Originally posted by Tjompen1968 The trailing in the corners is probably due to lens coma.
Probably not coma but geometric distortion and poor tracking with wide and ultra wide lenses is the likely cause.
Originally posted by osbourne one-nil Also, I know there's a table out there which shows the recommended tracking times for a given focal length, but I can't find it anywhere...can anyone point me in the right direction?
The table you are looking for
is this one that gives tracking time for the O-GPS1 which should match the inbuilt ability of the K-1. However for going after deep sky objects I find the provided tables to be on the optimistic side of things by a lot and often find that I can get good result at 1/4 the time suggested.
The astrotracer ability in the cameras that support it functions as an alt-az mount that also does field rotation. It is dependent on knowing your latitude fairly precisely (a +/- a few hundred meters north south is good enough), what cardinal direction the camera is pointed, and how it is oriented in relation to the center of the earth. It gets this info from the compass, level sensors, and GPS and then does a bunch of math to figure out how much to move the sensor. If you look at the tables for the O-GPS1 it gives times depending on declination however most people don't understand declination correctly. A declination of 90 degrees is not looking straight up into the sky at the zeniuth and a declination of 0 is not looking straight out at the horizon. Instead a declination of 90 degrees means that camera is point at the celestial pole and if you are in the norther hemisphere you would be very close to having polaris centered in the frame. A declination of 0 degrees means you would have the camera pointed along the celestial equator and a good object basically on it is the upper most star in Orion's belt which is really close. If you are pointed directly at the celestial pole all of the movement is rotational, and if you look at the tables you will find that point at a declinatio nof 90 always gives the longest tracking time and is independent of focal length. this makes sens as the movement in the frame is all angular speed and the sensor can only rotate so much so the time it takes the stars to rotate the most the sensor can is about 5 minutes. However if you are pointed along the celestial equator the movement is entirely linear so the linear speed of the stars is all that matters. Here focal length matters since with longer focal length lens things move across the frame faster which is why you see decreased tracking time with longer lenses. Depending on where you have the camera pointed between the celestial pole and celestial equator there will be varying amounts of linear and rotational movement needed for accurate tracking.
Now on to quirks of astrotracer beyond it being rather finicky to get calibrated well. The biggest one that comes to mind is that with wide and ultra wide lenses it will almost always produce some trailing in the corners. The only time when it wouldn't is when you have it pointed exactly at the celestial pole in which case it it is functioning as a equatorial mount with a very short tracking ability. The reason for the trailing is caused by 2 things. The first is the geometric distortion that these lenses have that tends to be worse in the corners and along the edge. This distortion causes the tracking to not be as accurate as you move from the center of the frame out to the edges and corners. The other issue is that these lenses cover such as huge area that the amount of rotational movement vs linear movement varies substantially across the frame such that as you move from the center of the frame the tracking gets worse. As mentioned before this isn't a problem when point at the celestial pole since all the movement in the frame is rotational, but if you point it at the celestial equator the movement of the sensor will be entirely linear but as you move away from the celestial equator there will be more of a rotational component to the star movement.
The nice thing is that with wide and ultra wide lenses the need for tracking is greatly diminished as you can get very good results using the rule of 200 (a better variation of the rule of 500) which basically says to use as your maximum untracked exposure time 200/(focal length). So with my 12mm lens I can use a 15 second exposure and get really good results, but in reality since the stars are so small in the frame found I can push it to 20s and still get pretty good results but at 30 I don't like the trails. With a 50mm lens I can do 4 seconds untracked, but with my 400mm I could only do .5s untracked. The reason to use 200 instead of 500 is that 500 was from the film era where reciprocity failure was a thing so it worked well enough, but 200 works better with modern digital sensors that don't suffer from reciprocity failure. However this still takes advantage of the fact that our sensors have a bayer mask on them and interpolate pixels and to get truly sub 1 pixel movement with things along the celestial equator you would have to use 50/(focal lenght) and I have done some shots like that with some really long glass just to see if it was possiable. I did some moon shots at f/20, 2000mm, ISO 100, and 1/40s that way because I could and the f/20 wasn't by choice but a results of the f/10 mirror lens and 2x convert in the mix so I could get it to mount and still achieve infinity focus.
I recently got a small equatorial and the 2 biggest benefits I've found with it are first that I don't have to recompose all the time. Once I get an object framed up with a short lens I just put the camera in continuous low shooting mode and filp the switch on one of my release cables and let it take pictures until I decide to pack up. The second benefit is that with playing around with getting a good polar alignment does take longer than calibrating astrotracer it doesnt' get thrown off by things like astrotracer does so I can get good alignment up in places like the Iron Range of northern MN where astrotracer never seems to get a good calibration or any other place with magnetic items or magnetic fields. With wider lenses like a 50mm one doesn't need even a very good polar alignment to get good results at 30s per shot as I found out the other day with my first real attempt. I do need to get an intervalometer so that I can go beyond 30 second exposures with it.
I still use astro tracer as my little equatorial can't support my big lenses by themselves so I either shoot untracked or using astrotracer with them. I use astrotracer all the time with my SMC A* 400/2.8 and will even throw the 1.4X-L converter in the mix to have a 560mm f/4 and have had astro tracer work great. Granted for deep sky objects I still am stacking and the tracking times to get good results are still pretty short but I can consistently get 20s shots at 400mm and 10s shots at 560mm all the time that don't shot any trailing. Eventually I will move up to also having a big equatorial that can support a 16lbs lens and the camera and other gear you hang off of it but for now I am still using astrotracer for the big glass. I often am running multiple cameras and the last time I was out I had the 12mm lens not tracking at all but continuously shooting 30 second shots so I could do a star trails image with Polaris and the milky way, a 50mm lens on the equatorial following Cassiopeia through the sky shooting continuous 30 second shots, and I was using astrotracer with my 400mm on Andromeda.