From: "mommoteandcoyote" 
To: "Sidor . Kurt" 
Cc: 
Reply-To: "mommoteandcoyote" 


Kurt,

How large can I print..."*WOW!!!!"*  Now this is getting real
interesting. Fine work... And now ...the scrutiny

Coyot‚
----- Original Message -----
From: "Sidor . Kurt" 
To: 
Sent: Monday, January 13, 2003 12:28 PM Subject: Re: ATM Ultimate Optical
Capability, A possible Mathematical Model
Experiment


>
> Dear List,
>
> At my current job I have been designing optical encoders utilizing
> diffractive optics principals.  I have numerous Mathcad files utilizing
> Fresnel and Fraunhoffers models for simulating diffractive effects.  With
> slight dimensional scaling I have run a few simulations of Raleighs and
> Dawes criterions for an ATM size 6" diameter aperture case.
>
> Lambda = 550 nM (0.00022") wavelength of light
> D = 6 inches, mirror diameter
>
> Raleigh Criterion: "Stars are said to be "just
resolved" when the center
of
> one Airy disc falls upon the first minimum of the second Airy disc"
> (according to Hect, OPTICS, third edition)
>
> For a 6" diameter 1.22*Labmda/D = 0.92 arcseconds
>
> Dawes says stars can be resolved at 4.5/D seconds of arc, or in our case
> 0.77 arcseconds. (Smith, MODERN OPTICAL ENGINEERING)
>
> I plotted some Mathcad graphs of Fraunhoffer diffraction patterns
separated
> at these spacings of 0.92 and 0.77 arcseconds respectively.
>
> The results can be seen here:
>
>
http://images.andale.com/f2/115/106/3663062/1042483409819_RALEIGHDAWES1.JPG
>
> The separate Airy disc intensities are plotted on the left with the
> mathematical summations plotted to the right.
> The Raleigh separation shows a "contrast" of 28% change in
the intensity
> from the brightest peak of one Airy disc to the dimmer "shade of gray"
that
> resolves it from the next one.  Due to the slope of the Airy discs central
> bright core when you reduce the spacing from 0.92 arcseconds to 0.77
> arcseconds this intensity "contrast" reduces to only a 4%
difference from
> the brightes peak to the "shade of gray".  This result implies that a
> "contrast" change as small as 4% could be detected by Dawes
defining his
> "limit".
>
> I then created a new model of summing the intensities of 100 Airy discs
> defining an object 5 arcseconds wide for the same Fraunhoffer pattern
> created by a 6" aperture.  This was identical to the previous model using
> only two to define two stars but now I am creating an
"extended" object by
> mathematically putting them all next to eachother.  Then I removed one of
> the sections in the middle of my source simulating a dark line 0.05
> arcseconds wide.  The resulting change in the surface intesity of my 5
> arcsecond object was a 6% "contrast" change.  This contrast change is
> greater then what the Dawes criterion of 4% contrast needs as a minimum.
>
> The plot of this dark line (0.05 seconds wide) against a 5 arcsecond
object
> can be seen here:
>
>
http://images.andale.com/f2/115/106/3663062/1042483417451_RALEIGHDAWES2.JPG
>
> 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
> 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.
>
> Regards,
>
> Kurt Sidor
> Mechanical Engineer
> Dynamics Research Corp.
> Encoder Division
>
>
>
>
>
>

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