excitation upon emission from 2 LEDs

I came across a problem:

I have 2 LEDs with different emission spectra (blue and green). I have 1 molecule with a known excitation spectrum (channelrhodopsin2 protein). I turn on 1 LED at a time.

I want to approximately estimate the ratio of the (level of excitation generated upon green over blue emission) in the full spectrum.

I initially thought it was the dot-product between the emission and excitation functions. But my colleague told me that I have to add the lambda and he offered equation 3 from this website

:

$$J = \int_o^{\infty} F_D(\lambda)\epsilon_A(\lambda) \lambda^4 d\lambda$$

• FD(λ) is the normalized emission spectrum of the donor
• $\epsilon_{A}$ standards for the molar absorption coefficient of the acceptor
• λ is the wavelength.

I'm not sure how this equation applies to the problem at hand, in special I don't know what should the exponent from lambda be.

I have measured the power of both LEDs, and I don't care about the real level of excitation, just the ratio between the excitation generated from the 2 LEDs.

• re: "I don't care about the real level of excitation, just the ratio...". You can't get the ratio without assuming something about the power. Is the peak intensity of green and blue LEDs assumed to be the same, or is the area under the peak assumed to be the same, or is the electrical power assumed to be the same?!? After that decision it is just a matter of doing the integral. – MaxW Mar 2 '16 at 4:22
• We measured the power at the peak intensities for both LEDs. We assume the peak is the same, not the integral. – fritz_da_silva Mar 2 '16 at 10:50
• We measured the power at the wavelength of peak intensity for both LEDs. We assume the peak intensity is the same, not the integral. During the experiment, we applied the same power (at the peak intensity) on the blue and on the green LEDs. – fritz_da_silva Mar 2 '16 at 11:06
• @MaxW, what integral are you talking about? does it involve multiplying $\lambda$ or not? – fritz_da_silva Mar 3 '16 at 10:15