Experience in the use of polarization
standards for determining the parameters
of instrumental linear polarization for
small telescopes 0.7–2.6m with
photoelectric polarimeters
Nikolai Kiselev and Vera Rosenbush
Main Astronomical Observatory of the National Academy of
Sciences of Ukraine, Kyiv
Calibration Workshop
Zurich, Switzerland, 23-24 January 2013
1
1
Outline of presentation
Target objects and values of their polarization parameters
Instruments and methodology of polarimetric observations
Strategy of the instrumental calibration:
 Correct estimation of the polarization parameter’s accuracy;
 Instrumental linear polarization and some problems with using
unpolarized standards;
 Efficiency of polarimeter, zero point of the instrumental position angles
and problems with polarized standard
Conclusions
2
Comets Satellites
Asteroids
Stars
10,0
V, зв. вел.
10,5
0.6
0.6
0.4
0.4
0.2
0.0
0.2
-0.2
0.0
11,0
11,5
Iapetus, Pv = 0.6
Enceladus, Pv = 1.04
Rhea, Pv = 0.8
-1.0
-0.2
7
6
-0.4
5
-0.6
-0.8
-1.2
-1.4
0
2
4
6
8
10
12
14
64 Angelina, Pv = 0.48
4
Herbig
Ae/Be star
WW Vul
P
3
-1.0
2
Phase angle, deg
0.6
-1.2
0.4
1
0
-1.4
0.2
0
2
4
6
8
10
12
14
Phase angle, deg
That is those values where
the errors of instrumental
polarization may distort the
true polarization values of the
investigated objects.
-0.2
-0.4
-0.6
-0.8
Europa, Pv = 0.68
-1.0
-1.2
-1.4
0
2
4
6
8
Phase angle, deg
10
12
14
180
160
град
0.0
Polarization, %
P, %
-0.6
-0.8
Multi-decadal measurements
of polarization. Target objects
are:
comets,
asteroids,
satellites of planets, and some
types of variable stars. Eeach
program object has own
values of polarization degree.
V
12,5
-0.4
Polarization, %
Polarization, %
12,0
140
120

100
900
950
1000
1050
JD 2440000+
1100
3
Telescopes
the 0.7-m telescope of
the Gissar Observatory
(Tadjikistan)
the 1.0-m RCC telescope of
the Sanglok Observatory
(Tadjikistan)
the 0.7-m telescope
of the Chuguev
observation Station
of Kharkiv Univ.
the 2.6-m Shain
telescope of the Crimean
Astrophysical
Observatory
4
Methodology of aperture photoelectric observations
The measurements are based on counting the photoelectron pulses. A high rotation frequency of the polarizer
( 33Hz) and the method of synchronous detection ensure a quasi simultaneous measurement of the polarization
parameters. In the simplest type of polarimeter to determine the parameters of the linear polarization we used
next expression:
I()=1/2(I0 + Q0 cos2 + U0 sin2) = 1/2 [1 + Pcos2( - )]
(1)
Stokes parameters I0, Q0, U0 of incident light have been determined from the four counters
N1, N2, N3, N4 recorded the signal in the course of quarter period (±/4) of rotation of the polaroid
I0=1/ (N1 +N2)=1/ (N3 +N4);
U0 = ½(N1 – N2);
Q0 = ½(N3 – N4)
Polarimeter of the 2.6 m Shain telescope based on the use of modulation formula by Serkowski (1974)
I() = 1/2(I0 + 1/2Q0 +1/2Q0 cos4 +1/2U0 sin4 -V0 sin2) (2)
where  is the angle between the optical axes of the analyzer (a quarter-wave plate /4) and a fixed analyzer
(Glan prism). The simultaneous measurement of all four Stokes parameters necessitates measurements for
8 orientation angles with 22.5° increments.
The expressions (1) and (2) are used for determination of polarization parameters of target objects as well
as instrumental polarization (standard stars).
5
Correct estimation of the errors of polarization parameters
As a rule, the errors are estimated in two
ways. First of all, the random error can
be estimated from the statistics of the
accumulated pulses using the following
formula (Shakhovskoy&Efimov, 1976):
 oP   o,q   o,u 
 100 1
2
N
(1 
1
)
R
N - the number of photoelectron pulses accumulated for
the object
 - the ratio of the accumulation times for the object and
the background sky
R - the ratio of the average pulse rates for the object and
the background sky.
Another estimate: the errors are
defined as the standard of random
variables for separate measurements
of Stokes parameters qi and ui
The greater of the two average errors serves as the final estimate
of the error of polarization measurements of targets and standard stars.
Errors found on dispersion parameters ui and qi individual
measurements vs errors based on statistics of pulses
For a sufficient number of measurements
(n>20), two errors are close to each other.
The final errors of the polarization
parameters of the object take into account
the random and systematic (instrumental)
components. Therefore it is important that
the instrumental errors were less than the
random ones.
2
 q   02,q   inst
,q ;
2
 u   02,u   inst
,u
Therefore it is important that the instrumental errors
were less than the random ones.
7
Use of standard stars for determining the
parameters of instrumental polarization
HD
111395
154029
111395
102870
114710
214923
165908
u_obs
0.080
0.056
0.008
0.012
0.057
0.068
0.069
Mean
0.050
+/-0.011
sigu
0.030
0.027
0.028
0.028
0.027
0.026
0.026
q_obs
-0.061
-0.055
-0.119
-0.061
-0.053
-0.070
-0.040
sigg P_cat
0.030 0.020
0.027 0.040
0.028 0.020
0.028 0.017
0.027 0.018
0.026 0.050
0.026 0.002
sigP_cat
0.032
0.035
0.032
0.014
0.014
0.020
0.007
PA_cat
21
177
21
162
116
40
39
sig PA_cat
39
24
30
2
2
12
4
-0.066
+/-0.010
As a rule observations of nearby unpolarized stars are carried out to measure the
instrumental polarization.
1. Because the standards with zero polarization is not much need to use the
standards with a small degree of polarization, preferably with different angles
of polarization.
2. Parameters of instrumental polarization must be determined independently for
each period of observation of target objects.
8
Determination of the instrumental parameters of polarization
8
Instrumental parameters u and q, %
P_cat= 0.986*P_obs + 0.063
+/-0.074
+ /- 0.027
6
HD 204827
5
P_cat, %
The 0.70-m telescope
Filter V
0.20
7
4
HD 7927
3
HD 198478
2
HD 187929
u_ins = 0.050 +/- 0.011 %
0.10
0.00
-0.10
q_ins = -0.066+/-0.010 %
1
-0.20
HD 188326
HD 191854
0
0
1
2
3
4
5
6
7
1
8
2
3
4
5
6
7
8
9
the number of measurement
P_obs, %
50
50
CRL 2688
P_cat = 1.056 * P_obs - 0.078
+/-0.005
+/- 0.071

obs
cat, deg
40
P_cat, %
30
20
45
Mean  39.7 +/- 1.9 deg
40
35
10
HD 204827
30
0
0
10
20
30
P_obs, %
40
50
40
60
80
100
 cat , deg
120
140
160
9
Conclusion
1. It is important to make sure that the instrumental
polarization is stable and small and/or or determined with
high accuracy for each period of observations of target
objects.
2. Number and distribution of standards with zero degree of
polarization of a highly unsatisfactory.
3. We define the degree of polarization of polarized standards
not only for the determination of the zero point instrumental
angles, but also to correct the observations of target objects.
4. There are no standards with a high degree of polarization in
the range of 8-40 percent and more.
5. To carry out work on the characterization of the polarization
of the new standards should be used spacecraft polarimeters
as well as new ground-based observations.
10
Main sources of systematic errors
High-quality polarimetric observations of astronomical objects must be based on
a careful analysis of and correction for all systematic errors. The main sources
of systematic errors are the following:
• instrumental polarization;
• instrumental depolarization;
• relative errors in the radiometric calibration of different channels (for
differential measurement techniques);
• imperfections of the polarization analyzer;
• errors in the zero point of position angles;
• polarization of the background skylight;
• and some others.
Thanks for attention
Acknowledgments
We thank Dr. Hervé Lamy and Dr. Hans
Martin Schmid for support to participate
in the Calibration Workshop of the COST.
12