1 Nikolai Kiselev and Vera Rosenbush Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv Calibration Workshop Zurich, Switzerland, 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 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 parameters 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

CometsSatellitesAsteroidsStars Herbig Ae/Be star WW Vul V P 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. 3

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 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(I 0 + Q 0 cos2 + U 0 sin2 ) = 1/2 [1 + Pcos2( - )](1) Stokes parameters I 0, Q 0, U 0 of incident light have been determined from the four counters N 1, N 2, N 3, N 4 recorded the signal in the course of quarter period (± /4) of rotation of the polaroid I 0 =1/ (N 1 +N 2 )=1/ (N 3 +N 4 ); U 0 = ½(N 1 – N 2 ); Q 0 = ½(N 3 – N 4 ) Polarimeter of the 2.6 m Shain telescope based on the use of modulation formula by Serkowski (1974) I( ) = 1/2(I 0 + 1/2Q 0 +1/2Q 0 cos4 +1/2U 0 sin4 -V 0 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): 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. 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 q i and u i

Errors found on dispersion parameters u i and q i 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. 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 u_obs sigu q_obs sigg P_cat sigP_cat PA_cat sig PA_cat Mean / / 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 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