ISIS spectropolarimetry user guide

1. Basic characteristics
   
2. Polarisation optics
   
3. Preparation before a run
   
4. Afternoon settings and calibrations
   
5. Configuring the telescope
   
6. Acquiring targets and taking data
   
7. Data reduction
   
8. Useful observing commands and information

Basic characteristics


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ISIS is a modulation polarimeter with a double-beam analyser (a calcite plate) and a rotating half-wave and quarter-wave retarder, enabling linear and circular spectropolarimetry observations to be performed. In the standard configuration, where the half-wave plate is mounted on top of the quarter-wave plate, the unvignetted field of view is about 130 and 35 arcsec for linear and circular spectropolarimetry observations, respectively.

It's usually recommended to use only one arm of ISIS at a time to avoid the use of a dichroic, which introduces reflected light from its rear surface along the slit into the polarisation spectrum. However, Bagnulio and Landstreet (A&A 618, 113, 2018) have demonstrated that observations of circular polarisation of spectral lines can be successfully carried out using both arms simultaneously, significantly improving observing efficiency.

The instrumental polarisation as measured from zero-polarisation standard stars is p = 0.07 +/- 0.04 %.

A polaristion modulator (see graphic below) consists of a waveplate and an analyser. Rotation, or periodic modification, of the waveplate modifies the incident polarisation in a time-varying manner, and the analyser converts this into an intensity modulation which is then measured on the CCD.








A schematic plot of the ISIS polarimeter with representative beam cross-sections and polarisation ellipses can be found here (note that FOS is no longer in use). The physical dimensions of the ISIS polarisation modulator and slit area can be found in this graphic.

For linear polarimetry, a standard sequence of exposures is:
• exposure 1 with half-wave plate at 8.0 deg
• exposure 2 with half-wave plate at 53.0 deg
• exposure 3 with half-wave plate at 30.5 deg
• exposure 4 with half-wave plate at 75.5 deg

where exposures 1 and 2 yield the Stokes Q parameter, and exposures 3 and 4 yield the Stokes U parameter. A recipe for deriving the Stokes parameters can be found in section 3.2 of the ISIS Spectropolarimetry Users' Manual

For circular polarimetry, a standard sequence of exposures is:
• exposure 1 with quarter-wave plate at 95 deg
• exposure 2 with quarter-wave plate at 185 deg

The angle of the half-wave (quarter-wave) plate which provides the maximum brightness difference between the ordinary and extraordinary rays is the zero angle. Theoretical zero angles should be 0 (90) degrees for linear (circular) polarimetry measurements, but for ISIS the actual zero angle is around 8 (95) degrees. The exact value of the zero angle depends on wavelength and ISIS configuration, and will be determined by your support astronomer.


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Polarisation optics


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The polarisation optical elements, following the optical path from sky to detector, are:


Polarisers

There are three different choices of polariser (located in the main colour-filter slide in the WHT A&G box):

• MF-POL-PAR and MF-POL-PER: these are two linear polarisers (both transmit a linearly polarised beam perpendicular to each other). MF-POL-PAR is normally used to find zero angles during the set-up preparation. MF-POL-PER is not used much.
• MF-POL-CIR: circular polariser which is in fact elliptically polarised, and thus its use is not recommended.

Retarder waveplates

These are mounted above the slit. They are effective over the wavelength range 300-1100 nm. They can be inserted/retracted and set to any position angle, or rotated continuously at a maximum speed of 1 Hz. The available retarder plates are:

• Half-wave (λ/2) plate
• Quarter-wave (λ/4) plate


Rotating the half-wave plate by n degrees results in a rotation of the polarisation vector of the incident beam of 2n degrees. The quarter-wave plate converts circular polarisation into linear polarisation, so that the calcite plate (linear beam-splitting polariser) can detect its presence. Rotating the quarter-wave plate rotates the linear polarisation incident on the calcite plate.


The standard configuration has the half-wave plate mounted above the quarter-wave plate in the beam, so that the quarter-wave plate is closer to the slit. The table below lists the unvignetted field of view according to the plate position.

Wave plate	Position	Unvigneted FoV (arcsec)
Half-wave	Closer to the slit	~145
Half-wave	Further from the slit	~130
Quarter-wave	Closer to the slit	~35
Quarter-wave	Further from the slit	~16


Note that the quarter-wave plate really only allows observations of point sources due to its limited unvignetted field.

The quarter-wave and half-wave plates can be interchanged, to optimise the FoV for a particular application. This has to be done when ISIS is off the telescope, and so you should communicate this change request to your support astronomer well in advance of your run.

The dekker masks

The polarisation dekker slide is placed above the slit to avoid overlap between the two sets of spectra produced by the calcite slab analyser.






The choice of dekker position will depend on the nature of targets to be observed. The table below describes the characteristics of each dekker mask.



Dekker slide position	ICS command	Aperture (arcsec)	Separation (arcsec)
out	dekker 1	-	-
1	dekker 2	5	8.1
2	dekker 3	5	18.0
3	dekker 4	5	36.1
4	dekker 5	5	22.6
5	dekker 6	5	27.1
6	dekker 7	5	31.6
7	dekker 8	clear	-
8	dekker 9	clear	-

For point sources a dekker with three apertures, one for the source and two for the sky, can be used. Each aperture generates two beams. In the polarisation dekker slide, positions 1-3 have three apertures. The default option has the dekker slide in position 2 (ICS command "dekker 3"), in which the ordinary and extraordinary beams of the target and sky are aligned next to each other so that the CCD can be windowed to reduce the readout time. This default dekker-slide position has three apertures of 5 arcsec width, spaced by 18 arcsec. Therefore the total width is 41 arcsec, and the unilluminated space between the slots is 13 arcsec. The separation of the o and e rays is 8 arcsec.

Dekker slide positions 1 and 3 are not usually used. Position 1 is a specially designed sky-compensation dekker (see page 23, section 5.3 of the Users' manual for more details). Position 3 was designed for FOS (The Faint Object Spectrograph), which is no longer in operation. Note that this dekker introduces additional vignetting when used with the quarter-wave plate.

For extended sources the comb dekkers (in dekker slide positions 4-6) are used. They have different duty ratios, thus one has to plan in advance the size and number of position offsets along the slit to allow sampling of the full spatial extent of the slit. There are other comb dekkers on a different dekker slide, although these are rarely used.

The analyser


• Calcite slab: this is located immediately below the slit. It is a Savart plate which equalizes focus for both polarisations and reduces polarisation anomalies within ISIS. It produces two beams, the ordinary (o) and extraordinary (e) beam, which are both 100% polarised, but orthogonally. The o and e beams are separated from each other by between 2.1 mm (at 10000Å) and 2.6 mm (at 3000Å). The relative intensity of these beams depends on the percentage of polarised light in the incoming beam. The analyser is effective over the wavelength range 330-1100 nm.


• Polaroid: in principle, the polaroid analyser can be used for occasions when full spatial sampling, uninterrupted by the dekker structure, is mandatory. However, it is rarely used.

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Preparation before a run


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• Choose a dekker position according to the nature of the targets to be observed.


• Using a dichroic is in general not recommended for spectropolarimetric observations due to the reflected light from the rear surface of the dichroic. This reflected light is displaced along the slit, partly into the spectrum of the other polarisation, and this may compromise the polarimetry measurements.

  If observations are needed using the red and blue arms it is usually recommended to alternate between the two arms, and not use them simultaneously. However, if one is interested in e.g., the polarisation of emission lines and not too worried about continuum contamination from the ghost reflection in the dichroic, then simultaneous observations in the two arms can be considered. Also, Bagnulio and Landstreet (A&A 618, 113, 2018) have demonstrated that observations of circular polarisation of spectral absorption lines can be successfully carried out using both arms simultaneously. Of course, this capability significantly improves observing efficiency.



• Using the GG495 order-sorting filter in the red arm should not introduce any extra polarisation or problems (see e.g. Harries et al., 2002, MNRAS 337, 341, who used the GG495 filter with the R1200R grating centered at 6560 Å).


• The Stokes Q and U parameters, and hence also the polarisation angle, are defined relative to some instrumental coordinate system. It's therefore convenient to keep the orientation of the instrument fixed relative to the sky (i.e., set the Cassegrain rotator tracking), but equally, it is important to keep the relative orientations of the telescope and ISIS constant (this will mean there is only one global system to calibrate for the polarisation zero-point). Our compromise recommendation is to track in angle during the entire observation, but to aim at having the slit vertical halfway through the observation. You can plan this using ING's Object Visibility web-page, selecting 'Parallactic angle' in Options.

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Afternoon settings and calibrations


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As you proceed to set up ISIS for spectropolarimetric observations, various components specific to this mode of ISIS will appear on the ISIS Mimic window (see graphic).


1. Set the dekker position

To set the default position of the dekker (called POL18ARCSEC, which has a gap of 18 arcsec between the centre of the central dekker slot and the centre of the left or right dekker slot), type:

SYS@taurus> dekker 3

Other dekker positions are listed here.


2. Put the retarder plate in the beam

Deploy the half-wave plate (for linear spectropolarimetry) or the quarter-wave plate (for circular spectropolarimetry) in the light path:

SYS@taurus> hwin (for linear) or qwin (for circular)

To take half-wave or quarter-wave plate out of the beam, type:

SYS@taurus> hwout or qwout


3. Put the Savart plate in the beam

To move the Savart plate into the light path, type:

SYS@taurus> fcp calcite

To move the Savart plate out of the beam, type:

SYS@taurus> fcp_out


4. Setup the detector

Set the appropriate window and readout speed of the detector in the usual way, using the windows below as a reference. But, these need to be checked empirically.

SYS@taurus> window red 1 "[840:1190,1:4200]"

SYS@taurus> window blue 1 "[890:1240,1:4200]"


5. Take calibrations

Take the usual set of calibrations described in the ISIS cookbook.

For the flat fields use the same polarimetry components in the light path as for your observations, except for the dekker, for which it's recommended to take two sets of flat fields. The first set should be taken with the dekker slide in the clear position (type SYS@taurus> dekker 9). Next, insert your required dekker in the beam, and take another set of flat fields. Note that roughly double the exposure time will be needed compared to flat fields taken at dekker position clear; when the dekker slide is in the clear position each pixel is illuminated by both the ordinary and extraordinary rays.

To take flat fields, set the half-wave (quarter-wave) plate to the angle where the contrast between the ordinary and extraordinary rays is minimized. For ISIS this is around 30.5 or 75.5 deg for linear, and around 185 deg for circular spectropolarimetry.

If you want to take sky flat fields in addition to the tungsten lamp flat fields, ask the telescope operator to point the telescope to the Arago point (telescope azimuth = Sun azimuth - 180 deg and elevation ~ 20 deg at sunset), where the degree of the sky polarisation is close to zero. The Arago point lies about 20 deg above the antisolar point when the sun is close to (or just below) the horizon.

It's important not to change any sensitivity parameters of the system between taking calibrations and science observations. This applies particularly to gratings, grating settings and filters.


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Configuring the telescope


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1. Focusing the telescope

To find the focus of the telescope with ISIS for spectropolarimetric observations, follow the usual focusing procedure. Choose some bright star (a brighter star is needed than for the normal ISIS observations, e.g., V ~ 6-8 mag). The usual telescope focus is 0.2 (0.1) mm lower when using a half-wave (quarter-wave) plate compared to the ISIS focus without a wave plate. This means that the telescope focus will be around 97.65 and 97.75 mm for the linear and circular spectropolarimetry, respectively.

Once the value of the focus is determined, set the value by, e.g.,

SYS@taurus> focus 97.65

If you are doing both linear and circular spectropolarimetry, it's recommended that you add all necessary focus changes to your observing scripts, or automate focus changes using a GUI hwp (qwp) "Dfocus" setting of -0.2 (-0.1) mm for linear (circular) spectropolarimetry observations.

Make sure you determine the telescope focus well. An out-of-focus image can lead to polarisation effects if the image is sampled asymmetrically with the spectrograph slit. In this case, one samples a specific part of the primary mirror and will see a polarisation imprint due to the oblique incidence on that part of the mirror. With accurate focusing, all parts of the primary contribute equally, and the average polarisation effect is zero.


2. TV and autoguider focus

It may be necessary to decrease the TV focus by 1500 microns and the autoguider focus by a few hundred microns. The telescope operator will take care of this.

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Acquiring targets and taking data

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1. Acquiring objects

Point the telescope to your target and type:

SYS@taurus> agslit

Due to the thickness and field vignetting of the retarders they have to be retracted from the optical path to acquire a target:

SYS@taurus> hwout (or qwout)

After the acquisition is finished and auto-guiding is on, the wave plate can be inserted back into the beam:

SYS@taurus> hwin (or qwin)

In the acquisition camera you should see an image resembling the image below, where the vertical thick apertures are the dekker slots. Inside the dekker slots, and towards their lower extremes, it's possible to distinguish shadowed areas. These are the edges of the dekker, which are visible because of the 7.5 deg tilt of the dekker with respect to the slit-view camera (the slit jaws are inclined to the optical axis of the telescope at an angle of 7.5 degrees to allow the acquisition TV to view the reflected skylight off the polished slit jaws).

At the upper extreme of the dekker slots there are thin horizontal lines visible. These are the interfaces of the metal plates of adjacent dekkers, visible in this image of the polarisation dekker slide.

Finally, the dekker selected for observing has in the upper part of the slots another shadowed area, which is the ISIS slit. The target should be acquired in the intersection between the central dekker slot and the ISIS slit, as shown here. Sometimes, particularly for bright targets, it's necessary to move the source out of the ISIS slit to be able to see the dekker shape clearly.







2. Taking data

Once the acquisition is complete, the telescope operator should close the autoguider loop (if necessary), and you can start your science exposures. Take data using the spectropolarimetry scripts located in /home/whtobs/isis_scripts:

SYS@taurus> linpolscript <camera> <int time> <title> [nloop] (linear polarimetry)

SYS@taurus> cirpolscript <camera> <int time> <title> [nloop] (circular polarimetry)

where nloop is the number of loops, and defaults to one if not specified.

Here are examples of scripts for linear and circular spectropolarimetry, which will take 4 and 2 images, respectively, at zero angles determined by your support astronomer. The zero angles are different for the red and the blue arm of ISIS, and also vary with other spectrograph settings like the central wavelength. Your support astronomer will modify the scripts to contain the correct zero angles for your run.

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Data reduction

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You can use the CCD2POL in TSP (The FIGARO Time Series/Polarimetry Package), which is installed on the ING computers as part of Starlink, to analyse your data. The idea is that you can quickly reduce your data immediately at the telescope, to confirm that the polarisation and position angle are consistent with expectations (quick-look). For rigorous data reduction, you can extract the ordinary and extraordinary rays for the target and sky apertures, and make a cube of these extracted spectra, which will then be an input for CCD2POL.

Documentation for FIGARO is available here, documentation for TSP is available here, and documentation for convert is available here.

Start a terminal session on a data reduction computer, e.g., whtdrpc1 as user whtguest and move to the scratch directory where your data are located. Load the FIGARO, TSP and CONVERT packages:

figaro
tsp
convert

Now you can use CCD2POL, which reduces CCD spectropolarimetry data. This function expects four spectra in each frame, corresponding to the ordinary and extraordinary rays for each of two apertures (A and B). These spectra are combined to derive a polarisation spectrum in TSP format. ISIS data have usually six spectra for three apertures B (sky), A (target), and B (sky). Choose two apertures, one containing the target spectrum and one for the sky. The input data are expected to have the Y axis as the dispersion direction (which is the case of ISIS data).

To run the function CCD2POL, type:

ccd2pol

Here is an example of ccd2pol input parameters:



POS1	FIGARO Input file for 0.0 degrees	r1806752.fit[1]
POS2	FIGARO Input file for 45.0 degrees	r1806753.fit[1]
POS3	FIGARO Input file for 22.5 degrees	r1806754.fit[1]
POS4	FIGARO Input file for 67.5 degrees	r1806755.fit[1]
ASTART	Start column for the A aperture data	147
BSTART	Start column for the B aperture data	228
OESEP	Separation of ordinary and extraordinary spectra	36
WIDTH	Number of columns to include in each extracted spectrum	10
APERTURE	Aperture containing star (A or B)	A
BIAS	Bias level to be subtracted from data	3016
READNOISE	CCD readout noise (electrons/pixel)	3
PHOTADU	CCD gain (photons per ADU)	1.16
ALGORITHM	Data reduction algorithm (OLD or RATIO)	RATIO
OUTPUT	Output Dataset	@result


In the example above the spectra are laid out in columns with the aperture A spectrum in columns 147 to 156 (ordinary) and columns 183 to 192 (extraordinary), and the aperture B spectrum in columns 228 to 237 (ordinary) and columns 264 to 273 (extraordinary).

The two algorithms (OLD or RATIO) differ in the method used to compensate for transparency variations between the observations at two plate positions. The RATIO algorithm works very well on bright stars, but can fail on faint objects (or on 100% polarised calibration sources) through attempting to take the square root of a negative number. Under these circumstances the OLD algorithm should be used.

The variances on the polarisation data are calculated from photon statistics plus readout noise.

If you want to plot results, you can use the function PPLOT, which plots a polarisation spectrum:

pplot

Here is an example of the pplot input parameters:



INPUT	Stokes Data to Plot	@result
BINERR	Error per bin (per cent)	0.5
AUTO	Autoscale Plot	TRUE
LABEL	Label for plot	''
DEVICE	Plot Device	@xwindows


Finally, if you want to calculate the polarisation P and the position angle Theta for a polarisation spectrum, use the PTHETA function:

ptheta

Here is an example of the ptheta input parameters:



INPUT	Polarisation Spectrum	@result
LSTART	First Wavelength to Use	800
LEND	Last Wavelength to Use	3500


The input in this example is in pixels.

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Useful observing commands and information

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Commands to move the half-wave (quarter-wave) plate

SYS@taurus> hwin (qwin), moves retarder plate in

SYS@taurus> hwout (qwout), moves retarder plate out

SYS@taurus> hwp <angle> (qwp <angle>), moves retarder plate to requested angle (0-360 deg)

SYS@taurus> hwprot <rate> (qwprot <rate>), rotates retarder plate at requested rate (0 - 1 Hz)

SYS@taurus> hwstop (qwstop), stops the rotation of retarder plate

Continuous rotation for both half- and quarter-wave plates has a time-out of 12 hours (in case it's forgotten to stop it).

Other useful commands

SYS@taurus> fcp calcite, moves the Savart plate into beam

SYS@taurus> fcp_out, moves the Savart plate out of beam

SYS@taurus> dekker 3, chooses the standard position of the polarisation dekker

SYS@taurus> mainfiltnd MF-POL-PAR, selects polariser in the main colour filter unit

SYS@taurus> mainfiltnd 1, removes polariser in the main colour filter unit

In case the retarder plates don't move, type:

SYS@taurus> inhw (inqw), which initialises the half-wave (quarter-wave) plate.

Reference system

The angle of the half-wave and quarter-wave plate is relative to the instrumental reference. The orientation of the calcite block and the slit are fixed with respect to ISIS. So if the ISIS slit is at the parallactic angle, the angle of the retarder plate relative to north will depend on where on the sky the telescope points.

A note on circular polarimetry

Because the quarter-wave plate is not exactly quarter-wave for all wavelengths, the circular polarimeter is partly sensitive to linear polarisation. If you suspect linear polarisation in your source, you can depolarise it by continuous rotation of the half-wave plate ahead of the quarter-wave plate in the beam (which is default configuration of the retarders). This should eliminate systematic errors due to linear polarisation, and invert but otherwise leave intact, the true circular polarisation.

If linear polarisation of your source is strong, you must determine to what extent the telescope converts linear to circular polarisation. The way to do this is to set up ISIS for circular polarisation, but observe a strongly linearly polarised star. Obtain two complete observations, with a rotator angle difference of 90 degrees. External circular polarisation will constant, but converted linear polarisation will be inverted in the two observations.

Instrumental polarisation zero-point

To 'depolarise' a zero-polarisation star completely, observe it twice, with a difference of about 90 degrees in rotator angle. In the Alt-Az frame, the average of the two observations represents the pure instrumental zero-point. The converse holds for a representation in the equatorial coordinate frame: the average is purely the stellar polarisation.

Photon noise calculation

An absolute error in the Stokes parameter ~ 1/√ N_total , where N_total is the number of photons per resolution element. So for example, in order to determine one Stokes parameter to a degree-of-polarisation accuracy of 0.005, 4x10⁴ photons per resolution element are required. To obtain both linear Stokes parameters with that accuracy, we need two such observations. For more details see Section 3.8.1 of the ISIS Spectropolarimetry Users' Manual.

More information

Some more information about ISIS spectropolarimetry can be found in the ISIS Spectropolarimetry Users' Manual. Although this is an old document and some specific detail isn't valid anymore, it contains invaluable background discussion on the broader aspects of spectropolarimetry with ISIS.