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Another Q: Dark Noise/Dark Current

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  • Orlando Andico
    So here s another situation which has me scratching my head. The older Kodak sensors (e.g. KAF-1603..) are rated at 0.9 e-/sec dark curent at 0 Celsius. Now
    Message 1 of 12 , Mar 12, 2013
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      So here's another situation which has me scratching my head.

      The older Kodak sensors (e.g. KAF-1603..) are rated at 0.9 e-/sec dark
      curent at 0 Celsius.

      Now there's some other figure floating around that the
      undifferentiated sky fog at a dark sky site is c.a. 2 e-/sec.

      So.... I know this is very crude, but does that imply that you will
      get no better than 3 dB SNR? (every time you get 2 electrons from your
      object, you also pick up almost 1 electron from dark current). Or is
      that 0.9 e-/sec from SBIG excessively pessimistic? it still means the
      SNR is going to be low, because prolonging your exposure to get more
      signal also gets you a proportional amount of dark current...
    • Ron Wodaski
      Signal and noise don t work that way, you ll be glad to know. :-) The relationship is quadratic, not linear, and so longer exposures will (slowly) drive down
      Message 2 of 12 , Mar 12, 2013
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        Signal and noise don't work that way, you'll be glad to know. :-) The relationship is quadratic, not linear, and so longer exposures will (slowly) drive down the noise (uncertainty) level.

        As as far as unwatned signal (e.g., skyglow) is concerned, that is a bit more pessimistic. But the photons of your target are always being added to the unwanted signal, and you will also see a little improvement from a longer accumulated exposure time.

        At a dark site, the sky background might be 50 ADU, while your signal is 100 ADU. Nice margin. At a bright site, the background might be 500 ADU or more - but your signal is still 100 ADU. Now, the noise inherent in the signal is the square root of the signal, so in addition to the read noise there is shot noise. The trick, therefore, is that you need a dim enough background level to be able to pull out your signal. So you can't image M33 during the daytime, but you can get at least the brighter parts of it even in a suburban backyard. <g>

        Ron Wodaski



        On Mar 12, 2013, at 12:45 PM, Orlando Andico <orly.andico@...> wrote:

        > So here's another situation which has me scratching my head.
        >
        > The older Kodak sensors (e.g. KAF-1603..) are rated at 0.9 e-/sec dark
        > curent at 0 Celsius.
        >
        > Now there's some other figure floating around that the
        > undifferentiated sky fog at a dark sky site is c.a. 2 e-/sec.
        >
        > So.... I know this is very crude, but does that imply that you will
        > get no better than 3 dB SNR? (every time you get 2 electrons from your
        > object, you also pick up almost 1 electron from dark current). Or is
        > that 0.9 e-/sec from SBIG excessively pessimistic? it still means the
        > SNR is going to be low, because prolonging your exposure to get more
        > signal also gets you a proportional amount of dark current...
        >
        >
        > ------------------------------------
        >
        >
        >
        >
      • Stan
        ... Or expose long enough to improve the S/N as necessary. Whatever the S/N is for a given exp it will improve by 1.4x for every doubling of exp time (assuming
        Message 3 of 12 , Mar 12, 2013
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          --- Ron Wodaski <yahoo@...> wrote:
          > ... need a dim enough background level to be able to pull
          > out your signal.

          Or expose long enough to improve the S/N as necessary. Whatever the S/N is for a given exp it will improve by 1.4x for every doubling of exp time (assuming the conditions remain the same).

          Ignoring all camera noises (i.e. examining the virtual image):
          suppose sky = 100e- and object-signal = 10e- (both are photon counts from the angular extent of the object; pixels are irrelevant because we are ignoring camera noise). Then a 1 sec exp would yield S/N = 10/sqrt(10+100) = 0.95. Object S/N must be at least 3 for the object to be detected, so it would be invisible in a 1 sec exp. But a 10 sec exp would yield S/N = 10*10/sqrt(10*10 + 10*100) = 3 and now the object is visible.

          One could image M33 in daylight but it would require a humongous amount of time/signal to overcome the sky flux (probably at least a few weeks worth).

          Stan

          (edited for typos)
        • geoff
          ... Not to mention the fact that you would need very short exposures to avoid saturating the camera with sky signal, so read noise would also be a big factor.
          Message 4 of 12 , Mar 15, 2013
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            --- In ccd-newastro@yahoogroups.com, "Stan" <stan_ccd@...> wrote:
            >
            > One could image M33 in daylight but it would require a humongous amount of time/signal to overcome the sky flux (probably at least a few weeks worth).
            >
            > Stan
            >
            > (edited for typos)

            Not to mention the fact that you would need very short exposures to avoid saturating the camera with sky signal, so read noise would also be a big factor. Still, if someone had time on their hands it would be an interesting project--maybe try a bright open cluster, rather than a faint galaxy.
            >
          • Ron Wodaski
            No, read noise would not be a factor. The noise inherent in the unwanted signal (the bright sky) would utterly swamp read noise as a factor. it would simply be
            Message 5 of 12 , Mar 15, 2013
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              No, read noise would not be a factor. The noise inherent in the unwanted signal (the bright sky) would utterly swamp read noise as a factor.

              it would simply be a matter of exposing long enough to make the small difference in brightness between the sky and the target resolve into an image by accumulating signal the old-fashioned way: by overcoming the shot noise with lots of data.

              Ron Wodaski



              On Mar 15, 2013, at 4:39 PM, geoff <ghsmith45@...> wrote:

              >
              >
              > --- In ccd-newastro@yahoogroups.com, "Stan" <stan_ccd@...> wrote:
              >>
              >> One could image M33 in daylight but it would require a humongous amount of time/signal to overcome the sky flux (probably at least a few weeks worth).
              >>
              >> Stan
              >>
              >> (edited for typos)
              >
              > Not to mention the fact that you would need very short exposures to avoid saturating the camera with sky signal, so read noise would also be a big factor. Still, if someone had time on their hands it would be an interesting project--maybe try a bright open cluster, rather than a faint galaxy.
              >>
              >
              >
              >
              >
              > ------------------------------------
              >
              >
              >
              >
            • Stan
              ... It is possible to calculate the exp time necessary to achieve a particular SNR for an object by knowing the flux of the object and the ratio of object to
              Message 6 of 12 , Mar 16, 2013
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                --- Ron Wodaski <yahoo@...> wrote:
                > it would simply be a matter of exposing long enough to make
                > the small difference in brightness ...
                > by overcoming the shot noise with lots of data.

                It is possible to calculate the exp time necessary to achieve a particular SNR for an object by knowing the flux of the object and the ratio of object to sky brightness:

                SNR = sqrt(t) * f/ sqrt(f + f*r)
                Where t = time (seconds)
                f= total flux of object (detected photons per second)
                r = ratio of sky/object

                some simple algebra yields:
                t = SNR^2 * (1+r)/f

                approximation for large r:
                t = SNR^2 * r/f

                An object S/N > 3 is required for certain detection so a good approximation is:

                t = 10 * r/f

                I guestimate that daytime sky (varies by alt-az, time of day, atmosphere...) is about a million times brighter than the brighter parts of a bright galaxy. A 12-14" aperture and decent camera might detect about 1000 photons/sec from that galaxy (for the extent of the brighter area). So:

                t = 10 * 1,000,000 / 1,000 = 10,000 sec = 2.8 hours

                The sky would quickly swamp a CCD and thus require a fast video camera. 30fps would generate about a quarter million frames. That's actually not so bad, I've handled that many doing high speed intensified DS imaging.

                So with the right equipment it might not be terribly difficult to image a galaxy in the daytime. I might try it except that I do not have a goto mount and so the real challenge would be to aim the scope and guiding would be nearly impossible so it would have to be very well polar aligned and such. But it might be interesting to image a random patch of daytime sky for several hours...

                Stan

                (revised and replaced this msg)
              • larryl
                Stan, I am always impressed with your knowledge of signal/noise calculations etc. Would you recommend a good book for this subject matter? The Statistics 101
                Message 7 of 12 , Mar 17, 2013
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                  Stan,

                  I am always impressed with your knowledge of signal/noise calculations etc. Would you recommend a good book for this subject matter? The Statistics 101 book does not cover this. ;-)

                  Thanks.

                  Larry Leitch


                  --- In ccd-newastro@yahoogroups.com, "Stan" <stan_ccd@...> wrote:
                  >
                  > --- Ron Wodaski <yahoo@> wrote:
                  > > it would simply be a matter of exposing long enough to make
                  > > the small difference in brightness ...
                  > > by overcoming the shot noise with lots of data.
                  >
                  > It is possible to calculate the exp time necessary to achieve a particular SNR for an object by knowing the flux of the object and the ratio of object to sky brightness:
                  >
                  > SNR = sqrt(t) * f/ sqrt(f + f*r)
                  > Where t = time (seconds)
                  > f= total flux of object (detected photons per second)
                  > r = ratio of sky/object
                  >
                  > some simple algebra yields:
                  > t = SNR^2 * (1+r)/f
                  >
                  > approximation for large r:
                  > t = SNR^2 * r/f
                  >
                  > An object S/N > 3 is required for certain detection so a good approximation is:
                  >
                  > t = 10 * r/f
                  >
                  > I guestimate that daytime sky (varies by alt-az, time of day, atmosphere...) is about a million times brighter than the brighter parts of a bright galaxy. A 12-14" aperture and decent camera might detect about 1000 photons/sec from that galaxy (for the extent of the brighter area). So:
                  >
                  > t = 10 * 1,000,000 / 1,000 = 10,000 sec = 2.8 hours
                  >
                  > The sky would quickly swamp a CCD and thus require a fast video camera. 30fps would generate about a quarter million frames. That's actually not so bad, I've handled that many doing high speed intensified DS imaging.
                  >
                  > So with the right equipment it might not be terribly difficult to image a galaxy in the daytime. I might try it except that I do not have a goto mount and so the real challenge would be to aim the scope and guiding would be nearly impossible so it would have to be very well polar aligned and such. But it might be interesting to image a random patch of daytime sky for several hours...
                  >
                  > Stan
                  >
                  > (revised and replaced this msg)
                  >
                • Stan
                  ... Not any single book (haven t written it yet ). But one of the most succinct books that influenced much of my thinking in this area has been Howell s
                  Message 8 of 12 , Mar 17, 2013
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                    --- "larryl" <k3fit@...> wrote:
                    > Would you recommend a good book for this subject matter?
                    > The Statistics 101 book does not cover this.

                    Not any single book (haven't written it yet <g>). But one of the most succinct books that influenced much of my thinking in this area has been Howell's "Handbook of CCD Astronomy". Added to that is some acquired knowledge and training in statistics and information theory.

                    Once you orient your thinking to an information theory approach (object analysis) with some basic statistical tools then it isn't that difficult to devise particular analyses for imaging issues.

                    In that regard: It looks like I will conduct a workshop on an informal information theory approach to AI at the upcomming 2013 AIC.

                    Stan
                  • Stan
                    ... On second thought: There are some complications not considered in the first msg. The most serious problem is CCD PRNU (Photon Response Non-Uniformity), an
                    Message 9 of 12 , Mar 17, 2013
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                      --- "Stan" <stan_ccd@...> wrote:
                      > might not be terribly difficult to image a galaxy in the daytime

                      On second thought:

                      There are some complications not considered in the first msg. The most serious problem is CCD PRNU (Photon Response Non-Uniformity), an inherent variation of pixel sensitivity (QE) within an individual CCD. Generally for AI PRNU is trivial and is easily calibrated out via flats. But the impact of PRNU increases with sky and object fluxes and it would be extremely difficult to produce a flat that could deal with the enormous sky flux of this situation.

                      The pixel noise from flat fielding (pffn)=(s+sky)/flatSN

                      A typical AI master flat made from 20 frames, each with avg 30ke-, has S/N near 700. Flat effect on the object varies by sampling (n pixels within object) but let's say the object subtends 100x100 pixels (10k) so if we used a typical AI flat (S/N = 700) in this situation then:

                      pffn = (10,010,000,000/10k) / 700 = 14.3ke-/pix

                      that is not at all trivial and must be included in the S/N eq:

                      object S/N with flat effect = sqrt(t) * s / sqrt(s + sky + p*ffn^2)

                      using the prior numbers:

                      S/N with no PRNU/flat = sqrt(10k) * 1k / sqrt(1k + 1k*1m)
                      = 100* 1k/31.6k = 3

                      S/N with flat = sqrt(10k) * 1k / sqrt(1k + 1k*1m + 1k*14.3k^2)
                      = 100 * 1k / sqrt(1b + 204b) = 0.0004

                      It could be hopeless to create a flat with sufficient S/N to reasonably overcome this dynamic. You could make a 3 hour flat but the flat target would have to be impeccable because the slightest defects would "print thru" (e.g. you could not use the sky because at that level it would be too disturbed by "invisible" stars and such).

                      So it may be completely hopeless to actually image a galaxy in daylight without significant offset/drizzle, which can overcome much of this problem by averaging out PRNU / flat error. I've not yet calculated how much dithering would be necessary but any dithering is very problematic because there are no guide stars and so it would require an ultra-precise mount with a coordinated control link to the image stream so that the stacking software could know how to align the frames.

                      This would be a very difficult challenge!

                      Stan
                    • Stan
                      ... I take that back. You could use a diffusion screen on the aperture. Of course, the scope should have absolutely no light leaks. So if you took a 3-4 hour
                      Message 10 of 12 , Mar 17, 2013
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                        > ... make a 3 hour flat but ... you could not use the sky...

                        I take that back. You could use a diffusion screen on the aperture. Of course, the scope should have absolutely no light leaks.

                        So if you took a 3-4 hour daylight screen-sky-flat and a 3-4 hour image that tracked well then it might be possible...

                        Stan
                      • Ken Harrison
                        I d also recommend Howell s book. It covers the whole subject of astronomical CCD s very well (and gives some interesting stuff on spectroscope applications!)
                        Message 11 of 12 , Mar 17, 2013
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                          I'd also recommend Howell's book.
                          It covers the whole subject of astronomical CCD's very well (and gives some
                          interesting stuff on spectroscope applications!)



                          On 18 March 2013 03:01, Stan <stan_ccd@...> wrote:

                          > **
                          >
                          >
                          > --- "larryl" <k3fit@...> wrote:
                          > > Would you recommend a good book for this subject matter?
                          > > The Statistics 101 book does not cover this.
                          >
                          > Not any single book (haven't written it yet <g>). But one of the most
                          > succinct books that influenced much of my thinking in this area has been
                          > Howell's "Handbook of CCD Astronomy". Added to that is some acquired
                          > knowledge and training in statistics and information theory.
                          >
                          > Once you orient your thinking to an information theory approach (object
                          > analysis) with some basic statistical tools then it isn't that difficult to
                          > devise particular analyses for imaging issues.
                          >
                          > In that regard: It looks like I will conduct a workshop on an informal
                          > information theory approach to AI at the upcomming 2013 AIC.
                          >
                          > Stan
                          >
                          >
                          >



                          --
                          "Astronomical Spectroscopy - The Final Frontier" - to boldly go where few
                          amateurs have gone before....
                          http://tech.groups.yahoo.com/group/astronomical_spectroscopy/?yguid=322612425
                          "Astronomical Spectroscopy for Amateurs" - Springer
                          "Grating Spectroscopes - How to use them" - Springer


                          [Non-text portions of this message have been removed]
                        • lmleitch02
                          Thanks guys. I will get it and start reading. Larry
                          Message 12 of 12 , Mar 18, 2013
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                            Thanks guys. I will get it and start reading.
                            Larry


                            --- In ccd-newastro@yahoogroups.com, Ken Harrison <kenm.harrison@...> wrote:
                            >
                            > I'd also recommend Howell's book.
                            > It covers the whole subject of astronomical CCD's very well (and gives some
                            > interesting stuff on spectroscope applications!)
                            >
                            >
                            >
                            > On 18 March 2013 03:01, Stan <stan_ccd@...> wrote:
                            >
                            > > **
                            > >
                            > >
                            > > --- "larryl" <k3fit@> wrote:
                            > > > Would you recommend a good book for this subject matter?
                            > > > The Statistics 101 book does not cover this.
                            > >
                            > > Not any single book (haven't written it yet <g>). But one of the most
                            > > succinct books that influenced much of my thinking in this area has been
                            > > Howell's "Handbook of CCD Astronomy". Added to that is some acquired
                            > > knowledge and training in statistics and information theory.
                            > >
                            > > Once you orient your thinking to an information theory approach (object
                            > > analysis) with some basic statistical tools then it isn't that difficult to
                            > > devise particular analyses for imaging issues.
                            > >
                            > > In that regard: It looks like I will conduct a workshop on an informal
                            > > information theory approach to AI at the upcomming 2013 AIC.
                            > >
                            > > Stan
                            > >
                            > >
                            > >
                            >
                            >
                            >
                            > --
                            > "Astronomical Spectroscopy - The Final Frontier" - to boldly go where few
                            > amateurs have gone before....
                            > http://tech.groups.yahoo.com/group/astronomical_spectroscopy/?yguid=322612425
                            > "Astronomical Spectroscopy for Amateurs" - Springer
                            > "Grating Spectroscopes - How to use them" - Springer
                            >
                            >
                            > [Non-text portions of this message have been removed]
                            >
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