I have a problem similar to reflection of multiple thin films. I have light coming in from medium 1 and I want to find the total reflected intensity after being reflected inside 2 layers. However, I want to account for the fact that the surface area of medium 4 is smaller than the light's spot size and so some of the light is lost.
I already derived the total reflection for the regular 2 layer case: (I am assuming a zero incident angle) $$R =\left| r + \frac{tt'r_{34}e^{i\delta}}{1-r'r_{34}e^{i\delta}} \right|^2 $$ $r$ is the total reflected electric field amplitude from the first layer only, $t$ total transmitted amplitude through the first layer( $r'$ and $t'$ are in the opposite direction), $r_{34}$ is the reflection Fresnel coefficient for the n3-n4 boundary and $\delta$ the phase corresponding to the n3 layer.
Now I want to take into account that not all of the light transmitted through the first layer hits the last boundary. I thought about just multiplying the second term in my expression by some factor, say 0.5, which would make the transmitted amplitude smaller. However, since this will effectively multiply the complex electric field amplitude I am not sure if that make sense.