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Now everything was fine up til the point where he said:

"Now, if we want to know the total field at point Z, then we need to add together every point in the aperture. That is, we need to integrate across the aperture to get the field at point Z. To get this, we'll have to know a little more physics. Specifically, the fields from a point source can be modeled as:"

As I understand it, he is treating every point on the aperture as a point source, I do not understand why this is so.

(Btw, does anyone like the username, couldn't do spherical cow so had to think of something else physicists always use to simplify problems)