ASTRO: OT; maximum exposure time, read noise and cooling

I want to share one more thing with the group loosely related to the RBI
issue. As shown in the previous note about RBI and Thermal Diffusion, there
are advantages in running cameras colder: it lengthens the time constant for
the leakout of the filled traps using the Cassini / Galileo solutions for
RBI

For a given camera system it is common in the professional literature to set
the maximum practical exposure time that a camera should be used is that
exposure time where the shot noise of the accumulated dark signal is equal
to the readout noise of the camera.

Let's explore what happens when we have two arbitrary cameras we want to
compare that have different read and cooling performance specs but use the
same sensors


Assume the following specs for the two cameras:

Camera A:

10 electron read noise

0.03 electron/second/pixel dark current generation rate at -20C operation,
and that's as cold as it will run with cooling margin

100,000 electron well capacity

Camera B:

5 electron read noise

0.03 electron/second/pixel dark current generation rate at -20C operation,
but the camera can run to -40C with cooling margin. Assume dark current is
halved for a 5C drop in temperature

100,000 electron well capacity

-----
Problem: compute the maximum practical exposure time for Cameras A and B
with the criteria that the max practical exposure time is that amount of
exposure time when the shot noise of the dark signal equals the read noise


Solution: Camera A
Dark_signal_shot_noise = sqrt(dark_signal_in_electrons) = 10 electrons

dark_signal_in_electrons = 10 ^2 = 100 electrons/pixel

At 0.03 electrons/second/pixel generation rate, the maximum practical
exposure time would be 100/0.03 = 3333 seconds or a bit short of one hour

Camera B:

Dark_signal_shot_noise = sqrt(dark_signal_in_electrons) = 5 electrons

dark_signal_in_electrons = 5 ^2 = 25electrons/pixels

At 0.03 electrons/second/pixel generation rate, the maximum exposure time
would be 833 seconds or a bit short of 15 minutes

In order to expose for the same 3333 seconds as Camera A, the dark current
generation rate will need to be reduced:

Problem #2 Compute the desired maximum dark current generation rate and what
temperature is needed to hit that spec:

3333*desired_dark_current_generation_rate = 25 electrons/pixel

desired_dark_current_generation_rate = 25electrons/pixel /3333 seconds =
0.007501 electrons/sec/pixel

starting from 0.03 electrons/sec/pixel and desiring 0.007501
electrons/sec/pixel we need to reduce the dark current by a factor of four
(3.999467 to be exact)

So since it takes a 5C drop to reduce the dark current generation rate by a
factor of two it would mean the sensor needs to operate at --30Cto be able
to expose for 3333 seconds and not have the shot noise of the dark signal
exceed the read noise (-20C - 2 * 5C) = -30C


but there's mo

Problem #3: compute the dynamic range of the two cameras above with the
second camera running at the colder temperature


Solution:

Camera A: dynamic range = full well / read noise = 100,000 / 10 = 10,000
or 80 dB (20 Log10(dynamic range)

Camera B: 100,000 / 5 = 20,000 = 86dB

so the camera B has twice the dynamic range as the camera A with the poorer
read noise and cooling.

Implication

So what happens if Camera A is redesigned to have the same 5 electron read
noise but has no cooling improvement? Reducing the read noise without
improving the cooling will reduce the maximum practical exposure to about 15
minutes instead of the one hour before.

It still has the dynamic range improvement, but the maximum practical
exposure time is reduced by a factor of four

So one really should check to see if the cooling needs to be improved if you
find a way to improve your read noise otherwise you may not be able to fully
exploit the potential of the camera's read noise improvement with exposure
times that you may want to use.

Richard