Design and Performance Analysis of a Highly Efficient Polychromatic Full-Stokes Polarization Modulator for the CRISP Imaging Spectrometer
A.G. de Wijn, J. de la Cruz Rodríguez, G.B. Scharmer, G. Sliepen, P. Sütterlin
DD RAFT VERSION F EBRUARY
3, 2021Typeset using L A TEX twocolumn style in AASTeX63
Design and Performance Analysis of a Highly Efficient Polychromatic Full-Stokes Polarization Modulator for the CRISPImaging Spectrometer
A.G. DE W IJN , J. DE LA C RUZ R ODR ´ IGUEZ , G.B. S
CHARMER , G. S
LIEPEN , AND
P. S ¨
UTTERLIN High Altitude Observatory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307, USA Institute for Solar Physics, Department of Astronomy, Stockholm University, AlbaNova University Centre, SE-106 91, Stockholm, Sweden
ABSTRACTWe present the design and performance of a polychromatic polarization modulator for the CRisp ImagingSpectroPolarimeter (CRISP) Fabry-Perot tunable narrow-band imaging spectropolarimer at the Swedish 1-mSolar Telescope (SST). We discuss the design process in depth, compare two possible modulator designs througha tolerance analysis, and investigate thermal sensitivity of the selected design. The trade-offs and proceduresdescribed in this paper are generally applicable in the development of broadband polarization modulators. Themodulator was built and has been operational since 2015. Its measured performance is close to optimal between500 and 900 nm, and differences between the design and as-built modulator are largely understood. We showsome example data, and briefly review scientific work that used data from SST/CRISP and this modulator.
Keywords: instrumentation: polarimeters INTRODUCTIONOur knowledge of solar magnetism relies heavily on ourability to detect and interpret the polarization signatures ofmagnetic fields in solar spectral lines. Consequently, newStokes polarimeters are designed to have the capability to ob-serve the solar atmosphere in a variety of spectral lines over awide wavelength range. One immediate instrument require-ment stemming from this need for wavelength diversity isthat the polarization modulation scheme must be efficient atall wavelengths within the working range of the spectropo-larimeter. (For the definition of polarimetric efficiency seedel Toro Iniesta & Collados 2000.) Typically, one attempts toachieve this goal by achromatizing the polarimetric responseof a modulator. This, for instance, is the rational behindthe design of super-achromatic wave plates (Serkowski 1974;Samoylov et al. 2004; Ma et al. 2008). Tomczyk et al. (2010)argued that for many instruments achromaticity is too stronga constraint, and instead proposed the concept of the poly-chromatic modulator that is efficient at all wavelengths ofinterest, but has polarimetric properties that vary with wave-length.In this paper, we present the development process ofa modulator for the CRisp Imaging SpectroPolarimeter(CRISP) Fabry-Perot tunable narrow-band imaging instru-
Corresponding author: A.G. de [email protected] ment (Scharmer 2006; Scharmer et al. 2008) at the Swedish1-m Solar Telescope (SST, Scharmer et al. 2003). First, wecompare the performance of two possible modulator designs,and use a Monte-Carlo tolerance analysis to evaluate theirrobustness. We analyze the sensitivity of the modulator tothermal conditions, and present the opto-mechanical packag-ing and electrical interfaces. The modulator was constructedand tested at the High Altitude Observatory (HAO). We com-pare as-built properties to those of the design. Finally, weshow some example polarimetric observations made usingthis modulator.This modulator was designed and built to replace a mod-ulator based on Liquid Crystal Variable Retarders (LCVRs).LCVRs are electro-optical devices that have a fixed fast axisorientation, but, as the name implies, can be set to any retar-dance within some range by applying an AC voltage. LCVRsgenerally have much slower switching speeds than Ferro-electric Liquid Crystals (FLCs). In contrast to LCVRs, FLCshave a constant retardance but switch their fast axis orienta-tion between two states separated by a switching angle, typ-ically around ◦ . The LCVRs in the old CRISP modulatorhad to be “overdriven” and the modulator state order had tobe optimized in order to switch during the
10 ms readout timeof the CRISP cameras. More importantly, however, thermalsensitivities of the setup forced polarimetric calibration morefrequently than desired (van Noort & Rouppe van der Voort2008).We limit ourselves to designs that use FLCs because theirfast switching speed allows the state of the modulator to be a r X i v : . [ a s t r o - ph . I M ] F e b D E W IJN ET AL .changed in less than the allotted
10 ms , thus allowing forthe highest possible modulation rate. Fast modulation is de-sirable because seeing-induced crosstalk between Stokes pa-rameters that is a dominant source of error in ground-basedpolarimeters is less at higher modulation rates (Lites 1987;Judge et al. 2004; Casini et al. 2012a). Also, it is of impor-tance in maximizing the overall efficiency of the polarimeter.Many present-day CCD and CMOS detectors allow simulta-neous exposure and readout so that the switching speed of themodulator becomes the limitation in the overall duty cycle—and thus efficiency—of the modulator.For a recent review of instrumentation for solar spectropo-larimetery we direct the reader to Iglesias & Feller (2019).Rodenhuis et al. (2014) present a more general review of in-strumentation for measurements of polarized light. DESIGNA computer program was developed at HAO to determinecomponent parameters for a given modulator design (Tom-czyk et al. 2010). This program was used successfully to de-sign the modulators for the ProMag, CoMP-S, SCD, Chro-Mag, and UCOMP instruments built or under constructionby HAO (Elmore et al. 2008; Kuˇcera et al. 2010; Kuceraet al. 2015; de Wijn et al. 2012). More recently, it, or sim-ilar programs derived from it or independently implementedby others, have been used to design modulators, e.g., for theDKIST (Harrington & Sueoka 2018). The code can use sev-eral different merit functions. We choose to minimize themaximum of the deviation of the modulation efficiency (cid:15) Q , (cid:15) U , and (cid:15) V in Stokes Q , U , and V from the optimal value of / √ for balanced modulation at a number of user-specifiedwavelengths, normalized by the efficiency (cid:15) I in Stokes I . Itis possible to bias the modulation efficiency to prefer linearor circular polarization. However, such schemes are of lim-ited use because the SST is not a polarization-free telescope(Selbing 2005).We study two designs: one consisting of two FLC devicesfollowed by one fixed retarder that we will refer to as theFFR design, and one consisting of an FLC, a fixed retarder,a second FLC, and a second fixed retarder that we will re-fer to as the FRFR design. The HAO-designed instrumentsmentioned above all use the FFR design. Others have imple-mented FRFR designs (e.g., Gandorfer 1999; Keller & SolisTeam 2001; Iglesias et al. 2016) The FFR design has 5 freeparameters, whereas the FRFR design has 7 (see Table 1).Both have significant freedom to optimize the design overwide wavelength ranges.All modulators discussed here were optimized for bal-anced modulation, i.e., equal efficiency in Q , U , and V , at16 equidistant wavelengths over the 500—900 nm operatingwavelength range of the CRISP instrument. We allow theprogram to choose the retardances of the FLCs and the re- Table 1.
FRFR and FFR modulator designs. The orientation valueof the FLCs refers to the bisector of the two fast axis positions thatare separated by ◦ .Component Retardance Orientationwaves at 665 nm degreesFRFRFLC 1 .
429 0
Retarder 1 .
181 121 . FLC 2 .
324 17 . Retarder 2 .
543 109 . FFRFLC 1 .
490 0
FLC 2 .
248 112 . Retarder 1 .
228 108 . tarders, as well as the orientations of the second FLC and theretarders. Experience has shown that the best configurationshave an orientation very close to or ◦ with respect to theorientation of the analyzing polarizer for the bisector of thefirst FLC. We therefore fix the orientation of the first FLCat 0 degrees to eliminate one free parameter. The switchingangle of an FLC is sensitive to both temperature and drivevoltage (Gisler 2005; Gisler et al. 2003). Hence, we assumethat we can adjust the drive voltage at a given operating tem-perature so that the FLC switching angles are 45 degrees. Wealso account for dispersion of birefingence for all elements ofthe modulator using measurements from similar optics.The program can use several different optimization tech-niques. We first use a Latin Hypercube Sampling algorithm(McKay et al. 1979) to probe the parameter space. We use alarge population size of 25,000 but only 5 iterations in whichwe shrink the parameter space around the best solution. Wethen apply a downhill simplex method (Nelder & Mead 1965)to refine the solution. To increase confidence that we did notfind a local minimum, we repeat the search several times andcheck that we consistently find the same solution. The result-ing designs are summarized in Table 1.The next step is to evaluate the robustness of the designusing a Monte-Carlo tolerancing method. Efficiencies werecalculated for a total of 1000 modulator realizations with pa-rameters chosen from a uniform distribution around the de-sign values. The width of the distributions was chosen tobe the vendor-supplied accuracies for the retardances of thedevices of
50 nm for the FLCs and for the retarder.For the orientation we assume an error of up to 1 degree.Experience has shown that alignment of the optics with thisaccuracy is possible by hand with a simple lab setup. Theswitching angle of the FLCs is assumed to be 45 degrees withinsignificant error. FLCs typically have large manufacturingerrors in their retardances. Since as-built retardances will beknown prior to assembly of the modulator, the tolerancing HE CRISP P
OLYCHROMATIC M ODULATOR . and . waves, and aretarder with a value of . waves, at the reference wave-length of
665 nm . The tolerancing procedure would then re-optimize the modulator design to find optimal angles of . and . ◦ for the second FLC and the retarder. Then, theprocedure will perturb all the angles to account for mountingerrors, to, say, − . , . , and . ◦ , and finally calculatethe efficiencies of this modulator realization.The resulting expected modulator performance is shown inFigs. 1 and 2. An even better result can be achieved by re-optimizing the retardances of the fixed retarders in addition tothe orientations after the as-built FLC retardances are known.This was not pursued for the CRISP modulator due to timeconstraints, and because the design is shown to be tolerant toexpected manufacturing errors.Figures 1 and 2 show that both designs are well-behaved.The nominal FRFR design exhibits better overall perfor-mance than the FFR design, which is not surprising in viewof its higher number of degrees of freedom. The toleranceanalysis shows that the FRFR design is considerably less re-sistant to manufacturing errors than the FFR design, partic-ularly in (cid:15) V between 500 and 800 nm. We show this designhere to demonstrate the importance of performing a toleranceanalysis. It is possible to find other FRFR designs that haveslightly worse performance, but are more robust against man-ufacturing errors. However, the FFR design performs verywell over this wavelength range and has the benefit of oneless component, and thus results in a thinner stack of opticswith fewer interfaces. In our case, we select the FFR designprimarily because the modulator must fit in a tight space inthe existing CRISP optical setup.There is considerable freedom to pick a reference wave-length. Our experience has shown that a wavelength at orslightly below the middle of the operational range is a goodchoice for practical reasons. Here, we picked
665 nm , alsobecause the program chooses to use FLCs with retardancesthat are equal to λ/ and λ/ at that wavelength within themargin of error. We fix these components at those valuesout of convenience and optimize the fixed retarder and com-ponent orientations. We find that the orientation of the 2ndFLC does not change. The fixed retarder value and orienta-tion change slightly to . λ and . .FLCs with these specifications were procured from CitizenFinetech Miyota. The FLC used in these devices is MX8068.A polycarbonate retarder was procured from MeadowlarkOptics. THERMAL ANALYSIS . . . . (cid:15) I . . . . (cid:15) Q . . . . (cid:15) U
500 600 700 800 900 λ [nm]0 . . . . (cid:15) V Figure 1.
Theoretical I , Q , U , and V efficiencies with tolerancesfor the FRFR design. Solid curves: design performance of the mod-ulator as a function of wavelength. Horizontal dotted lines: theoreti-cal efficiencies for a perfectly balanced and optimally efficient mod-ulator. Vertical dashed lines: lower and upper bound of the designwavelength range. The grayscale background shows the expectedspread of performance as a result of component and constructiontolerances. The switching angle of FLCs is somewhat sensitive to tem-perature. Gisler et al. (2003) measured it as a function oftemperature and found a mostly linear relationship with a co-efficient of − . ◦ / K . This coefficient is specific to the FLC.Gisler (2005) shows an example measurement with a coeffi-cient of − . ◦ / K . For this analysis we use the larger, moreconservative value.We evaluate the effect of temperature change of the mod-ulator following a procedure similar to Lites & Ichimoto(2013). We follow the notation of del Toro Iniesta & Col-lados (2000) and refer the reader to that work for a rigorousmathematical treatment of polarimetric measurements. TheStokes vector S is modulated into a vector of intensities I .The modulation can be described by a modulation matrix O , I = O S . (1) D E W IJN ET AL . . . . . (cid:15) I . . . . (cid:15) Q . . . . (cid:15) U
500 600 700 800 900 λ [nm]0 . . . . (cid:15) V Figure 2.
Theoretical I , Q , U , and V efficiencies with tolerancesfor the FFR design in the same format as Fig. 1 A demodulation matrix D is used to recover the Stokes vec-tor, S = D I . (2)A difference in temperature of the modulator during observa-tions and calibrations will result in a mismatch of the mod-ulation and demodulation matrices. We denote with O (cid:48) and D (cid:48) the modulation and demodulation matrices derived fromthe calibration, and with S (cid:48) the inferred Stokes vector, S (cid:48) = D (cid:48) I . (3)We can then relate the inferred Stokes vector S (cid:48) and the realStokes vector S through an error matrix, S = X S (cid:48) . (4)It is easy to see that we now have X D (cid:48) = D , (5)and using D (cid:48) O (cid:48) = I we find X = D O (cid:48) . (6)For our error analysis, we can calculate the modulation ma-trix O (cid:48) from the unperturbed design, and demodulation ma-trices D for several switching angles to determine the per-missible change in temperature. . . . I Q U V . . . Q . . . U
600 800Wavelength [nm]0 . . . V
600 800Wavelength [nm] 600 800Wavelength [nm]
Figure 3.
The | X − I | matrix elements for the error introduced by . change in temperature assuming a − . ◦ / K coefficient forthe switching angle of the FLCs. The first column of the matrix isomitted because it is identically . Gray areas are outside the limitsgiven in Eq. 7. Limits must be imposed on every element of the matrix X .The diagonal elements represent a scale error that is muchless sensitive than crosstalk errors. The scaling on I is uncon-strained after normalizing S by I . Furthermore, the elementsin the Q and U columns can be scaled by the maximum ex-pected linear polarization signal, and those in the V columncan be scaled by the maximum expected circular polarizationsignal. We follow Ichimoto et al. (2008) and adopt maximaof e = 0 . of I for the crosstalk error between Stokes Q , U , and V , a = 0 . for scale error, p l = 15% of I for lin-ear polarization, and p v = 20% of I for circular polarization.We then find | X − I | ≤ .
333 0 .
333 0 . .
001 0 .
050 0 .
007 0 . .
001 0 .
007 0 .
050 0 . .
001 0 .
007 0 .
007 0 . , (7)where, e.g., the second and third element of the top row aregiven by the ratio a/p l , and the second and third element ofthe last column are given by the ratio e/p v . HE CRISP P
OLYCHROMATIC M ODULATOR Figure 4.
A cross-section view of the modulator with major com-ponents labeled. Optical components are shown in dark blue: 1. en-trance window; 2. FLC 1; 3. FLC 2; 4. fixed retarder; and 5. exitwindow. The mechanical assembly is color-coded by its major com-ponents: 6. pressure plate (dark green); 7. oven (gray); 8. optic hold-ers (yellow); 9. inner mount assembly (light green); and 10. Delrinshell (light blue). See the text for details on the mechanical design.
Figure 3 shows the X − I matrix elements for the error in-troduced by the change in switching angle for a . changein temperature. The Q -to- U term is the worst offender and isjust below the limit at
500 nm .There are other contributors to X than changes in switch-ing angle with temperature. E.g., the retardances of the FLCsand the retarder also have a small temperature dependence.The polarimetric calibration procedure also has a finite accu-racy (van Noort & Rouppe van der Voort 2008). We do notexplicitly model these effects here, since the switching angleis expected to be the dominant source of error. For example,polycarbonate retarders have typical temperature coefficientsaround . / nm / K , and a change in temperature isrequired to exceed the permissible error. Instead we assign afraction of the permissible error to changes in switching an-gle and set the requirement for thermal stability to ± . . OPTO-MECHANICAL DESIGNFigure 4 shows a cross-section of the modulator. The me-chanical design borrows heavily from the HAO Lyot filter de-signs used in the CoMP, CoMP-S, SCD, and ChroMag instru-ments. The modulator optics are glued into mounts that allowthe optic to be oriented to any angle using a RTV silicone.The mounts consist of two parts. The inner part is round andholds the optic. It can be oriented to the desired angle andglued to the hexagonal outer part that is indexed to the innermount assembly. The optics stack is assembled between par-allel windows using index-matching gel. The windows reston O-rings in their mounts. The entrance window mount isspring-loaded against the inner mount assembly with 4.4 N.The inner mount assembly is inserted in an oven consistingof an aluminum tube with a silicone rubber heater elementand aerogel insulation wrapped around it. An off-the-shelfprecision temperature controller is used to stabilize the ovento . ◦ C to better than . ◦ C. The modulator is encased in a Delrin housing. Electrical connections for the FLCs and theheater system are routed to two D-subminiature connectorson the housing.A custom controller based on an Arduino Uno micro-controller board was built to drive the FLCs. The cam-era software sends a voltage sequence to the controller viaa serial interface, which is preloaded into two Burr-BrownDAC714 digital-to-analog converters (DACs). A synchro-nization pulse is then used to update the voltages when thechopper that controls the exposure of the cameras is closed.The FLCs are primarily capacitive loads, with capacitance ofabout
80 nF . The DACs are capable of driving , whichis more than adequate to drive the FLCs between states inunder a millisecond. The controller also resets the voltageto zero after a few seconds of inactivity as a safety featurebecause the FLCs may be damaged if driven by a constantvoltage for a prolonged period of time. PERFORMANCEThe components of the modulator must be accuratelyaligned to ensure proper functioning of the assembled de-vice. HAO has a facility Lab Spectropolarimeter (LSPM)test setup for polarimetric characterization of optics that wasused to test components of the CRISP modulator after theywere mounted.The LSPM consists of relay optics that feed light from ahalogen bulb through, in order, a calibration package thatconsists of a polarizer and a retarder in individual rotationstages, the sample under test, and a polychromatic polariza-tion modulator and analyzer, into an Ocean Optics USB4000fiber-fed spectrograph. This setup allows for characteriza-tion of the full Mueller matrix of the sample as a function ofwavelength. The spectrograph covers the wavelength rangefrom about nm to about nm, though signal levelsare low under nm.We solve for retardance and fast axis position of a linear re-tarder that matches the Mueller matrices derived from LSPMmeasurements as a function of wavelength. Figure 5 showsthe results for the three CRISP modulator components. Thefigure also shows the design retardances and fast axis posi-tions. The λ/ and λ/ FLCs have measured retardances of . λ and . λ at
665 nm , and mean switching angles of . ◦ and . ◦ . The fixed retarder is measured at . λ .All three components show a curious increase in the fast axisposition at the shortest wavelengths. However, the signallevel is low, and it may be that the effect is the result of sys-tematic errors in the measurement.As discussed in Sect. 2, we can re-optimize the design withthese values. However, we made our measurements at roomtemperature. The measurement should have been performedat the operating temperature of ◦ C because component re-tardance has some temperature dependence. Using the re- D E W IJN ET AL . − − A x i s A n g l e s [ d e g ] A x i s A n g l e s [ d e g ]
500 600 700 800 900Wavelength [nm]108 . . . . . A x i s A n g l e [ d e g ] . . . . . R e t a r d a n ce [ w a v e s ] . . . . R e t a r d a n ce [ w a v e s ] . . . . R e t a r d a n ce [ w a v e s ] Figure 5.
Solid lines: retardances (orange) and fast axis positions(blue) of the -wave FLC (top panel), the -wave FLC (middlepanel), and the retarder (bottom panel), as determined by a fit to theMueller matrix inferred from LSPM measurements at room tem-perature. The panels for the FLCs show two fast axis positions for ± drive voltages. Dashed lines: fast axis bisector. Dotted lines:design retardances and fast axis positions. In these measurementsthe signal level drops below acceptable levels around
550 nm . tardance values at room temperature we find fast axis an-gles for the 2nd FLC and the fixed retarder are . and . . However, if we assume the retarder will haveits design retardance at ◦ C , the fast axis positions revertto the nominal design. The FLC switching angles are largerthan the nominal ◦ design, but also expected to decrease ata higher operating temperature, possibly to angles below ◦ (Gisler et al. 2003; Gisler 2005). We choose not to change themodulator design because of the unknown effect of tempera-ture on the component retardance and FLC switching angle,and because only marginal improvement of performance isexpected.The modulator was first assembled with air gaps, and oncethe proper relative alignment of the components was con-firmed using the LSPM, the modulator was assembled in itshousing using Nye OCF-452 optical coupling fluid on theglass interfaces. The purpose of the coupling fluid is to re-duce internal Fresnel reflections between the surfaces of the . . . . (cid:15) I . . . . (cid:15) Q . . . . (cid:15) U . . . . (cid:15) V
500 600 700 800 900Wavelength [nm]0 . . . . (cid:15) Q U V Figure 6.
Modulation efficiencies of the modulator. The top fourpanels shows the efficiency in Stokes I , Q , U , and V . The bot-tom panel shows the RSS of the efficiencies in Stokes Q , U , and V .Solid black lines: modulation efficiencies of the assembled modula-tor measured with the LSPM. Solid green lines: design efficiencies.Solid orange lines: modulation efficiencies expected from the mea-surements in Fig. 5. Blue crosses and diamonds: modulation effi-ciencies measured at the telescope in the transmitted and reflectedbeams, resp. The horizontal dotted line in each panel shows thetheoretical maximum efficiency for a balanced modulation scheme. optics. Nye OCF-452 was used because it has a refractive in-dex that is well-matched to the Corning XG glass of the FLCsand the BK7 glass of the retarder and windows. Internal Fres-nel reflections at the optical interfaces of the components arelimited to below the × − level.The fully assembled modulator was brought to operatingtemperature and tested again on the LSPM. The LSPM pro-duces measurements of the Mueller matrix of the modulatorin each of its 4 states. We simulate a perfect analyzer in Q to calculate modulation efficiencies, shown as a function ofwavelength in Fig. 6. HE CRISP P
OLYCHROMATIC M ODULATOR ◦ switching angle. In reality, thecomponents have imperfections such as chromatic variationof the fast axis, and the actual dispersion of birefringence isdifferent from the model. This can be seen in Fig. 5. Thesolid blue lines are not horizontal, and the solid and dottedorange lines are not parallel. The FLC switching angle isalso not exactly ◦ . Lastly, bulk rotational alignment of themodulator to the analyzer was not included in the analysis.The efficiencies of some modulator designs, in particular thetraditional rotating retarder, are invariant under rotation ofthe modulator with respect to the analyzer. This design is notinvariant, and rotation of the modulator results in depressedefficiencies.Figure 6 also shows the modulation efficiencies computedfrom the Mueller matrices of the measured components inorange. They show good agreement with the measured effi-ciencies of the assembled modulator. We attribute the differ-ences mostly to the components not being measured at oper-ating temperature. There are also likely small differences inthe relative orientation of the components in the assembledmodulator compared to the individual measurements.The CRISP instrument is intended for high-resolutionimaging. The modulator, therefore, must have low trans-mitted wavefront distortion (TWD). Because the internal op-tics are coupled using an index-matching gel, the TWD isdominated by the by the entrance and exit windows. Fortu-nately, excellent quality windows are inexpensive and com-monly available. The TWD of the assembled modulator wasmeasured using a Zygo interferometer. It was found to be .
20 waves at
632 nm
RMS over the clear aperture afterremoval of the tilt component, but including .
14 waves ofpower that introduces primarily a shift in focus position.The modulator was installed at the SST in October 2014.CRISP uses a polarizing beamsplitter to analyze the polar-ization signal in two orthogonal directions simultaneously(de la Cruz Rodr´ıguez et al. 2015). This kind of setup isknown as a dual-beam polarimeter and allows for the re-moval of crosstalk resulting from atmospheric seeing fromStokes I to Stokes Q , U , and V (Casini et al. 2012a). Mea-sured modulation efficiency averaged over the field of viewfor the transmitted and reflected beams at five wavelengthscommonly used for solar polarimetry are given in Table 2and also shown in Fig. 6 as blue crosses and diamonds. Table 2.
Modulation efficiencies measured at the telescope aver-aged over the field of view.Wavelength (cid:15) I (cid:15) Q (cid:15) U (cid:15) V (cid:15) QUV
Transmitted . .
992 0 .
500 0 .
588 0 .
560 0 . . .
996 0 .
573 0 .
591 0 .
539 0 . . .
991 0 .
506 0 .
608 0 .
554 0 . . .
993 0 .
576 0 .
579 0 .
536 0 . . .
933 0 .
570 0 .
504 0 .
501 0 . Reflected . .
988 0 .
485 0 .
572 0 .
543 0 . . .
997 0 .
557 0 .
572 0 .
524 0 . . .
986 0 .
506 0 .
607 0 .
549 0 . . .
994 0 .
576 0 .
579 0 .
530 0 . . .
951 0 .
563 0 .
497 0 .
493 0 . It is not possible to directly compare the efficiencies in theindividual Stokes parameters. The telescope measurementsinclude all the optics on the tables, which include a numberof mirrors and lenses, a dichroic beamsplitter, the CRISP pre-filter, a gray beamsplitter, and the CRISP etalons. These ele-ments cannot be separated from the modulator. The calibra-tion procedure fits all optics on the table between the calibra-tion optics and the polarization analyzer as one modulationmatrix (van Noort & Rouppe van der Voort 2008). In effect,all optical elements between the calibration optics and the po-larimetric analyzer together act as the modulator. There areoblique reflections that may cause some mixing of all Stokesparameters due to retardance of the mirror coatings, and thereference frame of polarization of these measurements is notnormal to the optical table. It is still valuable to compare theperformance in the telescope to the design performance andlab measurements, but this can only be done in an aggregateway, i.e., by comparing the RSS of the efficiencies in Stokes Q , U , and V , (cid:15) QUV = (cid:113) (cid:15) Q + (cid:15) U + (cid:15) V . (8)The overall agreement of the performance in the telescopesetup and the assembled modulator is very good. The largestdifference in the RSS of the efficiencies in Q , U , and V is . in the reflected beam at . .The transmitted and reflected beams show very similar be-havior. The differences in efficiencies between the beams areon the order of a few percent, and may result from differencesin the contrast of the polarizing beamsplitter in the transmit-ted and reflected beams, or from polarizing components inthe telescope such as the wide-band beamsplitter that has ahighly uneven ratio of the transmitted and reflected light.The overall performance is excellent with the lowest effi-ciencies only slightly below (cf. the optimum and bal- D E W IJN ET AL .anced efficiency of . ). The RSS of the efficiencies inStokes Q , U , and V are , , , , and forthese 5 wavelengths. CONCLUSIONThe trade-offs and procedures described in this paperwere employed to design the polarimetric modulator for theCRISP instrument, but can be applied to the design of modu-lators for other instruments. We chose to omit some steps thatcould result in somewhat improved performance of the mod-ulator. If schedule permits, it is possible to incrementally op-timize the design with measured optic properties. We couldhave delayed the purchase of the retarder until the FLCs,which have the largest errors, had been characterized at op-erating temperature, so that the value of the retarder couldhave been optimized for the as-built FLCs. While this de-sign with only three components is robust, such incrementalre-optimization may be necessary to guarantee acceptable ef-ficiencies for modulator designs with more optical elementsthat cover larger wavelength ranges (Snik et al. 2012).We did not specifically consider polarized spectral“fringes” in our design process. A description of polarizedspectral fringes can be found in reviews by Lites (1991),Semel (2003), and Clarke (2004). They are interference pat-terns that are produced by reflections between parallel sur-faces in a system with polarization optics, such as the compo-nents of the modulator, that are difficult to characterize (Har-rington et al. 2017) and remove (Rojo & Harrington 2006;Casini et al. 2012b; Casini & Li 2019). Snik et al. (2015) op-timized components to suppress polarized fringes for theirapplication by ensuring that the periods of the fringes aremuch smaller than the spectral resolution of their instrument.This approach cannot be applied in modulators using FLCs(or LCVRs) because the FLC layer thickness that determinesthe period of the fringes is set by the required retardance.Because the FLC layer is very thin, fringes caused by re-flections at the FLC-glass interfaces have periods of ten ormore of nanometers (Gisler et al. 2003), i.e., much larger thanthe CRISP bandpass of less than ten picometers (Scharmeret al. 2008). These fringes will consequently be relativelystable over the CRISP bandpass and therefore will be nearlycompletely removed in the polarimetric calibration. Fringescaused by reflections between surfaces at larger optical dis-tance have smaller periods and can be a problem. For those,the only available option is to reduce the amplitude of fringesby reducing the amplitude of Fresnel reflections from the in-terfaces of the optical elements. The use of optical couplingfluid is therefore not only required to address etaloning, butalso to suppress these fringes.The polarimetric modulator described here has been in usefor science observations at the SST starting with the 2015observing season. Example data of a sunspot are shown in Fig. 7. The data reduction procedures are described in de-tail by de la Cruz Rodr´ıguez et al. (2015) and L¨ofdahl et al.(2018). These data can be fit using forward-modeling proce-dures to derive quantitative measures of atmospheric param-eters, most notably the strength and direction of magneticfield. For example, Kuridze et al. (2018) studied the struc-ture and evolution of temperature and magnetic field in a flar-ing active region using full-Stokes CRISP observations in theCa II line at . , Vissers et al. (2019) used similar datain combination with data from the IRIS mission (De Pontieuet al. 2014) to study Ellerman bombs and UV bursts, Vis-sers et al. (2020) inferred the photopheric and chromosphericmagnetic field vector in a flare target and studied their differ-ences, Libbrecht et al. (2019) used CRISP observations in theHe I D line in a study of a flare, Morosin et al. (2020) andPietrow et al. (2020) studied chromospheric magnetic fieldsin plage targets and estimated a canopy mean field strengthof
400 G in the chromosphere, and Joshi et al. (2020) studiedvery small-scale reconnection in the solar photosphere usingCRISP polarimetry and CHROMIS (Scharmer et al. 2019)observations in H β .Figure 8 shows a region of quiet sun with the line-of-sight component of the magnetic field inferred from full-Stokes observations of the Fe I . line profile using aspatially-regularized Milne-Eddington inversion method (dela Cruz Rodr´ıguez 2019). This example highlights the powerof CRISP combined with this modulator. Quiet-sun magneticfields are weak and difficult to detect. Telescopes and in-struments that achieve high spatial resolution, have adequatespectral resolving power, and have high system efficiency arerequired to study them. We refer the interested reader to Bel-lot Rubio & Orozco Su´arez (2019) for a comprehensive re-view of observations of quiet-sun magnetic field.The high throughput and efficiency of CRISP with thismodulator also enables observations in many lines with po-larimetry while maintaining sufficient cadence for studies ofdynamic events. Such multi-line observations were used byLeenaarts et al. (2018) in a study of chromospheric heatingin an emerging flux region. They used the STiC code (de laCruz Rodr´ıguez et al. 2019) to simultaneously interpret thesignals from several lines. Esteban Pozuelo et al. (2019) usedthe same code in a similar way to study penumbral microjets. HE CRISP P
OLYCHROMATIC M ODULATOR x [arcsec] y [ a r cs e c ] I x [arcsec]Q x [arcsec]U x [arcsec]V − − λ − λ [ ˚A] I − − λ − λ [ ˚A] − Q − − λ − λ [ ˚A] − U − − λ − λ [ ˚A] − V Figure 7.
Example spectro-polarimetric data of AR12471 in the Fe I lines at . . The observation was recorded on 2019-05-10 around09:10 UT. Top row: images of the Stokes parameter in the blue wing of the .
25 nm line at −
90 mA from line center. Spectra at the black,red, and blue crosses are shown in the bottom row. The locations of the spectral sampling are indicated by crosses.
ACKNOWLEDGMENTSWe acknowledge R. Casini for the development of thecodes used for optimization and tolerancing of the modu-lator designs. This material is based upon work supportedby the National Center for Atmospheric Research, which isa major facility sponsored by the National Science Founda-tion under Cooperative Agreement No. 1852977. CRISPand the modulator were funded by the Marianne and Mar-cus Wallenberg Foundation. This research has made use ofNASA’s Astrophysics Data System, NumPy (van der Waltet al. 2011), matplotlib, a Python library for publication qual-ity graphics (Hunter 2007), Astropy, a community-developedcore Python package for Astronomy (Astropy Collaborationet al. 2018, 2013), and the IPython package (Perez & Granger2007). The acknowledgements were compiled using the As-tronomy Acknowledgement Generator.REFERENCES
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