The correction procedure consists essentially in applying all the specified corrections according to the distribution of the relevant photons over the detector face, within the accepted time intervals. All the necessary information is contained in the descriptor header which is always associated to the binned data to be corrected. Only the photons which contributed to the binned data are taken in consideration in the correction procedures. When Projection is set in correction mode via the SET/PROJECTION command, this is done automatically during data binning in Projection (this is applicable for PSPC data only, anyway).
A histogram of the photon distribution over the detector face -- or simply a histogram of the photon distribution along the off axis angle when allowed by reasons of symmetry -- is created as a first step. There are two possible modes which may be chosen in the construction of the histogram, either the photon or the attitude mode (in the automatic correction performed in Projection run in correction mode, only photon mode is used).
In photon mode the detector histogram
is derived from the detector coordinates (XDET, YDET columns)
of the contributing photon.
To each one of the histogram bins, (xdet,ydet) or offax, the
corresponding number of photons 
or 
is written.
Next, since the vignetting affects also the shape of the
detector histogram, this must be also corrected.
Without such a correction for the
detector histogram, the correction would
be strongly underestimated in case of survey data (in principle,
in a survey observation the
source photons are uniformly distributed over the detector face, therefore
the detector histogram will include all the off axis angles; but, because
of the vignetting effect, less photons than expected
will be observed at high off axis angles, and the detector histogram
will be then distorted in the direction of the smaller off axis angles,
where the vignetting effects are minor).
In attitude mode the detector histogram is not build from the relevant photons distribution on the detector face, but from the satellite attitude information. Given the sky pixel coordinate (xsky,ysky) of a given point on the sky, the correction procedure calculates the corresponding detector coordinates (xdet,ydet) for each determination of the satellite attitude within the accepted times intervals. In the ROSAT-PSPC case the satellite attitude is available every 1 second of time and the coordinate transformation from sky to detector pixels is given by
where s and d are the sky and detector pixel sizes,
x and y are the position of the
instrument optical axis expressed in sky pixels, 
is the
roll angle, and xdetcen and ydetcen are the coordinates of the
detector center expressed in detector pixels. x, y and 
are read from the available attitude table. In this case is valid
the relation
where 
is the geometrical (i.e. excluding the dead
time effects) exposure time for the specified
point (xsky,ysky), and 
the time resolution of the
satellite attitude determination ( 
s in the ROSAT-PSPC
case).
From the previous description it should be evident that the photon mode must be chosen in the correction of spectra or light curves which are derived from extended objects (such as SNRs, or background portions of the sky, or even distributions of many point-like sources). It is also correct to choose the photon mode for point-like sources. The attitude mode can be chosen only in the correction of spectra or light curves derived from point-like sources (in practice, the choice of the attitude mode is useful just for low counts point-like sources).
As shown above, the geometrical exposure time 
for the specified sky coordinate (xsky,ysky) is computed
during the spectral correction in attitude mode.
The exposure time is generally equal to the extension of the accepted times,
but it is less than that in the case of slew data (like in the
ROSAT survey) -- because the source may not have been always exposed
while the detector was operative -- or in the case of pointing data
when a source is very close to the detector edge
or to other non-sensitive parts of the detector (as the ribs of the
ROSAT-PSPC). In those specific cases, if the attitude mode is
not used the total exposure time of the source might be overestimated.
Since the attitude mode cannot
be used within Projection run in correction mode, such a correction
can be applied afterwards via the usual correction commands.
If the data were already corrected within the Projection run they will
be not corrected again, and only the exposure will be computed.
The dead time correction, when requested, is taken into account
both in attitude and in photon mode
while building the detector histogram. When a detector coordinate
is determined (from the attitude solution or from the input photon list)
the corresponding histogram bin is increased by the life time factor 
(and not by 1).
Once the detector histogram is produced, the data correction can be performed.
In the spectral correction the aim is to calculate the instrumental effective area as a function of the energy. For the spectra which have been already corrected within Projection this is always the effective area on-axis, and therefore it is not necessary to compute a special correction vector for each spectra in this case.
In the calculation of the correction vector all the instrumental effects for which a correction was requested are included (in the ROSAT-PSPC case, beyond the XRT effective area there may be included the effects of the Boron filter transmission and the loss of photons due to the PSF).
It must be pointed out that the dead time correction is only an approximation in attitude mode, while it is exact in photon mode. This can be easily seen in the following:
Let's N be the total measured counts from an X-ray source. What are
the dead time corrected counts? Assuming that the count rate from
the source is changing, second after second, as 
,
and assuming that the corresponding life times are 
(which depend on the total count rate
on the entire detector), than the corrected counts are given by
This is exactly what is done in photon mode, where each single photon is
corrected for the local life time factor 
.
In attitude mode, since the count rate information 
is missing (there is no access to photons), all time bins are weighted
equally. This is equivalent to calculating the corrected total counts
as
This correction is different from the previous one
whenever the count rate 
and the life time 
are not
constant. As a conclusion, dead time correction in photon mode is
in general preferable.
In the correction for a light curve the aim is to calculate a sequence of as many correction factors as many are the time bins which compose the light curve. The same procedure used in the spectral correction is repeated for each of the time bins. A detector histogram is created for each single time bin, and the corresponding spectral correction vector is integrated over the energy interval specified in the creation of the light curve. The integral is compared to the same integral at the instrument optical axis. The ratio between the two integrals defines the correction factor for that specific time bin.
Such a spectral approximation is dropped anyway when running Projection in correction mode. In this case, each single photon is corrected according not only to its detector position, but also for its specific energy. Therefore this mode should be preferred whenever a more accurate light curve correction is required.
By multiplying a light curve by its correction vector, it is obtained the light curve which would have been observed if the source were always on-axis. Also this task is performed automatically in Projection run in correction mode, and the correction factor column is not written in output.
A dead time correction should be avoided in light curves having bin size less then about 10 seconds. Below this level the dead time correction lacks precision.