Bull. Astr. Soc. India (2014) 42, 165–183
A new three-band, two beam astronomical photo-polarimeter
G. Srinivasulu1∗, A. V. Raveendran2, S. Muneer1†, M. V. Mekkaden3,
N. Jayavel4, M. R. Somashekar1, K. Sagayanathan1, S. Ramamoorthy1,
M. J. Rosario5 and K. Jayakumar6‡
1Indian Institute of Astrophysics, Bangalore 560034, India
2399, "Shravanam", 2nd Block, 9th Phase, J P Nagar, Bangalore 560108, India
3No 82, 17E Main, 6th Block, Koramangala, Bangalore 560095, India
4No 22, Bandappa lane, New Byappanahalli, Bangalore 560038, India
5210, 4th Main, Lakshmi Nagar Extn, Porur, Chennai 600116, India
624, Postal Nagar, Ampuram, Vellore-632009, India
Received 2014 July 23; accepted 2015 May 05
Abstract. We designed and built a new astronomical photo-polarimeter that can mea-
sure linear polarization simultaneously in three spectral bands. It has a Calcite beam-
displacement prism as the analyzer. The ordinary and extra-ordinary emerging beams
in each spectral bands are quasi-simultaneously detected by the same photomultiplier
by using a high speed rotating chopper. A rotating superachromatic Pancharatnam
halfwave plate is used to modulate the light incident on the analyzer. The spectral
bands are isolated using appropriate dichroic and glass filters.
We show that the reduction of 50% in the efficiency of the polarimeter because
of the fact that the intensities of the two beams are measured alternately is partly com-
pensated by the reduced time to be spent on the observation of the sky background.
The use of a beam-displacement prism as the analyzer completely removes the polar-
ization of background skylight, which is a major source of error during moonlit nights,
especially, in the case of faint stars.
The field trials that were carried out by observing several polarized and unpo-
larized stars show the performance of the polarimeter to be satisfactory.
Keywords : instrumentation: polarimeters – techniques: polarimetric – methods: ob-
servational, data analysis
∗email: gs@iiap.res.in
†email: muneers@iiap.res.in
‡email: jayakumar.kanniah@gmail.com
166 G. Srinivasulu et al.
1. Introduction
There was a need for an efficient photo-polarimeter for observations with the 1-m Carl Zeiss
Telescope at Vainu Bappu Observatory, Kavalur. The single spectral band, star–sky chopping
polarimeter, which was built by Jain & Srinivasulu (1991) almost a quarter century ago, was
the only available instrument for polarimetric studies (Ashok et al. 1999; Parthasarathy, Jain &
Bhatt 2000; Manoj, Maheswar & Bhatt 2002; Raveendran 1999, 2002). The star-sky chopping
procedure makes the instrument very inefficient, thereby underutilizing the available telescope
time.
A project to build a new photo-polarimeter for observations of point sources was initiated
in the Indian Institute of Astrophysics quite sometime back. Unfortunately, due to unforeseen
reasons there were delays at various stages of the execution of the project. There were several
ongoing programmes in the Institute which required accurate multiband polarimetry: studies of
Herbig Ae/Be stars (Ashok et al. 1999), Luminous Blue variables (Parthasarathy et al. 2000),
Young Stellar Objects (Manoj et al. 2002), R CrB stars (Kameswara Rao & Raveendran 1993),
RV Tauri stars (Raveendran 1999), Mira variables that show long-term modulations in their
brightness at light maximum (Raveendran 2002) and T Tauri stars (Mekkaden 1999).
The new polarimeter, which was designed and built in the Institute, was mounted onto the 1-m
telescope and observations of several polarized and unpolarized stars were made during April–
May 2014, to determine its suitability for efficient astronomical observations. Due to prevalent
poor sky conditions, the instrument could be used effectively only on a few nights during this pe-
riod. The instrument was found to have a very high mechanical stability, but a comparatively low
polarization efficiency of 94.72%. Since we suspected the scattered light inside the instrument to
be the reason for such a low value for the efficiency, we blackened the few internal mechanical
parts which were left out earlier, and again made observations during February–April 2015.
In this paper we discuss the details that have gone in the selection of the analyzer and give
brief descriptions of the component layout, the control electronics, and the data acquisition pro-
cedure and analysis. Details of the polarimeter and the data reduction procedure can be found in
Raveendran et al. (2015). We also discuss the results of the observation made during February–
April 2015, which were carried out to evaluate the performance of the instrument.
2. Choice of the analyzer
In order to reduce the adverse effects of the atmospheric scintillation, seeing and transparency
variation, which usually limit the accuracy of any polarimetric measurement, it is imperative to
measure simultaneously both the emerging beams, ordinary and extra-ordinary, from the ana-
lyzer. The two basically different types of analyzers that are usually employed in astronomical
polarimeters are: (1) beam-displacement prisms made of Calcite (Piirola 1973; Magalhaes & Vel-
loso 1988; Scaltriti et al. 1989; Schwarz & Piirola 1999) and (2) beam-splitting prisms of Wol-
A new astronomical polarimeter 167
Sky Star Sky
Beam displacement prism
Overlapping region
Rotating chopper
Focal plane diaphragm
Star (ordinary) + Sky
Star (extra−ordinary) +sky
Fabry lens
Photocathode
Figure 1. Working principle of the polarimeter.
laston or Foster design (Magalhaes, Benedetti & Roland 1984; Deshpande et al. 1985; Kikuchi
1988; Hough, Peacock & Bailey 1991)
We adopted a design for the polarimeter incorporating a Calcite beam-displacement prism so
that most of the spectroscopic nights that are available at the site can be utilized for polarimetric
observations. The working principle of the polarimeter is illustrated in Fig. 1. An astronomi-
cal polarimeter based on this principle was first built by Piirola (1973). A beam-displacement
prism divides the incident light, producing two spatially separated emerging beams with mutually
perpendicular planes of polarization. The background sky, which acts as an extended object, il-
luminates the entire top surface of the beam-displacement prism, and hence, produces two broad
emergent beams whose centres are spatially separated. There will be considerable overlap be-
tween these two beams about the geometrical axis of the prism, and wherever the beams overlap
in the focal plane of the telescope that portion remains unpolarized by the prism and gives the
background sky brightness directly. The situation is different with respect to the starlight; the
star being a point source, there will be no overlap between the two emergent beams from the
prism. The net result of these two effects is that we observe two images of the star with mutually
perpendicular planes of polarization at the focal plane, which are superposed on the unpolarized
168 G. Srinivasulu et al.
background sky. Two identical apertures are used to isolate these images, and a rotating chop-
per is used to alternately block one of the images allowing the other to be detected by the same
photomultiplier tube.
The main advantages of such an arrangement are: (i) The contribution of background sky po-
larization is completely eliminated from the data, thereby, facilitating the observations of fainter
stars during moonlit nights without compromising on the accuracy that is achievable during dark
nights. This is possible because the background sky is not modulated, it just appears as a constant
term that can be removed from the data accurately. (ii) Since the same photomultiplier tube is
used to detect both the beams quasi-simultaneously, the effect of any time-dependent variations in
its sensitivity as a result of undesired variations in the operating conditions of the associated elec-
tronics, like, variations in HT supply, is negligible. (iii) The quasi-simultaneous detection of both
the beams using a fast rotating chopper essentially eliminates the adverse effects of the variations
in sky-transparency and significantly reduces the errors due to atmospheric scintillation for bright
stars. Scintillation noise is independent of the brightness of the star and dominates the photon
noise for bright objects; with a 1-m telescope the low frequency (< 50 Hz) scintillation noise is
expected to be larger than the photon noise for stars brighter than B = 7.0 mag at an airmass of
1.0 (Young 1967). The averaging of the data by the process of long integration will reduce the
scintillation noise only to a certain extent because of its log-normal distribution. The frequency
spectrum of scintillation noise is flat up to about 50 Hz; the noise amplitude decreases rapidly
above this frequency and it becomes negligibly small above 250 Hz. With the fast chopping of the
two emergent beams alternately and the automatic removal of the background sky polarization, it
is possible to make polarization measurements that are essentially photon-noise limited.
The two factors that determine the overall efficiency of a polarimeter attached to a telescope
are (Serkowski 1974a): (i) the faintest magnitude that could be reached with a specified accuracy
in a given time, and (ii) the maximum amount of information on wavelength dependence that
could be obtained during the same time. It is evident that the former depends on the efficiency
in the utilization of photons collected by the telescope and the latter on the number of spectral
bands that are simultaneously available for observation. In the beam-displacement prism-based
polarimeters, where the image separation is small, the intensities of the two beams produced by
the analyzer are measured alternately using the same detector, and hence, only 50 per cent of
the light collected by the telescope is effectively utilized. In polarimeters using Wollaston prism
as the analyzer, the two beams, which are well-separated without any overlap, can be detected
simultaneously by two independent photomultiplier tubes, fully utilizing the light collected (Ma-
galhaes et al. 1984; Deshpande et al. 1985). For simultaneous multi-spectral band observations
that make use of the incident light fully, the beams emerging from the analyzer will have to be
well-separated so as to accommodate a large number of photomultiplier tubes, making the result-
ing instrument both heavy and large in size (Serkowski, Mathewson & Ford 1975), and hence,
not suitable for the 1-m telescope. Usually, in Wollaston and Foster prism-based polarimeters,
which have the provisions for simultaneous observations in multi-spectral bands, different spec-
tral bands are distributed among the two emergent beams, and hence, at a time only 50 per cent
of the light collected in each spectral region is made use of (Kikuchi 1988; Hough et al. 1991).
A new astronomical polarimeter 169
The background sky polarization has to be determined accurately and removed from the ob-
ject plus sky data when there is no overlap between the emergent beams, and a significant fraction
of the time spent on object integration will have to be spent for such observations if the objects are
faint. In beam-displacement prism-based polarimeters, time has to be spent only to determine the
brightness of the background sky, and for the maximum signal-to-noise ratio, it is only a negligi-
ble fraction of the object integration time even for relatively faint objects; the available time for
observation can be almost entirely utilized to observe the object, as indicated by the analysis pre-
sented in section 5.3 on optimum sky background observation. Therefore, the non-utilization of
50 per cent light in beam-displacement prism-based polarimeters does not effectively reduce their
efficiency much, especially, while observing faint objects where the photons lost actually matter.
The provisions for multi-spectral band observations can be easily incorporated in the design,
making beam-displacement prism-based polarimeters to have an overall efficiency significantly
higher than that of the usual Wollaston or Foster prism based polarimeters. Another advantage
of these polarimeters is that they can be easily converted into conventional photometers, just by
pulling the beam-displacement prism out of the light path.
3. Layout of the components
The layout of the polarimeter indicating the positions of the main components is shown schemat-
ically in Fig. 2. A super-achromatic halfwave plate of Pancharatnam design is used to rotate
the plane of polarization of the incoming light falling on the analyzer, and thereby, to modulate
the intensities of the two emergent beams from the analyzer (Frecker & Serkowski 1976). The
position angle of the effective optical axis of a Pancharatnam retarder is wavelength-dependent.
This would cause difficulties in the accurate determination of the position angle of polarization
when broad spectral bands, as in the present case, are used for observations because corrections
that are to be applied to the observed position angles would depend on the energy distribution
of the observed objects. Such an inconvenience is usually avoided by introducing another sta-
tionary identical Pancharatnam plate immediately after the rotating plate in the light path. The
introduction of such a half-wave plate ensures that the signal modulation is only a function of the
relative positions of the effective optical axes of the two half-wave plates, which is wavelength-
independent. The rotating halfwave plate, which acts as the modulator of the incoming light, is
the first element in the optical path of the polarimeter, and hence, avoids the detection of any spu-
rious polarization produced by any optical components used in the polarimeter. The two identical
half-wave plates of 19 mm clear aperture used in the polarimeter are acquired from Bernhard
Halle Nachfl. GmbH, Berlin, Germany.
The analyzer is a cross-mounted, double calcite block with a 20 mm clear aperture and a total
thickness of 28 mm, which produces identical ordinary and extraordinary images at the focal
plane of the telescope. This component is also acquired from Bernhard Halle Nachfl. GmbH.
Since the separation between the emergent beams is a function of wavelength, the images will be
slightly dispersed. The image strips have a linear size of 0.318 mm in the spectral interval 320–
990 nm with the centre-to-centre distance of the two images being 2.292 mm. The images can be
isolated for observation using one of the two sets of twin identical diaphragms of 20 and 25 arc
170 G. Srinivasulu et al.
Glan−Taylor prism
HWP (Rotating)
HWP (Fixed)
Calcite block
Chopper
Diaphragm disc
Neutral density filter
Electronic shutter
UG1 Fabry
ETL 9893Q/350
U−band Reflecting dichroic filter inside B2F−type housing
Fabry BG12
ETL 9893Q/350
inside B2F−type housing B−band reflecting dichroic filter
VRI band filter slide
Fabry
Hamamatsu R943−02 inside FACT50 model housing
Figure 2. Schematic layout of the main components of the polarimeter. In the instrument the U and B bands
are mutually perpendicular, making it more compact.
sec in diameter mounted on a manually rotatable disc. The calcite block is placed in the light
path immediately after the stationary half-wave plate. The rotating chopper isolates alternately
the ordinary or extra-ordinary image for detection by the same photomultiplier. The chopper has
four slots, two for each of the images, and therefore the effective chopping frequency is double
the rotational frequency of the chopper.
The isolation of the spectral regions into the three bands for simultaneous observation is
achieved by using two dichroic filters, one to reflect the ultra-violet part of the incoming light
and the other to reflect the blue part of the spectrum from the light transmitted by the first. The
dichroic filters used are obtained from Custom Scientific, Inc., Arizona, USA. The reflective
coatings required for the dichroism are done on 2 mm thick glass substrates. The two reflected
beams are detected by two separate uncooled photomultiplier tubes. The bi-alkali photocathodes
of these tubes along with the Schott glass filters inserted in front of them produce spectral bands
that approximate the U and B bands of Johnson. The light transmitted by both the dichroic filters,
A new astronomical polarimeter 171
Figure 3. Combined response of the filter-detector combination.
Table 1. Filter-detector combinations.
Spectral Mean wavelength
Band Filter combination λ0 (nm) Photomultiplier tube
U UG1 (1 mm) 357 ETL 9893Q/350B
B BG12 (1 mm) 437 ETL 9893Q/350B
V BG18 (1 mm) + GG495 (2 mm) 561 Hamamatsu R943-02
R OG570 (2 mm) + KG3 (2 mm) 652 ′′
I RG9 (3 mm) 801 ′′
which fall in the VRI spectral bands, is detected by a cooled photomultiplier tube with a GaAs
photocathode. The observations are made sequentially in V , R and I bands using suitable filter
combinations mounted on a sliding filter-holder. The Schott glass filters that are used have clear
apertures of 25 mm diameter. The combined responses of the dichroic mirrors, glass filters and
detectors are plotted in Fig. 3. The V passband approximates that of Johnson’s, while the R and
I passbands approximate those of Cousins (Bessel 1979, 1993). The selection of the required
glass filters are based on the filter-detector combinations used by Piirola (1973) and Hough et
al. (1991); these authors also have employed dichroic filters to isolate spectral regions in their
multiband polarimeters. The details of the filter-detector combinations used are given in Table 1.
172 G. Srinivasulu et al.
The mean wavelength, calculated using
∫
∫λ S (λ) δλλ0 = ,
S (λ) δλ
is also given in the table against the respective spectral band; S(λ) is the wavelength-dependent
responses plotted in Fig. 3.
The pulse amplifier-discriminators of Model ETL AD6 and Hamamatsu Model C9744 are
used to interface the ETL 9893Q/350 and Hamamatsu R943-02 photomultiplier tubes, respec-
tively, to the pulse counters. The uncooled ETL 9893Q/350 photomultiplier tubes used in the U
and B bands give dark counts which are less than 10 counts s−1 at an ambient temperature of
about 25◦C when operated at an anode voltage of 2300 V. These are mounted in uncooled am-
bient ETL B2F-type housings, while the Hamamatsu tube used in the VRI channel is mounted
in a FACT 50 model housing, which is of forced air-cooled type and cools about 50◦C below
an ambient temperature of 20◦C. The dark counts given by the cooled tube when operated at a
cathode voltage of –1900 V are also less than 10 counts s−1.
A Glan-Taylor prism of 24.5 mm clear aperture, also acquired from Bernhard Halle Nachfl.
GmbH, can be inserted in the telescope light path to produce a fully polarized beam that is nec-
essary to measure and periodically check out the constancy of the polarization efficiency of the
instrument. Facilities for wide angle-viewing and diaphragm-viewing have also been provided in
the instrument for the easy acquisition of the object for observation.
4. Control electronics
All the polarimeter functions are performed by two PIC family PIC16F877A1 microcontrollers.
One microcontroller controls both the step motor coupled to the half wave plate and the servo
motor coupled to the chopper wheel. The second microcontroller interfaces with the Linux ma-
chine, which is used to operate the polarimeter, through the standard serial communication with
the RS232C protocol. The two microcontrollers in the instrument communicate between them
through the built-in SPI Bus.
We have used a command-based communication protocol, wherein the computer acts as the
master and the microcontroller as a slave unit. Always the commands are generated from the
computer and sent to the microcontrollers, which interpret and execute them, and then respond
indicating the status of the execution to the computer. We followed this scheme to avoid any
communication clash between the computer and the microcontrollers, and to identify the errors,
if any, quickly.
A new astronomical polarimeter 173
5. Data acquisition and reduction procedure
5.1 Observations
The photomultiplier pulses corresponding to the intensities of the two emergent beams from the
beam-displacement prism are counted separately over a full rotation of the halfwave plate at the
specified equal angular intervals, starting from a reference position. The actual counting time
interval for each beam over a rotational cycle of the chopper depends on its frequency of rotation
since the latching pulses for the electronic pulse counters are derived from the positional sensors
of the chopper. When the integrated counting time over several rotational cycles of the chopper
equals to what is specified, the counting is stopped, and the resulting counts are stored. The
halfwave plate is then moved to its next position, and the process is repeated at all the required
positions. The entire procedure is counted as one cycle. The cycle can be repeated till the required
accuracy in the measurement is achieved. After each cycle, the counts are added to the previously
stored counts at the respective position of the halfwave plate. Before a new cycle begins the
halfwave plate is always brought to its reference position. In order to give equal weightage to
the observations in the data reduction, the number of counts accumulated at all positions of the
half-wave plate should be of the same order. This requires that under poor sky conditions the
observations should be repeated over several cycles of rotation of the half-wave plate, with a
smaller integration time at each position of the halfwave plate. Usually, the observations in U
and B bands will last longer than those in V , R and I bands. The integrations in U and B can be
continued till integrations in the other bands are completed successively.
The procedure is the same for the object and the sky background that has to removed from
the object plus sky background counts before the data reduction. As shown in section 5.3 on
optimum background sky observation, the time to be spent on sky integration is usually a small
fraction of the time spent on the object integration. The optimum number of sky cycles for an
observed number of object cycles and the optimum number of object cycles for an observed
number of sky cycles, which are computed from the relative brightnesses of the object and sky,
are displayed on the monitor.
After each cycle, the linear polarization, the position angle and the gain-ratio, and their prob-
able errors are displayed on the monitor. If the sky background is observed first, the displayed
values will represent the actual values, otherwise they will only be approximations. Once the
integration of the object is terminated, the final values of the Stokes parameters Q and U, the
polarization (P%), the position angle (θ◦) and the mean Julian day of observation are stored in
appropriate files.
5.2 Data reduction
The pair of counts registered at each position i of the halfwave plate depends both on the Stokes
parameters I, Q and U of the incident light and the angle ψi between the optical axes of the two
174 G. Srinivasulu et al.
halfwave plates at that position as given below:
N i1 =
1
2 G1 (I + Q cos 4ψ
i + U sin 4ψi) Tatm and
N i = 12 2 G2 (I − Q cos 4ψi − U sin 4ψi) Tatm ,
where the subscripts 1 and 2 refer to the beams polarized in the principal plane of the first plate
of the calcite block and the plane perpendicular to it, respectively. The parameters G1 and G2
are the net efficiencies for the two light beams, which include the transmittances and reflectivities
of the various optical elements in the light path and the quantum efficiencies of the cathode of
the photomultiplier tube, and Tatm is the atmospheric transmittance integrated over the period of
observation. Taking the ratio of the counts accumulated in the two channels,
N ii 1 1 + q cos 4ψ
i + u sin 4ψi
Z = =
N i2 α (1 − q cos 4ψi −
,
u sin 4ψi)
where α (= G2/G1) is the ratio of the efficiencies of the two channels (gain-ratio), and q and u
are the normalized Stokes parameters, (Q/I) and (U/I).
There will be M such ratios corresponding to the M positions of the halfwave plate over its
full rotation at which the photons in the two beams are counted. The Stokes parameters and the
gain-ratio are solved using the least-square method from these M ratios. The normal equations
are solved using the Cracovian matrix elimination method (Kopal 1959) because it also gives the
weights required to calculate the probable errors in the parameters that are solved for from the
resulting standard deviation of the least square fit.
The percentage linear polarization P, position angle θ and their probable errors, P and θ, are
calculated from
√
P (%) = q2 + u2 × 100 ,
√ 2 θ = tan
−1(u/q) ,
(q  )2q + (u u)2
P (%) = × 100 andp √
28.65 (q  )2 + (u  )2
θ (degree)
u q
= ,
p2
where q and u are the probable errors in q and u, determined from the least square solution.
5.3 Optimum background sky observation
As already mentioned, the time to be spent on sky integration is usually a small fraction of the
time spent on the object integration for the minimum error in the polarization determined, which
arise from the statistical fluctuations in the photons counted. If ni and ni1 2 are the observed star
A new astronomical polarimeter 175
plus background sky counts at the ith position of the halfwave plate, and s1 and s2 are the scaled
background sky counts due to the two beams,
N i = ni1 1 − s1 and N i2 = ni2 − s2.
If we assume the gain-ratio to be unity, which is expected to be close to unity in normal cases,
the conditions for least square give
∑
(Z2 − ∑1) cos 4ψ (1 + Z )2 ∑ ∑i i i sin2 4ψi − (Z2i − 1) sin 4ψi (1 + Z 2i) sin 4ψi cos 4ψiq = ∑ .
(1 + Z 2 2
∑ 2 2 ∑ 2 2
i) cos 4ψi (1 + Zi) sin 4ψi − ( (1 + Zi) sin 4ψi cos 4ψi)
Further, if we assume that the observed polarization is small so that the squares and higher order
terms in q and u can be neglected, and that the measurements are done over a full rotation of the
halfwave plate at equal angular intervals, the expression for the differential in q can be written as
∑ ∑ ∑
M n∗ δq = Xi (1 + Z ) δnii 1 − X ii (1 + Zi) Zi∑δn2 − δs1 Xi (1 + Zi) +
δs2 Xi (1 + Zi) Zi , (1)
where
Xi = Zi cos 4ψi − q (1 + Z ) cos2i 4ψi − u (1 + Zi) sin 4ψi cos 4ψi
and n∗ is the counts corresponding to the Stokes parameter I, the intensity due to the object alone.
The gain ratio of the beams α is usually close to unity and q  1, making the counts ni1’s
and ni2’s, and the statistic√al errors in their determination similar. Since photons obey Poisson
statistics, we have σn = n, in general. Assuming σni = σni = σn and σs1 = σs2 = σs , using1 2
the law of propagation of errors, from Equation 1 we get
{ }
(σ )2
4
q = 2 (σn)
2 + 2.5 M q2 (σ 2s) .
M n∗
If n̄ and s̄, respectively, are the averages of the observed object plus background sky and back-
ground sky counts at various positions of the rotating half-wave plate in one second and if the
object is observed for to and background for tb seconds at each position of the half-wave plate,
then
n∗ = 2 (n − s) = 2 to (n̄ − s̄) ,
(σ 2 2 2 2n) = to n̄ and (σs) = (to/M tb) M tb s̄ = to s̄/M tb .
Making use of these values we get the probable error in q as
( ) 1
0.6745 n̄ 2
 2
s̄
q = √ + 2.5 q .
M (n̄ − s̄) to tb
There will be a similar relation for the other normalized Stokes parameter u. It is clear from the
176 G. Srinivasulu et al.
Figure 4. Plot of the optimum fraction of the time to be spent on background sky observation with the
beam-displacement- and Wollaston prism-based polarimeters against the sky-background to star brightness
ratio. The dashed lines show the corresponding asymptotic values.
above that the errors in q and u due to statistical fluctuations in the accumulated counts depend
on the values of q and u themselves. When q = u, p = q. Accordin√g to the above relation for
the error due to photon noise q = u, when q = u, i.e., when q = p/ 2. This implies that for a
given linear polarization p, the observations would yield a minimum error in p if q = u, all other
parameters being the same. The highest possible error in P due to photon fluctuations, which
occurs when either q = p and u = 0, or u = p and q = 0, is obtained by replacing q by p in the
above equation as
( ) 1
67.45 n̄ s̄ 2
P(%) = √ + 2.5 p2 .
M (n̄ − s̄) to tb
For an efficient use of the telescope time, we should distribute the total time available between
the object and background sky observations such that the signal-to-noise ratio is a maximum, or
equivalently, the error in P is a minimum. Differentiating the expression for (P)2 with respect to
to, the time spent on object integration, and equating it to zero, we get the condition for P to be
A new astronomical polarimeter 177
a minimum as √
tb 2.5 s̄
= p . (2)
to n̄
In polarimeters where the beam separation is large, the moon lit background sky will be mod-
ulated by the rotating half-wave plate because of its polarization. The intensities of the ordinary-
and extraordinary-components at each position of the half-wave plate should be measured sepa-
rately and removed from the object plus background data. When we deal with such a situation,
s i1 and s2 appearing in the above equations should be replaced by the corresponding s1’s and s
i
2’s,
which have uncorrelated statistical errors. The equation for (P)2 then would be modified to
( ) 1
2
P(%) = √ 67.45 n̄ s̄+ ,
M (n̄ − s̄) to tb
and the condition for P to be a minimum as √
tb s̄
= .
to n̄
Fig. 4 shows the fraction of the time to be spent on background sky observations as a function
of the ratio of the background brightness to the object brightness with two different types of po-
larimeters, one with well separated ordinary- and extraordinary-beams as in the case of Wollaston
or Foster prism-based polarimeters, and the other with overlapping ordinary- and extraordinary-
beams as in the case of beam-displacement prism-based polarimeters. In the case of overlapping
beam polarimeters the fraction of time to be spent on background observation increases with the
polarization of the object and at low polarization levels, which is usually encountered in stellar
polarization measurements, it is negligibly small, indicating that most of the available time can
be spent on observing the object, and thereby, partially compensating for the loss in efficiency in
not utilizing 50 per cent of the light collected by the telescope.
6. Observational validation
The two main parameters of a polarimeter that determine its suitability for observations are the
polarization it produces for an unpolarized beam and its ability to measure correctly the degree of
polarization of a polarized beam without causing any depolarization; during February–April 2015
we observed unpolarized stars with and without the Glan-Taylor prism in the telescope beam to
determine these two. Observations during April–May 2014 were made with different settings of
the chopper speed, number of positions of the halfwave plate over a full rotation, integration times
and diaphragm sizes, in order to look for any dependency on their values. Since we could not
find any obvious differences in the results of those observations, all the observations made during
February–April 2015, which are discussed here, were done with a chopper frequency of 50 Hz,
25 positions of the halfwave plate over a full rotation, integration time of 1-s, and diaphragms of
20 arc sec diameter. In addition to the UBVRI bands, another broad spectral band which included
both the R and I bands was also used for the observations. We refer to this band, which has a
mean wavelength of 712 nm, in this paper as R′.
178 G. Srinivasulu et al.
Figure 5. Plots of instrumental Q (%) and U (%) against the mean wavelength of the corresponding spectral
band. The dashed lines show the averages of the corresponding quantities in the BVRR′I bands.
Figure 6. Plots of polarization efficiency and position angle against the mean wavelength of the correspond-
ing spectral band. The dashed lines show the corresponding mean values.
6.1 Instrumental polarization
We observed the unpolarized stars, HD 42807, HD 65583, HD 90508, HD 98281, HD 103095,
HD 100623, HD 125184 and HD 144287, on several occasions. The average values of the ob-
served Q (%) and U (%) in the UBVRR′I bands are plotted against the mean wavelengths of the
spectral bands in Fig. 5. It is clear that the polarization produced by the telescope-polarimeter
combination, which is usually referred to as the instrumental polarization, is small. The instru-
mental polarization, apparently, increases slightly towards the ultraviolet. It is nearly constant in
the V − I spectral region.
A new astronomical polarimeter 179
Figure 7. Plot of observed polarization against that available in the literature. The observed polarization
has been corrected for the wavelength-dependent polarization efficiency and the instrumental polarization.
The straight line indicates an efficiency of 100 per cent for the polarimeter. The number inside the brackets
indicates the number of observations obtained in the corresponding spectral band.
6.2 Polarization efficiency
A total of 161 observations of several unpolarized stars were made with the Glan-Taylor prism
in the light path of the telescope beam to determine the polarization efficiency of the instrument,
which is the numerical value obtained by the instrument for an input beam that is 100% polarized.
In the top panel of Fig. 6 we have plotted the individual values of the polarization efficiencies
obtained by us in UBVRR′I spectral bands against the corresponding mean wavelength. The
polarization efficiency has a slight wavelength dependence, with lower values in the V−R spectral
region. The mean polarization efficiency is 99.206% and its total amplitude of variation in the U−
I spectral region is 0.271%. The position angle of polarization observed, which is plotted in the
bottom panel of Fig. 6, also shows a slight wavelength dependence. The wavelength dependence
observed is almost an inverted and scaled-down version of the variation of the position angle of
the effective optical axis theoretically computed for a super-achromatic halfwave plate (Serkowski
1974b), indicating that the fixed super-achromatic halfwave plate in the beam does not fully
compensate for the variation in the position angle of the effective optical axis of the rotating plate
because of the slight, but unavoidable errors in their fabrication. The total amplitude of variation
in the position angle is only 0.92◦ and the wavelength-dependent offset in the position angle can
be incorporated in the data reduction procedure easily.
180 G. Srinivasulu et al.
Figure 8. Plot of observed position angle against that available in the literature. The observed position angle
has been corrected for the wavelength-dependent offset. The straight line has a slope of unity. The number
inside the brackets indicates the number of observations obtained in the corresponding spectral band.
6.3 Observations of polarized stars
During the observing runs we observed the polarized stars, HD 21291, HD 23512, HD 43384,
HD 147084, HD 154445, HD 160529, HD 183143, HD 58439, HD 94473, HD 127769 and
HD 142863 in UBVRR′I bands. Most of the above objects were observed several times during
the observing runs. The first 7 objects are considered to be standard polarized stars, and are
normally used to determine the offset in the measured position angles from the standard equatorial
coordinate system. Hsu & Breger (1982) have reported polarizations and position angles for these
objects in UBVR bands. For the other 4 stars, Mathewson & Ford (1970) have given polarization
measurements in the B spectral band. The above 4 stars were included in the present observations
so as to have an extended range in the polarization and brightness for the observed polarized
stars. In Fig. 7 we have plotted the polarization determined by us in UBVR bands against the
corresponding value available in the literature. The observed polarization has been corrected for
the wavelength-dependent polarization efficiency of the instrument. It is clear from Fig. 7 that
there is an excellent agreement between the measured polarization and the corresponding value
available in the literature. A linear least square fit to the data plotted in the figure gives a value of
1.004±0.001 for the slope.
We have plotted in Fig. 8 the position angles observed by us in UBVRR′ against the corre-
sponding values available in the literature. The position angles in R′ band were obtained by an
A new astronomical polarimeter 181
Figure 9. Plot of polarization in UBVRR′I bands observed against the inverse of the corresponding effective
wavelength. The solid (Pmax = 3.73±0.01, λmax = 556±2 nm) and dashed (Pmax = 3.73±0.01, λmax = 558±2
nm) lines show the computed interstellar polarization curves using the data obtained by us and Hsu & Breger
(1982), respectively.
interpolation of the data given in Hsu & Breger (1982). It is clear that the agreement between
the measured values and those available in the literature is very good. The observed position
angles were corrected for the wavelength-dependent position angle of the effective optical axis
of the rotating halfwave plate. The offset in the position angles was determined by a least square
fit to the combined data plotted in Fig. 8. The offset obtained using such a procedure would be
better than the value determined using a single standard polarized star, since, the position angles
of some of the standards are found to vary by more than 1◦ (Hsu & Breger 1982).
In Fig. 9 we have plotted the averages of the polarization observed in UBVRR′I bands against
the corresponding inverse of the effective wavelength, which were computed using the responses
of the filter-detector combinations, the UBVRI magnitudes in the Johnson’s system and the av-
erage extinction coefficients in those bands observed at Kavalur, for one of the polarization stan-
dards, namely, HD 154445. The airmass of observation was taken as 1.5. The figure also shows
the observations of Hsu & Breger (1982) and Serkowski et al. (1975); the effective wavelengths
of these observations were computed using the empirical relations given by the respective au-
thors. The airmass of observation was taken as 1.0, while computing the effective wavelengths
of the observations of Hsu & Breger (1982). The position angle of polarization of the object is
plotted in the bottom panel of the figure.
We have also plotted in Fig. 9 the interstellar polarization curves, computed using the empir-
ical relation given by Serkowski et al. (1975). The Pmax, the maximum value of polarization,
182 G. Srinivasulu et al.
and λmax, the wavelength at which the maximum occurs, of the present data were derived using
a least square fit of the empirical relation. Hsu & Breger (1982) have given Pmax and λmax for
their data. It is clear from the figure that the present observations are in excellent agreement with
those of Hsu & Breger (1982).
7. Conclusions
A new polarimeter for simultaneous observations in three spectral bands, U, B and V , or R, or I
was designed and built in the Indian Institute of Astrophysics. A cross-mounted Calcite beam-
displacement prism acts as the analyzer, and the modulation of the intensities of the emergent
beams is achieved by a rotating superachromatic halfwave plate. Combinations of dichroic and
Schott glass filters are used to isolate the spectral bands. In each spectral band the emergent beams
from the analyzer are quasi-simultaneously detected by the same photomultiplier tube using a
fast rotating chopper. The operation of the polarimeter is done using a Linux machine. All the
functions of the polarimeter are controlled by the electronics built around PIC microcontrollers.
Since the background sky is not polarized when a beam displacement prism is used as the
analyzer, time has to be spent only to determine the brightness of the background sky. We show
from an analysis of the propagation of errors that the time to be spent on background observation
is only a small fraction of the object integration for an optimum error in the observed polarization,
which arise from the statistical fluctuations in the photon counts. This advantage partially offsets
the loss in the efficiency of beam displacement prism-based polarimeters in not utilizing 50% of
the light collected by the telescope.
The polarimeter was mounted onto the 1-m Carl Zeiss telescope at Vainu Bappu Observatory,
and several unpolarized and polarized stars were observed during February–April 2015 to test its
suitability for efficient astronomical observations. An analysis of the data collected showed the
performance of the polarimeter to be quite satisfactory. The instrumental polarization, which in-
cludes the telescope contribution also, is found to be small. Observations with the Glan-Taylor
prism in the light path show that both the polarization efficiency and the position angle of po-
larization are slightly wavelength-dependent; however, the total amplitudes of variation in the
U − I spectral region are only 0.271% and 0.92◦ . The mean polarization efficiency is found to
be 99.206%. Both the polarization and position angles of standard polarized stars obtained using
the polarimeter are in excellent agreement with those available in the literature.
Acknowledgments
We gratefully acknowledge the keen interests shown by Professors H. C. Bhatt and P. Sreekumar,
and Shri A. V. Ananth in putting the instrument in operation at the telescope. We thank Professors
G. V. Coyne, F. Scaltriti, and A. M. Magalhaes for their prompt responses to our queries, which
helped us in finalizing the optical layout, and Professor F. Scaltriti for sending copies of the
drawings of the polarimeter at Torino Astronomical Astronomical Observatory. Several of our
A new astronomical polarimeter 183
colleagues helped us at various stages; Mr P. K. Mahesh, Mr P. M. M. Kemkar, Mr P. U. Kamath,
Dr D. Suresh and Dr G. Rajalakshmi helped us in the preparation of the Auto CAD drawings of
the mechanical parts of the polarimeter; Professor T. P. Prabhu helped us in acquiring the dichroic
mirrors and glass filters; Mr N. Sivaraj helped us in checking the photomultiplier tubes and the
pulse-amplifier-discriminators; the staff at Vainu Bappu Observatory helped us in carrying out
the observations using the instrument; we thank all of them. We thank Professor T. P. Prabhu also
for critically going through the manuscript and making valuable suggestions for improving the
quality of the paper.
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