Re: ATM Airy disk frustrations

[Donald Taylor <dtaylor@unlinfo.unl.edu>]

Reading what Dwight has said about diffraction and Airy discs, I would like
to offer the following comment for what it is worth.

In regard to diffraction it sounds like there is too much emphasis on the
effects of edges. If you look at the text book presentation of Huyghens
principle applied to wave fronts you see that every point in the wave front
acts as a point source for a new spherical wave and that it is the combined
results of all of those point sources adding up that creates the next
wavefront surface.   That being the case it is not just the effect of the
point sources along the edges that creates the diffraction effects.  It is
all of those missing point sources outside of the aperture as well as those
missing because of obstructions that causes the diffraction effects. At
least thats how I understand it. If it were only the point sources along the
edge then it shouldn't matter for example how wide the obstruction of a
secondary vane was only how long or what shape it has, but instead it is all
of those point sources blocked by the width of the vanes as well that
affects the diffraction pattern.

 When one calulates diffraction effects mathematically you integrate the
amplitudes contributed by the point sources taking into account the phase.
The result is affected by what is missing from the area integrated as well
as what is in the area.  The edges are just the boundaries of the areas
integrated. Hope that isn't sounding too technical and that it is
illuminating and not confusing or worse yet wrong.
                         Don Taylor

lifedata@voy.net wrote:
> 
> I started reading.  "Airy disk" didn't appear immediately, but it
> said Airy described "defraction disk."
> 
> OK, diffraction disk.

Hi Jim
 At I understand it, when treating light as a wave,
every edge that the light must go past creates
point sources. In the case of a telescope like
a refractor, the outer edge of the telescope
produces this ring of light that broadcast radially
from each spot along the outer edge. Now, let us
look what happens when we focus the light down to
a spot. We have the light that came straight in
from the star and the slightly off angle fan of light
from the entire outer ring of the telescope.
At the center of the Airy disk, the angle is so
small that the light adds constructively. As
one moves to the side of center, the angle of the
light diffracted from the ring ( but focused to
a spot ) now is out of phase with the straight
light from the star. As one goes farther out, we
get the alternating light and dark rings.
 Now we get to the size of the disk. If we made
an imaginary lens that had infinitely adjustable
focal length we would find that at vary short focal
lengths ( close to wave lengths of light ) the disk
would be quite small with a lot of rings. As the focal
length extended to more macro sizes that we are used
to, most of these rings have spread into a wide faint
area that we don't see them. Because the center angles
are now changing quite slowly as we go farther out,
the disk and first ring seem to be mostly stationary.
The length difference between the straight light
and the hypotenuse diffracted light keeps the distance
to the canceled light ring relatively constant.
( This was what I didn't think about when we had a
discussion on placing mask in front of the mirror. )
So, the Airy disk, is an artifact of the aperture of
the telescope. The amount of energy in the disk and
in the rings can be effected by adding more edges,
such as secondary mirrors and supports. The angle of
the diffracted light and the straight light is what
creates the slight, 1/2 wave difference in travel
to the focus, causing the first dark ring. This of
course defines the Airy disk size.
 I hope I'm not to far off, maybe others can correct or
enhance what I've said.
Dwight

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