imhotep
Vendor - Optical Supports
Reged: 02/14/07
Posts: 1718
Loc: Floriduh
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My paper has all the formulas you need and I put them in an Excel spreadsheet but here is a quick and dirty way to find the values.
First I shoot what I want for a sub-frame exposure, recently 10 minutes for M51 at a dark site, to verify the object can take the exposure without blooming or saturating from LP. I then measured the background signal minus bias. For my 10m frame it was 800 ADU - 100 ADU bias. That leaves 700 ADU LP signal. Noise equals sqrt(LP signal) / sqrt(camera gain) = sqrt(700)/sqrt(1.3) = 23.2 ADU RMS. Now I want to drive the final stacked noise to around 6 ADU. That takes (noise per frame / final noise)^2 = (23.2 / 6)^2 = ~16 frames. I had plenty of time to shoot 16 10-minute frames so that is what I did. If I didn't then I would have used a shorter exposure and fewer frames.
If you do not know the gain of your camera then you can simply use the sqrt(LP signal). It should be guaranteed to result in at least the number of frames you need to drive the final noise below whatever value you set (start with 6). If you find the number of frames too small then increase your exposure time if you can.
The number of frames from the formula is around the maximum number of frames where adding more frames no longer improves the final picture. If you don't believe it then shoot at least twice as many and compare the result of stacking just the number the formula recommends with stacking all the frames. If you see a visible difference then lower the final noise value so it recommends the larger number of frames and do the experiment again. Try to find the final noise value that no longer seems to improve the stacked picture. It isn't going to be 1.
Edit - Addendum
The above assumes the exposure is long enough that LP noise is the dominant noise and not camera read noise. If that is not true then you will have to stack more frames than the formula gives and the new formula is at least #frames = (read noise / final noise)^2.
Excellent explanation. Thank you for attempting to bring the technical apsects of these equations down to a practical point where a user can "plug and chug".
A few questions:
1. How can I go about determining the value for my camera's gain? I'm currently shooting with a Rebel XT.
2. In your example above, where did the target value of 6 ADU for the final stacked image come from? Does this value serve as an all-around good target for most situations, or is it taken from one of the tables in your paper (and is therefore based upon another factor that the user must know and be ready to input into the table)?
3. After taking the prelimenary test photo to check for blooming and LP saturation, which software is used to read the background signal off of it? Also, where does the bias value come from?
Chuck, I thoroughly enjoyed reading your paper. I'm barely competent enough with mathematics and image processing theory to keep up. Thank you for taking the time to educate us.
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Curt
www.opticalsupports.com
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Chuck Anstey
scholastic sledgehammer
Reged: 01/17/05
Posts: 960
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I didn't say anything about how many frames to stack, just how long the subs should be.
I agree I may have taken your statement slightly out of context. I took it you implied that all of this discussion is irrelevant to 30 second exposures and I disagree with that sentiment.
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But as you point out in the next post, there isn't really a "wall of diminishing returns", but a curve. So that makes the number of frames to be a mixture of other factors and still not a calculation. It is a matter of trial and error, personal taste, and time.
The number of frames to stack is not arbitrary and definitely has a calculation to achieve the "best" there can be. All I said was that your imaging system may have a different final noise value where you hit the "wall". It is a curve but it is hyperbolic and has a very sharp "knee". I had some sub-frames to stack where stacking 28 was visibly better than 14 but that 56 was visually indistinguishable from 28. I called that a wall. Now maybe it was really 24 or 26 but I didn't really care. The formula said somewhere around 28-32 frames but I was going to bed so I just let it keep shooting to see what I could get and it turned out the equation held up.
You may disagree with my research and find out something I missed. I disagreed with John C. Smith's article because it didn't hold up against my own experience. I did the math and research and figured out why. I am sure someone will take my research even farther and come up with even better formulas that take more variables into account.
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jgraham
Postmaster
Reged: 12/02/04
Posts: 11575
Loc: Dayton, Ohio
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Clownfish; you might find digital imaging a little more forgiving than you expect. I normally save all of my uncombined images as it is those I finally work with, but I also go ahead and have the software align and combine in real-time just to see how things are going (and I like to play with the image as it builds). To keep things simple I set the minumum match quality to zero so it stacks all of the images no matter how bad they are. Now keep in mind I'm not guiding so I take'm as I get'm. Normally things go along rpetty well, but you get the occasional 'bounce', and wobble, and gust of wind, and what you'll see on the image is uauslly a minor disturbance (because statistically it is minor) and it quickly fades into the background mush. I could very well just use the image combined in real-time, but by having the source images I can go back and sift through them and pick and choose the ones I want (and run them through functions like drizzle offline). I'll also often find little details that got lost like satellites crawling across the field.
Sooo, again, I think you'd find that digital imaging is more forgiving than you'd think.
Heh, heh, I also found I could do a fair job of simulating film if I just locked the black point at zero and the white point at 65535 and let'r go. Of course that's not quite accurate because you'd fix a lot of the image in the darkroom, but it's pretty close.
One last point (I promise) when I shoot wide fields that are comparable to a full 35mm frame, the acceptance rate is pretty near 100% (keeping all of the frames). The biggest problem is when an airplane flies through the field. I'll be doing some wide field work if this weather ever clears.
-John
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-John
The best advice on imaging I've ever been given... don't forget to look! 
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ClownFish
Post Laureate
Reged: 04/26/05
Posts: 6254
Loc: Baghdad, Iraq
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Thanks for the details John. Now if I ever can accept a computer at my scope I'll be there. Right now I really enjoy the primitive side - and all those cables and electronic hardware distract from the joy of a simple setup (for me folks - please do not take this personal slam against computer lovers).
CF
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Learn all about Polar Alignment and Manual Guiding on my website at www.PetesAstrophotography.com! Or visit my Foreign Service Blog!
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jgraham
Postmaster
Reged: 12/02/04
Posts: 11575
Loc: Dayton, Ohio
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Clownfish; now I'm with you on that. If I ever get the chance to get out under some truly dark skies I'd prefer to have my eye up to an eyepiece. About the only photography I'd do would be to have a patrol camera set up on a curved-bolt tracker. You've got one picture of M51 I just love, it reminds me of an opportunity I had about 30 years ago to observe from Cades Cove in the Smoky Mountains with my homebuilt 6" RFT. It was the first and only time I've seen the arm between the two galaxies visually.
One of these days...
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-John
The best advice on imaging I've ever been given... don't forget to look!
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Chuck Anstey
scholastic sledgehammer
Reged: 01/17/05
Posts: 960
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Imhotep,
First my paper is based upon temperature contolled CCD imaging. While the general principles should hold up for uncooled imaging, the amount of camera noise may be a moving target depending on outside temp, length of exposure, and number of frames shot in a row.
1. How can I go about determining the value for my camera's gain? I'm currently shooting with a Rebel XT.
The only way I know to compute the gain is to measure the LP noise across several frames and use the formula Measured noise = sqrt(LP signal) / sqrt(gain) and solve for gain. I'm not sure how accurate that really is in the real world. I will be working with Craig Stark, author of PhD guiding and Nebulosity, to create a program to do this in the near future.
2. In your example above, where did the target value of 6 ADU for the final stacked image come from? Does this value serve as an all-around good target for most situations, or is it taken from one of the tables in your paper (and is therefore based upon another factor that the user must know and be ready to input into the table)?
The factor of 6 to 7.5 ADU comes from my paper where the Poisson distribution becomes more normal at around lambda = 15 so you need 15 ADU from the signal to easily detect it from its own noise. To get enough separation from the background (theortically 0), a noise value of half that has the background and the lowest desired signal touch at one standard deviation (0 + 7.5 = 15-7.5). If you prefer more frames then you go lower to lambda = 12 and the noise goes to 6 ADU.
3. After taking the prelimenary test photo to check for blooming and LP saturation, which software is used to read the background signal off of it? Also, where does the bias value come from?
I used CCDSoft but that is for my SBIG camera. For the XT I assume you would convert RAW into 16-bit per color TIFF files and then you can measure it from Photoshop. The bias is 100 for my camera but the XT may subtract out the bias before creating the RAW picture. You would have to take a few instant dark frames and then measure the background value of the RAW picture.
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ribuck
sage
Reged: 11/01/05
Posts: 329
Loc: Newcastle, England
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All,
Whilst I appreciate everyones input, I would just like to point out that the question I asked was a simple question about the accuracy of a particular mount, and it's abilities for imaging unguided.
I had hoped to get feed back from others who had experience of this mount, but unfortunately this posting seemed to have been hijacked and blown way out context of the original question, with mathematical discussions on calculating exposures.
I would like to remind people that I did post this in the beginners forum and it can be very frustrating for newbies like myself who are trying to learn when we get bombarded with unnecessary information.
Please don't think i am not grateful for peoples help, i really am, but please bare this in mind in the future peeps.
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ClownFish
Post Laureate
Reged: 04/26/05
Posts: 6254
Loc: Baghdad, Iraq
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While I appreciate that straying from the topic may lead to confusion, I do not feel we strayed too far from the evolving discussion.
You also asked specific questions to help keep this going and evolving, and your original question was answered several times, with varying degrees of opinion.
You: Quote:
i'm basically taking away form this that there is no set hard and fast rule and that it all depends on your setup.
I would only say the thread was hijacked if you hadn't asked questions that drive the answers:
You: Quote:
I always thought it better to do 10x 2 minute exposures than 40x 30sec , as you pick up more detail in the longer exposure. Am i wrong ?
You: Quote:
This has always been a question of mine when i see peoples stunning images where they have taken different lengths of luminance exposures to the RGB, i never understood how they came up with these numbers.
Most of the discussion in this thread dealt with tracking on low-cost mounts, and exposure calculations. I don't feel we went too far off topic. But if I did, and caused some confusion, please accept my apologies!
Clear Skies to you!
CF
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Learn all about Polar Alignment and Manual Guiding on my website at www.PetesAstrophotography.com! Or visit my Foreign Service Blog!
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ribuck
sage
Reged: 11/01/05
Posts: 329
Loc: Newcastle, England
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Clownfish, I'm just dont think going into mathematical formula's is the right place in a beginners forum, in the main Imaging forum Yes, but not in a beginners forum.
I just want to stress again that i do appreciate everyones help, but for beginners that level of discussion is a bit advanced for beginners in my mind.
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Chuck Anstey
scholastic sledgehammer
Reged: 01/17/05
Posts: 960
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Quote:
ok, well if anyones up for an experiment, lets get someone to do 10x2 min exposures and 4x5 min exposures of the same subject using the same kit and site and see what we end up with. Anyone game ?
I answered your question quite clearly and maybe more than you intended but it required mathematics and empirical results for a complete answer. I make no assumptions about the math skill of the readers and being an advanced imager doesn't mean you are better at math or statistical analysis or that beginners are not. I hope for the ones that do understand the math that some are happy to find a way to calculate exposures and sub-frame counts instead of having to do lots of experiments to find the same answer.
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Charlie Hein
Postmaster
Reged: 11/02/03
Posts: 11211
Loc: 26.06.08N, +80.23.08W
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Hold on folks - I don't want to see this conversation devolve or to see anyone taking offense here.
You make a very good point, Chuck - but I can also clearly see ribuck's viewpoint on this as well... the math involved is definitely a part of the issue, but folks can also sometimes get the sense (rightly or wrongly) that their original question just got "run over" with a response that wasn't *quite* what they were looking for. That doesn't mean that they aren't *interested* in what you're talking about by any means.
What happens here is that the answers they were actually looking for (which was in this case about the average exposure length one could expect to get from a particular type of mount) tend to get buried in the more esoteric "side" discussion which is drawing a lot more posts than the original question is. This can be an especially sticky situation when the poster isn't on multiple times during the day like a lot of us are. I for one felt the need to PM ribuck with a pointer to a post that answered his original question because of this.
There's no question of intent or malice here but even so, unintentional or not it's "sort of" a thread hijack in a sense. I wish I knew a good way to deal with it, but I don't - nobody really did anything *wrong*.
I do have a suggestion that would help with the sensitivity over the issue with the math... I think that you (or anyone who posts on these subjects for that matter) *should definitely* make some assumptions with regard to math skill when you discuss formulas such as these - especially and particularly in the case of the Beginners forums. These forums have a very large readership who are keenly interested in astronomy and astrophotography but who also may not have had any exposure to the math at all - for example, many simply aren't old enough to have taken this level of math in school yet (or they are only just now taking it).
My strong suggestion would be to turn every opportunity to discuss these subjects into an even wider educational experience than you already do. I suggest that when you discuss a mathematical formula - especially in a "beginner's" forum - you should always take the extra time to explain the formula you're talking about so that your audience completely understands how to use it.
After all, it's a lot like handing a caveman a power drill and not telling him he has to plug it in to make it work (no offense to you cavemen out there). If a person can't understand how to use a tool, it's worthless to them.
I hope that you understand that I'm not in any way trying to put you on the spot about this, Chuck. I really feel that this should be happening with anyone who is discussing mathematical tools. I also understand that there's going to be a certain percentage of folks whose eyes will glaze over regardless of how you present the material...
...that said, if when you do this even one person gets the lightbulb switched on with regards to the math, you have turned it from a stumbling block to an even greater enabler for that person. That's a really valuable thing.
Charlie
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Weston CSC:
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imhotep
Vendor - Optical Supports
Reged: 02/14/07
Posts: 1718
Loc: Floriduh
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Chuck, thank you for your answers. This is helping, I think I'm almost there.
Regarding the equation:
1. Measured Noise = √(LP signal) / √(gain)
I notice that this equation is the same as the one I first replied to (see #1506845 above):
2. Noise equals sqrt(LP signal) / sqrt(camera gain)
On the right side of the =, both 1 and 2 are the same, so I assume we are solving for basically the same thing. In my case, since I do not know what my camera's gain is, I guess I have two unknowns. So if I measure the noise across several dark frames, thus determining a value for "measured noise", wouldn't I then be eliminating the need to know what my camera's gain is? I'm probably doing a terrible job of asking this question. If so, I apologize.
Assuming what I just said is close to being right, my next step is to learn how to measure the noise from my RAW files in photoshop. I'm experienced with RAW shooting and PP in Adobe Camera RAW. What I'm not clear on is how to measure the LP signal from the images. Am I just looking for the brightness value of the pixels in the converted TIFF(i.e. 0 - 255)? Or, am I going to sum the individual RGB values together?
Neither of those seem right actually. In order to come close to a value like you did above (700 ADU), the pixel values of my image would have to be near white, and obviously they won't be. They should be black.
If I can get a brief explanation on how to measure the noise from the TIFFs in photoshop, I'll be golden
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Curt
www.opticalsupports.com
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Chuck Anstey
scholastic sledgehammer
Reged: 01/17/05
Posts: 960
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I wasn't offended and I'm sorry I didn't adjust my post more to not sound that way.
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Please adjust your display so you can just barely differentiate the darkest two boxes in the picture's calibration bar before evaluating the picture. If they are easily distinguished (typical LCD) reduce your gamma to see an accurate picture. Otherwise shadow detail that should be hidden or very dark will be easily seen and look unnatural and overprocessed.
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Charlie Hein
Postmaster
Reged: 11/02/03
Posts: 11211
Loc: 26.06.08N, +80.23.08W
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Quote:
I wasn't offended and I'm sorry I didn't adjust my post more to not sound that way.
I'm very glad to hear it - I wanted to be certain of it and now I am...
Charlie
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Weston CSC:
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ribuck
sage
Reged: 11/01/05
Posts: 329
Loc: Newcastle, England
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Hey Guys, I appreciate all the help, it's just that when you're completely new to all this it can be hard to grasp what people are talking about when you are not familiar with all the components involved. I'm keen to learn, it's just a steep learning curve.
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ribuck
sage
Reged: 11/01/05
Posts: 329
Loc: Newcastle, England
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But i suppose to be fair i'm picking up birs of it, so something must slowly be sinking in.
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ClownFish
Post Laureate
Reged: 04/26/05
Posts: 6254
Loc: Baghdad, Iraq
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One thing about CN, is that when you ask a question, 10 others out there have the same thought or similar one, and just didn't dare ask. Then we start to answer it, but the question evolves long after your original question was answered. So we tend to just keep on answering questions and the end result looks totally different than the beginning.
Keep those questions coming!!!
CF
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Learn all about Polar Alignment and Manual Guiding on my website at www.PetesAstrophotography.com! Or visit my Foreign Service Blog!
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ribuck
sage
Reged: 11/01/05
Posts: 329
Loc: Newcastle, England
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I guess from now on once i get the information i need i'll just treat the rest as a bonus weather I understand it or not.
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ClownFish
Post Laureate
Reged: 04/26/05
Posts: 6254
Loc: Baghdad, Iraq
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That's the spirit!
CF
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Learn all about Polar Alignment and Manual Guiding on my website at www.PetesAstrophotography.com! Or visit my Foreign Service Blog!
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Jeremy@za
professor emeritus
Reged: 02/28/05
Posts: 704
Loc: Cape Town, South Africa. 33 56...
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Clownfish - sorry to hijack, but looking at your imaging setup - is that a .975" eyepiece in your guidescope?
J
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