The Fibre Resolved OpticAl and Near-Ultraviolet Czerny–Turner Imaging Spectropolarimeter (francis)

Abstract

The solar physics community is entering a golden era that is ripe with next-generation ground- and space-based facilities, advanced spectral inversion techniques, and realistic simulations that are becoming more computationally streamlined and efficient. With ever-increasing resolving power stemming from the newest observational telescopes, it becomes more challenging to obtain (near-)simultaneous measurements at high spatial, temporal and spectral resolutions, while operating at the diffraction limit of these new facilities. Hence, in recent years there has been increased interest in the capabilities integral field units (IFUs) offer towards obtaining the trifecta of high spatial, temporal and spectral resolutions contemporaneously. To date, IFUs developed for solar physics research have focused on mid-optical and infrared measurements. Here, we present an IFU prototype that has been designed for operation within the near-ultraviolet to mid-optical wavelength range, which enables key spectral lines (e.g., Ca ii H/K, H$\beta$, Sr ii, Na i D₁/D₂, etc.) to be studied, hence providing additional spectral coverage to the instrument suites developed to date. The IFU was constructed as a low-budget proof-of-concept for the upcoming $2\text{ m}$ class Indian National Large Solar Telescope and employs circular cross-section fibres to guide light into a Czerny–Turner configuration spectrograph, with the resulting spectra captured using a high quantum efficiency scientific CMOS camera. Mapping of each input fibre allows for the reconstruction of two-dimensional spectral images, with frame rates exceeding $20\text{ s}^{-1}$ possible while operating in a non-polarimetric configuration. Initial commissioning of the instrument was performed at the Dunn Solar Telescope, USA, during August 2022. The science verification data presented here highlights the suitability of fibre-fed IFUs operating at near-ultraviolet wavelengths for solar physics research. Importantly, the successful demonstration of this type of instrument paves the way for further technological developments to make a future variant suitable for upcoming ground-based and space-borne telescope facilities.

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., 2022a; 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 ($j=\frac {1}{2}$, $j'=\frac {1}{2}$; 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 2-m-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).

2 Instrumentation

In 2018, a relatively small budget (∼$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 $\sim 2\,\text{--}\,3\text{ s}$ 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 ($\sim 100\text{ m s}^{-1}$) 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 $10\text{ km s}^{-1}$ (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 $\sim 2\,\text{--}\,3\text{ s}$ 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 $<3\text{ s}$, a spectral resolution no more than a few tens of mÅ, with sensitivity to key chromospheric spectral lines with wavelengths as low as $\approx 390\text{ nm}$, 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 ∼$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 Instruments.¹ 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, three unique holographic reflection gratings were selected, comprising 4320, 3600, 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, 3600, and 2400 lines/mm gratings employed in the francis instrument were manufactured by Richardson Gratings,² with the area of each grating equal to $102\times 102\text{ mm}^{2}$.

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 has been adapted from the Teledyne Digital Imaging article US20130182250A1 (https://patents.google.com/patent/US20130182250A1).

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 $1.5\text{ m}$ 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.

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 Optica,³ comprising a 40 μm diameter silica core, a 4 μm thick silica cladding, and a 3.5 μm thick polyimide coating, providing a total diameter of 55 μm for each fibre and a numerical aperture, $\mathit{NA}=0.22\pm 0.02$. 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 $1.127\times 0.960\text{ mm}^{2}$, providing an occupied area of $1.082\text{ mm}^{2}$. Each fibre core has a surface area of $1.257\times 10^{-3}\text{ mm}^{2}$, hence 400 fibres cover a total area of $0.503\text{ mm}^{2}$, 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).

The two-dimensional fibre array is housed at the centre of a circular brass ferrule with a diameter of $10\text{ mm}$ (see the left panel of Figure 2). The brass end is polished to a flatness that is < 1 μm, 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 spectra.⁴ Over the $1.5\text{ m}$ 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 $22.0\text{ mm}$, which required a larger brass ferrule to accommodate this increased dimension over the original two-dimensional layout that utilised a $10\text{ mm}$ diameter brass ferrule.

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 $1.082\text{ mm}^{2}$, with light transmission provided by the cores of the optical fibres with an effective area of $0.503\text{ mm}^{2}$, hence providing a filling factor of approximately 46.5%. The brass end of the ferrule is polished to a flatness that is < 1 μm, 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 $22.0\text{ mm}$ 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 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 ($28\text{ mm}$ 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 μm 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 μm) that was larger than the diameter of the fibre cores (40 μm) 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.

Table 1 Overview of prototype francis fibre characteristics employed during the August 2022 commissioning phase.

2.3 Wavelength Order Filters

The transmission profile of the DST spans the near ultraviolet ($\sim 350\text{ nm}$) 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, three lines were chosen: (i) Ca ii H/K at $\sim 395\text{ nm}$, (ii) Ca i at $\sim 423\text{ nm}$, and (iii) Na i D₁/D₂ at $\sim 589\text{ nm}$, with the final filters manufactured by Semrock.⁵ Each filter was mounted in a circular housing with an aperture diameter of $50\text{ mm}$ 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.

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 $376\,\text{--}\,424$, $411\,\text{--}\,439$, and $574\,\text{--}\,600\text{ nm}$, respectively. Each filter allows for the isolation of prioritised spectral lines, including the Ca ii H & K lines (396.847 and $393.366\text{ nm}$, respectively, highlighted using vertical dashed black lines), the Ca i line ($422.673\text{ nm}$, indicated with the vertical dotted–dashed line), and the Na i D₁ & D₂ line pair ($589.592\text{ nm}$ and $588.995\text{ nm}$, respectively, highlighted using the vertical dotted black lines). Each bandpass filter has transmissions $>90$% at the wavelengths of interest.

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 $11\times 11$ μm² pixels to form an imaging area that is $22.53\times 22.53\text{ mm}^{2}$. 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 μm, resulting in a final length of $22.0\text{ mm}$ 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 μm, 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 $22.53\text{ mm}$ 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 Koolance⁶ EX2-1055 liquid cooling system was employed, which has a cooling capacity of $900\text{ W}$ (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 $560\text{ nm}$, with QEs $>60$% across the entire wavelength range sampled by francis ($390\,\text{--}\,700\text{ nm}$; 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 $390\,\text{--}\,700\text{ nm}$, hence this camera provides QEs $>60$% across the useable wavelength domain. This image is 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, two liquid crystal variable retarders (LCVRs) were purchased from Meadowlark Optics,⁷ each with a UV coating to allow operation within the wavelength range of $390\,\text{--}\,600\text{ nm}$ and a large clear aperture of $40.6\text{ mm}$ 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 $\approx 5\text{ ms}$ to switch from one-half to zero waves (i.e., low to high voltage) and $\approx 20\text{ ms}$ to switch from zero to one-half wave (i.e., high to low voltage).

However, care must be taken with the LCVRs as their organic properties means they can become degraded if exposed to wavelengths $<380\text{ nm}$. To protect the LCVRs, a custom high-pass filter was sourced from Laser 2000⁸ that offers $\approx 0$% transmission for wavelengths $<250\text{ nm}$, 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 $260\,\text{--}\,310\text{ nm}$ that peaks at $\approx 10$% ($\mathrm{OD}\ge 0.977$), although this is beneath the atmospheric cut-off wavelength of $\sim 310\text{ nm}$ found at ground-based telescope facilities (Erlick et al., 1998; Lee et al., 2019). Transmission remains $\approx 0$% ($\mathrm{OD}>6$) up to $\approx 382\text{ nm}$, before rising steeply to $>83$% ($\mathrm{OD}\le 0.080$) at $\approx 388\text{ nm}$. Transmission remains $>87$% ($\mathrm{OD}\le 0.060$) across the operational spectral range of $390\,\text{--}\,700\text{ nm}$ as shown in Figure 5, with a mean transmission of 97.1% ($\mathrm{OD}=0.012$).

Figure 5

The transmission curve of the custom high-pass filter manufactured to protect the polarisation optics from wavelengths $\le 380\text{ nm}$, 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 $260\,\text{--}\,310\text{ nm}$ 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 $390\,\text{--}\,700\text{ nm}$.

Typically, once the light has passed through the two 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., 2022a; 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 $0\text{ V}$ applied, the optical beam is rotated by $90^{\circ}$, while the application of a 8 V/$2\text{ kHz}$ AC square-wave signal causes the optical beam to pass straight through the optical shutter without rotation. Timescales are $0.4\text{ ms}$ and $5.0\text{ ms}$ 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 $40.6\text{ mm}$ to accommodate future telescope facilities operating with large beam sizes and has a UV coating to enable use with wavelengths as low as $390\text{ nm}$. Once the modulated beam has been rotated (or not), an ultrabroadband ($300\,\text{--}\,2700\text{ nm}$ 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.

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 $<380\text{ nm}$ that are damaging to the organic material within the LCVRs. The unpolarised light then passes through the two 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 that 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, beams (1) and (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).

The polarisation optics include three components (two LCVRs and one 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 two 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 coordinates ($-86''$, $-491''$), 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 $\approx 1{\,}.{\!\!}''5$ across the diameter of each fibre, providing a ideal compromise between high spatial sampling and overall field-of-view coverage. Of course, placing $\approx 1{\,}.{\!\!}''5$ across the entire 55 μm fibre diameter means that only the transmitting core will sample $\approx 1{\,}.{\!\!}''1$ across its 40 μm 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 $\approx 29{\,}.{\!\!}''3$/mm, which was facilitated through use of a focusing lens with a $200\text{ mm}$ focal length (acting on an $\approx 22\text{ mm}$ 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 and $588.995\text{ nm}$, respectively. A $25\text{ ms}$ 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 $23\text{ s}^{-1}$. Hence, $50{,}000$ spatially-resolved spectral images were obtained across the $36\text{ min}$ 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 $100\text{ ms}$ exposure time to provide Stokes $I$ sunspot spectra, centred on the Ca ii H/K absorption line pair at 396.847 and $393.366\text{ nm}$, respectively, with an imaging rate of $9\text{ s}^{-1}$, hence obtaining 200 spectral images in just over $20\text{ s}$ 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 $0{\,}.{\!\!}''077$ per pixel, providing field-of-view sizes equal to $77''\times 77''$. 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 $0{\,}.{\!\!}''084$ per pixel, providing a field-of-view size equal to $172''\times 172''$, 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.

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 $\approx 0{\,}.{\!\!}''05$ ($\approx 36\text{ km}$).

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 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 that this process only needs to be completed once due to the use of the same fibre/camera orientation for all future observing campaigns.

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 blocker⁹ 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 six 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 six 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 ($\sim 0.5\text{ m}$ instead of the current $\approx 1.5\text{ m}$), which will help to make the overall fibre array more robust.

Figure 8

The completed mapping process to translate the linearised array back into the two-dimensional fibre group. Here, the green → blue → magenta → 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.

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.

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 → blue → white colour scale) on top of the black-and-white ROSA G-band context image.

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.

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.

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 and $588.190\text{ nm}$. 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.

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 spectrograph.¹⁰ 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 $0.002\text{ nm}$. 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 and $588.995\text{ nm}$, respectively, the strong Ne–Ar emission lines at 585.249, 588.190, and $594.483\text{ nm}$ 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 five fibres, spanning the detector pixels $1012 \le y{\mathrm{-pixels}} \le 1034$. 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, 588.190 and $594.483\text{ nm}$ fitted with a Gaussian and their central wavelengths compared to the expected values from the Ne–Ar source. The fitted Gaussian centroids were within $\pm 0.001\text{ nm}$ of the expected emission peak wavelengths, which is consistent with the $0.002\text{ nm}$ 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 $589.000\text{ nm}$, a wavelength sampling of $\Delta \lambda =0.008\text{ nm}$ and an overall spectral range spanning $580.758 \le \lambda \le 597.250\text{ nm}$ 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 and $407.784\text{ nm}$ 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 and $407.784\text{ nm}$ emission lines were within $\pm 0.001\text{ nm}$ of the expected peak wavelengths provided by the IntelliCal^® system. As such, for the 3600 lines/mm grating, a wavelength sampling of $\Delta \lambda =0.005\text{ nm}$ was established, providing an overall spectral range spanning $389.547 \le \lambda \le 400.459\text{ nm}$ 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 $585.249\text{ nm}$ was chosen as this was also within the wavelength window selected for the main solar observations. For the 3600 and 4320 lines/mm gratings, the strong Hg emission lines at 404.656 and $365.016\text{ nm}$ 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 $585.249\text{ nm}$ was found to have a measured line centre of $585.249\pm 0.001\text{ nm}$ and an FWHM of $0.037\pm 0.006\text{ nm}$, providing a spectral resolving power, $R_{2400}=15{,}817\pm 2742$. Similarly, for the 3600 lines/mm grating, the chosen Hg emission line at $404.656\text{ nm}$ was found to have a measured line centre of $404.656\pm 0.001\text{ nm}$ and an FWHM of $0.024\pm 0.002\text{ nm}$, providing a spectral resolving power, $R_{3600}=16{,}860\pm 1058$. Finally, for the 4320 lines/mm grating, the chosen Hg emission line at $365.016\text{ nm}$ was found to have a measured line centre of $365.016\pm 0.001\text{ nm}$ and an FWHM of $0.018\pm 0.001\text{ nm}$, 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 $585.249\text{ nm}$ (left panel), $404.656\text{ nm}$ (middle panel), and $365.016\text{ nm}$ (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.

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, 3600, 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 μm, which was employed during the initial commissioning phase of the francis instrument.

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/μm) 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 μm slit width, which is almost a factor of 5 larger than the pixel size on the imaging camera (11 μm), hence allowing this simplified estimate to be used. Hence, for the 2400 lines/mm grating, which provides a linear dispersion of $d\lambda /dl = 0.00072\text{ nm/}\upmu \text{m}$, a slit width of 50 μm equates to a theoretical FWHM of $0.036\text{ nm}$ and a resolving power of $R_{2400}=16{,}306$. Similar calculations for the 3600 and 4320 lines/mm gratings, which have associated linear dispersions of 0.00045 and $0.00032\text{ nm/}\upmu \text{m}$, provide theoretical FWHMs of 0.023 and $0.016\text{ nm}$, 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, 3600, 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.

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 μm slit width was chosen so that all light propagating down the 40 μm (core diameter) fibres would pass through into the spectrograph, hence minimising modal interference noise. However, this resulted in exposure times of 25 and $100\text{ ms}$ for the Na i D₁/D₂ and Ca ii H/K observations, which provided associated spectral frame rates of 23 and $9\text{ s}^{-1}$, respectively. Importantly, in the case of the Na i D₁/D₂ observations running at a maximal frame rate of $23\text{ s}^{-1}$, an exposure time of $\approx 40\text{ ms}$ 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 μm → 20 μm) would provide theoretical FWHMs of 0.014, 0.009, and $0.006\text{ nm}$ for the 2400, 3600, 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 $R \sim 40{,}000\,\text{--}\,55{,}000$ 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 $R \sim 40{,}000\,\text{--}\,55{,}000$ 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., 2022a) 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 and $588.995\text{ nm}$, respectively, were obtained, in addition to a short $\approx 20\text{ s}$ burst (200 spectral images) of Ca ii H/K spectra at 396.847 and $393.366\text{ nm}$, 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 ($25\text{ ms}$ for Na i D₁/D₂; $100\text{ ms}$ 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 ($25\text{ ms}$ for Na i D₁/D₂; $100\text{ ms}$ 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.

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 $25\text{ ms}$ 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).

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., $\sim 700\text{ nm}$).

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 $580.758 \le \lambda \le 597.250\text{ nm}$ for the Na i D₁/D₂ observations and $389.547 \le \lambda \le 400.459\text{ nm}$ 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 ($585.249\text{ nm}$) 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 ($404.656\text{ nm}$) 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.

It must be noted that each fibre core is 40 μm in diameter (see Table 1), while the Princeton Instruments Kuro 2048B camera employed has $11\times 11~\upmu \text{m}$² pixels. Hence, each fibre core will span over three 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 three $y$-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., $\lambda$ × 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 $23\text{ s}^{-1}$.

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.

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.

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 ($\ge 23\text{ s}^{-1}$).

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 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 $\Delta \lambda =0.008\text{ nm}$ 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.

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 $581.3\,\text{--}\,596.3\text{ nm}$ (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, $\Delta \lambda =0.008\text{ nm}$ pixel⁻¹, employed across the detector.

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 ${\Delta \lambda =0.005}\text{ nm}$ pixel⁻¹ is employed across the detector, providing spectral coverage spanning approximately $390\,\text{--}\,400\text{ nm}$. 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.

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 $389.55\,\text{--}\,400.08\text{ nm}$, 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, $\Delta \lambda =0.005\text{ nm}$ pixel⁻¹, employed across the detector.

Overall, Figures 9, 14 and 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 $\sim 3\text{ s}$ 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 μm, which results in a spectral line FWHM of $\approx 0.018\text{ nm}$. 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 $\approx 0.006\text{ nm}$, 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 $393.366\text{ nm}$, 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 $1000\text{ Hz}$) 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 $390\,\text{--}\,700\text{ nm}$. 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.