Telescope Resolution, FWHM, and HFR

[@DevilleJean]

James, this is one of the best technical explanations I have come across. Makes me really understand more in-depth what I am actually doing during my astro sessions. Keep up the good work!

[@Aero19612]

Great! Thanks for watching, Jean!

[@hbmike47]

Hi James. Thank you for putting this out here. There is not much on YT when it comes to physics and engineering in astrophotography. You are raising the bar. Clear skies!

[@Aero19612]

What can make astrophotography more fun, you ask? More math, physics, and engineering, of course! Thanks for watching, Mike!

[@stevenadam3730]

Enjoyed this video immensely and I found your technical tutoring very easy to understand. I'll be tuning into a few more for sure. Thanks Steve

[@Aero19612]

Thanks Steven! You're welcome back anytime...plenty of room

[@NMukkavilli]

Man I never thought I’d see a Bessel function of any kind after year 2 maths in engineering! Great video, thanks

[@Aero19612]

They’re hiding under rocks, just waiting to pounce. Thanks for watching!

[@louisrosner7902]

Great video. Now I understand why the HFRs are a little bit greater with my SCT than my 102 refractor. Thought it was just the focus routine. Very informative. Scary formulas but you made them almost too easy to understand. Keep up the great work.

[@Aero19612]

Glad you didn't kick your SCT to the curb before this! Thanks, Louis!

[@astrophotonics9470]

Always enjoy James in depth technical analysis, a refreshing change from the run of the mill cookie cutter Astro Shill channels.

[@Aero19612]

Thanks for watching!

[@salomon1639]

Thanks for your insight. You always make a complex topic easier to understand. I recently installed a falcon rotator and had a hard time achieving the proper spacing for back focus as recommended by ZWO (Back focus of 56 mm and I was off by 1 mm) . My image focus was normal. Maybe you can make a video discussing this topic and the significance of minor measurement changes with back focus and its real impact on image focus and resolution. Again thanks for your analytic videos and your hard work and attention to detail.

[@Aero19612]

Thanks for watching, Salomon! Yes, there is some unplowed territory where back focus is concerned. One issue I don't have a good grasp on is the manufacturing variability and the permissible error. I'm still "scarred" by my experience with trying to find optimal back focus for my Explore Scientific ED102 and field flattener. Still have stretched stars.

[@jiffijoff9780]

Just wanted to throw in a THANKS for this explanation. Its very helpful. Cheers.

[@Aero19612]

You're quite welcome. Thanks for watching!

[@math2cool]

You just created the primmer (be it at a rather high level) on this subject. Thank you - because I love days where I understand more than I did when I awoke. (PS - double integral - sweet!)

[@Aero19612]

Haha. Well, I'll lose what few subscribers I have if I play the "integral" card too often. Thanks for watching!

[@jameschase9002]

Hi James - In case you don't already know... APT has just released version 3.88 which includes their new auto-focus routine. I would very much enjoy seeing your evaluation of it.

[@Aero19612]

Hey James. Yes, I got the email and am looking forward to giving it a shot: clouds, rain, work. Rinse and repeat. I have installed v3.88. Thank you for your efforts in leading APT in this development. You should be very proud of your contribution. Thank you! It's a huge must-have feature for APT.

[@Aero19612]

Haha. My apologies! My reply above must have been rather confusing. I got you confused with one of the guys I have spoken with who started the work on the new auto-focus routine in APT. He had asked some questions about my Excel curve fit spreadsheet. In any event, I have finally given the new APT auto-focus aid a quick test with my SCT (I just put out a video on it). It worked well for me. Time will tell. They’ve got to integrate it with the imaging session control scripts. Sorry for the confusion, James!

[@JohnMcGFrance]

Thanks James. Very interesting. Especially in regard to under/over sampling which can worry people with scope and camera combinations that are supposedly far from ideal. Most of us can’t afford to buy a camera with different pixel size just to match a new scope! I think most experienced astroimagers know that it’s the seeing and attaining precise focus that makes the most difference. This shows up clearly in PI if you use the subframe selector tool to analyses subs. Frames from the exact same scope camera combination can vary markedly in FWHM in one inaging run. I’m sure you’ve seen it but in case not PHD2 now has guiding using multiple stars allowing better guiding with shorter guide cam exposure times as it cancels out some of the variations caused by seeing. Possibly a good comparison video for you to do? I’m hoping to test it soon, but no clear skies in the coming week according to the forecasts. Have a great 2021 and look forward to more of your highly informative videos.

[@Aero19612]

Thanks for watching, John! Yep, my sense is that too much is made about under- and over-sampling. Plenty of other, more critical, things to worry about in this hobby...starting with the bank account. I've been hearing about "multi-star guiding" for years and am pleased that PHD2 has incorporated into the latest (dev) version. Unfortunately, where I need most help with guiding is with my SCT and I use an OAG where there may only be 1 star to guide with. I'll try it out with my GT81 and Redcat 51 where that OAG sees more stars. The multi-star guiding option may be most (only?) useful for folks with wide angle guide scopes rather than OAGs.

[@grahamwhite75a]

Love your clarity in explaining the topic. Thanks.

[@Aero19612]

Thanks Graham!

[@thomascoverdale2193]

I learn so much from your videos!! Thanks you for sharing your knowledge and expertise! Tom

[@Aero19612]

Thanks for watching, Thomas!

[@maciejpyziak8426]

Hi James very interesting video. I’ve watched it about twice to get a grasp on it. I recently got William Optics Zenithstar 61 APO with the 61 field flatter. Camera that I purchased for it is ASI 183MC Pro Pixe Size 2,4 nm The sensor size it’s quite small. 13.2-8.8mm 20 megapixels. Do you think that was a wise choice to do it. Or I should’ve went different route. Thanks for the feedback James in advanced. I wish you and your subscribers many clear skies. Thanks again Mike

[@Aero19612]

Thanks for watching, Mike! Sure! You made a great choice. The smaller pixel size (2.4 um vs my 3.8 um) leaves you with a slightly over-sampled image (i.e., you can take full advantage of the scope's optical design). I am a little under-sampled with my William Optics scopes (but with atmospheric effects, my combo is just fine). If anything, you'd rather be over sampled, like your setup. As I say in the video, companies like ZWO aren't in the business of selling cameras that don't pair well with telescopes. Enjoy your scope and camera,

[@scottrk4930]

Hello James . I started to cringe when I saw the Formulae in the Video Preview window but I'm glad I stuck it out until the end . I always learn something new from your Videos . Cheers ./SRK

[@Aero19612]

I know. I thought about it. I hope I never get too "mathy" on the channel, but it is nice to show the "big picture" once in a while. Also, I've never seen how optical folks come up with the theoretical HFR so I thought I'd show my approach for those more knowledgeable than I to set me straight.

[@montygiavelli8125]

Another great video. It's been a long time since I've done double or triple integration but I get a lot out of your presentations. thanks, Monty

[@Aero19612]

Thanks Monty! Nothing says "fun" like double integration!

[@jehocking24]

Very nicely done you gave very good visual explanation and I understand it much much better thank you

[@malcolqwe2]

amazing explanations, thanks for posting!

[@Aero19612]

Thanks for watching, Malcolm!

[@redabdab]

Excellent video thanks! I learned a lot! Question; if all stars are point sources why do some look larger than others in photos? In other words, why is there no brightness (magnitude) term in the formula for FWHM or HFR?

[@Aero19612]

Right. I used a "normalized"" magnitude. In a real starfield, as you say, stars look different. They all have the shape, but not the same height. Imagine a variety of curves like that but with different magnitudes. And imagine a noise floor. Some of the stars will barely poke above the noise floor and you only see the top. With others, you see more of the star shape rising above the noise, and with the brightest stars, you see most of the PSF. Anyway, that's the way I think about this issue!

[@guibraproductions2120]

Really interesting video, it helps a lot in my master thesis! thanks! :)

[@Aero19612]

Glad it helped!

[@AstroQuest1]

Stupendous video James! Thanks for dragging me down the Rabbit Hole as well. I took some notes while watching it. Does NINA store the autofocus points somewhere, I was wondering how you made the the comparison graphs? Cheers Kurt

[@Aero19612]

Why should rabbits have all the fun. The NINA autofocus files are stored in: C:\Users\[your user name]\AppData\Local\NINA\AutoFocus in the ".JSON" format. It's an ascii file format so it readable in a text editor.

[@AstroQuest1]

@@Aero19612 Ha Ha, Thanks James.

[@toddnoseworthy1447]

Love your technical videos!! I've wondered if focusing routines could use the number of stars detected to confirm best focus, or at least to supplement the other method chosen. What do you think. Sharper focus usually means more stars detected.

[@Aero19612]

Thanks for watching, Todd! I've wondered the same thing: kzbin.info/www/bejne/nZqQY2SjqLp-gZY My SCT produces odd HFR results and the number of stars seems more reliable. I haven't noticed that for the shorter focal length refractors.

[@RobB_VK6ES]

A way out there thought James. Do you think it possible to harness the inaccuracies of the mount and sample the star using the slightly different locations on the sensor? It occurs to me this would be similar a vernier scale where by using two coarse scales it is possible to resolve a finer interval Now reality sets in with reduced seeing :(

[@Aero19612]

Hey Rob. I'm not sure you're "way out there." Isn't that the whole idea of dithering followed by drizzle integration to improve resolution. I joke sometimes when I say that my CGEM already has an automatic dither feature.

[@arnaudmarie2892]

I understand the reasoning of this video in the case of a monochrome sensor. But how can we apply this reasoning to a Bayer matrix color sensor. Indeed, the apparent resolution of the Bayer matrix is lower than that of a monochrome matrix.

[@Aero19612]

A very good question, Arnaud. At worst, double your pixel size. But I don't think things are quite that easy. The interpolation algorithm should "recover" some of that lost resolution.

[@BrentMantooth]

Great video, don't fear the math for with it there is much power. Thanks and keep it up!

[@Aero19612]

Haha. Just remember: Math is as scared of us as we are of it

[@scottrk4930]

Actually , if you are looking for a future Topic , how about explaining "Diffraction Limited" when applied to OTA's ? My EdgeHD flaunts this in the White Paper but I still can't get my head around it in practical , User-friendly terms . Cheers ./SRK

[@Aero19612]

If it were a snake....I think my video is about "Diffraction Limits" for OTAs. That is, the resolution of your OTA is limited by the diffraction of light by the edge of the aperture. Resolution (FWHM) = 1.22 lamda / D (180/pi)(3600) arc-sec, where lamda = 0.55 micro-meter D = 203200 micro-meter (203.2 mm = aperture of Edge HD8)

[@scottrk4930]

@@Aero19612 Ouch ! Sorry , don't remember hearing or seeing the Term Diffraction Limited in your Video and since I don't understand this Term I could not connect the dots . I'll have another watch and see if anything clicks for me ./SRK

[@Aero19612]

Haha. No worries. I didn't mention "diffraction limited" in the video. I should have. I'll look a little more into the term, but I'm guessing that's what it refers to.

[@patwicker1358]

Nice clear explanation of what could have been a real "egg-head' presentation.

[@Aero19612]

Darn it! I was going for "egg head". I'll do better next time. Thanks for watching, Pat!

[@realair5472]

Hi James. You are such a good teacher. I wonder if you have elaborated regarding the resolution for the complete system including guiding? E.g. what is the impact of a guiding performed (in terms of Arcseconds) on paar or under the telescope resolution? Will the guiding just cause noise that can be reduced by increasing the number of subs or are there other considerations? How much better does the guiding need to be (e.g with 50 subs) compared to the telescope resolution in order to use the full capability of the telescope resolution?

[@Aero19612]

Thanks for watching! The number of subframes cannot "erase" the effect of poor guiding. More subframes (imaging time, really) = improved signal to noise ratio. But the resolution of those images is governed by aperture of the scope, pixel size, seeing, and guiding. Poor guiding reduces resolution. Your only hope is to perform guiding that (1) compensates for periodic error of the mount (2) error in polar alignment, and (3) compensate for gear train harmonics in the RA axis. You want to avoid "chasing the seeing," which only exacerbates the seeing. Hope that helps...

[@realair5472]

@@Aero19612 Thank you. I have now also seen your Dawes vs Nyquist clip. Incredible good explained (I had to watch it several times to fully understand it). I have now for the first time understood why I would benefit of smaller pixels in my Redcat 71 setup (my pixelsize is the famous 3,76 um) given that my guiding is good enough. Is there a formula of how the guiding error affects (degrades) the total resolution?

[@Aero19612]

Not sure of a formula for guiding effect on resolution. A big part of the problem is that guiding is just a "glimpse" of the true seeing. The atmospheric waviness occurs at a much faster rate than guiding so that seeing-smeared light is affecting your image even without considering the guiding effect. In other words, PHD2 could tell you that you have "perfect" guiding, but there is still seeing effects and dense atmosphere effects without seeing. In the end, we get the seeing we get and can only do our best not make it worse with our guiding.

[@AstroQuest1]

Hi James, I have another question? At 14:26 minutes in you list the FHWM value of 2.77 um for your William Optics and compare it to your pixel size of 3.8 um. Where or how did you calculate that number. - Cheers Kurt

[@Aero19612]

Hey Kurt. The formulas are at 5:30. In that case it looks like I wrote down the RedCat instead of the GT81. I'm also using the "actual" F-ratio with F = focal length/aperture For the GT81: F = 385mm/81mm = 4.753 for the Redcat: F = 250mm/51mm = 4.902 Using 550 nm = 0.550 um for green light, Diameter of green FWHM = (1.029)(0.550 um)(4.902) = 2.77 um (for Redcat) = (1.029)(0.550 um)(4.753) = 2.69 um (for GT81) Hope that clears it up!

[@AstroQuest1]

@@Aero19612 Thank you James, it does clear it up! I was getting confused with the sensor resolution calculations in arcseconds. I have seen so many internet feeds with people spouting off numbers with more confusing explanations often contradicting themselves. Your presentation really clears things up for me. My current setup AT115 with the ASI1600 fortunately works well but I just ordered an Edge HD8 so along with a ASI294 so I wanted understands what to expect.

[@BruceMallett]

Excellent, thanks!

[@Aero19612]

Thanks for watching, Bruce!

[@BillRichards82]

Can you please show the math you used to compute the FWHM numbers on the slide at 15:15 (i.e. show the actual numbers in each equation)? When I plug in the values, I'm getting totally different results and I cannot figure out what I'm doing wrong. For example, for the C9.25, I get: [(1.029 * 0.550 um * 10) / (2350 * 1000)] * (180/Pi) * 3600 = 0.49674" Where am I going astray?

[@Aero19612]

Hi Bill: You are showing the FWHM in arc-sec and your value is correct. I'm showing the FWHM in um on my camera's pixel array. Also, I'm using the focal length as determined by a plate solve (2218 mm instead of 2350 mm per theory) 1.029 Lamda F = 1.029 (0.550 um) (2218 mm/235 mm) = 5.34 um Now, let's convert this into arc-sec: (5.34 um)/(2218 mm * 1000 um/mm)(180 deg/pi)*(3600 arc-sec/deg) = 0.4966 arc-sec Hope that helps!

[@BillRichards82]

@@Aero19612 Thank you!

[@neverfox]

At one point you give the HFR formula of 0.471* lambda * F, and later show the HFR min of 1.86 for the WO. When I try to solve for lambda, I get 0.831 (1.86 / 0.471 / 4.75), which isn't anywhere close to a visible light wavelength, at least not as typically reported in nm. Is there something about the units I'm not getting right?

[@neverfox]

I guess the 1.86 result is short of ideal so if wavelength is in micrometers and you're using green, that would mean "optimal" is 1.23 HFR. Is that right? So in this case conditions are such that you're focus is "as if" the wavelength was 831nm when it's really 550nm.

[@Aero19612]

Nice try! The 1.86 is the number that NINA reports as the HFR, but NINA does not say if their number is measured in pixels, arc-sec, microns, etc. so you really don't know what to compare it to. There's another issue at play here too. The 0.471 lambda F formula applies to the ideal point source (i.e., no atmosphere, no seeing, no guiding). The NINA autofocus HFR includes atmospheric dispersion and seeing effects (but not guiding, because I don't guide during autofocus). Thanks for watching!

[@patricezink5595]

Hi James, I tried to use your formula for my scope/camera, but I don't understand how you calculate the FWHM for your different scopes. Here is what I get versus you: William Optics F/4.75 : me 1.029*0.55*4.75=2.69 you 2.69 Redcat F/5 : me 1.029*0.55*5=2.83 you 2.77 Explore Scientific F/6.9 : me 1.029*0.55*6.9=3.90 you 3.88 C9.25 F/10 : me 1.029*0.55*10=5.66 you 5.34 Could you tell me what I'm doing wrong? Thanks

[@Aero19612]

Hi Patrice, You're doing just fine. The difference is caused by me using an Excel spreadsheet where I calculate the focal ratio using the focal length I get from plate solving an image rather than the theoretical focal length. For example, with my SCT, I get a focal length of 2218 mm instead of the theoretical 2350 mm. So my actual F/# is 2218/235 = F/9.44 instead of "F/10". The Redcat has a focal length of 250 mm and an aperture of 51 mm, so it's an F/4.9 instead of "F/5". Hope that explains it! Thanks for watching!

[@georgehatfield9473]

I came across a relatively new method of incorporating narrowband data into RGB and luminance images and I'm wondering if you have any experience with it. Charles Hagen developed the method which he describes on his website (night photons) under guides/advanced-narrowband-combination). It is dated November 2022. I've tried it, and it seems to work well, but I have not seen other references to this method other than Mike Cranfield's presentation on TAIC earlier this year (processing of NGC55). It involves using ColorCalibration to prepare an image of Ha lacking broadband data, along with Pixelmath methods to incorporate it into the red or luminance channel. I like this method since it does not require guessing as to the magnitude of multiplication factors to use in Pixelmath expressions designed to remove red channel "contamination."

[@Aero19612]

Interesting. Thanks for pointing this out. I still use the 2-step method but am certainly willing to try another method.

[@Aero19612]

I tried the ChannelCombination + BackgroundNeutralization approach. It works well. I also tried LinearFit on Red with Ha as the reference and then did the PixelMath subtraction. Seemed like I got better results with that approach. Could be just that data set. I didn't have as much luck when I tried to combine the nonlinear NewHa into the nonlinear RGB using his PixelMath. May need to play with parameters. But I did break the nonlinear RGB into R, G, and B and then blended the nonlinear NewHA into the R and recombined. That worked fine.

[@georgehatfield9473]

@@Aero19612 Thanks for looking into it! I'll give the split RGB method a try. Did you notice he has processes for most of the steps available to download (top of the page).

[@andyevans29]

Hi James, great video and well explained, I wish I had come across your channel a couple of years ago. It's seems you and I have (as of 2 years ago for you) exactly the same scopes, except I have WO GT 102. That being said now I have the edge HD 9.25, the stars are a lot more bloated than with my refractors, which is to be expected as you pointed out. My question is, as Astronomy tools shows I'm oversampled with my edge HD 9.25, 0.7X reducer and ZWO 2600MM Pro, would you advise binning, and would you also advise binning when collimating? Many Thanks Andy

[@Aero19612]

Thanks, Andy! First, being oversampled is not a problem, per se. but you’re not gaining anything either. You can shoot in Bin1 and then downsample to Bin2 in PixInsight ( or other software you may be using). You should not be losing true resolution if you bin on-camera, but binning after collecting the images gives you options. It also gives you 4x the file sizes, if that matters to you. If you have a project completed with Bin1, try converting those 8mages to Bin2 and reprocessing it. Then, see what you think.

[@Aero19612]

ooops. I would collimate in Bin1

[@andyevans29]

@@Aero19612 Hi James, thanks for the info, after rewatching your video I agree Bin 1 just to keep the resolution. I picked up a Hotech Advanced CT laser scanner today so I'll be collimating over the weekend, hopefully this should also help with bloated and egg shaped stars. Thanks again for the advice and keep producing your informative videos.

[@krzysztofchmielewski9246]

Hi. 11:06 the focal length for WO GT81 is 478mm. Yours 385 is coming from using reducer/flattener?

[@Aero19612]

That's correct. The 385mm is with the FLAT6Aiii installed.

[@jesuschrist2284]

In nina when looking at most recent sub, what is a good hfr?

[@Aero19612]

That’s a tough question because it depends upon seeing (and guiding) and aperture of the scope you’re using. You should get smaller HFR for larger diameter aperture and better seeing. I have NINA write the FWHM into the file name for use later, but not the HFR.

[@jesuschrist2284]

@@Aero19612 as a noob, i think its tough to determine if my subs are any good while im imaging.

[@chrisstrobel3439]

I need the dummies version of this 🙄

[@Aero19612]

Haha. Who knows, maybe I'm the dummy! If you can stand it, try watching it again. Thanks for giving it a go, Chris!