From: MitchAlsup{at}aol.com
To: KSidor{at}drc.com, atm{at}shore.net
Reply-To: MitchAlsup{at}aol.com



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In a message dated 1/13/2003 1:36:01 PM Central Standard Time, KSidor{at}drc.com writes:


> This does not imply that a 6" telescope can "resolve"
(as one would
> classically use the word) 0.05 arcseconds but it does imply that one could
> detect the prescence of a dark feature that small against a brighter
> background although its "gray" width would be quite subtle. 
I would guess
> that Martian "canals" would fall into this category.
>
> Before I created my model of an "extended" object 5 arcseconds wide, I
> tried
> using smaller objects.  I tried 1.8 arseconds, twice the Raleigh criteria.
> My results were poor and I could not "resolve" dark features
against it.  I

Consider this from an energy-centric point of view:

When the subtension of the wire is smaller than an airy disk, the wire does
not cease to exist in the image, it remains imaged; with the size of airy
disks,
but the energy illuminating the airy causally degrades by the ratio between
the actual width of the line and the width on an airy disk.

This would imply that if you set your model to dark wire on bright
background and set the wire width to a fraction of an airy that you could
see that the bright
background was blocked by the opaquing wire as a grey streak. This would
prove that the obsever could detect the wire even though the wire is
thinner than
the optical resolution limit of an airy disk.

> believe the cause of this is the slope of the central bright spot in the
> Airy disc.  This slope itself is too wide and my "extended"
object of only
> 1.8 arcseconds would not create a "plateu" of uniform
"flat" light
> intensity
> across its middle width, it just looked like a wide Airy disc.  In other
> words the diffractive edge effects washed out the small features because
> they were too close to the edge of the object to be
"resolvable".  You need
> to be some finite distance in from the edge before any change in contrast
> can be detected.  I then increased my width to 5 seconds of arc and got a
> good looking "flat" plateu.
>
> Any thoughts?  This is all just a mathematical model, I lack the personal
> experience of being an experienced observer of things like Saturns ring
> divisions or Martian canals.  I'm just an engineer who's worked with
> diffraction too much in the last few years.
>

Kurt:

Nice attack at a sticky problem.


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In a message dated 1/13/2003 1:36:01 PM
Central Standard Time, KSidor{at}drc.com writes:


This does not imply that a
6" telescope can "resolve" (as one would
classically use the word) 0.05 arcseconds but it does imply that one
could detect the prescence of a dark feature that small against a
brighter background although its "gray" width would be
quite subtle.  I would guess
that Martian "canals" would fall into this category.

Before I created my model of an "extended" object 5 arcseconds
wide, I tried
using smaller objects.  I tried 1.8 arseconds, twice the Raleigh
criteria.
My results were poor and I could not "resolve" dark features
against it.  I

Consider this from an energy-centric point of view:

When the subtension of the wire is smaller than an airy disk, the wire
does not cease to exist in the image, it remains imaged; with the
size of airy disks,
but the energy illuminating the airy causally degrades by the ratio between

the actual width of the line and the width on an airy disk.

This would imply that if you set your model to dark wire on bright
background
and set the wire width to a fraction of an airy that you could see that the
bright 
background was blocked by the opaquing wire as a grey streak. This
would prove that the obsever could detect the wire even though
the wire is thinner than
the optical resolution limit of an airy disk.

believe the cause of this is
the slope of the central bright spot in the
Airy disc.  This slope itself is too wide and my
"extended" object of only
1.8 arcseconds would not create a "plateu" of uniform
"flat" light intensity
across its middle width, it just looked like a wide Airy disc.  In
other
words the diffractive edge effects washed out the small features
because they were too close to the edge of the object to be
"resolvable".  You need
to be some finite distance in from the edge before any change in
contrast can be detected.  I then increased my width to
5 seconds of arc and got
a
good looking "flat" plateu.

Any thoughts?  This is all just a mathematical model, I lack the
personal
experience of being an experienced observer of things like Saturns
ring divisions or Martian canals.  I'm just an engineer
who's worked with diffraction too much in the last few
years.

 Kurt:

Nice attack at a sticky problem.


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