Wed, 03/09/2016 - 06:37
Hello, Hopefully someone expert in this area could provide a quick answer. If one were using a 25" f/3.0 telescope with perfect optics, what would be the expected average (and "best") FWHM size obtained in ARC SECONDS, given typical well-matched commercial CCD systems, mounts, guiding, medium length exposures, say up to 60 sec.
Of course the answer would depend on seeing too, so lets assume good seeing. I am mainly interested to know what the typical observer's (not-saturated) image sizes come out to be with larger aperture instruments under good conditions. I suspect, there comes a point of lessening returns as aperture goes up?
Thanks!
Mike
Hi Mike,
an approximate formula that is used very often is:
resolution (in arcsec) = 122 / telescope diameter in millimeters
Exact formula would be:
resolution (in radians) = 1.22 * wavelength / telescope diameter,
where wavelength and telescope diameter must be expressed in the same units. To convert from radians to arcseconds, just multiply the result by 206265 (arcseconds in radian). Still the first equation is IMHO enough to estimate expected diameter of Airy disk.
In general, the diameter of diffraction image depends on telescope aperture linearly (~1.2" for 10cm instrument, 0.12" for 1m intrument, 0.012" for 10m instrument). Resolution would not lessen if you would take a refractor. In reflectors, additional diffraction effects caused by additional mirrors in the light path will change the result a bit. Major player is still atmosphere. At best observatories on ground, seeing of 0.5-0.3 arcseconds is typically considered extremely good. Observatories in Antarctics could be exeptions ;-) To go further, adaptive optics is needed to compensate atmospheric turbulence and it's effects on image.
Tõnis
[quote=Tonisee]
an approximate formula that is used very often is:
resolution (in arcsec) = 122 / telescope diameter in millimeters
[/quote]
Hi Tonis, What I am looking for is the ACTUAL FWHM achieved in practice with typical CCD system vs. the theoretical airy disk.
For example, when running the BSM system at my location, it has a 65mm aperture, so the airy disk is about 2 arc seconds, however when it is running its usual imaging, the best FWHM is around 7 arc seconds. That is taking into account all the factors of the actual operating system.
My question is would one expect this ratio of actual FWHM/theoretical FWHM = 7/2 = 3.5 a general rule that would apply for all apertures as well?
Mike
Hi Mike,
BSM is primarily limited by the CCD resolution, which is about 4.5 arcsec for your system. Since you typically end up with 1.5-2.0 pixels per fwhm when focusing, that is why you end up with ~7arcsec resolution. It is determined by the equipment in this case and not the sky.
When you start using larger telescopes, say in the 20-40cm range, you are in a transition zone. If well matched to the diffraction limit of your telescope, and the optics quality is excellent, then your limitation is the atmosphere and any ground-effect causes. Since the aperture is about the same size as the atomospheric cells (20cm or smaller), you often have variable seeing, where you can get some extremely good moments mixed in with blurring, which is why things like Registax work so well on the planets. Beyond 40cm, usually the seeing is consistent because the telescope aperture averages over several atmospheric cells - you never see that moment of good seeing. I have seen nights on the WIYN telescope where it just stayed at 0.7arcsec for hours, and nights on the USNO 1.5m telescope where it stayed consistently at 3arcsec. At any given site, there is a mix of ground-level seeing (say, airflow over adjacent buildings) and high-level seeing (say, the jet stream).
So for bigger telescopes, it depends on where you've sited the telescope and what efforts you've made to improve the ground-level seeing, such as ventillation and mirror support. At USNO-Flagstaff, the 1.5m telescope had nonimal seeing of 1.1arcsec. 100 meters away, the 1.0m telescope had nominal seeing of 2.0arcsec. OC61 has 1.5-2.0arcsec seeing. TMO61 averages closer to 1.0arcsec, mostly due to its location on an isolated mountain peak. I'd say for the typical amateur, low-elevation, backyard installation, the average seeing will be 2-3arcsec (and that is about what I get with the 80cm telescope in NH).
Usually at any site, about 10% of the time the seeing will be much better than average. The trick is to make use of those good conditions!
Arne
Once again, Arne has nailed the answer! It comes from experience and long-term understanding of the questions.
In case any of you were wondering, he is my #2 Hero. Number 1? A. U. L., of course!
Lew
[quote=HQA]
When you start using larger telescopes, say in the 20-40cm range, you are in a transition zone. If well matched to the diffraction limit of your telescope, and the optics quality is excellent, then your limitation is the atmosphere and any ground-effect causes.
[/quote]
Thanks for the good information Arne. I generally have pretty good seeing at both sites here, certainly sub-arcsecond happens frequently. One other issue you didn't mention, and I wonder if it could even become a dominant factor is the guiding. How many typical commercial mounts and drives are able to consistently track down to one arc second precision for 60 sec exposures, even if perfectly polar aligned?
I ask this because in the course of running BSM-Hamren, which uses a fairly common CGEM mount, even if I get the polar alignment "spot on", most longer exposures show defects in the tracking. Commonly, the images will be elongated into ellipses or "egg shapes", show zig-zags, or even "double stars", where the mount tracked ok part of the exposure, then something "slipped", and it tracked again! Obviously these commercial mounts have imperfections in their gears, motors, manufacturing tolerances and alignments, and I wonder if ANY reasonable priced commercial mount is capable of consistent sub-arcsecond tracking for long exposures?
Mike
Google for example: mount periodic error
and select Images. There is quite a lot of different ones..
Most of the commercial mounts have pretty ugly PE curves.. If you dare, add Meade (or other common brand name(s)) in front of the 'mount' when searching ;-)
Our Paramount ME here has few arcseconds from peak to peak (without correction).
Tõnis
Having problems posting. Hopefully this is not posted twice.
The Astro-Physics mounts are close to if not sub arc-sec if you are running APCC software and have PEM on. You are not going to get much better than that without encoders. I am pretty sure the paramount mounts are also sub arc sec with no current encoder capabilities. The 10 Micron mounts, which come with encoders are also reported to be highly accurate with little to no PE. Most of these mounts are way north of $8,000 with the encoders starting somewhere around $15,000.
I have a commercial mount, whether you consider it typical or not. It is an AP1600. I have not modeled it on the sky since I last demounted the OTA (just lazy I guess) so I am just using normal sidereal tracking and usual through the scope guiding using the second chip of an STXL camera. I have PEC turned off, but the mount does have absolute encoders which significantly, but probably not completely, reduce the benefit of periodic error correction.
Attached is an Excel spreadsheet of a typical tracking log covering about a 45 minute period. The seeing that night averaged about 4.6 pixels (3.3 arcsec) which is just a little less than average for my site. Guiding exposures were 5 seconds. Keep in mind that with seeing of over 3 arcseconds the airy disk is moving around quite a bit, with 5 second guiding exposures. So some of the offset, I don't know how much, is due to the airy disc wiggling around. From the overall statistics at the bottom of the file, you will see that there is some drift in RA and DEC. I have polar aligned fairly well but I won't swear I am spot on the refracted pole. Also as I mentioned above, I am simply tracking at the sidereal rate since I have not run a sky model. I had guiding aggressivness set at 8 in Maxim.
Mike, at one point I was having many of the same guiding problems you mentioned. I was getting better images without guiding than with it. Everything had been working correctly but I had changed computers and had to setup Maxim from scratch. It turns out that the problem I had was that in setting up Maxim I had set Auto guider control to "Control Via Telescope" rather that "Control Via Ascom Direct" I could see from the guiding log that guiding commands were being delayed and were occurring out of sync or not being sent to the telescope at all when they clearly should be. when I changed to Ascom Direct, everything returned to normal immediately. This may not apply to your situation if you are using, for exmple, relays inputs instead of the ASCOM interface to guide. However, if you are using the ASCOM interface, try changing this setting.
By the say a found an extremely thorough and quantitative web site dealing with Polar alignment. It is the best I have seen anywhere: http://canburytech.net/DriftAlign/index.html
The overall statistics are as follows and all the details are in the attached spreadsheet.
In Pixels
OffsetX
OffsetY
Corr X
Corr Y
Max
1.3
2.11
0.27
0.11
MIN
-1.57
-1.17
-0.33
-0.21
RANGE
2.87
3.28
0.6
0.32
AVG
-0.0982
0.343689
-0.02061
-0.0315
RMS
0.495324
0.546782
0.101611
0.051109
Includes long term drift
1σ
0.485548
0.428578
0.09951
0.040544
Excludes drift
2σ
0.971095
0.857156
0.199021
0.081089
Excludes drift
3σ
1.456643
1.285734
0.298531
0.121633
Excludes drift
In arcsec
OffsetX
OffsetY
Corr X
Corr Y
Max
0.9698
1.57406
0.20142
0.08206
MIN
-1.17122
-0.87282
-0.24618
-0.15666
RANGE
2.14102
2.44688
0.4476
0.23872
AVG
-0.07326
0.256392
-0.01537
-0.0235
RMS
0.369512
0.407899
0.075802
0.038127
Includes long term drift
1σ
0.362219
0.319719
0.074235
0.030246
Excludes drift
2σ
0.724437
0.639438
0.148469
0.060492
Excludes drift
3σ
1.086656
0.959158
0.222704
0.090738
Excludes drift
Brad Walter, WBY
Attached is a spreadsheet that demonstrates the seeing variability Arne Mentioned. The Telescope is a 250mm (~10") corrected Tak Mewlon Dahl-Kirkham. The diffraction limit for this telescope is about 0.5 arcsec. My STXL camera has 9 micron pixels which for the corrected Mewlon gives almost exactly 0.75 arcsec per pixel. My location in central Texas is where coastal air masses meet the those from the Hill country. That means my seeing isn't great. 3.0 to 3.5 arcsec is normal; 2.5 significantly better than average; 2.0 great and 1.0 almost unknown. On the other side, 4 arcsec is poor, but not uncommon, and at above 5 arcsec I start taking calibration frames. There are nights that the seeing is so bad that FocusMax won't converge on a position.
The attached spreadsheet shows a series of 20 x one-second V images of the b Per field taken on 3/5/2015 UT over a period of about 10 minutes. All 3 stars are far from the center of the field and I focused on the center. The Coma of the corrected Mewlon is pretty small over the 38 x 25 arcmin FOV, but there is some small increase in the FWHM far away from the center. Other factors prevail, however since the FWHM does not increase consistently with distance from the image center HIP 20296 and b Per are at almost identical distances (b Per is a few pixels closer) and check star 55 is very slightly less than half the distance of the the other two stars.
Consistently for all 3 stars measured (Target, Check, Comp) the FWHM varied across images by over 100% from the minimum value and the standard deviation (of the sample) ranged between between 1.1 and 1.2 pixels also for each star across all images. The Range of FWHM for the three stars within a single image was about one-tenth of the range of FWHM of any single star across the 20 images taken over about a 10 minute period and about 20% for the analogous comparison of standard deviations.
No refocusing was done during this set of images. The telescope was well cooled and the air temperature was decreasing slowly (fraction of a degree per hour..
With our 0.6 meter club telescope, however, we rarely see ranges in FWHM (in arcsec) over short time spans that approach one-half this amount. The comparison, however, is far from perfect since the club scope is located over 100 miles distant with typical seeing of around 2.5 arcsec.
Brad Walter, WBY
Brad, Thanks for your input. Your detailed information and data is very useful as always :) Let me say, I was mainly using the BSM situation here as an example of tracking issues. In reality, even though the tracking is variable from image to image (as you find too), it appears Maxim DL or something is adjusting for the errors, since I see FWHM on many trailed stars is still close to that of the untrailed stars. Overall, I think for the mission of BSM, this CGEM mount is ok for its job.
My main thrust of this thread is more about my 25" f/3.0 reflector telescope soon to come online. I have been thinking whether to use it purely as a visual scope (easy mounting!) or try to get it setup as an imaging system. In the latter case, be it true CCD or DSLR, I am going to need an accurate tracking mount for good performance at the image scales in question (75" F.L.) I don't have a whole lot of money to spend on a high-end mount, especially one that can handle a 100+ pound telescope, so I am planning to build my own mount from whatever convenient parts I can locate. Seems likely I will use large pillow block ball bearing or needle bearings as the principal component in a standard GEM setup, though I may also try making a large fork mount. Not sure if these types of bearings allow good precision motions though, as they are generally designed for higher RPM usage, not small back and forth as in a mount.
Mike
What optical design is it. 25" f/3 numbers suggest Newtonian to me but that is just a guess. If it is a Newtonian and you want to do visual as well as imaging I don't think GEMs and Equatorial Forks will work well. A "C" ring design (like the Las Cumbres 1m telescopes use might be better. See the attached image. This one is installed on raised pedestals since it is never used for visual work. something like this installed at floor level would keep the eyepiece about as low as you can have it with anything except an equatorial platform. LCOGT is open source so you might be able to get plans for this mount from them and scale them down.
Brad, Walter, WBY
Hello Michael
Just as a couple of points on the curve. I have a Mewlon 300, much like Brads, but with a corrected focal length of 3000mm. I use an Tak EM500 mount and its advertised PE is 2.5-3.5 arc secs without correction. I have no issues with 5 minute unguided exposures. Polar alignment is very good. I also have a second one at a remote observatory, and its performance is the same.
At Maria Mitchell, we also have a CDK-17 on top of another Tak EM500. Its focal length is 2936 mm and we have no issues with 5 minute exposures.
We also have a 24 inch RC on a custom mount. It has a 24 inch Byers Gear, and its even better. We can go 10 minutes with no signigicant isuues. Its 24 inch f5.6, or a focal length of 3450 mm.
So without autoguiding, 5 minute subs are possbile with a 25 inch f3 which is 1950 mm.
The bad news is the Tak Em500 mounts are about $15K. Used on Amart ? The big 24 inch Byers Gear with PE observed below 1, is priceless. Not made any more.
Gary
Hope this helps.