# The Fibre Resolved opticAl and Near-ultraviolet Czerny-Turner Imaging
Spectropolarimeter (francis)

David B. Jess  Samuel D.T. Grant  William Bate  Jiajia Liu  Shahin Jafarzadeh
Peter H. Keys  Luís E. A. Vieira  Alisson Dal Lago  Fernando L. Guarnieri
Damian J. Christian  Doug Gilliam  Dipankar Banerjee  Astrophysics Research
Centre, School of Mathematics and Physics, Queen’s University Belfast,
Belfast, BT7 1NN, UK  Department of Physics and Astronomy, California State
University Northridge, Northridge, CA 91330, USA  Deep Space Exploration
Lab/School of Earth and Space Sciences, University of Science and Technology
of China, Hefei, 230026, China  CAS Key Laboratory of Geospace Environment,
Department of Geophysics and Planetary Sciences, University of Science and
Technology of China, Hefei, 230026, China  Max Planck Institute for Solar
System Research, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany  Rosseland
Centre for Solar Physics, University of Oslo, P.O. Box 1029 Blindern, 0315
Oslo, Norway  National Institute for Space Research (INPE/Brazil), São José
dos Campos, São Paulo 12227-010, Brazil  Big Bear Solar Observatory, 40386
North Shore Lane, Big Bear City, CA 92314, USA  National Solar Observatory,
University of Colorado Boulder, 3665 Discovery Drive, Boulder, CO 80303, USA
Aryabhatta Research Institute of Observational Sciences, Nainital, 263000,
Uttarakhand, India

###### keywords:

Astronomical instrumentation, Solar atmosphere, Solar radiation,
Spectrometers, Spectropolarimetry

.tifpng.pngconvert #1 .tif

##  1 Introduction

The solar physics community has recently benefited from a number of improved
telescopes and instruments that enable the dynamics of the Sun’s tenuous
atmosphere to be studied with unprecedented spatial, temporal, and spectral
resolutions, while also sampling the different polarisation states of the
incident light (see, e.g., the recent review by Jess et al., 2023). Such
facilities include the CRISP/CHROMIS instruments on the Swedish Solar
Telescope (SST; Scharmer et al., 2003, 2008; Scharmer, 2017), ROSA/HARDcam
imagers on the Dunn Solar Telescope (DST; Dunn, 1969; Jess et al., 2010b,
2012b), balloon-borne experiments such as Sunrise (Solanki et al., 2010;
Barthol et al., 2011; Berkefeld et al., 2011), space-based telescopes
including the Interface Region Imaging Spectrograph (IRIS; De Pontieu et al.,
2014), Solar Orbiter (Müller et al., 2013, 2020), and Parker Solar Probe (Fox
et al., 2016), and of course pioneering ground-based telescopes such as the
Daniel K. Inouye Solar Telescope (DKIST; Tritschler et al., 2016; Rimmele et
al., 2020; Rast et al., 2021).

Irrespective of whether a space-based, balloon-borne or ground-based facility
is employed, it has always been a goal of the instrument teams to maximise the
trifecta of (near-)simultaneous spatial and spectral information obtained
across different polarisation states at high temporal cadences. Traditional
instruments, which include Fabry-Pérot interferometers (e.g., see the recent
review by Bailén, Orozco Suárez, and del Toro Iniesta, 2023) and scanning
slit-based spectrographs, are unable to obtain simultaneity between spatial
information and the associated spectra, either through the need to scan in
wavelength space (e.g., Fabry-Pérots) or raster across a field of view (e.g.,
slit-based spectrographs). Of course, with constantly improving detector
sensitivities and more efficient optical configurations becoming commonplace
in instrument designs over the last decade-or-so (e.g., Jaeggli et al., 2010;
Kiselman et al., 2011; de Wijn et al., 2012; Puschmann et al., 2012, 2013;
Rimmele et al., 2020; de Wijn et al., 2022; Jaeggli et al., 2022), the
temporal restrictions are now significantly less of a challenge with regards
to scientific analyses of the data. Furthermore, multi-slit variations of
slit-based spectrographs can be considered an in-between solution that offers
better temporal resolution over their single slit counterparts. However, due
to the fundamental design of these instruments, they are inherently unable to
obtain strict simultaneity of their wavelength and spatial samplings.

In recent times, there have been a number of significant developments in the
construction of integral field units (IFUs) suitable for solar observing. As
described by Iglesias and Feller (2019), IFUs currently come in three distinct
formats: image slicers, microlens arrays, and fibre-fed bundles, each with
their own technical processes to capture two-dimensional (2D) images and
disperse the incident light into simultaneous cubes of [$x$, $y$, $\lambda$],
where $x$ and $y$ are the spatial dimensions and $\lambda$ is the wavelength
coverage sampled. Thus, it is possible to simultaneously acquire spectral
information across a 2D field-of-view, and when performed at high cadences,
enables dynamic solar events to be examined with high degrees of precision.
Recently, the Diffraction Limited Near Infrared Spectropolarimeter (DL-NIRSP;
Jaeggli et al., 2022), the Multi-Slit Image Slicer based on collimator-Camera
(MuSICa; Calcines, López, and Collados, 2013), the Microlens Hyperspectral
Imager (Mi-Hi; van Noort et al., 2022), the GREGOR Infrared Spectrograph
(GRIS; Collados et al., 2012; Dominguez-Tagle et al., 2022), and microlens-
etalon coupled spectrographs (e.g., Ranganathan et al., 2018) have all been
prototyped, constructed, and tested with great success. Indeed, there are a
number of conceptual IFU designs that have been put forward as first-light
instruments on the planned European Solar Telescope (EST; Quintero Noda et
al., 2022), which is a European led, 4.2 m on-axis facility due to be
operational within the next decade. While IFUs for solar science are in their
relative infancy, more advancements have been made in the night-time community
(see the overview provided by Abell et al., 2009), with the James Webb Space
Telescope employing the Mid-Infrared Instrument (MIRI; Wells et al., 2015) and
the Near-Infrared Spectrograph (NIRSpec; Jakobsen et al., 2022) instrument,
which employ long-slit configurations similar to an image slicer arrangement
(Regalado Olivares et al., 2022). Of course, the need for IFUs to place both
spatial and spectral domains on a single detector chip naturally results in a
reduced field-of-view size, which unfortunately is a limiting factor in any
instrument that attempts to observe a three-dimensional data space with two-
dimensional detectors. This effect can be minimised during the design phase by
using larger format detectors and smaller diameter fibres to better match the
diameter of each fibre to the pixel size of the imaging camera.

Fabry-Pérot interferometers, slit-based spectrographs, and IFU spectrographs
are all valuable tools in the field of astrophysics, each with its own set of
advantages and disadvantages. The choice of which spectrograph to use depends
on the specific research objectives and observational conditions. The
asynchronous nature of the data taken by Fabry-Pérot interferometers and slit-
based spectrographs may result in undesired effects due to changing
atmospheric conditions between each exposure, or through the failure to
capture dynamic solar features that evolve on timescales less than the typical
scan/raster duration (Scharmer, 2006; Schlichenmaier et al., 2023). IFUs
attempt to mitigate this challenge by acquiring spectral and spatial
information simultaneously, although they are typically forced to utilise a
smaller field-of-view size and/or a reduced spatial resolution (Iglesias and
Feller, 2019). Due to IFUs attempting to sample three data dimensions
([$x,y,\lambda$]) with two-dimensional detectors, they become naturally less
efficient in the use of imaging detector pixels than their Fabry-Pérot
interferometer and slit-based spectrograph counterparts. This means that even
with full detector pixel usage efficiency, the field of view would remain
smaller than for a comparable Fabry-Pérot instrument at the diffraction limit
(Allington-Smith, 2006; Hagen and Kudenov, 2013). However, for cases where
simultaneous spatial and spectral sampling is paramount, the benefits of IFUs
can outweigh the drawbacks of a reduced field of view and/or reduced spatial
resolution. For example, it has been shown that the study of impulsive shock
waves in sunspot umbral atmospheres can be negatively influenced by the time
required for scanning Fabry-Pérot instruments to construct spectral profiles
(Felipe, Socas-Navarro, and Przybylski, 2018; Yurchyshyn et al., 2020), hence
making an IFU the ideal choice of instrument.

To date, many IFUs have been developed to work primarily in the
(near-)infrared portion of the electromagnetic spectrum, including DL-NIRSP,
the SpectroPolarimetric Imager for the Energetic Sun (SPIES; Lin, 2012; Anan
et al., 2019), and GRIS. However, the blue/green portion of the
electromagnetic spectrum offers numerous spectral lines for examination of the
lower solar atmosphere, including recent studies involving Ca ii H/K (e.g.,
Jafarzadeh et al., 2013; Grant et al., 2015; Jafarzadeh et al., 2017b; Mathur
et al., 2022; Morosin et al., 2022), H$\beta$ (e.g., Abbasvand et al., 2020;
Rouppe van der Voort et al., 2021; Kowalski et al., 2022; Kuridze et al.,
2022), Na i D1/D2 (e.g., Jess et al., 2010a; Kuridze et al., 2016; Chae et
al., 2017), as well as other magnetically-sensitive lines that have not yet
been fully exploited for solar research (e.g., Ca i 422.7 nm; Capozzi et al.,
2020), none of which are interspersed with telluric lines. Furthermore, it has
been shown that the Ca ii H & K lines, with effective Landé $g$-factors of
$g_{\mathrm{H}}=1.333$ and $g_{\mathrm{K}}=1.167$, respectively, are highly
suited for circular polarisation studies (Martinez Pillet et al., 1990),
especially since due to the atomic transition of the Ca ii H line
($j=\frac{1}{2}$, $j^{\prime}=\frac{1}{2}$; Stenflo, Baur, and Elmore, 1980;
Landi Degl’Innocenti, 1984), no linear polarisation is produced in the core of
this line due to resonance scattering. Motivated by such cutting-edge studies,
it now appears timely to pursue the construction of an IFU dedicated to the
blue/green portions of the electromagnetic spectrum. Furthermore, the lower
wavelengths associated with these regions, when compared to (near-)infrared
alternatives, allows for thinner cladding thicknesses around each fibre core
(Goto et al., 2015) that helps to promote a better observational filling
factor of the 2D fibre array without needing to employ microlenses, which (if
used) come at an additional financial cost.

Here, we report on the design, construction, commissioning and science
verification of a new fibre-fed IFU named the Fibre Resolved opticAl and Near-
ultraviolet Czerny-Turner Imaging Spectropolarimeter (francis), which is
initially put forward as a prototype instrument for the proposed Indian
National Large Solar Telescope (NLST; Hasan et al., 2010; Dhananjay, 2014).
The NLST will be a state-of-the-art 2m-class telescope, built close to the
Chinese border in Merak, designed for high-resolution studies of the solar
atmosphere. Merak, which is in the Himalayan mountain region at an altitude
greater than 4000 m, has an extremely low water vapour content, resulting in
excellent conditions for optical and infrared observations. Furthermore, the
NLST will be the second largest solar telescope in the world when it sees
first light in the latter stages of the decade and will be ideally situated
15.5 hours ahead of the world’s largest solar telescope (DKIST) in Hawaii,
offering the unique ability to provide unrivalled 24/7 ground-based
observations of evolving solar phenomena when combined with other world-class
optical facilities, such as the those available in North America (e.g., the
DST and Big Bear Solar Observatory, BBSO; Goode et al., 2010), the Canary
Islands (e.g., the SST and GREGOR; Schmidt et al., 2012), and China (e.g., the
New Vacuum Solar Telescope, NVST, and the Chinese Large Solar Telescope, CLST;
Liu et al., 2014; Rao et al., 2015, 2020).

Figure 1.: A simplified schematic of the internal configuration of the
Princeton Instruments IsoPlane® 320 spectrograph housing. ‘A’ represents the
linearised fibre array that is aligned with the spectrograph slit, ‘B’ is a
concave toroidal-shaped collimating mirror with an off-axis angle, $\alpha$,
‘C’ is the chosen diffraction grating (either 4320 lines/mm, 3600 lines/mm, or
2400 lines/mm) with angles of incidence and refraction, $\alpha_{g}$ and
$\beta_{g}$, respectively, ‘D’ is the aspheric aberration correction mirror
with an angle of incidence, $\beta_{pl}$, ‘E’ is the concave focusing mirror
with an angle of incidence, $\beta$, and ‘F’ is the spectral imaging detector
placed at a maximum angle, $\delta$, to the focal plane. The background image
is adapted from Princeton Instruments hardware specification documents.

##  2 Instrumentation

In 2018, a relatively small budget ($\sim$$120k USD) was secured to design,
build, transport and test an IFU, which would act as a prototype instrument
for the upcoming Indian NLST facility. The primary science objectives of the
NLST revolve around studying the nature and subsequent consequences of solar
magnetism (Hasan, 2010; Hasan et al., 2010). As outlined by Singh (2008), the
NLST aims to investigate the role of magnetohydrodynamic (MHD) waves in the
supply of energy flux across different layers of the solar atmosphere,
including the determination of their periods across a wide range of spatial
and temporal scales. This scientific objective is supported by others,
including the study of dynamically evolving structures that rely on high-
cadence observations, examination of large-scale features (including pores,
sunspots, and entire active regions) and their role in triggering rapid plasma
motions, such as those associated with flares, filament eruptions, coronal
mass ejections, etc.

Recent work by Ramesh et al. (2016) examined the typical evolutionary
timescales of dynamic features in the solar atmosphere and stipulated that a
temporal cadence of $\sim 2-3$ s is required to study such processes with the
NLST. While investigating potential instrumentation for the NLST, Singh (2008)
stated that a spectral resolution of a few mÅ is required to adequately
resolve the velocity signatures ($\sim 100$ m/s) associated with MHD waves in
the solar photosphere. However, for chromospheric MHD wave signatures, which
motivated the design of the francis instrument and often have wave amplitudes
exceeding $10$ km/s (Jess et al., 2023), the spectral resolution required for
chromospheric lines (e.g., Ca ii H/K) can often be relaxed to several tens of
mÅ (Tomczyk et al., 2016). Furthermore, the observation of dynamic MHD wave
phenomena, such as the development of umbral flashes in sunspot atmospheres,
requires both high time resolution (consistent with $\sim 2-3$ s as stated
above) and simultaneous sampling of the entire sunspot umbra, hence making an
IFU the logical choice of instrument. Finally, Sankarasubramanian, Hasan, and
Rangarajan (2010) and Ramesh et al. (2016) provide a list of crucial spectral
lines that are required to be observed as part of NLST operations to address
the scientific objectives, including the Ca ii K, H$\beta$, and H$\alpha$
absorption lines. As a result, the francis instrument prototype has the
overarching goals of being able to obtain complete spectral mapping of a two-
dimensional field of view with a temporal cadence of $<3$ s, a spectral
resolution no more than a few tens of mÅ, with sensitivity to key
chromospheric spectral lines with wavelengths as low as $\approx 390$ nm,
including Ca ii K, H$\beta$, and H$\alpha$.

For simplicity and to minimise the number of additional components needed
(e.g., microlenses and additional mirrors), a fibre-fed IFU was chosen over
its image slicer and microlens array counterparts. With a budget of
$\sim$$120k USD, it was necessary to obtain all components required for the
production of the final instrument, including:

  * •

Fibre optics (including the array assembly and mapping);

  * •

Spectrograph housing (including adjustable entrance slits);

  * •

Diffraction gratings (including movable mounts);

  * •

Digital camera for acquiring observed spectra;

  * •

Polarisation optics;

  * •

High-pass and bandpass filters (including filter wheels);

  * •

Calibration lamps spanning near-UV and optical wavelengths;

  * •

Acquisition PC and data storage infrastructure;

  * •

Control software (spectrograph, camera, polarisation optics, etc.);

  * •

Water cooling and circulation hardware;

  * •

Transportation cases; and

  * •

Shipping and travel costs associated with the commissioning time.

Below, we breakdown all of the components selected for the final instrument
prototype, before discussing first-light commissioning observations in Section
3.

###  2.1 Spectrograph

As a result of the limited budget, it was decided to centre the build on the
well-established Czerny-Turner spectrograph housing produced by Princeton
Instruments111Princeton Instruments are part of the Teledyne Imaging Group —
www.teledyneimaging.com. The Princeton Instruments IsoPlane® 320 spectrograph
housing was chosen due to its rugged cast steel construction and previous
successful scientific applications in laboratory and optical astrophysics
(e.g., Wu et al., 2016; Kafle et al., 2021; Cousin et al., 2022).

In this configuration, light is incident on the slit plane as a divergent
beam, which propagates to a concave toroidal-shaped collimating mirror with an
off-axis angle, $\alpha$ (see Figure 1). The light is subsequently reflected
as a collimated beam and directed towards the chosen diffraction grating. For
the prototype IFU presented here, 3 unique holographic reflection gratings
were selected, comprising of 4320 lines/mm, 3600 lines/mm, and 2400 lines/mm
variants. Holographic gratings, unlike ruled diffraction gratings, are
produced by exposing the underlying photosensitive material to the
interference pattern produced by two interfering laser beams. The interference
pattern creates a finely structured (periodic) pattern on the surface, which
is then chemically treated to expose a sinusoidal surface pattern capable of
precise control over light dispersion (Labeyrie and Flamand, 1969; Baldry,
Bland-Hawthorn, and Robertson, 2004). Holographic gratings were selected here
due to the optical techniques used in their manufacture not introducing the
spacing errors and/or surface irregularities often found in traditional ruled
gratings. This helps to not only provide consistent linear dispersion
properties, but also suppresses stray light and ghosting artefacts when high-
density gratings are required (Steiner et al., 2013). The 4320 lines/mm, 3600
lines/mm, and 2400 lines/mm gratings employed in the francis instrument were
manufactured by Richardson Gratings222Richardson Gratings are part of the
Newport Corporation — www.newport.com, with the area of each grating equal to
$102\times 102$ mm2.

Following reflection off the concave toroidal-shaped mirror (labelled ‘B’ in
Figure 1), the collimated beam strikes the grating with an angle of incidence,
$\alpha_{g}$, and is diffracted as a dispersed beam with an angle of
refraction, $\beta_{g}$. The diffracted beam from the chosen holographic
reflection grating is directed towards an aspheric aberration correction
mirror (which is rotationally symmetric) with an angle of incidence,
$\beta_{pl}$, before being deflected towards an aspheric concave focusing
mirror with an angle of incidence, $\beta$. Following reflection from the
final focusing mirror, the convergent beam forms images of the dispersed input
light on to a detector placed in the focal plane. Here, the detector may be
placed with a maximum angle, $\delta$, to the imaging plane, in order to
capture spectral images that are close to being free from axial and field
aberrations (i.e., is approximately anastigmatic). A simplified schematic of
the Princeton Instruments IsoPlane® 320 spectrograph housing, including
internal optics and the diffraction grating, is shown in Figure 1.

###  2.2 Fibre bundle

To feed the spectrograph, an optical fibre bundle was designed to capture an
approximately square two-dimensional field-of-view, then linearise the fibres
into a one-dimensional array that can be placed against the entrance slit of
the spectrograph. Initially, when the project began, the available bench space
at the NLST was unknown due to the ongoing design phase. Thus, a $1.5$ m long
optical fibre bundle was chosen to ensure it had the capability to function
with different configurations at the future telescope site. Shorter fibre
bundles would help minimise the risk of stress-related fibre breakages (El
Abdi et al., 2008), but this risk was deemed necessary as part of the
prototype trialling of the instrument. However, to help protect the fibre
bundle from excess stress being exerted on the fibres, the final bundle was
encased using shrink-fit PVC monocoil tubing.

Figure 2.: Left: A view of the two-dimensional fibre end, where the 400
optical fibres are arranged in a closely packed $20\times 20$ hexagonal
configuration, which is seen as the dark rectangular region towards the centre
of the brass ferrule. The surface area covered by the fibre array is $1.082$
mm2, with light transmission provided by the cores of the optical fibres with
an effective area of $0.503$ mm2, hence providing a filling factor of
approximately $46.5$%. The brass end of the ferrule is polished to a flatness
that is $<1~{}\mu$m, enabling a back reflection to be captured by an
additional camera to help with fibre alignment. Right: The linearised end of
the fibre bundle, where all 400 fibres are arranged in a one-dimensional
configuration that is $22.0$ mm long, which is seen in the image as the narrow
dark band spanning the centre of the brass ferrule. The linearisation of the
fibre array enables the propagated light to pass through the entrance slit of
the spectrograph and, with the mapping of the fibres known, two-dimensional
spectral images to be reformed following calibration.

As the primary goal was to obtain spectra in the near-UV and blue portion of
the electromagnetic spectrum, we were able to utilise thinner cladding
thicknesses around the optical fibre cores (Goto et al., 2015), yet still
retain total internal reflection along the fibres for maximum ray (critical)
angles $<10^{\circ}$. Circular cross-section fibres were provided by FiberTech
Optica333FiberTech Optica — https://fibertech-optica.com, comprising of a
$40~{}\mu$m diameter silica core, a $4~{}\mu$m thick silica cladding, and a
$3.5~{}\mu$m thick polyimide coating, providing a total diameter of
$55~{}\mu$m for each fibre and a numerical aperture, $NA=0.22\pm 0.02$. At the
two-dimensional array end of the fibre bundle, a $20\times 20$ closely packed
hexagonal configuration was chosen to maximise the filling factor of the
fibres to light, providing a total of 400 individual fibres to be placed in
the focal plane of the incident beam. The final dimensions of the two-
dimensional array is $1.127\times 0.960$ mm2, providing an occupied area of
$1.082$ mm2. Each fibre core has a surface area of $1.257\times 10^{-3}$ mm2,
hence 400 fibres cover a total area of $0.503$ mm2, providing an overall
filling factor of $46.5$%. This is a comparable filling factor to the DL-NIRSP
IFU commissioned on DKIST (Jaeggli et al., 2022).

Table 1.: Overview of prototype francis fibre characteristics employed during the August 2022 commissioning phase. Fibre parameter | Value
---|---
Number of fibres | 400
Bundle configuration | $20\times 20$
Fibre cross-sectional shape | Circular
Fibre material | 100% multi-mode silica
Fibre core diameter | 40.0 $\mu$m
Fibre cladding thickness | 4.0 $\mu$m
Fibre coating thickness | 3.5 $\mu$m
Total fibre diameter | 55.0 $\mu$m
Fibre packing configuration | Hexagonal
2D fibre end |
Dimensions of bundle group |  $1.127\times 0.960$ mm2
Bundle group termination | Stainless steel ferrule with brass insert
Dimensions of bundle group ferrule | 10 mm diameter / 50 mm length
Linear fibre end |
Dimensions of linearised fibre group |  $22{\,}000\times 55$ $\mu$m2
Linearised fibre group termination | Stainless steel ferrule
Dimensions of linearised group ferrule | 28 mm diameter / 100 mm length
Numerical aperture ($NA$) | $0.22\pm 0.02$
Overall length of fibre array | 1.5 m
Fibre array sheathing | Black PVC monocoil tubing

The two-dimensional fibre array is housed at the centre of a circular brass
ferrule with a diameter of $10$ mm (see the left panel of Figure 2). The brass
end is polished to a flatness that is $<1~{}\mu$m, which enables the ferrule
to provide a back-reflection image that can be captured by another camera to
assist with the co-alignment between the observed spectra and the targeted
field-of-view. For this purpose, a ROSA (Jess et al., 2010b) CCD camera was
employed to capture the back-reflection image, which allows use of the master
ROSA synchronisation trigger to ensure simultaneity between contextual/back-
reflection imaging and the acquired spectra444Note — the back-reflection setup
is affectionately known as the Detecting the Orientation of the bUndle Group
camera (DOUGcam), in honour of the tireless assistance provided by D. Gilliam
during the initial commissioning run of francis.. Over the $1.5$ m length of
the optical fibre, the $20\times 20$ configuration of the fibre bundle is
linearised into a one-dimensional array prior to being mounted at the entrance
slit of the spectrograph (see the right panel of Figure 2). Here, all 400
fibres arranged side-by-side provide an array length equal to $22.0$ mm, which
required a larger brass ferrule to accommodate this increased dimension over
the original two-dimensional layout that utilised a $10$ mm diameter brass
ferrule.

As discussed by Resisi, Popoff, and Bromberg (2021), multi-mode fibres are
sensitive to various types of fluctuations, such as thermal, acoustic, or
mechanical vibrations, which can induce modal interference as a result of
changes in the phase of the guided modes. Here, the permitted number of
transversal electromagnetic modes within an idealised circular cross-section
fibre is proportional to the square of the fibre-core radius (Daino, Marchis,
and Piazzolla, 1980; Hill, Tremblay, and Kawasaki, 1980). Experimental
characterisation of optical fibres by Baudrand and Walker (2001) revealed that
modal noise is reduced when the energy is spread out over more permitted
modes. Furthermore, Baudrand and Walker (2001) found that lower wavelengths
provide higher numbers of available modes within the same fibre. Hence, the
combination of large-diameter fibre cores and the blueward wavelength regime
intrinsic to the francis instrument is ideal for minimising transmitted modal
noise within the fibres. To further minimise modal interference, the fibre
bundle is securely clamped to the optical bench and remains fixed throughout
the duration of any solar observing campaign, which helps to mitigate time-
varying modal interference patterns arising from telescope vibrations and/or
accidental movements of the fibre bundle. Furthermore, to protect the brass
ferrule from damage when being mechanically clamped to the entrance slit of
the spectrograph, it was compression fit inside a larger ($28$ mm diameter)
stainless steel tube, which is visible around the outside of the brass insert
in the right panel of Figure 2.

Finally, the ferrule housing the linearised array is positioned in-line with
the entrance slit, which is operated with a slit width of $50~{}\mu$m to
ensure all light from the individual fibres is allowed to propagate into the
spectrograph. Leading on from the discussions above concerning modal
interference patterns with multi-mode fibres, it must be highlighted that
inherent fibre properties (e.g., imperfections at the core-cladding interface)
can produce time-varying speckle patterns at the fibre exit that are modulated
by any unconstrained mechanical stresses and/or temperature shifts (Epworth,
1979). As described by Goodman and Rawson (1981), and experimentally
demonstrated by Lemke et al. (2011), the fraction of the illuminated fibre end
face that is ultimately transmitted to the imaging detector plays an important
role in ensuring the response of the instrument remains stable with time. It
is important to note that a reduction in the transmitted fraction of light
coming from the fibre does not necessarily only stem from the use of a narrow
slit at the entrance to the spectrograph (i.e., a slit width less than the
diameter of the fibre core), but will also result from overfilling the
diffraction grating in an attempt to increase the spectral resolution. For the
initial commissioning of the francis instrument, we chose to implement a slit
width ($50~{}\mu$m) that was larger than the diameter of the fibre cores
($40~{}\mu$m) to ensure modal interference noise was minimised in the captured
spectra. This approach, in addition to the scrambling processes (see, e.g.,
Avila and Singh, 2008) inherent to fibres, also help to minimise uncertainties
from different spatial and angular information arising from variable seeing
conditions, since the light that is coupled into the fibres largely results in
a similar response from the spectrograph and thus helps to stabilise the
signal (Lemke et al., 2011). An overview of the optical fibre bundle employed
is provided in Table 1.

Figure 3.: Transmission profiles of the three different bandpass filters
selected to prevent conflicting spectral orders from contaminating the final
spectral images. The shaded blue, green, and red bandpass filters span
$376-424$ nm, $411-439$ nm, and $574-600$ nm, respectively. Each filter allows
for the isolation of prioritised spectral lines, including the Ca ii H & K
lines ($396.847$ and $393.366$ nm, respectively, highlighted using vertical
dashed black lines), the Ca i line ($422.673$ nm, indicated with the vertical
dot-dash line), and the Na i D1 & D2 line pair ($589.592$ nm and $588.995$ nm,
respectively, highlighted using the vertical dotted black lines). Each
bandpass filter has transmissions $>90$% at the wavelengths of interest.

###  2.3 Wavelength order filters

The transmission profile of the DST spans the near ultraviolet ($\sim 350$ nm)
through to the far infrared. Light incident on a diffraction grating produces
multiple orders, whereby monochromatic light at a certain wavelength appears
at more than one angle of diffraction. As a result, the superposition of
different orders of diffracted light on the detector can lead to ambiguous
spectral data. Hence, bandpass filter sets were purchased to help eliminate
conflicting spectral orders and allow for unambiguous capture of spectral
signatures from solar sources.

Specific spectral lines were prioritised for the purposes of obtaining
suitable bandpass filters. In total, $3$ lines were chosen: (1) Ca ii H/K at
$\sim 395$ nm, (2) Ca i at $\sim 423$ nm, and (3) Na i D1/D2 at $\sim 589$ nm,
with the final filters manufactured by Semrock555Semrock are part of the IDEX
Health & Science corporation — https://www.idex-hs.com/semrock. Each filter
was mounted in a circular housing with an aperture diameter of $50$ mm to
accommodate a wide range of future optical beam sizes. At the wavelengths
corresponding to the prioritised spectral lines, each bandpass filter has a
transmission exceeding $90$%, which helps to maximise light reaching the
spectrograph (see Figure 3). The selected filter is placed upstream of the
two-dimensional fibre head, thus pre-selecting the wavelengths of interest
before being guided into the spectrograph by the fibre bundle.

###  2.4 Camera and data storage

To image the resulting spectra, a Princeton Instruments Kuro 2048B scientific
CMOS camera was selected. This camera has a back-illuminated $2048\times 2048$
pixel2 imaging array and utilises $11\times 11~{}\mu$m2 pixels to form an
imaging area that is $22.53\times 22.53$ mm2. A large imaging area was
necessary to accommodate all 400 optical fibres once re-formatted into a
linearised array. As highlighted in Table 1, each fibre has an outer diameter
of $55~{}\mu$m, resulting in a final length of $22.0$ mm once linearised prior
to entry into the spectrograph. Due to the spectrograph employing a $1:1$
magnification, each imaged fibre also has a total diameter of $55~{}\mu$m,
resulting in its information being spread across $\approx 5$ detector pixels,
thus creating an oversampled final spectral image. However, importantly, the
imaging chip length of $22.53$ mm is able to accommodate all 400 optical
fibres within a single frame. The Kuro 2048B camera has a well depth of
$80{\,}000$ e- and provides $16$-bit readout at a maximum rate of $23$ frames
per second. A readout noise of $1.5$ e- (rms) is maintained using liquid-
assisted cooling, providing a dark current of approximately $0.7$ e-/pixel/s
at $-25\,^{\circ}$C. For this setup, a Koolance666Koolance —
https://koolance.com EX2-1055 liquid cooling system was employed, which has a
cooling capacity of $900$ W (or $3071$ BTU/hr) with a $25\,^{\circ}$C liquid-
ambient delta temperature at a circulation rate of $4.5$ litres/min. A peak
quantum efficiency (QE) of $>95$ % is found at approximately $560$ nm, with
QEs $>60$ % across the entire wavelength range sampled by francis ($390-700$
nm; see Figure 4 for more details).

Figure 4.: The quantum efficiencies (QEs) of the Princeton Instruments Kuro
2048B scientific CMOS camera chosen to image the fibre-resolved spectra.
francis operates within the wavelength range of $390-700$ nm, hence this
camera provides QEs $>60$ % across the useable wavelength domain. This image
is kindly reproduced from the Teledyne Imaging Group resource centre
(https://www.photometrics.com/learn/imaging-topics/quantum-efficiency).

The camera utilises a rolling shutter and communicates to the storage PC using
a USB 3.0 interface. Basic setup (e.g., exposure times, windowing and binning
functions, etc.) is controlled via Princeton Instruments LightField® software
that is installed on the main storage PC. Here, the PC employed is a simple
Microsoft Windows-based laptop that is connected via a USB 3.1 (10 GB/s)
interface to an external hard disk enclosure running two 4 TB solid-state
disks in a RAID-0 configuration. Data is saved directly from LightField® on to
the 8 TB disk, enabling several hours of unbroken observations to be
accumulated. Additionally, the ROSA synchronisation box (see Jess et al.,
2010b, for more information) can be connected to the Kuro 2048B camera by way
of a TTL voltage signal, allowing the camera sequence to be triggered by the
master ROSA machine for microsecond precision spectra/imaging capabilities.

###  2.5 Polarisation optics

To enable polarimetric measurements of the incident light, a number of
additional polarisation optics can be placed upstream of the fibre bundle. As
discussed by Okamoto (2006), it is not typical for the polarisation state of
light to be maintained while propagating through fibre optics. Aspects that
are often difficult to alleviate completely, including mechanical vibrations,
temperature variations, and slight bending of the fibre bundle can readily
manipulate the final polarisation state of the output light (Jaeggli et al.,
2022). As a result, it was decided that any polarisation optics introduced
should be placed upstream of the fibres, hence pre-selecting the polarisation
state to be transmitted and imaged, thus minimising potential impacts caused
by the fibres themselves. To accomplish this, 2 liquid crystal variable
retarders (LCVRs) were purchased from Meadowlark Optics777Meadowlark Optics —
https://www.meadowlark.com/, each with a UV coating to allow operation within
the wavelength range of $390-600$ nm and a large clear aperture of $40.6$ mm
to facilitate future optical setups that may employ large beam sizes. The
LCVRs are also temperature controlled via a digital interface, and offer
typical response times of $\approx 5$ ms to switch from one-half to zero waves
(i.e., low to high voltage) and $\approx 20$ ms to switch from zero to one-
half wave (i.e., high to low voltage).

Figure 5.: The transmission curve of the custom high-pass filter manufactured
to protect the polarisation optics from wavelengths $\leq 380$ nm, which can
damage the organic material found in the LCVRs. The typical spectral range of
francis is highlighted using the shaded green region that is bounded by the
vertical black dotted lines, while the blue hashed regions denote spectral
windows that are outside of the initial instrument specifications. The bump of
enhanced transmission between $260-310$ nm is not a concern since it falls
below the typical atmopsheric cut-off wavelength found at ground-based
telescope sites. The average transmission of this high-pass filter is $97.1$%
across the spectral range of $390-700$ nm.

Figure 6.: A schematic of the components making up the polarisation optics for
the francis spectrograph. Incident light from the telescope is denoted by the
black circular shape in the upper-left corner. The light rays, highlighted
using solid green tracers, then pass through a high-pass filter to remove
wavelengths $<380$ nm that are damaging to the organic material within the
LCVRs. The unpolarised light then passes through the 2 LCVRs to produce a
modulated beam, where the polarisation state is still unknown, but modified by
the LCVRs in a pre-determined way. Two possible components of light output by
the LCVRs are shown for visualisation purposes using blue and red arrows, each
of which are polarised perpendicular to one another. A twisted nematic liquid
crystal cell (i.e., an optical shutter) is then used to rotate the beam by
either $0^{\circ}$ or $90^{\circ}$, producing the unrotated beam (1) and the
rotated beam (2), respectively, which are indicated in the figure (note: a
conventional dual-beam setup employs a polarising beam splitter or a Wollaston
prism to negate the need for an optical shutter; see the main text for more
information). Finally, the beam can then be analysed by passing through the
linear polariser to produce a measurable intensity signal corresponding to the
modulated polarisation state produced by the combination of the LCVRs, optical
shutter, and linear polariser. Here, beam (1) and beam (2) can be selected
independently from one another by using the optical shutter to rotate the beam
by $0^{\circ}$ and $90^{\circ}$, respectively. The modulated light then forms
an image on the two-dimensional fibre array, for propagation into the
spectrograph for subsequent Stokes imaging. Optical component images provided
courtesy of 3DOptix (https://3doptix.com).

However, care must be taken with the LCVRs as their organic properties means
they can become degraded if exposed to wavelengths $<380$ nm. To protect the
LCVRs, a custom high-pass filter was sourced from Laser 2000888Laser 2000 —
https://photonics.laser2000.co.uk that offers $\approx 0$% transmission for
wavelengths $<250$ nm, or an equivalent optical density (OD; where the OD is
the negative of the base-10 logarithm of the transmission that varies between
0 and 1) of $\mathrm{OD}>6$ (see Figure 5). There is a slight increase in
transmission between $260-310$ nm that peaks at $\approx 10$%
($\mathrm{OD}\geq 0.977$), although this is beneath the atmospheric cut-off
wavelength of $\sim 310$ nm found at ground-based telescope facilities (Erlick
et al., 1998; Lee et al., 2019). Transmission remains $\approx 0$%
($\mathrm{OD}>6$) up to $\approx 382$ nm, before rising steeply to $>83$%
($\mathrm{OD}\leq 0.080$) at $\approx 388$ nm. Transmission remains $>87$%
($\mathrm{OD}\leq 0.060$) across the operational spectral range of $390-700$
nm as shown in Figure 5, with a mean transmission of $97.1$%
($\mathrm{OD}=0.012$).

Typically, once the light has passed through the 2 LCVRs, a dual-beam
configuration will separate the polarisation states of the modulated beam,
using either a polarising beam splitter or a Wollaston prism, and image these
states independently (e.g., Nagaraju et al., 2008; de Wijn et al., 2022;
Jaeggli et al., 2022). However, implementing a dual-beam setup here would be
beyond the scope of the current prototype, especially if additional imaging
detectors and optics were required. Even if the single Princeton Instruments
Kuro 2048B camera was employed to capture both modulated states in the most
simplistic configuration, this would halve the available spectral range, which
is something we wanted to avoid. As a result, for the francis prototype, we
decided to implement a combination of both a twisted nematic liquid crystal
cell (i.e., an optical shutter, also obtained from Meadowlark Optics) and a
linear polariser to sequentially alternate each modulated polarisation state
through the spectrograph. In this configuration, the optical shutter is able
to rotate the output beam from the LCVRs by either $0^{\circ}$ or $90^{\circ}$
through the application of a high-frequency voltage source. With $0$ V
applied, the optical beam is rotated by $90^{\circ}$, while the application of
a $8$ V/$2$ kHz AC square-wave signal causes the optical beam to pass straight
through the optical shutter without rotation. Timescales are $0.4$ ms and
$5.0$ ms for $0^{\circ}\rightarrow 90^{\circ}$ and $90^{\circ}\rightarrow
0^{\circ}$ beam rotations, respectively. Like the LCVRs, the optical shutter
is temperature controlled with a clear aperture of $40.6$ mm to accommodate
future telescope facilities operating with large beam sizes and has a UV
coating to enable use with wavelengths as low as $390$ nm. Once the modulated
beam has been rotated (or not), an ultrabroadband ($300-2700$ nm operating
range) linear polariser is used to analyse the output beam by creating a
measurable intensity signal corresponding to the modulated polarisation state
produced by the combination of the LCVRs, optical shutter, and linear
polariser, which is then focused on the two-dimensional ($20\times 20$) fibre
array before being propagated into the spectrograph for subsequent spectral
imaging. A schematic of the polarisation optics are shown in Figure 6 for
easier visualisation.

The polarisation optics include three components (2 LCVRs and 1 optical
shutter) that require computer control to ensure the beam modulation is
synchronised with the spectrograph (if adjusting the chosen grating and/or
central wavelength of the spectral range) and acquisition camera (to make sure
spectral images are not obtained during the modulation transition phases).
Thankfully, the digital control interfaces provided by Meadowlark Optics (for
the 2 LCVRs and the optical shutter) and Princeton Instruments (for the Kuro
2048B sCMOS camera) come complete with the necessary software development kit
(SDK) to enable the instrument hardware to be paired with and controlled by
the LabVIEW® software provided by National Instruments. LabVIEW® is a
graphical programming environment that enables the automation of LCVR/optical
shutter configurations, diffraction grating rotations, and image acquisitions
to ensure that the liquid crystals have settled in their selected states
before exposing the camera to the modulated incident light. While it is
possible to configure the liquid crystals, diffraction gratings, and camera
settings manually, it is significantly more robust and streamlined to pair all
pieces of hardware (using their respective SDKs) under the same software
umbrella. This type of solar instrumentation automation using the LabVIEW®
environment has been successfully demonstrated in a number of previous
projects (e.g., Kotani et al., 2010; Bethge et al., 2011; Bailey, Cotton, and
Kedziora-Chudczer, 2017; Ren and Wang, 2020).

##  3 Instrument commissioning and science verification

The francis instrument was designed and constructed, with final laboratory
tests being conducted on-time towards the start of 2022. However, at this
stage, construction of the Indian NLST had not yet commenced. As a result, it
was decided that initial science verification should be performed on another
facility, notably the Dunn Solar Telescope (DST), in the Sacramento Peak
mountains, New Mexico, USA during the summer of 2022. Due to busy scheduling
at the DST, we were only able to be granted 10 days of telescope time during
the latter stages of August 2022. Thankfully, following a few days of
intermittent sunshine and poor seeing conditions while the instrument was
being setup and focused on the optical bench, the weather improved and we were
presented with a few continuous hours of cloudless skies and excellent
atmospheric seeing. For the first stage of instrument commissioning presented
here, the polarisation optics were not utilised, which was a consequence of
the limited (10-day) observing time available to the team to setup, test,
refine, benchmark, then pack away the complete instrument. However, as
discussed in Section 3.7 below, addition of the polarisation optics is a
priority for the next observing campaign with francis.

###  3.1 Data overview

The data sequence presented here as part of the science verification process
was obtained between 18:03 – 18:39 UT on 2022 August 29. A sunspot group
within active region NOAA 13089 was observed under excellent seeing
conditions, which was positioned at heliocentric co-ordinates
($-86^{\prime\prime}$, $-491^{\prime\prime}$), or S23.9E5.7 in the
conventional heliographic co-ordinate system. High-order adaptive optics
(Rimmele, 2004) were utilised to further improve the image quality. Due to the
finite number of optical fibres available, it was decided that the $20\times
20$ two-dimensional array bundle should cover an approximate $30\times 30$
arcsec2 field-of-view. This configuration would place $\approx
1{\,}.{\\!\\!}^{\prime\prime}5$ across the diameter of each fibre, providing a
ideal compromise between high spatial sampling and overall field-of-view
coverage. Of course, placing $\approx 1{\,}.{\\!\\!}^{\prime\prime}5$ across
the entire $55\,\mu$m fibre diameter means that only the transmitting core
will sample $\approx 1{\,}.{\\!\\!}^{\prime\prime}1$ across its $40\,\mu$m
diameter. Nevertheless, this sampling interval would ensure the complete
field-of-view sampled by francis was approximately $30\times 30$ arcsec2. To
accomplish this, the focal plane of the DST was required to have a spatial
sampling of $\approx 29{\,}.{\\!\\!}^{\prime\prime}3$/mm, which was
facilitated through use of a focusing lens with a $200$ mm focal length
(acting on an $\approx 22$ mm pupil), resulting in an $f$/9 beam placed on the
francis ferrule. Importantly, this produced a ray angle $<2^{\circ}$, which is
significantly lower than the maximum permissible for the fibre bundle
($10^{\circ}$).

For the francis data presented here, the $2400$ lines/mm holographic
diffraction grating was implemented to sample the Na i D1 & D2 absorption line
pair located at $589.592$ nm and $588.995$ nm, respectively. A $25$ ms
exposure time was used for the Na i D1/D2 observations to acquire Stokes $I$
spectra of the sunspot region, which provided a spectral imaging rate of $23$
s-1. Hence, $50\,000$ spatially-resolved spectral images were obtained across
the $36$ min duration of the observing sequence. Immediately after the Na i
D1/D2 acquisitions were complete, the $3600$ lines/mm diffraction grating was
employed with a $100$ ms exposure time to provide Stokes $I$ sunspot spectra,
centred on the Ca ii H/K absorption line pair at $396.847$ nm and $393.366$
nm, respectively, with an imaging rate of $9$ s-1, hence obtaining $200$
spectral images in just over $20$ s of observing time.

In addition to the francis instrument, the Rapid Oscillations in the Solar
Atmosphere (ROSA; Jess et al., 2010b) and Hydrogen-Alpha Rapid Dynamics camera
(HARDcam; Jess et al., 2012b) imaging systems were utilised to provide
simultaneous contextual imaging of the field-of-view captured by the
spectrograph. ROSA images consisted of blue continuum (5.2 nm bandpass filter
centred at 417.0 nm), G-band (0.9 nm bandpass filter centred at 430.5 nm), and
Ca ii K (0.1 nm bandpass filter centred at 393.3 nm) filtergrams taken with
platescales of $0{\,}.{\\!\\!}^{\prime\prime}077$ per pixel, providing field-
of-view sizes equal to $77^{\prime\prime}\times 77^{\prime\prime}$. The G-band
and 417.0 nm continuum channels were acquired at frame rates of 30.3 s-1,
while the Ca ii K images were obtained at frame rates of 4.3 s-1. HARDcam
images provided H$\alpha$ (0.025 nm filter centred on the line core at 656.281
nm) filtergrams with a platescale of $0{\,}.{\\!\\!}^{\prime\prime}084$ per
pixel, providing a field-of-view size equal to $172^{\prime\prime}\times
172^{\prime\prime}$, which was obtained at a frame rate of 35 s-1. Following
the methods described by Wöger, von der Lühe, and Reardon (2008), speckle
reconstruction algorithms were implemented to improve the final imaging data
products. For the present science verification of francis data products, only
sample G-band and Ca ii K images have been employed for co-alignment purposes,
with the remainder of the contemporaneous imaging data left for future follow-
up science projects.

Figure 7.: The optical layout employed for the commissioning of the francis
instrument during the summer of 2022 at the DST (left panel). Highlighted,
using yellow boxes, are the core components of the observational setup,
including the placement of contextual ROSA/HARDcam/DOUGcam imagers, the
control and data storage PCs, the fibre bundle (including the orientation of
two-dimensional and linearised array ends), and the spectrograph and
associated imaging hardware. The right panel shows the method employed to map
the two-dimensional fibre bundle to its linearised array prior to connection
to the spectrograph. Here, an optical blocker, in the form of a rigid bus
pass, is attached to a bi-directional platform controlled by micrometers,
which provides the ability to translate the optical blocker in front of the
fibre array one row/column at a time. It is then possible to observe what
corresponding rows disappear from the spectral image captured by the francis
sCMOS camera and relate these to the individual rows/columns occulted by the
optical blocker, hence creating a process to re-map the linearised fibre
spectra back into a two-dimensional field of view. Note, this process only
needs to be completed once due to the use of the same fibre/camera orientation
for all future observing campaigns.

The Helioseismic and Magnetic Imager (HMI; Schou et al., 2012) present on the
Solar Dynamics Observatory (SDO; Pesnell, Thompson, and Chamberlin, 2012)
provided a contextual continuum image that was employed to co-align the images
obtained from the DST with the full-disk HMI observations. The SDO/HMI
continuum images were processed following the standard hmi_prep routine within
sswidl, following which $80\times 80$ arcsec2 subfields were extracted from
the processed data with a central pointing close to that of the ground-based
image sequences. Using the SDO/HMI continuum context image to define absolute
solar coordinates, the ROSA G-band observations were subjected to the cross-
correlation techniques described by Jess et al. (2013, 2016, 2017, 2020) to
provide sub-pixel co-alignment accuracy between the imaging sequences,
ultimately providing an accuracy down to approximately one tenth of an SDO/HMI
pixel, corresponding to $\approx 0{\,}.{\\!\\!}^{\prime\prime}05$ ($\approx
36$ km).

Finally, the polished brass fibre ferrule, which houses the two-dimensional
($20\times 20$) fibre array, produced a back-reflection image that was
captured by DOUGcam (see Section 2.2 for more information). Here, DOUGcam
employed the same imaging optics as the rest of the ROSA channels, providing a
consistent imaging platescale that enabled a straightforward way to map the
two-dimensional fibre array directly on to physical features on the solar
surface. A top-down perspective of the observational setup and optical layout
is shown in the left panel of Figure 7.

Figure 8.: The completed mapping process to translate the linearised array
back into the two-dimensional fibre group. Here, the
green$\rightarrow$blue$\rightarrow$magenta$\rightarrow$white colour scale
represents each sequential fibre core along the linearised array, which is
displayed as a function of the spatial dimensions (in mm) along the $20\times
20$ fibre head. For added visual clarity, the numbering system used is also
highlighted at the beginning of each row, as well as at the ends of the first
and last rows. It can be seen that fibre numbers $211$, $212$, $215$, $219$,
$221$, and $281$ are absent, which indicates these are damaged fibres and
unable to propagate light efficiently to the end of the bundle.

Figure 9.: A full disk continuum intensity image acquired by SDO/HMI at 17:12
UT (upper left). The red box denotes the field-of-view captured by the ROSA
instrument at the DST. The upper-right panel displays a sub-field of the full
SDO/HMI image that is now identically sized to that of the ROSA time series,
where the middle-left panel displays a sample ROSA G-band image acquired
simultaneously at 17:12 UT. The middle-right panel depicts a simultaneous
DOUGcam image, which was created by imaging the light reflected off the brass
fibre ferrule, enabling the locations of each individual fibre to be mapped to
its corresponding location on the solar surface. Note, the intensities
corresponding to back reflections from the fibre bundle have been rescaled for
visual clarity, since the majority of light is transmitted down the fibres and
not reflected to the DOUGcam imager. The lower-left panel overplots the
positioning of the individual francis fibres using solid yellow contours on
top of the underlying ROSA G-band image, while the lower-right panel
interlaces a re-formatted two-dimensional continuum image derived from francis
spectra (using a black$\rightarrow$blue$\rightarrow$white colour scale) on top
of the black-and-white ROSA G-band context image.

###  3.2 Fibre mapping

In order to establish the mapping between the head of the fibre bundle and the
linearised array that is placed at the entrance to the spectrograph, a method
is required to illuminate individual fibres and track the corresponding
brightening at the opposite end of the fibre group. Typically, this process
can be accomplished in a laboratory environment by, e.g., computationally
rearranging the array based on intensity mapping between observed/simulated
data (Li et al., 2019) or back-illuminating the fibre bundle using precisely
focused LED light sources (Drory et al., 2015). In the case of francis, this
process was accomplished during the commissioning phase of the instrument.
Here, an optical blocker999Initially cardboard was chosen to act as the
optical blocker, but the edges of the cardboard were not sufficiently sharp to
abruptly block light to the individual fibres. Instead, a bus pass from the
Northern Ireland company, Translink, was chosen due to its sharp plastic
edges, which helped to mask individual rows/columns with high degrees of
precision (see the right panel of Figure 7). was attached to a bi-directional
platform that could be translated in the horizontal and vertical directions
using precise micrometers, before being placed in front of the two-dimensional
end of the fibre bundle (see the right panel of Figure 7). Next, the
horizontal and vertical micrometers were adjusted to progressively block out
portions of the light reaching the fibre array, with data saved after each
platform shift to investigate which corresponding rows of the imaged spectra
subsequently disappeared. By translating the optical blocker first
horizontally, and then vertically across the face of the two-dimensional fibre
array, it was possible to map not only the ordering of the fibres onto the
linearised array, but also to investigate whether any of the $400$ fibres were
damaged.

Following this process, it was found that the uppermost (i.e., fibre number
‘1’) and lowermost (i.e., fibre number ‘400’) rows of the spectral image
acquired by the Princeton Instruments Kuro 2048B sCMOS camera corresponded to
the lower-right and upper-left fibres, respectively, once re-mapped back into
its two-dimensional array. The complete re-mapping lookup image is shown in
Figure 8, where the beginning of each row is highlighted by its corresponding
fibre number. During this process it was noticed that $6$ fibres appeared to
be damaged, with almost zero transmission along the length of the fibre. Once
the re-mapping was complete, these fibres were found to correspond to fibre
numbers $211$, $212$, $215$, $219$, $221$ and $281$, as can be seen in Figure
8. Three of the six fibres (numbered $219$, $221$ and $281$) are close to the
edges of the two-dimensional fibre array and are, therefore, on the periphery
of the selected field-of-view. However, it is unfortunate that the three other
damaged fibres (numbered $211$, $212$ and $215$) are relatively central within
the two-dimensional array and, as a result, care must be taken to ensure these
damaged fibres do not compromise the overall science objectives of the
experiment when selecting the central solar pointing of the fibre head. As
discussed in Section 2.2, the $6$ damaged fibres may have arisen from the
relatively long fibre lengths chosen for this prototype instrument. However,
future fibre bundles will likely be able to utilise shorter lengths ($\sim
0.5$ m instead of the current $\approx 1.5$ m), which will help to make the
overall fibre array more robust.

With the linear/two-dimensional fibre re-mapping complete, it is possible to
use the back-reflection image from the fibre ferrule, which was imaged by
DOUGcam, to select regions of interest from the observed field-of-view and
extract their associated spectra for subsequent analyses. Figure 9 provides
contextual information for the data products utilised in the present science
verification study, including the fields-of-view captured by SDO/HMI, ROSA,
and DOUGcam, in addition to the spatial orientation of the two-dimensional
francis fibre head.

###  3.3 Wavelength calibration

Many options exist to calibrate the wavelength axis of an acquired spectrum,
including the comparison with a standard reference such as the solar atlas
compiled by Kurucz et al. (1984) using the Fourier Transform Spectrometer
(FTS; Brault, 1978, 1979) at the McMath-Pierce facility at Kitt Peak
Observatory, USA. However, this process can become more difficult if the
observations acquired are from regions away from solar disk centre and/or
include spectral lines that are more dynamic in their evolution. As such, to
calibrate the wavelength axis of spectra recorded by the francis instrument,
we utilised the Princeton Instruments IntelliCal® calibration source, which
includes both a mercury (Hg) and neon-argon (Ne-Ar) lamp that have been
strictly calibrated by National Institute of Standards and Technology (NIST)
processes.

Figure 10.: The left panel shows the custom 3D printed mount that enables the
two-dimensional fibre head to be exposed to light from the IntelliCal® Hg/Ne-
Ar calibrated reference lamps. The fibre head slots into the cavity seen
towards the left-hand side of the image, while the Hg/Ne-Ar lamp bolts
directly to the back of the mount, which minimises contamination from unknown
sources during the wavelength calibration process. The upper-right panel
displays a complete spectral image of Ne-Ar emission lines obtained by the
Kuro 2048B sCMOS camera using an exposure time of 10 s and displayed on a log-
scale for added visual clarity, with the most prominent emission lines being
visible at $585.249$ nm and $588.190$ nm. The colour bar provides an
indication of the detector counts accumulated during the calibration process.
Note that the observed bending of the spectral lines is a result of the short
focal length, off-axis optics used within the spectrograph housing and the use
of plane diffraction gratings, which is discussed in more detail in Section
3.3. The lower-right panel reveals a zoom-in to the spectral image to show the
visibility of individual fibres along the vertical axis of the camera.

The IntelliCal® system works in conjunction with the LightField® software to
minimise the need for user input. However, first it was necessary to subject
the two-dimensional fibre head to the output light from the calibration lamp,
without external contamination from stray light or unknown sources. To achieve
this, a custom mount was 3D printed that allowed the brass ferrule to be
inserted into a chamber that was illuminated by the Hg/Ne-Ar lamps. The left
panel of Figure 10 displays the 3D printed mount, which enables the
calibration lamps to be bolted securely to the housing, while offering an
insertion cavity for the fibre ferrule. The custom mount was secured to a
multi-axis platform fixed to the optical bench, which allowed the IntelliCal®
system to be easily placed into the optical setup without the need to move any
existing components. This meant that wavelength calibration could be
accomplished/checked multiple times each day using the automated approaches
available within the LightField® software.

Specifically, the IntelliCal® system employs an automated calibration routine
in which a non-linear least-squares refinement algorithm is derived that
minimises spectral intensity residuals with respect to a theoretical model of
the Czerny-Turner spectrograph101010More details of the process can be viewed
in the dedicated IntelliCal® technical note —
https://www.princetoninstruments.com/wp-
content/uploads/2020/04/TechNote_FullyAutoWavlengthCalibrationDataAccuracy.pdf.
The system simulates the entire observed spectrum so that the number of
observables is always equal to the number of horizontal pixels in the detector
array, here being equal to $2048$ in the case of the Princeton Instruments
Kuro 2048B sCMOS camera. Following the application of the IntelliCal®
approach, a typical rms error of the derived wavelength axis is found to be on
the order of $0.002$ nm. However, for completeness, spectral images of the
Hg/Ne-Ar lamps were also obtained using 10 s exposures to manually repeat the
wavelength calibration process once the data had been downloaded. The right
panel of Figure 10 displays a sample spectrum obtained using the Ne-Ar lamp,
alongside a zoom-in to reveal the individual fibres that are sampled along the
vertical axis of the image.

To accurately calibrate the wavelength array using the IntelliCal® Hg/Ne-Ar
reference lamps, it is important that there is sufficient overlap between the
selected wavelength range used for science observations and the window
employed for capturing the calibrated emission lines. As the spectral lines of
interest for data verification were the Na i D1 & D2 absorption line pair
located at $589.592$ nm and $588.995$ nm, respectively, the strong Ne-Ar
emission lines at $585.249$ nm, $588.190$ nm and $594.483$ nm were selected to
manually calibrate the wavelength domain since they overlap completely with
the wavelengths chosen for scientific purposes. Slight curvature of the
spectral lines, as seen in the upper-right panel of Figure 10, which is caused
by the effects of off-axis optics within the spectrograph housing and the use
of plane diffraction gratings (Zhao, 2003), is a common phenomenon in compact
spectrographs with short focal lengths (Qiu et al., 2022). As the spectral
curvature is symmetric about the mid-point along the $y$-axis of the slit
image, we created an initial calibration spectrum by integrating across the
central $5$ fibres, spanning the detector pixels $1012\leq
y{\mathrm{-pixels}}\leq 1034$. This spectrum was then plotted as a function of
the wavelength array provided via the IntelliCal® process, with the dominant
emission lines at $585.249$ nm, $588.190$ nm and $594.483$ nm fitted with a
Gaussian and their central wavelengths compared to the expected values from
the Ne-Ar source. The fitted Gaussian centroids were within $\pm 0.001$ nm of
the expected emission peak wavelengths, which is consistent with the $0.002$
nm rms wavelength uncertainty provided by the IntelliCal® software that
sampled more (faint) features within the selected spectral window. Thus, for
the $2400$ lines/mm diffraction grating chosen, with a central science
wavelength of $589.000$ nm, a wavelength sampling of $\Delta\lambda=0.008$ nm
and an overall spectral range spanning $580.758\leq\lambda\leq 597.250$ nm was
provided.

To calibrate the wavelength domain corresponding to the Ca ii H/K spectra
obtained using the $3600$ lines/mm grating, an identical approach was
followed, only now using the strong Hg emission lines at $404.656$ nm and
$407.784$ nm produced by the IntelliCal® calibration lamp. While these
wavelengths do not completely overlap with the wavelength region selected for
Ca ii H/K science observations, they are the closest (in wavelength) strong
emission features present within the spectral signatures of the lamp. As with
the Ne-Ar emission features described above, the fitted Gaussian centroids of
the $404.656$ nm and $407.784$ nm emission lines were within $\pm 0.001$ nm of
the expected peak wavelengths provided by the IntelliCal® system. As such, for
the $3600$ lines/mm grating, a wavelength sampling of $\Delta\lambda=0.005$ nm
was established, providing an overall spectral range spanning
$389.547\leq\lambda\leq 400.459$ nm for the scientific Ca ii H/K observations.

###  3.4 Resolving power

The resolving power, $R$, of a spectrograph is a defining characteristic that
indicates how closely (in wavelength space) two features can be, yet still be
resolved. The classical definition for the resolving power is,

$R=\frac{\lambda}{\Delta\lambda}\ ,$ (1)

where $\lambda$ is the wavelength of the features of interest and
$\Delta\lambda$ is the minimum wavelength separation these features need to
have to still be distinguishable. As a result, the selection of what defines
$\Delta\lambda$ is rather arbitrary. Traditionally, the Rayleigh criterion
(Rayleigh, 1879) has been employed, although there are ongoing debates
regarding exactly how close Airy disks need to be before they become
impossible to distinguish apart, which is fuelled by the fundamental works of
Sparrow (1916), Houston (1927), and Buxton and Oxon (1937).

In recent years, it has become common practice to adopt the measured full-
width at half-maximum (FWHM) as the definition of $\Delta\lambda$ in Equation
1 (Robertson, 2013). Hence, to get an accurate measurement of the FWHM of a
spectral line, it is desirable to utilise a feature that is isolated,
unblended, and unbroadened by mechanisms other than instrumental effects. As
such, the Hg/Ne-Ar calibration lamp offers an ideal spectrum from which to
measure the FWHMs across a variety of different wavelengths and diffraction
gratings. For the $2400$ lines/mm grating, the strong Ne emission line at
$585.249$ nm was chosen as this was also within the wavelength window selected
for the main solar observations. For the $3600$ lines/mm and $4320$ lines/mm
gratings, the strong Hg emission lines at $404.656$ nm and $365.016$ nm were
selected, respectively, where the former emission feature is close to the
wavelength window selected for solar observations in the Ca ii H/K region.

For each selected emission line, spectra from all $394$ operational fibres
were fitted with a Gaussian to extract both the fitted line centroids (i.e., a
measure of the absolute wavelength calibration and the quality of the spectral
curvature correction – see Section 3.5 for more information on the spectral
curvature correction steps taken) and their corresponding FWHMs. For the
$2400$ lines/mm grating, the chosen Ne emission line at $585.249$ nm was found
to have a measured line centre of $585.249\pm 0.001$ nm and a FWHM of
$0.037\pm 0.006$ nm, providing a spectral resolving power,
$R_{2400}=15\,817\pm 2742$. Similarly, for the $3600$ lines/mm grating, the
chosen Hg emission line at $404.656$ nm was found to have a measured line
centre of $404.656\pm 0.001$ nm and a FWHM of $0.024\pm 0.002$ nm, providing a
spectral resolving power, $R_{3600}=16\,860\pm 1058$. Finally, for the $4320$
lines/mm grating, the chosen Hg emission line at $365.016$ nm was found to
have a measured line centre of $365.016\pm 0.001$ nm and a FWHM of $0.018\pm
0.001$ nm, providing a spectral resolving power, $R_{4320}=20\,278\pm 1020$.
Figure 11 shows sample emission spectra captured by a single fibre using the
$2400$ lines/mm (left panel), $3600$ lines/mm (middle panel), and $4320$
lines/mm (right panel) diffraction gratings, where the fitted Gaussians are
also shown using a dashed red line in each panel. The numerical measurements
are also outlined in Table 2.

Figure 11.: The solid black lines are example spectral profiles captured by
the same fibre core for the $585.249$ nm (left panel), $404.656$ nm (middle
panel), and $365.016$ nm (right panel) calibration lamp emission lines using
the $2400$ lines/mm, $3600$ lines/mm, and $4320$ lines/mm diffraction
gratings, respectively. The dashed red lines denote the fitted Gaussian for
each emission profile, which determines the associated FWHM for that feature.

The resolving power can also be estimated theoretically by computing the FWHM
of the instrumental profile following Mohammadi and Eslami (2010),

$\mathrm{FWHM}=\frac{d\lambda}{dl}\times\mathrm{slit~{}width}\ ,$ (2)

where $d\lambda/dl$ is the linear dispersion of the spectrograph (nm/$\mu$m)
under the assumption that the entrance slit width is larger than the pixel
size of the imaging detector. For the first-light observations with francis we
employed a $50~{}\mu$m slit width, which is almost a factor of $5$ larger than
the pixel size on the imaging camera ($11~{}\mu$m), hence allowing this
simplified estimate to be used. Hence, for the $2400$ lines/mm grating, which
provides a linear dispersion of $d\lambda/dl=0.00072$ nm/$\mu$m, a slit width
of $50~{}\mu$m equates to a theoretical FWHM of $0.036$ nm and a resolving
power of $R_{2400}=16\,306$. Similar calculations for the $3600$ lines/mm and
$4320$ lines/mm gratings, which have associated linear dispersions of
$0.00045$ nm/$\mu$m and $0.00032$ nm/$\mu$m, provide theoretical FWHMs of
$0.023$ nm and $0.016$ nm, alongside theoretical resolving powers of
$R_{3600}=17\,921$ and $R_{4320}=25\,090$, respectively (see Table 2).

From inspection of Figure 11, alongside the information provided in Table 2,
it is clear that the instrument is almost achieving its theoretical resolving
power across the three different diffraction gratings. Specifically, for the
$2400$ lines/mm, $3600$ lines/mm, and $4320$ lines/mm gratings, the instrument
reached $97.0$ %, $94.1$ %, and $89.6$ %, respectively, of its theoretical
maximum resolving power values. The reduction in relative resolving power from
the lowest ($2400$ lines/mm) to highest ($4320$ lines/mm) resolution
diffraction gratings is likely the consequence of a slight optical coma in the
imaged spectra (seen as increased broadening in the red wing of the observed
spectral line; Tu et al., 2021) and/or a residual astigmatism caused by
imperfect focusing of both the tangential (wavelength resolution optimised)
and sagittal (fibre resolution optimised) focal planes provided by the
toroidal mirror within the spectrograph optics (see Figure 1). In the case of
Czerny-Turner spectrograph configurations, coma is introduced from chief rays
reflecting from mirrors rotated about its sagittal axis, which results in
broadening along the tangential (wavelength) directions of the image. On the
other hand, an astigmatism is commonly observed as the asymmetric broadening
of the image along the sagittal plane (i.e., along the fibre direction of the
image) when a detector is positioned for the tightest sagittal focus to
provide maximum wavelength resolution (Foreman, 1968; Lee, Thompson, and
Rolland, 2010). Typically, the toroidal mirror used in Czerny-Turner
configurations helps to correct for astigmatism by enabling both the
tangential and sagittal foci to cross at the centre of the focal plane.
However, while this works very well for the wavelength selected during the
design phase, it is natural for slight astigmatisms to manifest as user-
selected wavelength windows move away from the original design conditions.

Table 2.: Measurements of the line centre and FWHM for the strongest spectral lines that are part of the Hg/Ne-Ar calibration lamps using the $2400$ lines/mm, $3600$ lines/mm, and $4320$ lines/mm diffraction gratings. The measuring and theoretical resolving powers, $R$, are also displayed. All of the numerical values provided in this table are for a slit width of $50~{}\mu$m, which was employed during the initial commissioning phase of the francis instrument.  Dispersion | Emission |  | Measured | Measured | Theoretical | Theoretical
---|---|---|---|---|---|---
grating | line | Measured line | FWHM | resolving | FWHM | resolving
(lines/mm) | used (nm) | centre (nm) | (nm) | power ($R$) | (nm) | power ($R$)
|  | $585.249$ | $0.037$ | $15\,817$ |  |
$2400$ | $585.249$ | $\pm$ | $\pm$ | $\pm$ | $0.036$ | $16\,306$
|  | $0.001$ | $0.006$ | $2742$ |  |
|  | $404.656$ | $0.024$ | $16\,860$ |  |
$3600$ | $404.656$ | $\pm$ | $\pm$ | $\pm$ | $0.023$ | $17\,921$
|  | $0.001$ | $0.002$ | $1058$ |  |
|  | $365.016$ | $0.018$ | $20\,278$ |  |
$4320$ | $365.016$ | $\pm$ | $\pm$ | $\pm$ | $0.016$ | $22\,631$
|  | $0.001$ | $0.001$ | $1020$ |  |

Recently, Plowman et al. (2022) demonstrated a formal method to help remove
observed astigmatisms, whereby a spectral image can be modelled as an array of
localised basis elements with coefficients, helping to render it as a very
large, sparse matrix, which can be solved using linear least squares
optimisation. This approach has recently been applied to the Spectral Imaging
of the Coronal Environment (SPICE; SPICE Consortium et al., 2020) instrument
onboard Solar Orbiter (Müller et al., 2013), with great success demonstrated
in removing similar artefacts observed in SPICE spectral images. Importantly,
this technique provides an alternative approach to traditional deconvolution
methods (e.g., Poduval et al., 2013), which may be important if the point
spread function of the instrument varies across the image plane (something
that convolution approaches cannot account for). As such, future scientific
applications of the francis instrument will utilise the methods put forward by
Plowman et al. (2022) to help minimise the effects of instrument astigmatism
seen in Figure 11.

Importantly, future observing campaigns with francis will be able to utilise a
narrower slit for science observations. Initially, the $50~{}\mu$m slit width
was chosen so that all light propagating down the $40~{}\mu$m (core diameter)
fibres would pass through into the spectrograph, hence minimising modal
interference noise. However, this resulted in an exposure times of $25$ ms and
$100$ ms for the Na i D1/D2 and Ca ii H/K observations, which provided
associated spectral frame rates of $23$ s-1 and $9$ s-1, respectively.
Importantly, in the case of the Na i D1/D2 observations running at a maximal
frame rate of $23$ s-1, an exposure time of $\approx 40$ ms would still enable
an identical data rate to be achieved, although would likely result in
saturation of the detector due to the increased exposure time. As a result, it
is possible to combine slightly longer exposure times with a reduced slit
width to obtain better spectral resolutions without negatively impacting the
overall cadence of the science observations. For example, reducing the slit
width by just over half (i.e., $50~{}\mu$m $\rightarrow 20~{}\mu$m) would
provide theoretical FWHMs of $0.014$ nm, $0.009$ nm, and $0.006$ nm for the
$2400$ lines/mm, $3600$ lines/mm, and $4320$ lines/mm diffraction gratings,
ultimately producing resolving powers of $R_{2400}=40\,765$,
$R_{3600}=44\,800$, and $R_{4320}=56\,580$, respectively. It is possible to
reduce the slit width even more to help further improve the spectral
resolution. However, as noted above, Equation 2 is only valid for slit widths
that are larger than the pixel size on the detector. As a result, calculating
the theoretical resolving power for even narrower slit widths requires more
sophisticated approximations, such as those described by Casini and de Wijn
(2014).

Of course, reducing the slit width to values smaller than the diameter of the
fibre cores will result in a fraction of the illuminated fibre end face not
transmitting fully to the imaging detector. As discussed in Section 2.2, this
may increase the measured modal interference noise if the speckle pattern at
the fibre exit evolves on time scales similar to (or longer than) the camera
exposure times. This would have the unwanted consequence of varying the point
spread function, and hence response of the instrument, which would make
spectral flat-fielding difficult and differential photometry (necessary for
polarimetric measurements) extremely challenging. Many high-resolution
instruments in the nighttime astrophysical community have worked on promising
solutions to these difficulties, including the use of high-frequency fibre
agitators to ‘mix’ the modal interference patterns on much shorter timescales
and help maximise the resulting signal-to-noise ratio (e.g., Petersburg et
al., 2018). As a result, care must be taken when re-configuring the slit width
of the spectrograph to ensure instrument sensitivity (particularly to
spectropolarimetric measurements) is not compromised.

For comparison, resolving powers in the range of $R\sim 40\,000-55\,000$ are
similar to, if not higher than some current dual Fabry-Pérot interferometers,
such as the CHROMIS (Scharmer, 2017) and CRISP (Scharmer et al., 2008)
instruments that have resolving powers on the order of $R\sim 20\,000$ and
$R\sim 60\,000$, respectively (Rouppe van der Voort et al., 2017; Löfdahl et
al., 2021), but of course without the excellent spatial resolution that comes
from imaging-based instrument setups. Contrarily, some Fabry-Pérot imaging
instruments are optimised for very high spectral resolutions, with the
Interferometric Bidimensional Spectrometer (IBIS; Cavallini, 2006) having a
design resolution (measured from the FWHM of the instrumental profile) on the
order of $R\sim 200\,000$ (Reardon and Cavallini, 2008). Of course, while a
Fabry-Pérot instrument is in operation, it is necessary to scan the selected
spectral line with the minimum number of wavelength points to maintain a fast
line scan, while also preserving as much of the spectral sensitivity as
possible (Díaz Baso et al., 2023). Resolving powers on the order of $R\sim
40\,000-55\,000$ are consistent with modern filtergraphs, such as the space-
based HMI instrument (Schou et al., 2012), which are capable of high-precision
Doppler studies of the lower solar atmosphere. On the other hand, existing
slit-based spectrographs can obtain very high resolving powers, such as $R\sim
210\,000$ for the FIRS instrument, $R\sim 190\,000$ for the GRIS IFU, $R\sim
180\,000$ for the new Visible Spectro-Polarimeter (ViSP; de Wijn et al., 2022)
on DKIST, and $R\sim 170\,000$ for the Spectro-Polarimeter for Infrared and
Optical Regions (SPINOR; Socas-Navarro et al., 2006). These instruments obtain
increased resolving powers by using traditional low- or medium-density ruled
diffraction gratings (typically a few tens to a few hundreds of lines/mm), but
observing the resulting dispersed light in higher spectral orders. In order to
maintain efficiency when observing in higher diffraction orders, these
instruments typically employ steeper blaze angles (e.g., $63^{\circ}$ in the
case of the GRIS instrument) to ensure optimal dispersion of light. For the
diffraction gratings employed for use with the francis instrument, which are
holographic in nature, the efficiency at a particular wavelength will be
determined by the depth of the grooves formed by holographic methods (i.e.,
the modulation). As such, future upgrades to the francis instrument may
include the use of traditional ruled diffraction gratings operating at high
blaze angles to improve the efficiency of higher-order wavelength dispersion
captured by the detectors, hence helping to improve the spectral resolution.
Importantly, as highlighted by Tomczyk et al. (2016), it is still possible to
undertake high-precision chromospheric polarimetry studies with resolving
powers on the order of $R\sim 20\,000$ (particularly true for Stokes $V$
measurements of circularly polarised light), hence supporting the future
capabilities of the francis instrument.

###  3.5 Data reduction

As described in Section 3.1, $50\,000$ fibre-resolved spectral images centred
on the Na i D1 & D2 absorption line pair located at $589.592$ nm and $588.995$
nm, respectively, were obtained, in addition to a short $\approx 20$ s burst
($200$ spectral images) of Ca ii H/K spectra at $396.847$ nm and $393.366$ nm,
respectively. To calibrate these data into science-ready products, a reduction
pipeline was created to streamline the processing steps required. Each step of
the data reduction pipeline was applied independently to each of the Na i
D1/D2 and Ca ii H/K data products to ensure consistency and repeatability of
their respective calibrations.

First, an average dark frame was produced that was obtained with an identical
exposure time to that of the science observations ($25$ ms for Na i D1/D2;
$100$ ms for Ca ii H/K) by averaging over $1000$ frames captured under dark
conditions (i.e., the telescope beam blocked from the fibre head). Next, an
average flat field was created by de-focusing the telescope and slewing
randomly across the solar surface, albeit slightly offset from the active
region under investigation to ensure the solar $\mu$-angle, and hence
background light level, was preserved. A total of $1000$ exposures, each with
an identical exposure time ($25$ ms for Na i D1/D2; $100$ ms for Ca ii H/K) to
that of the science observations, were obtained. These observations were
subsequently averaged to create the flat-field frame, where the corresponding
Na i D1/D2 image can be visualised in the left panel of Figure 12.

Typically, for imaging observations, it is possible to simply subtract the
average dark frame and divide by the average flat field to produce an image
that is devoid of thermal and chip sensitivity degradations. However, this is
not directly possible for spectral observations since the average flat field
will still contain spectral signatures in the form of solar absorption lines.
Furthermore, as discussed in Section 3.3 and shown in the upper-right panel of
Figure 10, the acquired spectral images have an associated spectral curvature
due to the spectrograph optics utilised. Hence, it is necessary to compensate
for the slit image curvature along the $y$-axis before attempting to remove
the presence of absorption lines from the initial flat field. The offset
between the observed and absolute wavelengths (caused by the spectral
curvature) can be modelled by a quadratic function (Qiu et al., 2022),

$\lambda^{\prime}=C\lambda(y-y_{0})^{2}+\lambda\ ,$ (3)

where $\lambda^{\prime}$ and $\lambda$ are the observed and absolute
wavelengths at specific $y$ coordinates along the slit, $y_{0}$ is the
$y$-pixel position corresponding to the apex of the curvature (i.e., the point
of symmetry for the spectral curvature), and $C$ is a constant. Equation 3
clearly demonstrates that stronger spectral curvature is experienced at longer
wavelengths, hence will be more apparent towards the upper end of the spectral
range covered by francis (i.e., $\sim 700$ nm).

Figure 12.: The three stages of deriving a flat-field frame for the francis
instrument, shown here for the case of the Na i D1/D2 spectral window. The
left panel shows an average spectral image obtained by summing $1000$
individual exposures, each with an exposure time of $25$ ms to match that of
the science observations, where the telescope was de-focused and performed a
random slew across a quiescent region of the solar surface with a $\mu$-angle
consistent with the science field-of-view. The middle panel displays the same
average spectral image, only now with the spectral curvature corrected through
use of the quadratic function derived from data obtained with the Ne-Ar
calibration lamp. Finally, the right panel depicts the final flat-field frame,
where each of the spectral lines have been removed. The colour bar depicts the
image intensities in detector numbers, where the Princeton Instruments Kuro
2048B camera saturates at $\approx 64\,000$ DNs (i.e., 16-bit).

To calculate the curvature correction function, the spectra from each
horizontal row of the Ne-Ar (for Na i D1/D2 science observations) and Hg (for
Ca ii H/K science observations) slit images were extracted, with the strong
emission peaks fitted using a Gaussian profile. The wavelength offsets, as a
function of $y$-pixel position, enabled the quadratic correction function (see
Equation 3) to be derived, allowing the wavelength-dependent spectral
curvature to be corrected across the entire spectral imaging domain. Applying
the curvature correction function to the average flat-field frame produces the
intermediate image shown in the middle panel of Figure 12 for the Na i D1/D2
observations. Comparing the left and middle panels of Figure 12, it is clear
that the spectral curvature has been corrected but that the spectral lines are
still present, which need to be removed to form the final flat-field image. We
must note that Equation 3 corrects for the spectral curvature, but does not
compensate for any residual spectral skew that may be present. However, during
initial setup of the francis instrument, small adjustments to the orientation
of the grating mount were performed to ensure the wavelength dispersion was
along the horizontal rows of the imaging detector, thus minimising any
misalignment between the entrance slit and the direction of the diffraction
grating (see, e.g., Lites et al., 1991; Elmore et al., 1992; Esmonde-White,
Esmonde-White, and Morris, 2011, for more discussions on spectral skew
corrections).

To remove spectral lines from the final flat-field image, standard processes
are adopted (see, e.g., Jaeggli et al., 2010; Wang et al., 2013), whereby
first a spectrum is extracted for each $y$-pixel along the detector. Next, a
number of continuum locations are identified that are away from obvious
absorption profiles. As the flat-field image has already been corrected for
spectral curvature, the wavelengths of the continuum locations will remain
constant across all $y$-pixels of the detector. A second-order polynomial is
then fitted to the continuum data points, with the line of best fit tracking
the spectral sensitivity across the given wavelength range, in this case
$580.758\leq\lambda\leq 597.250$ nm for the Na i D1/D2 observations and
$389.547\leq\lambda\leq 400.459$ nm for the Ca ii H/K data products. The
fitted continuum for the Na i D1/D2 observations is shown in the right panel
of Figure 12. To finalise the flat-field image, the fitted continua (e.g., the
right panel of Figure 12 in the case of Na i D1/D2 observations) are divided
by their median value to produce a flat-field image correction map that can be
applied to subsequent science observations to correct for instrument spectral
sensitivity variations.

It must be noted that the panels shown in Figure 12 reveal a number of rows
that have relatively low intensities. This does not necessarily mean that the
instrument has poor light sensitivity associated with these $y$-pixels.
Instead, these rows of decreased intensity will correspond to the detector
pixels where no fibre core is imaged and, as a result, minimal light is
propagated through the entrance slit of the spectrograph and dispersed onto
these rows of the imaging detector. Some of the light present along these
darker rows will naturally arise from internal scattering within the optics or
from around the periphery of the fibre cladding, hence it is not expected for
them to have completely zero counts. Regardless, these rows are excluded when
the fibre-core spectra are extracted for further scientific study and
analyses. However, they are retained here to simplify and streamline the flat-
fielding processes applied to scientific observations.

Once the science spectral images have been calibrated, the next step is to
extract spectra corresponding to each of the $394$ working fibres. As
discussed in Section 3.2, fibres $211$, $212$, $215$, $219$, $221$, and $281$
transmit almost zero light down the length of the fibre bundle, hence it is
not possible to extract spectra for these specific fibre cores (see Figure 8
for their precise location on the two-dimensional fibre head). To pinpoint the
$y$-pixel on the spectral image corresponding to each fibre core, the
intensities of the brightest emission line ($585.249$ nm) from the Ne-Ar
calibration lamp (see Figure 10) were extracted as a function of the detector
$y$-pixel. Plotting this one-dimensional lightcurve as a function of the
$2048$ pixels along the $y$-axis of the camera allowed $394$ intensity peaks
to be clearly identified, which highlighted the $y$-pixel location of each
fibre core. For completeness, the same process was performed on the brightest
emission line ($404.656$ nm) from the Hg calibration lamp. Due to the fibre
ferrule remaining fixed in position at the entrance slit of the spectrograph,
the established $y$-pixel locations of the fibre cores remained identical,
irrespective of what wavelength region and/or calibration lamp was employed.

Figure 13.: Raw spectral images of the sunspot that was part of NOAA 13089,
captured on 2022 August 29 in the Na i D1/D2 (upper left; $2400$ lines/mm
grating) and Ca ii H/K (lower left; $3600$ lines/mm grating) wavelength
windows. The right panels depict the same spectral images, only after the
processes of dark-frame subtraction, spectral curvature correction, flat-
fielding, and fibre extraction have been applied. The colour bar depicts the
image intensities in detector numbers, where the Princeton Instruments Kuro
2048B camera saturates at $\approx 64\,000$ DNs (i.e., 16-bit). The dark
horizontal bands seen in the spectral images correspond to fibre cores that
sampled the sunspot umbra, hence have continuum intensities that are $\sim
40$% of their non-sunspot counterparts.

It must be noted that each fibre core is $40~{}\mu$m in diameter (see Table
1), while the Princeton Instruments Kuro 2048B camera employed has $11\times
11~{}\mu$m2 pixels. Hence, each fibre core will span over $3$ complete pixels,
which is consistent with the zoom-in image shown in the lower-right panel of
Figure 10. As a result, selecting a single $y$-pixel from the detector to
extract a spectrum from a chosen fibre core will underestimate the total flux
propagated by the fibre. Thus, for each of the $394$ identified intensity
peaks, the immediately neighbouring pixels (i.e., $\pm 1$ pixel) were used to
extract the associated science spectra from each fibre core. To do this, all
$3$ $y$-pixels associated with each fibre core location were averaged to
produce a final two-dimensional array that is $2048\times 394$ pixels2 in size
for each processed science spectral image (i.e., $\lambda~{}\times$ fibre
number). These smaller spectral arrays (i.e., $2048\times 394$ pixels2 instead
of the raw $2048\times 2048$ pixels2 sizes) are useful to minimise the amount
of disk space required to hold the processed files, especially considering the
Na i D1/D2 science observations presented here were acquired with a frame rate
of $23$ s-1.

Figure 13 displays ‘before’ and ‘after’ spectral science images of the sunspot
that was part of NOAA $13089$ on 2022 August 29. The left panels of Figure 13
are the raw spectral images obtained in the Na i D1/D2 (upper left) and Ca ii
H/K (lower left) wavelength windows, while the right panels display the same
images following the application of dark-field subtraction, spectral curvature
correction, flat-fielding, and fibre extraction. Dark horizontal bands are
visible in the processed spectral images shown in the right panels of Figure
13. These correspond to fibre cores that sampled the sunspot umbra, where the
associated continuum intensities are $\sim 40$% of their counterparts that
observed non-umbral locations.

With the linear/two-dimensional fibre mapping known (see Figure 8) and the
science observations processed onto a common wavelength axis, it is possible
to re-create two-dimensional images at precise wavelengths chosen by the
research team. The lower-right panel of Figure 9 overplots the ROSA G-band
context image with a two-dimensional francis image obtained at a continuum
wavelength just blueward of the Na i D2 spectral line. From Figure 9, it is
clear that the spatial re-mapping of francis fibres has worked incredibly
well, allowing precise spectral measurements to be studied alongside the
imaging observations, both of which were obtained with high temporal cadences
($\geq 23$ s-1).

###  3.6 Data verification

As discussed in Section 3.5, the francis data acquired during science
observations is reduced into a science-ready format via means of dark current
subtraction, correcting for spectral curvature, flat-fielding, and
transforming the dispersive $x$-axis array of the imaging detector onto a
calibrated wavelength grid. Once these steps have been performed, it is
possible to extract spectra corresponding to each individual fibre core and
examine the temporal, spatial and/or spectral evolution of the solar features
of interest.

Figure 14.: Sample spectra captured using the $2400$ lines/mm grating and
centred on the Na i D1 & D2 absorption line pair, spanning the complete
wavelength range of $581.3-596.3$ nm (upper panel). Solid red and blue lines
correspond to sample quiet Sun and umbral locations, respectively, while the
solid black line displays the quiet Sun FTS spectrum for comparison. The
intensity of each spectrum is normalised to the quiet Sun continuum intensity,
$I_{\textrm{c}}$, for easier comparison. The lower panel displays a zoom-in to
the Na i D1 & D2 line pair for better visual clarity. In both panels,
individual spectral measurements are indicated using the coloured crosses,
with a wavelength sampling, $\Delta\lambda=0.008$ nm pixel-1, employed across
the detector.

Figure 15.: The upper panels display the observational field-of-view
associated with the Ca ii H/K spectra, where the left and middle panels
display sample G-band and Ca ii K images, respectively, obtained by the ROSA
instrument that operated simultaneously with francis. The upper-right panel
also shows the ROSA Ca ii K field, only overplotted with the positioning of
the francis fibre bundle using solid yellow contours. Sample spectra captured
using the $3600$ lines/mm grating and centred on the Ca ii H/K line pair,
spanning the complete wavelength range of $389.55-400.08$ nm, is shown in the
lower panel. Solid red and blue lines correspond to sample quiet (i.e., non-
umbral) Sun and umbral locations, respectively, while the solid black line
displays the disk-averaged solar flux atlas spectrum for comparison. The
intensity of each spectrum is normalised to the quiet Sun continuum intensity,
$I_{\textrm{c}}$, for easier comparison. Individual spectral measurements are
indicated using the coloured crosses, with a wavelength sampling,
$\Delta\lambda=0.005$ nm pixel-1, employed across the detector.

Figure 14 displays sample spectra acquired during the observations of the
sunspot present in NOAA 13089 on 2022 August 29. The upper panel of Figure 14
displays the spectral window corresponding to the $2400$ lines/mm grating
centred on the Na i D1 & D2 absorption line pair, with a wavelength sampling
of $\Delta\lambda=0.008$ nm pixel-1 employed across the detector. The lower
panel of Figure 14 provides a zoom-in to the central wavelength region
encompassing the Na i D1 & D2 absorption lines. In each panel, the solid red
line corresponds to spectra extracted from non-umbral locations, while the
solid blue line reveals spectra obtained from the sunspot umbral core. It can
be seen that the umbral continuum has intensities that are $\sim 40$% of its
non-umbral counterpart, which is consistent with previous observations (e.g.,
Gosain, Mathew, and Venkatakrishnan, 2011; Rezaei, Beck, and Schmidt, 2012;
Grant et al., 2018, 2022; Li et al., 2022, to name but a few examples) and
validates the success of the flat-fielding processing outlined in Section 3.5.
Furthermore, in the lower panel of Figure 14, increased line broadening can be
seen in the spectrum extracted from an umbral location, which is consistent
with Zeeman effects previously observed (Zeeman, 1897; Oostra, 2017; Zhang,
2020). For comparison, the solid black lines used in Figure 14 display the FTS
atlas spectrum (Kurucz et al., 1984; Kurucz, 2005) that has been degraded to
match the instrumental resolving power ($R_{2400}\approx 15\,817$) of francis.
Very close agreement between the quiescent francis spectrum and that provided
from the FTS atlas reiterates the precise wavelength calibration performed
during the data reduction phase.

In a similar manner to the upper panel of Figure 14, the lower panel of Figure
15 displays non-umbral and umbral spectra using solid red and blue lines,
respectively, for the wavelength window obtained using the $3600$ lines/mm
diffraction grating centred on the Ca ii H/K absorption line pair. Here, a
wavelength sampling of ${\Delta\lambda=0.005}$ nm pixel-1 is employed across
the detector, providing spectral coverage spanning approximately $390-400$ nm.
The FTS solar spectrum is again degraded to match the resolving power
($R_{3600}\approx 16\,860$) of the francis observations and overplotted using
a solid black line. The FTS atlas is a disk-integrated flux spectrum and, as a
result, does not display any self-reversals at the core of the Ca ii H/K
lines. On the other hand, self-reversals are clearly visible in Figure 15,
particularly for the spectrum extracted from the umbral location, where
intense shock fronts (and their associated strong self-reversals) are commonly
expected (e.g., Beckers and Tallant, 1969; Socas-Navarro, Trujillo Bueno, and
Ruiz Cobo, 2000; de la Cruz Rodríguez et al., 2013; Henriques et al., 2017;
Houston et al., 2018, 2020; MacBride et al., 2021, to name but a few examples
employing Ca ii spectra). Even in the non-umbral location (red line in Figure
15), the extracted spectrum demonstrates self-reversals at the cores of the Ca
ii H & K lines, indicating that these locations are still not entirely
quiescent, which is a common feature regularly observed in the immediate
vicinity of solar active regions (Bjørgen et al., 2018; Leenaarts et al.,
2018) and often linked to a measure of magnetic activity (see, e.g., the
$S$-index; Wilson, 1968). As beam-splitters (instead of dichroics) were
utilised for the francis commissioning observations, it was possible to
simultaneously capture high-cadence Ca ii K imaging with ROSA while the
francis Ca ii H/K spectra were being obtained. The upper panels of Figure 15
display the two-dimensional fibre array coverage across the sunspot structure,
which provides a significant number of fibres sampling uniquely umbral,
penumbral, and quiescent (non-umbral) locations.

Overall, Figures 9, 14 & 15 display the capabilities of the francis instrument
in its current form. We have demonstrated its suitability to perform in-depth
studies of the lower solar atmosphere by combining a spatially-resolved, two-
dimensional field of view with excellent spectral coverage and rapid temporal
sampling. In its present form, the francis instrument significantly exceeds
the scientific requirements for temporal cadence of $\sim 3$ s that were
defined for the NLST by Ramesh et al. (2016). Furthermore, we have
demonstrated excellent data fidelity in key spectral lines defined in the NLST
science objectives (e.g., Sankarasubramanian, Hasan, and Rangarajan, 2010;
Ramesh et al., 2016), namely for the Ca ii H/K and Na i D1/D2 absorption
features. Finally, employing the $4320$ lines/mm grating, a spectral resolving
power of $R_{4320}\approx 20\,278$ was achieved using a slit width of
$50~{}\mu$m, which results in a spectral line FWHM of $\approx 0.018$ nm.
While this is not quite at the scientific requirements level of a several tens
of mÅ for chromospheric MHD wave diagnostics, we have shown how reducing the
slit width down to narrower values will significantly improve the subsequent
FWHM values to $\approx 0.006$ nm, which is consistent with the near-UV
spectrograph onboard IRIS (De Pontieu et al., 2014). As a result, the
performance of francis, demonstrated during the commissioning phase, is
encouraging as a baseline for future instrument upgrades, which will be
discussed in more detail in Section 3.7 below.

###  3.7 Current status and future upgrades

At present, the francis instrument is available as a common-user facility at
the Dunn Solar Telescope (DST), which is operated by the Sunspot Solar
Observatory Consortium (SSOC) that is led by New Mexico State University
(NMSU). As the Indian National Large Solar Telescope (NLST) is still in the
planning phase, it is not clear when francis will be transferred to the NLST
for integration testing. Thankfully, due to the rugged cast steel construction
of the spectrograph and hardened flight cases, it will be possible to move
francis to any other available telescope facility, even if temporarily, to
undertake scientific operations.

As discussed in Section 3.6, we have demonstrated the excellent data fidelity
provided by the francis instrument and, hence, its suitability for exciting
research projects involving observations of the lower solar atmosphere. In
particular, the extensive wavelength range provides many isolated spectral
lines, formed over a wide range of heights in the solar atmosphere, which
enables a multitude of wave propagation studies to be undertaken through the
analyses of oscillatory phase lags bridging different spectral features (e.g.,
continuing the works of Kneer, Mattig, and Uexkuell, 1981; Uexkuell, Kneer,
and Mattig, 1983; Mattig and Zerfass, 1991; Centeno, Collados, and Trujillo
Bueno, 2006, 2009; Jess et al., 2012a; Gafeira et al., 2017; Jafarzadeh et
al., 2017a, c; Kayshap et al., 2018; Grant et al., 2022; Guevara Gómez et al.,
2022, to name but a few examples). Furthermore, the rapid cadences associated
with francis data products will enable the development of highly dynamic shock
phenomena within the chromosphere to be examined with unprecedented
resolution. With this in mind, shocks developing in Ca ii bright grains (e.g.,
Carlsson and Stein, 1992, 1997; Mathur et al., 2022), sunspot umbral
observations (e.g., Rouppe van der Voort et al., 2003; de la Cruz Rodríguez et
al., 2013; Grant et al., 2018; Houston et al., 2018; Joshi and de la Cruz
Rodríguez, 2018; Anan et al., 2019; Houston et al., 2020), and other small-
scale atmospheric dynamics (e.g., Eklund et al., 2021; Wang, Yokoyama, and
Iijima, 2021; Hillier and Snow, 2023) can be examined with high temporal
resolution to better identify the mechanisms responsible for non-linear wave
behaviour. Finally, the simultaneous spatial sampling intrinsic to IFU designs
means that the spectral signatures of reconnection phenomena (e.g., through
the manifestation of solar flares) can be probed more readily since the field-
of-view of the francis instrument can be overlaid on top of the magnetic
neutral line to maximise the capture of associated flare kernels, alongside
the effects of chromospheric evaporation (e.g., Xuan et al., 1998; Hao et al.,
2017; Anan et al., 2018; Monson et al., 2021; Osborne and Fletcher, 2022).
Importantly, the ease of visualisation of francis data will enable scientific
discoveries to be identified, analysed, and interpreted in a timely manner.
Such novel visualisation capabilities are shown in Figure 16, where we
demonstrate how complementary high-cadence imaging and IFU spectroscopy (and
future spectropolarimetry) are able to work in harmony.

Figure 16.: Three-dimensional visualisations of francis data, alongside
complementary high-cadence images obtained by the ROSA instrument. Here, ROSA
G-band and Ca ii K line-core images are shown using black/white and blue
colour tables, respectively. In the left panel, the spatially-resolved francis
spectra, extracted from a window centred on the Ca ii K spectral line at
$393.366$ nm, is displayed with the wavelength axis orientated along the
vertical direction, where the Ca ii K line core is placed in the same plane as
the corresponding Ca ii K ROSA image. The right panel depicts spatially-
resolved intensities extracted from the francis spectra at photospheric (Ca ii
K continuum) and chromospheric (Ca ii K line core) heights, which are placed
on top of the ROSA G-band and Ca ii K line-core images, respectively. Hovering
above the ROSA Ca ii K image is a sample spectral cube ($x,y,\lambda$)
acquired instantaneously by the francis instrument, where the spectral
morphology of the underlying sunspot is clearly visible through the
examination of spatially-resolved absorption lines that are seen along the
vertical (wavelength) domain of the depicted sample cube. These types of novel
visualisation tools will greatly assist with the identification, extraction,
and analyses of dynamic solar features manifesting in francis data products.

In the short term, the francis instrument will continue to be developed and
refined by introducing the (single-beam) polarisation optics (see Section
2.5), developing a robust correction for residual wavelength-dependent
astigmatisms (see Section 3.4), and examining the effect on exposure times and
spectral sensitivity through use of narrower entrance slits. At present, we
are also laboratory testing the use of digital micromirror devices (DMDs;
Dudley, Duncan, and Slaughter, 2003; Lee, 2008), which are semi-conductor-
based optical micro-electrical-mechanical systems consisting of hundreds of
thousands of highly reflective tilted micromirrors. In particular, we are
investigating the suitability of DMDs to enable high-speed (upwards of $1000$
Hz) switching between orthogonal polarisation states, which may provide better
polarimetric precision over its optical shutter counterpart, while still
operating within a single-beam configuration to preserve the large wavelength
coverage. Similar methods to rapidly modulate the polarisation states have
been implemented by the Zurich Imaging Polarimeters (ZIMPOL; Povel, 1995) and
the Fast SpectroPolarimeter (FSP; Iglesias et al., 2016) instruments, which
are able to utilise fast charge transfer in the silicon chip architecture and
ferroelectric liquid crystals, respectively, to push polarimetric modulation
rates in excess of several hundred measured states each second. Importantly,
DMDs consume relatively little electrical power and reliability tests have
shown very long lifetimes, with greater than $100{\,}000$ operating hours and
more than 1 trillion mirror cycles before failure (Douglass, 1998). This makes
DMDs a very attractive technology for both ground-based and space-borne
hardware due to their reliability, small size, and application longevity.

In the longer term, we will examine the cost effectiveness of implementing a
ruled diffraction grating with steep blaze angles (as an alternative to the
holographic gratings presently employed) to obtain spectra in higher spectral
orders to further improve the resolving power of the francis instrument. The
optical design of the francis instrument is also ideally configured to test
the feasibility of using volume holographic gratings (VHGs; Sinha et al.,
2004) as the dispersive elements for high-resolution solar spectropolarimetry.
Holographic gratings (such as those currently employed) and VHGs are two types
of gratings created using laser interference patterns. Holographic gratings
are surface relief structures, while VHGs are formed within the volume of the
component itself by introducing a periodic modulation of the refractive
indices embedded throughout the photosensitive material. When compared to
standard holographic diffraction gratings, the volumetric period modulation of
the refractive indices within VHGs enables them to diffract light over a wide
range of wavelengths with even higher efficiencies (Barden et al., 2000).
Additionally, the francis design may allow future evaluations of profile
classifications in near-real time based on a diffractive neural network
inscribed within the VHG itself (Psaltis et al., 1990). To further improve the
spectral resolving power, we will investigate a revised optical design to
increase the $f$-number of the optics, which will naturally boost the spectral
resolution achievable, although it is noted that this would be a major
revision and may be more suited to a second generation iteration of the
instrument.

##  4 Conclusion

In recent years, the solar physics community has expressed a strong need for
the acquisition of spectra with high spatial, spectral, and temporal
resolutions, including the capture of polarimetric information for use with
modern inversion routines. Furthermore, to combat potential analysis
difficulties associated with the non-simultaneity of traditional slit-based
rastering spectrographs and Fabry-Pérot interferometers, there has been a
monumental push towards the creation of integral field units (IFUs) to enable
contemporaneous high-resolution spectra to be obtained from a well-resolved,
two-dimensional field of view. To date, the majority of solar IFU designs have
focused on the mid-optical to infrared regions of the electromagnetic
spectrum, hence creating the motivation for an IFU dedicated to the near-UV.

Here, we describe the scientific goals, construction, commissioning, and
initial science verification of a new prototype IFU designed to operate within
the spectral range spanning approximately $390-700$ nm. The Fibre-Resolved
opticAl and Near-ultraviolet Czerny-Turner Imaging Spectropolarimeter
(francis) is a fibre-fed IFU that employs a compact design, holographic
diffraction gratings and a high-performance, large-format scientific CMOS
camera to obtain spectra from a re-mappable 400-fibre ($20\times 20$) imaging
array. Commissioning of the francis instrument took place in August 2022 at
the Dunn Solar Telescope in the Sacramento Peak mountains, NM, USA, with the
initial science verification focused on the intensity and wavelength
calibrations of Stokes $I$ spectral images linked to spectral windows
incorporating the Ca ii H/K and Na i D1/D2 Fraunhofer lines.

Following the successful commissioning, imminent upgrades to the francis IFU
include the addition of polarisation optics to allow the high-speed
acquisition of complementary Stokes $Q/U/V$ spectra, which will enable modern
multi-line spectropolarimetric inversion routines to be applied to the data.
As technology progressively becomes miniaturised, more reliable and,
ultimately, cheaper, longer-term upgrades will focus on the implementation of
high-speed digital micromirror devices (DMDs) and higher-order ruled
diffraction gratings to further increase the spectral sensitivity (and speed
of acquisition) of the measured polarimetry.

Ultimately, the future of IFUs for solar physics research is very promising.
The latest (and future) generations of solar telescopes, including the ground-
based DKIST, EST, and Indian NLST, as well as upcoming space-borne missions
(e.g., the Brazilian Galileo Space Solar Telescope, GSST; Vieira et al.,
2019), all have IFUs at the forefront of their proposed scientific hardware.
Hence, the francis instrument helps to pave this path by demonstrating its
suitability for near-UV observations with simultaneous high spectral, spatial
and temporal resolutions. Therefore, we hope that the francis instrument will
inspire and motivate next generation instrument developments as the community
looks forward to the scientific discoveries that await us over the next
decade.

#### Acknowledgements

D.B.J. and S.D.T.G. acknowledge support from the UK Space Agency for a
National Space Technology Programme (NSTP) Technology for Space Science award
(SSc 009). D.B.J. also wishes to thank the UK Science and Technology
Facilities Council (STFC) for the award of an Ernest Rutherford Fellowship
(ST/K004220/1) where this project was initially conceived. D.B.J. and S.D.T.G.
are also grateful to STFC for additional funding via the grant awards
ST/T00021X/1 and ST/X000923/1. D.B.J. and W.B. also wish to thank The
Leverhulme Trust for grant RPG-2019-371. The authors would like to offer
gratitude to Prof. Mihalis Mathioudakis and Prof. Francis Keenan, who offered
expert guidance throughout the project, including both on scientific and
financial issues, with the overall success of the project largely attributed
to their assistance. D.B.J. would also like to thank Dr Hans-Peter Doerr and
Dr Michiel van Noort for discussions linked to fibre interference patterns,
which helped direct francis instrument development. The authors wish to
acknowledge scientific discussions with the Waves in the Lower Solar
Atmosphere (WaLSA; https://www.WaLSA.team) team, which has been supported by
the Research Council of Norway (project no. 262622), The Royal Society (award
no. Hooke18b/SCTM; Jess et al., 2021), and the International Space Science
Institute (ISSI Team 502). Finally, D.B.J. would like to thank the anonymous
referee for their invaluable suggestions and comments that improved the
overall quality of the manuscript.

## Author Contribution

D.B.J. defined the instrument goals, designed the optical configuration,
assembled and calibrated the instrument in laboratory conditions, assisted
with the commissioning observations, reduced and verified the data, and wrote
the manuscript. S.D.T.G. assisted with laboratory calibrations, performed the
commissioning observations, helped reduce the scientific data, and wrote
sections of the manuscript. W.B. took part in laboratory calibrations,
assisted with the acquisition of commissioning observations, developed the
fibre remapping algorithms, and prepared figures for the manuscript. J.L.
worked extensively in the laboratory to align the instrument optics and
calibrate the initial spectra. S.J. and P.H.K. provided scientific vision,
assisted with text development, and examined the final spectra for inclusion
within the manuscript. L.E.A.V., A.D.L. and F.L.G. assisted with spectrograph
calibration knowledge, particularly in relation to the use of holographic
diffraction gratings, and enabled additional laboratory testing to be
performed within Brazil’s Instituto Nacional de Investigación Espacial del
Brasil (INPE) facility. D.J.C. assisted with advertising the instrument
capabilities within the United States and examined the calibrated spectra for
any irregularities. D.G. was the (invaluable) Chief Observer during the
commissioning observations of francis during August 2022 and pioneered the
optical configuration of DOUGcam, which has since become a permanent and
complementary part of the francis hardware. D.B. provided initial motivation
for the project and enabled D.B.J. to become part of the Indian NLST project.
All authors provided contributions towards the final manuscript in the form of
figures, text, and proofreading.

## Funding

UK Space Agency (UKSA): SSc 009. UK Science and Technology Facilities Council
(STFC): ST/K004220/1, ST/T00021X/1, ST/X000923/1. The Leverhulme Trust:
RPG-2019-371. The Royal Society: Hooke18b/SCTM.

## Data Availability

Due to the data volume (approaching 5 TB), the francis commissioning data is
available, in various stages of reduction format, directly from the lead
author (David Jess; d.jess@qub.ac.uk). Similarly, complementary ROSA/HARDcam
imaging observations can also be provided to interested parties upon request
via the same email address (data volume exceeding 10 TB).

## References

  * Abbasvand et al. (2020) Abbasvand, V., Sobotka, M., Švanda, M., Heinzel, P., García-Rivas, M., Denker, C., Balthasar, H., Verma, M., Kontogiannis, I., Koza, J., Korda, D., Kuckein, C.: 2020, Observational study of chromospheric heating by acoustic waves. Astron. Astrophys. 642, A52. DOI. ADS.
  * Abell et al. (2009) Abell, P.A., Allison, J., Anderson, S.F., Andrew, J.R., Angel, J.R.P., Armus, L., Arnett, D., Asztalos, S.J., Axelrod, T.S., Bailey, S., Ballantyne, D.R., Bankert, J.R., Barkhouse, W.A., Barr, J.D., Barrientos, L.F., Barth, A.J., Bartlett, J.G., Becker, A.C., Becla, J., Beers, T.C., Bernstein, J.P., Biswas, R., Blanton, M.R., Bloom, J.S., Bochanski, J.J., Boeshaar, P., Borne, K.D., Bradac, M., Brandt, W.N., Bridge, C.R., Brown, M.E., Brunner, R.J., Bullock, J.S., Burgasser, A.J., Burge, J.H., Burke, D.L., Cargile, P.A., Chandrasekharan, S., Chartas, G., Chesley, S.R., Chu, Y.-H., Cinabro, D., Claire, M.W., Claver, C.F., Clowe, D., Connolly, A.J., Cook, K.H., Cooke, J., Cooray, A., Covey, K.R., Culliton, C.S., de Jong, R., de Vries, W.H., Debattista, V.P., Delgado, F., Dell’Antonio, I.P., Dhital, S., Di Stefano, R., Dickinson, M., Dilday, B., Djorgovski, S.G., Dobler, G., Donalek, C., Dubois-Felsmann, G., Durech, J., Eliasdottir, A., Eracleous, M., Eyer, L., Falco, E.E., Fan, X., Fassnacht, C.D., Ferguson, H.C., Fernandez, Y.R., Fields, B.D., Finkbeiner, D., Figueroa, E.E., Fox, D.B., Francke, H., Frank, J.S., Frieman, J., Fromenteau, S., Furqan, M., Galaz, G., Gal-Yam, A., Garnavich, P., Gawiser, E., Geary, J., Gee, P., Gibson, R.R., Gilmore, K., Grace, E.A., Green, R.F., Gressler, W.J., Grillmair, C.J., Habib, S., Haggerty, J.S., Hamuy, M., Harris, A.W., Hawley, S.L., Heavens, A.F., Hebb, L., Henry, T.J., Hileman, E., Hilton, E.J., Hoadley, K., Holberg, J.B., Holman, M.J., Howell, S.B., Infante, L., Ivezic, Z., Jacoby, S.H., Jain, B., R, Jedicke, Jee, M.J., Garrett Jernigan, J., Jha, S.W., Johnston, K.V., Jones, R.L., Juric, M., Kaasalainen, M., Styliani, Kafka, Kahn, S.M., Kaib, N.A., Kalirai, J., Kantor, J., Kasliwal, M.M., Keeton, C.R., Kessler, R., Knezevic, Z., Kowalski, A., Krabbendam, V.L., Krughoff, K.S., Kulkarni, S., Kuhlman, S., Lacy, M., Lepine, S., Liang, M., Lien, A., Lira, P., Long, K.S., Lorenz, S., Lotz, J.M., Lupton, R.H., Lutz, J., Macri, L.M., Mahabal, A.A., Mandelbaum, R., Marshall, P., May, M., McGehee, P.M., Meadows, B.T., Meert, A., Milani, A., Miller, C.J., Miller, M., Mills, D., Minniti, D., Monet, D., Mukadam, A.S., Nakar, E., Neill, D.R., Newman, J.A., Nikolaev, S., Nordby, M., O’Connor, P., Oguri, M., Oliver, J., Olivier, S.S., Olsen, J.K., Olsen, K., Olszewski, E.W., Oluseyi, H., Padilla, N.D., Parker, A., Pepper, J., Peterson, J.R., Petry, C., Pinto, P.A., Pizagno, J.L., Popescu, B., Prsa, A., Radcka, V., Raddick, M.J., Rasmussen, A., Rau, A., Rho, J., Rhoads, J.E., Richards, G.T., Ridgway, S.T., Robertson, B.E., Roskar, R., Saha, A., Sarajedini, A., Scannapieco, E., Schalk, T., Schindler, R., Schmidt, S., Schmidt, S., Schneider, D.P., Schumacher, G., Scranton, R., Sebag, J., Seppala, L.G., Shemmer, O., Simon, J.D., Sivertz, M., Smith, H.A., Allyn Smith, J., Smith, N., Spitz, A.H., Stanford, A., Stassun, K.G., Strader, J., Strauss, M.A., Stubbs, C.W., Sweeney, D.W., Szalay, A., Szkody, P., Takada, M., Thorman, P., Trilling, D.E., Trimble, V., Tyson, A., Van Berg, R., Vanden Berk, D., VanderPlas, J., Verde, L., Vrsnak, B., Walkowicz, L.M., Wandelt, B.D., Wang, S., Wang, Y., Warner, M., Wechsler, R.H., West, A.A., Wiecha, O., Williams, B.F., Willman, B., Wittman, D., Wolff, S.C., Wood-Vasey, W.M., Wozniak, P., Young, P., Zentner, A., Zhan, H.: 2009, LSST Science Book, Version 2.0. arXiv e-prints, arXiv:0912.0201. DOI. ADS.
  * Allington-Smith (2006) Allington-Smith, J.: 2006, Basic principles of integral field spectroscopy. New A Rev. 50, 244\. DOI. ADS.
  * Anan et al. (2018) Anan, T., Yoneya, T., Ichimoto, K., UeNo, S., Shiota, D., Nozawa, S., Takasao, S., Kawate, T.: 2018, Measurement of vector magnetic field in a flare kernel with a spectropolarimetric observation in He i 10830Å. Publications of the Astronomical Society of Japan 70, 101\. DOI. https://doi.org/10.1093/pasj/psy105.
  * Anan et al. (2019) Anan, T., Schad, T.A., Jaeggli, S.A., Tarr, L.A.: 2019, Shock Heating Energy of Umbral Flashes Measured with Integral Field Unit Spectroscopy. Astrophys. J. 882, 161\. DOI. ADS.
  * Avila and Singh (2008) Avila, G., Singh, P.: 2008, Optical fiber scrambling and light pipes for high accuracy radial velocities measurements. In: Atad-Ettedgui, E., Lemke, D. (eds.) Advanced Optical and Mechanical Technologies in Telescopes and Instrumentation, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series 7018, 70184W. DOI. ADS.
  * Bailén, Orozco Suárez, and del Toro Iniesta (2023) Bailén, F.J., Orozco Suárez, D., del Toro Iniesta, J.C.: 2023, Fabry-Pérot etalons in solar astronomy. A review. Astrophysics and Space Science 368, 55\.
  * Bailey, Cotton, and Kedziora-Chudczer (2017) Bailey, J., Cotton, D.V., Kedziora-Chudczer, L.: 2017, A high-precision polarimeter for small telescopes. Mon. Not. Roy. Astron. Soc. 465, 1601\. DOI. ADS.
  * Baldry, Bland-Hawthorn, and Robertson (2004) Baldry, I.K., Bland-Hawthorn, J., Robertson, J.G.: 2004, Volume Phase Holographic Gratings: Polarization Properties and Diffraction Efficiency. PASP 116, 403\. DOI. ADS.
  * Barden et al. (2000) Barden, S.C., Arns, J.A., Colburn, W.S., Williams, J.B.: 2000, Volume‐Phase Holographic Gratings and the Efficiency of Three Simple Volume‐Phase Holographic Gratings. Publications of the Astronomical Society of the Pacific 112, 809\. DOI. https://dx.doi.org/10.1086/316576.
  * Barthol et al. (2011) Barthol, P., Gandorfer, A., Solanki, S.K., Schüssler, M., Chares, B., Curdt, W., Deutsch, W., Feller, A., Germerott, D., Grauf, B., Heerlein, K., Hirzberger, J., Kolleck, M., Meller, R., Müller, R., Riethmüller, T.L., Tomasch, G., Knölker, M., Lites, B.W., Card, G., Elmore, D., Fox, J., Lecinski, A., Nelson, P., Summers, R., Watt, A., Martínez Pillet, V., Bonet, J.A., Schmidt, W., Berkefeld, T., Title, A.M., Domingo, V., Gasent Blesa, J.L., Del Toro Iniesta, J.C., López Jiménez, A., Álvarez-Herrero, A., Sabau-Graziati, L., Widani, C., Haberler, P., Härtel, K., Kampf, D., Levin, T., Pérez Grand e, I., Sanz-Andrés, A., Schmidt, E.: 2011, The Sunrise Mission. Solar Phys. 268, 1\. DOI. ADS.
  * Baudrand and Walker (2001) Baudrand, J., Walker, G.A.H.: 2001, Modal Noise in High-Resolution, Fiber-fed Spectra: A Study and Simple Cure. PASP 113, 851\. DOI. ADS.
  * Beckers and Tallant (1969) Beckers, J.M., Tallant, P.E.: 1969, Chromospheric Inhomogeneities in Sunspot Umbrae. Solar Phys. 7, 351\. DOI. ADS.
  * Berkefeld et al. (2011) Berkefeld, T., Schmidt, W., Soltau, D., Bell, A., Doerr, H.P., Feger, B., Friedlein, R., Gerber, K., Heidecke, F., Kentischer, T., v. D. Lühe, O., Sigwarth, M., Wälde, E., Barthol, P., Deutsch, W., Gandorfer, A., Germerott, D., Grauf, B., Meller, R., Álvarez-Herrero, A., Knölker, M., Martínez Pillet, V., Solanki, S.K., Title, A.M.: 2011, The Wave-Front Correction System for the Sunrise Balloon-Borne Solar Observatory. Solar Phys. 268, 103\. DOI. ADS.
  * Bethge et al. (2011) Bethge, C., Peter, H., Kentischer, T.J., Halbgewachs, C., Elmore, D.F., Beck, C.: 2011, The Chromospheric Telescope. Astron. Astrophys. 534, A105. DOI. ADS.
  * Bjørgen et al. (2018) Bjørgen, J.P., Sukhorukov, A.V., Leenaarts, J., Carlsson, M., de la Cruz Rodríguez, J., Scharmer, G.B., Hansteen, V.H.: 2018, Three-dimensional modeling of the Ca II H and K lines in the solar atmosphere. Astron. Astrophys. 611, A62. DOI. ADS.
  * Brault (1978) Brault, J.W.: 1978, Solar Fourier Transform Spectroscopy. In: Godoli, G. (ed.) Future solar optical observations needs and constraints 106, 33\. ADS.
  * Brault (1979) Brault, J.W.: 1979, Solar Fourier transform spectroscopy. Osservazioni e memorie dell’Osservatorio astrofisico di Arcetri 106, 33\. ADS.
  * Buxton and Oxon (1937) Buxton, A., Oxon, M.A.: 1937, XLI. Note on optical resolution. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science 23, 440\. DOI. https://doi.org/10.1080/14786443708561813.
  * Calcines, López, and Collados (2013) Calcines, A., López, R.L., Collados, M.: 2013, MuSICa: the Multi-Slit Image Slicer for the est Spectrograph. Journal of Astronomical Instrumentation 2, 1350009\. DOI. ADS.
  * Capozzi et al. (2020) Capozzi, E., Ballester, E.A., Belluzzi, L., Bianda, M., Dhara, S.K., Ramelli, R.: 2020, Observational indications of magneto-optical effects in the scattering polarization wings of the Ca I 4227 Å line. Astron. Astrophys. 641, A63. DOI. ADS.
  * Carlsson and Stein (1992) Carlsson, M., Stein, R.F.: 1992, Non-LTE Radiating Acoustic Shocks and CA II K2V Bright Points. Astrophys. J. 397, L59. DOI. ADS.
  * Carlsson and Stein (1997) Carlsson, M., Stein, R.F.: 1997, Formation of Solar Calcium H and K Bright Grains. Astrophys. J. 481, 500\. DOI. ADS.
  * Casini and de Wijn (2014) Casini, R., de Wijn, A.G.: 2014, On the instrument profile of slit spectrographs. Journal of the Optical Society of America A 31, 2002\. DOI. ADS.
  * Cavallini (2006) Cavallini, F.: 2006, IBIS: A New Post-Focus Instrument for Solar Imaging Spectroscopy. Solar Phys. 236, 415\. DOI. ADS.
  * Centeno, Collados, and Trujillo Bueno (2006) Centeno, R., Collados, M., Trujillo Bueno, J.: 2006, Spectropolarimetric Investigation of the Propagation of Magnetoacoustic Waves and Shock Formation in Sunspot Atmospheres. Astrophys. J. 640, 1153\. DOI. ADS.
  * Centeno, Collados, and Trujillo Bueno (2009) Centeno, R., Collados, M., Trujillo Bueno, J.: 2009, Wave Propagation and Shock Formation in Different Magnetic Structures. Astrophys. J. 692, 1211\. DOI. ADS.
  * Chae et al. (2017) Chae, J., Lee, J., Cho, K., Song, D., Cho, K., Yurchyshyn, V.: 2017, Photospheric Origin of Three-minute Oscillations in a Sunspot. Astrophys. J. 836, 18\. DOI. ADS.
  * Collados et al. (2012) Collados, M., López, R., Páez, E., Hernández, E., Reyes, M., Calcines, A., Ballesteros, E., Díaz, J.J., Denker, C., Lagg, A., Schlichenmaier, R., Schmidt, W., Solanki, S.K., Strassmeier, K.G., von der Lühe, O., Volkmer, R.: 2012, GRIS: The GREGOR Infrared Spectrograph. Astronomische Nachrichten 333, 872\. DOI. ADS.
  * Cousin et al. (2022) Cousin, A., Sautter, V., Fabre, C., Dromart, G., Montagnac, G., Drouet, C., Meslin, P.Y., Gasnault, O., Beyssac, O., Bernard, S., Cloutis, E., Forni, O., Beck, P., Fouchet, T., Johnson, J.R., Lasue, J., Ollila, A.M., De Parseval, P., Gouy, S., Caron, B., Madariaga, J.M., Arana, G., Madsen, M.B., Laserna, J., Moros, J., Manrique, J.A., Lopez-Reyes, G., Rull, F., Maurice, S., Wiens, R.C.: 2022, SuperCam calibration targets on board the perseverance rover: Fabrication and quantitative characterization. Spectrochimica Acta 188, 106341\. DOI. ADS.
  * Daino, Marchis, and Piazzolla (1980) Daino, B., Marchis, G.D., Piazzolla, S.: 1980, Speckle and Modal Noise in Optical Fibres Theory and Experiment. Optica Acta: International Journal of Optics 27, 1151\. DOI.