How to calculate mode overlap with I(x,y) rather than E(x,y)

[Fixar Frazze]

Hi

I have a waveguide that is rectangular and multimode that I but-couple to a standard telecom SMF28 fiber. I have imaged the output of the waveguide and the fiber with a 25X microscope objective onto the chip of an IR-camera. Usually the mode overlap is calculated by cross-correlation of the electric field (E(x,y)). Like

$$\eta=\frac{(\int E_1*conj(E_2))^2}{\int |E_1]^2*\int |E_2]^2}$$

Now however I only have access to the intensity distribution I(x,y).

What do you think, can I justs take the square root of the intensity and perform the calculation and pretend the imaginary part is equal to zero?

 

[soarce]

Maybe you can use the spatial symmetry of the modes after mapping the measured intensity to some known mode (e.g. http://en.wikipedia.org/wiki/Transverse_mode)