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PSRCHIVE user documentation: pcmImportant Note: The following instructions contain a few intentional mistakes; the intent behind these is to demonstrate a wider variety of related tools and problem solving strategies. If you have limited time, first skim the instructions and then follow the correct path.
Measurement Equation Template Matching ExampleSuppose that you have a well-calibrated template that spans some wide band with some frequency resolution, and an observation that spans the same band with the same frequency resolution. You can match the observation to the template by running
pcm -H -S template.ar observation.arHere, -H is telling pcm to choose the number of harmonics to include as constraints (the fit is performed in the fluctuation frequency domain). You might get an error message like
Error::message mismatch between calibrator template.ar and observation.ar orientation mismatch: -135deg != 0degThis is telling you that the one of receiver parameters is configured differently in these files. To work around this, first have a look at the receiver parameters; e.g.
psredit template.ar | grep rcvr rcvr:name Receiver name MULTI rcvr:basis Basis of receptors lin rcvr:hand Hand of receptor basis +1 rcvr:sa Symmetry angle of receptor basis -90deg rcvr:rph Reference source phase 0deg rcvr:fdc Receptor basis corrected 1 rcvr:prc Receptor projection corrected 1 rcvr:ta Tracking angle of feed 0deg psredit observation.ar | grep rcvr rcvr:name Receiver name unknown rcvr:basis Basis of receptors lin rcvr:hand Hand of receptor basis +1 rcvr:sa Symmetry angle of receptor basis 45deg rcvr:rph Reference source phase 0deg rcvr:fdc Receptor basis corrected 0 rcvr:prc Receptor projection corrected 0 rcvr:ta Tracking angle of feed 0degAnnoyingly, none of the parameters mention the word orientation; but you notice that the difference in "Symmetry angle of receptor basis" is equal to 135 degrees and conclude that this is the parameter to change; e.g.
psredit -c rcvr:sa=-90 observation.ar -mTry again and if all goes well, you'll see messages like the following
pcm -H -S template.ar observation.ar pcm: loading archives pcm: loaded archive: observation.ar pcm: creating model pcm: not normalizing Stokes parameters pcm: loading and setting standard pcm: standard set in 0.00286 seconds pcm: adding observation using Receiver::tracking_angle=0 deg using Horizon::parallactic angle=85.7632044171018 deg pcm: solving model Calibration::SignalPath::solve failure exceeded maximum number of iterations=50 Calibration::SignalPath::solve failure exceeded maximum number of iterations=50 Calibration::SignalPath::solve failure exceeded maximum number of iterations=50 Calibration::SignalPath::solve failure exceeded maximum number of iterations=50 reduced chisq 1336.17590332031 reduced chisq 1100.93566894531 reduced chisq 873.789123535156 reduced chisq 605.220581054688 reduced chisq 424.234100341797 reduced chisq 299.593902587891 reduced chisq 178.428039550781 reduced chisq 109.12866973877 reduced chisq 75.0532836914062 reduced chisq 57.5628433227539 reduced chisq 43.3002166748047 reduced chisq 35.0598678588867 reduced chisq 28.5796070098877 reduced chisq 25.0979061126709 reduced chisq 23.4912281036377 reduced chisq 19.9330711364746 reduced chisq 18.8966464996338 ...The output can be plotted with
psrplot -p calm pcm.fitsand queried using psredit; e.g. to list all polarization calibrator solution parameters
psredit pcm.fits | grep pcal pcal:name Name of calibrator model van04e18 pcal:nparam Number of calibrator model parameters 7 pcal:nchan Number of frequency channels 128 pcal:mjd Epoch of calibration observation 52886.9590000000 pcal:freq* Centre frequency of each channel (MHz) pcal:wt* Weight assigned to each channel pcal:eqn*:name* Parameter name pcal:eqn*:desc* Parameter description pcal:eqn*:val* Parameter value pcal:eqn*:var* Parameter variance pcal:eqn*:chisq Chi squared pcal:eqn*:nfree Number of degrees of freedomTo see the names of the model parameters
psredit -c 'pcal:eqn:name' pcm.fits pcm.fits pcal:eqn:name=G,gamma,phi,el0,or0,el1,or1Channel index 64 is not special, but you must choose a channel that has a valid solution. At this point, you see that the model is parameterized in terms of the ellipticities and orientations of each of the receptors, when what you really want is a single parameter that describes the rotation about the line of sight, as in Equation 19 of Britton (2000). So now you rerun pcm with that model
pcm -H -S template.ar -m bri00e19 observation.ar... wait a while and when pcm is finished
psredit -c 'pcal:eqn:name' pcm.fits pcm.fits pcal:eqn:name=G,gamma,phi,b_1,b_2,r_1,r_2Now you have some boosts and rotations that have numerical indeces instead of letters, but they appear in the same order, so r_2 is r_v, the rotation about the line of sight. It's value in all frequency channels can be printed with
psredit -c 'pcal:eqn:val' pcm.fitsbut this spits out a long comma-separated list. You might want the values on separate lines in a single column, which can be achieved with
psredit -c 'pcal:eqn:val' pcm.fits -d '\n'and to get rid of the leading pcm.fits pcal:eqn:val=
psredit -c 'pcal:eqn:val' pcm.fits -d '\n' -Qqthis output can be redirected to a file named radians.txt and the radio frequency of each channel can be queried and saved to file with
psredit -c 'pcal:freq' pcm.fits -d '\n' -Qq > frequencies.txtPaste the two columns into a single file
paste frequencies.txt radians.txt > plot.txtwhich can be plotted with gnuplot, where you can also fit a wavelength squared functional form to the curve to estimate the RM.