Fraunhofer diffraction integra theorem

[pop_ianosd]

Homework Statement

This is not an actual problem, it is a general matter about the equation that describes the Fraunhofer diffraction;
So, for a given aperture(A), which is evenly illuminated from the left(let's say), the Electric Field complex amplitude at a point P(on the right-the screen) can be computed by the formula:

E$_{P}$ = K$\int$$_{A}$e$^{ikr}$dA,
where r is the distance from the surface element dA to the point P.

My questions concerns the fact that I have seen this integral being applied (in a physics book) to non-point surface elements dA, but to line surface elements(dA = Ldy).
The problem I see about this is that one cannot define a distance r between a point and a line-surface element.
The exact case was at calculating the diffraction pattern given by a rectangular (Width>>Height) aperture, and later for a circular aperture.
How is this possible?

Homework Equations

The Attempt at a Solution

 

[jbsteele]

I think we can consider the line surface element as a collection of point surface elements, each one with its own corresponding distance. The integral is then applied to the sum of all the point surface elements, which results in some way in the same integral being applied to the line-surface element. This means that the integral should not be applied directly to the line surface element, but rather it should be applied to the sum of all the point surface elements that are part of it.