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

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1. Feb 23, 2015

### 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

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