WALOP-South: A Four Camera One Shot Imaging Polarimeter for PASIPHAE Survey. Paper I -- Optical Design
Siddharth Maharana, John A. Kypriotakis, A. N. Ramaprakash, Chaitanya Rajarshi, Ramya M. Anche, Shrish, Dmitry Blinov, Hans Kristian Eriksen, Tuhin Ghosh, Eirik Gjerløw, Nikolaos Mandarakas, Georgia V. Panopoulou, Vasiliki Pavlidou, Timothy J. Pearson, Vincent Pelgrims, Stephen B. Potter, Anthony C. S. Readhead, Raphael Skalidis, Konstantinos Tassis, Ingunn K. Wehus
WWALOP-South: A Four Camera One Shot Imaging Polarimeter forPASIPHAE Survey. Paper I - Optical Design
Siddharth Maharana a* , John A. Kypriotakis b,c , A. N. Ramaprakash a,b,e , ChaitanyaRajarshi a , Ramya M. Anche a , Shrish h , Dmitry Blinov b,c,i , Hans Kristian Eriksen g , TuhinGhosh h , Eirik Gjerløw g , Nikolaos Mandarakas b,c , Georgia V. Panopoulou f , VasilikiPavlidou b,c , Timothy J. Pearson e , Vincent Pelgrims b,c , Stephen B. Potter d,j , Anthony C. S.Readhead e , Raphael Skalidis b,c , Konstantinos Tassis b,c , Ingunn K. Wehus g a Inter-University Centre for Astronomy and Astrophysics, Post bag 4, Ganeshkhind, Pune, 411007, India b Institute of Astrophysics, Foundation for Research and Technology-Hellas, Voutes, 70013 Heraklion, Greece c Department of Physics, University of Crete, Voutes, 70013 Heraklion, Greece d South African Astronomical Observatory, PO Box 9, Observatory, 7935, Cape Town, South Africa e Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA, 91125, USA f Hubble Fellow, California Institute of Technology, Pasadena, CA 91125, USA g Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, NO-0315 Oslo, Norway h School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni 752050, Odisha,India i Astronomical Institute, St. Petersburg State University, 198504, St. Petersburg, Russia j Department of Physics, University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa
Abstract.
The WALOP-South instrument will be mounted on the 1 m SAAO telescope in South Africa as part of thePASIPHAE program to carry out a linear imaging polarization survey of the Galactic polar regions in the optical band.Designed to achieve polarimetric sensitivity of 0.05% across a × arcminute field of view, it will be capableof measuring the Stokes parameters I, q and u in a single exposure in the SDSS-r broadband and narrowband filtersbetween . µm − . µm . For each measurement, four images of the full field corresponding to linear polarizationangles of ◦ , ◦ , ◦ and ◦ in the instrument coordinate system will be created on four detectors from whichthe Stokes parameters can be found using differential photometry. In designing the optical system, major challengesincluded correcting for the dispersion introduced by large split angle Wollaston Prisms used as analysers as well asother aberrations from the entire field to obtain imaging quality PSF at the detector. We present the optical design ofthe WALOP-South instrument which overcomes these challenges and delivers near seeing limited PSFs for the entirefield of view. Keywords: polarization, linear polarimetry, optical polarization, wide-field polarimeter, Wollaston Prisms, one-shotpolarimetry. * Siddharth Maharana, [email protected]
Optical polarimetry in nighttime astronomy began in the 1940’s with Hiltner and Hall’s pioneer-ing work on polarization measurement of stars, leading to the serendipitous discovery of interstellarpolarization. Since then, optical polarimetry has been used as an essential tool by astronomers tomake progress in understanding various classes of objects such as stars, active galactic nuclei, exo-planets and protoplanetary disks.
3, 4
With advancements in detectors, polarization optics hardwareas well as associated control systems, optical polarimeters with polarimetric sensitivity ( s ) better We define polarimetric sensitivity ( s ) as the least value and change of linear polarization which the instrumentcan measure, without correction for the cross-talk and instrumental polarization of the instrument. s is a measureof the internal noise and random systematics of the instrument due to the optics. Polarimetric accuracy ( a ) is themeasure of closeness of the predicted polarization of a source to the real value after applying the above corrections a r X i v : . [ a s t r o - ph . I M ] F e b han − in p (fractional polarization) have been made, eg. HIPPI-2 and DIPOL-2. But mostpolarimeters built to date have limited field of view (FOV) of about × arcminute or less. Sowhile we have extensive polarization measurements of many of the above mentioned individualclasses of objects, a large area ( > square degrees) continuous optical polarization map of thesky has been unavailable. Existing large stellar polarization catalogues include measurements ofnearly 3600 and 10000 individual stars by Berdyugin et al. and Heiles respectively in the opti-cal wavelengths, and a continuous map of square degrees of the galactic plane by the GPIPSsurvey in the near infrared wavelengths.Using two WALOP (Wide-Area Linear Optical Polarimeter) polarimeters as survey instru-ments, the PASIPHAE (Polar-Areas Stellar Imaging Polarization High Accuracy Experiment) pro-gram aims to create a unique optopolarimetric map of the sky. Such a map will enable astronomersto pursue answers to many open questions related to the physics of dust and magnetic fields in theinterstellar medium (ISM), which together are the main source of starlight polarization. A detaileddescription of the motivation and scientific objectives of the PASIPHAE survey can be found inthe PASIPHAE white paper by Tassis et al. Here we mention key highlights of the program:– In the northern and southern Galactic polar regions, cover > square degrees of the skyand measure polarization of about stars with polarimetric accuracy (a) of 0.1 %. Currentoptical polarization catalogues have polarization measurements of around stars. – The survey will be simultaneously carried out from the 1 m telescope at SAAO’s (SouthAfrican Astronomical Observatory) Sutherland Observatory, South Africa in the southernhemisphere and the 1.3 m telescope at Skinakas Observatory, Greece in the northern hemi-sphere by using the WALOP-South and WALOP-North instruments, respectively.– Using stellar polarimetry in conjugation with the GAIA mission’s distance measurements ofstars, carry out magnetic field and dust cloud tomography of the ISM. The methodology tocreate such a map has been discussed by Panopoulou et al. – The main science goal of the PASIPHAE program is to aid CMB B-mode polarizationsearches by identifying clean patches of sky suitable for the search as well as to improvethe foreground emission models by combining PASIPHAE’s tomographic map with polar-ized dust emission data.– Some of the secondary science goals are- (a) improving understanding of interstellar dust bytesting various physical models of grain alignment and size distribution, (b) finding the pathsof ultra high-energy cosmic rays though the Galaxy, (c) creating a catalogue of intrinsicallypolarized stars and finding associated systematic correlations with properties like the spectraltype and stage of the stars.Of the two WALOP instruments, WALOP-South is scheduled to be commissioned first in 2021.Both the WALOPs are currently under development at IUCAA, Pune. The unique scientific goalsof the PASIPHAE survey lead to a set of very challenging design and performance requirementsfor the optical system of WALOP instruments. using calibration techniques (Section 4.3). In this paper, we presentthe complete optical design of the instrument. The optical design of WALOP-North is similarto that of WALOP-South- the differences are due to the differences in the telescope optics (theyhave different f-numbers) as well as opto-mechanical interfaces. Section 2 describes the techni-cal goals of the instrument as driven by the scientific objectives of the PASIPHAE survey and thechallenges in realizing them. Section 3 explains the overall optical design and Section 3.3 givesa detailed description of the architecture and working of the polarization analyzer subsystem ofthe instrument, referred to as the polarizer assembly in this paper, which is the most complex andnovel subsystem of the instrument’s optical system. In Section 4, we show the performance ofthe design and Section 5 contains our conclusions and observations regarding the optical designof WALOP-South and its possible application to the design of other wide field polarimeters. Inaddition to the WALOP-South optical system, we designed new baffles for the telescope’s mirrorsto accommodate the wide FOV and an auto-guider camera. These are presented in Appendix Aand B respectively.
Based on PASIPHAE survey goals as well as the current state of the art optical polarimeter designtechnology and understanding, optical design goals for WALOP-South instrument were decided.These goals are captured in Table 1. The design goals for WALOP-North are same as WALOP-South.Most stars at high galactic latitude are expected to have p < . due to lower dust con-tent in these regions. To accomplish the scientific objectives of the PASIPHAE program, a widefield polarimeter with high accuracy ( a ) and high sensitivity ( s ) is needed. As the survey aims tomeasure p with a = < . as limited by photon noise, we aim to limit s = < .
05 % .The polarimeter will be capable of carrying out four channel one-shot linear imaging polarime-try in R broadband filter and narrowband filters lying between . µm to . µm . Previous opticalpolarimeters like RoboPol have demonstrated the benefit of one-shot linear polarimetry, whichavoids instrumental noise due to rotating components like Half Wave Plates (HWP) as well aschanging sky conditions such as airmass during the exposures to obtain better polarimetric sensi-tivity. Each of the four channels is imaged on a separate detector or detector area. A schematic ofthis concept is shown in Fig 1, where after passing through the polarimeter, four images of the in-put field along the ◦ , ◦ , ◦ and ◦ polarization angles are imaged on separate detectors. Thisapproach has three major advantages over conventional polarimeters which image all two or fourchannels on the same detector area. Firstly, the background sky is an extended object, so imagingthe four channels on different detectors reduces the sky background by a factor of four by avoidingoverlap of ordinary and extraordinary images from adjacent sky regions. Second, there is no in-termixing of images from different channels, enabling more accurate photometry and polarimetryin sky regions with higher stellar density. Finally, this approach allows extended object imagingpolarimetry for a large field, which has not been possible without using slit masks in previouspolarimeters like RoboPol and IMPOL, leading to obscuration of large regions of the FOV.The initial PASIPHAE survey goal with WALOP-South is to cover 1000 square degrees, mainlycovering the areas targeted by upcoming CMB B-mode search missions. With 200 available nightson the telescope per year, an average of 8 hours per night and 70% observation efficiency, we can3 l. No . Parameter Technical Goal s ) 0.05 %2 Polarimeter Type Four Channel One-Shot Linear Polarimetry3 Number of Cameras 4 (One Camera for Each Arm)4 Field of View × arcminutes5 Detector Size k × k (Pixel Size = µm )6 No. of Detectors 47 Primary Filter SDSS-r8 Imaging Performance Close to seeing limited PSF9 Stray and Ghost Light Level Brightness less than sky brightness per pixel.Table 1: Design goals for WALOP-South instrument optical system.Fig 1: Concept of four channel imaging with separate camera for each channel. The input fieldis split into four channels along the ◦ , ◦ , ◦ and ◦ polarization angles and imaged on fourseparate detectors without any overlap.cover a 1000 square degrees region in 16 months with a FOV of × arcminutes and measure p with a = < . for R = < . mag stars (with the obtained FOV of × arcminutes, theestimated survey period becomes 14 months).The median seeing FWHM (full width half maximum) at the Sutherland Observatory is 1.5 arc-seconds. Imaging the FOV on a k × k detector with pixel size of µm gives a plate scale of0.45 arcseconds per pixel, allowing better than Nyquist sampling. The PSF (point spread func-tion) should be close to seeing limited for median seeing conditions. While a larger PSF helps inspreading photons over more pixels and washing out pixel to pixel sensitivity variation, it comesat the cost of a higher measurement uncertainty from increased sky background.The stray light from objects outside the FOV and ghost light from field objects due to reflectionsfrom telescope baffles/instrument optics should be reduced to a level where their intensities at thedetector will introduce less than 0.05% polarization (less than s ). While this cannot be realisedfor very bright stars and moon if they are near the FOV, for most sources this can be achieved bykeeping their stray/ghost light levels below the sky background.4 .1 Challenges in making the WALOP-South Optical Design The main challenge in building WALOP-South is obtaining s = < . across the FOV. Wollas-ton Prisms (WP) are the most widely used linear polarization analyzers in optical astronomy dueto their high extinction ratios ( > ) as well as near symmetrical angular splitting of orthogonalpolarization states, making these suitable to be placed at a pupil plane. It was decided to use adouble WP system to create a four channel analyzer system (refer to Section 3.3.1 for a trade-offstudy between different candidate analyzer systems). While double WPs with separate imagingof four channels on different detector areas have been designed and implemented in astronomicalpolarimeters in the past, eg. in HOWPol using WeDoWo prisms and in RoboPol, these instru-ments have smaller FOVs for which WPs with split angles of around ◦ are sufficient. However,for WALOP-South’s field size, large split angles of the order ◦ to ◦ are required. WPs with suchlarge split angles introduce large spectral dispersion in broadband filters in the split beams due tothe dependence of split angle on wavelength. This is in addition to the usual problems of largeaberrations of off-axis objects due to the very wide field. WALOP-South will be mounted on the direct port of the 1 m telescope at SAAO’s SutherlandObservatory. Details of the telescope and site is captured in Table 2. The instrument has beendesigned to perform optimally for the temperature range and seeing conditions at the site.
Parameter Value
Telescope Type Cassegrain Focus and Equatorial MountPrimary Mirror Diameter 1 mSecondary Mirror Diameter 0.33 mNominal Telescope f-Number 16.0Altitude 1800 mMedian Seeing FWHM 1.5”Extreme Site Temperatures − ◦ C to ◦ C Table 2: Telescope and Site Details.
The optical model of WALOP-South was created and analyzed using the Zemax ® optical designsoftware. The complete instrument model is shown in Fig 2. The instrument can be dividedinto the following assemblies: a collimator, a polarizer and four cameras (one for each channel).The collimator assembly, beginning from the telescope focal plane is aligned along the z-axis andcreates a pupil where the polarizer assembly is placed. The polarizer assembly splits the incomingcollimated beam into four channels corresponding to ◦ , ◦ , ◦ and ◦ polarization angles,which are referred to as O1, O2, E1 and E2 beams respectively. Additionally, this assembly steersthe O beams along the +y and -y directions and the E beams along the +x and -x directions. Eachchannel has its own camera which images the entire field on a k × k detector. The obtained FOV5ig 2: Complete optical model of the WALOP-South instrument. It accepts the beam for thecomplete FOV from the telescope focal plane and through the collimator assembly creates a pupilwhich is then fed to the polarizer assembly. The polarizer assembly splits the pupil beam into fourchannels and steers them in +/- x and +/- y directions. The O1 and O2 beams correspond to ◦ , ◦ polarization while the E1 and E2 beams correspond to ◦ and ◦ polarization. Each channelhas its own camera assembly to image the complete field on a k × k detector.of the instrument is . × . arcminutes (see Section 3.3.4 for more details). The key designparameters of the optical design are listed in Table 3.While creating the optical design, a major consideration was to avoid the use of mirrors and as-pheric lenses. Mirrors introduce instrumental polarization due to reflections while aspheric lensesare relatively more difficult to fabricate and align in an optical assembly. In addition to these, thelength of the instrument must be restricted to less than . m from the telescope focal plane due tospace constraints at the telescope.Almost all the complexity of WALOP-South optical design resides in the architecture andworking of the polarizer assembly. Its design and working are explained in detail in Section 3.3.The collimator and camera assemblies are described in Sections 3.4 and 3.5.6 arameter Design Value/Choice Filter SDSS-rTelescope F-number 16.0Camera F-number 6.1Collimator Length 700 mmCamera Length 340 mmPupil Diameter 65 mmNo of lenses in Collimator 6No of lenses in Each Camera 7Detector Size × Pixel Size µm Sky Sampling at detector 0.5”/pixelTable 3: Values of the key parameters of WALOP-South Optical Design.
Our key requirements in deciding on a suitable polarization analyzer design were: (a) to achievefour channel beam-splitting as shown in Figure 1, (b) to achieve good PSFs at the detectors fromthe split beams for the entire FOV, and (c) to ensure that the split beams have high extinction ratios( > ) to achieve the required s . To decide on the most suitable architecture of the polarizersystem, we considered four broad types of polarization analyzer systems and a trade-off study wascarried out to find the most suitable solution. These were:1. Twin Wire-Grid Polarization Beam Splitters (PBS).2. Twin Glan-Taylor/Thomson Prisms.3. Twin Polarization Gratings.4. Twin Wollaston Prisms.A single Wire-Grid PBS separates the incident beam into two orthogonal polarization states(parallel and perpendicular to the direction of nano-wires in the PBS) and steers them in orthogo-nal directions- one polarization is transmitted while the other is reflected. These have been used intwo-channel polarimeters like MOPTOP to obtain on-sky accuracy of 0.25 % using a modulatingHWP. The advantage of using these is that their beam-splitting performance does not change sig-nificantly over large angles of incidence, or over the range of wavelengths of broadband filters likethe SDSS-r, which is a major problem with using crystal based polarizers like Wollaston Prisms,as described later. While the transmitted beam can have a very high extinction ratio of > , thereflected beam has extinction ratio of less than 100, which would compromise the sensitivity of theinstrument in a single shot polarimeter like WALOP-South.The Glan-Taylor Prisms also work in a very similar manner as the Wire-Grid PBS- orthogonalpolarization states are split and steered in orthogonal directions. Instead of nano-wires, Glan-Taylor Prisms use anisotropic optical properties of birefringent crystals like calcite to reflect oneof the polarizations using total internal reflection. Similar to Wire-Grid PBS, the reflected beam7as very low extinction ratio. Additionally, in general, these polarization beam-splitters suffer fromsevere degradation of polarization performance even for small angles of − ◦ away from normalincidence, whereas the collimated beam of WALOP-South at pupil has angles of up to ◦ .Polarization gratings (PG) have been used in astronomical spectropolarimetry to achieve0.1 % accuracy in four channel polarimeters, e.g. WIRC+Pol. An advantage of PGs for usein large FOV polarimeters is their availability in large aperture sizes, whereas a major problemassociated in employing PGs in imaging polarimeters is the large dispersion introduced in theoutgoing beams. Also, since PGs separate circular polarizations, a quarter-wave plate (QWP) isneeded in front of the PGs to make them separate linear polarization states, making them moresuitable for circular polarimetry than linear polarimetry.Finally, Wollaston Prism (WP) systems have been used in astronomy
14, 16, 17, 21 as the go-topolarization analyzer system. These separate the orthogonal polarization states (called E and Obeams) with high extinction ratios. For WALOP-South’s FOV, WPs with large split angles ( > ◦ )and apertures are needed to image the four split beams on different detectors. Also, the split angleof a WP depends on the wavelength, and for a broadband filter like the SDSS-r, there is largedispersion in the outgoing beams (Section 3.3.5, Figure 6).Since our main goal is to carry out sensitive polarimetry, we decided to go with twin Wollas-ton Prisms as the polarization analyzer system, with each Wollaston Prism having its own HWPin front, similar to the architecture of RoboPol’s polarization analyzer system. The dispersionintroduced by the Wollaston Prism system is corrected downstream in the optical design.
It consists of four sub-assemblies: (a) Wollaston Prism Assembly (WPA), (b) Wire-Grid Polar-ization Beam-Splitter (PBS), (c) Dispersion Corrector Prisms (DC Prisms) and (d) Fold Mirrors.The WPA, using the splitting action of the WPs, separates the beam at the pupil into O1, O2, E1and E2 beams- corresponding to the polarization angles of ◦ , ◦ , ◦ and ◦ respectively. ThePBS’ act as beam selectors, allowing both the O beams to pass through while folding the E1 andE2 beams along -x and +x directions. Fig 3 shows the overall working idea of the WPA and PBScomponents of the polarizer assembly, which in combination act as the polarization beamsplitterunit of the instrument. The collimated pupil is split equally between two BK7 wedges which isthen fed to the HWP + WP system to split into four channels. Then the two PBS’ steer the fourbeams in four directions. The need for the PBS’ is described in Sec 3.3.6. The DC Prisms are apair of glass prisms present in the path of each of the four beams after the PBS to correct for thespectral dispersion introduced by the WPA. Additionally, before the O-beams enter their respectivecamera assemblies, mirrors placed at ± ◦ to the y-axis in the y-z plane fold the beams into +yand -y directions. This folding was done to limit the length of the instrument to 1.1 m from thetelescope focal plane. Fig 4 shows the drawing of the WPA. The WPA is made of two parts, named as the Left Half andthe Right Half. Each half has the following optical components: a glass (BK7) wedge, a half-wave retarder plate (HWP), a calcite WP and a flat BK7 window. The aperture of all the elementsis mm × mm , making the overall WPA aperture mm × mm . The Left Half hasbeen designed to separate the ◦ and ◦ polarizations, from which the Stokes parameter q will be8ig 3: Schematic of the working of the polarizer assembly of the WALOP-South instrument. Incombination, the Wollaston Prism Assembly consisting of the two BK7 glass wedges, WollastonPrisms (WP) and Half-Wave Plates (HWP) and the two PBSs act as the polarization beamsplitterunit of the instrument. The collimated beam at the pupil is split equally between two BK7 wedgeswhich is then fed to the twin HWP + WP system to be split into four channels with the polarizationstates of ◦ , ◦ , ◦ and ◦ , and two PBSs steer these four beams in four directions. The changein the polarization state of the beams while passing through this system is annotated.obtained while the Right Half separates the ◦ and ◦ polarizations from which the u parameterwill be obtained. For this purpose, the Left HWP’s fast-axis is along ◦ and that of the Right one isat . ◦ with respect to the x-axis in the WPA coordinate system. While the right HWP effectivelyrotates the EVPA (electric vector polarization angle) of the beam by − ◦ , the left HWP has noeffect on the beam, and has been used to maintain similar optical path as the right HWP. BothWPs separate ◦ and ◦ polarizations. So while the right WP separates ◦ and ◦ polarizationsof the incoming beam, because the HWP has rotated the beam by − ◦ , it effectively separates ◦ and ◦ polarizations. At the exit face, a BK7 window is placed to provide a surface whichcan be anti-reflection (AR) coated. Calcite is a softer material than conventional glasses. Duringapplication of AR coatings, large mechanical and thermal stresses that develop on substrates couldbreak the large calcite wedges. The complete WPA is cemented together as one unit using theNorland 65 cement. This is a flexible cement which has been carefully chosen so as to withstandlarge stresses in WPs that will arise from anisotropic thermal expansion of calcite WPs whensubjected to large temperature variations such as that expected at SAAO’s Sutherland Observatory(Table 2). To ascertain the flexibility of the cement, sacrificial calcite WPs cemented with Norland65 were subjected to temperatures in range of − ◦ C to ◦ C in an environmental chamber.Due to extended FOV of WALOP-South, rays from non-axial field points arrive at large obliqueangles at the pupil. This angle α ’s approximate value can be found using Eqn 1 (also called OpticalInvariant equation), where D , p and θ are the telescope primary mirror diameter, pupil image9ig 4: Drawing of the Wollaston Prism Assembly (WPA). The optic axis of the calcite wedgesforming the Wollaston Prisms are marked. All length dimensions are in mm.Fig 5: Beam splitting action of the Left and Right Half of the Wollaston Prism Assembly (WPA)as seen from Y-Z plane. The right WP is rotated by ◦ with respect to the left Wollaston Prism.10iameter and the on-sky angle of the field point from center. Without the BK7 wedge, a fractionof rays from such sources will go on to hit the interface between the Left and Right Half, leadingto throughput loss and possible stray light from scattering at the surface. To avoid such a scenario,BK7 wedges with tilt angle of ◦ are used. Fig 10 shows the BK7 wedges bending the rays fromthe whole field such that none hit the interface. α = D × θp (1)The HWPs are made of Quartz-MgF plates designed to provide achromatic half-wave retarda-tion (within 0.515 to 0.480 λ ) over the wavelength range of . µm to . µm for normal incidence.Both the Left and Right HWPs are made by a × mosaic of mm × mm size HWPs. Thiswas necessitated due to unavailability of larger blanks of Quartz and MgF to create a single HWPof aperture mm × mm . In general, the retardance of a HWP is dependant on the absoluteand azimuth angles of incidence of the incoming beam with respect to the fast axis of the HWP. Due to the bending by the BK7 wedges, rays from the entire FOV have oblique angles of incidenceon both the HWPs, and hence undergo ’non-half wave’ retardation. This leads to cross-talk be-tween all the Stokes parameters, which has been considered and modelled as part of the calibrationmethod we have developed for the instrument (Section 4.3).Two identical calcite WPs are used as polarization analyzers. The polarization separation be-haviour of the WPs is shown in Figure 5. While both the WPs separate ◦ and ◦ (called O andE beams) polarizations, due to the HWPs in front of each WP, the O1 beam and O2 beams corre-spond to ◦ and ◦ while the E1 and E2 to ◦ and ◦ . The right WP is rotated by ◦ withrespect to the left WP. Hence, the O1 beam goes downwards and O2 beam goes upwards, and viceversa for E1 and E2 beams. This inversion of WPs was done so that the E1 and E2 and O1 and O2beams can be folded in opposite directions to each other to physically separate the four beams tocorrect for their dispersion, the need for which is explained in Section 3.3.5.The complete polarizer assembly is fabricated by Karl Lambrecht Corporation, Chicago, USA. A WP can be characterized by the following quantities: (a) aperture, (b) material, (c) wedge angle,(d) optic axis directions in the two wedges forming the WP and (e) extinction ratio. Of these, thematerial and the wedge angle decide the split angle of the WP.The minimum required split angle for a WP ( β min ) to separate the E and O beams such thatthey are fully separated on the detectors is given by Eqn 2. It is twice of the angle formed by theextreme field point in the direction of splitting at the pupil (which is y-axis in our case), given byEqn 1. For a FOV of . × . arcminute ( . ◦ × . ◦ ), the extreme vertical field point is . ◦ for which β min = . ◦ . β min = 2 × D × θp (2)Materials from which WPs of such large split angle can be created in the optical wavelengthsare α -BBO (Barium Borate), LiNbO (Lithium Niobate) and calcite. α -BBO and LiNbO havelower birefringence than calcite and are not available in large crystal sizes. Employing WPs madefrom either of these would lead to reduction in the pupil image size and consequently higher split11ngle requirement (Eqn 1) and hence larger dispersion and aberrations. Also, calcite has been usedin previous wide-field astronomical polarimeters such as SALT-RSS polarimeter. Calcite WPshave very high extinction ratios > .The approximate split angle ( β ) for a WP can be calculated using Eqn 3, where n e and n o areextraordinary and ordinary index of refraction and γ is the wedge angle of the WP. sin ( β n e − n o ) tanγ (3)The WP used in the WPA has a wedge angle of γ = 30 ◦ , for which the split angle comes outto be . ◦ at . µm (Figure 6). As can be seen, the split angle is larger than β min . We increasedthe FOV from . × . arcminutes to . × . arcminutes to take advantage of this largesplit angle without degrading the image quality. The plate scale for this FOV is 0.5”/pixel, so themedian seeing FWHM (1.5”) is sampled by 3 pixels. Although we could have increased the FOVfurther, it would lead to sparser PSF sampling at the detector and higher instrumental noise due topixel to pixel sensitivity variation of the CCD.As can be seen from Eqn 2, for the same telescope, if the pupil diameter is larger, WP withsmaller split angle is required which will introduce smaller dispersion. The issue of dispersionfrom calcite WPs is described in Section 3.3.5. So, while it is advantageous to make the pupillarger to reduce dispersion by using large aperture WPs, the upper limit is set by the availability oflargest calcite crystals. Additionally, making a large pupil makes the collimator design challenging.Hence we decided to use WPs with the largest available apertures- mm × mm . Birefringence ( δn = n e − n o ) of crystals and consequently the split angle of WPs depends on thewavelength (Eqn 3). Figure 6 shows the wavelength dependence of calcite’s birefringence and splitangle for the WALOP WPs. This split angle variation with wavelength leads to the outgoing E andO beams to have dispersion in the splitting direction. WPs with larger split angle introduce largerdispersion. There is significant change in the split angle within the SDSS-r band wavelengths of . µm to . µm . In case of WALOP WPs, this leads to dispersion in the y-axis direction in theoutgoing E and O beams corresponding to a spectral resolution R ∼ . The dispersion in theE and O beams are similar (but not equal) and in opposite directions. Hence the dispersion ofboth the E and O beams cannot be corrected by placing a suitable glass wedge after the WP exitsurface. Fig 7 shows the dispersion in the E and O images for a × arcminute FOV of theSALT-RSS polarimeter which employs calcite WPs as the polarization analyzer. As can be seen,the dispersion of the same stars is in the opposite directions between the top and bottom images. Inaddition to the WPs, the BK7 wedges at WPA entrance also introduce dispersion, but in the x-axis(horizontal). So, the outgoing beams from the WPA suffer from dispersion along both the x and ydirections.Most imaging polarimeters like RoboPol which do not image the entire FOV on separate de-tectors use WPs with small split angles (around . ◦ ), for which the dispersion is minimal andlower in value than other optical aberrations of the system. On the other hand, SALT-RSS (Fig 7)and HOWPol polarimeters image a large FOV on separate detectors, but do not correct for thedispersion by the WPs and are limited to carry out only narrow-band imaging polarimetry.12 .4 0.5 0.6 0.7 0.8 0.9 1.0 Wavelength ( m ) B i r e f r i n g e n c e Sp li t a n g l e ( d e g ) Fig 6: Dependence of birefringence and split angle of the WALOP Wollaston Prisms on wave-length.Fig 7: SALT-RSS two channel polarimeter image of the M30 globular cluster, which employscalcite Wollaston Prisms as the polarization analyzer. The E and O beams are imaged on the topand bottom half of the detector. The dispersion in the E and O images for a × arcminutefield is clearly visible. Also, the dispersion direction is opposite in the two images. This image isreproduced with permission, courtesy of Prof. Kenneth Nordsieck, the PI of the RSS instrument.13 C Prism No . Beam Glass Name Tilt Angle-X Tilt Angle-Y
Prism 1 O Beam S-TIH6 - . ◦ Prism 1 E Beam S-TIH6 - . ◦ Prism 2 O Beam S-BSL7 . ◦ -Prism 2 E Beam S-BSL7 . ◦ -Table 4: Details of the Dispersion Corrector Prisms used in WALOP-South optical model. As the dispersion due to the WPs in E and O beams is in opposite directions, the four beams need tobe separated physically so that the required correction can be applied on each beam. The wire-gridPBS is designed such that it allows the O-Beam to pass through but folds the E-Beam by actingas a mirror. Since the two beams have already been completely separated in the angle-space bythe WPA, the lower extinction ratio of the PBS for the E-Beam (which causes some fraction ofO-beams to be folded as well, but at different angles than E-beam) will not lead to any O-Beamrays reaching the detector of E-Beam cameras. Unlike other types of polarization beam splittersystems, wire-grid type have uniform performance for large angles of incidence of ± ◦ and areavailable in sizes required for WALOP-South instrument. The PBSs used in the WALOP-Southdesign are of aperture × mm , and have been fabricated by Moxtek, Inc., Utah, USA. Ithas nearly 90 % throughput for p (O Beam) and s (E Beam) polarizations for the transmitted andreflected beams respectively over the SDSS-r filter wavelengths. Each of the four beams have two DC Prisms- the first prism made of S-TIH6 glass corrects they direction dispersion and the second prism made of S-BSL7 (glass from Ohara catalogue withproperties identical to BK7) corrects the x direction dispersion. Each prism has one tilted and oneflat surface, as shown in Fig 8, 9 and 10. Details of the DC Prisms are captured in Table 4.
The collimator assembly begins from the telescope focal plane as shown in Fig 2, 8, 9 and 10. Itconsists of 6 spherical lenses placed axially along the z-axis. At the telescope focus, the field sizeis mm × mm , from which a pupil of of mm in diameter is formed. The choice of thepupil size was driven by the architecture of the polarizer assembly described in Section 3.3.4. Theeffective focal length of the collimator is . × mm and its total length is 700 mm. Each camera assembly consists of 7 spherical lenses. Fig 8 and 9 shows the optical path for O1 andO2 beams. The Polarization Beam-Splitter (PBS), described in Section 3.3, allows these beams topass straight through to be then folded towards the +y and -y directions by the Fold Mirrors. Fig 10shows the optical system for the E1 and E2 beams. The PBS folds these beams towards the -x and+x directions.The O1 and O2 cameras are identical to each other, i.e, they have identical lens prescriptionand air gaps. Similarly, the E1 and E2 cameras are identical to each other. Between the O andE beam cameras, while the glass types are same for corresponding lenses, their apertures and air14ig 8: O1 Beam Optical Path. After getting split by the Wollaston Prism Assembly (WPA), thePolarization Beam-Splitter (PBS) allows this beam to pass through it to the Dispersion Corrector(DC) Prisms. The fold mirror downstream then directs this beam along +y direction to its camera.separations are different. Also, between the O-Beam and E-Beam cameras, the radii of curvaturesand central thicknesses are same for the first five lenses but differ for the last two lenses. As adesign choice, we made the E and O beam cameras as similar as possible to reduce fabricationeffort and cost of the lenses. The f-number at the detectors is 6.12 and 6.06 for the E and O beamcameras, respectively, which corresponds to effective focal lengths of 6220 mm and 5993 mm.With k × k detectors of pixel size µm , the plate scale is 0.5 arcsecond per pixel. This allowsfor better than Nyquist sampling for the median seeing FWHM of 1.5 arcsecond at the SutherlandObservatory. The filter and the calibration HWP are located near the pupil image before the polarizer assembly,as shown in Fig 8, 9 and 10. The initial design idea was to use Johnson-Cousins R as the mainbroadband filter. In comparison to this filter, SDSS-r has a similar throughput but a smaller wave-length spread which helps in reducing the spectral dispersion introduced by the polarizer assemblyand provides better PSFs (refer to Section 4, Fig 12). Fig 11 compares the transmission profilesbetween the two filters. The SDSS-r filter used in WALOP-South instrument is of mm aperturefabricated by Asahi Spectra Co., Ltd. (ASC), Japan.Rotation of the calibration HWP to orientations that are multiples of ◦ deg, would in an idealinstrument interchange the intensities in the O and E beams. Any departure from this behaviourof the beams passing through the four cameras can be used to correct for any channel dependanttransmission variation. This offers an additional method to calibrate the instrument (Section 4.3)15ig 9: O2 Beam Optical Path. After getting split by the Wollaston Prism Assembly (WPA), thePolarization Beam-Splitter (PBS) allows this beam to pass through it to the Dispersion Corrector(DC) Prisms. The fold mirror downstream then directs this beam along -y direction to its camera.during main science observations. The aperture of the calibration HWP is mm × mm , andis made by a × mosaic of mm × mm size HWPs whose fast-axes are accurately alignedwith each other. As described in Section 2, the essential performance criterion for the instrument optical design is toobtain near seeing limited PSF for the entire FOV (within 1.5-2 times the median seeing Gaussianprofile). To carry out polarimetry with sensitivity of 0.05 %, all the photons from a star reachingthe detector need to be counted using aperture photometry. Larger PSFs sample larger sky areasand lead to higher measurement uncertainty. So, in judging the quality of PSFs obtained, whileFWHMs are a good measure of spatial resolution, for high sensitivity polarimetry, the ensquaredenergy radius containing all the starlight ( > .
95 % ) is a better measure. For example, Fig 12shows the PSF at the center of WALOP-South’s FOV for the Johnson-Cousins R and SDSS-rfilters. Although both have similar FWHMs, the radius corresponding to the > .
95 % ensquaredenergy is much larger for the Johnson-Cousins filter due to its extended spectral transmission tail,as shown in Fig 11.Figs 13 and 14 show the spot diagrams for the O and E beam cameras at different field points.As the optical path of the O1 and O2 beams is same, they have identical optical performance.Same is true of E1 and E2 beams. As can be seen, the dispersion introduced by the WPA hasbeen corrected by post-WPA optics. On an average, the centroid of the spot diagrams for allthe individual wavelengths within the SDSS-r filter fall within µm (less than a pixel) of each16ig 10: E1 and E2 Beam Optical Paths. After getting split by the Wollaston Prism Assembly(WPA), the two Polarization Beam-Splitters (PBS) fold these along -x and +x directions. Afterpassing through the Dispersion Corrector (DC) Prisms, each beam goes to its camera.17
00 550 600 650 700 750 800 850 900
Wavelength (nm) T r a n s m i ss i o n ( % ) Johnson-Cousins R SDSS-r
Fig 11: Comparison of the transmission profiles of the SDSS and Johnson-Cousins R filters. Whileboth filters have similar throughput, the SDSS-r has a narrower wavelength coverage which reducesthe dispersion by the Wollaston Prisms.Fig 12: Comparison of the PSF at the center of FOV for a 1.5” (median seeing) input beam atthe detector for Johnson-Cousins and SDSS R band filters. As can be seen, with Johnson-Cousinsfilter, we get an elongated PSF due to the residual dispersion from the Wollaston Prisms owing tothe filter’s broad spectral range while we get a symmetric PSF with the SDSS filter.other for the entire FOV for both E and O beams. The average RMS radius of both the beams isaround 11.5 µm for the whole field. For comparison, the RMS radius for a 1.5 arcsecond FWHMGaussian beam (median seeing at Sutherland) with the same plate scale as at the camera detectorsis 19.1 µm . The PSF obtained will be a convolution of the input Gaussian seeing beam with thespot diagram profile. The radius corresponding to 99.95% of the ensquared energy at differentpoints in the FOV for a 1.5” FWHM source for the E and O beams is captured in Table 6 undercolumn name Nominal . The averaged radius for both the beams is less than 75 µm or 5 pixels at18ig 13: Spot diagram for the O Beam cameras at the detector for different field points. Differentcolors represent rays of different wavelengths, as labeled in the image legend. RMS and GEOradius stand for the root-mean square and geometric radius of the spot diagrams, respectively. Theoptical performance of O1 and O2 beams are identical as they follow identical optical paths.the detector whereas for an ideal Gaussian this radius is 67.1 µm or 4.5 pixels at the detector.Tolerance analysis of the optical system was carried out to get an estimate of expected degrada-tion of spot sizes and ensquared energy radii due to tolerances in fabrication of optical componentsand mechanical mounts to hold the optics. Two compensators were defined - one is the separationbetween the primary and secondary mirrors of the telescope. The second compensator is the dis-tance of the detector from the last lens in each camera. We used the Monte Carlo (MC) simulationfeature of Zemax for this work. Table 5 shows the results for the spot radius based on 20,000Monte Carlo runs for the system. Table 6 lists the radius containing 99.95 % of the ensquaredenergy for median seeing conditions for the E and O beams in nominal as well as best and worstMonte Carlo simulation results at different field points. Even in the worst case scenarios, we getPSFs equivalent to Gaussian beams with FWHM of 1.6 and 1.3 times the seeing FWHM for the Oand E beams, respectively. While the WALOP-South instrument will be assembled and characterized in the lab at IUCAA ataround 1 Atm pressure and ◦ C temperature for which the design has been made, the atmospheric19ig 14: Spot diagram for the E Beam cameras at the detector for different field points. Differentcolors represent rays of different wavelengths, as labeled in the image legend. RMS and GEOradius stand for the root-mean square and geometric radius of the spot diagrams, respectively. Theoptical performance of E1 and E2 beams are identical as they follow identical optical paths.20arameter O-Beams E-BeamsRMS Spot Radius ( µm ) RMS Spot Radius ( µm )Nominal Spot 11.63 11.77Root-Sum-Square 17.1 15.37MC Simulation Best Case 11.72 11.7MC Simulation Worst Case 37.4 25.5MC Simulation Mean 17.54 15.72MC Simulation Std Dev 0.003 0.0018Table 5: Results of Monte Carlo simulations based tolerance analysis for the O and E beams.Root-Sum-Square radius is the RMS spot radius obtained if the offset in spot radius due to allmechanical and optical tolerances are added in quadrature.Sl. No Field Poisition O Beams E BeamsX Y 99.95 % EnsqauredEnergy Radius ( µm ) 99.95 % EnsqauredEnergy Radius ( µm )(in Deg) (in Deg) Nominal MC Best MC Worst Nominal MC Best MC Worst1 0 0 73 75 62 69 69 752 0.29 0 62 61 68 64 63 683 0 0.29 74 72 96 79 82 624 -0.29 0 66 66 66 66 66 825 0 -0.29 75 68 165 70 63 1146 0.29 0.29 86 76 150 82 82 677 -0.29 0.29 86 78 112 88 92 788 -0.29 -0.29 73 71 154 83 76 1409 0.29 -0.29 78 78 210 85 74 12710 0.15 0.15 70 68 68 66 68 6411 -0.15 0.15 74 74 68 68 70 6512 0.15 -0.15 62 64 90 65 63 82Field Average 73 71 109 74 72 85Table 6: For an input 1.5” (median seeing) beam, radius containing 99.95% of the ensquaredenergy of the PSF for the E and O beams in nominal design and the best and worst case MonteCarlo simulation realizations.pressure at the Sutherland Observatory is 0.78 Atm due to its higher altitude and the temperaturemay change from − ◦ C to ◦ C during observations. Changes in pressure and temperature leadto change in thickness, curvature and refractive index of the optics and separation between opticalelements due to expansion/contraction of metallic components used as optics holders and spacers.The estimated change in the RMS spot radius for different temperature conditions is shown inthe
Before Compensation column of Table 7. This image degradation effect can be compensatedby adjusting the separation between the detector and the last lens in each camera. Using Zemax,thermal tolerancing was carried out on the optical design. As can be seen from the achievedRMS spot radius after compensation in Table 7, we can get to within 1.1 times the nominal RMSspot radius using this compensator system for all the temperature conditions at the SutherlandObservatory. 21emperature(in Celsius) Pressure(in Atm) O Beams E BeamsRMS Spot Radius ( µm ) RMS Spot Radius ( µm )BeforeCompensation AfterCompensation BeforeCompensation AfterCompensation25 1 11.63 - 11.79 --10 0.78 17.1 12.5 16.7 12.080 0.78 17.3 12.19 17.05 11.9410 0.78 17.55 11.92 17.36 11.8420 0.78 17.7 11.76 17.65 11.7830 0.78 17.9 11.7 17.9 11.77Table 7: Thermal tolerancing results for WALOP-South optical model. Stray and ghost light analysis for the entire WALOP-South optical system including the telescopemirrors and baffles was carried out using the non-sequential mode of Zemax. As part of the study,we created point sources inside and outside the FOV and light rays were traced through the system.Using Zemax’s Path Analysis feature, all paths of stray and ghost light from each source reachingthe detectors were identified and controlled in the optical as well as optomechanical model of theinstrument so that for any source the ghost/stray light intensity at the detector is less than × − of it’s total intensity incident on top of the telescope tube. For most sources barring the extremelybright ones ( < mag ), its stray and ghost light will be undetectable on WALOP-South detectorsas it will be fainter than the background sky. The major source of ghost light from inside FOVobject is due to reflection from the lens surfaces at the beginning of the cameras. To controlthe ghost light as well as improve instrument’s throughput, we used high efficiency AR coatings( R < . ) for all optical surfaces. Fig 15 shows the ghost image pattern from a source at thecenter of the FOV. For a total input power of 100 Watts incident on top of the telescope tube, × − Watts of power reaches the detector as ghost image.Fig 16 shows the stray light irradiation for an object in the vicinity of the FOV (source position:x, y = 19.2, 19.2 arcminute) at one of the four detectors. For a total input power of 100 Watts atthe telescope, . × − Watts of power reaches the detector.
To achieve high accuracy linear polarimetry of . across the FOV, we need to accurately obtainthe value of the real linear Stokes parameters of a star from those measured by the instrument.All optical elements can introduce instrumental polarization and cross-talk in the following ways:(a) due to oblique angles of incidence, which leads to preferential transmission of one orthogonalpolarization over the other , (b) due to stress birefringence in the optics, as a result of thermal andmechanical stresses on the optics. Over and above these, we expect the main source of instrumentalcross-talk to arise from the non half-wave retardance from the HWPs in WPA, as described inSec 3.3.3.So the measured value of the linear Stokes parameters by the instrument will depend on theinput polarization of the source (cross-talk) and the instrumental zero point (instrumental polariza-tion). To correct for these effects and obtain high accuracy polarization values, we have developed22ig 15: Ghost image formed for an object at the center of the FOV at one of the four detectors. Fora total input power of 100 Watts at the telescope, × − Watts of power reaches the detector asghost light.a detailed model for on-sky calibration of the instrument. For this purpose, we have placed a mov-able linear polarizer at the beginning of the instrument (after the telescope optics and before thefirst collimator lens), which will be removed from the optical path during the main observations.This polarizer will be used to provide as input linearly polarized light with different EVPAs tothe instrument, which will be used to create a mapping function between the instrument’s mea-sured and real polarization values of stars. Additionally, the model uses standard polarized andunpolarized stars for building as well as testing the accuracy of the model. We have tested andvalidated this scheme by using the Zemax optical model of the instrument and have achieved bet-ter than 0.1 % accuracy over the entire FOV. We will test the calibration model on sky during thecommissioning of WALOP-South instrument and details of the model and results obtained will bepublished as a separate paper.
We have described the complete optical model of the WALOP-South instrument which meets allthe design goals to successfully carry out the PASIPHAE Survey. Scheduled for commissioning in2021, it will be a unique wide field polarimeter. In one shot, it allows determination of I , q and u with four channels simultaneously imaged on separate detector/camera operating over a broadbandfilter wavelength range. We have elaborated the key challenges in creating the design, namely thedispersion introduced by large split angle Wollaston Prisms and aberrations due to the very widefield. With WALOP-South optical design, we expect to obtain within 1.6 times the seeing limitedPSF for the entire FOV after correcting for these effects.23ig 16: Stray light irradiation pattern for an object in the vicinity of the FOV (source position: x,y = 19.2, 19.2 arcminute) at one of the four detectors. For a total input power of 100 Watts at thetelescope, . × − Watts of power reaches the detector.While we have developed the optical model to work for the SDSS-r filter and narrowband filterswithin the wavelengths of . µm − . µm , the prescription presented can be implemented withminor modifications to design polarimeters to work over other broadband filters. It can also beused to design polarimeters with larger FOV by using WPs with larger aperture than those usedin WALOP-South, most likely by employing a mosaic of smaller WPs, without increasing thesplit angle and associated spectral aberrations from the WPs. Also, of interest is the possibilityof carrying out low-resolution imaging spectropolarimetry in WALOP-South like polarimeters bytaking advantage of the dispersion created by WPs by not correcting for the dispersion. Appendix A: Baffles Design
Telescope baffles are used to prevent direct stray light from sources outside the FOV of the in-strument to reach the telescope focal plane and propagate into the instrument. An efficient bafflesystem should achieve this objective with minimal obstruction to light from sources inside theFOV. The existing baffles at the 1 m SAAO telescope were optimized for a narrow FOV of 12 ar-cminutes in diameter. The throughput with these baffles at the telescope focal plane for the radialextent of WALOP-South FOV (the extreme field point is at a distance of . ◦ from the center) isshown in Fig 17 a. While this baffle allows high throughput for objects up to a radius of 6 arcmin-utes, there is a steep drop in throughput for farther objects. In order to get uniform throughput forthe entire WALOP-South FOV, we designed a new baffle system for the telescope’s primary andsecondary mirrors using the method described by Kumar et al. Fig 17 b shows the throughput at24ig 17: Comparison of throughput at the telescope focal plane between the previous baffles andthe new baffles for the telescope designed to accommodate WALOP-South’s FOV.
Baffle Length (mm)
Outside Diameter (mm)Primary 1673.6 236.2Secondary 610.3 424.2Table 8: Dimensions of the new telescope baffles designed for the 1 m SAAO telescope.the telescope focal plane with the new baffle system. Table 8 captures the dimensions of the newbaffles. The new baffle system has been optimised for a FOV of 30 arcminutes in diameter, andthere is minor drop in throughput for farther field points. The average throughput for the completefield is 80.3% in comparison to 72.8% from the previous baffles.
Appendix B: Guider Camera Design
As WALOP-South will be mainly observing the southern Galactic polar regions where there areless number of stars available per square degree, there is sparsity of available guide stars. Addi-tionally, the guider camera field must lie outside of the main science field as any guider optics andassociated mechanical structure may lead to reflection of light leading to stray light on the detector.As can be seen in Fig 17, the throughput from the telescope is lower outside the science field. Theauto-guider camera for the instrument needs to have a large enough FOV to be able to find guidestars for all fields to be covered in PASIPHAE survey. We estimate a minimum required FOV areaof 200 square arcminutes for the guider camera. The guider camera designed for WALOP-Southis a modified version of the guider camera on the 1 m Lesedi Telescope at SAAO’s SutherlandObservatory. Fig 18 a shows the FOV for the guider camera which is located near the telescopefocal plane. This region spanning 540 square arcminutes will be patrolled using two linear stageson which the camera optics, consisting of a pick-off mirror and a lens doublet, and a Lodestar X2CCD detector will be mounted. The pick-off mirror will be moved to the position of the light beampath coming from the target guide star and folded sideways to be imaged on the detector aftercorrection of aberrations by the lens doublet. Fig 18 b shows the PSF obtained (FWHM = 2.2”)for median seeing FWHM of 1.5”. 25ig 18: (a) Schematic of the available FOV for WALOP-South guider camera and (b) PSF at theguider camera detector across the FOV.
Acknowledgments
The PASIPHAE program is supported by grants from the European Research Council (ERC) undergrant agreement No 771282 and No 772253, from the National Science Foundation, under grantnumber AST-1611547 and the National Research Foundation of South Africa under the NationalEquipment Programme. This project is also funded by an infrastructure development grant fromthe Stavros Niarchos Foundation and from the Infosys Foundation.We are thankful to Vinod Vats at Karl Lambrecht Corp. for his inputs and suggestions onvarious aspects of the polarizer assembly design and fabrication and Prof. Kenneth Nordsieck forsharing his experience and ideas on thermal properties of calcite Wollaston Prisms.We thank the anonymous reviewers of the paper whose comments and suggestions helpedimprove the paper.
References
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Appl. Opt. , 2581–2582(1970).23 H. Gu, X. Chen, C. Zhang, et al. , “Study of the retardance of a birefringent waveplate at tiltincidence by mueller matrix ellipsometer,” Journal of Optics , 015401 (2017).24 M. C. Simon, “Wollaston prism with large split angle,” Appl. Opt. , 369–376 (1986).25 C. M . Senthil Kumar and A. S. Kiran Kumar, “Design and analysis of optimum baffle for acassegrain telescope,” Appl. Opt. (2), 180–185 (2016). Siddharth Maharana is an astrophysics PhD student at the Inter-University Centre for Astronomyand Astrophysics, Pune, India. He received his Bachelor in Mechanical Engineering from CentralUniversity, Bilaspur, India in 2015. He is currently working on the design and development of theWALOP instruments for PASIPHAE survey. His areas of interest are polarimetric instrumentationand data analysis.
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A. N. Ramaprakash
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Chaitanya Rajarshi
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Ramya M. Anche
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Shrish
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Dmitry Blinov
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Hans Kristian Eriksen
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Tuhin Ghosh
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Eirik Gjerløw
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Nikolaos Mandarakas
Not Available 28 eorgia V. Panopoulou
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Vasiliki Pavlidou
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Timothy J. Pearson
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Vincent Pelgrims
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Stephen B. Potter
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Anthony C. S. Readhead
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Raphael Skalidis
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Konstantinos Tassis
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Ingunn K. Wehus
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List of Figures ◦ , ◦ , ◦ and ◦ polarization anglesand imaged on four separate detectors without any overlap.2 Complete optical model of the WALOP-South instrument. It accepts the beamfor the complete FOV from the telescope focal plane and through the collimatorassembly creates a pupil which is then fed to the polarizer assembly. The polarizerassembly splits the pupil beam into four channels and steers them in +/- x and +/- ydirections. The O1 and O2 beams correspond to ◦ , ◦ polarization while the E1and E2 beams correspond to ◦ and ◦ polarization. Each channel has its owncamera assembly to image the complete field on a k × k detector.3 Schematic of the working of the polarizer assembly of the WALOP-South instru-ment. In combination, the Wollaston Prism Assembly consisting of the two BK7glass wedges, Wollaston Prisms (WP) and Half-Wave Plates (HWP) and the twoPBSs act as the polarization beamsplitter unit of the instrument. The collimatedbeam at the pupil is split equally between two BK7 wedges which is then fed to thetwin HWP + WP system to be split into four channels with the polarization statesof ◦ , ◦ , ◦ and ◦ , and two PBSs steer these four beams in four directions.The change in the polarization state of the beams while passing through this systemis annotated.4 Drawing of the Wollaston Prism Assembly (WPA). The optic axis of the calcitewedges forming the Wollaston Prisms are marked. All length dimensions are inmm.5 Beam splitting action of the Left and Right Half of the Wollaston Prism Assembly(WPA) as seen from Y-Z plane. The right WP is rotated by ◦ with respect to theleft Wollaston Prism. 29 Dependence of birefringence and split angle of the WALOP Wollaston Prisms onwavelength.7 SALT-RSS two channel polarimeter image of the M30 globular cluster, which em-ploys calcite Wollaston Prisms as the polarization analyzer. The E and O beams areimaged on the top and bottom half of the detector. The dispersion in the E and Oimages for a × arcminute field is clearly visible. Also, the dispersion directionis opposite in the two images. This image is reproduced with permission, courtesyof Prof. Kenneth Nordsieck, the PI of the RSS instrument.8 O1 Beam Optical Path. After getting split by the Wollaston Prism Assembly(WPA), the Polarization Beam-Splitter (PBS) allows this beam to pass through itto the Dispersion Corrector (DC) Prisms. The fold mirror downstream then directsthis beam along +y direction to its camera.9 O2 Beam Optical Path. After getting split by the Wollaston Prism Assembly(WPA), the Polarization Beam-Splitter (PBS) allows this beam to pass through itto the Dispersion Corrector (DC) Prisms. The fold mirror downstream then directsthis beam along -y direction to its camera.10 E1 and E2 Beam Optical Paths. After getting split by the Wollaston Prism As-sembly (WPA), the two Polarization Beam-Splitters (PBS) fold these along -x and+x directions. After passing through the Dispersion Corrector (DC) Prisms, eachbeam goes to its camera.11 Comparison of the transmission profiles of the SDSS and Johnson-Cousins R fil-ters. While both filters have similar throughput, the SDSS-r has a narrower wave-length coverage which reduces the dispersion by the Wollaston Prisms.12 Comparison of the PSF at the center of FOV for a 1.5” (median seeing) input beamat the detector for Johnson-Cousins and SDSS R band filters. As can be seen, withJohnson-Cousins filter, we get an elongated PSF due to the residual dispersionfrom the Wollaston Prisms owing to the filter’s broad spectral range while we geta symmetric PSF with the SDSS filter.13 Spot diagram for the O Beam cameras at the detector for different field points.Different colors represent rays of different wavelengths, as labeled in the imagelegend. RMS and GEO radius stand for the root-mean square and geometric radiusof the spot diagrams, respectively. The optical performance of O1 and O2 beamsare identical as they follow identical optical paths.14 Spot diagram for the E Beam cameras at the detector for different field points.Different colors represent rays of different wavelengths, as labeled in the imagelegend. RMS and GEO radius stand for the root-mean square and geometric radiusof the spot diagrams, respectively. The optical performance of E1 and E2 beamsare identical as they follow identical optical paths.15 Ghost image formed for an object at the center of the FOV at one of the fourdetectors. For a total input power of 100 Watts at the telescope, × − Watts ofpower reaches the detector as ghost light.16 Stray light irradiation pattern for an object in the vicinity of the FOV (source po-sition: x, y = 19.2, 19.2 arcminute) at one of the four detectors. For a total inputpower of 100 Watts at the telescope, . × − Watts of power reaches the detector.307 Comparison of throughput at the telescope focal plane between the previous bafflesand the new baffles for the telescope designed to accommodate WALOP-South’sFOV.18 (a) Schematic of the available FOV for WALOP-South guider camera and (b) PSFat the guider camera detector across the FOV.