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Ïîèñêîâûå ñëîâà: m 87 jet
INSTRUMENT SCIENCE REPORT
FOC­057
TITLE: The FOC Polarizing Filters
AUTHOR: P. E. Hodge DATE: 4 October 1994
ABSTRACT
This report describes preliminary calibration of the FOC polarizing filters. The approximate
position angles of the filters were determined to be as follows. The POL0 filter passes light
with electric vector parallel to the sample direction. The POL60 polarization direction is
60 ffi counterclockwise from POL0, as projected onto the sky, and the POL120 polarization
direction is 120 ffi counterclockwise from POL0 as projected onto the sky. These position
angles should be correct to within 10 ffi , and more accurate values will be obtained by further
analysis of existing data. Additional observations will be needed to measure the image shifts
and the relative throughputs of the polarizing filters.
0 DISTRIBUTION:
FOC Project: D. Eaton, B. G. Taylor, R. Thomas, N. Towers
IDT: entire FOC IDT
TIB: D. Baxter, J. C. Blades, C. Cox, P. Greenfield, W. Hack, R. Jedrzejewski, A. Nota, F. Paresce,
W. Sparks, All Instrument Scientists
SCARS: D. Bazell, D. Gilmore, P. Hodge
SESD: W. Baggett, M. Miebach
SPD: F. Macchetto
USB: B. Gillespie
ST/ECF: H.­M. Adorf, P. Benvenuti, A. Caulet, R. Fosbury, R. Hook

1 Introduction
The f/96 relay of the FOC contains three linearly polarizing filters with nominal position
angles of 0 ffi , 60 ffi , and 120 ffi . These filters are described in some detail in the FOC Instrument
Handbook (Paresce, 1990). Observations of Lick Hff 233 and of the knot A region of the jet
of M 87 were taken with the FOC in the blue and ultraviolet through the polarizing filters
for the purpose of determining the orientations of the filters. Polarization maps were created
from these data. The map of M 87 was compared with 2 cm VLA map (Owen, Hardee,
Cornwell, 1989), which was taken as a reference for what the polarization directions should
be. The polarization directions for Lick Hff 233 were assumed to be radially symmetric
around a star, which itself was not visible. Lick Hff 233 is listed as a polarization standard
by Bohlin et al. The observations of M 87 allow a possible ambiguity in the orientations of
the polarizing filters. The observations of Lick Hff 233 resolve the ambiguity, and further
analysis should yield improved calibration of the filter position angles.
2 Observations
The M 87 observations were taken on 1991 April 3, proposal 1521. After a target­acquisition
image, each of the six exposures for polarization was of 1500 seconds duration. Three
exposures were taken through the F430W filter, one with each of the polarizing filters, and
then three exposures were taken through the F220W filter, one with each polarizing filter.
After the first two images through the F430W filter (0 ffi and 60 ffi polarizing filters), the
telescope was moved in order to include knot C in the field of view. The third F430W image
and all three F220W images were taken at the new pointing direction.
The observations of Lick Hff 233 were taken on 1991 Nov 21, proposal 3873. Each exposure
was 1500 seconds, and the same filters were used as for M 87. The telescope was not moved
between exposures.
3 Data Reduction and Analysis
The M 87 observations were not deconvolved. The Lick Hff 233 observations were decon­
volved using the Wiener filter method using filter type = geometric, signal model = Markov,
and noise model = Poisson.
2

The F220W observations of Lick Hff 233 were not used because the signal was so weak,
about eight counts peak brightness in each image.
As mentioned earlier, the third M 87 F430W image was taken at a different pointing position
from the first two. The offset between the images was not available in the post­observation
trailer file, so the offset was estimated by displaying the first and third images using the
IRAF display task, blinking between the two images, and shifting one image relative to the
other until the match was reasonable. Pixel [1,1] of the third F430W image corresponds to
pixel [129,234] of the first and second images. We estimate the uncertainty in this procedure
to be a few pixels. This method would have been more reliable if the degree of polarization
were not so high. The region which is common to all three of the images was extracted, and
this region was further reduced to exclude portions of the border.
Although the Lick Hff 233 observations were taken at the same telescope pointing, the
second image appeared to be offset three pixels to the right with respect to the first and
third images, based on the location of the peak brightness. This is not a reliable measure
of offset, however. We know the peak brightness is not the location of the star because the
polarization vectors are not radially symmetric around that point.
The background level for M 87 was measured for each image by taking averages in regions
away from the jet, and the values of about 15 counts for F430W and one count for F220W
were subtracted from the images. No background was subtracted from the Lick Hff 233
observations because the nebulosity extended to the edges of the field. As long as the
background is the same for all three images---of course, we don't know that this is the
case---the background will not affect the polarized flux or direction of polarization.
Reseau marks are located about every 60 pixels. Two reseau marks in relatively bright
regions of each M 87 image were filled in using values from neighboring pixels. Other reseau
were either faint or invisible because of low count rates in the surrounding regions, and they
were not modified. For Lick Hff 233, on the other hand, the nebulosity covers a wider area,
so the entire grid of reseau marks was replaced (using imedit) in those images.
The three polarizing filters differ somewhat in throughput. The 60 ffi filter has a short­
wavelength cutoff near 220 nm, while the 0 ffi and 120 ffi filters extend below 150 nm (Paresce
1990). When the polarizing filters are combined with F430W, the difference in throughput
is less than one percent. With the F220W filter, on the other hand, the throughput of
the 60 ffi filter is only about 2/3 that of the other two polarizing filters. In order to have
any confidence in the polarization measurement for M 87 with F220W, this factor must be
accurately determined. The reflectivities of the HST mirrors, the transmission curves of the
various filters, and the sensitivities of the detectors were measured prior to launch. Horne
3

(1989) has written a program XCAL to calculate the throughput of the HST with various
instrument configurations and different spectral distributions of the incident light. We used
XCAL to calculate the relative throughput of the three polarizing filters together with either
the F430W or F220W filter, and then we used these values to normalize the M 87 images.
When running XCAL, we specified that the input light was unpolarized and had a power­law
spectral distribution. We estimated that the spectral index of knot A was +1 (F – increases
with decreasing wavelength), based on the F430W and F220W fluxes. Only the POL60
image of Lick Hff 233 was modified for normalization; it was divided by 1.007.
The relative throughputs of the various filter combinations for spectral indexes of 0 and +1
are given in the table below.
filters throughputs for spectral index
0. +1.
F430W+POL0 0.999935 0.999901
F430W+POL60 1.007410 1.008335
F430W+POL120 1.000065 1.000099
F220W+POL0 1.000255 1.001148
F220W+POL60 0.759097 0.689160
F220W+POL120 0.999745 0.998852
The three images in a set were block averaged to improve the signal­to­noise and then
were combined to give Stokes parameters I, Q, and U in units of counts. An IRAF script
polfoc.cl was used to do the image arithmetic, convert Q and U into polarized flux and
position angle, and write the results to a table and to a text file that could be plotted using
the fieldplot task. Using the notation im0, im60, im120 to represent the images taken
through the polarizing filters POL0, POL60, POL120 respectively, the Stokes parameters
were determined as follows:
I = im0 + im60 + im120
Q = 2 \Delta im0 \Gamma (im60 + im120)
U = (im60 \Gamma im120) \Delta
p
3
These equations are based on the following assumptions and conventions. Stokes parameter
Q is taken to be positive in the increasing sample direction and negative in the increasing line
direction. The position angles of the three polarizers are assumed to differ from each other by
4

exactly 60 ffi . The POL0 filter passes light with electric vector parallel to the sample direction.
The POL60 polarization direction is 60 ffi counterclockwise from POL0, as projected onto the
sky, and the POL120 polarization direction is 120 ffi counterclockwise from POL0.
The polarization maps for M 87 and Lick Hff 233 based on the above equations are shown
in Figures 1, 2, and 5.
4 Ambiguity
It was not especially clear (at least to me) how to interpret the documentation regarding
the polarizing filters. Two lists that give positions of filters in the filter wheels have the
polarizers in different filter holes. An engineering drawing of a polarizing filter shows a line
and implies that it indicates the filter orientation, but is the line the electric field direction
or the apex of the prism? In the drawing of the filter wheel, which side are we looking at?
We consider it to be a reasonable assumption that the three polarizing filters are oriented
at 60 ffi intervals, at least as a start. Beyond the assumption of regular spacing, however, any
arrangement of the filters was considered fair game. That's not as bad as it may sound. One
has only to consider an arbitrary rotation of the set of filters as a whole, and a mirror image
with arbitrary rotation.
The position angles of polarization in the strongly polarized regions in the M 87 images are
for the most part either parallel or perpendicular to each other. In this situation there are two
arrangements of the three polarizing filters that give identical results. The two arrangements
are mirror images of each other around the direction of polarization. Polarization maps based
on the alternative arrangement are shown in Figures 3 and 4. The direction of polarization in
knot F in the F430W images (at approximately [90,30]) is not consistent with the alternate
arrangement of the filters, but this evidence is not very convincing since knot F is close to
the lower edge of the image, and the total flux is only about 60 counts per pixel in that
region.
The observations of Lick Hff 233 resolve this ambiguity because the position angles in the
field of view vary continuously over a range of about 90 ffi . The mirror­image arrangement of
the filters was tried with different position angles in 30 ffi increments, as shown in Figure 6.
Since none of these maps resembles what we expect for a bipolar nebula, we conclude that
the arrangement of the polarizing filters discussed in the previous section is correct.
5

5 Discussion
One count per pixel per 4500 seconds of exposure through a polarizing filter corresponds to
23.1 magnitude per square arcsecond for F430W and 20.6 magnitude per square arcsecond
for F220W. The magnitude scale is referred to as ST magnitude. The factor for converting
count rate into F – , which can then be converted to ST magnitude, is computed during
routine calibration and written into the image headers. This computation uses code based
on XCAL.
Two important questions have not been resolved. The throughputs of the three polarizing
filters should be checked to verify or improve the ground­based measurements. This requires
observations of an unpolarized object of known spectral energy distribution. This is especially
critical if the F220W filter is to be used for polarization observations since the POL60 filter
cuts off within the F220W bandpass. The second issue is to accurately determine the image
shifts introduced by the polarizing filters. This requires observations of one or more stars
with fixed HST pointing for all polarizing filters. While the image shifts could be measured
if the stars were polarized, there is a possibility that the PSF depends on polarization
(Paresce, private communication), so the use of unpolarized stars may give more reliable
results. Determining the throughputs and image shifts will require additional observations.
Further analysis of the existing Lick Hff 233 images should reveal any overall rotation of
the set of polarizing filters and possibly also any deviation from 60 ffi spacing of the filters.
Polarization maps rotated 10 ffi from nominal show a distinct asymmetry, so we believe the
filter position angles are correct to within 10 ffi .
6 References
Bohlin, R. C., Turnshek, D. A., Willaimson, R. L., Lupie, O. L., Koornneef, J., Morgan,
D. H. 1989, An Atlas of Hubble Space Telescope Photometric, Spectrophotometric, and
Polarimeteric Calibration Objects, STScI Publication.
Horne, K. 1990, XCAL User's Manual, Version 1.1.
Owen, F. N., Hardee, P. E., Cornwell, T. J. 1989, Ap.J., 340, 698.
Paresce, F. 1990, FOC Instrument Handbook, STScI Publication.
6

7 Figure Captions
Figure 1. Polarization map of the knot A region of the M 87 jet with the F430W filter,
assuming the filters are arranged as described in the text. The length of each line segment
is proportional to the polarized flux, and the lines have been rotated 90 ffi to show magnetic
field direction. The numbers on the X and Y axes are pixel numbers in the image. The
north and east directions and the image scale are shown in the right margin.
Figure 2. Polarization map of the knot A region of the M 87 jet with the F220W filter,
assuming the filters are arranged as described in the text. The length of each line segment
is proportional to the polarized flux, and the lines have been rotated 90 ffi to show magnetic
field direction. The numbers on the X and Y axes are pixel numbers in the image. The
north and east directions and the image scale are shown in the right margin.
Figure 3. Polarization map of the knot A region of the M 87 jet with the F430W filter. This is
similar to Figure 1 except that it is based on the assumption of an alternative arrangement of
the polarizing filters. This arrangement is related to that discussed in the text by a reflection
around a line tilted 15 ffi from lower left to upper right.
Figure 4. Polarization map of the knot A region of the M 87 jet with the F220W filter. This
is based on the alternative arrangement of the polarizing filters, as described for Figure 3.
Figure 5. Polarization map of Lick Hff 233 with the F430W filter, assuming the filters
are arranged as described in the text. The length of each line segment is proportional to
the polarized flux, but in contrast to Figures 1--4 the orientation shows the electric field
direction. Polarization by dust scattering of light from a star would give line segments that
are perpendicular to the direction toward the star, in good agreement with what we see in
this figure.
Figure 6. Each of these six maps shows the polarization (electric field direction) of Lick Hff
233 with the F430W filter, but they are based on the assumption that filters POL60 and
POL120 are interchanged. The six maps differ from each other by simple rotations of the
position angles in 30 ffi increments, which corresponds to a rotation of the set of polarizing
filters as a whole. None of these maps resembles what we expect for dust scattering.
7