I would suggest that optical power is not equal to electrical power, it more like the electrical power into the device generates both light and heat where the ratio of light to heat is the efficiency of the device. So the optical power is the electrical power times the efficiency. I'm not sure how you are measuring photon density, but it usually is greatly influenced by the lenses in the setup.
Assuming the responsivity is just the efficiency of the detector, as long as you can measure the input and the output of the detector it shouldn't matter what is held constant. Measuring the input optical power is tough as it involves figuring out how much optical energy is reaching all parts of the surface of the detector and none of the sources emits a uniformly distributed light pattern. The efficiency may also depend on the flux level.
Thank you . Just a follow up question
Most LEDs come with brightness measured in millicandela. I learned to convert MCD into watts by first converting MCD into lumens and then into watts. For this, luminosity function was used which has various values between 0 and 1 . Now, if i have a UV LED for which the luminosity function value is zero, how can one convert MCD into watts ?
Also, in the literature, usually authors mention watts/cm^2 of a LED given the luminous intensity/m^2 data. Any idea how to get luminous intensity/m^2 value?
UV emitters are easy since they are usually specified in mW / steradian. Converting steradians to square meters is pretty straightforward - just multiply the steradians by the square of the distance.
MCD is a unit that only applies to visible light since it includes responsivity of the human eye. UV and IR light would all be 0 MCD regardless of power.