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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

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

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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

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Comets Satellites Asteroids Stars

12,5

12,0

11,5

11,0

10,5

10,0

гр

ад

JD 2440000+

V, з

в. в

ел.

P, %

0

1

2

3

4

5

6

7

900 950 1000 1050 1100100

120

140

160

180

HerbigAe/Be starWW Vul

V

P

0 2 4 6 8 10 12 14Phase angle, deg

-1 .4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Pol

ariz

atio

n, %

64 Angelina, Pv = 0 .48

0 2 4 6 8 10 12 14Phase angle, deg

-1 .4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Pol

ariz

atio

n, %

Iapetus, Pv = 0.6

Enceladus, Pv = 1.04

Rhea, Pv = 0.8

0 2 4 6 8 10 12 14Phase angle, deg

-1 .4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

Pol

ariz

atio

n, %

Europa, Pv = 0.68

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.

That is those values where the errors of instrumental polarization may distort the true polarization values of the investigated objects.

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Telescopes

the 0.7-m telescope of the Gissar Observatory (Tadjikistan)

the 0.7-m telescope of the Chuguev observation Station of Kharkiv Univ.

the 1.0-m RCC telescope of the Sanglok Observatory (Tadjikistan)

the 2.6-m Shain telescope of the Crimean Astrophysical Observatory

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Methodology of aperture photoelectric observationsThe 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).

 

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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):

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.

)1

1(1

2

100,, RNuoqooP

The greater of the two average errors serves as the final estimate

of the error of polarization measurements of targets and standard stars.

Another estimate: the errors are

defined as the standard of random

variables for separate measurements

of Stokes parameters qi and ui

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,

2,0

2,

2,0 ; uinstuuqinstqq

Therefore it is important that the instrumental errors were less than the random ones.

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Use of standard stars for determining the parameters of instrumental polarization

HD u_obs sigu q_obs sigg P_cat sigP_cat PA_cat sig PA_cat

111395 0.080 0.030 -0.061 0.030 0.020 0.032 21 39

154029 0.056 0.027 -0.055 0.027 0.040 0.035 177 24

111395 0.008 0.028 -0.119 0.028 0.020 0.032 21 30

102870 0.012 0.028 -0.061 0.028 0.017 0.014 162 2

114710 0.057 0.027 -0.053 0.027 0.018 0.014 116 2

214923 0.068 0.026 -0.070 0.026 0.050 0.020 40 12

165908 0.069 0.026 -0.040 0.026 0.002 0.007 39 4

Mean 0.050 -0.066

+/-0.011 +/-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.

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Determination of the instrumental parameters of polarization

1 2 3 4 5 6 7 8 9the num ber of m easurem ent

-0 .20

-0.10

0.00

0.10

0.20

Inst

rum

enta

l par

amet

ers

u an

d q,

% u_ ins = 0 .050 + /- 0 .011 %

q_ins = -0 .066+/-0 .010 %

The 0.70-m telescopeFilter V

0 10 20 30 40 50P_obs, %

0

10

20

30

40

50

P_c

at, %

P_cat = 1.056 * P_obs - 0.078 +/-0.005 +/- 0.071

C R L 2688

H D 204827

0 1 2 3 4 5 6 7 8P_obs, %

0

1

2

3

4

5

6

7

8

P_c

at, %

P_cat= 0 .986*P_obs + 0 .063 + /-0 .074 + /- 0 .027

H D 187929

H D 188326H D 191854

H D 198478

H D 7927

H D 204827

40 60 80 100 120 140 16030

35

40

45

50

ob

s

M ean 39.7 + /- 1 .9 deg

ca

t , de

g

cat , deg

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Conclusion1. 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.

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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.

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