The redistribution function of the CCD's is parameterized per CCD and per node. The model is described in [1] with an update described in [2]. It combines the X-ray absorption probability in silicon with an empirical parameterization of the generated charge signal, which is then folded by a Gaussian for noise representation.

The probability for absorption of a photon in silicon at the depth
is given by

with the mean absorption length in silicon . For a given photon
of energy (in eV), and absorption at , the
collected charge (in eV) is parameterized with the
empirical model

with a threshold for charge detection , and being a parameter that defines the scale of the collected charge.

The charge probability density then is

From (3) follows that

and hence

Reforming (3) into

(7) |

allows to eliminate from (6), and yields

which gives the response probability of an ideal CCD to an incident
photon of energy with the parameters and which are
specified in the CCF `REDIST`.

To this function a partial event tail is added that has a
constant probability density for all charges less than the incident
energy, and zero above:

is the differential amplitude of the total fraction of partial
events . It is
and its value is
defined from

is parameterized as

with the parameters , , and , which are specified in the CCF
`REDIST`.

Finally
is convolved with a Gaussian
to represent the Fano-noise and the amplifier noise. The (in
eV) of this Gaussian can be written as

It has to be noted that the result of the this function, as far as described so far, is in units of energy. In order to be able to compare with data, which are in units of PI, the output of this function has to be converted to PI, taking the relationship between the definition of PI and energy into account.

Note that the Si escape peak is not included in the current model.