Theoretical alignment accuracy

Following the amazing performance of the refreshed AZ-EQ6 mount a few nights back, I started to wonder what the theoretical limits of polar alignment might be, given the practicalities of turning the mount’s adjustment knobs in the field.  I had managed a six-minute shot of Vega – see my last post – with no trailing, and no external guiding.  That’s just the mount doing what it’s supposed to do, and doing it rather well.

All other things being equal – and with the caveat that in the real world this is never the case – we can consider that there are two variables in the system:  the inaccuracy of the polar alignment and the length of the exposure.  The more the error in aligning the mount, the greater the difference between the axis of rotation of the camera and the axis of rotation of the Earth.  This difference will show as trailed stars, and the length of the trail will increase with the duration of the exposure.

Given my setup of the Nikon D90 on the Altair Wave 115/805, the sensor resolves the image to 1.41 arc seconds per pixel.  My calculations* are very encouraging, as they suggest that if the mount is aligned to within a very achievable half a degree of the celestial pole, the drift will not show as a complete pixel for 10 minutes.  Even an exposure of 4 minutes will only drift a tenth of a pixel.

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More practice, experimentation and experience will show just how far the real world parameters are from this ideal.

*Many thanks to Abhijit Pendse for his most generous assistance and guidance on the maths of this problem, through the Facebook page for Astrophotography/ Amateur Astronomy Enthusiasts.

Perfect alignment

I’ve been having a really troubling time with my new AZ-EQ6 equatorial mount.  I say new, but I bought it about a year ago – second hand – and it has puzzled and infuriated me ever since.

First up, the previous owner had snipped the power supply cable and wired it to a mains adapter.  No problem there, so I undid his modification and wired it back to a “cigar lighter” plug for use with a battery pack.  Despite all the care in the world, I somehow got it wired to the wrong polarity and promptly blew the mother board as soon as I switched it on.

Embarrassing.  Took it to the “repair and service division” of one of the UK’s best known retailers, who smiled sympathetically, wagged a finger, tut-tutted and said they would check it out.  Days turned into weeks, weeks turned into months, gentle reminders turned into an increasingly despairing string of phone calls and emails, and eventually they returned it, fixed.  Their apology for the shameful delay was not to charge me.  Fair enough.  We have since made up – you can’t stay angry all your life now, can you?

There’s no doubt that the AZ-EQ6 is a fabulous mount.  Some evolutionary changes and some revolutionary changes make it so much better than the standard EQ6, so my expectations were really high.  On my old EQ3 mount, I could polar align by eye and track with a 300mm telephoto lens for up to 8 minutes without star trails.  It took a lot of practice, but I could do it time after time.  Here’s Comet C/2011 L4 (PANSTARRS) from May 2013 at those settings:

PANSTARRS approaching Cepheus 300mm f/5.6, ISO 800, 8 min. Single 8-minute frame.

PANSTARRS approaching Cepheus
300mm f/5.6, ISO 800, 8 min.
Single 8-minute frame.

The AZ-EQ6 is a heavy beast, and I use it out of the back of the car.  Incidentally, it lives in my basement, so each astro-session starts with lugging the boxes up the stairs and out the front door to the car.  Practice makes perfect, however, and I can set it up in the dark in about five minutes, then run through the alignment routine and we’re good to go.

Except we weren’t good to go.  It just didn’t work very well.  The “advanced polar alignment” routine, using feedback from the star-aligned telescope to adjust the polar alignment of the mount, kept producing crazy results.  Crazy adjustments, endless frustrations.  I resorted to drift alignment, convinced that I must be getting something wrong but baffled as to what that might be.

Then we hit rock bottom.  Drift aligning produced near-perfect levels of polar alignment, but the stars still trailed for anything over 60 seconds of exposure, even at a relatively modest 300mm focal length telephoto lens.  After several sessions it occurred to me that the drift was entirely in RA, and the mount drive was therefore running slightly fast.  There was no drift at all in Dec.  I sent an email to SkyWatcher to ask them how to fix it.

The moment I sent that email, it came to my attention that there were a couple of “firmware updates” on the Skywatcher website: one firmware update for the motor drives, one for the handset.  The list of “fixes” for these updates read like a copy of my list of queries.  Maybe, just maybe, I wasn’t doing anything wrong at all.  Could it really be that the mount was inherently faulty?

I downloaded the updates and reflashed the motor drive and handset according to the instructions.  The polar alignment feedback routine is now slightly different, so I took the first opportunity to test it out last night.  After dodging clouds to complete two iterations of the alignment routine, I watched the sky cloud over leaving just one star visible: Vega on the western horizon.  Nothing else to do but take photos of Vega.  Here’s the result – first a couple of frames through the 300mm telephoto lens, spaced 7 minutes apart:

Vega at 20:19 300mm telephoto.

Vega at 20:19
300mm telephoto.  Field of view 4.5º x 3.0º

Vega at 20:26 300mm telephoto.

Vega at 20:26
300mm telephoto.  Field of view 4.5º x 3.0º

That looks good, but it’s not the position of Vega that caught my eye, as that’s impossible to tell without layering the frames together.  It’s the stars at the edge of the frame.  I had become so accustomed to seeing them drift off between frames.

Next, a single five-minute frame:

Vega for 5 minutes. 300mm telephoto.

Vega for 5 minutes.
300mm telephoto. Field of view 4.5º x 3.0º

The image is poor quality because the clouds kept coming and going, but the important thing is that it appears not to be drifting.  On the other hand, I could do that with the old EQ3:  the AZ-EQ6 was supposed to do better than this.

Okay, last test before the clouds completely finish the evening.  Prime focus through the Altair Wave 115/805.  That’s a focal length of 805mm.  I leave the shutter open for six minutes while I start to pack stuff away:

Vega for 6 minutes. 805mm prime focus.  Field of view 1.7º x 1.1º 1.4 arc seconds per pixel

Vega for 6 minutes.
805mm prime focus. Field of view 1.7º x 1.1º
1.4 arc seconds per pixel

A bit fuzzy from the cloud, but it looks pretty solid to me.

That’s six minutes, unguided.  Happy days.  That’s what I believed I had bought in the AZ-EQ6, but had begun to think I’d made a mistake.  Next clear sky, I’ll see how far it can go!