POLICAN: A Near-infrared Imaging Polarimeter at the 2.1m OAGH Telescope
R. Devaraj, A. Luna, L. Carrasco, M. A. Vázquez-Rodríguez, Y. D. Mayya, J. G. Tánori, E. O. Serrano Bernal
DDraft version March 8, 2018
Typeset using L A TEX twocolumn style in AASTeX61
POLICAN: A NEAR-INFRARED IMAGING POLARIMETER AT THE 2 . Devaraj R., A. Luna, L. Carrasco, M. A. V´azquez-Rodr´ıguez, Y. D. Mayya, J. G. T´anori, andE. O. Serrano Bernal Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica,Luis Enrique Erro (Received —; Revised —; Accepted —)
Submitted to PASPABSTRACTPOLICAN is a near-infrared imaging linear polarimeter developed for the Cananea Near-infrared Camera (CANICA)at the 2 . − . µ m) half-wave plate (HWP)as the modulator and a fixed wire-grid polarizer as the analyzer. CANICA has a 1024 × .
32 arcsec / pixel and provides a field of view of 5 . × . . The polarimetric observations arecarried out by modulating the incoming light through different steps of half-wave plate angles (0 ◦ , ◦ , ◦ , ◦ ),to establish linear Stokes parameters ( I, Q , and U ). Image reduction consists of dark subtraction, polarimetric flatfielding, and sky subtraction. The astrometry and photometric calibrations are performed using the publicly availabledata from the Two Micron All Sky Survey. Polarimetric calibration includes observations of globular clusters andpolarization standards available in the literature. Analysis of multiple observations of globular clusters yielded aninstrumental polarization of 0.51%. Uncertainties in polarization range from 0.1% to 10% from the brightest 7 mag tofaintest 16 mag stars. The polarimetric accuracy achieved is better than 0.5% and the position angle errors less than5 ◦ for stars brighter than 13 mag in H -band. POLICAN is mainly being used to study the scattered polarization andmagnetic fields in and around star-forming regions of the interstellar medium. Keywords:
Instrumentation: Polarimeters, Methods: Data Analysis, Techniques: Polarimetric, Mag-netic fields, Polarization
Corresponding author: Devaraj [email protected] a r X i v : . [ a s t r o - ph . I M ] M a r Devaraj et al. INTRODUCTIONImaging polarimeters offer great opportunity to studyvarious astrophysical topics ranging from galactic re-gions to extragalactic sources such as active galactic nu-clei (AGNs). Polarimeters built to function in opticalwavelength are plenty (e.g. IAGPOL, IMPOL, Dipol-2, RoboPol; Magalh˜aes et al. 1996; Ramaprakash et al.1998; Piirola et al. 2014; King et al. 2014), but they arelimited to provide only partial insight into some of thescience cases. On the other hand, near-infrared (NIR)polarimetry offers a unique window to observe new re-gions, revealing different physical phenomena. One ofthe main subjects of interest for polarimetric studieswith 2 m class telescopes is the interstellar dust andcool galactic star-forming regions. The linearly polar-ized light from the stars, caused by dichroic extinction(Hall 1949; Hiltner 1949) from dust grains, which arealigned to local magnetic fields (Davis & Greenstien1951; Lazarain & Hoang 2007), is very useful in under-standing the interplay of interstellar matter and mag-netic fields. Combining theory and observations, we canbegin to understand dust properties and magnetic fieldsfrom dense cores to star-forming regions in and aroundmolecular cloud complexes (e.g. Jones 1989; Nishiyamaet al. 2009; Chapman et al. 2011). Existing NIR po-larimeters like SIRPOL (Kandori et al. 2006) and Mimir(Clemens et al. 2007) have been used to conduct vari-ous observations and surveys like GPIPS (Clemens etal. 2012a) to study the magnetic fields in the galacticmedium. Additionally, NIR polarimetry can aid in in-vestigating the circumstellar structures of young stellarobjects (YSOs) whose radiation is scattered by dust andis observed as infrared reflection nebulae (Tamura et al.2006; Hashimoto et al. 2008). Polarization data fromspiral galaxies can be used to study galaxian magneticfield properties and the field’s orientation to the disk(e.g. Jones 1997; Clemens et al. 2013; Montgomery &Clemens 2014).With all of these diverse astrophysical topics to ex-ploit, and considering that only few NIR polarime-ters are available, we built a new instrument calledPOLICAN to function as an imaging linear polarime-ter. POLICAN operates at the 2 . POLICAN: Polarimetro Infrarojo para CANICA pleted in the year 2012 with the support of funding fromthe Mexican science agency CONACyT.POLICAN consists of basic polarizing elements: arotating super-achromatic (1 − . µ m) half-wave plate(HWP) as the modulator and a fixed wire-grid polar-izer as the analyzer. These are housed in an externalassembly placed between the telescope and CANICA asshown in Figure 1.To meet the scientific requirements and to obtain goodquality polarization data, it is important to make POLI-CAN function well and to understand its characteristicsand operational behavior. Obtaining accurate polari-metric data requires optimization of observation meth-ods and a robust data processing and analysis tool kit.Further, a detailed calibration of the instrument is nec-essary to calculate the true polarization. This led todevelopment of various strategies and methods for oper-ation and calibration of POLICAN. Additionally, soft-ware pipelines were developed for handling the largeamounts of data to be processed into science-quality re-sults. The core of POLICAN capabilities depends on theCANICA characteristics, which have been characterizedand evaluated in Devaraj et al. (2017); hereafter Paper I.POLICAN incorporates a mechanical design similar toSIRPOL and most of its calibration scheme are derivedfrom the Mimir team’s approach (Clemens et al. 2012b).Preliminary descriptions about POLICAN are reportedin Devaraj et al. (2015, 2017a). In the following sections,we present the instrument overview, polarimeter opera-tion, observational properties, data processing methods,calibration, and observational results of POLICAN. INSTRUMENT OVERVIEWThe reflector telescope at the OAGH observatory is aRitchey-Chr´etien configuration on an equatorial mountwith a primary mirror of 2 . . (cid:48)(cid:48) J (1 . µ m), H (1 . µ m)and K (cid:48) (2 . µ m) including other multiple narrow bands.The camera unit is made up of a cryostat assembly in-cluding collimator, filter wheels, focusing system and adetector. The detector is a HgCdTe HAWAII array of1024 × .
32 arcsec / pixeland provides a field of view (FOV) of 5 . × . .CANICA is operated using a correlated double sampling(CDS) readout method, and hence the raw data deliv-ered after POLICAN observations are the CDS images.Details of CANICA construction and design are pre- OLICAN Figure 1.
Block diagram and exterior photos of POLICAN attached to CANICA and the telescope. The polarimeter unit is amechanical assembly consisting of a half-wave plate and a polarizer operated at room temperature. The assembly is coupled toCANICA on one end and to the telescope on the other end with the help of a rotating adapter. sented in Carrasco et al. (2017). A complete descrip-tion of CANICA characteristics and performance arepresented in Paper I.2.1.
Polarimeter
The CANICA has a light entrance window that is off-centered with respect to the cryostat so as to align itwith the optical axis designed to accommodate filterwheels. To adjust for the displaced entrance window, anadapter couples the telescope and the CANICA. As a re-sult, it was observed that the polarimeter POLICAN canbe implemented in the space next to the adapter puttingthe polarizing elements externally to the CANICA atroom temperature (see Figure 1).POLICAN’s polarizing elements consists of a retarder(half-wave plate) and an analyzer (wire-grid polarizer).The retarder is a super-achromatic (1 − . µ m) HWPof diameter 50 mm, which is made by cementing pairs ofMgF and Quartz plates. It has very low path differenceof ± .
04% and the change in orientation of the opticalaxis is negligible ± . ◦ across the entire spectral range.The retarder is manufactured by Bernhard Halle Nachfl,Germany. The analyzer is a holographic high extinctionratio (HER) polarizer of diameter 71 mm deposited ona CaF substrate, with a large spectral range from 1 − µ m. It has a grid spacing of 4000 lines/mm with atransmission efficiency of 84% at 2 . µ m. The polarizeris manufactured by Specac company, UK.The polarizing elements are housed inside an alu-minum mechanical assembly with a detachable system.The detachable system can be manually removed from the beam along a translating stage, so as to switch theobservations between normal photometry and imagingpolarimetry. The change in back focal length duringeach mode is corrected by positioning the secondary mir-ror accordingly. The top and bottom ends of the me-chanical assembly are provisioned with circular flangesfor attaching to the telescope and to CANICA. The flex-ure in the mechanical assembly due to the weight ofCANICA at different declinations is found to be neg-ligible. The adapter for coupling POLICAN with thetelescope is a rotating system that can be used to orientthe instrument. The entire setup with the adapter isaligned to a setting of 328 ◦ to orient the observationsalong north-up and east-right direction on the detector.Figure 2 shows a zoomed view of the mechanical assem-bly with the stepper motor, HWP, and the polarizer.Details of the mechanical assembly design and construc-tion are presented in V´azquez-Rodr´ıguez (2012). OPERATION AND CONTROLLinear polarimetric observations can be achieved froma combination of rotating modulators and analyzerswhereby the orthogonal components of polarization areproduced. Dual-beam polarimeters (e.g. PLANET-POL, DBIP, MMTPOL; Hough et al. 2006; Masieroet al. 2007; Packham et al. 2012) that have a Glan-Thompson prism or a Wollaston prism as analyzerscan produce two orthogonal polarizing components si-multaneously for a single position of the modulator,thereby operating faster and reducing sky-dependentnoise. However, they are restricted to observing well
Devaraj et al.
Figure 2.
Blown-up view of the mechanical assembly of the polarimeter. The polarizing elements: half-wave plate and thepolarizer are attached to a tubular case fixed onto a base plate. The half-wave plate is secured on a rotating unit connected toa stepper motor. The base plate is attached to set of rails that can move the unit in and out of the light path manually. separated or isolated sources across a fairly narrowerfield. POLICAN, on the other hand, is designed to op-erate in a single-beam mode which has the advantageof observing both point and extended sources with amedium FOV. However, it must compromise on time ca-dence and deal with the effects of sky-dependent noise.Such a design of POLICAN requires a minimum of fourmodulation angles to obtain the polarizing componentsneeded to establish the linear Stokes parameters (Shur-cliff 1962). The change in the polarization state of thelight as it passes through different optical componentscan be described by a Mueller matrix formalism (Clarke2010). From analysis of Mueller matrices, we find thatthe input linear Stokes parameters I , Q , and U can beestablished from the output lights intensity, by modulat-ing the incoming light with four HWP angles of the firstquadrant—0 ◦ , ◦ , ◦ , ◦ . Appendix A describesthe detail derivation of the modulation scheme with theuse of Mueller matrices. Other sets of HWP angles fromdifferent quadrants can be used similarly to obtain theStokes parameters. The results from each quadrant canthen be combined to reduce HWP dependent errors.However, with POLICAN setup, we chose only the an-gles of the first quadrant to limit the large integrationtime during observations. The control for HWP rotation for modulation is han-dled by a stepper motor that is integrated into the po-larimeter mechanical assembly. The stepper motor con-nects to the HWP with a gear-to-gear transmission sys-tem and the rotation delivered is followed in precise stepangle of 0.3 ◦ . The reference home position of the HWP(i.e. the zero-phase axis) is identified by a Hall effect sen-sor. Connection to the motor controller from the mainobservation computer is through a RS232 serial com-munication line. The stepper motor unit is providedby Parker Motion Control Systems, USA, and the mo-tor controller program is a software in the Visual BA-SIC. To simultaneously achieve control of CANICA andPOLICAN, the stepper motor control and the CANICAcontrol are integrated. This allows for scripted observa-tions to be acquired in sequence for each HWP angle ateach dithered position. OBSERVATION GOALSThe chief scientific goal of POLICAN is to study mag-netic fields in the star-forming regions of the nearby (dis-tances ∼ few kpc) interstellar medium (ISM). Hence, itwas important to define various observational propertiesto carry out polarimetric studies meeting the scientificrequirements. OLICAN
Area coverage
Most of the polarimeters available in the NIR can ei-ther do wide-field, large-scale surveys (e.g. Mimir, SIR-POL), spanning a few tens of parsecs, or use adaptiveoptics to study narrow field regions (e.g. ZIMPOL, GPI;Roelfsema et al. 2010; Perrin et al. 2015), across scalesof 100 − ∼ . to 200 arcmin .4.2. Waveband
At NIR bands, the magnetic field information in theISM obtained from starlight polarization is revealed dueto dichroic extinction. While K -band offers the bestwindow to probe regions of high extinction ( A V ), thethermal emission from the sky is large. On the otherhand, at J -band the sky emission is low, but the A V values probed are limited. The H -band offers the bestcompromise, where we can sufficiently probe regions ofmoderate A V with low thermal emission from the sky.Hence, current observations with POLICAN are concen-trated in H -band, which are presented in this article.However, calibration and study of sources in J and K -band is being carried out simultaneously.4.3. Sensitivity and sampling goals
The starlight polarization information from the red-dened stars in the ISM is usually weak, of the order of1% −
5% (Mathewson & Ford 1970). To accurately per-form starlight polarimetry for studying magnetic fieldproperties requires measurements with polarization un-certainties below 1% (Clemens et al. 2012a). Further, tohave adequate stellar density for tracing magnetic fieldat sub-parsec scales means the angular sampling mustbe greater than 10 −
20 reliable sources per square ar-cmin. From the Two Micron All Sky Survey (2MASS)(Skrutskie et al. 2006) data, to reach the above angu-lar sampling we need to observe magnitude depths of13 −
14 mag in the galactic plane between latitudes b ± ◦ .Hence, to achieve a polarization uncertainty of around1% for stars as faint as 13 mag (e.g. Figure 13) requiresper image exposure times ranging from 30 s to 40 s in H -band with POLICAN.4.4. Signal-to-noise ratio goals
The accuracy of polarimetric measurements also de-pends on the source signal-to-noise ratio (S/N). 2MASSdata reached 15 mag at a S/N of 10 in H -band. Weaim to obtain a S / N >
10 for 15 mag sources in orderto reach the best polarimetric accuracy. This can be achieved by combining more number of images acquiredper field for each HWP. Hence, we considered typicallya minimum of 15 images are required for each HWP an-gle, leading to a total of 60 images for a given observingfield. This leads to a total integration time of around 30to 40 mins for a given field.Essentially, these values and estimates form the ba-sis for starlight polarimetry with POLICAN. However,observations of extragalactic and other sources can becustomized to have different integration times as desired. OBSERVATION SCHEMEGround-based images obtained in the NIR are con-taminated by the atmospheric sky emission (OH line andthermal continuum emission), sky transmission noise,and thermal emission from the telescope and optics.Successfully isolating these effects during data process-ing is essential to consider in an observing scheme. Astandard practice for observing in the NIR is to ob-tain multiple images using telescope dither. This fa-cilitates estimating the aforementioned “sky” contribu-tions. Typically, a minimum of five dithered images issufficient to establish the sky image. However, as notedin the previous section, we want to obtain more imagesper field to boost the S/N of the combined image. Hence,with POLICAN, we implemented a sequence to acquire15 dithered images for each HWP angle for a given ob-serving field.The Stokes parameters are calculated by the differ-ence in flux between two orthogonal polarization mea-surements (see Section 6.2). The flux difference is moreaccurate when the two orthogonal polarizations are ob-tained in sequence, as the change in sky transmission isminimum (Clemens et al. 2012a). Based on this, we de-signed the observing scheme such that the HWP imagescorresponding to each Stokes parameter are acquiredconsecutively for each dithered position (i.e. in the order0 ◦ and 45 ◦ for Stokes Q , 22.5 ◦ and 67.5 ◦ for Stokes U ).This sequence is followed for all the 15 dither positionsleading to a total of 60 images per observed field.The dithering strategy varies depending on the fieldof interest and size of the source.1) For studying magnetic field properties throughstarlight polarimetry, the sequence of observations con-sists of 15 dithers distributed in a non-repetitive randompattern within a diameter of 30 arcsec around the tar-geted center. The dither size of 30 arcsec makes sure thatthe extended emission from bright stars do not overlapin each image.2) For studying scattered polarization from extendedsources, the sequence of observation consists of a dither-ing pattern of 8 source images and 7 off-field images. Devaraj et al.
Figure 3.
Images displaying various characteristics of a normalized master flat image. The first panel shows the flat imagemarked with detector pixel values in physical coordinates. The dark corners in the image are formed due to vignetting. The center panel shows a 3D surface plot of the normalized flat image that reveals the illumination profile and some large-saleaspects of pixel-to-pixel variations. The last panel shows row and column cuts through a particular region of pixels across theflat image.
The source and off-field images are obtained alterna-tively. The off-field images are taken by dithering com-pletely outside the source field in one or more differentcardinal directions (typically along the north-south di-rection).To obtain the dark contribution, a set of 10 dark im-ages are acquired at the end of the observing night forall values of exposure time used. The 10 darks for eachexposure are then averaged to obtain mean dark images.The automatic image acquisition sequence for obser-vations is passed to the telescope control system by aJavaScript from the main computer operated by theobserver. The script includes functions for telescopedither, camera exposure time, and HWP rotation. Theuser can modify each parameter as desired. Once thescript is run, user intervention is not needed. A log ofthe POLICAN observing runs conducted to date is savedboth in hard copy and in digital format. On a typicalnight, POLICAN produces around 600 images, whichapproximately sum up to 2 . Flat fielding strategy
There are both temporal and spatial variations in thedetector that affect the quality of the images. Temporalvariations from noise and sky amplify with spatial varia-tions introduced by non-uniform illumination and pixel-to-pixel variations in the detector. Other effects includedust on the HWP, which rotates during modulation andis not canceled in the Stokes combination scheme. Tocorrect for all of the above effects, a suitable flat-fieldingstrategy is required. Because polarimetric observationsvary with each HWP angle, the flats should be obtainedat the same HWP angles. Based on Mimir calibration (Clemens et al. 2012b)methods, we implemented a similar technique for ob-taining these “polarimetric flats.” The flats consistedof sequence of images ( ∼ − empirical estimation) ac-quired with dome lights ON and OFF for each HWPangle. Exposure times were set so as to fill half of thefull-well-depth in the ON images. The lights ON andOFF images are differenced to eliminate the effects ofdark counts and thermal backgrounds. The differencedflats are then averaged to obtain a master flat with highS/N. This is repeated for each HWP angle to obtainfour master flats. The master flats are normalized usingthe mean value obtained from a region of 40 ×
40 pixelsin the central zone [460:500, 540:580] of the detector.Figure 3 shows different characteristics of a normalizedmaster flat. The center panel shows the 3D surface plotof the normalized master flat where the illumination pro-file is seen along with large-scale non-uniform pixel-to-pixel variations. The last panel shows row and columncuts obtained for a particular region of pixels. DATA PROCESSINGThe images obtained with POLICAN contain a num-ber of instrumental effects in addition to the NIR atmo-spheric contamination, leading to a challenge to obtainhigh-quality, linear polarimetric data. These include1) the non-linear response of the detector array pixels;2) the dark current that is pixel, time, and tempera-ture dependent; 3) the bad pixels, about 0.2% spreadacross the detector array; 4) the non-uniform illumina-tion profile and the pixel-to-pixel variations; 5) detectorcrosstalk effects, seen as residual negative charges in dif-ferent quadrants; 6) the atmospheric sky emission andtransmission that varies with time and position; and 7)
OLICAN
Basic data processing
Stage 1: The first stage of data processing that willlead to science-quality images uses a custom pipelinecalled
POLREDUCE , developed in the IRAF environ-ment. Image display and interactive functions are car-ried out with the help of SAO DS9 software. The in-dividual dithered images obtained for a given set of ob-servation are associated based on their HWP angle andfilter band. The corresponding mean dark images andpolarimetric flats are grouped in the same set. The re-duction process is carried out separately for each HWPangle leading to four science-quality images. The stepsin reduction are as follows:1) The first step in reduction involves non-linearitycorrection. The correction coefficients are estimated bycharacterizing the illumination response of each pixelusing dome flats as described in Paper I. Using the cor-rection coefficients, the individual images are correctedfor each pixel to establish linearity corrected images.2) Next, the images are subtracted with the mean darkimage to remove the dark count contribution.3) The non-uniform illumination, pixel-to-pixel varia-tions, and any effects introduced by the HWP are cor-rected by flat fielding using polarimetric flats (see Sec-tion 5.1).4) The individual dithered images after Step 3 arestacked and median combined using the imcomb task toobtain the sky image. The images are then subtractedwith the sky image to obtain the reduced “clean” im-ages. The reduced images have an offset in their zerolevel introduced by the median sky. Image Reduction and Analysis Facility (IRAF) is distributedby the National Optical Astronomy Observatory, which is oper-ated by the Association of Universities for Research in Astronomy(AURA) under a cooperative agreement with the National ScienceFoundation. http://iraf.noao.edu/
A modal filter is applied to each image with a 3 σ lowerand upper threshold. The modal value gives the zerolevel offset, which is then subtracted from the reducedimages, resulting in uniform background nearly to zero.The images are next corrected for detector crosstalk ef-fects as described in Paper I.Step 4 is slightly modified if the reduction is car-ried out for extended sources. Because dithering is per-formed as alternating source and off-field, only the off-field images are median combined to obtain the sky im-age. The rest of the procedure remains the same.5) Because the images are shifted because of dithering,they have to be aligned before combining. The aligningprocedure is carried out by selecting the centroids ( Xcen and
Y cen ) of a common star in all of the images. Usingthe centroids, the shift in each image, both in X and Y directions, is computed, keeping the first image as ref-erence. From the computed image shifts, the ditheredimages are aligned using the imalign task. The alignedimages are next average combined with a minmax rejec-tion to produce the final reduced image.Image aligning and combination remains the same forextended sources with only the source images used inthe process.6) The final corrected image is then transformed to theequatorial system with north-up and east-left direction.Next, the image is cropped to the central 4 × ,which removes major optical aberrations (as shown inPaper I).7) The last step in the pipeline involves finding allof the point sources using the daofind task, with a de-tection threshold of 5 σ . The source positions as cen-troids Xcen and
Y cen are stored in a file. Additionally,all the important parameters involved in the reductionprocess are saved and can be used in future for rapidre-processing.Steps 1 to 7 are performed for all four sets of imagescorresponding to each HWP angle, obtaining the finalreduced images and source positions. The reference im-age used in aligning all four sets of images is the same,and hence the final four reduced images are matched inthe image coordinate system. The reduced images andresults form the basis for polarimetric analysis, which isexplained in Section 6.2.6.1.1.
Astrometry corrections
Observations made with POLICAN have astrometricinformation updated to the image headers based on tele-scope and dithering data. These values were found todiffer by a few arcsec to a few arcmin when comparedwith astrometric-based coordinates. The images werealso found to have rotation offsets of a few degrees and
Devaraj et al. to possess slight geometric distortions. Hence, scientificanalysis of the reduced images required accurate astro-metric corrections. Existing astrometry software suchas astrometry.net (Lang et al. 2010) failed to obtaincorrect solutions, due large offsets in POLICAN imageheaders, leading to the necessity of implementing a cus-tomized program. This is carried out in two steps, bothrelying on the astrometric information provided by thepublicly available 2MASS data.The first step involves making coarse corrections tocenter the images such that the astrometric errors arewithing a few arcsec. A reference star is chosen in theimage, and its corresponding 2MASS coordinates areobtained. The image header is then updated for thecentral reference value (CRVAL) with the 2MASS coor-dinates of the reference star. This transforms the imagefield with astrometric information close to the true co-ordinates. Users satisfied with this information have thechoice to skip the second step and move directly to po-larimetric analysis. Most of the time this is the casefor observations of extended sources. However, starlightpolarimetry requires further corrections.The second step involves obtaining solutions to rec-tify the image rotation and geometric distortions. Thisis performed with the help of tasks in IRAF imcoords package. As the images at this stage have a roughly ac-ceptable astrometry, the 2MASS catalog for all the pointsources in the field are obtained within a given searchradius. Next, the
Xcen and
Y cen for a minimum ofsix point sources in the image are associated with their2MASS coordinates. These are then used to obtain theplate solutions in the equatorial system. The astrometrycorrection for one HWP image is sufficient to correct theother 3 HWP images, as they are aligned with respectto each other. The astrometry information of the firstimage is directly copied to the other three, making themequal both in image and celestial coordinates.6.2.
Polarimetric Analysis
Stage 2: The second stage of polarimetric data pro-cessing is carried out using a pipeline developed in In-teractive Data Language (IDL). The pipeline is called
FLX2POL , and it combines functions and proceduresthat are found in the IDL Astronomy Library (Lands-man 1993) and in the Coyote Graphics Library . Themain steps in polarimetric analysis are to accuratelymeasure the flux of sources; establish the Stokes param-eters; and compute polarizations, position angles, andtheir corresponding uncertainties. Table 1.
Aperture ranges used for Pho-tometry.Source S/N Photometric Apertureat 10 pixels Radius (pixels) <
10 710 - 50 850 - 100 9100 - 500 10500 - 1000 111000 - 5000 125000 - 10000 13 > The output file from Stage 1 consists of source posi-tions for all point sources. The first step is to matchsource positions among the four HWP images and ob-tain a common identification and location list. Thesource-matching algorithm selects the centroids
Xcen and
Y cen for all sources in the four HWP imagesand runs a cross-correlation search within a given ra-dius, typically 2 pixels ( ∼ . (cid:48)(cid:48) aper routine adapted from theDAOPHOT (Stetson 1987) package. The pipeline in-cludes two runs of photometry that allow aperture selec-tion for obtaining accurate flux values. The first run ofphotometry involves calculating the S/N of the sourcewith an optimum aperture radius. In the second run,the final flux of the source is measured with an aper-ture whose value is chosen depending on the S/N of thesource. The necessity of aperture selection based on S/Nis required, as the PSF of the sources vary both in timeand across the FOV as shown in Paper I.Based on magnitude growth analysis (Howell 1989;Stetson 1990), we find that an aperture radius of 10 pix-els is optimum for photometry. Using this radius, weperform first run of photometry and obtain the S/N ofall the sources. Next, a new aperture is chosen betweena range of 7 to 14 pixels (empirical estimation) for eachsource depending on its S/N (see Table 1). Using thenew aperture, a second run of photometry is performed OLICAN I , I . , I , I . .The Stokes I , Q , and U in the instrumental referencesystem are now computed as follows: I = ( I + I + I . + I . ) / Q = ( I − I ) /I (2) U = ( I . − I . ) /I (3)These are then scaled by polarization efficiency η androtated by the HWP zero-phase offset angle, θ (see Sec-tion 7.2) to obtain the equatorial Stokes values. The po-larization efficiency η was obtained from SIRPOL mea-surements (Kandori et al. 2006), as both instrumentsuse the same polarizing elements from the same manu-facturers. The η values are J = 0 . H = 0 . K = 0 . Q eq = ( Qcos (2 θ ) − U sin (2 θ )) /η (4) U eq = ( U cos (2 θ ) + Qsin (2 θ )) /η (5)Next, the Stokes values are corrected for instrumentalpolarization, derived from globular cluster observations(see Section 7.1): Q c = Q eq − Q inst (6) U c = U eq − U inst (7)Finally, the corrected Stokes values are combined toform the equatorial degree of polarization, P eq , and theposition angles, P.A , measured from the north-up toeast-left direction: P eq = 100 (cid:112) Q c + U c (8) P.A = 12 tan − (cid:18) U c Q c (cid:19) . (9)The P.A values have an ambiguity in the calcula-tion because the arctangent function produces values be-tween − π/ π/ ◦ . The polariza-tion uncertainty σ P is computed from the correspondingStokes errors which is described in Appendix B. The cal-culated polarization values have a positive bias becauseof the quadrature combination of the Stokes parameters. The Ricean correction prescription of Wardle & Kron-berg (1974) which works well for polarization S/N valuesgreater than 2 (i.e. P/σ P ≥
2) is used for de-biasing thepolarization values as follows: P = (cid:113) P eq − σ P (10)Photometric measurements for each source is next ob-tained from the deep co-added intensity image calcu-lated from the four HWP images as in equation 1. Basedon the previously obtained image source list, aperturephotometry is performed on all the sources to obtaintheir magnitude values. A broad zeropoint correction oninstrumental magnitudes is applied by using the averagezeropoint value. The source coordinates are convertedfrom pixel values to celestial coordinates using the xyad routine, which uses the astrometric information avail-able in the image header.The values of polarimetric analysis together with as-trometric and photometric measurements are combinedto form a catalog of results. The catalog contains thesource information as follows: ID , RA , DEC , Xcen , Y cen , P %, P err , P.A , P.Aerr , M ag , M agErr , Q %, U %, Qerr , U err
Polarization visualization are carried out by producingmap of vectors representing P and P.A for each sourceusing a separate customized program (e.g Figure 14).Polarimetric analysis for extended sources remain sim-ilar to the above description. Because the four HWPimages are aligned with each other, the surface bright-ness in each pixel is used for analysis instead of flux ofa point source. The Stokes parameters and polariza-tion values are obtained in order up to equation 10 foreach pixel. The results are then stored into an imagearray. The visualization and map making procedure iscarried out by binning the polarization values in eachpixel, with a certain threshold as required by user. Foreach bin, a vector is plotted to represent the P and P.A value (e.g Figure 8). POLARIMETRIC CALIBRATIONDesign factors and optical setup introduce instrumen-tal polarization that need to be carefully removed tofaithfully recover the true polarization. As the po-larizing elements in POLICAN are located ahead ofCANICA, the only contribution for instrumental po-larization should be the telescope mirrors. POLICANis designed for single-beam linear polarimetric observa-tions with just two polarizing components: the HWPand polarizer. There exists no room for other optical ele-ments such as prisms in the setup for producing artificialpolarization for calibrations. Hence, all the calibrationneeds to be done through observations of astronomical0
Devaraj et al.
Figure 4.
Distribution of mean instrumental Stokes (cid:104) Q (cid:105) and (cid:104) U (cid:105) values from 37 observations of globular cluster M5.The mean Stokes values for each observation are representedby plus symbol. The final grand mean of all the 37 meanStokes values is represented by a circle with plus symbol. objects. For POLICAN, we used two standard steps ofpolarimetric calibration as described for the Mimir in-strument (Clemens et al. 2012b): 1) removal of instru-mental polarization across the FOV from observations ofglobular clusters and 2) converting instrumental polar-ization position angle to equatorial position angle fromobservations of polarimetric standards. In the followingsections, we describe the methods and results obtainedfor polarimetric calibration.7.1. Globular Clusters
Globular clusters are known to have stars with low po-larization levels. Clusters with large angular extent areuseful to calculate the instrumental polarization acrossthe entire FOV. Mimir calibration observations of mul-tiple globular clusters (M2, M3, M5, M12, M13 etc . )showed that M5 has polarization values below 0 .
1% withlow color excess E ( B − V ), representing the best clus-ter with distributed stars. Hence, we concentrated onobserving only M5 to determine the instrumental polar-ization for POLICAN. M5 observations were conductedin various runs over a period of three years from 2013to 2016. In total 37 sets of clear sky observations wereobtained, which was used for analysis. The images wereacquired using dithering methodology for 15 positionsas described for extended sources in Section 5. In allobserving runs, the image acquisition order remained same, with exposure time set to 20 s. The M5 fieldswere distributed to fall on the detector center as wellas at different quadrants of the detector. This allowedto have distributed polarization values in all the pixels,making it feasible to map the instrumental polarizationacross the entire FOV.The images from each observation were reduced as de-scribed in Section 6.1. All the stars in each field wereselected and analyzed up to calculations of Stokes val-ues in equatorial system (i.e. up to equation 5), as de-scribed in Section 6.2. By the time of analysis, the HWPzero-phase offset angle θ was determined and hencewe converted the Stokes values into equatorial system.Next, the polarimetric and photometric values of thestars were obtained up to equation 10, omitting equa-tion 6 and 7. This produced a catalog of results forthousands of stars in each observing field. The resultswere filtered to obtain Stokes values only for bright starswith low polarimetric uncertainties. (i.e. for stars withmag <
13 and σ P < . (cid:104) Q (cid:105) and (cid:104) U (cid:105) were calculated from the individual Stokes valuesof the selected sample of stars. These were then com-bined to form the grand mean Stokes value (cid:104) Q inst (cid:105) and (cid:104) U inst (cid:105) . Figure 4 shows the distribution of mean Stokes (cid:104) Q (cid:105) and (cid:104) U (cid:105) in plus symbol for the 37 observations ofM5. The grand mean Stokes value is shown at thecenter with a circle and plus symbol. The estimatedvalues of grand mean instrumental Stokes values are (cid:104) Q inst (cid:105) = − . ± . (cid:104) U inst (cid:105) = 0 . ± . Q and U values for all the stars were exam-ined by a histogram and a Gaussian was fitted to thedistribution as shown in Figure 5. The peak of the his-togram matched with the peak of the Gaussian fit, whichrepresented the final instrumental Stokes value of POLI- In each plot of Gaussian fit, µ indicates the peak value ofthe Gaussian fit, and σ indicates the standard deviation of theGaussian fit. OLICAN Figure 5.
Histogram of instrumental Stokes Q % and U % for combined values of 10,700 stars in the 37 observations of globularcluster M5. The histograms are fitted with a Gaussian to calculate the mean and standard deviation of the distribution.The combined data of all the Stokes values produced the final instrumental polarization for POLICAN as Q inst = − . U inst = 0 .
11% with P inst = 0 . CAN. The values were estimated to be Q inst = − . U inst = 0 . .
02% levels when compared with the grandmean Stokes value. The uncertainties in the instrumen-tal Stokes σ Qinst and σ Uinst were taken as the standarddeviation of the fit, which gave σ Qinst = 0 .
42% and σ Uinst = 0 . × . Figure 6 showsthe map of instrumental Stokes Q inst and U inst , alongwith the P inst value computed from the former Stokesvalues. The variations in instrumental Stokes, both Q and U , across the FOV are around ± . Q inst and U inst are calculated to be − .
50% and 0 . . Polarimetric Standards
POLICAN’s mechanical assembly and the polarizingelements are fixed along their axis and mounted sta-tionarily to the telescope. It is not definitive that theHWP zero-phase angle is aligned to the equatorial north.This results in calculations of polarization position an-gle to be based in the instrumental coordinates. Hence, it is important to determine the HWP zero-phase off-set, to correct the position angle to standard equatorialsystem. Observation of polarimetric standards are thebest way to determine the offset angle. Mimir’s calibra-tion observations of polarimetric standards provided alarge sample of stars for the study. They were mainlyderived from Whittet et al. (1992), who studied wave-length dependence of polarization. The H -band filtercentral wavelength and bandwidths remained the samefor POLICAN and Mimir, which avoided any correctionsfor wavelength dependence.A large number of calibration observations duringeach run were directed towards two bright standardstars that are available during most times of the year.These were HD38563C and CygnusOB221 in the fields ofOrion and Cygnus. Here, we present results obtained forHD38563C which was observed for a total of 19 nightsduring a period of 6 months.The observation scheme for HD38563C was similar topoint sources as described in Section 5 with exposuretime set to 5 s. The HD38563C field was targeted to fallon the detector center to avoid any effects introducedby optical aberrations. The images were reduced andanalyzed up to equation 6 and 7 as described in Sec-tion 6.2, to obtain the corrected Stokes values Q c and U c . The only change in the analysis was that the HWPoffset angle was set to zero. The instrumental polariza-tion calculated from globular clusters remained in theinstrumental system for this analysis.2 Devaraj et al.
Figure 6.
POLICAN instrumental polarization map ofStokes Q inst , U inst and P inst across the central 4 × FOV, obtained from observations of globular cluster M5.The contours for Q inst , U inst and P inst start at -0.7%, -0.2%, 0.3% and are stepped in increasing order of 0.04%,0.06% and 0.05% values up to 10 contour levels. Figure 7.
Polarimetric calibration results of standard starHD38653C for 19 different nights of observation. The toppanel shows distribution of polarization values with their er-ror bars against different nights. The dashed line representsthe published value of 3.73%. The bottom panel shows dis-tribution of calculated position angles with their error bars.The position angle values are corrected for HWP zero-phaseoffset. The dashed line represents the published value of 71 ◦ . The individual Stokes values, Q c and U c from each ofthe 19 observations were averaged to obtain the meanStokes value. Next, the mean Stokes value was used tocompute the Ricean corrected polarization and positionangle as described in equation 8 to 10. The computedposition angle was then compared with the Mimir’s pub-lished value to find the difference. The difference gavethe HWP zero-phase offset angle for POLICAN, whichwas determined to be 139 ◦ .Figure 7 shows results of HD38563C corrected for posi-tion angle for all the 19 observations. Results from eachobserving night are represented by a black-filled circlewith their corresponding error bars. The final computedmean polarization and position angle are expressed onthe top left corner of each panel. Overall observationsshowed good agreement with published values. Overthe course of the last few years, there were times whenthe motor sensor failed to locate the HWP home posi-tion. This was corrected immediately and the sensor wasbrought back to the original setting to keep the homeposition constant, in turn the offset angle for POLICANremained consistent. OBSERVATIONS
OLICAN SIRPOL Sh2106 H−band polarization
Published image (2009)
Figure 8.
SIRPOL and POLICAN H -band polarimetric observations towards Sh 2-106. The left panel is a published imageof 7.7 × by Saito et al. (2009). The right panel shows POLICAN results for FOV of 4 × . The length of thevectors represent the degree of polarization and their orientation represents the position angle. The vectors are plotted only forvalues above 3 σ for every bin of 3 × POLICAN saw its first light at the end of 2012. Overthe past few years, the majority of the observations wereconcentrated towards polarimetric calibration and pilotstudies. These observations were spread evenly in eachsemester for an average telescope time of around 7 to 8weeks in a year. Early science proposals were targetedfor well known sources to provide comparison of POLI-CAN results with the literature data. In parallel, a fewnew regions of interest were also observed to complimentthe current studies with priority. These included galac-tic molecular clouds, H ii regions, planetary nebulas, andpost-AGB stars.The starlight polarimetry towards the center of thegalactic plane is usually around 3% polarization due tothe presence of large columns of dust. These regionsprovide a good starting point for pilot studies. TheGPIPS survey (Clemens et al. 2012a) spanning from18 ◦ ≤ l ≤ ◦ and − ◦ ≤ b ≤ ◦ , contains an ex-cellent catalog of polarimetric data for comparing thePOLICAN observations.To evaluate the performance of POLICAN, we ob-served two regions that represented good examples ofscattered polarization and starlight polarimetry. Theywere Sharpless H ii region Sh 2-106 and the GPIPS fieldnumber 182. In the following sections, we present theobservation details for each of them.8.1. Scattered polarization
Sh 2-106 is an emission nebula estimated to be at adistance of 600 pc in the Cygnus constellation. At thecenter of the nebula is a young massive star (type O8) ofapproximately 15 solar masses, which emits jets of gasforming a bipolar structure. We carried out H -band po-larimetric observation towards the central 4 × region surrounding the massive star. The observationscheme was similar to extended sources as described inSection 5 with exposure time set to 20 s. Image reduc-tion and analysis followed the steps described in Sec-tion 6.1 and 6.2. The final polarimetric results weresaved into an image array.Analysis of the results showed that the region sur-rounding the central star had high polarization levels to ∼ σ ,binned for every 3 × Devaraj et al.
Figure 9.
The GPIPS field 182 and its surrounding regions are shown in the background image from 2MASS H -band survey.The 10 ×
10 arcmin FOV of Mimir instrument centering GP182 is shown in black box. The POLICAN pointings for mappingthis entire region are shown by blue box with each field marked in its observing order from R1 to R15. The FOV for eachPOLICAN pointing is 4 × . to have a clear distinction of nebulosities and circum-stellar matter. Such observations with POLICAN willhelp to obtain scattered polarization at smaller scalesmaking it vital for star-forming studies.8.2. Starlight polarization
The GPIPS field 182 (hereafter GP182) is centeredaround the galactic coordinates of l = 20 .
456 and b = − .
645 with a size of 10 ×
10 arcmin . Clemens etal. (2012c) showed that GP182 field contains high stel-lar density with significant polarization detections. Fur-ther, the stars in the field have high polarization S/N( P S/N = P/σ P ) and their galactic position angles areoriented along the galactic plane. Hence, GP182 field isan ideal region for evaluating POLICAN’s performance.We chose a total region covering 20 ×
12 arcmin formapping GP182 and its surrounding areas. The usefulFOV with POLICAN is 4 × , therefore the ob-servations need to span multiple pointings to cover theentire region. By equally placing 4 × fieldsdistributed over the entire region, we obtained a totalof 15 pointings for POLICAN. Figure 9 shows the back-ground 2MASS image overlaid with 10 arcmin field of GP182 in black color. The 15 POLICAN 4 arcmin fieldsare shown in blue color and are marked from R1 to R15,based on their observing orders. The fields are not over-lapped with each other, as the full FOV of POLICAN is5 . × . and during image reduction they arecropped to 4 arcmin fields.GP182 observations with POLICAN were conductedfor four nights during 2017 April. Each field was ob-served with 15 dither positions totaling 60 images for allthe HWP angles. The exposure time was fixed to 20 swith a dither diameter of 30 arcsec. During each nightthree to four fields were observed and started at the sameuniversal time to keep the airmass and time-dependentvariations minimum. The total clock time taken to com-plete the 15 fields was 7 . OLICAN ii in the ISM. Given the largeclock time for such observations, the regions are limitedto sizes within 20 ×
20 arcmin . Figure 10.
Histogram distribution and cumulative valuesfor POLICAN, GPIPS, and 2MASS stellar detections towardthe GP182 region. The horizontal axis gives the H -bandstellar magnitude. About 50% of POLICAN detections havestars brighter than 14 mag. The other half detections reachmagnitudes as faint as 18 mag.9. RESULTS9.1.
Stellar properties
The combined starlight polarimetric catalog towardsGP182 region for all the 15 POLICAN fields resultedin a total stellar count of 13,635 stars. These were ob-tained by selecting sources above 5 σ in the deep co-added intensity image. Out of this entire stellar pop-ulation, 9556 stars had definite polarization detections.They formed the essential sample of stars for all futureanalysis. Analyzing 2MASS survey data for the sameregion, we find the number of stellar count obtained is4453 stars. This showed that POLICAN observationshad twice the number of detections to 2MASS. Simi-larly, analyzing GPIPS data for the same region, weobtain a total of 7230 stars with definite polarizationdetections. This indicated the number of polarizationdetections with POLICAN is much higher for the cho-sen integration time. Figure 10 shows the stellar counthistogram against magnitude for POLICAN, GPIPS and2MASS data. Also plotted is the cumulative distribu- tion function for each data. It is seen that POLICANobservations reached depth of many orders better than2MASS. The majority of stars were in the magnituderange from 13 mag to 16 mag, with 50% probability ofdetection for 14 mag stars. The stellar density achievedwith POLICAN in this region is about 30 −
40 stars persquare arcmin, meeting the sampling goals as describedin Section 4.
Figure 11.
Plot of S/N and magnitude error for all thePOLICAN stellar detections towards GP182 region. Thehorizontal axis gives the POLICAN H -band stellar magni-tude. The S/N achieved is better than 10 for stars up to15 . Photometric properties
The photometric results obtained from the deep co-added intensity image for the 9556 polarization detec-tions were analyzed for their magnitude properties. Be-cause the photometric values had only broad correctionson the magnitudes, as described in Section 6.2, a postcorrection was implemented to obtain accurate magni-tude values. This was carried out by zeropoint correc-tions using the 4453 2MASS matched stars, as describedin Paper I. The resultant photometry showed that thestars in GP182 region spanned magnitude ranges from7 mag to 18 mag. Errors in photometric magnitudeswere below 1% up to 13 mag stars and 10% up to15 . . Devaraj et al.
Figure 12.
Photometric comparison of POLICAN and 2MASS H -band magnitudes for 4453 matched stars towards the GP182region. The error bars in horizontal and vertical axis represents POLICAN’s and 2MASS magnitude errors. The dispersion inmagnitude difference is below 0 .
05 mag for stars up to 11 mag. the desired signal-to-noise ratio goals described in Sec-tion 4.The 4453 2MASS matched stars were compared withtheir magnitudes for estimating photometric accuracy.The difference in POLICAN and 2MASS magnitudes areplotted against their magnitude along with their corre-sponding magnitude errors in Figure 12. The dispersionin magnitude differences were better than 0 .
05 mag upto 11 mag stars. For stars up to 13 mag, the dispersionwas around 0 . . Polarimetric properties
The polarimetric data available for all the 9556 starsprovided a full range of polarization properties. Un-certainties in polarization ( σ P ) values are useful to cal-culate the polarization S/N ( P S/N ). Examining thepolarization uncertainty against the magnitude showedPOLICAN observations had polarization uncertaintiesof 1% up to 13 mag and 2% up to 14 mag. This matchedour polarization sensitivity goals as described in Sec-tion 4. Figure 13 shows the log plot of polarization un-certainty against POLICAN magnitude for stars from 7to 18 mag.The reliability of polarization data can be determinedfrom combination of σ P , P S/N and magnitude. Clemenset al. (2012c) classified the stellar polarizations basedon their reliability into usage flags (UF) to allow easyidentifications. As magnetic field studies using POLI-CAN’s starlight polarimetry have well-established ob-
Figure 13.
Plot of polarization uncertainty in log scaleagainst POLICAN H -band magnitude for 9556 stars towardsthe GP182 region. The dashed line represents reliable polar-ization classification from UF = 1 to 3 category. The high-quality polarization values are within UF = 1 and have po-larization uncertainties less than 1% with magnitudes below13 mag. serving goals and scheme (Section 4 and 5), it will beuseful to classify POLICAN data. Based on the ob-served polarization properties, we formed a new set ofusage flags for POLICAN data as follows: UF = 1 rep-resented the high-quality polarization values having σ P OLICAN Figure 14.
The GP182 region is shown in the background image from the 2MASS H -band survey. The polarization valuesare plotted for common stars with UF = 0 category matched in the GPIPS and POLICAN data. The blue vectors representPOLICAN observations and the red vectors represent GPIPS data. A reference vector in black at the bottom left indicates 5%polarization. Table 2.
Polarimetric Usage Flagsfor POLICAN.Usage Flag POLICAN dataUF = 0 σ P < & mag < & P S/N > . σ P < & mag < σ P < & mag < σ P > & mag > within 1% and magnitude < P S/N > . σ P within2% and magnitude < PERFORMANCEAfter establishing POLICAN’s GP182 stellar photo-metric and polarimetric properties, the results could becompared with the GPIPS data. The polarimetric datafrom GPIPS survey was derived from
GPIPS data re-lease 3.1 . This included the most recent version withthe best compilation of up to date data. Individualstars from POLICAN and GPIPS data were matchedto obtain common detections. A total of 1298 stars hadcommon detection for UF = 1 category, with also com-mon detection in the 2MASS data. Out of these, therewere 817 stars that matched UF = 0 category. Figure 148
Devaraj et al.
Figure 15.
Plot of differences in GP182 polarization values between POLICAN and GPIPS data for 1298 stars with UF = 1category. The left panel shows difference in degree of polarization against 2MASS H -band magnitude. The differences arewithin 1.5% for majority of the stars. The right panel shows differences in position angle against 2MASS H -band magnitude. Figure 16.
Histogram of differences in GP182 polarization values between POLICAN and GPIPS data for 1298 stars withUF = 1 category. The histograms are fitted with a Gaussian to calculate the mean and standard deviation of the distribution.The polarization values have standard deviation better than 0.5% with the position angle values below 5 ◦ . shows the background 2MASS image of GP182 regionwith polarization vectors for UF = 0 stars. The polar-ization values of POLICAN are overlaid in blue vectors,with the GPIPS values overlaid in red vectors. Visually,the polarization vectors align with each other in theirlength and position angle.The values of UF = 1 subset form the core infor-mation to determine POLICAN’s polarimetric accuracyand performance. Since UF = 1 are considered reliable and high-quality data, they need to equal the GPIPSdata consistently. Comparison of both the data setswere carried out for all the 1298 matched stars. Thedifferences between POLICAN and GPIPS stars wereestablished by subtracting their individual polarizationvalues. The difference in polarization percentage werebelow or around 0 .
5% for stars brighter than 11 mag.For fainter stars the difference reached up to ∼ . ◦ OLICAN Table 3.
Summary of POLICAN performance.Quantity Value CommentsPlate scale 0.32 arcsec/pixel On the detectorField of view 4 × Cropped from 5 . × . Photometric accuracy < . < < ◦ For stars with UF = 1Instrumental polarization 0.51% Q inst = − .
50% and U inst = 0 . ◦ Correction angle for stars brighter than 11 mag. For fainter stars, the dif-ference in position angle reached up to ∼ ◦ , with someexceeding it. Figure 15 shows the plot of POLICANand GPIPS polarization and position angle differencesagainst 2MASS H -band magnitude.A histogram examination of the polarization differ-ences gives the accuracy of POLICAN. In Figure 16 weshow the histogram distribution for both polarizationand position angle differences. A Gaussian is fitted foreach distribution to determine the peak and standarddeviation. The peak in the polarization and positionangle differences are close to zero, indicating there isno offset in the calculated values. This means that thepolarimetric efficiency, HWP zero-phase offset angle, in-strumental polarization and polarization de-biasing, arewell established for POLICAN. Because the data set rep-resented high-quality UF = 1 stars, the standard devi-ation of the Gaussian fit should give the polarimetricaccuracy of POLICAN. From the fit, we see that thepolarization accuracy is found to better than 0.5% andthe position angle accuracy is below 5 ◦ . The values ofaccuracy are minimum and within the expected levels ofuncertainties with POLICAN data.The established accuracies with POLICAN allow toobtain precise calculation of magnetic field strengthsusing Chandrashekar & Fermi (1953) method. Over-all, POLICAN’s UF = 1 subset showed good agreementwith archival data, adequately meeting the polarimetricgoals for magnetic field studies. SUMMARYWe have described the important aspects in the op-eration, data processing, calibration, and performanceof the newly developed polarimeter: POLICAN, at the2 . .
32 arcsec / pixel and use-ful FOV of 4 × enables deep high-resolutionmedium field linear polarimetric imaging. The observa-tion schemes are optimized to study polarization prop-erties of both point sources and extended sources in theinterstellar medium. POLICAN’s large data sets of rawimages are handled by the robust image reduction andanalysis techniques implemented into custom pipelinesin IRAF and IDL environment.Polarimetric calibrations were carried out from obser-vations of globular clusters and polarimetric standards.The analysis of 10,700 stars from 37 observations of glob-ular cluster M5, determined the instrumental polariza-tion to be 0.51%. Observations of polarimetric standardHD38563C, determined the HWP zero-phase offset an-gle to be 139 ◦ . Pilot studies were carried out for bothextended and point source regions to obtain POLICAN’sobservational results and performance. Scattered po-larization was compared with SIRPOL data for Sh 2-106 object. Starlight polarimetry was compared withGPIPS data for GP182 field. Mapping a GP182 regionof 20 ×
12 arcmin produced 9556 polarization detectionsreaching sensitivity many orders better than 2MASSsurvey. The polarimetric data were classified with usageflags to deem their reliability. A total of 1298 stars withreliable polarization under UF = 1 category were com-pared with the GPIPS data. POLICAN achieved po-larization accuracy better than 0.5% and position angleerrors below 5 ◦ up to 13 mag stars in H -band. The en-tire performance of POLICAN is summarized in Table 3.Based on background starlight polarimetry, POLICANdata can be used to trace the plane-of-sky magnetic fielddirections in the interstellar medium. Various observa-tions on star-forming regions are being conducted to-wards the galactic plane to study their magnetic field0 Devaraj et al. properties. POLICAN features all characteristics of asensitive NIR polarimeter capable of delivering reliablepolarization data in the coming years.We would like to thank the anonymous referee for use-ful comments on improving the article. We thank allthe OAGH staff for their help in development and ob-servations with the instrument. We are deeply indebtedto the the valuable comments and feedback providedby Dan Clemens, Boston University, on improving thedata processing techniques and calibration methods. Wethank Eswaraiah Chakali, NTHU Taiwan, for helpfuldiscussion on polarimetric analysis. This work has beencarried out at Instituto Nacional de Astrof´ısica, ´Opticay Electr´onica, M´exico, with support from CONACyTunder the project CB-2012-01 182841. D.R. with CVU555629 acknowledges CONACyT for the grant 370405.SAOImage DS9 software is developed with the fund- ing from the Chandra X-ray Science Center (CXC),the High Energy Astrophysics Science Archive Center(HEASARC) and JWST Mission office at Space Tele-scope Science Institute. This work makes use of dataproducts from the Two Micron All Sky Survey, which isa joint project of the University of Massachusetts andthe Infrared Processing and Analysis Center/CaliforniaInstitute of Technology, funded by the National Aero-nautics and Space Administration and the National Sci-ence Foundation. This research used data from theBoston University (BU) Galactic Plane Infrared Polar-ization Survey (GPIPS), funded in part by NSF grantsAST 06-07500, 09-07790, and 14-12269. GPIPS used theMimir instrument, jointly developed at BU and Low-ell Observatory and supported by NASA, NSF, and theW.M. Keck Foundation.
Facility:
OAGH (CANICA, POLICAN).APPENDIX A. STOKES PARAMETERS AND MUELLER MATRICESThe Stokes parameters define the polarization state of a non-coherent electromagnetic radiation. Originally describedby G. G. Stokes in his classic paper Stokes (1852), the Stokes parameters were re-introduced to modern astronomyby Chandrashekar (1947), who denoted the polarization states by I , Q , U and V . The Stokes parameters can becombined to form a vector S as S = IQUV (A1)where I is the total intensity of the radiation; Q is the intensity difference between horizontal and vertical linearlypolarized components; U is the intensity difference between linearly polarized components oriented at ± ◦ ; and V isthe intensity of the circularly polarized radiation.When electromagnetic radiation interacts with matter, it is likely to change its polarization state. The changein polarization state can be algebraically represented by matrix transformations of the input Stokes vector and thefinal measured Stokes vector. Mueller (1948) described the matrix calculus for different states of polarization, eachrepresented by its 4 × S in and the final measured Stokes vector S out can be representedas S out = M pol ∗ M HW P ∗ S in (A2)where M pol is the Mueller matrix of the linear polarizer with fast axis oriented at 0 ◦ , and M HW P is the Mueller matrixof the HWP with arbitrary fast axis orientation θ . These are represented by their respective Mueller matrices (Shurcliff1962) as M pol = 12 − − and M HW P = cos (2 θ ) − sin (2 θ ) sin (2 θ ) cos (2 θ ) 00 2 sin (2 θ ) cos (2 θ ) cos (2 θ ) − sin (2 θ )
00 0 0 0 (A3)
OLICAN S out as S out = 12 I in + Q in ( cos (2 θ ) − sin (2 θ ) ) − U in sin (2 θ ) cos (2 θ ) − I in − Q in ( cos (2 θ ) − sin (2 θ ) ) + U in sin (2 θ ) cos (2 θ )00 (A4)The final measured intensity I out of the Stokes vector S out , depends on the HWP fast axis θ . As noted in Section 3,four HWP modulation angles are necessary for estimating the input linear Stokes parameters: Q in and U in . Giventhat θ can have number of values between 0 and 360 ◦ , we can chose values such that sine and cosine functions inequation A4 can cancel out to remain Q in and U in . The first four angles of θ that fulfill the conditions are at θ = 0 ◦ θ = 22 . ◦ θ = 45 ◦ θ = 67 . ◦ sin (2 θ ) = 0 and cos (2 θ ) = 1 sin (2 θ ) = 1 / √ cos (2 θ ) = 1 / √ sin (2 θ ) = 1 and cos (2 θ ) = 0 sin (2 θ ) = 1 / √ cos (2 θ ) = − / √ S out as I out , we get the output intensityfor each HWP angle as I = [ ± I in ∓ Q in ] I . = [ ± I in ∓ U in ] I = [ ± I in ± Q in ] I . = [ ± I in ± U in ] (A6)Now, we can re-arrange equation A6 to establish the input Stokes parameters as I in = ( I + I + I . + I . ) / Q in = I − I U in = I . − I . (A7) B. POLARIMETRIC ERROR ANALYSISPolarimetric analysis of point sources (mainly stars) are obtained by measuring the fluxes (integrated counts) on thestars in images corresponding to each of the orthogonal polarized components of linear Stokes parameters. The fluxmeasurement in POLICAN is performed through synthetic aperture photometry on brightness profiles of the stars inthe observed images based on the use of DAOPHOT package in IDL (see Section 6.2).The phot/aper function of the DAOPHOT package applied to the image with stars, measures the flux of a source invalues of analog-to-digital units (ADU) as follows (Stetson 1987): I s = I tot − ( area ∗ skymod ) (B8)where I s is the total flux measured of the source within an aperture, I tot is the total flux measured within an aperture, area is the total area of pixels in the aperture, and skymod is the sky/background modal value per pixel measuredfrom all the pixel values within a sky annulus (In IDL this is obtained by mmm ).The error in flux measurement σ s in ADU is given as follows: σ s = (cid:115) ( I s gN i ) + ( area ∗ skyvar ) + ( area ∗ skyvarnsky ) (B9)where skyvar is the variance in sky measurement per pixel for the final image, g is the gain in electrons/ADU, N i isthe number of images used for constructing the final image, and nsky is the number of pixels used in the sky annulusduring photometry.2 Devaraj et al.
Based on the equation of Stokes parameters as described in Section 6.2 and Appendix A, the error in Stokesparameters can be given by standard error propagation as follows: σ I = (cid:112) σ + σ . + σ + σ . σ Q = (cid:114) σ + σ I + ( QI σ I ) (B11) σ U = (cid:114) σ . + σ . I + ( UI σ I ) (B12)where σ , σ . , σ , σ . are flux errors for the fluxes I , I . , I , I . measured in each HWP angle.The Stokes parameters are next scaled by polarization efficiency η and rotated by the HWP zero-phase offset angle, θ as shown in equation 5. The corresponding Stokes errors in equatorial system are σ Qeq = (cid:115) ( cos θη σ Q ) + ( sin θη σ U ) (B13) σ Ueq = (cid:115) ( cos θη σ U ) + ( sin θη σ Q ) (B14)Next, the Stokes values are corrected for instrumental polarization as in equation 7 and are represented with theirerrors as σ Qc = (cid:113) σ Qeq + σ Qinst (B15) σ Uc = (cid:113) σ Ueq + σ Uinst (B16)where σ Qinst and σ Uinst are error in instrumental Stokes values calculated from globular cluster observations (seeSection 7.1).The final Stokes values are combined to give the equatorial degree of polarization P eq and the position angle P.A asin equation 8 and 9. The error in polarization is calculated as σ P = 100 P eq (cid:113) ( Q c ∗ σ Qc ) + ( U c ∗ σ Uc ) (B17)After obtaining the de-biased polarization value P as in equation 10, the P.A. uncertainty ( σ P.A ) is computed as σ P.A = 28 . σ P P ) (B18)REFERENCES Carrasco, L., Hern´andez Utrera, O., V´azquez, S., et al.2017, RMxAA, 53, 497Chandrasekhar, S. 1947, ApJ, 105, 424Chandrasekhar, S., & Fermi, E. 1953, ApJ, 118, 113Chapman, N. L., Goldsmith, P. F., Pineda, J. L., Clemens,D. P. 2011, ApJ, 741, 21Clarke, David 2010, Stellar Polarimetry, Wiley-VCHpublicationsClemens, D. P., Sarcia, D., Grabau, A., et al. 2007, PASP,119, 1385 Clemens, D. P., Pinnick, A., Pavel, M. D., & Taylor, B. W.2012, ApJS, 200, 19Clemens, D. P., Pinnick, A., Pavel, M. D. 2012, ApJS, 200,20Clemens, D. P., Pavel, M. D., & Cashman, L. R. 2012,ApJS, 200, 21Clemens, D. P., Pavel, M. D., & Cashman, L. R. 2013,ApJS, 145, 74Davis, L., Jr., & Greenstein, J. L. 1951, ApJ, 114, 206
OLICAN Devaraj, R., Luna, A., Carrasco, L., & Mayya, Y. D. 2015,IAU Symposium 305, 10, 175Devaraj, R., Luna, A., Carrasco, L., & Mayya, Y. D. 2017,RMxAA(Conf. Series), 49, 58Devaraj, R., Mayya, Y. D., Carrasco, L., et al. 2017, PASP,Accepted (Paper I)Hall, J. S. 1949, Science, 109, 166Hashimoto, J., Tamura, M., Kandori, R., et al. 2008, ApJL,677, L39Hiltner, W. A. 1949, ApJ, 109, 471Howell, Steve B. 1989, PASP, 101, 616Hough, J. H., Lucas, P. W., Bailey, J. A., et al. 2006,PASP, 118, 1302Jones, Terry Jay 1989, ApJ, 346, 728Jones, Terry Jay 1997, AJ, 114, 1393Kandori, R., Tamura, M., Kusakabe, N., et al. 2006,Proc. SPIE, 6269, 51King, O. G., Blinov, D., Ramaprakash, A. N., et al. 2014,MNRAS, 442, 1706Landsman, W. B. 1993, ASP Conf. Series, 52, 246Lang, D., Hogg, D. W., Mierle, K., Blanton, M., & Roweis,S. 2010, AJ, 139, 1782Lazarian, A., & Hoang, T. 2007, MNRAS, 378, 910Magalh˜aes, A. M., Rodrigues, C. V., Margoniner, V. E., etal. 1996, ASP Conf. Series, 97, 118Masiero, J., Hodapp, K., Harrington, D., & Haosheng Lin2006, PASP, 119, 1126Mathewson, D. S. & Ford, V. L. 1970, MmRAS, 74, 139Montgomery, J. D., & Clemens, D. P. 2014, ApJ, 786, 41Mueller, H., 1948, The foundations of Optics, J. Opt. Soc.Am., 38, 661Nishiyama, S., Tamura, M., Hatano, H., Kanai, S., et al.2009, ApJS, 690, 1648 Packham, C., Jones, T. J., Warner, C., et al. 2012,Proc. SPIE, 8446, 3RPerrin, M. D., Duchene, G. Millar-Blanchaer, M., et al.2015, ApJ, 799, 182Piirola V., Berdyugin A., Berdyugina S., 2014, Proc. SPIE,9147, 8IRamaprakash A. N., Gupta R., Sen A. K., Tandon S. N.,1998, A&AS, 128, 369Roelfsema, R., Martin, H., Schmid, H. M., et al. 2010,Proc. SPIE, 7735, 4BSkrutskie, M. F., Cutri, R. M., Stiening, R., et al. 2006, AJ,131, 1163Saito, H., Tamura, M., Kandori, R., Kusakabe, N., et al.2009, AJ, 137, 3149Shurcliff, W. A. 1962, Polarized Light: Production and Use,Harvard University PressStetson, P. B. 1987, PASP, 99, 191Stetson, P. B. 1990, PASP, 102, 932Stokes, G. G. 1852, Transactions of CambridgePhilosophical Society, 399-416Tamura, M., Kandori, R., Kusakabe, N., et al. 2006, ApJL,649, L29Vacca, W. D., Cushings, M. C., & Rayner, J. T. 2004,PASP, 116, 352V´azquez-Rodr´ıguez, M. 2012, INAOE, http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/779http://inaoe.repositorioinstitucional.mx/jspui/handle/1009/779