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.

HRC-I Quadratic Degapped Flat-Fields at XRCF Settings

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.

Projections: HRC-I Raw and Quadratic Degapped U-axis Coarse
Positions 25-35 Projections: HRC-I Raw and Quadratic Degapped V-axis Coarse
Positions 25-35 Projections: HRC-I Raw and Quadratic Degapped U-axis Coarse
Positions 50-60 Projections: HRC-I Raw and Quadratic Degapped V-axis Coarse
Positions 0-10

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

0-10 0-10
10-20 10-20
20-30 20-30
30-40 30-40
40-50 40-50
50-60 50-60

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.

HRC-I U-axis Degap 
Coefficients for XRCF settings HRC-I V-axis Degap 
Coefficients for XRCF settings

The × symbols are for the negative side of the tap and the box 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.

Quadratic vs Linear

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)"

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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