[Author Prev][Author Next][Thread Prev][Thread Next][Author Index][Thread Index]
Re: ATM More Spheroidalage
Richard,
I used a 10 inch diameter flat, one day, while standing on the deck of the
living quarters for visiting astronomers at The Big Bear Solar Observatory
at about noon casting light from Sol to the North wall of BBSO and it gave
an image more than one story tall, showed negligable asti due to off axis
bundles and did show some Sun spots.
The lack of discernable aberrations was due to preterbations of the hand,
I'm sure.
At 11:09 AM 08/24/2001 -0700, you wrote:
>
>This is all very interesting, but I am interested in building something out
>of a FLAT mirror. Does anybody have limits for size and focal length for a
>flat?
>
>It is my understanding that a flat is can be an exact fit for the first two
>terms of the power series for a parabola z = a + bx + cx^2. All that is
>necessary is for the third term to be less than (according to Tex) one wave,
>or about .5 microns.
>
>Reworking this, and adopting Texereau's 1 wave peak-to-valley criterion, we
>get the following possibilities (all dimensions in inches, assuming a
>wavelength of .000020 inches)...
>
> d f-length f-ratio
> 16 800000 50000
> 8 200000 25000
> 1 3125 3125
> 0.5 781.25 1562.5
> 0.2 125 625
> 0.1 31.25 312.5
> 0.04 5 125
>
>
>Although the 16 inch model, with its focal length of 12.6 miles may be
>beyond the means of less affluent ATM's, the smaller telescopes may provide
>satisfactory performance. These are truely marveleous optical systems.
>Becuase of the small aperture, care must be taken to avoid any central
>obstruction. However, because of the flat primary, these systems work well
>with tilted components. Even more intersting is that, since the primary
>has zero power, it can be converted into a lens with two flat sides. Since
>both sides are flat, the lens does not depend on the index of refraction of
>the glass, so you can use ordinary window glass, a microscope slide, a piece
>of saran wrap, or ... gasp.... AIR!
>
>Of course with such a small numerical aperture, this instrument is best used
>on bright objects, such as the sun. I have actually done this, and it
>works.
>
>So far the only technical problem has been getting the epoxy to bond to the
>air lens. I think this can be remedied by adding more mirror clips and
>edge support clamps at the radius of equilibrium.
>
>. . . Richard
>
>----- Original Message -----
>From: "Anthony Stillman" <atmer@flash.net>
>To: <atm@shore.net>
>Cc: <atmer@flash.net>
>Sent: Friday, August 24, 2001 3:29 AM
>Subject: ATM More Spheroidalage
>
>
>>
>> In his reply to "ATM Spherical mirrors", Guy Toutant quoted Texereau's
>"How
>> to Make a Telescope" who intern referenced A. Couder "Lunettes et
>> Telescopes"
>>
>> Couder's rule of thumb f^3=34.9*D^4, as echoed by Texereau contains hidden
>> within it a tolerable wavefront degradation criteria. In the preceding
>> paragraph Texereau implies that a telescope mirror, not blustered over by
>> an industrial worker needs an un-haphazardly figure of 1/10th wave or
>> better. The title of the table printed on page 19 states that the focal
>> ratios listed will satisfy Rayleigh's Criterion for the associated
>> diameters.
>>
>> Couder's rule is derived from the root of a three term expansion of the
>> difference between the saggitta of a sphere and a parabola. Specifically
>> this yields:
>>
>> min required focal ratio = (1/8) (mirror radius / degradation
>criteria)^(1/3)
>>
>> where the mirror radius and allowed profile difference are in like units.
>> Remember, this is a mirror, 1/8 wave profile error yields 1/4 wave
>> wavefront error, the so called Rayleigh Criterion.
>>
>> Reverse engineering Couder's rule of thumb we see that it amounts to one
>> wave wavefront error.
>>
>> wavefront error = (1 / 558.4)^3 cm = 574 nm
>>
>> Not exactly a quarter wave, but then given Texereau's propensities, not
>> exactly unexpected either.
>>
>>
>> Anthony
>>
>> PS Below is a table of minimum focal ratios required for spheroidal
>> mirrors. Differing wavefront criteria (in waves) and diameters (in
>> millimeters) are given. Lambda is 574 nm
>>
>> wavefront 1/10 1/8 1/4 1/2 1
>> diameter
>>
>> 80 mm 14.0 13.0 10.3 8.2 6.5
>> 100 mm 15.0 14.0 11.1 8.8 7.0
>> 150 mm 17.2 16.0 12.7 10.1 8.0
>> 200 mm 19.0 17.6 14.0 11.1 8.8
>> 250 mm 20.4 19.0 15.0 11.9 9.5
>> 300 mm 21.7 20.1 16.0 12.7 10.1
>> 400 mm 23.9 22.2 17.6 14.0 11.1
>> 750 mm 29.4 27.3 21.7 17.2 13.7
>>
>>
>>
>> PPS I know, a 30" sphere, silly silly, but I was curious.
>>
>>
>>
>
>
>
>
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
AXE* (*Astronomically Xenogenic Enterprises)
P.O. Box 14045
Tucson, AZ 85732-4045
USA
Voice 520.745.3024
Fax 520.745.0206
<http://www.axeoptics.com>
<owners@axeoptics.com>
^^Reach for the stars; the stretch will do you good!^^
***
Proud members of the Arizona Optics Industry Association
<http://www.aoia.org>
WRC