Reductions for the UBVRI Photopolarimeter at NOT

Version 1.2, 24.3.1993 Vilppu Piirola

A software package has been written for an IBM PC/AT type environment with HP-GL or PostScript compatible graphics device. Versions for the IDL graphics language have been developed at Helsinki Observatory, too. In general, the output files of the reduction programs can be further handled by other data analysis and graphics systems.

The raw data are stored by the polarimeter on standard 1.44 MB 3.5 inch floppy disks. Several nights' observations can be stored on one diskette, and normally the measurements of one night form a file.

1. Computing polarization parameters and raw magnitudes ( POLRED , CIRLI)

To carry out the first reduction step, you must have a file containing the position angle zero-point 'constants' to be used for the particular night. If you do not know the values, you can use those listed below (stored in the file COR.DAT in the C:\POLAR directory), and make any necessary correction at a later reduction step. The file is of the form:
17.4
.74 3.2 .0 -3.7 -3.6
where the first line gives the zero-point correction, CP, of position angle in degrees and the second line the wavelength dependent part of the position angle correction, CPA, in degrees. The five columns from left to right correspond to the U, B, V, R, and I, bands, respectively. The file is read in free format and a space must be used as the separator between the columns.

To start the reduction, type POLRED, and the program will ask you the output file name, and the input and constant file names. After completing the reductions of one file, a new input file name is asked. In this way the results of several nights can be stored in one output file, if desired. To exit, type END.

POLRED interpolates the background intensity between each sky measurement, if the star number or diaphragm has not been changed, otherwise the first background value is used. The program calculates the Stokes parameters Px and Py for linear polarization from the eight integrations made in different orientations of the half-wave retarder. Error estimates are calculated both from the photon statistics (E1) and from the least square fit to the eight integrations (E2). If E2 > 2E1, the integration with the largest residual is searched and discarded, and the remaining seven integrations used only. This helps in rejecting occasional disturbances due to bad guiding or strong RF-sources (sparking relays etc.). A message is given each time when the rejection has been made. Normally this may happen a few times per night and should not be worried about too much, unless rejections appear frequently, which in most cases indicates star drifting close to the edge of the diaphragm.

As shown in the Instructions for the use of the UBVRI photopolarimeter, the second line of the data file (after the header line) must give the date, starting with the measurement code 9, and the third line must be the command for polarimetric mode, starting with the code 8. Similarly, the last line of each night's data must be followed by a line starting with number 9, to indicate the end of the night (see an example of data aquisition file ).

If the polarimeter is used in the simultaneous linear & circular polarization mode, the first reduction step is carried out with CIRLI. This program provides an easy way of correcting the PC clock drift. Any number of clock comparisons can be provided in a file of the format:

hh mm ss hc mc sc
.. ..  etc. .. ..
where 'hh mm ss' give the true UT time and 'hc mc sc' the PC clock time at the corresponding moment. CIRLI interpolates the clock correction between successive clock comparisons. If no clock comparisons were made during the observations, the following file (e.g. CLO.DAT) can be written:
18 0 0 18 0 0
6 0 0 6 0 0
This means adopting the PC system clock as the true UT time. CIRLI asks the input and clock comparison file names and the output file names for linear and circular polarization. The position angle zero-point correction asked can be given zero, and any possible correction found necessary can be made at a later step.

2. Computing averages, nightly means, and normal points ( KOKPOL )

To execute KOKPOL, you must first write a file specifying the identification numbers of the stars for which average polarization values are to be computed. The star file is of the format (e.g. file STAR.STA in the C:\POLAR directory):
32 0 0 0 0
123 0 0 0 0
45678 0 0 0 0
23456 7214.3962 0.1234567 12.52 -24.16
Each line gives the star identification number, epoch of zero phase (with last four digits of Julian Date), the period (days), and the coordinates alpha and delta in decimal form, to be used for heliocentric correction of the normal points. Irrelevant information is replaced with zeroes.

KOKPOL asks the necessary file names, and in a self- explanatory way the desired averaging procedures. The output file from POLRED (an example) is used as the input file for KOKPOL. If the data are spread in several files, the program PICKUP should be run first to pick up the observations of the stars specified in the star file shown above. Also the DOS command COPY can be used to collect the data into one file. At the end of the execution the names of the output files created for plotting the nightly means (PLOTFIN.SA) and the polarization normal points (PLOTFIL.SA) are shown, if applicable. The output file PR.AA contains the results in a tabular form for printer (see example).

The weighted averaging procedure uses the inverse square of the estimated error for each observation for weighting. The error estimate is taken either from the least square fit of the double cosine curves to the eight integrations in the different positions of the half-wave retarder (E2 in Table 2), or from the photon statistics (E1 in Table 2), whichever is greater. This prevents weights having values larger than the theoretical maximum corresponding to photon noise limit, which could happen if only the least square fits with only eight data points in each observation were relied.

3. Making additional corrections for instrumental constants

If the average values obtained with KOKPOL for the standard stars deviate systematically from the catalogue values, the results stored in the output files of POLRED can be corrected with the program ADDCOR and then recalculated with KOKPOL. The instrumental corrections for ADDCOR are given from a file of the form (file COR.ADD in the C:\POLAR directory)

1.4
0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
0. 0. 0. 0. 0.
where the first line gives the additional correction required for the position angle zero-point in the V band (CP) and the second line the wavelength dependent part, i.e. corrections required relative to the V band (CPA). The two last lines give the instrumental polarization produced by the telescope optics, Px and Py, in the UBVRI bands, respectively (in percents). If desired, the corrections can also be given from the keyboard, as asked by the program. The constants for POLRED may also be updated by the amounts used by ADDCOR, which removes the need of running ADDCOR again for the subsequent nights, at least for a typical run of less than 1-2 weeks.

The zero-point of position angle CP and its wavelength dependent part CPA are best determined from observations of large polarization standard stars. Note that the corrections given in the constant file are added to the observed values, both in the case of CP and CPA. Usually CPA(V)=0.0 since the corrections for other bands are taken relative to the V band.

The instrumental polarization parameters Pxi and Pyi are determined by averaging the observed Px and Py parameters of a sample of zero-polarization standard stars with a special program KOKINST (not yet implemented for NOT), which is a modification of KOKPOL, and includes rotation of the observed polarization vectors from the equatorial to the telescope optics coordinate system. This is required because of the field rotation in an alt-az telescope changes the relative orientation of the polarimeter and the telescope optics. The instrumental polarization produced by the telescope has been found to be very small, and zero values can so far be used in the file COR.ADD for most applications.

4. Photometric reductions for the UBVRI photopolarimeter (preliminary)

If the instrument was used in the sky-chopping photometric mode, the first reduction step is carried out by the program FOTMON . For data obtained in the non-chopping (single channel) mode the corresponding program is FOTMO. In the latter case the background measurements must be designated with the measurement code 3 (first digit in the record containing the star number). If more than one background measurement are made, the values of background are linearly interpolated with time for each star integration, if the star number is not changed between the sky measurements.

The raw photometric data obtained during polarization measurements, and stored in the output file of POLRED, can be extracted and written in a more compact file by the program FOTLI (see Table 5). This also brings the data into the same format as used in the output files from FOTMON and FOTMO. The magnitudes stored in the polarization data file are averages from eight integrations corresponding to one complete polarization measurement. A better time resolution is provided by the program FASTFOT , which computes magnitudes from the individual integrations of the original data file. The version FASTFO applies a clock comparison file similarly as CIRLI.

For further reduction steps a file containing the necessary information on the observed stars must be given (e.g. file STAF.STA in the C:\POLAR directory):

1234 6789.1234 0.123456 12.45 16.72 0.0038 0 0 0 0 0
67321 0. 0. 11.68 24.54 0. 9.432 .249 .362 .453 .395
where the columns give the star number, T(0), period (days), RA and DEC in decimal form, Heliocentric correction (days), V, U-B, B-V, V-R, and V-I. The magnitude and colour data are given for comparison stars only, and must be zeroes for the objects (variables). The heliocentric correction can be given zero, in which case the program computes it each time when the star number is changed, using the coordinates RA and DEC and the epoch of observation (J.D.).

There are two programs for simple differential photometry reductions, FOTLIM , which lists UBVRI magnitudes, and FOTLIN , for V, U-B, B-V, V-R, R-I indices, both programs with extinction reduction based on the coefficients provided in data sequences inside the program. This is a satisfactory arrangement for differential photometry in cases where the object and the comparison star are not too far from each other, when the spectral type and location on the sky are concerned. The zero-point correction can be interpolated between each comparison star observation with the program FOTOUT , which uses the output file from FOTLIM or FOTLIN as the input, and lists the final results for the program star observations in the output file. More sophisticated photometric reduction packages are under developement for the PC/AT versions of the programs.

The UBVRI light curves consisting of the individual photometric measurements (integrations) can be plotted with the program HSPLOT . To give the header and scaling for the plot, three lines must be added in top of the output file of FOTOUT. For example:

RE2107-05 1992 Oct 25/26
2107 .0 0 8773.6928 0.08676861
0.5 17.2 18. 18. 17.5 17.1
........ data lines from FOTOUT ..........
The first line gives the header, the second line from left to right: star no, phase shift (if any), location of phase zero in the plot (0-9), time of zero phase T(0), period, and the third line from left to right: scale/div (mag), and the origin (=bottom) of mag scales in the UBVRI bands. The T(0) and period can be given zeroes, in which case the phase values calculated by FOTLIM in the file are used.

Light curves can also be plotted against Julian Date, by the program HSPLOTJD . For this case the second line of the above example file must give from left to right: star no, lower limit of JD interval, and the upper limit of the JD interval to be plotted.

Photometric normal points can be calculated by FOTNORM , from the same file as is used for plotting the individual integration light curves, i.e. there must be the three lines (shown above) in the beginning of the output file from FOTOUT. In particular, the T(0) and Period values must be given, since they are needed for FOTNORM. The photometric normal points stored in the ouput file of FOTNORM can be plotted by PLOTA4M directly, without editing the file, although for fine tuning of the plot the mag-scale and origin values may be altered in the file.

5. Plotting programs for polarization and photometric results

A number of self-explanatory plotting programs in Fortran are available in versions for IBM PC/AT, utilizing the HP-GL language (see Figs. 1-4). The plots can be viewed on the screen e.g. by the HPP command, which is a batch file for PRINTGL software. HPO shows an A4 sheet in vertical orientation. The previewing of plots offers reasonably good and fast possibilities for 'fine-tuning' of the plotted diagrams.

The plots can be converted into a PostScript file (PLOT.PS) for printing, by the command HPS <file.plt>, where <file.plt> is the name of the HP-GL plot file created by one of the programs summarized below. HPS appends new plots to the PLOT. PS file, and hence several plots (sheets) can be printed from the same file. The PLOT.PS file must be deleted before creating a new PostScript file for another set of plots for printing with a laser. The HP LaserJet printers can also be set to a mode to print graphics directly from the HP-GL files.

PLOTA4L - plotting normal points of the degree of polarization P (%) as a function of phase. Uses the file (PLOTFIL.SA) created by KOKPOL as the input file.

PLOTA4C - the same for circular polarization

PLOTPA4 - the same for position angle (P.A) of the linear pol.

PLOTAL - plotting nightly mean values of polarization (from file PLOTFIN.SA) or normal points (file PLOTFIL.SA) of polarization as a function of phase. The range is given for each colour band separately.

PLOTPA - the same for position angle (P.A.)

PLOTAP - plotting P (%) and P.A. on the same sheet (A4) from the normal point file (PLOTFIL.SA)

PLOTAXY - plotting nightly means or normal points of the Stokes parameters Px and Py as a function of phase. Scaling is done automatically, either independently in each band or having the same scale/div in each band as instructed from the keyboard.

JDPLOTP - plotting polarizations as a function of Julian Date.

JDPLOTXY - the same for Px and Py

JDPLOTA - the same for position angle

JDPLOT - plotting P and P.A. as a function of J.D.

HSPLOT - plotting UBVRI magnitudes as a function of phase from a file created by FOTLIM & FOTOUT. See section 4 for input file format (file STAF.STA).

HSPLOTJD - like HSPLOT, but plotting vs. Julian Date (see section 4 for input file format).

PLOTA4M - Plotting normal points of UBVRI magnitudes with error bars, created by FOTNORM.

COUNTS - is a batch file for plotting onto the screen the raw photon counts obtained in the polarimetric modes. This is useful for checking the stability of background values and the atmospheric transparency. After running COUNTS it is possible to adjust the scales by changing the corresponding parameters in the third line of the file APU.DAT (created by COUNT) like with the programs HSPLOT, HSPLOTJD and PLOTA4M before. The plot can then be redrawn by COUNTPLO and viewed by HPO.

HPO - is a batch file to start PRINTGL for screen previewing a plot. The /FV parameter specifies a standard VGA display, and /FV+ an enhanced 800x600 mode with a multisync monitor. If you know the type of the graphics card, you can give the specification by e.g. /FV+$54 for ATI 1024x768 (Gateway), and /FV+$58 for Paradise 800x600 graphics cards (see PRINTGL.DOC for further details). The parameter /M0.78 defines magnification 78 % to fit the upright A4 sheet to the screen, and can be modified as necessary. Example of HPO.BAT:

printgl /FV /O3 /WAF /M0.78 /P%1 %2 %3 %4 %5 %6 %7 %8 %9
HPP - is like HPO but the A4 sheet is plotted horizontally to fill the whole screen.

HPS - creates a Postscript file (PLOT.PS) from a HP-GL file. New plots are added to the previous PLOT.PS file. Example: HPS hsplot.plt

HP - is another previewing program which works faster than PRINTGL. It also has zooming capabilities, but does not give as good HP-GL emulation as PRINTGL.



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