From: stanleymm@e... Date: Mon Sep 3, 2001 10:18 pm Subject: Re: S/N & f-ratio (was Latest ARGO Images) --- In SBIG@y..., "Ron Wodaski" wrote: << I can understand that one could gain something by taking the time to learn all of the theory, but I am immersed in the practical side ... >> The equation for S/N is very rich and it's not possible to reduce it to simple maxims, but here are a few. Enjoy! Stan Exp times: 1) Increasing the exp time by 2x will increase the S/N by approximately 2x for short exp up to the point where sky glow becomes significant. At that point ("sky limit") the S/N will rise by about 1.4x for every 2x increase in exp time. Until you reach another limit that is imposed by the quality of your flat-field, at which point the S/N barely increases with exp time. (there are other limits as well, esp seeing for stellar S/N). 2) Breaking up an exposure into shorter sub-exposures will significantly decrease (hurt) the S/N if the sub-exps do not reach into the "sky limit". If each sub-exp has achieved "sky-limit" then there is no significant S/N harm in doing them (compared to a single long exp). Note: you must take measurements and do the math in order to know your "sky limit". Binning: 1) Binning short exp will dramatically increase the S/N (compared to unbinned) but binning long exp ("sky limit") will have little effect on S/N and can even harm it if the image is undersampled. 2) Binning (2x) is essentially S/N equivalent to decreasing the f- ratio by 1 stop, except for very short exp (in which case shortening the FL is better). Resolution: 1) For stellar and small feature S/N, resolution and sampling are significant determinants. Finer resolution = greater S/N, unless it is undersampled. 2) Actual resolution is determined not only by FWHM but also S/N. Filters: 1) Filters can improve S/N by selectively removing sky-glow while retaining most of the signal. If the signal's spectral profile is similar to sky-glow (e.g. stars & moonlight) then the filter will harm S/N. Resampling (resizing): Resampling will proportionally affect the "pixel S/N" (which is roughly correlated with "visual appearance") in approximately the same way as changing the f-ratio or binning. It will have no effect on "object S/N". F-ratio: Changing f-ratio (with constant aperture) will affect the "pixel S/N" in approximately the same way as resampling. . It will have only a small effect on "object S/N". From: stanleymm@e... Date: Tue Sep 4, 2001 10:05 pm Subject: Re: S/N & f-ratio - Stan --- In SBIG@y..., "John Smith" wrote: > A nice summary, Stan. I seem to remember you wrote something a while > back about how to determine the sky limit. I think I recall 2000e- > for an ST-8E. Because of the damaged/missing SBIG archive here, I > wasn't able to find the original post. If you get a chance, would > you restate/repost the sky limit discussion? Thanks John, "Sky limit" is the zone where the sky noise overpowers the readout noise. A simple dictum would be to expose long enough so that camera noise is only about 10% of the background noise. For a cold camera (i.e. ignoring dark current) this occurs when the sky noise > 3x readout noise. For an ST-7/8 this means that the background "should" be at least 1,500 ADU (assuming gain=2.3). What that means is that if you expose long enough to get background count > 1,500 ADU then you will have essentially overcome the readout noise. Shorter exposures will suffer from a greater impact of the camera noise. So if you are doing sub-exposures then it's a good idea to make them long enough to pass that zone. To examine this further, I just did some recent investigations where I looked at the pixel S/N of objects of various intensities as a function of time. To assess the noise curves, I calculated a ratio of the "pure signal S/N" to "full S/N" and plotted it by exp time. This ratio basically tells you how close you are to "perfection". This ratio curve has a very steep beginning followed by a pronounced "elbow" where it flattens out. This "elbow" does not move very much (in terms of exp time) when you vary the dark current or signal strength. But it does move based on sky-glow &/or f-ratio. Basically the curves show that the exp times for overcoming ST-7/8 camera noise are in the range of 300-1200 seconds depending on sky- glow and f-ratio. For dark skies &/or slow f-ratio &/or filters you should expose for at least 20 minutes. For bright skies &/or fast f- ratio (unfiltered) you may be able to reduce the exp time to as little as 5 minutes. It is not advisable to do exposures less than 5 minutes because you are fighting a steep uphill battle against camera noise (bad news for "T&A"). If you want to explore these relationships for yourself, here is a simplified eq (primarily ignores flat and PSF) for determining the "pixel S/N": SNp = Sp*t / sqr-root(Sp*t + Bp*t + (1+1/x)*Dc*t + Rn^2*En) Where: t = time in seconds Sp = Signal count per second per pixel Bp = Sky count second per per pixel Dc = Dark current per second per pixel x = number of calibration dark frames Rn = readout noise per pixel En = number of sub-exposures for ST-7e/8e: Rn = 15e/pix Dc = 0.1e/sec/pix at –20C Bp = 2.5e/sec/pix for rural dark sky at f/10 Stan From: stanleymm@e... Date: Wed Sep 5, 2001 5:30 pm Subject: Re: S/N & f-ratio - Stan --- In SBIG@y..., "Mike Cook, AF9Y" wrote: > How did you derive 1500 ADU from the readout noise of 15e > and gain of 2.5 e/ADU? Mike, I made an error in the calculation for ST-7/8 "sky limit". The basic idea is that the sky noise should be at least 3x times the readout. Because noise adds quadratically, a 3x difference means that the readout noise only contributes about 5% to the total noise (sqrt(1^2 + 3^2) = 3.16 vs sqrt(3^2)=3 if there was no readout). That is important because the readout noise does not scale with time, so you should expose long enough to render it harmless. For ST-7/8 the readout noise is 15e so sky noise should be > 45e, which means that the background should be >2000e or 800 ADU (I have no idea how I came up with that 1,500 yesterday ). For an ST-10 the readout noise = 7e, so sky noise should be > 21e, which is a level of 440e or 660 ADU. Of course the ST-10's smaller pixels will accumulate the sky-glow at only 75% the rate of ST-7/8, so the actual difference in exp times is not much. Stan From: stanleymm@e... Date: Thu Sep 6, 2001 4:33 pm Subject: Re: S/N & f-ratio - Stan --- In SBIG@y..., "Mike Cook, AF9Y" wrote: > Shouldn't you divide instead of multiplying 440e by > 1.5e/ADU to obtain the objective ADU number? That > would give a result of 294 instead of the 660. Yes of course, sorry about that. My further comments were based on e counts and are still valid (I try to always think in term of e, not adu). (I've got to stop trying to work and do these msgs at the same time. Or least I've got to start proofing...) > Also, SBIG shows the readout noise of the ST-10E as 11e. > You used 7e. The Kodak spec sheet says 7e is normal, and that is consistent with what I measured for an actual ST-10. But the spec sheet also says the chips may run as high as 12e (maybe SBIG selected a conservative number). So, (hopefully) the "final" correction is: ******************************************************** For ST-7/8 the readout noise is 15e so sky noise should be >45e, which means that the background should be >2000e or 800 ADU. For an ST-10 the readout noise = 7e, so sky noise should be > 21e, which is a level of 440e or 300 ADU. Of course the ST-10's smaller pixels will accumulate the sky-glow at only 75% the rate of ST-7/8, but the difference in exp times is still quite significant. These figures are based on Kodak nominal specs. There is significant variations, so you should measure your own camera. ******************************************************** OK, now find the latest error! Stan