Hi Greg. Thanks for posting. Will try to answer your questions one at a time. Regards Ray
Is the relationship between pixel size and focal length though a division of their squares though? How did you figure that?
Originally from first principles, but this general form seems to be widely used in astronomy - as an example, it is a simplification of equation 4 in http://arxiv.org/pdf/1401.5473v1.pdf Also, it is not focal length, but FNumber
Something must be a little off as it does not match my experience with various scopes.
I doubt using a 200mm RC with a KAF8300 is going to take 12 times longer to get the same signal to noise ratio.
Depends on the camera, but with the chosen examples, that's what happens. If you are looking at ADU signal values from the chip, you might not think that this is the case due to camera gain differences, but the sensitivity difference (based on SNR in the detected charge) will be 12 - but only if the other system has a big pixel 16803.
Doesn't it more come down to aperture not focal length? And QE.
Aperture is included in the FNo and the equation has a QE term. I agree that aperture determines how many photons get in to the system, but the fl and pixel area determine how many end up in a pixel (and hence what the SNR is) - you can't look at any part of the system in isolation.
I take it when you worked out those average QEs you took the same samples of each of the sensors QE graph? 16803 has peak 60% QE and so does KAF8300.
the QE used in the equation is the average over the bandpass, not the peak. These kodak chips do not have a very flat spectral response (maybe I should have included the 3200 in one of the examples - that is pretty good)
I have noticed a drop in sensitivity with oversampling but its not that dramatic.
It is scary how much damage oversampling can do. The simplest way to be convinced of this is to imagine what would happen if you imaged with a 2x Barlow in your scope - I am sure that you would agree that the signal will take a huge hit if you did (try it!) - what you would be doing is simply changing the sampling by 2x (the aperture remains the same), but you would end up with 1/4 the signal in each pixel and need to image for 4x as long to compensate.
From my experience only I would rate a 200mm RC at F8 and KAF8300 taking 4x longer to reach the same signal to noise than a 300 F3.8 an 16803 camera. Perhaps 5X max but unlikely 12X.
would really need measured SNR to check this, but what you may possibly be basing this on is a 4x-5x difference in time to get to the same ADU values. Since an 8300 camera has about 2.5x the gain of a 16803, the time to equal SNR would be 10x-12.5x, which agrees with the equation .
For example my RHA is 305/F3.8. If I take an image of something that I have imaged several times with different scopes it sure is faster but not 12X. So perhaps that pixel/focal length formula is not correct.
The formula uses FNo and pixel area. It seems to be widely used in other guises - I am pretty sure that it is OK.
Camera read noise comes into it as well. What do you think?
Read noise only determines how long the subs should be - this approach assumes that they are long enough that shot noise from the sky is dominant, so read noise does not come into it. It is also assumed that dark current is under control (but that is a given with modern cameras and broadband imaging)