gpmatthews wrote:Simple explanations of complex phenomena are rarely comprehensive!
Now
there is a pithy quote if I've ever heard one.
This issue of
"Is it diffraction or is it spatial filtering?" has been bouncing around in my head since you guys raised the question.
It got so bad that I finally went back to the basic math & physics and programmed up some simulations from first principles. When I say "basic" and "first principles", I mean really low level stuff -- brute force solution of the wave equation using purely local calculations on a fine grid. No formal analysis, nothing Fourier, not even any phase and amplitude calculations -- nothing but grid cells and finite approximations to 2nd derivatives -- subtract, multiply, add.
Then I looked at the simulation results and asked, "How would I describe what I see here?"
The results provided an interesting perspective on terminology.
When I started with plane or spherical waves and allowed them to propagate freely, they just marched right across the simulation grid. I looked at them and said to myself "Light travels in straight lines."
But it doesn't, really. That's just my human interpretation of the solution of the wave equation.
When I imposed an obstacle, I observed that waves appeared even in areas "behind" the obstacle, in what would be "shadow" areas when I
imagined that light travels in straight lines. I looked at those waves and said to myself, "Oh, this is diffraction -- the light is bending or spreading behind the obstacle."
Again, this is just my human interpretation.
When I ran plane waves through an aperture, I observed interference patterns, and I said to myself "Oh, this is diffraction too -- it looks just like the pictures in
Wikipedia."
Then I tried converging spherical waves, corresponding to a point source imaged through a perfect lens. (That's "perfect" as in no aberrations. I don't want to get into the other kind of "perfect" that has to do with negative refraction.)
When I ran those converging waves through an aperture, I observed interference patterns and noted that there was no sharp focal point. Instead, in what should have been the focal plane, I observed a fuzzy concentration of waves.
When I made the aperture smaller, I observed that the interference patterns got more obvious, and in the focal plane, the fuzzy concentration spread out farther. But still, I'm looking down on the whole simulation and the interference pattern is blatantly obvious. "Diffraction", I said. "Diffraction, diffraction, diffraction!"
Then I went one more step. (This one was a thought experiment because actually coding it up and getting it to run would have taken way too long.) Instead of a point source imaged through a perfect lens, I imagined an array of point sources, each having a different intensity so as to construct a patterned "subject". And I further imagined that rather than looking down on the whole simulation, I could only see the pattern of energy projected on the focal plane.
You know what happened? That pattern in the focal plane looked remarkably like what I'd get if I took the sharp pattern of the original subject, and just ran a blurring filter over it.
Suddenly my brain wanted to switch gears and think in terms of spatial filtering.
I think what's determining my favorite model is complexity of the pattern being imaged. If the pattern is simple -- a point source or a plane wave -- then I find it feasible to think about the waves directly. When the pattern gets complex the waves become too messy to deal with, but the spatial filtering model works fine.
So is the observed blurring "because of diffraction" or "because of spatial filtering"???
To play devil's advocate, I don't think it's either one.
I think the observed blurring is just because that's what light does, and you can choose to call it "diffraction" or "spatial filtering" as you prefer. If you do the mathematics carefully enough, you get the same result from either standpoint.
Graham Stabler wrote:To put it another way, if you put a coat on you get warmer but you would not say the cause of the temerature increase was heat you would say it was insulation.
That sounds reasonable at first read.
But on the other hand, suppose you swathe yourself in layers of really good insulation, and end up dying because your body temperature gets too high.
In that case, I'll wager the medical examiner's certificate will list the cause of death as "overheating", not "overinsulating".
By analogy, the images must get fuzzy because of too much diffraction, not too much filtering.
Ah, language -- you gotta love it!
--Rik
Edit: fix spelling error.