bhobba said:
When a "photon" gets to a material, it is absorbed... phonon...may create a new photon
Ah, but look at the bigger picture, Bill. That description covers only a single photon passing through a transparent material of undefined shape. But I'm talking about the
pattern of photons processed by a
telescope.
Let me explain where the Fourier transform comes into it:
Here's a very simple telescope, with one lens. Real telescopes have more lenses and mirrors, but they're essentially doing the same thing.
Incoming photons are focussed by the lens (on the left) to an image sensor (on the right).
The coloured lines represent the paths of individual photons.
All of the photons from a source are near parallel, so e.g. the photon paths "a1" and "a2" are from a "red source".
The telescope focusses light such that we get distinct images of the "red source" and "green source" on the image plane.
Notice that
all of the photons collected from a source, from the whole surface of the lens, are brought to a
single point.
Now: how is that a
Fourier transform?
The incoming photons can be described as a function of
position and
momentum.
Photons from different sources have different momentum vectors. But they may have the same
position - for example, a2 and b2 pass through the same point on the lens.
At the image plane, the
momentum of the photons has been transformed into
position (light from different sources goes to different points)
The
position has been transformed into
momentum (light from different parts of the lens arrives at different angles).
I'm sure you will recognise that's the essence of what a Fourier transform does!
The field of Fourier Optics, where we manipulate light using concepts from Communications Theory, is a fascinating one. There's an introduction here;
https://en.wikipedia.org/wiki/Fourier_optics
And that's what I referred to earlier.
Finally; my example telescope is handling an ensemble of photons, a "pattern" as I called it, but we're talking about quantum events here. What will happen with a single isolated photon?
To answer that, I call upon a wonderful property of photons. They don't affect each other.
The behaviour of a huge ensemble of photons arriving together, is the same as if they arrive one by one and we slowly accumulate the image. Every description of the Young's experiment will remind you of that.
And it's important to understand why that is; it's because the Wave Function of the single photon behaves as an ensemble of photons would. The Wave Function impacts the whole of the lens, it gets focussed as I described, and it defines the single photon's probability distribution to match exactly the image that a large ensemble of photons would form.
Has anybody any questions?
David
