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How much different is doubling the ISO vs. summing the pixel values from 2 shots? (at a very basic level, ignoring fancy image processing, image compression, etc)

When taking a shot of the night sky (ISO=400, shutter=1 second, fixed aperture because smartphone), if I want more starlight, I can:

  1. Double the shutter time to 2 seconds
  2. Take 2 back-to-back shots and sum the pixel values.
  3. Double the ISO from 400 to 800
  4. Blindly double the pixel values
  5. Get the median pixel value from a bunch of shots, and double that.

For digital cameras my understanding is that:

  • 1 and 2 are ELI5 the same (if you ignore details like compression and where in the pipeline all the image enhancements happen)
  • 3 and 4 are kinda similar, but better to do 3 because you might catch more low-light details. But either way you are trying to do more with the same amount of capture-time, so you will get noise. this is where I'm most confused - doubling the ISO feels far better than boosting the pixels after the fact
  • 5 is the odd one out - it improves things, but doesn't really map to any of 1-4. But if your scene isn't moving, may as well try it!

... am I correct or completely confused w/r/t ISO and shutter speed?

  • 1 and 2 are different because AFAIK noise in the sensor increases with exposure time. Maybe not much between 1s and 2s, but definitely a problem between 1 and 30s. So astrophotographers take several "short" shots and sum them (this also averages out some of the noise). – xenoid Aug 23 '18 at 20:05
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    @BenjaminH Yes. See photo.stackexchange.com/questions/41848/… – xenoid Aug 23 '18 at 22:43
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    @MichaelClark Yep. The Poisson distribution changes between a single and another at twice the exposure, becoming more like a Normal distribution. Most noticeable in deep shadows. Of course the shot noise distribution of two exposures added together is also Poisson and is the same as that of a single, but doubled exposure. The gamma of the distribution is doubled. – doug Aug 24 '18 at 18:29
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    It seems to me that the largest advantage of many short exposures vs. fewer longer exposures is in the area of full well capacity for the brightest objects in the sky. When combining many frames the brighter objects can be masked and processed differently to preserve color that would be lost in longer exposures that fully saturate all three color channels. – Michael C Aug 24 '18 at 18:34
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    @MichaelClark Absolutely! Well capacity is a primary reason for stacking lower exposure shots to keep values below where they clip or become non-linear. – doug Aug 24 '18 at 19:26
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For #1 and #2.

Doubling exposure and stacking two exposures are going to be similar, but not exactly the same. Doubling exposure means you get twice as much signal, for a single unit of read noise. Taking two exposures means you get the same total signal as doubling exposure across both shots, but you end up with two units of read noise.

Depending on how shallow your exposures are (you said night sky, i.e. milky way?), stacking two exposures might result in a bit more noise than taking a longer exposure. HOWEVER, if this is indeed a milky way shot, a longer exposure is more likely to trail the stars more. So you have to decide, longer star trails or more noise?

Dark current will actually not be worse with either of these two options. Dark current shot noise is a time-dependent thing. You have the same total amount of time with one doubly-long exposure as with two stacked exposures, so your total dark current is the same. Now, things get interesting when you start talking about stacking many exposures...that can have distinct advantages, if you do it right. By right, I mean you would need to dither (shift the frame a little bit across subs), and ideally for night sky imaging, you would either use dark calibration with a separate master dark, or use LENR (long exposure noise reduction) to remove the dark pattern. Stacking many dithered and calibrated subs can produce a much cleaner image than taking a much longer single exposure, and if you don't want a star trails image, taking shorter subs and aligning them (ideally while imaging on a tracker of some kind) will average out various noise terms and produce a much, much cleaner image.

For #3 and #4.

Neither of these will be as good as #1 or #2. Doubling ISO, or digitally multiplying the raw data, does not increase signal. It simply changes the amplification of the signal. Doubling ISO is better than digitally multiplying, and depending on what ISO settings you are using, you might be better increasing ISO anyway (i.e. if you have 6e- read noise at ISO 400 and 4e- read noise at ISO 800, and you are doing shorter exposures for milky way images, then stacking many exposures at the higher ISO will again produce better results). Note that read noise scales as the square, so increasing ISO is more like the difference between 36 and 16, rather than 6 and 4.

Digitally multiplying the signal is, for any low light use case, utterly useless. With low light, particularly night sky or astrophotography, you want more REAL SIGNAL. You only get more signal by exposing. Amplifying (increasing ISO) will reduce read noise to some degree, but it still does not get you more signal in and of itself. Digitally multiplying, however, neither reduces read noise nor increases signal.

For #5.

I am not exactly sure what you are saying here. I think I gather that you mean stacking many exposures. I am not sure what you mean by "double that"...that what? And how?

No matter what you do, for low light, night sky, astrophotography stuff...MORE SIGNAL is what you want. The only way you get more signal is to expose more. For night sky (really wide field and milky way stuff), the best way to expose more is to get a tracker of some kind. Lightrack, SkyTracker/Polari, Star Adventurer, these will all counteract the rotation of the earth, and allow you to get much longer than the few seconds exposures you can normally get with DSLRs on fixed tripods these days (don't even bother with the 600/500/400 rules, totally useless, pixels are far too small for these to apply these days. Even at very short focal lengths, you will usually only get a few seconds of exposure before trails start.) A tracker can let you expose for up to minutes, if you are imaging under dark enough skies. That is the first and best way to improve your IQ, because it gets you more signal, and uses that signal to bury read noise.

Even with a tracker, there are limits to how long you can expose. With night sky, milky way and astrophotography, you can basically never have too much exposure. I've created astrophotography images with nearly 50 hours of total integrated exposure, and I could have used double or triple that! ;) Wide field mikly way images don't generally require that much, however they can benefit from 30, 60, 90 minutes of total integration on a tracker if you can muster it...that is when the fainter nebular colors (notably hydrogen alpha) in the milky way nebula start to come out. To get that kind of exposure, you have to stack, no matter how you slice it. You might get 2, maybe 3 minute exposures with a tracker and a DSLR, in which case you might stack 10-15 of those kinds of exposures to create a cleaner, richer, more colorful night sky image.

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