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ROSAT PSPC

Calibration Corrections Applied to Individual PSPC Events

ROSAT PSPC

Calibration Corrections Applied to Individual PSPC Events

http://heasarc.gsfc.nasa.gov/docs/bios/turner.html http://heasarc.gsfc.nasa.gov/docs/bios/imgeorge.html http://heasarc.gsfc.nasa.gov/docs/bios/snowden.html http://heasarc.gsfc.nasa.gov/docs/bios/ryusaf.html
Mail Code 660,
NASA/GSFC,
Greenbelt, MD 20771
G. Hasinger
Astrophysikalisches Institut Potsdam
An der Sternwarte 16
14482 Potsdam
Germany

Version: 1995 Oct 30 (Draft)

SUMMARY

This document gives a summary of all the calibration corrections applied to individual PSPC events during their conversion from their arrival position & pulse height (PH) channel to their corrected coordinates & pulse-invariant (PI) channel.

This memo is essentially a copy of the original MPE memo TN-ROS-ME-ZA00/027 (Hasinger & Snowden, 1990), but updated and expanded to refer to the FITS versions of the calibration files available from the http://heasarc.gsfc.nasa.gov/

Intended Audience: http://heasarc.gsfc.nasa.gov/docs/rosat/rosgof.html and http://heasarc.gsfc.nasa.gov/docs/software/ftools/ftools_team.html

LOG OF SIGNIFICANT CHANGES

Release	Sections Changed	Brief Notes
Date
1995 Sep 21		Internal Draft
1995 Oct 13		First Public Release
2012 Aug 31	all	Minor corrections by MFC

1 INTRODUCTION

Each event detected in the ROSAT PSPC is tagged onboard with a number of pieces of information, including its arrival time, its position and its nominal pulse height. On the ground this information is transfered to the 'Event File' in the columns TIME, RAWX & RAWY, and PHA respectively (for files in RDF format - see Table 1 for the corresponding column names for earlier formats).

However, to facilitate data analysis, the Standard Analysis Software System (SASS) applies corrections for a number of effects. Here we describe the corrections required to convert from the raw detector coordinates of an event to the linearized detector coordinates, and from the observed pulse-hight channel of an event to the pulse-invariant (PI) channels. These corrected values are then also transferred and stored in the DETX, DETY & PI columns of the Event file (Table 1), respectively.

These corrections are applied within the SASS processing and have been described in the MPE Memo TN-ROS-ME-ZA00/027 "Calibration Corrections to individual PSPC events" (Hasinger & Snowden, 1990).

1.1 Overview of Inputs & Outputs

The corrections described in this memos are performed on an event-by-event basis, using the following observed (`raw') parameters from the Event file:

observed PH bin of each event
observed X & Y coordinates of each event in raw detector coordinates
time-tag for each event

and producing the following corrected/derived parameters, which are written back into the Event file:

corrected pulse invariant bin PI of each event
corrected coordinates X₃ & Y₃ of each event

The names of the columns used to store these parameters in the various FITS file formats used for ROSAT PSPC data are summarized in Table 1. However readers are reminded that all PSPC datasets available from the http://heasarc.gsfc.nasa.gov/ archives have been converted to RDF format.

Table 1: Column Names used to store the i/p & o/p parameters

Parameter		FITS File Format
Symbol	Description	RDF	US-Rev0	German-Rev0

Input Parameters
t	Time-tag of event	`TIME`	`TIME`	`TIME`
X	Raw X-axis position	`RAWX` f	-	-
Y	Raw Y-axis position	`RAWY` f	-	-
PH	Raw pulse-height bin	`PHA`	`PHA`	`RAW_AMPL`

Output Parameters
X₃	Linearized X-axis position	`DETX`	`DX`	`XDET`
Y₃	Linearized Y-axis position	`DETY`	`DY`	`YDET`
PI	Derived pulse-invariant channel	`PI`	`PI`	`AMPL`

f - available in the *_raw.fits file

2 THE CORRECTIONS

2.1 Correction for non-linearities in the ADC

The ADC (analogue-to-digital converter) within the PSPC electronics introduces small variations ( < 3%) in the width of the PH channels. The effective width of each channel has therefore been determined from a large number of ground calibration measurements and subtracting a smooth spline function.

Inputs & Outputs

Inputs:

observed PH bin of each event (from Event file)
lower & upper boundaries (ADC₁ & ADC₂) on each effective ADC bin (from Calibration file)

Outputs:

effective PH bin, PH₁, for each event

Method

The non-linearity of the ADC is corrected by drawing a random number RAN(0,1) between zero and one, and calculating the effective PH bin, PH₁ from the observed PH bin as follows:

PH₁ = ADC₁(PH) + RAN(0,1)×(ADC₂(PH) − ADC₁(PH))

(1)

Files

SASS:
The effective boundaries of each channel are stored in a calibration file: ADC_BINS.DAT, which is a simple ASCII table with 256 rows, each row containing the two reals giving the lower (ADC₁) & upper (ADC₂) boundaries of the effective channel. The SASS subroutine which uses this is CADC (within CT module).
http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_intro.html:
The effective boundaries of each channel are stored in the calibration file: adc_bins.fits
Format: FITS BINTABLE, with 256 rows, and 3 columns where:
- column PH_1 gives PH₁ corresponding to ADC_LO
- column ADC_LO gives ADC₁
- column ADC_HI gives ADC₂

Notes

In the MPE Memo TN-ROS-ME-ZA00/027 "Calibration Corrections to individual PSPC events" (Hasinger & Snowden, 1990), this correction is described in slightly different terms. A different input calibration file is described, which contains the lower edge ADC₁ along with the width of each bin (instead of the upper edge, ADC₂, described above). Clearly this is a minor difference, and presumably reflects a change made to SASS sometime after 1990.

2.2 Correction for saturation of the detector gain

For high energy photons, the gain of the PSPC detector begins to saturate (ie there is a fall-off in the signal amplication and a loss of linearity between incident photon energy and channel). This is a relatively minor effect, only noticeable above ∼ 1 keV and has been modelled using ground calibration measurements.

Inputs & Outputs

Inputs:

effective PH bin, PH₁, for each event (after correction described in Section 2.1)
channel,B_Al, in which the peak of the onboard Al calibration source is expected to occur (interpolating between the nearest two measurements to the time of the observation)
Algorithm and associated parameters to perform correction (the coefficients C₁, C₃, defined below)

Outputs:

corrected PH bin, PH₂, for each event

Method

The corrected PH bin, PH₂ is constructed as follows:

PH₂ =

⎧
⎪
⎨
⎪
⎩

PH₁

if PH₁ < C₂

PH₁ + C₁ ×(PH₁ − C₂)^C₃

otherwise

(2)

with

C₂ = 0.62777 ×B_AL + 4.453

(3)

where B_Al is the channel in which the peak of the line from the onboard Al calibration source is expected to lie. B_Al is calculated by (linearly) interpolating between the results from Prescott fits to the Al calibration observations immediately before & after the observation. For the nominal gain, B_AL ≅ 151, giving C₂ ≅ 99 (equivalent to ∼ 1 keV).

Files

SASS:
The coefficients are hard-wired into the code in the SASS subroutine CGS (within CT module) with the following values:
C₁ = 5.5×10⁻²
C₃ = 1.74
along with equation 3.
http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_intro.html:
The values of the coefficients C₁ & C₃ are currently not available in the CALDB
The results of the Prescott fits to observations using the Al calibration source are stored in the calibration files: alkhist_v1_b.fits and alkhist_v1_c.fits (for PSPCB & PSPCC respectively)
Format: FITS BINTABLE, with several columns, the most important of which are:
- column ISCC giving the time, as measured by the spacecraft clock, of each observation using the Al calibration source
- column ALK_BIN the peak of the onboard Al calibration source based upon Prescott fits (in cases where more than one Al calibration observation was carried out on a given day, the value stored in ALK_BIN is the mean). Interpolating between the nearest two values in ALK_BIN for a given observation date gives B_Al.

2.3 Temporal Gain Correction

The gain (ie pulse hight as a function of energy) of the PSPC changes slowly due to variations in gas density, composition, high voltage, pressure and temperature. The temporal gain G(t) is measured by fitting Prescott functions to the data regularly obtained from the on-board Aluminum K_α calibration source.

Inputs & Outputs

Inputs:

effective PH bin, PH₂, for each event (after correction described in Section 2.2)
channel,B_Al, in which the peak of the onboard Al calibration source is expected to occur (interpolating between the nearest two measurements to the time of the observation)

Outputs:

corrected PH bin, PH₃, for each event

Method

The corrected PH bin, PH₃, is given by:

PH₃ = PH₂ ×(D₀ + D₁ ×B_AL+ D₂ ×B_AL²+ D₃ ×B_AL³)

(4)

where
D₀ = 4.543085
D₁ = − 5.135878×10⁻²
D₂ = 2.518324×10⁻⁴
D₃ = − 4.562700×10⁻⁷
and B_Al is the channel in which the peak of the line from the onboard Al calibration source is expected to lie. B_Al is calculated by (linearly) interpolating between the results from Prescott fits to the Al calibration observations immediately before & after the observation.

Files

SASS:
The coefficients D₀-D₃ are hard-wired into the code in the SASS subroutine CTG (within CT module) along with equation 4.
http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_intro.html:
The values of the coefficients D₀-D₃ are currently not available in the CALDB
The results of the Prescott fits to observations using the Al calibration source are stored in the calibration files: alkhist_v1_b.fits and alkhist_v1_c.fits (for PSPCB & PSPCC respectively)
Format: FITS BINTABLE, with a number of columns, the most important of which are:
- column ISCC: the time, as measured by the spacecraft clock, of each observation using the Al calibration source
- column ALK_BIN: the peak of the onboard Al calibration source based upon Prescott fits (in cases where more than one Al calibration observation was carried out on a given day, the value stored in ALK_BIN is the mean). Interpolating between the nearest two values in ALK_BIN for a given observation date gives B_Al.

2.4 Electronic Position Correction

The electronic correction removes the small-scale nonlinearities which are introduced by the PSPC wires. This correction can be measured and applied to the X & Y positions of an event independently, but in both cases is a function of pulse-height.

Inputs & Outputs

Inputs:

observed X & Y coordinates of each event in detector coordinates (from Event file)
effective PH bin, PH₃, for each event (after correction described in Section 2.3)
the functions R₁, R₂ & R₃, and S₁, S₂ & S₃ defined below

Outputs:

corrected positions X₁ & Y₁ of each event

Method

The correction is calculated from the pulse-height (after application of the temporal gain correction) using a parabola. The corrected position along the X-axis is then calculated using:

X₁ = R₃(X) + R₂(X)×PH₃ + R₁(X)×(PH₃)²

(5)

and the corrected position along the Y-axis using:

Y₁ = S₃(Y) + S₂(Y)×PH₃ + S₁(Y)×(PH₃)²

(6)

Files

SASS:
The SASS subroutine which performs this is DCORE (within CT module).
http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_intro.html:
No files currently available

2.5 Spatial Gain Correction

The spatial gain correction (SGC) corrects for variations in the gain due to variations in the distance between the anode wires. This correction is therefore only dependent on the Y-coordinate of each event.

Inputs & Outputs

Inputs:

Y-coordinate Y₁ of each event (after correction described in Section 2.4)
effective PH bin, PH₃, for each event (after correction described in Section 2.3)
the functions L, H_A & H_F defined below (from Calibration files)

Outputs:

corrected pulse invariant bin PI of each event

Method

The correction can be separated into a position-dependent low-frequency term (L) and two high-frequency terms - one energy-dependent (H_A), and one position-dependent (H_F). The amplitude of H_A is assumed to be a smooth function of the penetration depth. The pulse-invariant PI bin is calculated using:

PI =

PH₃

L(Y₁) + H_A(PH₃) ×H_F(Y₁)

(7)

The shape of H_A is calculated from measurements at 1.49 keV and thus is normalized to unity at this energy.

Files

SASS:
The position-dependent terms L and H_F are stored in calibration files: GAIN_KOR3_B.FITS and GAIN_KOR3_C.FITS (for PSPCB & PSPCB respectively) which are simple ASCII tables with 800 rows, each row containing the two reals giving the lower L & H_F.
The energy-dependent term H_A is stored in the calibration file GNAMPL_NEW.DAT which is a simple ASCII table with 256 rows, each row containing a single real representing H_A.
The SASS subroutine which uses this is DCORG (within CT module).
http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_intro.html:
The values of the position-dependent terms L and H_F are stored in a calibration files: gain_kor3_b.fits and gain_kor3_c.fits (for PSPCB & PSPCB respectively)
Format: FITS BINTABLE, with 800 rows, and 3 columns where:
- column Y_1 gives Y₁
- column SGC_LF_Y gives L for the position Y₁
- column SGC_HF_Y gives H_F for the position Y₁
The values of the energy-dependent term H_A are stored in a calibration file: gnampl_new.fits (valid for both PSPCs)
Format: FITS BINTABLE, with 256 rows, and 2 columns where:
- column PH_3 gives PH₃
- column SGC_HF_E gives H_A for the value of PH₃

Notes

SASS has been applying the spatial-gain correction based upon the electronically-corrected X coordinate, and this introduced spurious variations in PI channel, as the electronically-corrected Y coordinate should have been used. The http://heasarc.gsfc.nasa.gov/docs/software/ftools/rosat.html task pcpicor recalculates the event file PI column using the Y coordinate.

In the MPE Memo TN-ROS-ME-ZA00/027 "Calibration Corrections to individual PSPC events" (Hasinger & Snowden, 1990), calibration files with different names are referred as being used by SASS. However the memo implies their contents are the same as that described above, hence the name change presumably reflects a change made to SASS and/or the stored values sometime after 1990.

2.6 Window Correction

The window correction removes the large-scale distortions due to the bulging of the detector window as a result of the internal gas pressure versus the external vacuum.

Inputs & Outputs

Inputs:

coordinates X₁ & Y₁ of each event (after corrections described in Section 2.4)
PI bin, PI, for each event (after correction described in Section 2.5)
the functions G_A, G_X & G_Y defined below

Outputs:

corrected coordinates X₂ & Y₂ of each event

Method

The correction is both a function of position and energy, but it is assumed that these components can be separated into separate terms. The energy-dependent term G_A is assumed to be a smooth function of penetration depth. The shape of the Golden Disk is taken from measurements at 0.93 keV, thus G_A is normalized to unity at this energy. The corrected position along the X-axis is then calculated using:

X₂ = X₁ − G_A(PI) ×G_X(X₁, Y₁)

(8)

and the corrected position along the Y-axis using:

Y₂ = Y₁ − G_A(PI) ×G_Y(X₁, Y₁)

(9)

Files

SASS:
The SASS subroutine which performs this correction is DCORW (within CT module).
http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_intro.html:
The values of the energy-dependent term G_A are stored in a calibration file: scal3.fits
Format: FITS BINTABLE, with 256 rows, and 2 columns where:
- column PI gives PI
- column WC_GA_E gives G_A for the value of PI
The values of the position-dependent terms G_X & G_Y are stored in calibration files: tabi_093_j.fits, where i = x or y for G_X & G_Y respectively, and j = b or c for PSPCB & PSPCC respectively.
Format: FITS IMAGE array of dimensions 512×512, where
- axis-1 X₁
- axis-2 Y₁
- stored value is G_X or G_Y

Notes

In the MPE Memo TN-ROS-ME-ZA00/027 "Calibration Corrections to individual PSPC events" (Hasinger & Snowden, 1990), the sign of the correction vectors G_X & G_y is in the opposite sense to that given in equations 8 & 9 (ie TN-ROS-ME-ZA00/027 implies the values in G_X are −1 times those actually stored in the calibration files). This presumably reflects a change made to SASS and/or the stored values sometime

2.7 Plate-scale Non-linearities

The plate-scale varies slightly across the field-of-view due to the use of the (essentially) flat detector compared to the curved surface representing the points at which the XRT is perfectly focussed.

Inputs & Outputs

Inputs:

coordinates X₂ & Y₂ of each event (after corrections described in Section 2.6)
location (X_opt,Y_opt) of the XRT optical axis in detector coordinates,
algorithms and coefficents listed below

Outputs:

corrected coordinates X₃ & Y₃ of each event (the linearized detector coordinates, stored in the DETX & DETY columns of the Event file - Table 1).

Method

The effect of this has been simulated by ray-tracing experiments to give the shift in the centre-of-mass of the point-spread-function as a function of off-axis angle.

X₃ = X_opt + R ×cosδϕ

(10)

Y₃ = Y_opt + R ×sinδϕ

(11)

where

R = r − (4.1305 ×10⁻² × r^0.63)

(12)

r =

√

(δX)² + (δY)²

(13)

δX = X₂ − X_opt

(14)

δY = Y₂ − Y_opt

(15)

δϕ = arctan

δY

δX

(16)

and (X_opt,Y_opt) is the position of the optical axis in detector coordinates, where
X_opt = 4119.0
Y_opt = 3929.0

Files

SASS:
The SASS subroutine which performs this correction is FCOR (within CT module).
http://heasarc.gsfc.nasa.gov/docs/heasarc/caldb/caldb_intro.html:
No files currently available

REFERENCES

G. Hasinger and S Snowden, 1990 TN-ROS-ME-ZA00/027

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