e- / DN Uncertainty

[roger smith x294]

Posted to CCD-world:
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Paola and Jim,

My experience supports Jim's formula for the error in the
estimate of e-/ADU.  We developed an IRAF task last year which
acquires the data and plots variance versus mean for thousands of 
evenly distributed points in only a few minutes.  With so many points
the linear growth in the scatter with increasing signal is very
vivid, making it clear that the slope (ADU/e-) cannot be
estimated any better at higher signal levels.  It is also clear
that with more points (or more pixels per point) the estimate of
the slope is indeed more accurate.

Signal level only ceases to be relevant once the shot noise is
greater than the read noise.  If one is using only a *single*
point to estimate the slope (not recommended), then shot noise
must be very much greater than read noise.   

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So, why am I measuring variance curves with thousands of points
anyway?   I wanted away of estimating where the variance curve
becomes non-linear which was both accurate and fast.  Such a
curve allows me to select the linear range when estimating the e-
/ADU, but more importantly I find that variance curves are the
most robust measure of saturation level.  This may be the
only accurate method when high contrast test targets cannot be
projected onto the CCD, such as during the daytime on the
telescope.

We mount LEDs and a diffusing screen to provide flat illumination
of the CCD to within a few percent, then flash the LEDs for about
1 ms before each parallel shift to produce a linear increase in
intensity with line number and minimal intensity variation along
each line.  To eliminate photo-electrons detected by the serial
register, the serial register is flushed between the flashing the
LED and the parallel shift.  An nominally identical pair of such
images is acquired.

The variance of the difference of corresponding lines is then
plotted against the sum of their means, excluding columns which
are contaminated by known defects.  Since both the variance and
mean are doubled by this calculation, the slope is still ADU/e-.
The subtraction of similar frames eliminates the contribution of
pixel to pixel sensitivity variation from the statistics.  Such
variations have already been averaged out to a large extent by
accumulating the signal at many positions on the CCD: the greater
the signal, the greater is the amount of averaging. 

A 20 point boxcar average makes even small deviations from linear
easy to see in spite of the scatter in the individual variance
data: remember that scatter in variance goes down linearly with
number of points averaged (not as the square root).

Roger
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