I'm trying to figure out the missing step here, in a problem about X-ray crystallography. I am referring to the attached image:
In the image, A= electron density, Z= distance traveled, λ= X-ray wavelength, p = electron position. It shows two electrons hit by an X-ray, and then excited in all directions. In this case, only one of those directions, S', is considered. rj= pj - p1.
Working off the basics of the image, suppose now there are n electrons, e1,…,en at positions, p1,…,pn. And the X-ray scattering from ej is:
Xj=Aj∗exp(2πi * pj* S/λ)
I have understood that equation, but I do not understand how to use that to derive that the total scattering from all n electrons is:
X=F∗exp(2πi * p1 * S/λ) , where F=∑1<=j<=n Aj∗exp∗(2πi * rj * S/λ)