**Gain**

In CCD imaging, gain refers to the magnitude
of amplification a given system will produce. Gain
is reported in terms of electrons/ADU (analog-to-digital
unit). A gain of 8 means that the camera digitizes
the CCD signal so that each ADU corresponds to 8
photoelectrons.

The system gain of a Photometrics camera is typically
set so that the full well of the CCD matches the
full range of the digitizer (at 1x gain). The cameras
gain can also be selected under software control
to meet the needs of a given application. For example,
the gain can be increased to 4x when the application
is photon starved and a high-sensitivity mode is
required. Alternatively, the gain can be reduced
to 1/2x when the application is photon-shot-noise
limited and a high SNR mode is required. Because
gain refers to the amplification of a system and
the gain reported in CCD imaging is actually inverse
amplification, the meaning of gain is not entirely
intuitive. As gain increases, the reported gain
value decreases. For example, if the system gain
(1x) is 8e-/ADU, then the high-gain (4x) mode would
be 2e-/ADU.

A simple method to calculate the system gain
is shown below:

- Collect a bias image (zero-integration dark
image) and label it "bias".
- Collect two even-illumination images and
label them "flat1" and "flat2".
- Calculate a difference image: diff = flat2
- flat1.
- Calculate the standard deviation of the
central 100 x 100 pixels in the difference image.
- Calculate the variance by squaring the standard
deviation and dividing by 2 (variance adds per
image, so the variance of the difference image
is the sum of the variance of flat1 and flat2).
- Calculate a bias-corrected image by subtracting
the bias from one of the flat images and label
it corr: corr = flat1 - bias.
- Obtain the mean illumination level by calculating
the mean of the central 100 x 100 region of
the corr image.
- The mean divided by the variance equals
the gain: gain = mean /variance.

A more rigorous method is that of Mortara and
Fowler (*SPIE Vol. 290 Solid State Imagers for
Astronomy* (1981) pp. 28-33), which essentially
involves repeating the above procedure for a series
of illumination levels over the full range of the
CCD full well. In addition, their method recommends
collecting four or more flat images at each exposure
level and averaging them to improve the precision
of the measurement. The authors also provide the
theory supporting the method. Another rigorous,
excellent method that can be used to calculate gain
is the photon-transfer technique of Janesick et
al. (*Optical Engineering Vol. 26* (10) (1987)
pp. 972-980).