1. The problem statement, all variables and given/known data

I’m learning light interference and confused by the concepts. Like the figure I attached below, while computing the "interference" of the intersection point on the CCD, I used to do this ($E$ represents the electric field):

$E_{CCD}=E_1 \cdot e^{i (\omega t + \frac{2 \pi}{\lambda} l)} + E_2 \cdot e^{i (\omega t + \frac{2 \pi}{\lambda} (l+d \cdot sin \alpha))}$

I know this is wrong because electric field is directional and I should decompose it so that only components in the same direction add up — yet I’m not sure how to do it. Does a CCD detector respect the direction of fields?

2. Relevant equations
Described above.

3. The attempt at a solution
Described above.

Attached Images