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Last modified: 15 Dec 2011

URL: http://cxc.harvard.edu/ciao4.4/threads/psf/thread.html

Create a PSF

CIAO 4.4 Science Threads


Overview

Synopsis:

The Chandra Ray Tracer (ChaRT) gives the best available HRMA Point Spread Function (PSF) for a point source at any off-axis angle and for any energy or spectrum. The PSF libraries are used in this thread to create a PSF for a specific observation. A comparison of these methods is available from the ChaRT webpages.

[Updated] CIAO 4.4 is the last software release that will include the mkpsf tool. It will be removed from the next version of CIAO.

Purpose:

To create an image of the PSF for a source, and normalize it to the source flux. The PSF changes with source position and photon energy, and is created by interpolation of a library of pre-launch calibration files (the PSF hypercube library).

Related Links:

Last Update: 15 Dec 2011 - reviewed for CIAO 4.4: added note that mkpsf will be removed in the next CIAO release.


Contents


The PSF Libraries

To create a PSF for a source, the PSF library for the instrument of interest (i.e. ACIS or HRC) must be installed. These libraries are supplied as part of the CALDB and can be downloaded if they are not already available. The ACIS and HRC libraries are stored in $CALDB/data/chandra/acis/2d_psf/ and $CALDB/data/chandra/hrc/2d_psf/ respectively:

unix% ls -1 $CALDB/data/chandra/acis/2d_psf/
acisi1998-11-052dpsf1N0002.fits
acisi1998-11-052dpsf2N0002.fits
acisi1998-11-052dpsf3N0002.fits
acisi1998-11-052dpsf4N0002.fits
aciss1998-11-052dpsf1N0002.fits
aciss1998-11-052dpsf2N0002.fits
aciss1998-11-052dpsf3N0002.fits
aciss1998-11-052dpsf4N0002.fits
cxcpsflib.manual.ps@
README.txt

unix% ls -1 $CALDB/data/chandra/hrc/2d_psf/
cxcpsflib.manual.ps@
hrci1998-11-052dpsf1N0002.fits
hrci1998-11-052dpsf2N0002.fits
hrci1998-11-052dpsf3N0002.fits
hrci1998-11-052dpsf4N0002.fits
hrcs1998-11-052dpsf1N0002.fits
hrcs1998-11-052dpsf2N0002.fits
hrcs1998-11-052dpsf3N0002.fits
hrcs1998-11-052dpsf4N0002.fits
README.txt

The PSF changes with both the energy of the incoming photons and their location on the focal plane of the instrument, as described in the Chandra Proposers' Observatory Guide. Each library contains a grid of PSF images covering a range of energies and locations on the detector plane; linear interpolation of these images is used to create the requested PSF.

Currently the PSF library is evaluated at five energies - 0.277 keV, 1.4967 KeV, 4.51 keV, 6.4 keV, and 8.6 keV - for a range of positions that depend on which library is used. A summary of the available libraries is available in the PSF Library section of the CIAO dictionary. The recommended libraries are the f1 and f2 files for each detector; use the f1 library if the off-axis angle of the source is within the library's field of view, otherwise use the f2 library (see the PSF library manual (PS, 16pp) for the area covered by each library).


Get Started

Download the sample data: 1838 (ACIS-S, G21.5-09)

unix% download_chandra_obsid 1838 evt2,asol

In this thread we only use data in the energy range 0.3 to 8 keV; an image of the source region is also created:

unix% dmcopy "acisf01838N002_evt2.fits[energy=300:8000]" acis_1838_evt2.fits
unix% dmcopy "acis_1838_evt2.fits[bin x=3821:4320:1,y=4000:4499:1]" img_src_0.3-8keV.fits

Characterizing the Source

Several of the following steps require that you have a source region defined for your observation. Figure 1 shows the event file display in ds9 with the source region overlaid.

[Thumbnail image: The source region is defined as a green circle.]

[Version: full-size]

[Print media version: The source region is defined as a green circle.]

Figure 1: Source region defined on the data

The region defined in this example is circle(4069.5,4250.5,80).

What is the energy of the source? (dmextract)

For the dataset we are using, the source has a maximum at sky coordinates of (4069.5,4250.5). We use the dmextract tool to create an energy histogram of all photons that fall within 20 pixels of this location. Since we are not going to use this for spectral analysis, we set the output type to generic, and use a bin size of 0.1 keV to improve the signal-to-noise ratio:

unix% punlearn dmextract
unix% pset dmextract infile="acis_1838_evt2.fits[sky=circle(4069.5,4250.5,20)][bin energy=300:8000:100]"
unix% pset dmextract outfile=energy_histogram.fits
unix% pset dmextract opt=generic
unix% dmextract
Input event file  (acis_1838_evt2.fits[sky=circle(4069.5,4250.5,20)][bin energy=300:8000:100]): 
Enter output file name (energy_histogram.fits): 

You can check the dmextract parameter file that was used with plist dmextract.

The dmstat tool is used to find the maximum count rate from the histogram, followed by dmlist to locate the corresponding energy. For instance:

unix% dmstat "energy_histogram.fits[cols count_rate]"
COUNT_RATE[count/s]
    min:        0.00025473465771              @:        4
    max:        0.039865973932        @:        16
   mean:        0.013024549966
  sigma:        0.010659169807
    sum:        1.0028903474
   good:        77
   null:        0

unix% dmlist "energy_histogram.fits[count_rate > 0.03][cols energy,count_rate]" data,clean
#  ENERGY               COUNT_RATE
               1750.0     0.03770072934115
               1850.0     0.03986597393168
               1950.0     0.03387970947549

This shows that the maximum count rate is at 1.85 keV. For this thread, we choose to evaluate the PSF at an energy of 3 keV, which corresponds to a count rate of ~0.022 counts/s:

unix% dmlist "energy_histogram.fits[cols energy,count_rate][energy=2900:3100]" data,clean
#  ENERGY               COUNT_RATE
               2950.0     0.02585556775761
               3050.0     0.02190718056310

The peak in the spectrum may also be estimated from a ChIPS plot:

unix% chips
-----------------------------------------
Welcome to ChIPS: CXC's Plotting Package
-----------------------------------------
CIAO 4.4 ChIPS version 1 Friday, December 2, 2011

chips> make_figure("energy_histogram.fits[cols energy,count_rate]", "symbol.style=none")
chips> add_point(3050,0.022,"color=red style=circle")
chips> quit

The resulting plot is shown in Figure 2.

[Thumbnail image: A line plot of the energy histogram eV vs counts/s.]

[Version: full-size, PNG]

[Print media version: A line plot of the energy histogram eV vs counts/s.]

Figure 2: Plot of the spectrum

The red symbol is at ~3 keV, which is the energy at which the PSF will be extracted.


How far off axis is my source? (dmstat)

mkpsf uses the input SKY coordinates to determine how far off-axis the source is (see the Create a PSF Image File section), but it may be of interest to determine the off-axis angle for yourself as well. The location of the source in the focal plane of the detector can be found by using dmcoords.

In many cases, there will be more than one aspect solution file (pcad_asol1.fits) for an observation. All the files must be input, either as a list or as a stack. Here we use:

unix% cat pcad_asol1.lis
pcadf084244404N002_asol1.fits

unix% punlearn dmcoords
unix% dmcoords acis_1838_evt2.fits option=sky x=4069.5 y=4250.5 asolfile=@pcad_asol1.lis
unix% pget dmcoords theta
1.282061483350824

The off-axis angle of the source is 1.282 arcminutes.


Number of photons in the source (dmstat)

For this example, we use a simple method for estimating the number of source photons; namely dmstat with a circular aperture (radius of 80 pixels) to define the source counts and an annulus of width 10 pixels outside this for the background:

unix% punlearn dmstat
unix% pset dmstat centroid=no sigma=no
unix% dmstat "img_src_0.3-8keV.fits[sky=circle(4069.5,4250.5,80)]" 
EVENTS_IMAGE
    min:        0             @:        ( 4057.5 4171.5 )
    max:        83            @:        ( 4072.5 4246.5 )
   mean:        1.1521338579
    sum:        23136
   good:        20081
   null:        5840

unix% dmstat "img_src_0.3-8keV.fits[sky=annulus(4069.5,4250.5,80,90)]"
EVENTS_IMAGE
    min:        0             @:        ( 4069.5 4160.5 )
    max:        3             @:        ( 4150.5 4232.5 )
   mean:        0.063802083333
    sum:        343
   good:        5376
   null:        27385

You can check the dmstat parameter file that was used with plist dmstat.

The number of source photons is therefore: 23136 - 3.7647 * 343 = 21845. Note that the factor 3.7647 is used to scale the background counts to match the source count area, and is therefore the ratio of the source area to the background area; if you change your source or background area, then you'll have to change this number:

pi * r_src^2 / ( pi * (r_out^2 - r_in^2) )

= 80^2 / ( 90^2 - 80^2 ) = 3.76471

The regions used for calculating the source and background signals are accurate for this example case; they should be changed to match the particulars of each dataset. For example, the background region above would be incorrect for a large, extended source.


Create a PSF Image File (mkpsf)

The CIAO tool mkpsf creates a PSF image. If the requested coordinates and energy do not match those in the PSF library, then the output image is constructed by linearly interpolating the library data. We shall use the f1 ACIS-S library for the sky coordinates (4069.5,4250.5) and evaluate it at an energy of 3.0 keV. The pixel size and roll angle of the output image are taken from the infile parameter.

unix% punlearn mkpsf
unix% pset mkpsf coord=SKY x=4069.5 y=4250.5 energy=3.0
unix% pset mkpsf psflibfile=$CALDB/data/chandra/acis/2d_psf/aciss1998-11-052dpsf1N0002.fits
unix% pset mkpsf infile=img_src_0.3-8keV.fits
unix% pset mkpsf outfile=psf_3keV.fits
unix% pset mkpsf rotpts=9
unix% mkpsf
input coordinate system (SKY|DET) (SKY): 
PSF binning in x direction (0.25:256.0) (INDEF): 
PSF binning in y direction (0.25:256.0) (INDEF): 
PSF size in x direction (2:2048) (INDEF): 
PSF size in y direction (2:2048) (INDEF): 
input file (img_src_0.3-8keV.fits): 
energy in keV (0) (3): 
x (4069.5): 
y (4250.5): 
PSF library file (/soft/ciao/CALDB/data/chandra/acis/2d_psf/aciss1998-11-052dpsf1N0002.fits): 
output file (psf_3keV.fits): 
psflib data output basename ('.' to use output file) (): 
File psf_3keV.fits was created

The output image (psf_3keV.fits) is shown in Figure 3. You can check the parameter file that was used with plist mkpsf.


Normalize PSF to total counts in source (dmstat, dmimgcalc)

First, use dmstat to find the "signal" in the PSF image:

unix% dmstat psf_3keV.fits
AXAF_2DPSF
    min:        0             @:        ( 3942 4123 )
    max:        0.33929860592         @:        ( 4069 4250 )
   mean:        2.7752508086e-05
    sum:        1.8187883776
   good:        65536
   null:        0

and then dmimgcalc to normalize this image to the source counts (21845 counts). The PSF image is multiplied by 12011 (~= 21845/1.81878):

unix% punlearn dmimgcalc
unix% pset dmimgcalc infile=psf_3keV.fits infile2=none
unix% pset dmimgcalc weight=12011
unix% pset dmimgcalc operation=add
unix% pset dmimgcalc out=psf_3keV_norm.fits
unix% dmimgcalc
Input file #1 (psf_3keV.fits): 
Input file #2 (none): 
output file  (psf_3keV_norm.fits): 
arithmetic operation (add): 

You can check the parameter file that was used with plist dmimgcalc.

To check the signal in the normalized PSF model:

unix% dmstat psf_3keV_norm.fits
psf_3keV_norm.fits
    min:        0             @:        ( 3942 4123 )
    max:        4075.3155557          @:        ( 4069 4250 )
   mean:        0.33333537602
    sum:        21845.467203
   good:        65536
   null:        0

If the absolute normalization of the PSF is important, make sure that you read about the limitations of the PSF library.


Caveats

As discussed in the PSF library manual (PS, 16pp), the libraries contain weight information to account for the finite domain of the data (i.e. the fact that not all the simulated photons fell within the regions stored in the library). However, mkpsf currently cannot access this weight information, and so cannot account for the total number of photons used to create the PSF. Users should beware of this limitation if the normalization of the PSFs (i.e. the fraction of PSF photons that fall within the output region) is important (e.g. when attempting to calculate encircled energy fractions, calculating the PSF profile at large distances from a source).

Unless you specify a position and energy that corresponds to one of the grid points in the PSF libraries, mkpsf will use linear interpolation to create the model PSF. In this case, the model can only be considered an approximation to the true PSF, and must be used with care.

Energy

The two nearest energies to the energy used in this thread (3 keV) are 1.4967 keV and 4.51 keV. Figure 4 shows the PSFs extracted at these energies; the circle has the same radius in all three images.

The energies used to evaluate the PSFs are stored in the ENERGY_BINS block of the library:

unix% dmlist "$CALDB/data/chandra/acis/2d_psf/aciss1998-11-052dpsf1N0002.fits[ENERGY_BINS]" data
 
--------------------------------------------------------------------------------
Data for Table Block ENERGY_BINS
--------------------------------------------------------------------------------
 
ROW    ENERGY_BIN ENERGY              
 
     1          1               0.2770
     2          2              1.49670
     3          3                4.510
     4          4                 6.40
     5          5                 8.60

Position

The PSF library contains PSFs evaluated at a number of spatial locations (grid points) in the azimuth and elevation (off-axis angle) coordinate system (as discussed in the PSF library manual (PS, 16pp) and the CIAO dictionary). To find the nearest grid points to your source, convert the polar coordinates (PHI,THETA) to their cartesian values (azimuth,elevation). For the source used above, we have:

PHI   = 6.75  deg
THETA = 1.282 arcmin

which is

azimuth   = 0.15 arcmin
elevation = 1.27 arcmin

The four nearest positions in the f1 library are therefore (+1,0), (+2,0), (+1,+1), and (+2,+1) in (azimuth,elevation).

While you can extract the information directly from the AXAF_2DPSF block of the PSF library, the returned dataset will not be rotated to match your observation, the pixel size may not match, and the WCS information will not match that of your data. Here we show how to obtain the 4.510 keV ACIS-S PSF at the (+8,-4) position of the f1 library.

First we need to know which part of the library to extract. Listing the psf library file shows that the first two axes of the library are the spatial dimensions, #3 is the defocus setting, #4 is the energy, and #5,#6 are the grid position.

unix% dmlist "$CALDB/data/chandra/acis/2d_psf/aciss1998-11-052dpsf1N0002.fits[AXAF_2DPSF]" cols
  
--------------------------------------------------------------------------------
Columns for Image Block AXAF_2DPSF
--------------------------------------------------------------------------------
 
ColNo  Name                 Unit        Type             Range
   1   AXAF_2DPSF[256,256,1,5,21,11]              Real4(256x256x1x5x21x11) -Inf:+Inf            
 
--------------------------------------------------------------------------------
Physical Axis Transforms for Image Block AXAF_2DPSF
--------------------------------------------------------------------------------
 
Group# Axis# 
   1   1,2    PSF(PSFX) = (+0)[pixel] +(+0.250)* ((#1)-(+128.0))
                 (PSFY)   (+0)         (+0.250)  ((#2) (+128.0))
   2   3      Z                    = #3 
   3   4      AXIS4                = #4 
   4   5,6    DET(DETX) = (+4096.50)[pixel] +(+121.9512)* ((#5)-(+11.0))
                 (DETY)   (+4096.50)         (+121.9512)  ((#6) (+6.0 ))
 
--------------------------------------------------------------------------------
World Coordinate Axis Transforms for Image Block AXAF_2DPSF
--------------------------------------------------------------------------------
 
Group# Axis# 
   1   1,2    RELPOS(Y) = (+0)[mm] +(+0.0240)* (PSF(PSFX)-(+0))
                    (Z)   (+0)      (+0.0240)  (   (PSFY) (+0))
   2   3      DEFOCUS              = Z 
   3   4      ENERGY               = AXIS4 
   4   5,6    MSC(THETA) = (+0)[deg] +TAN-P[(+0.000136667)* (DET(DETX)-(+4096.50))]
                 (PHI  )   (+0)             (+0.000136667)  (   (DETY) (+4096.50)) 
   4   5,6    LSI(LSIY) = (+0)[mm] +(+0.0240)* (DET(DETX)-(+4096.50))
                 (LSIZ)   (+0)      (+0.0240)  (   (DETY) (+4096.50))
   4   5,6    AZEL(AZ) = (+0)[deg] +(+0.000136667)* (DET(DETX)-(+4096.50))
                  (EL)   (+0)       (+0.000136667)  (   (DETY) (+4096.50))

From the listed transformations, we find that:

  AZ = 0.000136667 * 121.9512 * ((#5)-(+11.0)) (degrees)
     = #5 - 11 (arcminutes)
  EL = 0.000136667 * 121.9512 * ((#6)-(+6.0))  (degrees)
     = #6 - 6  (arcminutes)

Therefore, (+8,-4) location corresponds to axis location (#5=19,#6=2) and an energy of 4.51 keV corresponds to #4=3 (from above). As there is only one defocus setting in the library, the following DM filter produces a (256,256,1,1,1) copy of the PSF image:

unix% dmcopy \
      "$CALDB/data/chandra/acis/2d_psf/aciss1998-11-052dpsf1N0002.fits[AXAF_2DPSF][#1=1:256,#2=1:256,#3=1:1,#4=3:3,#5=19:19,#6=2:2]" \
      psflib_4.51keV_p8_m4.fits

The resulting image is shown in Figure 5.

[Thumbnail image: The PSF image is displayed in ds9 with the "b" colormap.]

[Version: full-size]

[Print media version: The PSF image is displayed in ds9 with the "b" colormap.]

Figure 5: Image of off-axis PSF

The PSF is displayed with zoom=2.


Common Errors

A common mistake is to use the library of a different detector, for instance using aciss1998-11-052dpsf1N0002.fits when the ACIS-I array was at the telescope focus.



Parameters for /home/username/cxcds_param/dmextract.par


#--------------------------------------------------------------------
#
# DMEXTRACT -- extract columns or counts from an event list
#
#--------------------------------------------------------------------
        infile = acis_1838_evt2.fits[sky=circle(4069.5,4250.5,20)][bin energy=300:8000:100] Input event file 
       outfile = energy_histogram.fits Enter output file name
          (bkg = )                Background region file or fixed background (counts/pixel/s) subtraction
        (error = gaussian)        Method for error determination(poisson|gaussian|<variance file>)
     (bkgerror = gaussian)        Method for background error determination(poisson|gaussian|<variance file>)
      (bkgnorm = 1.0)             Background normalization
          (exp = )                Exposure map image file
       (bkgexp = )                Background exposure map image file
      (sys_err = 0)               Fixed systematic error value for SYS_ERR keyword
          (opt = generic)         Output file type: pha1 
     (defaults = ${ASCDS_CALIB}/cxo.mdb -> /soft/ciao/data/cxo.mdb) Instrument defaults file
         (wmap = )                WMAP filter/binning (e.g. det=8 or default)
      (clobber = no)              OK to overwrite existing output file(s)?
      (verbose = 0)               Verbosity level
         (mode = ql)              



Parameters for /home/username/cxcds_param/dmstat.par


        infile = img_src_0.3-8keV.fits[sky=annulus(4069.5,4250.5,80,90)] Input file specification
   out_columns = EVENTS_IMAGE     Output Column Label
       out_min = 0                Output Minimum Value
   out_min_loc = 4069.5,4160.5    Output Minimum Location Value
       out_max = 3                Output Maximum Value
   out_max_loc = 4150.5,4232.5    Output Maximum Location Value
      out_mean = 0.063802083333   Output Mean Value
    out_median =                  Output Median Value
     out_sigma =                  Output Sigma Value
       out_sum = 343              Output Sum of Values
      out_good = 5376             Output Number Good Values
      out_null = 27385            Output Number Null Values
    out_cnvrgd =                  Converged?
 out_cntrd_log =                  Output Centroid Log Value
out_cntrd_phys =                  Output Centroid Phys Value
out_sigma_cntrd =                  Output Sigma Centroid Value
     (centroid = no)              Calculate centroid if image?
       (median = no)              Calculate median value?
        (sigma = no)              Calculate the population standard deviation?
         (clip = no)              Calculate stats using sigma clipping?
       (nsigma = 3)               Number of sigma to clip
      (maxiter = 20)              Maximum number of iterations
      (verbose = 1)               Verbosity level
         (mode = ql)              



Parameters for /home/username/cxcds_param/mkpsf.par


#
# MKPSF -- retrieve PSF from library for given (energy,x,y) position
#
###########################################################################
#
#       COORDINATE SYSTEM parameters
#
         coord = SKY              input coordinate system
#
#       PSF binning parameters
#
       binspax = INDEF            PSF binning in x direction
       binspay = INDEF            PSF binning in y direction
#
#       PSF size parameters
#
      sizeoutx = INDEF            PSF size in x direction
      sizeouty = INDEF            PSF size in y direction
#
#       input file parameters
#
        infile = img_src_0.3-8keV.fits input file
#
#       PSF position parameters
#
        energy = 3                energy in keV
             x = 4069.5           x
             y = 4250.5           y
#
#       PSF library file parameters
#

    psflibfile = /soft/ciao/CALDB/data/chandra/acis/2d_psf/aciss1998-11-052dpsf1N0002.fits PSF library file

#
#       output file parameters
#
       outfile = psf_3keV.fits    output file
    outpsffile =                  psflib data output basename ('.' to use output file)
#
#       pixlib geometry parameter file
#
      (geompar = geom)            Parameter file for Pixlib Geometry files
#
#       PSF roll parameter
#
       (rotpts = 9)               number of pixel points in x or y direction for rotation
#
# debug print control
#
      (verbose = 0)               verbose mode
#
# system variables
#
      (clobber = no)              overwrite existing output file?
         (mode = ql)              



Parameters for /home/username/cxcds_param/dmimgcalc.par


# parameter file for dmimgcalc
        infile = psf_3keV.fits    Input file #1
       infile2 = none             Input file #2
       outfile = psf_3keV_norm.fits output file
     operation = add              arithmetic operation
       (weight = 12011)           weight for first image
      (weight2 = 1)               weight for second image
    (lookupTab = ${ASCDS_CALIB}/dmmerge_header_lookup.txt -> /soft/ciao/data/dmmerge_header_lookup.txt) lookup table
      (clobber = no)              delete old output
      (verbose = 0)               output verbosity
         (mode = ql)



History

14 Dec 2004 updated for CIAO 3.2: include dmcoords asolfile parameter
12 Dec 2005 updated for CIAO 3.3: default value of dmextract error and bkgerror parameters is "gaussian"; changes to dmstat parameter file
01 Aug 2006 corrected use of azimuth (phi) and elevation (also called the off-axis angle, theta)
01 Dec 2006 updated for CIAO 3.4: ChIPS version
16 Jan 2008 updated for CIAO 4.0: ChIPS plotting updated to CIAO 4.0 syntax; dmstat and dmlist are alternatives for finding the energy and count rate; filename and screen output updated for reprocessed data (version N002 event file)
09 Feb 2009 updated for CIAO 4.1: images are inline; added verbose parameter to dmstat output; calibration file paths updated for CALDB 4; Python and S-Lang syntax included for ChIPS commands
08 Feb 2010 updated for CIAO 4.2: ChIPS version; dmcoords asolfile parameter is automatic (not hidden)
12 Jan 2011 reviewed for CIAO 4.3: no changes
15 Dec 2011 reviewed for CIAO 4.4: added note that mkpsf will be removed in the next CIAO release.

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Last modified: 15 Dec 2011
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