Gain by Photon Transfer method

[roger smith x294]

Nick,

Gerry is right about the peak in the Fe55 histogram being a
quick, easy, and precise method to determine but to mention that
5.89 keV X-rays don't pass through a fused silica ("quartz")
dewar window.  To do the Fe55 test you have to replace the
optical window temporarily with a Beryllium, or build the Fe55
source into your dewar along with a method for retracting it into
an X-ray-tight shield.  This is great in a lab dewar but in real
applications one often has to locate the CCD too close to the
window to fit the Fe55 retractor because of back focal distance
requirements of the optics.

The "Photon Transfer" method is the standard way to measure gain. 
In practice this means taking pairs of identical flat field
exposures at various illuminations and plotting the variance of
the difference within each pair against the sum of the means, for
a region selected to be free of cosmetic defects.  The slope is
then the gain, in units of ADU/e-.   The differencing removes
pixel to pixel sensitivity variations, leaving only noise.  The
point at which the curve deviates from linear is the full well
capacity or saturation level and the Y-intercept is the square of
the read noise.  Read noise is more accurately obtained from a
zero length dark frame than extrapolating the variance curve. 
You can get the gain from just two illumination levels (4
frames), but it is safer to plot a curve to ensure that the
system is behaving itself.


The math is trivial.   For poission statistics....

          variance  = mean              (e-)      ........(1)

Define gain,   A    = number of ADU per electron

then 
     (A**2)variance = VARIANCE          (ADU)     ........(2)
and         A*mean  = MEAN              (ADU)     ........(3)

Substituting (2) and (3) into (1):

          VARIANCE  = A*MEAN            (ADU**2)  ........(4)


The variance of the difference is twice the variance of the shot
noise component of a single frame, so by plotting against the sum
of the means, the factors of 2 cancel.

Astronomers express "gain" in units of e-/ADU (the inverse of
gain) just to keep out the riff raff.


Roger Smith, CTIO