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RE: [APML] piggy back guide scope size
Guidescope information is useful for those shooting with refractors so I'll
provide some quantitative analysis.
To first order, the image scale (S) at the prime focus of an instrument of
focal length F is
S = 1 / F
in units of radians / length where the relevant length scale is whatever you
use to measure F (inches, meters, millilmeters, etc.) Convert this to
degrees by multiplying by 180 / pi:
S = (180 / pi) * (1 / F)
where now the unit are degrees / length. Again convert to arcseconds by
multiplying by 3600:
S = (180 / pi) * (1 / F) * (3600) ,
where now the units are arcseconds / length. Now let L denote the size of
one pixel in the autoguider. The angle subtended on the sky by that pixel
would be
S * L = (180 / pi) * (1 / F) * (3600) * L .
Further, assume that the autoguider can locate the centroid of the guide
star to within a fraction f of a pixel. (Michael Barber of SBIG has told us
previously that (approximately) f = 1/5 for the ST-4 and f = 1/30 for the
STV.) Thus, an autoguider of pixel size L, coupled to a scope of focal
length F, can guide to an accuracy
f * S * L = (180 / pi) * (1 / F) * (3600) * L * f .
Let's put in some numbers. For F = 1 m (i.e., 1000 mm) and L = 7.4 microns
(i.e., 0.0074 mm to put everything in consistent units), using f = 1/30
(these are the pixel size and f for the STV), we find:
f * S * L = 0.051 arcseconds.
Since that figure is considerably smaller than the Airy disk for typical
atmospheric conditions, this system has more than sufficient focal length to
guide with high accuracy.
Keep in mind that it does not pay to pile on barlows to increase the focal
length too dramatically with an autoguider. It turns out that if you do the
computation you'll find that the size of the first diffraction ring at prime
focus increases in size directly with the effective focal ratio. Thus if you
increase the focal ratio too much you blow up the size of the star image so
much that ultimately you might defeat the centroiding algorithms in the
autoguider. The ideal guide scope has focal length large enough to give sub
arcsecond accuracy with the autoguider yet has a focal ratio suffciently
small to create small stellar images without any optical distortion.
Practically speaking, anything in roughly the f/6 to f/12 range of focal
ratios works well.
The point is that we see that a 1 meter focal length gives plenty of guiding
leverage (if you will) and f/10 is a good focal ratio. This means that an
objective of the order of 100 mm would fit nicely. In practice, with this
autoguider you could easily use a focal length of 0.5 m and still have
excellent guiding, thus any guide scope of aperture greater than 50 or 60 mm
would be fine. Again, in practice it's easier to use bigger apertures for
your guidescope since they provide brighter star images. 90 mm is a nice
aperture without being too large and too expensive. A 90 mm f/11 achromatic
refractor is easily acquired rather inexpensively and works nicely with any
autoguider.
Greg Hartke
Sykesville, MD
> -----Original Message-----
> From: owner-astro-photo@seds.org [mailto:owner-astro-photo@seds.org]On
> Behalf Of cschur@cybertrails.com
> Sent: Tuesday, October 15, 2002 7:51 PM
> To: astro-photo@seds.org
> Subject: Re: [APML] piggy back guide scope size
>
>
> Larry, Id like to add a general formula for the guidescope is a
> magnification of 4 to 8x the taking FL in inches, and an aperture of 90mm
> as a minimum for good guide star selection. Often a 12mm
> eyepiece with 2x
> barlow is about right for guiding such a setup.
>
> Chris Schur
>
> > --- Larry McManus <lmcmanus@clearpointadv.com> wrote:
> >> Can anyone give me a minnimum size for a guide scope
> >> to go on my sc. I have
> >> a 6 x 6 Hasselblad connected to the visual back of
> >> my 8" sc and I need to
> >> come up with a setup to allow me to guide on long
> >> exposures.
> >
> > Hey Larry,
> >
> > Kent's right. Because of the moving mirror in SCTs,
> > you are best advised to use an OAG, like a GEG or
> > Taurus T III. You could be guiding away perfectly
> > through a guidescope and there can still be any number
> > of ways that your shots will be wasted. Flexure,
> > mirror rotation, focus shift, OTA contraction due to
> > falling temperatures. Guidescopes on a SCT are a
> > crapshoot.
> >
> > Alan
> >
> > __________________________________________________
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>
>
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