Issue |
A&A
Volume 507, Number 1, November III 2009
|
|
---|---|---|
Page(s) | 531 - 539 | |
Section | Astronomical instrumentation | |
DOI | https://doi.org/10.1051/0004-6361/200811315 | |
Published online | 08 September 2009 |
A&A 507, 531-539 (2009)
Fast imaging spectroscopy with MSDP
spectrometers. Vector magnetic maps with THEMIS/MSDP![[*]](/icons/foot_motif.png)
P. Mein1 - N. Mein1 - V. Bommier2
1 - Laboratoire d'Études Spatiales et d'Instrumentation en
Astrophysique (LESIA), Observatoire de Paris, CNRS, UPMC, Université
Paris Diderot, 5 Place Jules Janssen, 92195 Meudon, France
2 - Laboratoire d'Étude du Rayonnement et de la Matière en
Astrophysique (LERMA), Observatoire de Paris, CNRS UMR 8112, 5 Place
Jules Janssen, 92195 Meudon, France
Received 8 November 2008 / Accepted 16 July 2009
Abstract
Context. Multichannel subtractive double pass (MSDP)
spectrometers produce 3D data cubes
simultaneously across several line profiles. They do not suffer from
image convolution by any slit width, and synchronous observations
across all wavelengths avoid differential seeing effects. They are very
suitable for fast 2D spectroscopy.
Aims. (1) We review specifications and capabilities
of some existing MSDP spectrometers with respect to high-cadence
observations. (2) THEMIS/MSDP is designed for the spectropolarimetry of
strong lines. We propose new data reductions also suitable for the
spectropolarimetry of photospheric lines.
Methods. An off-line algorithm is described as a way
to increase the spectral resolution. Taking the opportunity of 3D data,
spatial interpolations are used around each solar point by only
assuming that intensity gradients
are constant in the range
.
The UNNOFIT inversion is used to compare vector magnetic maps deduced
from THEMIS/MSDP and slit-spectropolarimetry THEMIS/MTR data.
Results. Both results are in good agreement. In
active regions, the rms of the MSDP noise, calculated over
1 arcsec2, is less than 24 G
for the LOS magnetic field and less than 52 G for Bx
and 32 G for By.
The MSDP scanning speed is 10 times the speed of
slit-spectropolarimetry.
Conclusions. THEMIS/MSDP can provide vector magnetic
maps with typical temporal resolutions that are less than
1 min for small fields-of-view and 10 min for active
regions. This allows addressing a number of fast events. In the future,
MSDP instruments should efficiently complement single-slit spectroscopy
and tunable filters. Their main capabilities should be the multiline
aspect and the high temporal and spatial resolutions. New optical
devices, such as image slicers, should substantially increase the
signal-to-noise ratio. For polarimetric measurements, various
compromises are possible between speed, spatial resolution, and SNR.
A-posteriori image restorations, either using wide band proxies or
bursts of multi-wavelength short exposures, should help improving
signal-to-noise ratio and spatial resolution.
Key words: instrumentation: spectrographs - techniques: polarimetric - Sun: magnetic fields
1 Introduction
Fast evolving structures are being investigated more and more in solar
physics, especially in the low-density media of chromosphere and
corona. But velocity fields and magnetic fields observed at high levels
strongly depend on photospheric values, so spectropolarimetry of
different wavelength ranges are often required. Time scales smaller
than one minute characterize local events such as the triggering of
waves across sunspots (Tziotziou et al. 2007)
or
emerging fluxes and Ellerman bombs in active regions (Pariat
et al. 2007).
But short time scales not only concern small-size events. Instabilitiy
mechanisms must be investigated through magnetic field modifications
across full areas of active regions. Flares, CMEs, and slip-running
reconnections (Aulanier et al. 2006)
require
observing time scales typically as short as one minute, while
acceleration times of high-energy particles are generally shorter than
one second. In this context, large data fluxes
are needed more and more.
Table 1: Rough characteristics of some MSDP instruments (see Sects. 2 and 3).
Many advances have been made recently in the field of
high-cadence observations by tunable filters (Cauzzi et al. 2008;
Bello
Gonzales et al. 2008;
van Noort et al. 2008).
In this paper, we concentrate on multi channel subtractive double pass
(MSDP) spectrometers that produce synchronous wavelength data and avoid
differential seeing effects.
Unlike slit spectra, MSDP spectro-images do not suffer from any
convolution by slit widths and are not affected by spatial sampling
caused by scanning steps. The large scanning steps of MSDP are only
used to join successive 2D-fields. They can reach high spatial
resolution and provide large 3D data cubes
across several line profiles.
We review briefly the characteristics of some MSDP instruments, especially in view of high-cadence 2D spectroscopy. Then, we turn to spectropolarimetry and magnetic field observations. We present a new method of increasing the spectral resolution off-line. An example of a vector magnetic map observed with THEMIS/MSDP is given and compared to results derived from single-slit spectropolarimetry.
2 Synchronous field-of-view and data cube
MSDP instruments are presently attached to five telescopes: Meudon ST (Solar Tower, Mein 1977), LJR (Lunette Jean Rösch) at the Pic du Midi Observatory (Mein 1981), the German VTT at Tenerife (Mein 1991), the large Wroclaw coronagraph (Rompolt et al. 1994), and THEMIS (Mein 2002). All these instruments use a double pass of the light on the same grating, except THEMIS which includes two sequential echelle spectrographs, resulting in a very low stray light level.
We restrict this short review to instruments especially suited to observing large areas with high cadences. In particular, we do not present the LJR instrument, devoted to high spatial resolution. It is built to take advantage of the high resolution of the Pic-du-Midi seeing, together with the high quality of MSDP images that are not degraded by slit widths (see for example Malherbe et al. 2004; Roudier et al. 2006).
Table 1
presents some specifications in the cases of Meudon ST, German VTT, and
THEMIS. For VTT and THEMIS, two lines can be observed simultaneously,
and several observing modes are detailed.
Modes (1) and (2) of the German VTT, and modes (1),
(2), and (3) of Themis can be combined for different line strengths, as
indicated in Sect. 3. N and Wx
are respectively the number and the width of channels,
and
the focal lengths of telescope and spectrograph, l
the period of slits before the second pass, s the
bandwidth for each slit,
the wavelength distance between two successive channels (that is the
resulting wavelength sampling),
the number of channels used to
cover the line profile
,
p the pixel size (which might be reduced with CCDs
larger than
),
the spatial shift between two successive channels, nx
the number of channels used to cover the field-of-view
,
the
field-of-view in the perpendicular direction, A the
corresponding area and
the data cube. Wavelength intervals s,
,
and
are given for lines around 650 nm.
Figure 1
shows an example of MSDP spectro-image obtained at the Meudon Solar
Tower. In Fig. 2
we plotted the location of photons in the plane
,
where x is
the spatial coordinate parallel to the dispersion. The N
channels cover the parallelogram abcd (ab
= first channel, cd = last channel), but abcd
is not a rectangle because the wavelength increases across each
channel.
![]() |
Figure 1:
Example of MSDP data in the H |
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![]() |
Figure 2:
Photon distribution in the |
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Let us derive some useful relationships between parameters
characterizing MSDP instruments. The field-of-view is defined by a
field stop. We call Wx
and Wy
the lengths of the entrance window. In the y-direction,
Wy is
exactly the available field-of-view .
In the x-direction, the available field
may be smaller, according to the compromise with the total wavelength
range
needed around line centre:
![]() |
(1) |
This compromise is defined by an inscribed rectangle efgh (ef =





For a given range of wavelengths (for example 650 nm
as in Table 1),
if the blaze angles of gratings are similar in all instruments, we can
state that
![]() |
(2) |
where


![]() |
(3) |
where

![]() |
(4) |
We see in Fig. 2 that
![]() |
(5) |
and
![]() |
(6) |
where

![]() |
(7) |
In the case of large solar areas, such as active regions, the full field of view is recorded by scanning, with a spatial step


![]() |
(8) |
For comparison with other instruments such as tunable filters using successive exposures across a line profile, it is interesting to specify the useful Data Cube, which is is the product of A by the number of synchronous wavelengths defining the useful range

![]() |
(9) |
3 Specific capabilities
We again restrict this short review to the instruments listed in
Table 1.
The area A is a clue for the speed of the
instruments. From Eqs. (6) and (8) we see that
![]() |
(10) |
For a given




The MSDP of the Meudon Solar Tower is presently used for fast H
intensity and velocity maps of large active regions. The width of the
line, the large focal length of the spectrograph and the focal
reduction of the solar image account for a large observed field-of-view
with 6 simultaneous wavelengths. A system of prisms achieves a
scan of 5 successive exposures within 30 s and
produces maps larger than
arcmin.
Since 1981, many papers have been devoted to chromospheric events, such
as filament oscillations (Malherbe et al. 1981),
dynamical modelling of post-flare ejections (Mein & Mein 1982)
and correlations between ejecta and type-III bursts (Chiuderi-Drago
et al. 1986).
Recently MSDP data were used to calibrate prominence images obtained by
Hinode SOT (Heinzel et al. 2008).
Two lines can be observed simultaneously with modes 1
and 2 of VTT/MSDP. Mode 1 of Table 1 is generally used for
middle-strong lines (589.6 NaD1, 854.2 CaII, etc.)
and mode 2 for H.
Thanks to the good seeing of Tenerife, many topics were investigated,
either with H
alone, such as the dynamics of arch filament systems (Mein
et al. 1996)
and the non-LTE inversion of prominence profiles (Molowny-Horas
et al. 1999),
or with H
and 854.2 CaII, such as asymmetries of flare profiles (Mein
et al. 1997)
and Fourier analysis of sunspot oscillations (Tziotziou et al.
2007).
Two lines can also be observed simultaneously with THEMIS/MSDP
and the field-stop of arcsec,
with two possibilities. The first one uses the mode 1 for both lines:
chromospheric lines (517.3 MgI, 589.6 NaD1,
587.6 HeI, 854.2 CaII, etc.) or photospheric ones
(610.3 CaI, 630.2 FeI, etc. see next sections). The
second possibility uses simultaneously modes 1 and 2, the mode 2 being
devoted to a Balmer line (H
). A third possibility is to
use the mode 3 for H
alone, with the broad field stop
arcsec.
As with VTT/MSDP, chromospheric structures were targets of published
papers, as for example mottles and grains (Tziotziou et al. 2003).
But,
of course, since THEMIS is a polarization-free telescope, the main
applications of THEMIS/MSDP concern magnetic fields. We come back to
this point in subsequent sections.
4 Observing speed: MSDP and single-slit spectroscopy
It is interesting to qualitatively compare MSDP performances to
performances of single-slit spectroscopy with respect to resolution in
time. Let us concentrate on VTT (mode 1) and THEMIS (mode 1). If we
assume that slit spectroscopy and MSDP use the same field-of-view
versus y (
value) and that the length of the target in the y-direction
is less than
,
a full map is obtained in both cases by a single scan versus x.
The exposure times are generally shorter than 100 ms, while
the CDD readout and the telescope motions typically last 1 s,
so the scanning time does not depend very much on the exposure times,
and the ratio of observing times is close to the ratio of the number of
steps. For MSDP, scanning steps
must be smaller than
to ensure overlaps between exposures. Let us assume step sizes 10 and
5 arcsec respectively for VTT and THEMIS. If we assume that a
spatial sampling around 0.5 arcsec is needed for slit
spectroscopy, the corresponding scanning step is 0.5 arcsec,
so we get ratios 20 and 10 for observing times between slit
spectroscopy and MSDP.
Of course, slit spectroscopy provides more wavelengths than MSDP, with better spectral resolution. However, we see later that, in the case of narrow photospheric lines, methods do exist to increase the spectral resolution thanks to a little loss of spatial resolution. The resolution becomes similar to the resolution of typical slit spectroscopy, so that the high speed of MSDP can even be saved in that case.
5 Circular spectropolarimetry: LOS magnetic fields
Two MSDPs are attached to telescopes without coelostat. They are very suitable for polarimetry.
The LJR of Pic-du-Midi is a refractor. The site is well-known for excellent seeing, and compromises are required between speed, noise, and spatial resolution to take advantage of the seeing quality. As a result, circular spectropolarimetry was achieved with LJR/MSDP by recording successive bursts of 10 couples of Stokes spectro-images I+V and I-V. Maps of LOS magnetic field were summed after destretching (Malherbe et al. 2004). The seeing motions were deduced from local correlation tracking using images of the MSDP channel closest to the continuum (code by November 1986).
As mentioned before, we now restrict our discussion to teles-
copes fitted to fast scannings across large areas. THEMIS/MSDP is the
other instrument allowing accurate polarimetry. The spectral resolution
of mode 1 is quite suitable for measurements of Zeeman shifts of
middle-strong lines. In particular, many fast maps of line-of-sight
(LOS) magnetic fields were measured with THEMIS/MSDP. The scanning rate
is typically 1 arcmin square per 1 min of time.
Comparisons with SOHO/MDI were published (Berlicki et al. 2006).
Taking
advantage of the spatial resolution of MSDP spectro-images, we also
analysed facular flux tubes, and published several 2D models derived
from Zeeman shifts measured along the profile of 589.6 NaI D1
(Mein et al. 2007).
LOS photospheric magnetic fields from NaD2 were
also combined with H
and 854.2 CaII profiles to investigate barb endpoints of
filaments (Zong et al. 2003).
In a similar way, coordinated observations of NaD1
with Themis and H
with VTT have been combined to study the gradual phase of a flare
(Berlicki et al. 2005).
But vector magnetic field measurements require spectral resolutions fitted to photospheric lines. The next section shows how it is possible to increase the spectral resolution of THEMIS/ MSDP off-line for that purpose.
6 Vector magnetic fields: THEMIS/MSDP with increased spectral resolution
The finest spectral sampling provided by THEMIS/MSDP is 8 pm
(at 600 nm), with the band-width 4 pm, provided by
the 16 channels optics. This is not sufficient for polarimetry of
photospheric lines.
Successive exposures using small grating rotations (or small shifts in
the solar image) might be used to increase the number of wavelengths
and to improve the sampling. Such a method is used with tunable
filters. But MSDPs produce 3D data, so that it is possible to propose
an alternative method that is less seeing-sensitive and that does not
need any image destretching. To adapt the THEMIS/MSDP to photospheric
lines, it is possible to use a compromise between spatial and spectral
resolutions in the plane ,
without modifying the fast-scanning capabilities. The only condition is
that the intensity gradient
around a given point x and a given wavelength
must be roughly constant in the range
,
.
Figure 3
shows the corresponding interpolations in the plane
.
The plane (x,y) of 2D imagery is
not represented. Wavelength scales correspond to THEMIS mode 1
of Table 1
with the line 610.3 CaI. For a solar point at x
= 0, line profile intensities are measured at points A and D from
channels n and n+1
(wavelengths
and
). Let us
call B and C the points of channels n and n+1,
at solar locations
(with
arcsec),
which correspond to wavelengths
and
,
with
pm).
Let us call F and G the points x = 0 at the same
wavelengths as B and C.
![]() |
Figure 3:
Method of line-profile interpolation in the
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We assume that the spatial gradient of intensity
is constant around point E
,
so that
![]() |
(11) |
We can replace intensities at F and G by intensities at B and C to get intensity at point E by a cubic interpolation. Departures due to gradients are compensated for by symmetry (GE = EF). In this way, the spectral sampling of 8 pm (distance between A and D) is reduced to 4 pm. After similar computations of intensities at H and I, the final profile is obtained by new cubic interpolations between D, E, A, H for F and I, D, E, A for G.
Figure 4 shows examples of spectra deduced from MSDP data (intensities in arbitrary units, abscissae in numbers of channels).
![]() |
Figure 4:
Spectra derived from the 16 MSDP channels around 610.27 nm CaI
(deepest line). Stars correspond to points similar to A and D in
Fig. 3.
Rectangles correspond to points E, H, I, and black dots to points B and
C. Top: solar point with low value of
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In the case of polarimetric analysis, a grid is located at the primary focus in front of the analyser (Semel 1980). In all channels, the same fields of view are seen simultaneously in I+S and I-S ( S = +Q,-Q,+U,-U,+V,-V in the case of beam exchange). An example of spectro-image is shown in Fig. 2 of the paper devoted to THEMIS/MSDP (Mein 2002). For each solar point, intensities are interpolated inside the CCD matrix. The pixel size is close to 0.2 arcsec, and the accuracy of the geometrical calibration is around 0.1 arcsec, so thanks to synchronous observations, interpolations for I+S and I-S concern the same solar areas, smoothed by the same seeing blurring, with the accuracy close to the pixel size.
7 Full spectropolarimetry of NOAA 10960
On June 11, 2007, the active region NOAA 10960 was observed with
THEMIS/MSDP at 17:21 in the 610.27 nm CaI line (Lande factor
2.0). The exposure time was 200 ms and the local bandwidth
4 pm (see Table 1).
The field-of-view was
and the scanning time 12 mn. This corresponds to
0.5 arcmin square per minute of time. For comparison, MTR
observations had been performed with the same line across a smaller
field of view of the same region. The exposure time was 60 ms
and the slit-width 1 arcsec (spectral smoothing
6 pm). The field-of-view was
and the scanning time 38 mn.
The time delay between the middle points of both scans was
close to 42 mn. This target was the most active solar region
that we could observe in 2007. It was near the west limb (S05, W55).
Between both scans, the solar rotation is about 0.4 degree. It
modifies the spatial scale by less than 0.5%, which corresponds to arcsec
across a 60 arcsec field-of-view, and the rotation of the
magnetic vector leads to errors less than 7 Gauss when the
perpendicular component reaches 1000 Gauss. As a result, the
solar rotation can be neglected in the comparison of MSDP and MTR
results, except for the co-alignment (Sect. 9).
The polarimetry was the same in both modes. A grid was used in front of the polarization analyser, and Stokes parameters I+S and I-S were observed simultaneously as seen before. The grid period is 33.3 arcsec, and image restorations are obtained by 4 steps of 8.5 arcsec versus y. MSDP uses 5 grid periods and MTR 3 grid periods. The scanning steps versus x is 5 arcsec for MSDP and 0.7 arcsec for MTR. The y-scanning is performed inside the x-scanning loop for MSDP, but outside for MTR.
8 Noise and photon numbers: MSDP and slit spectropolarimetries
The CCD cameras used at THEMIS are different for MSDP and MTR, and it is difficult to directly investigate relative capabilities of the optics with respect to SNR. However, instrumental parameters can help to estimate the ratio of recorded photons in both modes, for a given solar area across the useful line profile. Let us choose for example a solar area of 1 arcsec2, which is fully covered by both modes in one exposure (the slit-width of MTR is 1 arcsec). The ratio is the product of several factors, which are mainly:
- -
- the efficiency of the interference filter that separates grating orders of MSDP (10 nm bandwidth), is around 70%;
- -
- four additional plane mirrors and 2 reflections in the prisms of the beam shifter (see Fig. 1 in the paper by Mein 2002) are introduced before the second pass of MSDP. Let us assume a ratio equal to 0.5;
- -
- before the second pass of MSDP, the spectrum is filtered by slits of 4 pm every 8 pm, while the full spectrum is recorded by MTR: ratio 0.5. This ratio becomes close to 1 in the case of profile calculations with the method presented in Sect. 6, because additional data are extracted from neighbouring solar points. However, this is equivalent to a spatial smoothing and cannot be considered in the estimate of the global number of photons;
- -
- although the first-pass grating (echelle grating, 79 grooves/mm, blaze 63.43 degrees) is close to the blaze angle, it is possibly less efficient than the grating used as predispersor by MTR (150 grooves/mm, blaze 2.15 degrees). We do not take it into account;
- -
- the exposure times are 200 ms for MSDP and 60 ms for MTR: ratio 3.3.




![]() |
Figure 5:
Vector magnetic map derived from THEMIS/MSDP data and UNNOFIT
inversion. The background colour shows the LOS magnetic field. The
transverse field is represented by dashes, the length of which are
proportional to the amplitude of the field (scale in Gauss).
The total field-of-view is |
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9 MSDP and MTR results with UNNOFIT inversion: departures and noise
MSDP data were reduced with the method described in Sect. 6. In both cases, line profile inversions were performed thanks to the UNNOFIT code (Bommier et al. 2007).
The MTR data were obtained with a slit width of
1 arcsec. To get comparable results, we used a
arcsec2
smoothing of MSDP data before UNNOFIT inversion and an additional
smoothing of 1 arcsec for MTR in the direction of the slit
before UNNOFIT inversion. Because the interpolation method of MSDP
profiles (Sect. 6) already includes additional data extracted
from neighbouring solar points, we only smoothed the Stokes profiles
over
arcsec2
to roughly mimic a global
arcsec2
smoothing.
Figures 5
and 6
show the maps of the vector magnetic field (Gauss) multiplied by the
filling factor, derived from MSDP and MTR data, respectively. North is
to the top, and west to the right. Scatter plots are presented in
Figs. 7-9 for
line-of-sight
magnetic fields B// and
transverse components Bx
and By.
Because the 180
ambiguity is not solved, one of the transverse components (here the x-component)
is always positive. Diamonds show the mean values in intervals of
100 Gauss. Vertical error bars correspond to the root mean
squares of departures in each interval (counted parallel to the
bisector). In most of the cases, scatter plots are well aligned along
the bisector and show that mean MSDP results are close to mean MTR
ones.
To compare the results more specifically, we compute, for each
component, the rms of departures between MSDP and MTR values:
![]() |
(12) |
where B is replaced by B//, Bx, and By successively. To distinguish active areas from the total field-of-view, the calculation is performed in two cases: d0 is the rms averaged over the full common field-of-view and d300 the rms averaged only over the areas where the mean modulus of the total magnetic field



![]() |
Figure 6:
Vector magnetic map derived from THEMIS/MTR data and UNNOFIT inversion.
The background colour shows the LOS magnetic field. The transverse
field is represented by dashes, the length of which are proportional to
the amplitude of the field (scale in Gauss). The total
field-of-view is |
Open with DEXTER |
![]() |
Figure 7:
Scatter plot of the LOS magnetic field multiplied by the filling
factor, deduced from UNNOFIT inversion; slit-spectroscopy versus MSDP. d0
and d300 are the rms of
departures averaged respectively over the total field-of-view and over
the areas where the vector magnetic field is larger than
300 Gauss. |
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![]() |
Figure 8: Scatter plot of the component Bx of the transverse magnetic field multiplied by the filling factor, deduced from UNNOFIT inversion; slit-spectroscopy versus MSDP. Definitions as in Fig. 7. |
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Figure 9: Scatter plot of the component By of the transverse magnetic field multiplied by the filling factor, deduced from UNNOFIT inversion; slit-spectroscopy versus MSDP. Definitions as in Fig. 7. |
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To get an upper limit
of the noise, we also compute, for the three components and in the same
cases, the rms of differences between the values obtained at a given
point (x,y) and the barycentre of
values obtained at 4 neighbouring points. We define
![]() |
(13) |
and
![]() |
(14) |
where B is replaced successively by B//, Bx and By, for MSDP and MTR results, with





The
and d values are lower for the full field than for
the spot. Let us concentrate on
and d300, which correspond
to active areas. The
values are upper limits of the noise, because they also include some
contribution from solar fluctuations across x and y.
For MSDP results, we get a noise less than 24 G for B//,
52 G for Bx
and 32 G for By
(Table 2).
For MTR, we get 28, 63, and 59 G, respectively. A large part
of the MTR
-values
is due to image distortions produced by seeing and pointing effects
between successive spectra (step 0.7 arcsec).
Table
2:
Upper limits
of the noise and rms of departures d between MSDP
and MTR results, averaged over the areas where the mean value of
B
is higher than 300 Gauss.
Table 3: Rough scanning times and temporal resolutions of THEMIS/MSDP (mode 1) for different polarimetric analysis.
Values of d300 are
higher than
values: 94 G for B//,
190 G for Bx
and
145 G for By.
They show some systematic departures between MSDP and MTR, probably due
to the time delay between both maps and to the different scanning modes
versus x and y (see
Sect. 7) resulting in additional image distortions. Residual
errors of co-alignment, slight rotations of telescope pointing, and
differential seeing effects are also disturbing the results. Finally,
especially in the case of spots, problems may arise from the MSDP CCD
camera, which is not perfectly linear at low light levels. In the
future, this camera should be calibrated more accurately.
10 Observing speeds for MSDP spectropolarimetry
Table 3
lists some cadences of THEMIS/MSDP observations in mode 1 of
Table 1.
Values of
and
are respectively the numbers of positions used to restore the full
field-of-view (y-steps smaller than the grid steps)
and to record the Stokes parameters,
and
are the scanning times for 1 x-step and for the
total target, and
is the solar area observed during 1 min of time.
Lines 1 and 2 correspond to polarimetric analysis with
synchronous I+S and I-S
(grid before the analyser). In principle
is sufficient. By taking
,
we get a large overlap between different parts of the field and avoid
edge effects. With polarization analysis, 30 arcsec are lost
at both ends of the field
to determine the accurate position of field-stop edges. The effective
field becomes
.
When
Stokes parameters are observed,
exposures are necessary for each scanning-step versus x.
To save overlaps, this step is also less than
.
It is currently
and the corresponding observed field-of-view
is restricted to
for one x scanning-step. Lines 3 and 4 are
extrapolations to the case of successive exposures I+S
and I-S, without grid analyser
and without Y-scanning. In lines 3 and 4, the times
are divided by
,
the number of successive exposures that were necessary to restore the
field-of-view split by the grid in lines 1 and 2. But then image
destretching becomes necessary before line profile inversion. Such a
mode is similar to a polarization analysis with modulator, and was used
at the LJR of Pic-du-Midi (Malherbe et al. 2004).
The speed of the instrument can be characterized by
.
The full spectropolarimetry of a 5 arcmin2
solar area does not need more than 10 min of time. Moreover,
the spatial overlaps versus x and y
might be reduced. In the case
and
,
the observing speed should be still increased by a factor 1.8 for items
(1) and (2).
11 Conclusion: capabilities of THEMIS/MSDP
We detailed in Sects. 1 to 4 some basic relationships between parameters of existing MSDPs, in the context of high observing cadences. In Sects. 5 to 10, we presented fast magnetic field measurements performed with THEMIS/MSDP in mode 1 of Table 1.
The spectral resolution is suited to strong lines, and LOS
magnetic fields can be measured simultaneously at 3 or
4 levels of the atmosphere, for example with lines NaD1 and H
(Sect. 5). But photospheric lines are required for vector
magnetic fields. Section 6 details a reduction software which
increases the spectral resolution by assuming some local conditions on
intensity gradients, inside neighbourhoods which do not exceed
.
To check the validity of results, observations with THEMIS/
MSDP and slit-spectroscopy THEMIS/MTR are compared in Sects. 7
to 9. Section 10 summarizes temporal resolutions of different
observing programmes of THEMIS/MSDP with mode 1 of Table 1. Performances
might be
improved with smaller values of
or faster cameras. A significant increase of cadences should be
obtained also by using polarimetry modulation and image destretching.
But in that case, accurate measurements imply high quality seeing.
THEMIS/MSDP can provide typical temporal resolutions smaller than 1 min for small fields, and 10 min for active regions. This allows to address a number of fast events mentioned in Sect. 1.
12 MDSP prospects
12.1 Spectral resolution
The spectral resolution is suited specifically to each one of the lines
observed simultaneously. But in the case of THEMIS, it is presently
limited by the slits of beam-shifters before the second pass on the
gratings. It can be increased by longer focal length spectrometers, or
by new optical systems. More powerful beam-shifters, with better
samplings and larger number N of channels, would
result also in a larger spectral coverage as well as a larger field of
view. Let us note that two additional methods can be used to increase
the spectral resolution. The first one is described in
Sect. 6. The second one would consist in reducing the spectral
sampling
thanks to successive exposures. Small translations of beam-shifters
(generally more accurate than grating rotations), can shift the
wavelengths. For example, positions
,
0,
would correspond to the sampling
.
This method is similar to the scanning used with tunable filters, but
needs image restoration.
12.2 Spatial resolution
Mirrors of spectrographs are used over large areas in case of multi-line MSDP, and astigmatism corrections are often necessary to provide spatial resolutions close to the diffraction limit, as far as the spectrograph optics is concerned. Cylindrical lenses can easily be put and adjusted in front of each transfer optics of CCD cameras. Such lenses are not present in THEMIS, but only in the MSDP of VTT, with two different corrections for the two lines.
The spatial resolution of THEMIS is also limited because the telescope is not equipped with adaptive optics. Instead, a tilting mirror corrects global shifts of the solar image at relatively high frequency. It is efficient, but not well suited to observations with grid. Since the mirror is put after the first focus, the image of the grid which is located before the analyser is moving at the output of the spectrometer, and flat fields cannot be used accurately. Adaptive optics, and in particular MCAO, should take the best advantage of images provided by MSDP. But even with AO, high spatial resolution implies short exposure times, reducing the signal-to-noise ratio.
Fortunately, it is possible to combine successive 2D multi-wavelength images with a ``wide-band image'', which can be deduced for example from the sum of all MSDP channels. A first reduction method, already used for circular polarimetry (Malherbe et al. 2004), consists in destretching by Local Correlation Tracking. Other more sophisticated ones, often used for filtergrams and based on speckle reconstructions (Keller et al. 1992; Bello Gonzalez et al. 2008; van Noort et al. 2008), can restore multi-wavelength intensity images across the line profile, before inversion. Let us note again that, while filtergrams of different wavelengths are generally obtained at different times, MSDP images of different wavelengths are simultaneous and not sensitive to differential seeing effects. Of course, fast CCD cameras are required to perform such observations.
12.3 Temporal resolution
The temporal resolution is proportional to the area observed synchronously, noted A in Eq. (8) of Sect. 2. It can be very high, thanks to the 3D character of MSDP data, although, as we have seen before, for high spatial resolution programmes, a number of successive exposures for image restoration leads to reducing the observing speed.
It is interesting to investigate the instrumental solutions
that can provide high-speed performances. We assume the best case, with
the width of channels Wx
equal to the useful field
(Eq. (1)). The total area of the output focal plane needed to
record the N channels is the sum S
defined by
![]() |
(15) |
It is determined by the size of camera mirrors and the number of lines observed simultaneously. From Eqs. (4), (6), (7), (8) we deduce
![]() |
(16) |
For a given instrument (a given ratio








Furthermore, it must be noted that the present numbers of MSDP channels do not exceed 16. It is obvious that new devicesshould be faster with greater numbers of channels (Eqs. (6), (7), (8)).
12.4 Signal-to-noise ratio
Photon fluxes and SNR can be increased in different ways. According to the items of Sect. 8, we see that the number of plane mirrors between both passes should be minimized as much as possible.
But a substantial improvement would consist in reducing dark intervals between slits defining MSDP channels. This should be possible, for example, by using image slicers, which should provide, in addition, a higher spectral resolution and more channels.
12.5 Conclusion
New MSDPs should provide multiline observations with spectral resolution and coverage suited to each line, high spatial resolution thanks to adaptive optics and image restoration, and high temporal resolution due to 3D data cubes. They should efficiently complement single-slit spectroscopy and tunable filters by addressing fast-evolving solar structures with very short time scales.
AcknowledgementsWe would like to thank the THEMIS team operating the telescope at Tenerife, and C. Coutard, R. Hellier, and A. Miguel, who performed many adjustments of MSDP instruments. We also thank the referee who proposed many improvements to this paper.
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Footnotes
- ... THEMIS/MSDP
- Based on observations made with the French-Italian telescope THEMIS operated by the CNRS and CNR on the island of Tenerife in the Spanish Observatorio del Teide of the Instituto de Astrofísica de Canarias.
All Tables
Table 1: Rough characteristics of some MSDP instruments (see Sects. 2 and 3).
Table
2: Upper limits
of the noise and rms of departures d between MSDP
and MTR results, averaged over the areas where the mean value of
B
is higher than 300 Gauss.
Table 3: Rough scanning times and temporal resolutions of THEMIS/MSDP (mode 1) for different polarimetric analysis.
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