Great answer Wavy !
Now add in a meridian flip and the problems are worse.
But again Tpoint has already been designed to consider these things as mentioned a, b, c and 1, 2, 3 and includes a total of nearly 30 repeatable mechanical errors in mounts and optical systems that affect telescope pointing.
Tpoint calls them Terms and anyone who has used it will be familiar with them. There are 6 basic terms that cover the basics of most mount and optical systems and will get you very close to perfect if you have a refractor thats rigid and collimated its often hardly worth persevering further, but the other two dozen or thereabouts will cover almost everything else.
Many terms are only likely to apply to one particular type of system or another - eg Refractor or Mirror or Nasmyth so you never need to use all of them.
Its not that Im trying to be a fanboy of Tpoint ! but the beauty is someone has done all the hard work already and its so easily implemented by an amateur without any additional hardware.
Any other method to truly yield high accuracy will necessarily have to make an attempt to cover all the very same Terms that Tpoint deals with - so why bother if its already done.
But if you are just seeking sub 2-4arcmin PA accuracy then of course its not needed and for many amateurs this is probably adequate for even medium to long length exposures with guiding as the field rotation is very minimal.
It just relies on doing some star mapping each time you setup your mount and system - once every so often if you have a fixed observatory setup and each time you setup in the field or if you drunkedly stumble into your telescope at night or the ground moves (eg heavy rain or passionate night - joke - we're amateurs)
But it really doesnt take that long unless you are also trying to solve all of the extra terms, and you dont need to understand how and why it works under the hood - just that it does work - it was originally developed for professional observatories to use - in fact I think it was originally developed for or in conjunction with the AAT at Siding Springs in NSW.
The accuracy of the results is dependent on the accuracy of your mapping and gear, although even poor mapping (eg visually or with equipment with lots of errors and instability - remember the errors have to be mechanically repeatable) can still yield reasonable results if you have enough mapped stars.
But mapping on screen using a camera at say 400% magnification means you are invariably within a pixel of the star's centre during mapping and any errors then get statistically "averaged out" of the equation anyway.
It doesnt deal with varying camera rotation angle and any inherent coaxial induced offset of the camera centre (ie the centre pixel of the camera image moves as the camera is rotated) - so you want a method for either keeping that fixed at least when initially mapping and preferably have the camera angle mechanically calibrated to some reference position when you first setup (preferably astronomical zero)
Dont mean to harp on about it but using the best tool for the job will give you great results and anything else is just an approximation because it comes with exceptions and all sorts of excluded cases.
One of the real benefits of using it (apart from accuracy) is that in two or three years time assuming you are using the same gear - you can go back to an old target you want to add more data to and start imaging again and you can use the same guide star in the identical same positons and this can be pointed by using one of the old images as the reference - it makes life so easy.
Your new images will then all register perfectly with the old ones (assuming you also have camera rotation either automated using ASCOM or manually set) since that will be recorded in the FITS header and can be translated directly into your planetarium software - at least with TheSky it does.
So you dont suddenly lose half your data after registraton becasue camera angle and image centres have shifted too much.
And you can save lots of time setting up and getting going.
I have to thank Eric for showing me how to use MaxIm to best extent for this !
Quote:
Originally Posted by Wavytone
It is feasible... the polar alignment error is a constant offset in altitude and an offset in azimuth. Mathematically the offsets can be computed from ONE short image taken near the east/west horizon and ONE short image near the zenith, provided you accurately know
a) the time the images were taken, and
b) the precise pointing of the telescope for each axis when each image was taken, ie from encoders or at worst, setting circles.
c) it assumes the mechanical axes of rotation of the mount and the optical axis of the scope are precisely orthogonal. They never are.
Notes:
1. the accuracy is fundamentally limited by the accuracy of the measurements of the telescope position in each axis. For example, if you used setting circles with 1-degree resolution the best accuracy you might achieve is +/- 0.5 degree. With encoders you can do significantly better, but there's another limitation...
2. orthogonality of the mount and optical axis - if the RA and dec axis aren't exactly perpendicular, nor the optical axis perpendicular to the dec axis, these introduce more errors in the calculation. Errors up to 1 degree or even more are not uncommon in commercial budget-grade mounts for the amateur market.
There are ways to measure these errors and correct them - this is fundamental to the precision of theodolites used in surveying - where accuracy of 1 arc second is considered common.
3. two images are not required.
The maths is also known as the "surveyors equation" as this is also the same as the method used for a 2-star astrometric fix to determine latitude and longitude in absolute coordinates using a theodolite. It is also the same maths in the heart of GOTO mounts to determine how to calibrate the mount using 2 stars, and to do the GOTO calculations.
Incorrect, study the spherical trig in say Smart's book. The the polar alignment error is a constant offset in altitude and an offset in azimuth, and is not a constant error in dec. Atmospheric refraction can be approximated using some formulae that take into account your site position, site altitude, air pressure and humidity but its not perfect, there are other variables in play (eg weather systems).
but it cant be perfect. It never is, because...
Yup, atmospheric refraction produces a vertical shift (ie in the apparent altitude) of a star - it appears higher in altitude than it really is. This produces an offset in its hour angle (ie RA) AND its declination - and worse, these offsets vary as the star moves across the sky.
So wherever you aim your polar axis, its really only an approximation and you DO need to guide in RA and dec to account for the changing offsets as the stars altitude changes.
Don't hypothesize - do the maths. It's describe in Smart's book "Spherical Trigonometry" and it isn't trivial - it is a significant challenge for someone with good highschool year 12 trig and calculus. I did all this 35 years ago to produce a program for determining position from 2-star alignments using a HP41CX... but don't ask me now.
Cheers, indeed.
Wavy.
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