An Easily Designed and Constructed Optical Polarimeter for Small Telescopes

Transcription

1 PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 125: , 2013 September The Astronomical Society of the Pacific. All rights reserved. Printed in U.S.A. An Easily Designed and Constructed Optical Polarimeter for Small Telescopes G. A. TOPASNA, D.M.TOPASNA, AND G. B. POPKO Department of Physics and Astronomy, Virginia Military Institute, Lexington, VA 24450; Received 2013 May 10; accepted 2013 July 18; published 2013 August 26 ABSTRACT. We have designed, constructed, and tested an optical polarimeter for use with the Virginia Military Institute (VMI) 0.5 m, f/13.5 Cassegrain telescope. Our instrument is based on the common dual-beam design that utilizes a rotatable half-wave plate and Wollaston prism to image starlight onto a CCD detector after it has passed through a broadband filter. The usable field of view is and the operational range of the instrument is nm. Measurements of unpolarized stars demonstrate that the instrumental polarization is 0:05%. Observations of seven standard stars were in agreement with their accepted values by an order of Δpð%Þ 0:23 for the degree of polarization and Δθð Þ 0:94 for the position angle. Online material: color figure 1. INTRODUCTION The measurement of stellar polarization has been instrumental in helping to determine the structure and constituents of the interstellar medium (ISM). From the early measurements by Hiltner (1949) and Hall (1949) to the current observations of today, stellar polarimetry has revealed information about the magnetic field of the galaxy and the intervening dust in the ISM, as well as the intrinsic polarization of some stars. Given the importance that polarization measurements and analysis have in helping astronomers understand astrophysical phenomena, it would be beneficial for astronomy and astrophysics students to actually obtain and analyze polarization measurements as part of their observational astronomy courses. Since most observational astronomy courses utilize small optical telescopes as part of the course instruction, an optical polarimeter is a natural choice. The optical polarimeter design should be simple enough that it can be easily modified and built to fit any particular telescope. A simple design that yields reliable, scientifically significant results is the dual-beam polarimeter. The dual-beam polarimeter design is common and saw its first astronomical use by Appenzeller (1967) and it has since then been replicated and improved upon by the introduction of CCD cameras and lenses for imaging [e.g., see Scarrott et al. (1983), Ramaprakash et al. (1998)]. The dual-beam design is simple enough that it can incorporate off-the-shelf optical and mechanical components that are readily available. Additional machining necessary to mount the optical and mechanic pieces together is typically minimal, making this an optimal design for a student project. Finally, the structure that houses and attaches the polarimeter to the back of the telescope can be as simple (or as involved) as the designers would like and required for their telescope. In this paper we present the design, construction, and testing of just such a simple dual-beam polarimeter that is used with the 0.5 m, f/13.5 Cassegrain telescope at Virginia Military Institute (VMI) observatory. It uses readily available off-the-shelf optical mechanical components and required a minimal amount of machining and construction to build. Section 2 describes the design and construction of the polarimeter, and 3 discusses our data reduction method. Section 4 presents our observations and analysis and an evaluation of the polarimeter s performance. Section 5 is our conclusion. 2. INSTRUMENT A cross-section of our polarimeter design is shown in Figure 1. The 22 mm diameter achromatic half-wave plate is from Karl Lambrecht Corporation (WPAC2-22). The double plate retarder is fabricated using magnesium fluoride and crystalline quartz and it is optimized for a wavelength range from 400 to 700 nm. It is housed in a compact motorized rotation stage from Thorlabs (PRM1-Z7) that has a maximum rotation speed of 24 s 1 and a resolution of 1. The Wollaston quartz prism is from Bernhard Halle Nachfl. GmbH (PWQ 30.30) with a usable spectral range from 0.23 to 2.8 μm and a 0.5 divergence angle. It has a mm cross section and is mounted in a 50.8 mm outside diameter cylinder. The prism is mounted inside a mm diameter coupling tube that connects the rotation stage to a filter wheel (Alata AFW50-9R from Apogee) that contains Johnson Cousins B, V, R, and I filters from Astrodon. 1 The filter wheel is connected to an Alta U6 CCD camera from Apogee which uses a Kodak KAF-1001E CCD 1 See

2 OPTICAL POLARIMETER FOR SMALL TELESCOPES 1057 Light Proof Mounting Enclosure 100 Rotation Stage HWP o e Filter Wheel Filter CCD Chip (24.58 mm sq.) Alta U6 Camera QE Curve/Filter Transmission (%) B V R I WP Wavelength (nm) 20 mm 83 mm 108 mm FIG. 1. Layout of the optical and mechanical components of the VMI polarimeter. [Half-wave plate (HWP) and Wollaston prism (WP).] imaging sensor. The imaging area of the sensor is 24:6 mm 24:6 mm with 24 μm 2 pixels in a array. The instrument we constructed was inspired by the IMPOL polarimeter that was designed and constructed by Ramaprakash et al. (1998). Whereas IMPOL is an imaging polarimeter with a movable grid in the focal plane and a field lens to image the focal plane on the CCD, our design only uses the same type of half-wave plate and Wollaston prism to image stars directly on the CCD. Similarly, the IMPOL was tested on a 1.2 m, f/13 telescope, whereas our is used on the 0.5 m, f/13.5 telescope. The polarization characteristics of the IMPOL and its optical components are thoroughly described by Ramaprakash et al. (1998), and they find that the amount of instrumental polarization to be less than 0.05%. Our analysis of polarized standard stars shows that the instrumental polarization of our instrument is also of this order. The transmission characteristics of the broadband filters were obtained by measurements in the Thin Films Lab at VMI using a Perkin Elmer Lambda 900 UV/Vis/NIR spectrophotometer. From these data we determined the mean wavelength λ o given by the expression TABLE 1 FILTER CHARACTERISTICS Filter λ o FWHM B V R I NOTE. All numbers are in nanometers. FIG. 2. Transmission curves of the broadband filters superimposed on the quantum efficiency curve of the Alta U6 CCD camera. Z λ 0 ¼ W Z λt ðλþdλ= T ðλþdλ; (1) W where T ðλþ is the transmission curve and the integration is carried over the spectral window W of the filter. The mean wavelength and FWHM for each filter are presented in Table 1 and the quantum efficiency of the CCD sensor and measured transmission curves for each filter are shown in Figure DATA REDUCTION Aperture photometry is performed on the two stellar point spread functions (PSF) in order to determine I o and I e, the ordinary and extraordinary flux, respectively. Measured on the image, the centroids of the two point spread functions are separated by 20 pixels, which corresponds to a separation of slightly less than 15. Given the small amount of separation between the ordinary and extraordinary images on the CCD, the polarimeter is limited to observation of point sources. The photometry was performed using Mira Pro UE software from Mirametrics. 2 The radius of the source aperture was determined by plotting growth curves and selecting an aperture radius where the S/N ratio was highest. A review of the growth curves that we plotted indicated that the aperture radius was typically 3 times the FWHM of the stellar profile. The background was determined from the median value in an annulus surrounding the source. Since the annulus contained the second stellar image, the width of the annulus was chosen so that the number of background pixels greatly exceeded those of the second stellar source. To remove most of the instrumental polarization, and to account for the response of the CCD sensor to different states of polarization, the normalized Stokes parameters q and u 2 See

3 1058 TOPASNA ET AL. are determined using the equations derived by di Serego Alighieri (1997) where q ¼ R q 1 R q þ 1 R 2 q ¼ Io 0 I e 45 I e 0 I o 45 u ¼ R u 1 R u þ 1 ; (2) R 2 u ¼ Io 22:5 I e 67:5 I e 22:5 I o 67:5 : (3) The percent polarization and position angle are then determined by the equations p 0 ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q 2 þ u 2 and θ ¼ 1 2 tan u q, respec- p tively, with the standard errors σ p and σ θ from repeated measurements determined by standard propagation procedures to be ½q 2 σ 2 q þ u 2 σ 2 uš 1=2 =p and ½q 2 σ 2 u þ u 2 σ 2 pš 1=2 =2p 2, respectively. Finally, in order to remove the bias inherent in the degree of polarization, we used the Wardle Kronberg estimator qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p ¼ p 2 0 σ2 p derived by Wardle and Kronberg (1974) and discussed by Simmons and Stewart (1985). 4. OBSERVATIONS AND ANALYSIS Observations of polarized and unpolarized standard stars were made during various moonless nights after astronomical twilight from November 2011 to October The polarimeter was used with the 0.5 m, f/13.5 Cassegrain telescope at the VMI observatory located at McKethan Park in Lexington, Virginia. The polarimeter was mounted so that the fast axis of the half-wave plate is parallel to the local meridian, making this the fiducial setting of 0 for the instrument. The CCD was thermoelectrically cooled to 20 C below ambient temperature, the particular star being imaged was centered on the CCD chip, and between 20 to 200 images were obtained with the half-wave plate at each position of 0, 22.5, 45, and All images were obtained with 2 2 binning to reduce read noise and a dark current was subtracted from each image. No flat-field images were used, as it was found that the image quality was reduced and subsequent analysis showed that the polarization measurements obtained were more accurate without flat fielding Unpolarized Standard Stars In order to determine the instrumental polarization we observed seven stars that have little or no polarization. Six of TABLE 2 MEASUREMENTS OF UNPOLARIZED STARS Star α (2000) a δ (2000) a Band mag a q (%) u (%) p (%) σ p (%) θ ( ) σ θ ( ) HD B V R I HD B V R I HD B V R I HD B V R I HD B V R I HD B V R I a Right ascension, declination, and magnitudes provided by the SIMBAD database operated at CDS, Strasbourg, France

4 OPTICAL POLARIMETER FOR SMALL TELESCOPES 1059 FIG. 3. Polarization measurements for six unpolarized stars. Open circle indicates the median instrumental polarization. these were from the nearby or unpolarized stars listed by Serkowski (1973), and one (HD ) was from the list of Matthewson and Ford (1970) and Clemens and Tapia (1990). Six of these stars were imaged in the B, V, R, and I bands with 20 images for each of the half-wave plate settings at 0, 22.5, 45, and 67.5, and the results of our analysis are presented in Table 2, showing the identification of the star, its right ascension and declination, the filter band, and the corresponding magnitude. Also shown are the measured values and associated uncertainties. A plot of the normalized Stokes parameters u (%) against q (%) for each filter is shown in Figure 3. An open circle in each plot indicates the median value of u (%) and q (%). These medians, which are taken as a measure of the instrumental polarization, are 0.02%, 0.01%, 0.05%, and 0.05% for the B, V, R, and I filters, respectively. This indicates an average instrumental polarization across all wavebands to be on the order of 0.03%, however, given the measurements in the R, and I bands a measurement of p is overall accurate to within 0:05%. A second estimate of the instrumental polarization was made using 200 measurements of the star HD in all four bands. A plot of the normalized Stokes parameters u against q is shown in Figure 4. The open circle in each of the plots shows the average value of the instrumental polarization to be (0:035 0:008) %,(0:047 0:008) %,(0:05 0:01) %, and (0:023 0:008) % for the B, V, R, and I filters, respectively. While the overall instrumental polarization is on the order of 0.04%, we take the limiting accuracy to be on the order of

5 1060 TOPASNA ET AL. FIG. 4. Instrumental polarization measurements for HD Open circle indicates the median instrumental polarization. 0.05% in any waveband and any measurement of polarization 0:05% is within instrumental polarization, and is therefore not considered measurable by our instrument Polarized Standard Stars (V Band) Seven standard stars with large, known interstellar polarization from the list by Serkowski (1974) were measured in the V band. A total of 200 images were obtained at each of the four standard angles of the half-wave plate, resulting in 200 measurements of q and u. Images were also obtained of unpolarized stars and the measured instrumental polarization was vectorially subtracted from the measured q and u values. The unbiased degree of polarization and position angle, along with their associated uncertainties, were calculated according to the method described in 2. We note that the position angle is reported in the conventional manner (with respect to a line of constant right ascension through the star with position angle increasing eastward). The results of our measurements are shown in Table 3, which displays the stars identifications, measured polarizations, position angles, and the published values of p, θ and the group that made the measurement. An examination of the results shows that our measurements are consistent with those of the listed authors. A weighted average of the published values from Table 3 is presented in Table 4 along with our measured values for comparison purposes. A very good agreement with the published values is indicated by the differences in degree of polarization and position angles which are on the order of Δpð%Þ 0:02 0:23 and Δθð Þ 0:03 0:94. The data are also shown in Figure 5, where the left-hand column is the degree of polarization (in percent) and the

6 OPTICAL POLARIMETER FOR SMALL TELESCOPES 1061 TABLE 3 V -BAND POLARIMETRY OF STANDARD STARS Measured Published Star p (%) θ ( ) p (%) θ ( ) Remarks HD ± ± ± ±0.1 Hsu et al. (1982) (ϕ Cas) ± ±0.5 Heiles (2000) Serkowski (1974) 3.23± ±0.8 Rautela et al. (2004) 3.35± ±1 Bailey et al. (1982) 3.298± ±0.22 Schmidt et al. (1992) 3.320± ±0.2 Bastien et al. (1988) HD ± ± ± ±0.7 Hsu et al. (1982) (9 Gem) ± ±1.3 Heiles (2000) Serkowski (1974) 3.05± ±0.3 Ramaprakash et al. (1998) HD ± ± ± ±0.1 Hsu et al. (1982) (O Sco) ± ±0.3 Heiles (2000) Serkowski (1974) 4.21± ±1 Baiely et al. (1982) 3.857± ±0.1 Bastien et al. (1988) 4.16± Tapia (1988) Weitenbeck (2004) 4.19± ±0.9 Chavero et al. (2006) 4.15± ±1.1 McDavid (1999) 4.12± Goswami et al. (2010) HD ± ± ± ±0.1 Hsu et al. (1982) 3.42± ±0.2 Heiles (2000) Serkowski (1974) 3.65± ±0.2 Ramaprakash et al. (1998) 3.78± ±0.47 Schmidt et al. (1992) 3.75± ±1 Bailey et al. (1982) 3.556± ±0.1 Bastien et al. (1988) 3.72± Tapia (1988) HD ± ± ± ±0.2 Hsu et al. (1982) 5.886± ±0.3 Heiles (2000) Serkowski (1974) 5.737± ±0.2 Clemens et al. (1990) 6.19± ±1 Bailey et al. (1982) 6.30± ±0.5 Schulz et al. (1983) HD ± ± ± ±0.2 Bastien et al. (1988) (η Aql) ± ±0.1 Heiles (2000) Serkowski (1974) 1.71± ±1 Baiely et al. (1982) HD ± ± ± ±0.2 Hsu et al. (1982) (55 Cyg) ± ±0.9 Heiles (2000) Serkowski (1974) 2.71±0.12 3±1 Baiely et al. (1982) right-hand column is the position angle (in degrees). The first data point in each row is our measurement and the remaining data points are taken from Table 3. The weighted mean value is shown by the solid horizontal line in about the middle of the box, and the 1σ confidence of the data set is represented by the dashed horizontal line above and below the mean value. In all instances, our measured values for both degree of polarization and position angle are within the 1σ confidence interval.

7 1062 TOPASNA ET AL. TABLE 4 COMPARISON OF V -BAND MEASUREMENTS WITH STANDARD STARS Measured Published (weighted average) Star p (%) θ ( ) p (%) θ ( ) Δp (%) Δθ ( ) HD ± ± ± ± (ϕ Cas).... HD ± ± ± ± (9 Gem)... HD ± ± ± ± (O Sco).... HD ± ± ± ± HD ± ± ± ± HD ± ± ± ± (η Aql).... HD ± ± ± ± (55 Cyg)... FIG. 5. Comparison of the degree of polarization measurements. The left column is the degree of polarization (percentage) and the right column is the position angle (degrees). The first data point in each row is the measurement from the VMI polarimeter. See the electronic edition of the PASP for a color version of this figure.

8 OPTICAL POLARIMETER FOR SMALL TELESCOPES 1063 FIG. 6. Wavelength dependence of polarization of HD (γ Gem). P max ¼ 3:00 0:01, λ max ¼ 0:526 0:005 μm, and θ V ¼ 170:2 0:2. Of the stars in our list, three of them (HD 43384, HD , and HD ) are listed by Hsu and Breger (1982) as being variable. Their analysis showed that these three stars are variable on the order of 0.3% in p and 1 in position angles with differing time scales of variability. Our polarization measurements of these three variable stars are within these limits Wavelength Dependence of HD In order to test the instrument s performance at other wavelengths, images of the polarized standard star HD (γ Gem) were obtained on 2012 January 27 in the B, V, R, and I wavebands and a plot of the polarization as a function of the mean wavelength of each filter is shown in Figure 6. It is well-known that the polarization of starlight depends on the wavelength according to the empirical relationship by Serkowski (1973) pðλþ=p max ¼ exp½ K ln 2 ðλ max =λþš; (4) where p max is the maximum degree of polarization (at the wavelength λ max ) and depends on the properties of grains in the interstellar medium. The parameter K was shown by Wilking et al. (1982) to be a function of λ max given by K 1:86λ max, where λ max is in microns. A nonlinear regression fit to the data is shown by the solid curve in Figure 6 and visually indicates a very good fit (r 2 ¼ 0:998). The maximum polarization is 3:00 0:01% and occurs at 0:526 0:005 μm, and K is found to be 0:98 0:07. The maximum polarization occurs in the V band and the position angle in the V band was found to be ð170:2 0:2Þ. The original determination of the maximum degree of interstellar polarization for HD was found by Serkowski (1974) to be 3.0% at λ max ¼ 0:53 μm and θðλ max Þ¼170. Later measurements by Hsu and Breger (1982) found that p max ¼ ð3:01 0:04Þ% at λ max ¼ð0:531 0:011Þ μm, and they list only the polarization angle in the V filter, which they found to be ð169:8 0:7Þ. It should be noted that position angle measurements by Hsu and Breger (1982) vary little from a mean value of 170 across measurements in their five filters (U, B, V, R, and [0.75]), and our measurements across the four filters B, V, R, and I also vary little from a mean value of Given the excellent agreement between our values and those of Hsu and Breger, we are confident in the instrument s ability to measure polarization at the B, R, and I wavebands. 5. CONCLUSION We have designed and constructed a two-beam polarimeter for use with the 0.5 m, f/13.5 telescope at the VMI observatory, demonstrating that a simple dual-beam polarimeter can be easily constructed for use with a small telescope to make precise astronomical observations. Our test of the polarimeter determined its instrumental polarization to be 0:05% in all four wavebands B, V, R, and I. Observations of seven standard stars indicate agreement on the order of Δpð%Þ 0:23 for the degree of polarization and Δθð Þ 0:94 for the position angle. This work is supported by a Jackson Hope Foundation Grant-in-aid of research at Virginia Military Institute. We would also like to thank VMI shop mechanic Grigg Mullen III for helping to design and build the structural components of the instrument. Appenzeller, I. 1967, PASP, 79, 467 Bailey, J., & Hough, J. H. 1982, PASP, 94, 618 Bastien, P., Drissen, L., Menard, F., Moffat, A. F. J., Robert, C., & St-Louis, N. 1988, AJ, 95, 900 Chavero, C., Gomex, M., Whitney, B. A., & Saffe, C. 2006, A&A, 452, 921 Clemens, D. P., & Tapia, S. 1990, PASP, 102, 179 di Serego Alighieri, S. 1997, in Instrumentation for Large Telescopes, ed. J. M. Rodriguez Espinosa, A. Herrero, & F. Sánchez (Cambridge: Cambridge Univ. Press), REFERENCES Goswami, A., Kartha, S. S., & Sen, A. K ApJ, 722, L90 Hall, J. S. 1949, Science, 109, 165 Heiles, C. 2000, AJ, 119, 923 Hiltner, W. A. 1949, Science, 109, 165 Hsu, J.-C., & Breger, M. 1982, ApJ, 262, 732 Mathewson, D. S., & Ford, V. L. 1970, MNRAS, 74, 139 McDavid, D. 1999, PASP, 111, 494 Ramaprakash, A. N., Gupta, R., Sen, A. K., & Tandon, S. N. 1998, A&AS, 128, 369

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