# Deriving HRC-I Degap for XRCF Settings

## Quadratic Degap Coefficients

Quadratic degap coefficients will not only stretch the data to fill in
the gap but will stretch by different fractional amounts relative to
the center of the tap to redistribute any peaking in the raw
distribution. The degap coefficients are derived from the raw
(undegapped) projections. The HRC UNIX Tools Data Analysis System tool
nmkdegap takes a projection and generates a
file with quadratic degap coefficients. The figure below shows the
result of applying the quadratic degap coefficients to the HRC-I "XRCF"
flat-field data set. The degap coefficients used are given
here.

The resulting histograms show some evidence for residual
gaps. Expanded views of a few sections of the histograms, comparing
the raw (undegapped) to the quadratic degapped data, are shown below.

The gap removal is not as complete as when using the linear coefficients, but the peaking toward the
center of the taps is smoothed out. Unfortunately, when there is a real
illumination variation (i.e. the expected distribution of events
across the tap is not constant), the derived quadratic coefficients
introduce discontinuities. See the
V-axis 0-10 projection for
the worst case of this problem. The stair-step shape of the quadratic
degapped projection compares unfavorably with the corresponding linear degapped projection. The derived
quadratic degapping coefficients might be improved by restricting the
range of positions along the opposite axis which are included in the
projection, so that the gradients are reduced. Or, it may be more
useful to modify the fit algorithm to allow for gradients across the
taps. This might be input via a template generated using the linear
degapped data.

## Expanded views of the projections

## Trends in the Quadratic Coefficients

It can be instructive to graphically view the degapping
coefficients. Trends in their value versus coarse position or versus
each other may provide information as to whether they have been
effected by some systematic effects. Below are plots of the linear and
quadratic coefficients as a function of U- and V-axis coarse position.

The × symbols are for the negative side of the tap and the symbols are for the positive
side. Evidence for the coefficients that cause the stair-step behavior
in the V-axis for low coarse position can be seen in the separation
between the positive and negative side coefficients. A similar thing
happens for the U-axis coefficients in the 50-60 range, where the
"saw-tooth" pattern is present in the undegapped data. Below the
quadratic coefficient is plotted versus the linear coefficient for the
U and V axes.

The coefficients form families of lines where the intercept with
the "b=0" line is the linear degap correction that will remove the
gap. The slopes are equal to 2 times this linear coefficient and where
a point lies along the line is related to how "peaked" the
distribution is toward the center.

Details of the linear degap coefficients can be found
here.

Back to "Deriving HRC-I Degap
for XRCF Settings (Flat Field Data)"

Back to "HRC Degapping Corrections"

*Dr. Michael
Juda*

*Harvard-Smithsonian Center for Astrophysics*

*60 Garden Street, Mail Stop 70*

*Cambridge, MA 02138, USA*

*Ph.: (617) 495-7062*

*Fax: (617) 495-7356*

*E-mail:
mjuda@cfa.harvard.edu*