If this question has been covered elsewhere, I apologize, I was unable to find it.
I am trying to develop an understanding of the significance of the read noise of a CCD camera for the quality of an image.
I have read everything I can find, but there is am implicit logical leap in much of that material, that I need help making explicit.
So far I understand that, simplistically, Full Well Capacity (Max signal) / Read Noise (Min signal) gives the effective dynamic range of a CCD. More dynamic range is better, because it allows a finer recording of subtle differences in light intensity. So, for example, with a FWC of 10,000 and a Read Noise of 10, there are 1,000 steps of dynamic range. With a FWC of 10,000 and a read noise of 6e, there are 1,666 steps of dynamic range.
This is where I am having my conceptual difficulty. I understand that the read noise establishes a floor for a signal (e.g. if read noise = 10e, then one needs 11e to create a signal, and the dynamic range expressed in electrons would be 10,000-10 = 9,990.
I don't understand how that translates into a dividing the full well capacity by the read noise to determine steps of dynamic range. There seems to be an assumption in this calculation that the size of each step of dynamic range of the sensor is equal to the read noise.
If read noise is 10e, is it not simply an adder to whatever number of electrons a photosite ends up capturing? A photosite that captures 7,000e will read off with 7010e (on average) for example, while one that captures 600e will read off with 610e (on average). In these terms, it seems an increase from 6e to 10e of read noise would be fairly de minimis. However, expressed in terms of steps of dynamic range, the increase in dynamic range is 2/3rds by going from 10e to 6e.
So, first thing, you are correct that dynamic range (in discrete steps of usable information) is FWC/RN. This is saturation point over noise floor...read noise isn't exactly min signal, it is the noise floor. So, for a camera that has 20,000e- FWC and 3.5e- read noise, you have 20000/3.5 = 5714 discrete steps of information.
You can convert this into decibels, or stops:
dB = 20 * log(FWC/RN)
stops = log2(FWC/RN)
stops = dB/6
So you have 75.14dB or 12.5 stops of dynamic range with 5714 steps.
NOW, onto your difficulty. You need more than 11e- signal to overcome read noise of 10e-. This is actually key to why dynamic range is useful. It tells us that the noise floor represents a DISTRIBUTION or BAND that determines the size of each DISCRETE STEP of useful information. You need to double the band, at a bare minimum, to be able to discern a new discrete level of information. So, to really be able to separate another value from your noise floor of 10e-, you need the signal to be 20e-. The read noise around this signal will distribute around its mean about the same as the read noise will distribute around the bias offset. So the two...the bias offset with read noise distributed around its mean and this new signal with read noise distributed around its mean...have become "separated" and are now discretely identifiable as different levels.
Now, you can repeat this process...to discern the next level of signal, it would at a minimum need to be another 10e- stronger than the previous, so you have 30e- vs. 20e- vs. 10e-, and three discretely identifiable levels of signal. Etc. etc. up through the saturation point.
Some visual demonstration is probably necessary here, so I'll try to come back later and add some images to demonstrate how this works in practice.
What is the relationship between the read noise and the necessary exposure time? I understand that generally, the advice is to expose for sub lengths sufficient to overwhelm read noise with sky noise, but how does that relate to the dynamic range of the camera?
So, while read noise defines the width of the bands of discretely discernible information, there is really more to it than that in an ACTUAL signal. An actual signal has other noises...dark current noise (minior in cooled cameras, could be significant otherwise) and shot noise (significant, eventually dominant). The relationship between read noise and signal is what helps you determine necessary exposure time. A signal must be strong enough that its intrinsic noise, its shot noise, is the primary driver of noise distributing around the mean signal level.
There are some simple rules that can help you experimentally determine what the necessary signal level is. At a minimum, you should aim for your weakest background sky levels to be approx. three times (3x) the read noise SQUARED (RN^2). Squaring the read noise is useful because the read noise is added in quadrature to other signals or noises when determining SNR, so to fully swamp read noise you want your signal to be stronger than the read noise squared. More optimally, you would want your mean background signals to be somewhere around 5-10xRN^2. Optimal in practice is usually considered to be 10xRN^2...as usually once you account for remnant FPN and dark current, it is unlikely that in practice you could ever really get better than 10xRN^2 (and in fact depending on remnant FPN 10xRN^2 may indeed already meet the "best possible" criteria as well.)
So if you have read noise of 10e-, the weakest signal in the image should be 3xRN^2, and at worst the mean background sky level should never be smaller than that, which means you would need your background sky signal to be 300e-! Now, more optimally, if you want to get better SNR on faint signals...then you would likely want your background sky mean to be somewhere around 500-1000e-! Actually getting a 1000e- signal could actually be quite difficult, especially with higher resolution imaging...so you can see the potential challenge here. In some cases, exposing long enough to get a 1000e- signal may simply be impossible, or at least impractical given other considerations (i.e. sub loss, airplane/sat/meteor trails, etc.)
This should in turn demonstrate some of the value of low read noise cameras. With only 2e- you would need only 12e- at a minimum and 40e- optimally. So it takes less exposure time per sub exposure to reach the optimal criteria. In fact, with very low read noise, it actually becomes much easier to reach the more optimal 10xRN^2 criteria.
Now, how does this all play into dynamic range? While swamping read noise is one part of the equation, that is the "left side of the histogram" or "dark signal" part of the equation. We also have the "right side of the histogram" or "bright signal" part of the equation...notably, stars. If you expose long enough to swamp the read noise optimally...what happens to your stars? It may be that you have enough dynamic range such that you can achieve 10xRN^2 without even getting close to clipping stars (very high DR)...or you may clip a few of them (moderate to high DR)...or you may clip a lot of them (low to moderate DR).
Dynamic range is the relationship between the noise floor, the saturation (clipping) point, and the degree of fineness that you separate that total signal range into. A camera with higher read noise, say 9e-, but a huge FWC (100,000e-) and very high dynamic range (13.2 stops) could be an extremely capable camera when used right. Used right, as in with sufficiently long exposures to swamp the read noise, which even though read noise is high with so much dynamic range (huge FWC) you don't necessarily have to worry too much about clipping stars...which might require more expensive, specialized equipment. A camera with lower read noise, say 2e-, but a more limited FWC (8200e-) and moderate dynamic range (12 stops) would still be a capable camera, but would also be easier to achieve more optimal results with, and would not necessarily require extremely expensive equipment. In other words...a lower read noise camera is much more accessible to a much wider range of astrophotographers. The cost of this accessibility is the increased possibility of some additional clipped stars (and, in practice there is also usually a reduction in bit depth as well, which will produce a less-fine signal...something that can be managed with technique.)
If read noise is as important as it seems to be, then as between two similarly priced cameras with the same sensor and cooling capabilities (say the SBIG 16200 with 10e read noise and the FLI 16200 with 6e read noise) why wouldn't one always choose the camera wit h the lower read noise? Note - not trying to start a conversation on the relative merits of these two brands (which both appear to be amazing), just trying to understand the theory here based on what I have been reading.
I know I must have a basic conceptual break here, so apologize if any of the questions above are wrongheaded, and appreciate any enlightenment this amazing community can bring!
In the case of the two examples you shared, they are the same sensor, but different qualities of readout electronics. Ignoring cost for the moment...there is ZERO reason to choose a 10e- RN camera over a 6e- RN camera if it is the same sensor. You lose dynamic range, and suffer for it. So cost aside, that is easy.
The differences here come into play when you factor in cost. Now, I guess the SBIG vs. FLI is a poor example here...looks like they cost the same (maybe the SBIG integrates a filter wheel?) So, yeah...really, there is no reason to get the camera with 10e- read noise. Remember...we really need to square the read noise to understand its full impact. So you are really comparing 100e- to 36e-...
A better example may be comparing the QHY or Moravian 16200 cameras with the FLI 16200. These other two cost about a third less or more than the FLI, but have read noise more similar to the SBIG. In these cases...COST would be the biggest factor. I mean, $8000 is a lot of money, and with the FLI you still need a separate filter wheel which is a couple thousand more, and if you can get the same sensor at 9-10e- PLUS the filter wheel for $3999, then that is a significant factor. The increase in read noise may well be a totally acceptable tradeoff, especially if you have the ability to use exposures long enough to sufficiently swamp the read noise. I think the SBIG probably integrates a filter wheel as well, I think many of their cameras do...and if that is the case, then there would still be a cost savings with the SBIG over the FLI.
Anyway...if cost is of no concern, or if there is no difference in cost and overall quality, then I would say read noise is indeed a primary driver of which camera to buy. Lower read noise has distinct benefits, especially if the FWC is maintained (since lower read noise with the same FWC means higher dynamic range!)
Edited by Jon Rista, 21 May 2019 - 02:02 PM.