PSF in-flight calibration for PN camera

IFC/CNR Ringberg, April 2-4, 2002

PSF in-flight calibration - PN

PSF in-flight calibration

for PN camera

Simona Ghizzardi

Silvano Molendi



ENERGY RANGES:

0.3 keV [200-400] eV

0.6 keV [400-800] eV

1.0 keV [800-1200] eV

1.8 keV [1200-2400] eV

3.7 keV [2400-5000] eV

6.5 keV [5000-8000] eV

10.0 keV [8000-12000] eV

DATA SAMPLE:

- 110 SOURCES (TARGET) included

OFF-AXIS ANGLES: from on-axis position up to 10 arcmin

- most of them are observed within 2 arcmin.



We adopt the same procedure and the same algorithm used for the two MOS cameras.

The pixel size of the PSF images is taken 1.1” .

According to the MOS results, the profile of the PSF is well represented by a King model:

PSF = KING + BKG

Analysis procedure and PSF model



King profile

core slope

Two shape parameters: core radius (rc) and slope ()

IT CAN BE INTEGRATED ANALYTICALLY IN rdr!!!



We merged the observations having

the same source target

the same pointing position

different filters and/or operating mode --->

---> different pile-up levels

The centroid is determined accounting for the mask of the detector

For each curve a good fitting range must be defined (points suffering

for pile-up must be excluded).

Building the radial profile



Algorithm for the averaged radial profile

•Energy selection and pattern (0-12) selection

BASIC METHOD

We bin the image (with larger bins at larger radii)

RADIAL PROFILE: dN/dA (the area is not 2r dr because of the mask)

each (squared) pixel is assigned to the (round) bin to which its CENTER belongs

for these pixels it works fairly

these pixels belong to two different bins in comparable fractions

the effect is less important at larger radiiADDITIONAL RECIPE ADDED TO THE BASIC PROCEDURE

We enclose each pixel in a circle.

If the circle is fully enclosed in the bin then the pixel is too.

If the circle is partly enclosed in another bin, the pixel may belong to two bins: we divide such pixels in NSUBPIXELS



The physical pixel size is 4.1”, not much smaller than

the core radius of the PSF.

The calibration of the core is quite tricky

The frame time is smaller than the MOS one.

The pile-up effect is less important

The effective area is larger than the MOS one.

Good statistics



In order to enhance the statistics, we fit simultaneously the different curves with different pile-up levels

PSF = King + BKG

e rc are the same

for each curve

BKG and the normalization

are different for each curve

for each energy and off-axis angle we derive and rc.

Fitting the radial profiles



rc = rc(E, )

= (E, )

SLOPE:

IT HAS A ROUGHLY CONSTANT

BEHAVIOR EVEN IF THE 2-D

BEST FIT DECREASES

FOR OFF-AXIS ANGLES

INCREASING.

CORE:CORE:

THE LINEAR DECREASING BEHAVIOR IS NOT WELL THE LINEAR DECREASING BEHAVIOR IS NOT WELL REPRESENTED BY THE 2-D FIT.REPRESENTED BY THE 2-D FIT.

2-D FIT:

THE 2-D FIT IS DRIVEN BY THE ON-AXIS POINTS.THE 2-D FIT IS DRIVEN BY THE ON-AXIS POINTS.

0.3 keV



rc = rc(E, )

= (E, )

SLOPE:



BEST FIT DECREASES

FOR OFF-AXIS ANGLES

INCREASING.

CORE:CORE:


2-D FIT:


0.6 keV



rc = rc(E, )

= (E, )

SLOPE:



BEST FIT DECREASES

FOR OFF-AXIS ANGLES

INCREASING.

CORE:CORE:


2-D FIT:


1.0 keV



rc = rc(E, )

= (E, )

SLOPE:



BEST FIT DECREASES

FOR OFF-AXIS ANGLES

INCREASING.

CORE:CORE:


2-D FIT:


1.8 keV



rc = rc(E, )

= (E, )

SLOPE:



BEST FIT DECREASES

FOR OFF-AXIS ANGLES

INCREASING.

CORE:CORE:


2-D FIT:


3.7 keV



rc = rc(E, )

= (E, )

SLOPE:



BEST FIT DECREASES

FOR OFF-AXIS ANGLES

INCREASING.

CORE:CORE:


2-D FIT:


6.5 keV



rc = rc(E, )

= (E, )

SLOPE:



BEST FIT DECREASES

FOR OFF-AXIS ANGLES

INCREASING.

CORE:CORE:


2-D FIT:


10. keV



rc = rc(E, )

= (E, )

SLOPE: SLOPE:

IT HAS A ROUGHLY CONSTANTIT HAS A ROUGHLY CONSTANT

BEHAVIOR EVEN IF THE 2-D BEHAVIOR EVEN IF THE 2-D

BEST FIT DECREASES BEST FIT DECREASES

FOR OFF-AXIS ANGLES FOR OFF-AXIS ANGLES

INCREASING. INCREASING.

CORE:

THE LINEAR DECREASING BEHAVIOR IS NOT WELL REPRESENTED BY THE 2-D FIT.

2-D FIT:


1.0 keV



rc = rc(E, )

= (E, )

SLOPE: SLOPE:






CORE:


2-D FIT:


1.8 keV



rc = rc(E, )

= (E, )

SLOPE: SLOPE:






CORE:


2-D FIT:

THE 2-D FIT IS DRIVEN BY THE ON-AXIS POINTS.

3.7 keV



BINNING

Data are not well represented by the 2-D data because they present a very large scatter.

The 2-D fit ( but also each 1-D fit for any fixed energy) is completely driven by the on-axis data.

We bin on the off-axis angle variable with bin 12” wide.



rc = rc(E, )

= (E, )

BINS for off axis angle: 12”

SLOPE:


BEHAVIOR

CORE:CORE:

IT LINEARLY DECREASES FOR IT LINEARLY DECREASES FOR

INCREASING OFF AXIS ANGLESINCREASING OFF AXIS ANGLES

2-D FIT:

0.3 keV



rc = rc(E, )

= (E, )


SLOPE:


BEHAVIOR

CORE:CORE:



2-D FIT:

0.6 keV



rc = rc(E, )

= (E, )


SLOPE:


BEHAVIOR

CORE:CORE:



2-D FIT:

1.0 keV



rc = rc(E, )

= (E, )


SLOPE:


BEHAVIOR

CORE:CORE:



2-D FIT:

1.8 keV



rc = rc(E, )

= (E, )


SLOPE:


BEHAVIOR

CORE:CORE:



2-D FIT:

3.7 keV



rc = rc(E, )

= (E, )


SLOPE:


BEHAVIOR

CORE:CORE:



2-D FIT:

6.5 keV



rc = rc(E, )

= (E, )


SLOPE:


BEHAVIOR

CORE:CORE:



2-D FIT:

10. keV



rc = rc(E, )

= (E, )


SLOPE: SLOPE:


BEHAVIORBEHAVIOR

CORE:

IT LINEARLY DECREASES FOR

INCREASING OFF AXIS ANGLES

2-D FIT:

1.0 keV



rc = rc(E, )

= (E, )


SLOPE: SLOPE:


BEHAVIORBEHAVIOR

CORE:



2-D FIT:

1.8 keV



rc = rc(E, )

= (E, )


SLOPE: SLOPE:


BEHAVIORBEHAVIOR

CORE:



2-D FIT:

3.7 keV



Profiles using the best fit values



Profiles using the best fit values



WHY SUCH A SCATTER ?

Out of time events can affect the slope of the profile

Pile up is less evident in the PN data. Are we neglecting a pile up effect?

Centroiding is very difficult because of the large size of the pixels. This makes the determination of the core uncertain especially for the Small Window op. mode.

…TO BE INVESTIGATED





FULL FRAME

SMALL WINDOW



















King Core Radius for PN



King Slope for PN



BEST FIT VALUES



ENCIRCLED ENERGY FRACTION



Range of Application



CONCLUSIONS

By using a large set of data we modeled the PSF profile with a King function and provided the best fit values of the core and of the slope as functions of the energy and of the off-axis angle.

To be done …

We must include in the sample some other off-axis sources to enlarge the region of the range of application.

Check on :

evaluation of the background in the Small Window measures

out of time events

pile-up

centroiding procedures

in order to reduce the scatter of the points

Documents

PSF in-flight calibration for PN camera