dunlap institute for astronomy & astrophysics · an ifts the product of the maximum resolution...

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Experimental AstronomyAstrophysical Instrumentation andMethods ISSN 0922-6435 Exp AstronDOI 10.1007/s10686-013-9330-9

Integral wide-field spectroscopy inastronomy: the Imaging FTS solution

J. P. Maillard, L. Drissen, F. Grandmont& S. Thibault

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Exp AstronDOI 10.1007/s10686-013-9330-9

ORIGINAL ARTICLE

Integral wide-field spectroscopy in astronomy:the Imaging FTS solution

J. P. Maillard ·L. Drissen ·F. Grandmont ·S. Thibault

Received: 2 May 2012 / Accepted: 11 February 2013© Springer Science+Business Media Dordrecht 2013

Abstract Long-slit grating spectrometers in scanning mode and Fabry–Perot inter-ferometers as tunable filters are commonly used to perform integral wide-fieldspectroscopy on extended astrophysical objects as HII regions and nearby galaxies.The goal of this paper is to demonstrate, by comparison, through a thorough reviewof the imaging Fourier transform spectrometer (IFTS) properties, that this instru-ment represents another interesting solution. After a brief recall of the performances,regarding FOV and spectral resolution, of the grating spectrometer, without and withintegral field units (IFU), and of the imaging Fabry–Perot, it is demonstrated that foran IFTS the product of the maximum resolution R by the entrance beam etendue U

is equal to 2.6 N × SI with N × N the number of pixels of the detector array andSI the area of the interferometer beamsplitter. As a consequence, the IFTS offers themost flexible choice of field size and spectral resolution, up to high values for bothparameters. It also presents on a wide field an important multichannel advantage in

J. P. Maillard (�)Institut d’Astrophysique de Paris, UMR7095 CNRS, Universite Pierre & Marie Curie,98 bis Blvd Arago, 75014, Paris, Francee-mail: [email protected]

L. DrissenDepartement de Physique, de Genie physique et d’Optique, Centre de Recherche en Astrophysiquedu Quebec, Universite Laval, 1045 av. de la Medecine, Quebec G1V 0A6, Canadae-mail: [email protected]

F. GrandmontABB Bomem, 585 Blvd Charest Est, Suite 300, Quebec, QC, G1K 9H4, Canadae-mail: [email protected]

S. ThibaultDepartement de Physique, Genie physique et Optique, Pavillon d’optique-photonique,Universite Laval, 2375, rue de la Terrasse, Quebec, G1V OA6, Canadae-mail: [email protected]

Author's personal copy

mailto:[email protected]




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comparison to integral field grating spectrometers, even with multiple IFUs. To com-plete, the few astronomical IFTSs, built behind ground-based telescopes and in space,for the visible range up to the sub-millimetric domain, are presented. Through twowide-field IFTS projects, one in the visible, the other one in the mid-infrared, thequestion is addressed of the practical FOV and resolution limits, set by the opticaldesign of the instrument, which can be achieved. Within the 0.3 to ∼2.5µm domain,a Michelson interferometer with wide-field diopric collimators provides the easiestsolution. This design is illustrated by a 11′ × 11′-field IFTS in the 0.35–0.90µmrange around an off-axis interferometer, called SITELLE, proposed for the 3.6-mCFH Telescope. At longer wavelengths, an all-mirror optics is required, as studiedfor a spaceborne IFTS, H2EX, for the 8–29µm range, a 20′ × 20′ field, and a highresolution of � 3 × 104 at 10µm. To comply with these characteristics, the interfer-ometer is designed with cat’s eye retroreflectors. In the same domain and up to the farinfrared, if the instrument aims only at a low spectral resolution (few thousands) anda smaller field (few arcmins2), roof-top or corner cube mirrors, as for the IFTS SPIREon the Herschel space telescope, are usable. At last, perspectives are opened, behindan ELT in the visible and the near infrared with the SITELLE optical combination,in the 2–5µm on the Antarctic plateau or in space up to longer wavelengths, withthe H2EX design, to provide the missing capability of global high spectral resolutionstudies of extended sources, from comets to distant galaxy clusters.

Keywords Instrumentation · Spectroscopy · Star formation · Gas kinematics · ISM

1 Introduction

With the advent of bidimensional detector arrays at almost all wavelengths, imag-ing surveys represent an important part of the observational programs in modernastronomy, conducted from ground and from space. Many ground-based telescopesare equipped with wide-field cameras able to accept more than 1 square degree fieldof view (FOV). Survey telescopes are in operation, as for example, the Visible andInfrared Survey Telescope for Astronomy (VISTA) [55], or the Panoramic SurveyTelescopes & Rapid Response System (Pan-STARRS) [24]. In space, the Wide-fieldInfrared Survey Explorer (WISE) [64] covered the entire sky at 3.4, 4.6, 12 and22µm in 2010. Many of these imaging surveys are conducted to probe the large-scalestructures of the distant universe. Detailed morphology of extragalactic and galacticsources are obtained in different spectral domains and, providing the adequate setof filters, spectral energy distribution (SED) of point sources can be retrieved. How-ever, the information on the chemical composition of the different species, and theirabundance variations across the field, are limited. Thus, the next step calls for theassociation of imagery and spectroscopy on wide fields.

Two classes of 3D-spectrometers, instruments providing spectral information onseveral points of an astronomical field, the multi-object spectrometers (MOS) andthe integral field spectrometers (IFS), have been developed. The proceedings ofthree international conferences which marked in the past recent years the develop-ment of 3D-spectroscopy in astronomy, from which several references given in the


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paper are extracted, are making a good introduction to the development of all thisinstrumentation. One can cite: “Tridimensional Optical Spectroscopic Methods inAstrophysics (1995)” [32], “Imaging the Universe in three Dimensions (2000)” [34],and “Science Perspectives for 3D-spectroscopy (2007)” [26].

With several arcmins fields on which spectral data are obtained only on selectedregions, MOS are favored as the spectroscopic complements to the extragalacticimaging surveys. Masks with slitlets, fiber positioners, or dynamic aperture shut-ters, are placed on the galaxies present in a wide deep field, and the light from allthe apertures is rearranged on the long slit of a grating spectrometer. For exam-ple, the WFOS project for the 30-m TMT [50] consists of two spectrographs witha 4.5′ × 5.4′ field each and as many as 750 slitlets on a single mask, for resolu-tions of 300 and 7,500. The BigBOSS instrument for the 4-m Mayall telescope aimsat simultaneously measuring 4,000 redshifts over a 3◦-diameter FOV by employing4,000 individual fiber positioners [56] feeding a set of 8 spectrographs (500 fiberseach) for a total wavelength coverage from 340 to 1,130 nm, at a spectral resolutionof about 5,000. On JWST, NIRSpec, the first MOS in space, is designed to producespectra of more than 100 individual sources between 0.6 and 5µm, over a 3.6′ × 3.4′FOV at R � 100, 1,000 and 2,700, by using programmable micro-electromechanicalsystems or MEMS [5].

With the IFS, spatially-resolved spectra are recorded on all the points of the field.Some authors [1] reserve the denomination to instruments in which all the data areobtained simultaneously, for one pointing of the telescope. In the paper, we adopta more general definition, by considering under that name all the intruments fromwhich the final product is the integral spectroscopy of a field, independently of thedata acquisition mode, implying a scanning operation or not. Two types of source callfor IFS, implying different instrumental solutions: (i) complex compact objects, and(ii) extended gaseous regions. The first class includes the circumstellar disks of youngstars, the envelopes of AGB stars, the halo of distant galaxies. For these objects, fewarcsecond fields are enough but, a high spatial resolution is desirable. The second cat-egory, on which the paper wants to focus, represents a large variety of sources whichhave in common an abundant content of atomic and molecular gas, the intergalacticmedium in galaxy clusters, nearby galaxies, the Galactic Center, galactic HII regions,planetary nebulae, supernovae remnants, the interstellar medium in young star clus-ters, comets near perihelion. For a global vision of these sources, several arcminsFOV are required. Often filled by a low density gas, a spectral resolution ≥104 isdesirable to study the entire velocity field and the variations of chemical abundance.Finally, a wide-field IFS compared to a MOS provides a serendipitous discoverypotential of unexpected sources since it does not pre-select particular regions in theobserved FOV.

In the paper, the more commonly used IFSs are examined, long-slit grating spec-trometers without and with integral field units (IFU), parallel spectrometers with IFU,in Section 2 and imaging Fabry–Perots in Section 3, to conclude on the limitations ofthese various solutions relative to field size, spectral resolution and spectral coverage.Then, Section 4 is devoted to the imaging Fourier transform spectrometer (IFTS),a relatively new technique, which represents a powerful solution often ignored, torespond to the scientific case of integral spectroscopy on wide-field sources. The


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relation between FOV and spectral resolution, making possible with a single instru-ment, integral spectroscopy on a wide field, with a continuous choice of spectralresolution, up to high values, on a broad enough spectral range, is analyzed. The lastpart of the section examines the multichannel advantage of the IFTS on a wide fieldin comparison to the competing techniques. Section 5 briefly describes the alreadybuilt astronomical IFTSs with their key characteristics. Then, the paper addressesthe question of the practical FOV and resolution limits impose by the optical designto image a wide field with an IFTS, through two projects, one named SITELLE inthe optical domain (Section 6) and the other one, H2EX, in the mid-infrared range(Section 7). For each spectral domain, perspectives are opened for other wide-fieldIFTSs which could provide new capabilities behind existing and future telescopes.

2 Dispersive integral field spectrometers

Different types of dispersive spectrometers are suitable to work as IFS, long-slit grat-ing spectrometers (LSGS), without and with IFU, in single and multiple mode, andslitless grating spectrometers.

2.1 Long-slit grating spectrometers

Wide-field spectral imaging can be obtained with a LSGS, simply by moving the slitin a raster pattern to map out a targeted region. However, the spectral resolution of agrating spectrometer matched to a telescope is related to its slit width by the relation:

R = 2 sin α

θ× WG

DT

(1)

where α is the angle of incidence on the grating, θ the angular slit width on the sky,WG the grating width and DT the telescope diameter, meaning that the higher thespectral resolution, the narrower the slit width, particularly behind a large telescope.To fully cover a wide field at high spectral resolution, the number of telescope point-ings of the narrow slit would become very large (see Section 4.4). In addition, witha high resolution LSGS, the spectral domain will be small since to image the full slitheight, a single echelle grating order is required. Consequently, this imaging modeis not much used at high spectral resolution, or only for a partial coverage of anextended object, with slit positions spaced by several seconds of arc, or in particu-lar directions to limit the number of pointing. Thus, this mode mode is better suitedto low spectral and spatial resolution mapping. For example, the supernova remnantCassiopeia A was completely mapped by the Infrared Spectrograph (IRS) aboard the0.85-m Spitzer telescope. The spectral resolution was around 600, for a spatial res-olution of ∼2′′ on the 5–15µm domain and of ∼8′′ on the 15–38µm domain, on afield respectively of 6.1′×5.9′ and 11.0′×7.8′ [57]. Note that the 3D structure of thesame object had been before partially explored by 73 long-slit optical spectra spacedby 4′′ [53].

A full 2D-field without slit scanning is obtained by placing in the telescope focalplane an IFU before the slit. Fiber bundles and mirror image slicers represent the two


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major solutions [1]. However, the maximum FOV remains equal to the slit area h×θ ,with h the slit height projected on the sky, and θ the angular slit width. For example,a slit height of 50′′ and a slit width of 1′′ will only give a 7′′ ×7′′ FOV. The number ofspectra depends on the number of spatial elements in the IFU, fiber or mirror slice, topave this field area. The fiber solution, with the interest of not requiring a relay optics,can be adopted for the visible and, with the adequate fibers, in the near-infrareddomain. The mirror image slicer presents the advantage to be achromatic, and thus, tobe usable for a wide spectral coverage, particularly in the infrared. However, a largenumber of slice increases the instrumental complexity since the portions of imageselected by each mirror slice have to be aligned with the long slit by a relay optics.So far, the largest slicers ever manufactured have been made of 48 elements [30].

On the ground, SINFONI installed behind an adaptive optics (AO) systems onthe VLT [40] and working in the J, H and K bands, is a typical example of such aninstrument. The available field sizes with the appropriate image slicer are respectively0.8′′ × 0.8′′, 3.0′′ × 3.0′′ and 8.0′′ × 8.0′′. The spectral resolution is of the orderof 3,000. In the instrumentation program of the E-ELT, HARMONI [60] is studiedto use the same technique, with a spectral coverage from 0.47 to 2.45µm, and thegoal of offering spectral resolutions up to 20,000, with spatial scales ranging fromseeing-limited imaging, on 5′′×10′′ FOV, to diffraction-limited resolution on 0.5′′ ×1′′ FOV. In space, MIRI [65] the JWST mid-infrared IFS, with a resolving poweraround 3,000, covers the full 5–28µm range in four channels associated to fieldsranging from 3.0′′ × 3.9′′ to 6.7′′ × 7.7′′.

In conclusion, the field size of an IFU, a few tens of arcsecond square, appears wellsuited to integral field spectroscopy of compact objects, such as particular distantgalaxies, circumstellar disks, exoplanet systems, or small crowded fields as in theGalactic Center, at the spatial resolution of a space telescope or of an AO system.The associated grating spectrometer generally provides a spectral resolution at mostof few thousands.

2.2 Multiple IFUs

To cover a larger field, the solution consists of paving the field with multiple IFUs.The Multi-Unit Spectroscopic Explorer (MUSE) [4] for the VLT is designed accord-ing to this rationale by covering a 1′×1′ field with 24 contiguous image slicers, whichimplies the same number of spectrometer modules, for a medium spectral resolutionof about 3,000 in the 465–930 nm range. Combined with an AO system, the spatialresolution aims to be of 0.2′′. The same concept is pushed much further with VIRUS(Visible Integral field Replicable Unit Spectrograph) [23] for the Hobby-Eberly Tele-scope, which consists of 150 identical spectrographs behind the 10-m telescope, fedby 75 fiber-coupled IFUs with a 1/3 filling factor, to cover a 22′ diameter FOV. Alltogether, they will produce around 33,000 spectra per exposure, covering the 350–550 nm domain. This solution leads to very huge instruments. However, its efficiencyis discussed in Section 4.4, through the example of MUSE.

With the progress of IFUs, instruments combining both, integral field spec-troscopy on small fields and the wide field of a MOS, have been developed, withthe concept of multiple deployable IFUs. This capability provides at optical and


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infrared wavelengths spatially resolved spectra, simultaneously on several targets ina wide field. The Fiber Large Array Multi-Element Spectrograph (FLAMES) in theGIRAFFE configuration [48] on the ESO VLT represents an example of this combi-nation with 15 IFUs, each covering a field of 2′ × 3′ within a FOV of 25′ diameterand, in a single exposure, a spectrum of about 20 nm at R = 33,000 and 60 nm atR = 11,000 in the 360–930 nm domain. This solution certainly increases the scien-tific output of a MOS. However, the largest part of the environment of the sourcesremains unexplored, which can be only obtained by a true wide-field IFS.

2.3 Slitless spectrometers

For the particular case of groups of point sources with strong emission lines, suchas clusters of distant galaxies or clusters of hot stars, a simple solution consists ofplacing a grism in front of the objective of a wide-field imaging camera which trans-forms it into a slitless spectrograph [39]. Only the degree of overlapping of spectra onthe bidimensional detector limits the separation of individual sources. To control theseparation of spectra to study single extended objects, the grism has been combinedwith a microlens array placed in the telescope focal plane. This TIGER-type design[2] providing a 33′′ × 41′′ FOV was used for the SAURON project [3], a survey ofearly-type galaxies at R � 1,500 in the visible. This solution has been transposed inthe near-infrared with the cryogenic OH-Suppressing InfraRed Integral field Spec-trograph (OSIRIS), instrument on Keck II [29] working near the diffraction limit ofthe telescope behind the AO system, up to a 6.4′′ × 6.4′′ field at a spectral resolu-tion of 3,800. All these instruments are also well suited to small field projects at lowspectral resolution, the true FOV depending on the spatial resolution.

3 The imaging Fabry–Perot

Fabry–Perot (F–P) interferometers in imaging mode have been in common use forlong, both at optical and infrared wavelengths, to study the distribution and the veloc-ity field of extended gaseous regions from one emission line of the gas. The spectralresolution R depends on the interference order p which is used to analyze a line pro-file, and the finesse F of the F–P, ratio of the interval between two consecutive peaksof the Airy function by the peak full width at half maximum, with:

R = p × F . (2)

Thus, to reach a high spectral resolution, a high-order F–P of high finesse is required.Technological developments based on piezo-electrically actuated gap scanning mech-anism make possible to maintain the gap spacing and parallelism with a highprecision from a spacing of a few microns up to several hundreds of microns. For agiven spacing, the maximum FOV which can be accepted by the F–P is determinedby the ring diameter at which the fringe contrast on the detector array becomes null,as defined in Section 4.1 (8) for the IFTS, the other imaging, interferometric device.Hence, the FOV diameter of an imaging F–P can be usually of several arcminutes,for a resolving power of the order of ten thousands.


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3.1 The high-resolution imaging Fabry–Perot

A high finesse (≥50) being more easily obtained on a narrow spectral range, special-ized imaging F–Ps have been built to carry surveys on one line, in particular Hα, agood indicator of star formation rate in galaxies. Successful surveys of this line havebeen carried out on the Galactic plane and on large sets of nearby spiral galaxies.For example, on the Virgo cluster [12], three facility F–Ps on four different tele-scopes have been used, CIGALE at OHP, MOS/F–P at CFH and FANTOMM at the1.6-m Mont Megantic Observatory, the 3.6-m CFH and the 3.6-m ESO telescope.The FOVs ranged from 13.6′ with FANTOMM behind the 1.6-m telescope to 4.2′and 3.6′ behind the 3.6-m telescopes with pixel sizes of 0.49 and 0.42′′. The spec-tral resolutions were ranging between ∼7,950 and 21,000, depending on the order inuse. In this case, the explored spectral range centered on Hα was equal to 1.08 nm or494 km s−1 for the lowest resolution and 0.56 nm or 259 km s−1 at the highest reso-lution. Going to long wavelength means a F–P with a large gap between the plates toreach a high order. For example, the South Pole Imaging Fabry–Perot Interferometer(SPIFI) [46] is a direct imager operating in the 205µm submillimeter windows on a5.4′ × 5.4′ FOV and a resolution of about 5,000. In conclusion, the high resolutionimaging F–P can make possible IFS, in very different spectral domains, on severalarcmins field, but strictly on a very narrow spectral range, allowing to study a singleline fitted to the F–P.

3.2 The imaging tunable filter

A low-order, medium-finesse F–P (10–20) and long-range piezo-electric transducersto scan the parallel plates make the basis of an imaging tunable filter. The instru-ment can isolate a narrow spectral band over a broad, continuous spectral range,providing blocking-order filters in contiguous passbands. Taurus, the tunable filteron the 3.9-m Anglo-Australian Telescope represents the prototype of this type ofspectro-imaging device, allowing spectral resolutions of 100–1,000, attainable in the370–1,000 nm domain over a ∼10′ circular field [6]. Such tunable filters have beenput in operation behind new ground-based telescopes. The Maryland-Magellan Tun-able Filter (MMTF) on the Magellan-Baade 6.5-m telescope at Las Campanas [61]provides a FOV up to 27′ in diameter at four different wavelengths, through fourdifferent order-blocking filters between ∼500 and ∼900 nm, with resolutions goingfrom ∼360 to ∼1,000. OSIRIS on the 10.4-m GranTeCan telescope [13] offers a sim-ilar low-resolution imaging mode with a blue and a red-optimized F–P tunable filteron a 7.8′ FOV. In space, the Tunable Filter Imager (TFI) [16] (R � 100), designed towork in the 1.6–2.5µm and 3.2–4.9µm domains on a 2.2′ × 2.2′ FOV, is part of theJWST instrumentation.

Two visible wide-field imaging instruments, the Brazilian Tunable Filter Imager(BTFI) on the SOAR telescope [59] (3′ FOV behind an AO module) and 3D-NTT forthe NTT telescope [38] (17′ and 7′ FOV) can offer medium resolution (∼1,000) andalso higher resolution up to ∼20,000, by combining a low-order F–P on 3D-NTT,or an imaging Bragg tunable filter [7] on BT FI , with a high-order F–P. In the low-resolution mode, only the tunable filter is placed in the beam. It serves as selecting


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filter for the high-order F–P in the high-resolution mode. The high-resolution capac-ity of the device depends on the finesse value attained on the high-order F–P andits uniformity over all the visible range, which represents a critical challenge. Thisconcept improves the choice of spectral resolution and of accessible lines comparedto the standard imaging F–P. However, in high-resolution mode the spectral domainwhich can be explored in a scan remains very narrow, making this device suited tothe analysis of a set of well-isolated emission lines.

4 The imaging FTS

Another technique for integral field spectroscopy has been proposed with the Imag-ing FTS which results from the coupling of a FTS with a bidimensional detector.It was developed first at the CFH Telescope by a prototype named BEAR [32, 34](Section 5.1). The entrance FOV is directly imaged on the detector array (Fig. 1). Astep-by-step scanning mode of the optical path difference (OPD), controlled fromthe fringe signal of a laser through the interferometer, is mandatory, a major dif-ference with a standard FTS. Moved by equal steps, the OPD is stopped after eachstep to integrate and record an image of the field (Fig. 1). The IFTS for astronomical

Fig. 1 Principle of the Imaging FTS data acquisition. At each step of the Michelson interferometer OPDan image of the entrance field is recorded on the 2D-detector array, to record an interferometric data cubefrom which the spectral cube is computed


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observations is generally based on a dual-port Michelson interferometer to accessto the two output beams for a maximum efficiency. Thus, two 3D-data cubes areacquired with x and y as the field coordinates and z as the OPD. The interfero-grams I1x,y(δ) and I2x,y(δ) (3) and (4), functions of the OPD δ, extracted from eachresolved element in the field, contain the spectral information. Bx,y(σ ) representsthe spectral energy distribution as a function of the wavenumber σ , of the observedextended source at the x, y point of the field, multiplied by the spectral response ofthe instrument and the transmission of the filter in use. The classical expression of I1and I2 is:

I1x,y(δ) = 1

2

∫ ∞

0Bx,y(σ )[1 + cos(2πσδ)]dσ (3)

I2x,y(δ) = 1

2

∫ ∞

0Bx,y(σ )[1 − cos(2πσδ)]dσ (4)

from which by FFT, the spectral data cube is generated (see Section 4.3). The IFTSkeeps the general properties of the FTS which can be revised in the textbook on“Fourier transform spectrometry” [15]. The field properties, specific to the imagingmode, are analyzed in the next sections.

4.1 Field size and spectral resolution properties

The famous formula, R� = 2π (valid also for the spectroscopic F–P), with R theresolving power and � the solid angle of the input beam under which the entranceaperture is seen in the interferometer, expresses the classical luminosity property ofthe standard FTS for a given spectral resolution (also called the “etendue advantage”or “Jacquinot’s advantage” compared to a slit spectrometer). This property is revisitedfor the Imaging FTS matched to a telescope, by studying in this configuration therelation between the imaged FOV and the maximum spectral resolution as a functionof the instrumental parameters. The entrance field of angular diameter θ on the sky,imaged by the telescope of diameter DT onto the Npxl×Npxl pixels array of the IFTS,corresponds at the edge of the field, within the interferometer of beam diameter DI ,to a maximum angle of incidence imax:

imax = θ × (DT /2DI) . (5)

If a binning factor bf is used in the data processing (Section 4.3), N = Npxl/bf ,and the effective pixel size translates into a small angle di:

di = 2imax/N . (6)

At δ0, the OPD measured on the axis of the fringe pattern, which is supposed tocoincide with the direction of the field center, a ring of order k, for a monochromaticline of wavelength λ, has an angular radius αk equal to:

αk = (2λ/δ0 × k)1/2 . (7)


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For a monochromatic source, the fringe signal recorded on one of the N pixels byscanning OPD presents a contrast , ratio of the fringe amplitude to the contin-uum intensity, with Imax the peak intensity and Imin the minimum intensity of thefringe:

= Imax − Imin

Imax + Imin. (8)

At large OPD the ring pattern centered on the 2-D detector becomes more and moreclosely spaced towards the detector edge. As a result, measured on a pixel row orcolumn crossing the field center, is a decreasing function towards the detector edge. has been computed by a special program written under IDL, at λ, for the instrumentalparameters DT , DI , and the plate scale θ/Npxl, as a function of the entrance fieldradius for a given OPD or, as a function of δ0 for a given FOV θ , as shown in Fig. 2computed from the instrumental parameters of the H2EX IFTS (see Section 7.1). Asseen in the figures, the resulting function has the general expression of the absolutevalue of a sinc function.

The fringe contrast becomes null for a certain value of OPD (Fig. 2, left) or acertain value of the field radius (Fig. 2, right). The position of the first zero of the function gives the theoretical maximum FOV which could be imaged by an IFTSdefined by the set of basic instrumental parameters (DT , DI , N , λ) at a given OPD or,the maximum OPD, noted δmax, which could be explored for a given field. To deter-mine this position, at large OPD, the ring becomes closely spaced and a derivation of(7) is valid. With dαk the angular fringe spacing, it comes:

αk dαk = λ/δ0 dk . (9)

Between two close consecutive rings we have dk = 1. The fringe contrast

becomes equal to zero where the fringe spacing is just equal to the pixel size

Fig. 2 function at the edge of the field considered for the H2EX project, at left, as a function of OPDfor a 20′ field radius. At right, the plate scale of 2.34′′/pixel (40′ on a 1K × 1K array) is kept, giving

as a function of the field radius for the 18.70 cm on-axis OPD (R = 32,000 at 9.7µm). At this OPD,

becomes null at a field radius of 1,643′′ (or �0.9◦ FOV), and for a 40′ FOV, at OPD = 25.47 cm, as givenby (11)


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expressed by dαk = di. This condition happens at an angular ring radius αk = imax.With di defined by (6) and for δ0 = δmax, (9) becomes:

imaxdi = λ/δmax . (10)

Finally, from (10) with (5) and (6), it comes:

δmax = λ2N

θ2 ×(

DI

DT

)2

. (11)

Thus, the corresponding maximum FOV θmax for the on-axis OPD δmax is:

θmax =(

λ2N

δP

) 12 ×

(DI

DT

). (12)

R0 the maximum resolving power corresponding to δmax is equal to:

R0 = σ/dσ = δmax

0.603 × λ(13)

with dσ the FWHM of sin(2πσδmax)/2πσδmax, the FTS instrumental lineshape(ILS). From (11) and (13) it comes:

R0 = 3.33N

θ2max

×(

DI

DT

)2

. (14)

This formula can be put under another form to remind the classical R × � productrecalled above. At the numerator, the θ2

max ×D2T product represents the etendue U of

the beam accepted by the telescope of collecting area ST with:

U = ST × � = (π2/16)θ2max × D2

T . (15)

Thus, with SI the area of the interferometer parallel beam, in practice the beamsplitterarea, it can be written from (14):

R0 × U = (3.33π/4) N × SI = 2.61 N × SI (16)

Thus, from (16), for an IFTS the R0 × U product is constant, which means that theincrease of the maximum resolution R0 implies to reduce the FOV and inversely. Onthe other hand, to allow a wide field and a high maximum spectral resolution, theR0 × U product of an IFTS can be increased in two ways, by the number of pix-els of the array for a same field (see Section 4.3.1) or by the beamsplitter diameter.This last parameter implies bigger optical pieces and therefore, a bigger instrumentand a higher cost. However, the gain R0 × U going as the square of the beam diame-ter, a moderate increase can make possible a significant gain on the possible FOV orresolution. In Section 6.1 is seen that the increase of this diameter also helps the opti-cal design of the interferometer collimators since it decreases the maximum incidentangle imax within the interferometer (5).

4.1.1 Effective spectral resolution of an IFTS as a function of OPD and field size

The decrease of the fringe contrast with OPD for an off-axis point of the field (Fig. 2,left) leads to an apodization of the ILS, meaning an effective spectral resolution


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which is reduced compared to the on-axis value (Fig. 3, left). The spectral resolutiondecreasing towards the edge of the field, is not uniform over a wide field for aninstrument aimed at a high spectral resolution (Fig. 3, right). From the computationof the function, it results that if the OPD for a given field, or the field radius for agiven OPD, is pushed to reach the first zero of the function, as shown from Fig. 3,the resolution at the field edge, Rmax−off−axis, is only:

Rmax−off−axis = 0.70 × R0 . (17)

From Fig. 3, left R0 is equal to 44,000 while at the edge of the 20′ field radius theresolution is only 30,800. To reach this minimum resolution an OPD equal to 17.8 cmis enough at the field center while it must be pushed up to 25.5 cm, in the ratio of 0.70between the two values from (17). In other words, the observing time is increasedat least by 43 % compared to the time which would be needed for a resolution of�30,000 over the FOV without the self-apodization effect. Consequently, to acquireIFTS data over a wide field with a spectral resolution as uniform as possible, onesolution consists of limiting the max OPD or field size well below the maximumvalues defined by the first zero of the function. In the example given in Fig. 3, left,for an OPD limited to 18.70 cm a resolution of 32,000 is reached at the field center,which goes down to 27,200 at the field edge, or 85 % of the central value for a fieldradius of 20′. This minimum resolution (OPD = 15.86 cm at the field center) impliesa less important increase, anyway still 18 %, of the OPD needed at the field center.In fact, the only solution to keep a uniform high spectral resolution over a widefield consists of adequately matching the DI diameter of the interferometer, whichincreases the R × U product (16). For example, computing with the parameters ofFig. 2, but with DI = 100 mm instead of 50 mm, the resolution of 32,000 is constantover the 40′ FOV since the fringe contrast remains ≥94 % at 9.7µm over the wholefield at the maximum OPD.

Fig. 3 Variation of the spectral resolution at the edge of the field (+ − + line) computed up to the firstzero of the functions shown in Fig. 2, at left with OPD, at right across the field. The tangent to the curvesshows the on-axis resolution, illustrating (17) at the max OPD and at the max field. The lower horizontalline marks the maximum resolution reached for the nominal on-axis OPD (at left), or for the nominal fieldradius (at right)


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4.1.2 Effective spectral resolution of an IFTS based on an off-axis interferometer

In the early days of the payload definition of the James Webb Space Telescope(JWST), called at that time the Next Generation Space Telescope (NGST), the sci-entific interest of a low-resolution, wide-field IFTS for extragalactic astronomy inthe 1–15µm domain, had been stressed by Graham et al. [21]. Three teams [22, 41,52] presented an IFTS project for NGST in response to the call for proposals. Twoprototypes of ground-based wide-field IFTS in the visible have resulted. Both werebased on a common optical concept, a Michelson interferometer used off-axis, asshown in Fig. 4. While in the standard Michelson one output beam returns towardsthe source, by giving a tilt to both flat mirrors, of 7◦ in this model, the two outputbeams become accessible, which doubles the useful signal (23). One such instru-ment was developed at LLNL (Lawrence Livermore National Lab.) [22] and testedon the 3.5-m Apache Point Observatory [63]. The other one, SpIOMM (SpectrometreImageur de l’Observatoire du Mont Megantic) (Section 5.2), from Laval University(Quebec City), was installed on its 1.6-m telescope, where it is still in operation.

The off-axis design presents the advantage of giving access to the two outputbeams of the interferometer without the need of corner cube mirrors, and as such,to provide a compact interferometric block with only two mirrors against six. How-ever, a consequence of this choice for an IFTS is to prevent the capability of highspectral resolution on a wide field. The drop of modulation efficiency at the edge ofa wide field becomes rapidly important by increasing OPD. As shown in Fig. 5, leftfor the SITELLE IFTS (Section 6.1) developed around the off-axis design, variesbetween 0.68 and 0.31 across the 11′ FOV while the modulation efficiency of an on-axis interferometer would remain on any point of the field always ≥96.5 % at thesame maximum OPD, over the same FOV. Indeed, the off-axis angle io−a to con-sider in the computation of the function is the sum of the true field radius (θ /2)plus twice the tilt angle β of the flat mirrors needed to access the two output beams,projected on the sky, which gives:

io−a = θ/2 + 2 β × DI/DT . (18)

Fig. 4 Schematic diagram of the off-axis IFTS developed at LLNL. From A1, the focal plane of thetelescope, the two resulting output beams are focused by the L2 systems on the cameras C1 and C2. In theinterferometer, the FOV center makes a 14◦ angle with the center of the fringe pattern


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Fig. 5 At left: variation between 0.68 and 0.31 of the fringe contrast at λ = 370 nm, for the SITELLEIFTS (Section 6.1) across the 11′ FOV, in the direction of the off-axis angle, for a max OPD of 0.67 cm(R = 30,000 on axis). At right: spectral resolution with OPD (+−+ line) at the most off-axis edge of thefield and the on-axis resolution for comparison

A tilt angle β as small as possible is preferable. For SpIOMM β is equal to 8◦, but forSITELLE, β = 15.5◦. In addition, the scanning of OPD introduces a shift d betweenthe two interfering beams equal to:

d = 2 × OPD × tan(βoff−axis) (19)

with βoff−axis the angle of incidence of the beam axis on the interferometer mirrors,limiting the flux to the area of the intersection between the two beams. Hence, ifSITELLE instead of working in the near-UV had been designed to work at 2.5µm ata spectral resolution of �25,000 (Fig. 5, right), the required OPD would be of 3.9 cminstead of 0.67 cm at 370 nm. The resulting shift d would reduce the fringe contrastfunction (Fig. 5, left) by a supplementary factor of 0.85, and the useful field by thesame factor. The drop would become even more important for the same resolution atlonger wavelengths. Thus, the off-axis solution appears able to combine wide fieldand relatively high spectral resolution towards the UV. This design could be adoptedfor a wide-field IFTS in the thermal infrared, only providing a low spectral resolu-tion instrument (∼100–1,000), which was in fact the resolution and spectral domainconsidered for the instrument based on this concept initially proposed for the futureJWST.

A dynamic alignment system of the mirror’s interferometer becomes absolutelynecessary to continuously correct the tilt of the moving mirror induced by its scanningmotion. Such a system of alignment is avoided by the use of corner cubes or cat’seye mirrors (see Section 5.1). Indeed, for a tilt angle θ between the two interferingwavefronts, parallel fringes are formed and the integrated intensity on the circularpupil of radius r gives the modulation efficiency (ME) at the wavelength λ (20) [62]with:

ME = 2J1(2πrθ/λ)

2πrθ. (20)

The application of (20) shows that the tolerance becomes particularly severe towardsshort wavelengths as illustrated in Fig. 6 for λ = 350 nm, the shortest wavelengthof the SITELLE spectral domain. The same equation can also be used to deduce the


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Fig. 6 Modulation efficiency of an interferometer at λ = 350 nm as a function of the tilt (in µrad) betweenthe two plane wavefronts for pupil sizes from 50 to 120 mm

tolerances on the right angle between the mirrors of a corner cube, since an error inone of these angles translates into a tilt of the outcoming wavefront, illustrating thedifficulty of making good corner cube mirrors for the blue and at shorter wavelength.Finally, this consideration convinces to adopt an off-axis design for the near-UV andvisible SITELLE IFTS.

4.2 Data acquisition

The data acquisition of an astronomical IFTS consists of recording N images witheach output camera, obtained by scanning the OPD by N steps of size p from thezero-OPD to the maximum OPD. This data cube will provide after data process-ing (Section 4.3) a final spectral data cube where the limit of resolution dσFWHM,generally expressed in cm−1 with p in cm, is equal to:

dσFWHM = 0.603/(N × p) . (21)

To p it corresponds a free spectral range �σ = 1/2p on which dσFWHM is constant,computed to match the full bandpass at zero-level of the filter isolating the spectraldomain under study. �σ can be as wide as needed, the classical multiplex propertyof the FTS, a major difference with the F–P imager (Section 3). Then, the minimumnumber of images N to record along the OPD is equal to the number M of spectralelements in �σ with M = �σ/dσ .


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On the BEAR IFTS [34] (Section 5.1), the number of image to acquire in a dataacquisition has been made equal to Nstep = N + 50, by starting the data record-ing 50 steps before zero-OPD. The exact zero-OPD position was determined in thedata processing (Section 4.3) from the short [−50, +50] steps symmetrical interfero-gramm at the beginning in each elementary interferogram. From this determination,a secondary interferogram was computed, exactly starting at zero-OPD. However,this data acquisition mode implies a perfectly compensated pair of beamsplitter andbeamcombiner to produce over all the spectral domain of the instrument an achro-matic OPD, while a not-compensated beamsplitter is tolerated by recording data from−δmax to +δmax. The BEAR method presents the very important advantage to cut bya factor two the number of images in the recorded data cube, and hence, to reduceby the same factor the overhead time in the total observing time. This considera-tion is crucial for a high-resolution wide-field IFTS, particularly for ground-baseddata where the available observing time is limited. Indeed, with Nstep the total num-ber of recorded images, the effective total observing Tobs to acquire a data cube isequal to:

Tobs = Nstep × (τ + thead) , (22)

with τ the integration time at each step and thead the overhead time coming fromthe sum of different components: readout of the array, storage of each image, andeventually, stabilization time of the moving mirror. For an efficient observing timeτ � thead is desirable. A wide-field IFTS supposes large format arrays, and thenthead can be dominated by the readout time—e.g. a time of 2.7 s is reported for thereadout of a low-noise 1K × 1K Si:As array [65] in the low-background JWST spaceconditions. Such overhead time would mean one hour lost on the total observingtime for a data cube of ∼1,300 images, which represents a typical value for ≥104

resolution data on a narrow-band filter. In such an environment, in order to be inphoton noise-limited conditions, the integration time τ must also be long enough forthe photon noise in the recorded images to be at least ∼5 times the readout noise. Allthese constraints lead to limit Nstep. Thus, a high spectral resolution imposes to usenarrow-band filters, well adjusted to the lines of interest.

4.3 Data processing

Data processing of a wide-field, high-resolution IFTS implies to manipulate a largevolume of data equal to two data cubes of Nstep × N2 pixels. For example, con-sidering SITELLE (Section 6.1), with these two 2K × 2K arrays and one thousandimages coded in 16 bits, the volume of data for a single observation becomes equalto 128 Gigabits, without applying a binning factor. Thus, the processing of such datavolume implies the access to enough computing power. With the BEAR instrument(Section 5.1) a complete IFTS data reduction package written under IDL was devel-oped [34]. Necessarily, it starts by standard image processing operations whichinclude bias subtraction, flat fielding, bad pixel correction and cosmic hits cleaning.The final cube of interferograms is built by the N2 differences (23) between the cor-responding interferograms I1x,y(δ) and I2x,y(δ) (3) and (4) from the two cleaned


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output cubes. These differences provide the full interferometric signal at each pointand cancel the continuum level since:

Ix,y(δ) = I1x,y(δ) − I2x,y(δ) =∫ ∞

0Bx,y(σ ) cos(2πσδ)dσ . (23)

For ground-based data, the sum of the two output interferograms from a bright starof coordinates Sx and Sy in the field (24) recovers the total flux Sx,Sy(δ) of the starreceived from:

Sx,Sy(δ) = I1Sx,Sy(δ) + I2Sx,Sy(δ) = η(δ)

∫ ∞

0BSx,Sy(σ )dσ . (24)

By normalizing the maximum of this function to 1, it provides a recording of η(δ),the variation of atmospheric transmission along the data acquisition by which, eachinterferogram Ix,y(δ) can be divided for correction.

The computing of the spectral data cube represents the last major step of the dataprocessing. If the data acquisition is based on the record of 50 steps before zero-OPDas made on the BEAR IFTS (Section 5.1) the computation of the precise zero-OPDposition for each interferogram has to be performed first. Only if the data acquisitionis made from −δmax to +δmax this determination is not needed. Then, a big loop ismade, pixel by pixel, over the N2 interferograms Ix,y(δ) (23) to create by FFT the N2

corresponding spectra, building the first spectral cube prior to complementary dataprocessing operations (Sections 4.3.2 and 4.3.3).

4.3.1 Spatial resolution of the spectral images

Working as a direct imager (as the imaging F–P) the IFTS can keep in the finalspectral cube the spatial resolution of the images recorded in the data acquisition,limited by seeing, or by adaptive optics or by diffraction of the telescope. Computingfor each interferogram its FFT and placing the resulting spectrum at the same x, y

coordinates, the spatial resolution and the astrometry of the interferometric cube isdirectly transferred to the spectral cube, without having to proceed to any reconstruc-tion of the field, as it must be performed with a slit instrument (Section 2.1). For ascanning LSGS the image reconstruction depends on the pointing precision of eachslit position. For a system with a mirror image slicer, it relies on the image qualityand the alignment of all the optical elements of the IFU (slicer stack, pupil mirrors,reimaging system on the slit).

However, preliminary operations on the raw data are needed. After the standardimage processing operations, a removal of the pointing errors and of the instrumentalflexures, which occurred along the data acquisition, has to be applied. A registrationof the hundreds of recorded images of both output cubes is made by using as referencetwo widely separated bright stars in the field (except for moving objects as comets forwhich another method is needed) to correct each image in translation and rotation.

Also, some conditions have to be put on the spatial sampling of the recordedimages. Considering (16), for a same field, simply by increasing N , the number N ofpixels of the detector array, the R × U product could be increased, meaning the pos-sibility of any maximum spectral resolution on a wide field. However, a high value


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of N is equivalent to a low energy level received on each pixel, and to an interfero-gram from a pixel giving after FTT a corresponding spectrum with a poor S/N ratio.Particularly, for seeing-limited ground-based observations, such a factor has to beapplied to fit the seeing conditions. An oversampling of the PSF would produce aphotometric noise in each individual interferogram due to the variable flux seen byeach pixel, which will translate into an excess noise in the resulting spectrum. Thus,for a best use of the available energy the plate scale must be fitted to the PSF of theobservations, in seeing or diffraction-limited conditions. For the observation of weakregions, the application to the raw images of a binning factor (6) several times thePSF, may be even necessary. Applying a binning factor to the recorded images, from(16), the maximum reachable spectral resolution on the data will be divided by thisfactor, which can be of 2 or 3 or more, compared to the maximum resolution withoutbinning. Off course, low resolution data will not be affected (Fig. 3) by this operationand the S/N ratio multiplied at least by the binning factor.

From (16), it can also be inferred that behind a diffraction-limited telescope, pro-viding an IFTS with N large enough to fit the spatial resolution of the telescope onthe observed field, a higher maximum spectral resolution can be reached on the samefield, than in seeing-limited condition. The possible increase in spectral resolution isdirectly proportional to the gain in spatial resolution, with the same S/N ratio whenlimited by the photon noise of the source, with a gain on the S/N ratio equal to thebinning factor when limited by the photon noise of the sky background. For an IFTSbehind an AO system, which so far has never been done, the discussion is more com-plex and will depend on the Strehl ratio of the system, a low ratio meaning extendedwings of the PSF limited by the seeing, which must be taken into account.

4.3.2 Phase curvature correction

An off-axis point of the imaged field corresponds to a parallel beam in the interfer-ometer with an angle of incidence i. It results in the spectral data cube that the surfaceaffected to a given wavenumber σ0 is in fact a paraboloıd instead of being a plane,since in the approximation valid for small angles:

σ ′ = σ0 (1 − i2/2) . (25)

Thus, for an absolute wavenumber calibration of the data cube a phase curvature cor-rection must be applied to the spectrum extracted from each pixel of the field, whichsupposes a correct estimate of the corresponding angle i. This operation requires aprecise determination of the coordinates in the field of the fringe pattern center, wherei = 0. The recording of a cube from a monochromatic source illuminating the fullFOV of the instrument, acquired in the observing conditions, makes possible to deter-mine this origin and then, to check the precision of the curvature correction (Fig. 7).On a wide-field instrument, the lineshift velocity correction to apply can becomelarge. As an example, with the parameters of the instrument given in Fig. 2 the veloc-ity shift would reach 3,000 km s−1 at the edge of the 40′ FOV for the 9.7µm H2 line.This shift must be taken into account in the determination of the step size associatedwith the filter used to isolate this line. The true width to consider is equal to the filterwidth at the baseline level, plus the maximum off-axis lineshift, 97 nm in this case.


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+ at field center

* at field edge, not corrected

- at field edge, corrected

Fig. 7 Instrumental lineshape of the BEAR instrument from an airglow OH line near the 2.12µm H2 line,which provides a uniform no-velocity line over the field. The lineshift between the edge (∗ line) and thecenter of the field (+ line) translates into a velocity shift of 9 km s−1. The ILS at the field edge, recenteredafter application of the phase curvature correction is shown (− line)

Note that for an off-axis IFTS (Section 4.1.2) the velocity correction becomes muchlarger since at the field center i is already equal to twice the mirror off-axis angle(18). In addition, the fringe pattern center being out of the FOV makes the precisedetermination of i in each point of field very critical for an accurate correction.

4.3.3 Background subtraction and photometric calibration

The final part of the data processing is devoted to the background subtraction andthe photometric calibration. No spectral calibration, except the phase correctiondescribed in the previous section, is needed, specific advantage of the FTS, provid-ing a well-defined reference line for the OPD control. For space data in the infraredthe spectral cube has to be corrected from the thermal background emission spectrum(see for example Fig. 10). Possibly, this spectrum can be retrieved from an area ofthe field free of source, easier to find with wide-field data. Otherwise, an offset datacube, as close as possible from the observed field for the same background emissionmust be acquired. A low resolution and an appropriate binning are applied to increasethe S/N ratio of this spectrum. Estimated for the same pixel size and sampled withthe same number of spectral elements, it can be subtracted to each spectrum of thespectral cube. For ground-based observations in the visible and the near-infrared thespectra of the observed field are mixed with the sky airglow emission. The spectrumextracted from a region out of the sources make possible to identify the airglow linesto put to zero the corresponding plans in the spectral cube.


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Finally, the flux calibration supposes the acquisition of a data cube from a cali-bration source (a photometric standard star or a blackbody source) through the samefilter, with the same OPD step size than the cube under calibration. A low spectralresolution is enough, the important point being a high S/N ratio. The calibrated spec-tral cube is obtained by the division of each spectrum of the spectral cube by thecalibration spectrum, sampled with the same number of spectral elements.

4.4 The IFTS multichannel advantage

To estimate the multichannel advantage of a wide-field IFTS by comparison to aLSGS, we assume that both instruments have the same global throughput, observe thesame FOV, with the same plate scale, at the same limit of resolution dσ , and over thesame spectral domain �σ . For sensitive astronomical applications, the interferometeris modified to give access to the two complementary output beams, and thus, eachbeam produces an image of the entrance field on a Npxl × Npxl pixels detector array(no binning factor). Assuming that the imaged slit length corresponds to Npxl, theLSGS needs a camera with a 2Npxl × Npxl array, for a 2-pixel sampling of eachspectral element. In an IFTS data acquisition, the number n of spatial elements of thefield is equal to N2

pxl, thus M times larger than for the LSGS, as presented in Table 1.In other words, M adjacent slit positions are needed for the LSGS to gather the

same number n that an IFTS observing the same field. As a typical example, thisfactor reaches a value of ∼ 1200 to record simultaneously the Hα and the nearby[NII] and [SII] emission lines on a HII region at a resolution of 20,000 over a 40 nmspectral range, as has been obtained with an IFTS (see Fig. 8). Hence, the classicalcomparison of signal-to-noise ratio between grating spectrometer and FTS must berevised when considering the imaging mode. The comparison is generally made onthe continuum level w of a single point source (a star in astronomical applications)observed by both instruments with the same total observing time T , over the samespectral range �σ , assuming the same throughput. In the photon noise-limited casefrom the source, this comparison leads to conclude on a multiplex disadvantage ofthe FTS, since the S/NFTS ratio obtained on the continuum level is:

S/NFTS = (w dσ T )1/2/M1/2 , (26)

giving a gain in S/N ratio of M1/2 in favor of the grating spectrometer. The situationis even worse in presence of a parasitic background emission. In the imaging mode,the conclusion becomes different. Bennett [8] made a comparison between the three

Table 1 Number n of spatialelements recorded in one LSGS& IFTS data acquisition

Spectrum coverage.................. �σ

Spectral resolution.................. dσ

Detector size............................ 2Npxl × Npxl

Nb. of spectral elements........... M = �σ/dσ

LSGS IFTS

n ≤ N2pxl/M n = N2

pxl


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Fig. 8 Image of a 12′ × 12′ eastern section of NGC 6992 in the Cygnus Loop Supernova remnant withSpIOMM, in Hα and the close [NII] line. The blue color shows filaments moving towards the observerwhile red filaments are moving away. Spectra of two small regions (5 pixels) are compared. The Dopplershift is of ∼90 km s−1

types of 3D-spectrometers we have examined, from the point of view of the signal-to-noise ratio performances. The discussion was placed in the infrared, in the context ofthe preparation of the future JWST instrumentation. We reconsider this comparisonstrictly in the photon-noise limited case from the signal of the source, condition whichcan prevail in the near-UV, the visible and the near infrared on the ground, and inspace, up to roughly 20µm (Fig. 10) and in the far infrared with modern missions.Still under the same conditions of comparison of a field with a w continuum level, theintegration time for an elementary data acquisition of the LSGS is reduced to T/M .This leads to S/NLSGS, to be:

S/NLSGS = (w dσ T/M)1/2 . (27)

It turns out from (26) and (27) that:

S/NIFTS = S/NLSGS (28)

as already reported by Bennett [8]. Thus, the IFTS becomes as efficient as a gratingspectrometer in imaging mode when observing an extended continuum level source.This remark is important since it means that absorption lines are also quite observ-able. For example in nearby galaxies, it can provide a direct access to the distribution


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of the old stellar population. On a wide-field emission-line source as a HII region,always in the photon noise-limited case for both instruments, for a line of intensityQ times more intense than the mean surface brightness w of all the emission withinthe �σ bandpass, it comes:

S/NIFTS = √QS/NLSGS . (29)

In this case, the IFTS definitely becomes more efficient than the LSGS by a factor√Q. Note that all these comparisons are made under the assumption that no time

is lost at each pointing of the slit of the LSGS, and that the consecutive pointingsare strictly adjacent on the field, which creates severe constraints on the pointingprecision, in particular for a space instrument. For the IFTS, it is only assumed(Section 4.2) that thead � τ .

However, with a multiple IFU configuration (Section 2) to obtain a direct imag-ing FOV equal to the IFTS field the MUSE-type IFS [4] recovers the same advantageover the IFTS than given in (26). In the case of an extended emission-line source thefactor of gain is still equal to

√M/Q. On a large spectral range (a high M number),

the theoretical advantage of the MUSE-type instrument can remain important. Notethat this advantage is obtained to the price of a huge and complex instrument, whichlimits the direct field size. For example, the MUSE FOV is equal to 1′ × 1′ while theSITELLE IFTS (Section 6.1), designed to work also in the visible range, offers a FOV112 times bigger. To cover the same field, the

√M/Q factor would be divided by 11,

which partly compensates the IFTS disadvantage. In addition, MUSE is designed fora fixed resolution of 3,000 while SITELLE can work at variable resolution, in partic-ular, at higher resolution. Also in this comparison, the same optical transparency isassumed for both instruments. In fact, from the combination of IFU optics, gratingefficiency and collimating optics, the global optical throughput of the MUSE spec-trograph within the common spectral range (550–850 nm) is typically of 25 % whileit reaches at least 60 % for the IFTS.

4.5 Flexibility

In conclusion, an IFTS provides the maximum flexibility in the choice of all the basicparameters: spectral resolution, field size, spectral domain, compared to any otherspectro-imaging device, making possible to comply with a large variety of scien-tific cases, extragalactic and galactic as well. A wide FOV can be matched to a highspectral resolution, of major interest for the study of cold and ionized gas regions,in the giant star forming regions. In the same exposure, the galaxies of a cluster andthe intergalactic gas, or the individual stars and the interstellar gas, can be observed,which is not possible with a MOS. In addition, a wide-field IFTS gains an importantserendipitous discovery potential in the observed fields. An IFTS presents an impor-tant multichannel advantage as shown in Section 4.4 when compared to a LSGS inthe observation of wide-field emission-line sources. Observation of absorption linesis also possible. Finally, all these properties can be fitted to any spectral domain,from the UV to the submillimetric range, as shown in the next section from existingastronomical IFTSs.


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5 Review of the current astronomical imaging FTSs

The following review concentrates on five astronomical instruments working ontargeted sources. FTS in orbit around a planet, such as the Planetary Fourier Spec-trometer (PFS) onboard Mars Express [19] or the Composite Infrared Spectrometer(CIRS) on the Cassini orbiter around the Saturn system [27], are not considered sincethey are producing spectral images, but from a single or a few pixels detector, bycombining the fast recording of individual spectra and the satellite motion. With theadvent of sensitive detectors for the far-infrared and the submillimetric region, twospatial instruments plus one ground-based instrument have been developed, since theFTS remains the only technique able to obtain spectroscopic data on a large spectralrange in these long wavelength domains.

5.1 BEAR

A high-resolution FTS for the 1–5.5µm domain (InSb detectors) has been activelypart, since 1983, of the CFH Telescope instrumentation [31, 33–35], up to the decom-missioning of the f/35 infrared focus in 2001, at which the instrument was working.The interferometer was using in each arm a cat’s eye mirror, an afocal, three-reflexionsystem, composed of a concave mirror and a small mirror at its focus, which, as acorner cube mirror, makes possible to access the two output beams, and is insensi-tive to a rotation around its apex. The FTS was capable of a 60 cm maximum OPD(R = 5 × 105 at 2µm). The detection of the molecular ion H+

3 in the Jovian aurorae,the study of the deuterium abundance in the solar system, the probing of Venus deepatmosphere from the observation of its night-side, the detection of the hot and coldgas in the environment of typical embedded high-mass young stellar objects wereamong the first the scientific highlights of the CFH/FTS [33]. Since the CFH/FTSwas recording data in a step-by-step mode, the possibility of an imaging mode wasconsidered as early as 1990 from a first test with a CCD camera. This mode, laternamed BEAR (Bidimensional Experience with Array Receiver), was developed byusing the near-infrared CFHT camera equipped with a 256 × 256 HgCdTe detectorarray, making it the first facility astronomical IFTS. An optical interface imaged thetwo output beams side-by-side on the camera, using 128 × 128 pixels for each beam.Since the FTS was not initially designed for this mode, the usable FOV was only24′′ in diameter. The full operation of the BEAR mode really started in mid-1996,completed by the development of a specialized data reduction package under IDL.The main astronomical targets of BEAR were emission line sources fitting the avail-able field, such as young planetary nebulae [14], star forming regions [45], the innerregion of the Galactic Center [49]. From spectral images at ∼10 km s−1 resolutionon atomic and molecular lines, in particular Brγ and the 2.12µm 1–0 S(1) H2 line,unique results on the structure and the dynamics of all these sources were obtained.

5.2 SpIOMM

The IFTS called SpIOMM, in operation behind the 1.6-m Mont Megantic Telescope[9, 17], provided its foremost usable data in 2007. Derived from the instrumentation


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proposals for NGST, the instrument was developed in close collaboration betweenLaval University and ABB-Bomem, an industrial company located in QuebecCity. Thus, the interferometer design is based on an off-axis configuration (seeSection 4.1.2). It offers a 12′ × 12′ FOV, clear demonstration of the IFTS ability toprovide integral field spectroscopy on a wide field. The spatial resolution is limitedby the seeing quality of the site. Hence, the instrument designed for a pixel size of0.5′′ (1340×1300 E2V CCD) provides data in a 2×2 binning mode. The main scien-tific interests of the team, combined to the small telescope aperture, leads to typicalresolutions of ∼1,500 in the 450–850 nm range, domain of its maximum efficiency.In practice, the observations are usually performed in a blue (450–520 nm) and a redfilter (650–680 nm) to isolate the most diagnostic-rich emission lines such as Hα,Hβ, HeI, [SII], [NII] and [OIII] lines, in galactic nebulae and nearby galaxies [11,28, 54]. Figure 8 shows a good example of a full field spectral image.

5.3 FTS-2 for the SCUBA-2 camera

The Submillimetre Common-User Bolometer Array (SCUBA) in its second version,represents the first large-format CCD-like camera for submillimetric astronomy,operational at the James Clerk Maxwell Telescope (JCMT). The camera is made oftwo superconducting bolometers arrays operating at both 450 and 850µm, which canbe observed simultaneously. With 4 sub-arrays of 32 × 40 pixels at each wavelengthband, the camera provides a nominal FOV of 8′ × 8′ at both wavelengths. FTS-2 isdesigned to use SCUBA-2 as detector array. The interferometer is based on a foldedMach-Zehnder configuration similar to the SPIRE optical layout (see Section 5.5),but with corner cube instead of roof-top mirrors. The maximum OPD reaches 100 cm,equivalent to a limit of resolution (FWHM) of 0.006 cm−1 which corresponds to amaximum resolution of ∼2,000 at 850µm and ∼3,700 at 450µm. In each band, thetwo output ports use two sub-arrays, giving a circular FOV of 3′ on 32 pixels indiameter. Due to the limited mounting space available for FTS-2 with the SCUBA-2feed optics, the maximum FOV is significantly reduced because of a vignetting ofthe beam at large travel distance of the moving mirror assembly. Thus, two baselineobserving modes are defined, one called “SED mode” on the full FOV, for a limit ofresolution of ∼0.1 cm−1 and a “spectral line mode” on a small field at the maximumresolution. The first mode represents an important science driver on the chemistryof star forming regions. Details on the instrument built at University of Lethbridgeand delivered to Hawaii in 2010, are given by Naylor et al. [42] and Gom andNaylor [20].

5.4 FIS-FTS on AKARI

An IFTS dedicated to the 80–170µm (85–130 cm−1) domain was part of the Far-Infrared Surveyor (FIS) onboard AKARI, launched in 2006 [25]. The satellite with a68-cm telescope, cooled down at 6 K, on a solar synchronous polar orbit, operated inthe cold mode for one year and half. The Martin–Puplett interferometer was able ofa maximum unapodized resolution equal to 0.19 cm−1. The FIS-FTS was equippedwith a short (SW) and a long (LW) wavelength photoconductive detector array. In the


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spectroscopic mode, only a band of each array was used of 3 × 20 and 3 × 15 pixels.They covered 85–130 cm−1 and 60–88 cm−1 ranges, on pixel scales of 26.8′′ and44.2′′ respectively, giving an imaging spectroscopic capability with higher resolutionthan previous ISO/LWS spectral images. After correction of a serious problem oflinearity from the photoconductive detectors, results were obtained on several activegalactic star-forming regions [47].

5.5 SPIRE on Herschel

The Spectral and Photometric Imaging Receiver (SPIRE) [43] is one of the threeinstruments in operation on the ESA 3.5-m Herschel space observatory, launchedin May 2009. The telescope is passively cooled at ∼85 K, the spacecraft being inorbit around the L2 point. SPIRE contains an imaging photometer and an IFTS, bothfor the far-infrared domain, to observe the early stages of star formation. The IFTSis based on a Mach–Zehnder dual-port interferometer with a single, back-to-backscanning roof-top mirror assembly which modulates the optical path in both arms. Adifferent array of feed horn-coupled Ge bolometer at each output makes possible tocover simultaneously two bandpasses, a short wavelength array (SSW of 37 pixels,194–312.5µm) and a long wavelength array (SLW of 19 pixels, 303–671µm), theboundaries being the points where the spectral intensity reaches half of its averagein-band value. Mapping with the IFTS can be made with intermediate or full imagesampling. The instrument FOV reaches 2.6′ and the maximum limit of resolution0.04 cm−1, meaning a resolution of 1,000 at the center of the SSW band and of 500 atthe center of the SLW band. The chemistry of the galactic star forming regions formsthe main scientific cases for the instrument. The first detection of the fundamentalrotational transition of CH+ has been secured in the Orion Bar and in two compactHII regions [44].

6 IFTS design in the optical domain

The practical FOV limits within the theoretical performances seen in Section 4.1 isset by the optical design of the wide-field collimators, which depends on the spectraldomain. The situation is examined first in the 0.3 to ∼2.5µm range.

6.1 The SITELLE project

A project of IFTS directly derived from SpIOMM (Section 5.2), named SITELLE(Spectrometre Imageur a Transformee de Fourier pour l’Etude en Long et en Largede raies d’Emission) [18], resulting from a collaboration between Laval University(Quebec), Institut d’Astrophysique de Paris (France) and ABB as industrial partner,has been proposed for the 3.6-m CFH Telescope on Mauna Kea, in a response to acall for proposal due by October 1st, 2008. The final contract between Laval Univer-sity and ABB has been signed in September 2011. Compared to SpIOMM, the newinstrument is optimized for the blue and the near UV. The goal in particular is toaccess the [OII] 372.7 nm line in ionized nebulae, diagnostic of oxygen abundance,


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with a good sensitivity. It should also make possible to reach z ≥ 2 Lyα galaxies.The characteristics of SITELLE are summarized by the following parameters:

– a wide imaging field of 11′ × 11′,– an optical combination with wide-field, AR-coated glass collimators, deliver-

ing a seeing-limited image quality across the full field (�0.6′′ FWHM) throughnarrow-band filters,

– a dual-output interferometer made by two flat, enhanced silver-coated mirrors,used off-axis as shown in Fig. 4, for an optimum optical efficiency,

– a maximum useful OPD of ±5 mm,– a broad spectral coverage, from 350 to 970 nm with 2K × 2K CCDs of high

quantum efficiency in the blue,– a direct mounting at the f/8 Cassegrain focus for a minimum relay optics,– a high-throughput instrument with a goal of 70 % over the main spectral range.

On the spectral domain of SITELLE, a fully refractive optical combination can beused, making possible to adopt classical wide-field, achromatic collimators. Figure 9shows the optical layout with the corresponding spot diagrams for a 11′ × 11′ FOV.To reach the required seeing-limited image quality, the parallel beam diameter hasbeen increased to 90 mm, limiting the maximum incidence angle within the interfer-ometer to 3◦40′ (5). This beam diameter also limits the rapid fall of the modulationefficiency at the edge of the field at high spectral resolution, resulting from the off-axis design of the interferometer (Fig. 5, left). With a maximum useful OPD limitedto 5 mm the maximum spectral resolution can be of ∼20,000 at 370 nm, with a dropof modulation efficiency across the field at this OPD of only 0.81 to 0.56 insteadof 0.68 to 0.31 as shown in Fig. 5, left for a maximum OPD of 6.7 mm. The maxi-mum resolution is of ∼8,000 at 900 nm. Consequently, over all its spectral range ofsensitivity, SITELLE appears well suited to scientific programs requiring a resolu-tion ≤104. With these conditions, the off-axis IFTS represents the best solution toprovide the highest optical efficiency towards the UV, which is one of the scientificdrivers of SITELLE. However, as for SpIOMM, a dynamic alignment system of theinterferometric flat mirrors has to be implemented, which adds some complexity tothe OPD control.

6.2 Applications of the SIT ELLE optical combination

The dioptric collimators of SITELLE (Fig. 9) could be fitted to the near infrared,from 0.8 to 2.3µm, where the thermal background remains relatively low, for anon-cryogenic, seeing-limited instrument on ground. In this case, an on-axis inter-ferometer should be proposed, with two roof-top mirrors to access the two outputbeams, and provide a spectral resolution ≥2×104 on a 15′ FOV behind a CFH-classtelescope. At 0.8µm from (20) (Fig. 6) the tolerances on the tilt angle between theinterfering wavefronts is less severe and monolithic roof-top mirrors, simpler to fab-ricate than corner cube mirrors, could be made with the required tolerances on theright angle. Thus, a dynamical alignment system of the mirrors would be no longerrequired, making a simpler OPD control system.


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Fig. 9 On top: optical combination of the SITELLE IFTS at the f/8 CFH telescope focus, showing thewide-field entrance collimator (f � 715 mm) and one output collimator (f/2.65). The interferometer placedin between, with off-axis flat mirrors as in Fig. 4, is not shown. The total free distance of the interferometerzone is equal to 1.2 m. The pupil image of 90 mm diameter is formed in the middle, on the beamsplitter.Below: Spot diagrams for a Hα filter (650–680 nm), at the field center, at 0.7 of the field edge, at the fieldedge and at a field corner, for the 11′ × 11′ FOV. The black circle represents 1′′ on the sky, showing animage FWHM of ∼0.6′′ across the field, compatible with a 2 × 2 binning mode on reading the 2K × 2Kdetector array

The on-axis SITELLE optical layout could be scaled up to a 39-m E-ELT [51] inthe visible or the near infrared. To keep the same maximum incident angle inside theinterferometer (5), the beam size within the interferometer (DI ) should be increasedto 16 cm, which remains a reasonable size, and the FOV limited to a ∼1.8′ diameter.A spectral resolution up to ∼50,000 at 0.5µm on such a field (modulation efficiencydecreasing to 68 % at the field edge for the corresponding OPD, observable at adap-tive optics-limited spatial resolution (plate scale of 0.2′′/pixel), behind an ELT, wouldprovide unique scientific capabilities.


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7 IFTS optical design and technical issues in the mid-infrared

7.1 A high spectral resolution wide-field IFTS: the H2EX space project

The Molecular Hydrogen Explorer proposal, H2EX in short, was submitted in June2007, in response to the ESA 2015–2025 Cosmic Vision Call, as a medium classspace mission. The understanding of the dynamics and the energetics of the moleculargas in the formation of galaxies, stars and giant planets, formed the central scientificcase. The study of the distribution of H2 in the intergalactic medium of galaxy clus-ters, the halo of nearby galaxies and giant galactic molecular clouds, called for aninstrument able to detect the largest quantity of gas. Thus, the mission was designedto observe the first rotational lines of H2 at 28.2, 17.0, 12.3 and 9.7µm. Knowingthat the line widths of the emission lines can go from a few km s−1 in the interstellarmedium to several hundreds of km s−1 in external galaxies, a complete flexibility inthe choice of resolving power was also required. An IFTS appeared as the most suitedsolution to associate a wide field in order to perform unbiased surveys. Space is pro-viding the ideal place for such an instrument in the thermal infrared. With a passivelycooled spacecraft in orbit around the L2 point of the Sun-Earth system, the IFTScan be zodiacal-light limited up to ∼20µm, as shown in Fig. 10. For spectroscopy,all the bandpasses are perfectly clear and for imagery, the angular resolution reachesthe diffraction limit of the telescope. No parasitic scintillation noise on the interfer-ogram signal, as it happens on ground, limits the SN ratio. Last, space enables longobserving time of the same field, important for deep surveys.

To work in the thermal IR, an all-mirror combination must be developed.The design was directly inspired from BEAR with cat’s eye retroreflectors in the

Fig. 10 Total background flux seen by H2EX for a 1.2′′/pixel image sampling. The thermal componentis computed for two passively cooled optics temperatures which are possible to reach. Position of the fourfirst rotational H2 lines to be observed are marked


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interferometer arms. They are mounted in parallel on the same carriage to movein a push-pull motion, and to realize a compact assembly (Fig. 11). The maximumOPD was set to 187 mm to reach a resolution of 32,000 at 9.7µm, meaning 11,000at 28.2µm. From Figs. 2 and 3 a 40′ FOV with a 50 mm parallel beam diameterappeared theoretically compatible with the maximum OPD. However, the FOV hadfinally to be limited to 20′ and the beam diameter increased to 80 mm to obtain animage quality matched to the diffraction limit at 10µm of a 1.2-m telescope. Withthese parameters the fringe contrast remained ≥97 % across the whole field forR � 30,000 at 9.7µm. Cat’s eye mirrors were introduced because of the propertyof this combination to provide a pupil imagery within the interferometer. By imag-ing with the foreoptics the entrance pupil on the beamsplitter and mounting thesesystems as Offner relays, at zero-OPD the pupil is exactly reimaged on the beam-combiner, making possible to keep a high modulation efficiency even with the strongdivergence of the wide field beam at large OPD.

In the submitted proposal [10], the interferometer was fed by an afocal telescopewith a fast (f/0.75) primary mirror delivering a useful beam of 1.2 m, followed byan Offner relay matched to the cat’s eye mirrors. After the proposal submission, adifferent optical design was studied in which the telescope was based on a Ritchey–Chretien configuration and the entrance Offner relay was replaced by an asphericfield mirror imaging the entrance pupil on the first beamsplitter and an off-axisparabolic mirror as entrance collimator (Fig. 11), in order to make the H2EX IFTStransposable to a more classical telescope [37].

Fig. 11 Final optical layout of H2EX showing the 1.2-m R-C telescope, the field mirror, the off-axisparabolic entrance collimator and the interferometer, with the two beamsplitters and the two parallel cat’seye mirrors in position of maximum OPD. For clarity, the two imaging assemblies, a 3-off-axis mir-ror wide-field corrector on each output beam, are not installed. The overall size of the IFTS behind thetelescope is equal to �1.2 × 0.80 × 0.60 m


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7.2 Perspectives in the infrared domain

Finally, the H2EX mission has not been selected. However, all its scientific objec-tives remain fully pertinent for a new project. On the ground, in an infrared site asDome C on the Antarctic plateau, exceptional because of the very low temperature,the extremely dry conditions and the length of continuous observing time, an IFTSwith the H2EX design for the K, L, M windows (2–5µm), regions of optimum gaincompared to mid-latitude infrared sites, has been proposed [36]. Scaled to H2EX theFOV could be of 10′ × 10′ and the maximum resolution of 150,000 at 2 µm. Infar-infrared astronomy, the next challenge consists of building a 3.5-m aperture cryo-genic telescope, SPICA (SPace Infrared telescope for Cosmology and Astrophysics),launched at L2 and cooled below 10 K by cryocooler, to achieve the ultimate sen-sitivity. An IFTS, SAFARI, with a 2′ × 2′ FOV for a medium resolution of 2,000at 140µm, is proposed for the payload [58]. In this domain at long wavelength, themodulation efficiency with the field size is no longer a problem, and the spectral res-olution remains low. Thus, cat’s eye retroreflectors as used on H2EX are no longerneeded. The simplest optical design consists of using roof-top or corner cube mirrorsin the interferometer, which can be built with the required tolerances, as has beendone in SPIRE (Section 5.5), which represents the third possible optical combinationfor an Imaging FTS.

8 Conclusion

Nowadays, the main interest of FT spectroscopy in astronomy is no longer basedon the mono-pixel FTS, except possibly for special cases of extremely high spec-tral resolution on stellar or solar system planetary sources, but relies on the ImagingFTS, as proven by the analysis of all its properties as integral wide-field spectrom-eter, from the UV to the far infrared, at low to high spectral resolution. As such, itwould represent the ideal instrument for global studies of a large choice of extendedastronomical sources, from comets to distant galaxy clusters. However, from the pre-sentation made in the two last sections, in the optical and the mid-infrared domain,an IFTS combining both a wide field and a high spectral resolution is still missing.The SITELLE project (Section 6.1) in the visible provides a 11′ × 11′ field but with aresolution capability of ∼104, and H2EX (Section 7.1) in the thermal infrared, whichhad this goal, has not been selected. To alert the community on the potential benefitof the Imaging FTS represents the main goal of this paper.

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