too close to the target.

For the UV led:

• find in the datasheet the graph that shows the radiation pattern of the LED optics. This will give you a relative radiant intensity at different angles.
• compute the apparent angular size of the target as seen from the LED
• compute what percentage of the total radiant power falls within that angle. You could estimate this by comparing angles if the radiation pattern is very flat with a sharp fall-off. Otherwise you may have to tabulate the data from the graph and integrate to find the area under the curve.
• divide by the area of the circle that corresponds to that angle at the distance of the target to get W/cm2.
• Thank you, just a follow up clarification. can i convert mcd into lumens by making use of " Ω(solid angle) = 2(pi)(1-cos(θ) ) where θ is the apex angle of the light cone a.k.a half the viewing angle ? Then, after converting lumens to watts, i divide by the area of the circle projected on the target by the light cone ? Note that the target is large enough to accommodate the circle. May 29, 2022 at 14:36

Divide the Watts by the area to be illuminated.

Area is length multiplied by breadth. measured in centimetres will give you cm^2.

So if you have a lamp with an output of 1000W and an area of 100cm^2, the W/cm^2 will be:

1000/100 = 10 W/cm^2


However, that may be an average as the light output will not likely be evenly spread.