7. Results for Residual-Seeing Case · 2020. 1. 22. · Instrument Slit Slit FPI FPI Modulation...

Detection of polarized light with ATST

7. Results for Residual-Seeing Case

In the following we introduce the effects of seeing and the correction thereof by a simulated adaptive opticssystem (as described in Sect. 5.). We do so by convolving the Stokes signals with different PSFs generatedbased on the simulated phase screens (see Sect. 5.3). How is this convolution performed? Obviously, thedifferent modulation schemes and the different instrumentapproaches (slit/grating based or two-dimensionaltuning, different number of accumulations, integrations times) will now play a mayor role.

For a slit based instrument, all wavelength points are detected instantly and time is encoded in one ofthe spatial dimensions (slit position, scan direction) andin each individual modulation state that adds to theoverall accumulation. Therefore, we have to convolve each of those modulation states at a particular slitposition with an individual PSF.

For a two-dimensional tunable filter polarimeter, both spatial dimensions are detected instantly and timeis encoded in the wavelength position (scan direction) and in each individual modulation state that adds tothe overall accumulation at that particular wavelength position. Therefore, we have to convolve each ofthose modulation states at a particular wavelength position with an individual PSF.

In order to somewhow restrict the number of possible calculations, we decided to concentrate first onthe following applications:

• Slit-based spectropolarimeter:

1. Continuously rotating retarder at the GOS and in the Coud´e laboratory with 16 mixed modula-tion states per full revolution, an exposure time of 10 ms and32 accumulations. In this case, weneed 16×32= 512 10 ms PSFs per slit position.

2. Switching LCVRs in the Coude laboratory with 4 mixed modulation states, an exposure time of100 ms and no accumulations. In this case, we need four 100 ms PSFs per slit position.

• Two-dimensional tunable filter polarimeter:

1. Switching LCVRs in the Coude laboratory with 6 defined modulation states, 71 wavelengthpoints, an exposure time of 33 ms, and no accumulations. In this case, we need 6× 71= 42633 ms PSFs per wavelength scan.

2. Switching LCVRs in the Coude laboratory with 4 mixed modulation states, 71 wavelengthpoints, an exposure time of 33 ms and no accumulations. In this case, we need 4× 71= 28433 ms PSFs per wavelength scan.

Before we start to look at the results of those modeling experiments, we would like to demonstrate whyit was so important and in fact crucial to include realistic (and controlled) variations of the Fried parameterr0 and the consequential variations of the Strehl value achieved by the AO system in the generation of theevolving phase screens. In Fig. 27 we display the individualStokes profiles of the FeI 630.25 nm lineat P2 along slit#2 for a different number of accumulations (32,16,8,4,colored) achieved with a rotatingretarder placed at the GOS when seeing and AO correction is included. The individual PFSs that wereused for the convolution are representative for a 10 ms exposure time. Although the PSFs are intrinsicallydifferent, they are characterized in a statistical sense bythe same Fried parameterr0 which was about10 cm. As can be easily seen, the shapes of the output spectralprofiles are completely independent from thenumber of accumulations applied, all spectral profiles overlap contradicting practical experience. Typically,increasing the number of accumulations and using exposure times that are comparable to or longer than theatmospheric correlation time at the observed wavelength compromises spatial resolution and thus shouldlead to significant visible changes in the spectral profiles.Figure 28 shows the same spectral profiles wheneither much longer exposure times (100 ms, 500 ms) and no accumulations are used or the same 10 ms PSFis applied during all of the 32 accumulations. Again, all spectral profiles overlap.

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Figure 27: Individual Stokes profiles of the FeI 630.25 nm line at P2 along slit#2 for different number ofaccumulations (32,16,8,4,colored) with varying 10 ms PSFs. Seeing and AO correction included.Black:original profile. Modulation performed at the GOS.From left to right: StokesI, StokesQ/I, StokesU/IandStokesV/I. Calculations are for hour angle of 0◦.


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Figure 28: Individual Stokes profiles of the FeI 630.25 nm line at P2 along slit#2 for different exposure timesand accumulations. Seeing and AO correction included.Black: original profile.Purple: 32 accumulationswith varying 10 ms PSFs.Blue: 32 accumulations with using the identical 10 ms PSF (no. 100). Green: 1accumulation with varying 100 ms PSFs.Orange: 1 accumulation with varying 500 ms PSFs. Modulationperformed at the GOS.From left to right: StokesI, StokesQ/I, StokesU/Iand StokesV/I. Calculationsare for hour angle of 0◦.


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Figure 29: Individual output Stokes profiles of the FeI 630.25 nm line at P2 along slit#2 for different Strehlvalues using 1 accumulation.Black: original profile.Purple: varying bewteen 0.1–0.9 Strehl.Blue: Strehlof 0.1 using 5 realizations.Green: Strehl of 0.5 using 5 realizations.Orange: Strehl 0.9 using 5 realizations.Red: Original synthesized input spectra convolved with one 10 ms PSF. Modulation performed at the GOS.From left to right: StokesI, StokesQ/I, StokesU/Iand StokesV/I. Calculations are for an hour angle of0◦.

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Instrument Slit Slit FPI FPIModulation states 16 mixed 4 mixed 4 mixed 6 definedModulation mechanism Rotating retarder LCVRs LCVRs LCVRsModulation location GOS/Coude Coude Coude CoudeExposure time [ms] 10 100 33 33Accumulation [number] 32 1 1 1PSFs [number] 512 4 284 426Acquisition time/slit, scan [sec] 5.12 0.4 9.370 14.058Wavelength points [number] 71 71 71 71Start 1 (s1) purple 0.132 0.147 0.123 0.102

0.814 0.871 0.802 0.714Start 2 (s2) blue 0.109 0.096 0.115 0.092

0.781 0.748 0.785 0.672Start 3 (s3) green 0.051 0.081 0.096 0.077

0.474 0.676 0.707 0.593Start 4 (s4) orange 0.046 0.067 0.083 0.067

0.357 0.741 0.644 0.518Start 5 (s5) red 0.069 0.009 0.079 0.066

0.497 0.0006 0.617 0.516

Table 1: Overview of modeled scenarios. For each of the different starting points the upper and lowervalues in each column refer to the average Fried parameterr0 (given in [m]) and the average Strehl value,respectively, calculated over the duration of the data acquistion. The different starting points s1 to s5 areindicated byvertical red linesin Fig. 6.

It is/was very suspicious, that the application of one PSF (over and over again) already leads to the strongdeformation of the StokesI signal. Particularly from this we take that the Strehl valueachieved by the AOmust have been rather low (and obviously consistantly low).We concluded that the generated residualphase screens were not realistic enough since they did not reflect variations of the Strehl as a consequenceof largerr0 fluctuations during modulation and detection (or acquisition) of the Stokes parameters. Figure 29demonstrates the effect of PSFs that reflect Strehl variations between 0.1 and 0.9 for different situations. Asexpected, now the profiles change significantly as expected.For a very good Strehl value of 0.9 the outputStokesI signal starts to resemble the original input StokesI profile, while for a very low Strehl value of 0.1,the StokesI profile appears very deformed as we argued before.

We come now to the results of the actual modeling approach which we have limited to the applicationsmentioned above. First, it seems most interesting to compare the output Stokes parameters when differentinstrument approaches are taken for different conditions of seeing and efficiencies of AO correction (seeSect. 5.3 and Fig. 6). Since the individual approaches implydifferent exposure times and different periods oftime to acquire the output Stokes data we have to be careful when comparing results that are obtained underdifferent seeing conditions and AO correction efficiencies(Stehl values) as visualized in Fig. 6. Therefore,the following assumption is made: all instruments start at the same time but are not synchronized. We chose5 different starting points that are indicated in Fig. 6 (s1 to s5,vertical red lines). Table 1 gives detailedinformation about those starting points and the instrumentspecifics. Furthermore, Fig. 84 through Fig.??in Sect. C in the appendix visualize the starting points and sequence length of the data acquistion directlycompared to the seeing and AO correction conditions.

Figures 30 and 31 give a first impression of those differenceswhen different instrument approaches aretaken during the observing process. We depict two differentsituations: one where the StokesV/I signal is

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Figure 30: Individual Stokes profiles of the FeI 630.25 nm line at P2 along slit#2 for different instrumentapproaches, modulation location, modulation schemes, andaccumulations and exposure times. Results forhour angle 0◦. Left to right: StokesI, Q/I, U/I andV/I. Dotted: reference profiles when no seeing andAO correction is included.Black: original input Stokes signal.Red: Modulation performed at the GOS.Purple: Modulation performed in the Coude laboratory. Seeing andAO correction is included. The seeingsample corresponds to conditions prevailing for starting point s1. No calibration is applied to the outputStokes signals.

large when compared to StokesQ/I andU/I corresponding to position P2 along slit#2 (Fig. 30), and onewhere the StokesV/I signal is comparable to StokesQ/I andU/I which corresponds to position P3 alongslit#2 (Fig. 31). correspond to very good seeing conditionsand high correction efficiencies reflected in largeStrehl values achieved by the simulated AO system (startingpoint s1). At this point, the Stokes profiles arenot calibrated or corrected for any crosstalk introduced bythe optics and the modulation location.

The differences we see are not un-expected. In general the seeing and AO correction appears to bevery efficient and residual seeing influences do not terriblydeform the individual StokesQ/I, U/I andV/Iprofiles. This is evident from the direct comparison with theblack dottedprofiles, which are the referenceprofiles and for which no seeing and AO correction is applied.Furthermore, the output Stokes profilesfor the 2D tunable instruments (Fig. 30 and Fig. 31,two lower rows) appearnoisier compared to both slit

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Figure 31: Same as Fig. 30 for spatial position P3 along slit#2 and hour angle 0◦. No calibration is appliedto the output Stokes signals.

applications. This is expected since the wavelength axis isalso the time axis, so different wavelengthsare affected by different seeing and AO correction conditions. Rather remarkable and surprising is thesignificant difference in the StokesI signal in Fig. 30 (first column) when a 4 mixed state modulationscheme and a 6 defined state scheme is used in combination witha 2D tunable instrument: the StokesIprofile deteced using the 4 mixed states scheme does not indicate any line splitting anymore. As we willsee later, this has to do with the very specific seeing conditions prevailing when the different wavelengthsand modulation states are detected. All other differences,when compared to the input Stokes profiles (blacksolid lines), are caused by the modulation location, the optical elements in the light path and the hour angle,which all have been discussed and summarized in Sect. 6..

We will now show how the profiles change when different seeingand AO correction conditions aresampled by varying the starting points. In the following we will show the output representative for hourangle 0◦. The corresponding profiles and there variations for other hour angles (15◦,30◦,45◦,60◦,75◦) can befound in the appendix in Sect.?? (see Fig.?? to Fig.?? and Fig.?? to Fig.??). Figure 32 and Fig. 33 showthe results for the two spatial positions P2 and P3 along slit#2. From those figures it is very obvious thatwhat is detected depends very much on how (and when) the different modulation states are exposed to the

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Figure 32: Same as Fig. 30 for different starting points s1 tos5 (different seeing samples, color coded) asdescribed in Table 1. Results correspond to hour angle 0◦. Dashed and dashed-dotted: Reference profileswith no seeing and AO correction applied.Black solid: input Stokes parameters.Dotted: Modulation at theGOS.Solid: Modulation in the Coude laboratory.

varying seeing samples and if accumulations have been used.When inspecting the spectral profiles only thesmoothest results are achieved consistently with the slit instrument in combination with a rotating retarder(16 mixed states, 10 ms short exposures, 32 accumulations) or two LCVRs (4 mixed states, 100 ms longexposures, no accumulations). However, for the worst seeing sample (red lines) the StokesI signal whensplitted (position P2, Fig. 32) for the long exposure 4 mixedstates application is significantly different, evenwhen compared with the 2D tunable applications: the profile is completely smeared out. This smearingseems to be unrelated to the actual spatial position and its direct environment. All spectra along slit#2 (notshown) (for that specific instrument application) are almost equally smeared, no spatial and spectral shapevariations are present. This is also valid for the corresponding Q, U andV profiles. We mostly recognizeStokesV shapes at all slit positions. The results for the other instrument applications are comparable anddepend rather on whether the input StokesV signal is stronger or rather comparable to the input StokesQand StokesU signals. In this context it is important to remember that theV → Q andV →U crosstalk is ofdifferent strength depending on the modulation location and varies with the hour angle. We see this reflected

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Figure 33: Same as Fig. 32 for spatial position P3 along slit#2. Results correspond to hour angle 0◦.

in the behavior of the StokesQ andU profiles of Fig. 32 and Fig. 33 when either the 2D tunable or theslitwith a rotating retarder approach is followed and the modulation is performed at the GOS or down in theCoude laboratoty. Please note, that depending on the time during the day (meaning the hour angle) also signchanges of StokesQ andU are involved, as can be clearly seen in Fig. 33 when theblack solid (originalinput signal) and thedashed and dashed-dotted(reference profiles) lines are compared.

At first sight, it appears surprising how well the 2D tunable applications behave. Depending on thestarting points we note slight differences in the profile shapes, which must result from the use of differentmodulation schemes and how they sample the seeing and AO correction conditions in a different way.However, based on the profiles presented so far there does notseem to be a very clear preference or tendencythat either the 4 mixed states modulation scheme or the 6 defined states scheme behaves more favourable.This will be further discussed in the next Section (Sect. 7.1).

In order to completely separate the influence of seeing and AOcompensation from the location of themodulation, the telescope, and the data acquisition using different instrument approaches, we will have totake out the latter influences of the output Stokes data. To this end we perform aperfect correction for thoseinfluences by applying the inverse of the corresponding influence matrices and telescope matrix (compareSect.??).

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Figure 34: Same as Fig. 32 after a perfect calibration applied.

7.1 Residual Crosstalk after a perfect Calibration

The important question now is: what is the source of the remaining differences, i.e., is there crosstalk leftthat can solely be ascribed to residual seeing present in theperfectly calibrated output Stokes signals? Torespond to and hopefully answer this question we revert again to scatter diagrams as a diagnostic tool as usedin Sect. 6.1 and Sect. 6.2. In this context, we try to rememberthat both, crosstalk from intensity into thepolarization states (I → Q,U,V ) and crosstalk amongst the polarization states (V ↔Q,U ), shows up in thosescatter diagrams in a very characteristic and distinct way.The intensity crosstalkI → Q,U,V manifests itselfas a vertical up- or down shift of the scatter pattern, while the polarized cross talkV ↔ Q,U, shows up as asystematic (linear) correlation of data points, manifested in a rotation of the scatter pattern w.r.t. the scatterpattern generated by the original input Stokes signal. The rotation angle depends on the time during the daywhen the data is acquired, i.e., the hour angle, because of the different amounts of instrumental crosstalkintroduced. However, after a perfect calibration this timedependence on the hour angle is taken out andany systematic detectable correlation between the Stokes parameters can only come from the influence ofresidual seeing variations.

Prior to showing and analyzing the scatter diagrams, Fig. 34and Fig. 35 visualize what the output Stokesparameters after a perfect calibration actually look like.Those Figures are basically identical to Fig. 32 and

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Figure 35: Same as Fig. 34 for spatial position P3 along slit#2.

Fig. 33 except for that the inverse of the corresponding influence matrices (MXGOS andMX

Coude, introduced inSect. 4.4) and the Mueller matrix of the telescope (MM1+M2) has been applied.

In general, the smoothest and most consistent results even when seeing conditions are variable and poorare achieved with the slit instrument in combination with short exposures (10 ms) and significant accumu-lations (upper panel). At first sight, it is surprising how poor the slit instrument using 4 mixed states, longexposures and no accumulations recovers the StokesQ signal when the input StokesV signal has been large(∼ 60%) and the linear polarization signals are very small (≤ 1%) (see Fig. 34,second panel top down). Inorder to understand why the starting points s5 and s4 (red, orange lines) behave so well in combination withthe 2D tunable instruments we have to look at Fig. 86 and Fig. 87 in Sect. C in the appendix. The sequencelength of a 2D tunable filter is usually much longer than compared to a slit instrument where all wavelengthsare detected at once instead of scanned in time. In our application we did not reduce the number of wave-length points to increase the cadence but rather keep the same spectral resolution as achieved with the slitinstruments. That does not necessarily reflect what is done in practice but makes a comparison of the resultsmuch easier. When inspecting Fig. 86 and Fig. 87 we realize that because of the sequence length the seeingsample s4 and s5 now cover considerably good and excellent conditions because we had towrap the 33 msPSFs and start from the beginning (s1) (because the AO simulation is only 25 ms long which obviously is

49


Instrument Slit Slit FPI FPIModulation states 16 mixed 4 mixed 4 mixed 6 definedModulation mechanism Rotating retarder LCVRs LCVRs LCVRsModulation location GOS/Coude Coude Coude CoudeExposure time [ms] 0.5/33/100 0.5/33/100 0.5/10 0.5/10Accumulation [number] 640/10/3 2560/40/13 66/3 66/3PSFs [number] 10240/160/48 10240/160/52 18744/852 28116/1278Acquisition time/slit, scan [sec] 5.12/5.12/5.12 5.12/5.12/5.12 9.372/8.520 12.780/14.058Wavelength points [number] 71 71 71 71

Table 2: Overview of additionally modeled scenarios.

not enough). We also want to note that the 4 mixed states modulation scheme now (clearly) reveals a betterperformance than the 6 defined states modulation scheme.

Figure 36 through Fig. 43 display scatter diagrams to visualize potential systematic correlations and thusdetectable crosstalk that might be still in the output Stokes signals caused by the sole presence of residualseeing. Remembering how the intensity (I →Q,U,V ) and the polarized (V ↔Q,U ) crosstalk manifests itselfin the scatter diagrams, we cannot see any obvious indication or traces of systematic detectable correlationsand , hence, crosstalk in any of the selected instrument applications (except for one, but we will come tothat). Instead, we observe the following:

Intensity crosstalk I → Q,U,V First, we note a characteristic spreading of the data points(coloredpointscompared toblack reference points), which is particularly obvious when looking at the bifurcated areas inthe scatter pattern caused within the spectral line by the StokesV lobes. This spreading basically reflects thatpoints with equal intensity, when compared to the input signal, are mostly moved or spread out to a largerStokesV/I signal. Second, there is no visual evidence of the distinct arrow-like shape distribution left intheQ/I andU/I versus StokesI scatter diagrams. We identified earlier that this pattern isa characteristicsignature ofV ↔ Q,U crosstalk (see Sect. 6.).

Polarized crosstalk V → Q,U We do not find direct and obvious evidence of a detectable sytematic cor-relation between the Stokes signals in the selected instrument applications. A systematic crosstalk fromV → Q,U should show up as a distinct arrow-like shaped pattern in diagrams of StokesQ,U versus StokesI (which it does not), and a systematic correlation of data points that shows up as a rotation against thereference points when StokesV is shown over StokesQ,U (see Sect. 6.) (which is not observed either).However, the lack of such behavior in the scatter diagrams does of course not imply that there are no seeinginfluences present, but rather that the effect of (residual)seeing manifests itself in a different way.

There is one application though that appears to behave slightly different, meaning that is seems tobe susceptible and prone to polarized crosstalk (V ↔ Q,U , see Fig. 39): the slit instrument where longexposure times are used in combination with a 4 mixed state modulation scheme and no accumulations. Inorder to understand this, we computed several additional applications, also to assure that our conclusionsare not scewed or biased by a certain choice of instrument application and configuration to begin with.We also added the special case of an ultra-fast modulation (i.e., ultra-short exposure times) combined withsignificant accumulation which to the addiationally modeled applications. These additional configurationsare summarized in Table 2.

50


Figure 36: Scatter diagrams of the FeI 630.25 nm output Stokes profiles for all spatial positions alongartificial slit#2. Left to right: StokesQ/I, U/I, andV/I versus StokesI. Top to bottom: different startingpoints s1 to s5 (color coded) reflecting different seeing conditions and AO correction efficiencies.Black:input Stokes parameters. Results are displayed for a rotating retarder with a slit instrument, 16 mixed states,10 ms exposures, and 32 accumulations after a perfect calibration is applied.

51


Figure 37: Scatter diagrams of the FeI 630.25 nm output Stokes profiles for all spatial positions alongartificial slit#2 for hour angle 0◦. Left to right: StokesQ/I versusV/I, U/I versusV/I, V/I versusQ/I,andV/I versusU/I. Top to bottom: different starting points s1 to s5 (color coded) reflectingdifferentseeing conditions and AO correction efficiencies.Black: input Stokes parameters. Results are displayedfor a rotating retarder with a slit instrument, 16 mixed states, 10 ms exposures, and 32 accumulations after aperfect calibration is applied.

52


Figure 38: Same as Fig. 36 for two LCVRs with a slit instrument, 4 mixed states, 100 ms exposures, and noaccumulations after a perfect calibration is applied.

53


Figure 39: Same as Fig. 37 for two LCVRs with a slit instrument, 4 mixed states, 100 ms exposures, and noaccumulations after a perfect calibration is applied.

54


Figure 40: Same as Fig. 36 for two LCVRs with a two-dimensional (FPI) instrument, 6 defined states, 33 msexposures, 71 wavelength points and no accumulations aftera perfect calibration is applied.

55


Figure 41: Same as Fig. 37 for two LCVRs with a 2D tunable (FPI)instrument, 6 defined states, 33 msexposures, 71 wavelength points and no accumulations aftera perfect calibration is applied.

56


Figure 42: Same as Fig. 36 for two LCVRs with a two-dimensional (FPI) instrument, 4 mixed states, 33 msexposures, 71 wavelength points and no accumulations aftera perfect calibration is applied.

57


Figure 43: Same as Fig. 37 for two LCVRs with a 2D tunable (FPI)instrument, 4 mixed states, 33 msexposures, 71 wavelength points and no accumulations aftera perfect calibration is applied.

58


Before we go into the details of all those results it is crucial to understand how the individual instruments(could) approach the sequencing of modulation and accumulation. There are several options that in practicemay not be viable because of timing constraints given by the response times of modulation and tuning (atthe present) in combination with how time scales of seeing and AO correction conditions are imposed, butthat are nevertheless very interesting from anacademic point of view. It should be mentioned again that inour modelling approach we neglected the switching and tuning times. The filter tuning times are usuallymuch faster than the liquid crystal switching times (for nematic liquid crystals). Switching times cruciallydepend on the properties of the liquid crystals in use. This was necessary, because the pool of PSFs is verylimited.

Modulation and Accumulation Sequencing For a slit-based instrument operated in combination witha continuously rotating retarder the only reasonable choice is to perform the accumulation after the mod-ulation states have been sequenced, meaning to repeat the sequencing of the modulation statesN times.Otherwise it would be a stepped rotating retarder anyways, asolution that might be slower in general. How-ever, a slit-based instrument with LCVRs has already two options to accumulate the modulation states. Thefirst option is, to accumulate each modulation state individually (accumulation option 1). The second op-tion is to perform the accumulation after the modulation states have been sequenced, meaning to repeat thesequencing of the modulation statesN times (accumulation option 2). For the 2D tunable instruments, thereare more options, because there is another time dependent variable, namely the tuned wavelength. We canimagine two different approaches to go through the modulation sequence for those instruments. The firstoption would be to detect all modulation states at the first wavelength, then at the second, then at the third,and so forth (modulation option 1). The second option would be to detect the first modulation state at allwavelengths, then the second one, then the third one, and so forth (modulation option 2). In practice, thecombination of modulation option 1 and accumulation option2 (VIP/TESOS, GFPI) and the combinationof modulation option 1 and accumulation option 1 (IBIS) are implemented.

In the following we will go through the different applications for the slit-based and the two-dimensionaltunable instruments separately. We will show for those additionally calculated applications in the follow-ing order: sample profiles after a perfect calibration has been applied, differences between the output andthe input Stokes profiles as an indicator of accuracy, scatter diagrams forI → Q,U,V andV → Q,U (notprepared yet!!!) and diagrams that visualize the Strehl statistics for the individual applications during dataacquisition.

7.1.1 Slit-based Spectropolarimeter

Figure displays the individual Stokes profiles at spatial position P2 along slit#2 resulting after a perfectcalibration has been applied. In this case a continuously rotating retarder in combination with a 16 mixedstates modulation scheme has been used. Fromtop to bottomwe show the results for different exposuretimes and number of accumulations. The total integration time to acquire the Stokes vector (exposuretime×number of accumulations×number of modulation states) for all of the applications is constant andequals 5.12 sec acting as a reference time. Thecolor coding demonstrates the differences between theoutput Stokes signals when the starting point for data acquistion is varied. For comparison, we also displaythe original input Stokes signal (black). First we note that the StokesI profiles do not differ from applicationto application. The reason is that the StokesI signal is always recovered by adding up all modulation states.Since we did not change the reference time of 5.12 sec, those profiles will only change their shape becauseof the different seeing and Strehl variations (starting points) encountered during data acquistion. A similarargument we speculate is valid for the StokesV parameter. However, the specifics of the demodulationin order to recover StokesQ andU in combination with the time scales and behavior of the seeing and

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Figure 44: Individual Stokes profiles of the FeI 630.25 nm line at P2 along slit#2 for a slit-based instrumentequipped with a rotating retarder using a 16 mixed states modulation scheme in combination with differentexposure times and accumulations for different seeing samples during data acquistion (color coded). Back:input Stokes signal.Left to right: StokesI, Q/I, U/I andV/I. Top to bottom: different exposure times andaccumulations. A perfect calibration has been applied to the output Stokes signals.

Strehl variations obviously have an unfavorable effect on the linear polarization signals. Figure 45 displaysthe difference between all output profiles (color coded) and the input signal (black) as a measure of thereal error (or accuracy). We note the tendency that the errors increase with increasing exposure time anddecreasing number of accumulations for the same starting point (seeing sample). This is particularly visiblein the linear polarization signals. The corresponding diagrams for spatial position P3 are shown in Fig. 98and Fig. 98 in the appendix in Sect.??.

Figure 46 shows the variation of the achieved Strehl value ineach of the modulation states duringaccumulation and data acquistion. Fromleft to right and top to bottomwe change the exposure time andnumber of accumulations and the starting point of the data acquistion, respectively. Thehorizontal linesindicate the Strehl value of a modulation state averaged over all accumulations, while thecurved linesdemonstrate how the Strehl value changes from accumulationto accumulation within the same modulationstate. We note that when increasing the exposure time and decreasing the number of accumulations (in order

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Figure 45: Same as Fig. 44 but difference signals between input and output signals.

to keep the total integration time of 5.12 sec a constant) thecurves for the individual modulation states startto differ in shape and the differences between their individual averages start to increase. We indicate thisincrease by calculating therms variation of those average Strehl values. Therms values increase typicallyby an order of magnitude from application to application (left to right), slightly depending on the variationof the Strehl with the number of accumulations for the individual modulation states (top to bottom).

We now come to the results from a slit-instrument that is equipped with two switching LCVRs using a4 mixed states modulation scheme. We skip showing the Stokesprofiles and error plots at the two differentspatial positions P2 and P3. Those can be inspected in Fig. 100 and Fig. 101, and Fig. 102 and Fig. 103 ofSect. E in the appendix. Instead we directly show in Fig. 47 the corresponding Strehl variations during dataaquisition. In this case, the accumulation was performed after the modulation sequencing (accumulationoption 2). We immediately notice that therms values are typically smaller when compared to the sameseeing sample (or start of data acquistion) in case a 16 mixedstates modulation scheme would have beenused (see Fig. 46). We argue that the 4 mixed states modulation scheme performs better, because there is4 times more time to evenly distribute the influence of the residual seeing and Strehl variations on the 4modulation states compared to a 16 mixed state modulation scheme. We try to corroborate this by a directcomparison of therms values achieved with a 4 and 16 mixed state modulation schemeversus exposure

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Figure 46: Strehl variation during modulation for the individual applications of a slit spectropolarimeterequipped with a continuously rotating retarder using a 16 mixed states modulation scheme during data ac-quisition.Left to right: different exposure times and accumulations.Top to bottom: different starting points(color coded) in oder to sample different seeing variations.Horizontal lines: Strehl value of a modulationstate averaged over all accumulations.Curved lines: Strehl variation of each of the 16 modulation statesduring accumulation. Forrms values see text for explanation.

time as shown in Fig. 48. Thesolid anddashedlines refer to results from the 16 and 4 modulation states,respectively. Thecolor codingrefers to the different starting points sampling differentseeing conditionsduring data acquistion. In general, alldashedlines are below thesolid lines.Please ignore all data points at50 ms.

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Figure 47: Strehl variation during modulation for the individual applications of a slit spectropolarimeterequipped with two switching LCVRs using a 4 mixed states modulation scheme during data acquisition.The modulation states are sequenced before the accumulation (accumulation option 2).Left to right: dif-ferent exposure times and accumulations.Top to bottom: different starting points (color coded) in oder tosample different seeing variations.Horizontal lines: Strehl value of a modulation state averaged over allaccumulations.Curved lines: Strehl variation of each of the 4 modulation states during accumulation.

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Figure 48: RMS variation of the mean Fried parameter (left) and Strehl value (right) characterizing anaccumulated modulation state versus esxposure time.Solid: Slit instrument with a continuously rotatingretarder using a 16 mixed states modulation scheme.Dashed: Slit instrument with two switching LCVRsusing a 4 mixed states modulation scheme.Colored symbols: different starting points sampling differentseeing variations.

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7. Results for Residual-Seeing Case · 2020. 1. 22. · Instrument Slit Slit FPI FPI Modulation...

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