spirou @ cfht : a nir échelle spectropolarimeter for ...astrolff/cfht_instruments/spirou.pdf ·...

SPIRou @ CFHT : a nIR échelle spectropolarimeter

for detecting Earth-like planets in the habitable zone of low-mass stars

Executive summary

SPIRou is a nIR spectropolarimeter proposed as a new-generation CFHT instrument mostly aimed at detecting Earth-like planets in the habitable zone of low-mass

stars and at investigating how magnetic fields impact star/planet formation.

We present here results of a feasibility study, discussing all relevant issues from the science drivers and corresponding instrumental specifications, to the optical design and associated technical developments, and to the operations and data processing.

No significant problem with SPIRou was identified throughout this study, that we conclude with a tentative budget, a preliminary agenda and a realistic project team.

SPIRou @ CFHT : a nIR spectropolarimeter

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Table des matières

Introduction 4

Main scientific drivers 4

Detecting Earth-like planets in habitable zones of low-mass stars 4

Investigating magnetised star/planet formation 5

Dynamo processes in brown dwarfs 7

Exploring stellar environments & envelopes 7

Other potential applications 8

Instrument specifications 8

Instrument concept & preliminary optical design 9

Overall concept & performances 9

SPIRou: a unique opportunity 10

Preliminary optical design & thermal background estimate 10

Development requirements 11

Identify a technical device providing a stable RV reference 11

Identify adequate glass & coating for the rhomb retarders 12

Modify the GIANO cryogenic bench/tank for SPIRou 12

Operations & data processing 13

Operations 13

Data processing 13

Development roadmap, project team & first cost estimate 14

Development roadmap 14

Project team 14

Tentative budget 15


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Appendix A : preliminary optical design of the cryogenics spectrograph (in French) 16

Appendix B : preliminary estimate of the instrument thermal background 60

Appendix C : preliminary study of nIR Fresnel rhombs for SPIRou 63

Appendix D : deriving accurate RVs from nIR spectra - the telluric-line issue 72

Appendix E : crushing down the activity-induced RV jitter with nIR spectropolarimetry 77


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1. IntroductionSPIRou is a nIR spectropolarimeter proposed as a new-generation CFHT instrument (to be implemented in 2014). Technically speaking, SPIRou is essentially a nIR version of ESPaDOnS/NARVAL with improved RV stability (1 m/s level), and consists of a high-resolution cryogenic échelle spectrograph fiber-fed from a Cassegrain achromatic polarimeter. It yields nearly complete spectral coverage in the JHK bands (ie from 0.9 to 2.4µm) at a spectral resolution of 50,000. The main science goal is to attempt detecting Earth-like planets in the habitable zone of low-mass stars and to investigate the role of magnetic fields in the star/planet formation process.

2. Main scientific drivers

a. Detecting Earth-like planets in habitable zones of low-mass stars

90% of the ~300 known exoplanets were discovered with the radial velocity (RV) method, which for Sun-like stars is limited to planets with masses larger than 10 Earth masses or in very close orbits. This is because habitable Earth-mass planets induce RV wobbles (a few cm/s around a Sun-like star) that are too small to be detectable with existing instruments. To investigate thoroughly the properties of Earth-like planets, and in particular those located in habitable zones (ie with surface temperatures allowing for the presence of liquid water), low-mass dwarfs are an extremely promising option. The RV wobble induced by an Earth-mass planet is more than an order of magnitude larger for an M dwarf than for a G star (~2 m/s for an Earth-mass planet around a 0.1 Msun star, see Fig 2), not only because the planet/star mass ratio is larger but also because the habitable zone is closer to the star (to ensure a similar stellar flux at the planet surface). Low-mass dwarfs vastly dominate the stellar population (8 of 9) in the solar neighborhood and are likely the hosts of most planets in our Galaxy. Systematic RV observations of nearby M dwarfs should thus provide a broader view on the diversity of planetary formation and yield a quantitative estimate of the fraction of habitable Earth-like planets about the Sun. However, M dwarfs will be difficult to observe with future space missions (eg DARWIN & TPF) aimed at investigating habitability of extrasolar planets due to their intrinsic faintness. Ground pre-launch preparation is thus essential for selecting the best few M dwarfs on which DARWIN & TPF could concentrate. While ground photometry can reveal a number of potential candidates through transits (eg the MEarth project, Irwin et al 2008, arXiv:0807.1316), spectroscopic observations are absolutely necessary both to obtain detections of non-transiting systems (only 1% of habitable planets in M dwarfs transit their star) and confirm the planetary nature of photometric candidates showing transits. Similarly, follow-up spectroscopic observations will be needed for all KEPLER transit detections. Presently, dwarfs with masses lower than 0.25 Msun are mostly out of reach of current optical extra-solar planet RV surveys as a result of their small sizes and low surface temperatures (fluxes of late M dwarfs peak at ~1.5 µm); exploring them therefore requires a high-resolution nIR échelle spectrograph providing simultaneously high RV accuracy (1 m/s), high throughput (15%) and wide single-shot spectral coverage (0.98-2.4 µm, ie the YJHK bands, to maximise the line content). Low


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Fig 1: artist view of the habitable planet around the M dwarf Gl 581 (©ESO)

mass stars apparently feature a rich nIR spectrum of atomic and molecular lines whose strengths increase at lower temperatures (eg McLean et al, 2007, ApJ 658, 1217), ensuring that potential planets generate detectable RV wobbles. The impact of telluric lines on the estimated RVs is minimised by observing from the driest non-polar observatory on Earth (ie MaunaKea) and can be further reduced with subtraction techniques (see Appendix D). By monitoring simultaneously the magnetic field topology of the host star (using the polarimetric capabilities of SPIRou), we can filter out efficiently the activity noise from the RV signal. Preliminary studies indicate that the activity-induced RV jitter of M dwarfs is smaller in the nIR (< 2 m/s, see also Appendix E) and roughly constant with spectral type (eg Endl et al, 2006, ApJ 649, 436). With the proposed filtering scheme, RV accuracies of 1 m/s should be attainable. A nIR spectropolarimetric survey of ~800 slowly rotating M dwarfs (out of the several thousand available within 50 pc) observed with a peak spectral quality of S/N=250 can be obtained with about 150 n/yr on a timescale of 7 yr. This corresponds to average observing times of about 0.5 hr per star (J=10, ie a M3 dwarf @ 40 pc or a M5 dwarf @ 18 pc) and per visit, with an average of 25 visits per star. Extrapolating from the (small) number of very-low-mass planets detected with HARPS/ESO indicates that at least 80 planetary systems hosting planets less massive than 20 Earth masses could be detected with SPIRou. Searching for massive planets around L dwarfs (detectable from spectra with S/N~40) is also very interesting; a 20 m/s RV accuracy survey of about 100 L brown dwarfs of different spectral types (limited at J<14) with SPIRou would require about 15 n/yr for 7 yr. SPIRou will also be very useful for detecting planets around young low-mass stars, and young M dwarfs in particular, yielding improved constraints on timescales of planet formation. Previous attempts at detecting planets around young stars have failed or produced false planet claims (eg Setiawan et al 2008, Nature 451, 38) due to their high level of intrinsic activity (magnetic fields & cool spots). Going to the infrared (where the spot/photosphere contrast is much lower, see Appendix E) will provide a drastic improvement by strongly reducing the activity jitter in the RV curve (by at least a factor of 5 between the V and H band, Huelamo et al 2008, arXiv:0808.2386). Several tens of K and M classical T Tauri stars featuring narrow spectral lines and mK < 10 should be accessible with SPIRou for such investigations.

b. Investigating magnetised star/planet formation

Whereas the understanding of most phases of stellar evolution made considerable progress throughout the whole of the twentieth century, stellar formation remained rather enigmatic and poorly constrained by observations until about three decades ago. One major discovery obtained at this time is that protostellar accretion discs are often associated with bipolar flows (eg Snell et al 1980, ApJ 239, L17), now known to be powerful, highly-collimated jets escaping the disc along its rotation axis. These jets (and in particular their collimation) have been attributed to the presence of magnetic fields and to the so-called magneto-centrifugal processes (eg Pudritz & Norman, 1983, ApJ 274, 677). Another important discovery is that low-mass magnetic protostars are rotating significantly


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Fig 2: detectability of a habitable planet as function of the host star mass and the instrument RV accuracy. Earth-like habitable planets are mostly accessible for nIR instruments.

slower than predicted by a non magnetized collapse (eg Bertout 1989, ARA&A 27, 351); this is likely due to the large-scale magnetic field coupling the protostar to its accretion disc (eg Königl, 1991, ApJ 370, L39). Both results demonstrate that magnetic fields play a central role throughout stellar formation. For exploring magnetic fields (through Zeeman polarisation of spectral lines) in star forming regions, and in particular in low-mass protostars and protostellar accretion discs, a nIR spectropolarimeter is optimally suited (with respect to an optical instrument), Zeeman splitting in magnetically sensitive spectral lines being much stronger in the nIR. Moreover, low-mass protostars are often quite cool, the youngest ones being often surrounded by a dust envelope (mostly opaque at visible wavelengths); studying them at nIR wavelengths is by far the optimal solution. By detecting Zeeman signatures in young stars/discs and by monitoring them as the stars/discs rotate, we will be able to model their large-scale magnetic topologies (eg Donati et al 2007, MNRAS 380, 1297, see Fig 4) and derive a wealth of brand new constraints on how magnetic fields impact the birth of stars and their planetary systems, how they participate in launching jets and how they control their angular momentum history. For this program, we need high spectral resolution (>50,000) to provide as much details as possible on the shape of Zeeman signatures; we also need the largest possible spectral domain accessible in a single exposure (ie 0.98-2.5 µm, the YJHK bands) to ensure that (i) we maximise the number of spectral lines from which Zeeman signatures are extracted and improve the accuracy to which magnetic fields are detected and modeled (ii) we collect as many different spectral proxies as possible (eg lines formed at the footpoints of accretion funnels, or at the inner rim of the accretion disc) to monitor the magnetospheric accretion processes simultaneously with (and further constrain) the magnetic topology. Magnetically sensitive Ti lines @ 2.22 µm, as well as CO lines @ 2.31 µm have often been used in this aim (eg Johns Krull 2007, ApJ 664, 975); many other atomic and molecular lines are also suitable for this purpose throughout the whole YJHK bands. With good RV stability (10 m/s), we can also investigate whether close-in giant planets are already present around forming protostars (ie before their disc is fully dissipated). With an efficient high-resolution nIR spectrograph like SPIRou, we should be able to access more than 200 young objects with mK<11 for such studies. This program would typically require as much as 50 nights/yr over a period of 5yr to investigate a large enough sample of protostars and protostellar discs and study how their large-scale magnetic topologies correlate with fundamental parameters (such as mass, age, rotation rate, outflow properties, disc density distribution) and vary on a timescale of a few yr (to look for activity or accretion cycles, or at planet migration within the inner regions of protostellar accretion discs like FUOrs).


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Fig 3: artist view of a protostellar accretion disc.

Fig 4: magnetosphere of the cTTS V2129 Oph derived with ZDI from sets of spectropolarimetric Zeeman signatures (Donati et al 2007).

c. Dynamo processes in brown dwarfs

In the last 20yrs, very-low-mass stars and brown dwarfs have triggered an enormous burst of interest. Very little was known about these objects before; despite considerable progress in recent years, their physics, internal structure and atmospheric properties are still poorly understood, with a number of important issues remaining unexplained. For instance, quantities as basic and fundamental as their radius and emergent spectra are still poorly reproduced by existing models; similarly, the magnetic topologies of late M and early L dwarfs are also poorly known, despite having an obvious impact on convection and therefore on the overall structure of these objects (eg Chabrier et al, 2007, A&A 472, L17). Radio observations demonstrate that strong large scale magnetic fields are likely present in brown dwarfs as late as at least L3 (Berger, 2006, ApJ 648, 629); spectropolarimetric data collected with ESPaDOnS (eg Donati et al 2006, Science 311, 633) demonstrate that large-scale magnetic topologies of M dwarfs can be reliably imaged, but late M and early L brown dwarfs are still out of reach due to their intrinsic faintness at optical wavelengths. Observing at nIR wavelengths should drastically improve the efficiency of spectropolarimetric studies and make them applicable to late M and early L brown dwarfs that radiate most of their photons between 1-2µm. Moreover, Zeeman splitting in magnetically sensitive spectral lines is much stronger in the nIR, where spectra show a large number of both atomic and molecular lines. A nIR spectropolarimeter thus offers a unique opportunity of studying dynamo processes in brown dwarfs and give us the key to understand why these objects rotate significantly faster than the mid-M dwarfs and strongly violate the radio/X-ray flux correlation applying to all cool stars including the Sun; it will also allow us to study how magnetic fields affect convection and impact the overall structure of brown dwarfs. Tomographic techniques applied to molecular lines can also be used to study "weather" patterns on brown dwarfs. For this program, we need high spectral resolution (>50,000) to provide as much details as possible on the shape of spectral lines and Zeeman signatures; we also need the largest possible spectral domain accessible in a single exposure (ie 0.98-2.5 µm, the YJHK bands) to ensure that we maximise the number of atomic (eg Ti @ 2.22µm) and molecular (eg FeH @ 1.00µm, CO @ 2.31µm) lines from which Zeeman signatures are extracted and improve the accuracy to which magnetic fields are detected and modeled. With an efficient high-resolution nIR spectropolarimeter, we are able to access more than 200 young objects with mJ<10 & mK<11 for such studies. This program would typically require as much as 25 nights/yr over a period of 5 yr to investigate a large enough sample of late M and early L brown dwarfs.

d. Exploring stellar environments & envelopes

SPIRou is also very well suited for studying spatially-extended circumstellar environments like protostellar dust cocoons, accretion discs and jets around young stars, winds around massive stars, excretion discs around Be stars or extended envelopes around cool giant stars. At nIR wavelengths in particular, the luminosity contrast between the central star and the surrounding accretion discs or dust envelopes are much smaller than at optical wavelengths, making their direct spectral investigation much easier. For instance, modeling CO molecular lines from


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Fig 5: artist view of a brown dwarf.

protostellar accretion discs can reveal the dynamics and physical properties (eg density & temperature) of the inner disc’s surface layers (eg Greene et al 2008, ApJ 135, 1421; Najita et al 2008, arXiv:0809.4267v1). By looking at the polarisation in line profiles, and in particular to how the scattering polarisation of emission lines formed in specific regions of the spatially-extended circumstellar environment (eg nIR emission lines from the Paschen series) differ from that of the continuum (mostly produced from the point-like central star), one can investigate the localisation, the geometry and to some extent the physical properties of the scattering medium at spatial scales that interferometry cannot yet reach (eg Takami et al 2006, ApJ 641, 357; Vink et al 2005, MNRAS 359, 1049; Kurosawa et al 2005, 358, 671). In particular, SPIRou will help alleviate limitations of existing studies. At nIR wavelengths, the effect of veiling (ie the dilution of the star+disc spectrum by an added hot featureless continuum, eg from accretion hot spots at the stellar surface) is lower than at optical wavelengths by a large factor, making the disc spectral features easier to observe and less ambiguous. Moreover, by monitoring how the line polarisation varies with time throughout several spectral lines simultaneously, SPIRou should disclose many more properties of scattering environments than presently possible and determine which of the various models (eg narrow accretion funnel vs accretion veils) best describes the observations. Such studies are crucial to understand the geometry and physical mechanisms at play in the star-disc interaction zone and inner disc regions where planets are expected to form and/or settle.

e. Other potential applications

SPIRou can also be used for many other front-line applications, from planetology to galactic and extragalactic astrophysics: ★ Chemistry & winds in the atmospheres of solar-system planets: High resolution spectra and precise

RVs (estimated from different sets of specific spectral lines) over the visible hemisphere of solar-system planets can tell us how winds distribute both horizontally and vertically in the planetary atmospheres. With its large nIR domain and high precision RVs, SPIRou will be particularly well adapted for such tasks and will usefully complement observations secured from space.

★ Chemical evolution & kinematics of the MilkyWay - stellar archeology: With its large spectral domain (eg compared to CRIRES@VLT), SPIRou will be highly competitive for measuring elemental abundances and velocities both in the bulge and in the distant regions of our Galaxy. It will also be very useful for studies on stellar archeology aiming at abundances of elements in giant stars whose spectrum is only accessible in the nIR (eg F & K) - to be compared with predictions of evolutionary models & nucleosynthesis.

★ Extragalactic astronomy & cosmology: SPIRou can also provide a wealth of information on topics like damped Ly-alpha systems, black holes in obscured AGNs, or absorption lines against GRBs @ z>2.5.

3. Instrument specificationsThe science requirements from the main drivers are as follows:★ spectral domain: 0.98-2.4 µm (w/ full coverage up to ~2 µm)★ spectral resolution > 50,000 (70,000 if possible)★ radial velocity accuracy < 1m/s★ S/N=150 per 3 km/s pixel in 1 hr @ J=12 & K=11★ thermal instrument background in the K band < telescope thermal emission, ie K>13.5★ all polarisation states accessible with >99% efficiency and <1% crosstalk over full spectral domain


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The corresponding instrument specifications are:★ peak throughput > 10% (telescope & detector included)★ stellar spectra recorded as 2 orthogonal polarisation channels (interleaved spectra) at all times,

with possibility of swapping polarisation state of both channel between successive exposures★ reference calibration spectrum recorded as third (interleaved) channel at all times★ retarders achromatic to < 1% over full spectral domain★ transmission tip/tilt module proving image stability (1 Hz) at entrance aperture ~ 0.02" and image

quality ~ 0.5"★ atmospheric dispersion corrector (ADC) providing correction up to airmass 2.7★ entrance pinhole within mirror and camera to provide viewing/guiding in a 1' field★ usual calibration facilities (flat field & thorium lamps) plus wavelength reference with high spectral

line density (>100 lines/order) and < 1 m/s stability★ fibre-fed bench-mounted cryogenic spectrograph cooled down to LN2 temperature (77 K) with

pressure (1 mbar) and temperature (0.01 K) control★ spot diagrams from spectrograph optics < 1 ccd pxl (~3 km/s) throughout full spectral domain

4. Instrument concept & preliminary optical design

a. Overall concept & performances

To meet the above listed specifications, SPIRou must consist of:★ a Cassegrain module collecting stellar light from a small (200 µm = 1.4") circular pinhole and

containing all optical components (Wollaston prism, rhomb retarders and achromats) needed for an achromatic polarisation analysis and an adequate focal reduction (f/8 to f/4). Interface with the telescope is achieved through another module including an atmospheric dispersion corrector, a transmission tip-tilt image stabilisation unit and a viewing/guiding camera looking at the entrance aperture; it also provides the usual spectral calibration facilities, as well as a stable wavelength reference module.

★ a 20 m triple fiber feed (2 object & 1 reference fibers) conveying the light to the spectrograph. Using ultra-low OH silica fibers (eg made of Suprasil 300, 100/110 µm core/clad diameters) ensures a transmission of 85% at 2 µm, 60% at 2.2 µm and ~10% at 2.4 µm. A 3 slice/fiber Bowen/Walraven image slicer coupled to a focal reducer (f/4 to f/8), both cooled down by a Peltier unit, provides the entrance slit for the spectrograph (1.85x0.07 mm). Light from all 3 fibers is recorded at all times.

★ a cryogenic spectrograph (dual pupil design) featuring a 15 cm pupil, 2 parabolic off-axis collimators (having 1.2m focal length), a R2 diffraction grating (with 23.2 gr/mm), a prism-train cross-disperser (providing 0.55 mm minimal inter-order separation at detector level) and a f/2 fully dioptric camera (32 cm focal length). With a 2k x 2k hawaii detector (18 µm pixels), orders #85 (0.98 µm) to #32 (2.4 µm) can be recorded simultaneously, ensuring 50 K spectral resolution with almost complete spectral coverage (full order coverage at 2 µm, 84% order coverage at 2.4 µm).

Being similar to ESPaDOnS, this design should provide a total throughput of 15% (atmosphere and detector included) - at J=12 and K=11, it should yield S/N=150 for a 1 hr observation. Pressure and thermal control should ensure RV accuracies similar to those achieved with HARPS. The spectrograph cryostat can be copied from GIANO, ie featuring a stainless steel cylinder (2m long & 1.3m wide) and containing an optical bench/tank filled with LN2 and on which all the spectrograph optics is mounted.


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http://www.bo.astro.it/giano/

http://www.bo.astro.it/giano/

To improve its RV stability, SPIRou will feature a fixed spectrograph configuration (as opposed to ESPaDOnS offering 3 different setups). All frames recorded with SPIRou will include 2 interleaved stellar spectra (one for each orthogonal state of the selected polarisation) and one spectrum of the RV reference cell.

b. SPIRou: a unique opportunity

As such, SPIRou fills a scientific niche and represent a unique opportunity. All existing nIR spectrographs have very narrow spectral domains:

instrument / telescope

spectral resolution

slit width

accessible domain

simultaneous coverage in single exposure

Pheonix / GEMINI 75 000 0.17” 0.8-2.5 µm 0.02 µm

NIRSPEC / KECK2 25 000 0.40” 0.9-2.5 µm 0.2 µm

IRCS / SUBARU 20 000 0.14” 1-3 µm 0.2 µm

CRIRES / VLT 40 000 0.5” 1-5 µm 0.02 µm

Very few instruments similar to SPIRou (with full coverage of the spectral domain in a single exposure) are in construction or in preparation :

instrument / telescope

spectral resolution

slit width full spectral domain

status

GIANO / TNG 50 000 0.50” 0.9-2.4 µm in construction (open 2010)

PRVS / GEMINI 50 000 fibre feed 0.9-1.8 µm abandoned

NAHUAL / GTC 50 000 0.175” 0.9-2.4 µm not funded yet

Only GIANO is being constructed at the moment (with commissioning planned for 2010). Moreover, neither GIANO nor NAHUAL are fiber-fed; for reaching the 1 m/s RV accuracy, both will therefore need to implement an absorption cell, known to strongly plague the instrument efficiency. Finally, as opposed to GIANO/NAHUAL, SPIRou implements polarimetric capabilities directly inherited from the ESPaDOnS/NARVAL experience. SPIRou therefore appears as a unique opportunity for carrying out all science goals.

c. Preliminary optical design & thermal background estimate

The key component of SPIRou is a cryogenic spectrograph (dual pupil design) featuring a 15 cm pupil, 2 parabolic off-axis collimators (with 1.2 m focal length), a R2 diffraction grating (with 23.2 gr/mm and 154x306 mm ruled surface), a prism-train cross-disperser (providing minimum inter-order separation of 0.55 mm at detector level) and a f/2 fully dioptric camera (32 cm focal length). Orders #85 (0.98 µm) to #32 (2.4 µm) can be recorded simultaneously on a Hawaii-2 detector with 18µm pixels. The optics provides spot diagrams (80% encircled energy) smaller than 1 ccd pxl throughout the full spectral domain (0.98-2.4µm) and over the ±5deg field. This design is significantly different than that of GIANO; in particular, it includes an efficient (>80% throughput) fully dioptric camera (whereas GIANO uses mirrors).


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A first (preliminary) optical design has been obtained (see Appendix A) matching all specifications; in particular, adequate optical quality is achieved throughout the whole wavelength domain. Several options (eg concerning the actual location of the cross-dispersor) are possible and will be studied in more details in the next design stage. One possible solution is shown on Fig 6 (see Appendix A for additional details on all options).

A preliminary thermal background budget of the instrument (see Appendix B) indicates that the main contributors are: ★ the polarimeter, and in particular the last

lens of the focal reducer★ both input and output optics of the image slicer

These 2 contributions are larger than the telescope thermal emission (the main contributor to the thermal background, at a level of K~13.5) if working at room temperature; the contribution of the cryogenic spectrograph itself remains small provided we implement a cold slit at the entrance. We will thus incorporate the polarimeter output optics into a small dewar cooled to ~250 K and featuring the output polarimeter lens on one side, the fiber-head holder on the other side and a polished baffle linking both. We will also put the whole image slicer into a similar device. With such a setup, we decrease the instrument thermal emission by an order of magnitude and ensure that it is smaller than the telescope thermal emission (see Appendix B for more details).

5. Development requirementsApart from the optical design and thermal background estimate (detailed above), several specific technical developments are required for SPIRou. The main issues are detailed below.

a. Identify a technical device providing a stable RV reference

To check that we indeed reach the 1m/s RV accuracy, monitor the short- and long-term RV stability and potentially compensate for small RV drifts of the recorded spectrum, we need to have a specific calibration module providing a very stable RV reference. While evacuated instruments with temperature/pressure control are intrinsically very stable (eg HARPS at a 1 m/s level), having such a wavelength reference module is nevertheless necessary, for regular stability checks at the very least. Experiments carried out with the PathFinder spectrograph @ Penn State University (Ramsey et al 2008, PASP 120, 887) suggest that a standard ThAr hollow cathode lamp is potentially usable in this purpose, and that a UAr hollow cathode lamp would provide a significantly higher line density in the nIR. However, prior experiments with such lamps (eg SOPHIE spectrograph) demonstrates that stability problems may arise when lamps are aging. We therefore aim at another more accurate option (keeping this one only as a backup). Another possibility is to use an athermal Fabry-Perot etalon (with both pressure and temperature control) in conjunction with a halogen lamp. The advantage of this option would of course be to provide a very high and regular density of lines throughout the whole spectrum (>100 of lines per order). The Geneva group is exploring this option in the framework of the CODEX/EXPRESSO ESO project at getting an ultra-stable calibration cell (1 cm/s), has started designing and building a stable


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Fig 6: Preliminary optical design of the SPIRou cryogenic spectrograph

Fabry-Perot unit and should start testing it on HARPS by early 2009. We are in close interaction with F Pepe - in charge of this experiment and our contact in Geneva - on this issue. Provided that their unit fulfills our less stringent specification of 1 m/s (highly probable), we will simply adapt their design to nIR wavelengths (in collaboration with them) and build a specific Fabry-Perot unit for SPIRou. A third solution is to implement a laser frequency comb with a Fabry-Perot filtering cavity (eg Li et al 2008, Nature 452, 610; Steinmetz et al 2008, Science 321, 1335); this promising solution is also very accurate and expected to provide accuracies of 1 cm/s. However, it is not completely clear how adaptable it is to our case (broad spectral domain, nIR) in a reasonable time-scale and budget. We will keep contact with the developers to ensure that we can switch to this third solution if needed. As the light from the wavelength reference module is brought to the instrument through an optical fiber, we can easily make provisions for future developments (such as the laser comp solution) if it turns out necessary for matching the specifications, or to improve further the accuracy of the reference cell.

b. Identify adequate glass & coating for the rhomb retarders

To obtain an achromatic polarimetric analysis over the whole spectral domain of SPIRou (0.98-2.4 µm), we need to find the adequate glass that can provide both the nominal retardation and the optimal transmission; we also need to check that ultra-low birefringence samples are available. The first preliminary study (see Appendix C) indicates that several options are possible. The 2 best solutions apparently consist in using S-FTM16 with MgF2 coating or ZnSe with CVD diamond (see Fig 7), both providing a nominal retardance within better than 0.5% over the whole wavelength range and field of view. In the next stage of the design study, we will order several chunks of both glasses and ask for accurate measurements of the residual stress birefringence.

c. Modify the GIANO cryogenic bench/tank for SPIRou

The spectrograph cryostat (copied from GIANO, see Fig 8) is a stainless steel cylinder (2m long & 1.3m wide) with standard multilayer thermal shield, containing an optical bench/tank (also copied from GIANO) isostatically mounted on a hexapod system and filled with LN2 (100 l). Pressure (10-5 mbar) and thermal (77 K) control within the cryostat ensures an ultra-accurate (0.01 K) long-term stability of the instrument. All optical components are installed on the bench via a 4 mm cover plate used as a thermal interface. Cooling the whole system requires ~400 l


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Fig 7: Retardance of a quarter-wave rhomb made of ZnSe with diamond CVD coating on full-reflection surface

Fig 8: The cryostat and bench/tank of GIANO, from which SPIRou will be adapated

of LN2 while maintaining the system at working temperature uses ~25 l/d. Temperature stability is obtained by controlling the pressure of the out-boiling gas within 1 mbar. The optical design that we have is different than that of GIANO. The physical dimensions are however similar, implying that we can almost exactly replicate the existing bench/tank design with minimal changes to the overall properties and performances. We will work out these changes in the next design stage, in collaboration with the GIANO team.

6. Operations & data processing

a. Operations

Operations of SPIRou will be very much like (and derived from) that of ESPaDOnS. As SPIRou is essentially a point & shoot instrument (with a unique instrument configuration), there will only be a very limited number of motors to operate (ADC, tip/tilt, calibration & density wheels in the interface module, rhombs in the polarimeter, shutters & focus in the spectrograph). In addition to those, we will need temperature and pressure controls for the cryogenics spectrograph. The overall instrument control is therefore expected to be fairly similar to that of ESPaDOnS. We expect to operate SPIRou in the very same way as ESPaDOnS, starting and ending each night with a series of calibration frames, and taking sequential series of 4 subexposures on each star we look at. We will then process spectra in real time with the automatic pipeline reduction routine and will derive polarised spectra, LSD profiles and accurate RVs on the fly. The whole operation of SPIRou will be mostly automated - as it is for ESPaDOnS - recording all calibration frames, taking all astronomical exposures on a given star, or reducing all collected data with a single command line.

b. Data processing

As for all instruments, we of course need to set-up an automatic reduction pipeline capable of turning series of raw spectropolarimetric frames into wavelength-calibrated polarised echelle spectra. We will mostly adapt Libre ESpRIT - the automatic reduction pipeline of ESPaDOnS & NARVAL - to the specific purpose of SPIRou; in particular, and following the HARPS & SOPHIE experience, we will incorporate all operations needed to match the 1 m/s precision in RV. We will also implement a new tool aimed at subtracting some telluric lines as accurately as possible. This is not crucial for reaching the expected performance of SPIRou; simply dropping all wavelength regions where telluric features are deeper than 5% to compute RVs ensures that the 'telluric jitter' is lower than 0.5 m/s while leaving at least 0.30 µm of useable domain (thanks to the very good nIR transparency of MaunaKea), ie 3 times larger than the HARPS domain used for M dwarfs (see Appendix D). Subtracting telluric lines may however help in further improving the efficiency of SPIRou and widening significantly (by ~50%, see Appendix D) the spectral range available for RV measurements. We will also have a similar tool for removing OH airglow lines from the sky background. Finally, we will also develop and implement a new tool aimed at correcting RV measurements from the intrinsic activity jitter of M dwarfs. The activity jitter from the majority of (weakly-active) M dwarfs is expected to be of a few m/s only in the nIR (see Appendix E), and will therefore not compromise the main goals of SPIRou. Correcting from this jitter will however further increase the performances of SPIRou. Spectropolarimetric results on mid M dwarfs obtained with ESPaDOnS (eg Morin et al 2008, arXiv:0808.1423; Donati et al 2008, arXiv:0809.0269) indicate that RV fluctuations correlate with the magnetic topologies; by working out in detail how activity jitters relate to the magnetic topologies (derived from the Zeeman spectropolarimetric signatures simultaneously collected


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with SPIRou), we will thus be able to model activity jitters (from the observed magnetic topology) and remove them (to some extent) from the RV data. This technique should thus further extend the range of SPIRou to both smaller planets and more active dwarfs.

7. Development roadmap, project team & first cost estimate

a. Development roadmap

The future project milestones are as follows:★ 2009: phase A study, concentrating on the development requirements listed above (modifications

in the cryogenics spectrograph mechanics, tests for a stable RV reference & testing various potential rhomb glasses)

★ 2010-2011: complete design study★ 2012-2013: construction & AIT★ 2014a: transport to CFHT & commissionning★ 2014b: open access to whole CFHT community

b. Project team

SPIRou is a collaborative project proposed jointly by Toulouse (LATT) and Grenoble (LAOG) and to which up to 5+ countries are involved worldwide (Taiwan, Canada, Switzerland, UK, USA). Listed below are the names of the persons involved in SPIRou.

For the project core team:★ PI : JF Donati, Toulouse★ PM : D Kouach, Toulouse★ IS : X Delfosse, Grenoble★ SE : E Artigau, tbc★ Optics: P Rabou, Grenoble & L Parès, Toulouse★ Cryogenics: M Bouyé, Toulouse & Ph Feautrier, Grenoble★ Mechanics: G Gallou, B Dubois, Toulouse★ Detector: SY Wang, Taiwan★ Control: S Baratchart, M Dupieux, Toulouse★ CFHT contact: G Barrick

All key people are therefore already identified and available to work on SPIRou (when needed). While we do not have a System Engineer position yet, we already have a very good candidate; E Artigau, a specialist in cryo-optomechanics from Montreal (Doyon's team) and presently working @ Gemini-S, is an optimal candidate for the job and is very interested in the position. We have therefore asked INSU for a position (matching the specific needs of SPIRou) in the coming years.

In a broader science context, many people are very interested with SPIRou, given the very unique science opportunity that it will represent for stellar/planet research in particular. A list of the core science team is given below: ★ France:

JF Donati, P Fouqué (Toulouse)X Delfosse, X Bonfils, J Bouvier, T Forveille, F Ménard, C Dougados (Grenoble)


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C Catala, E Lellouch (Meudon)C Moutou, M Deleuil (Marseille)V Hill (Nice)

★ UK:A Cameron, M Jardine, S Gregory, J Barnes

★ Switzerland:F Pepe, P Figueira

★ Canada:D Bohlender, J Landstreet, G Walker

★ Taiwan:SY Wang, DV Trung, J Lim

★ USA:E Shkolnik

c. Tentative budget

The total cost of Spirou is estimated to be about 3 M€.

The budget details (including a 20% overhead on all items), is:★ spectrograph optics: 1 M€★ spectograph cryomechanics: 1 M€★ Cassegrain module, RV reference module & polarimeter: 0.4 M€★ detector & detection control: 0.4 M€★ instrument control: 0.2 M€

This budget is fairly conservative, eg compared to the initial budget estimate of GIANO (1.3 M€). We are therefore very confident that the final budget will not exceed this amount.


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Appendix A : preliminary optical design of the cryogenics spectrograph (in French)

SPIROU

Design Optique Préliminairedu Spectrographe


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1.DESIGN OPTIQUE PRELIMINAIRE DU SPECTROGRAPHEbasé sur le design optique d'ESPaDOnS.

1.1Fente d’entrée

La fente d’entrée du spectrographe est formée par l’image de 3 fibres coupées en 3 tranches chacune par un dissecteur d’image de type Bowen-Walraven et une optique relais (la dissection s’effectue suivant la direction x).• D: diamètre de la gaine de la fibre, Φ: diamètre du coeur de la fibre

• Angle de dissection: θ• Angle d’inclinaison des fibres / dissecteur: ψ

• Longueur de la fente / fibre: LS = 3 Φ cos(θ)• Longueur de la fente totale: LST = 2 D cos(ψ) / sin(θ) + LS

• Distance inter-fentes: dS = (LST – 3 LS) / 2• Largeur de la fente: WS = Φ sin(θ)• Surface de la tranche centrale relative à la surface de la fibre: SC / S = (2θ + sin(2θ)) / π• Surface des tranches latérales relative à la surface de la fibre: SL / S = (1 - SC / S) / 2

Si la fente est inclinée d’un angle δ, pour atteindre une largeur de fente projetée de 3 WS:

• Angle d’inclinaison de la fente est de: sin(δ) ≈ 2 WS / LST

• La largeur projetée de la fente sur l’axe y est de: WSTY = WS cos(δ) + LST sin(δ)• La longueur de la fente totale projetée sur l’axe x est alors de: LSTX = LST cos(δ) + WS sin(δ)

Option 1 (image de fibre coupée en 3 tranches de largeurs égales):

Figure 1. Fente d’entrée option 1

• Angle de dissection: sin(θ) = 1 / 3, θ = 19.471221°• Angle d’inclinaison des fibres / dissecteur: ψ, cos(ψ) = (Φ / D) cos(θ) + sqrt(1 - (Φ / D)2) sin(θ)


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Option 2 (image de fibre coupée en 3 tranches de largeurs inégales):

Figure 2. Fente d’entrée option 2

• Angle de dissection: tan(θ) = D / (3 Φ)• Angle d’inclinaison des fibres / dissecteur: ψ = 0°

Application numérique (fibres 100/110 µm coeur/gaine à F/4) en entrée spectro F/8:• D: 220 µm, Φ: 200 µm

Option 1:• Angle de dissection: θ = 19.471221°, sin(θ) = 1 / 3, cos(θ) = 2 sqrt(2) / 3• Angle d’inclinaison des fibres / dissecteur: ψ = 5.148757°• Longueur de la fente / fibre: LS = 565.685 µm• Longueur de la fente totale: LST = 1880.359 µm• Distance inter-fentes: dS = 91.652 µm• Largeur de la fente: WS = 66.667 µm• Largeur des tranches de fente: 3 x 66.667 µm• Surface relative des tranches de fente: 29.179 %, 41.642 %, 29.179 %• Angle d’inclinaison de la fente: δ ≈ 4.066°, WSTY = 2.997 WS = 199.832 µm, LSTX = 1880.353 µm

Option 2:• Angle de dissection: θ = 20.136303° , sin(θ) = 0.344255, cos(θ) = 0.938876• Angle d’inclinaison des fibres / dissecteur: ψ = 0°• Longueur de la fente / fibre: LS = 563.326 µm• Longueur de la fente totale: LST = 1841.449 µm• Distance inter-fentes: dS = 75.736 µm• Largeur de la fente: WS = 68.851 µm• Largeur des tranches de fente: 65.575 µm, 68.851 µm, 65.575 µm• Surface relative des tranches de fente: 28.525 %, 42.950 %, 28.525 %• Angle d’inclinaison de la fente: δ ≈ 4.289°, WSTY = 2.997 WS = 206.360 µm, LSTX = 1841.442 µm


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Le dissecteur d’image génère une inclinaison en focalisation de la fente.

L’angle minimum d’incidence sur la lame dissectrice pour avoir une réflection interne totale est donné par:• sin(η) = 1 / nMIN, avec nMIN indice de réfraction minimum (pour la plus grande longueur d’onde).

L’angle de défocalisation moyen de l’image de la fente et son chromatisme à la sortie du dissecteur d’image sont donnés par:• tan(ϕ) = 1 /(nMOY tan(η)), avec nMOY indice de réfraction moyen sur la bande spectrale.• tan(Δϕ) = -Δn/nMOY sin(2ϕ)/2, avec Δn variation de l’indice de réfraction sur la bande spectrale.

Il est à remarquer que l’angle de défocalisation moyen β décroit quand l’indice de réfraction nMOY augmente et quand l’incidence sur la lame dissectrice α augmente.

L’angle de défocalisation moyen au niveau de la fente d’entrée du spectrographe et son chromatisme sont donnés par:• tan(ϕ’) = Gy tan(ϕ), avec Gy grandissement transverse de l’optique relais.• tan(Δϕ’) = -Δn/nMOY sin(2ϕ’)/2

Si le dissecteur d’image est fait en Infrasil,• nMIN = 1.43 à 2.5 µm, soit η > 44.37°.• nMOY = 1.44 sur la bande 0.95-2.5 µm, soit si α = 45°, tan(ϕ) = 1/1.44, ϕ = 34.78°• Δn = ± 0.0106 sur la bande 0.95-2.5 µm, soit tan(Δϕ) = ± 3.45e-3, Δϕ = ± 0.20°

Si la focalisation sur le dissecteur d’image se fait à F/24 (grandissement de l’image de la fibre d’un facteur 6), l’optique relais image la fente à l’entrée du spectrographe à F/8, soit: • Gy = 1/3 et tan(ϕ’) = 1/(3x1.44), ϕ’ = 13.03°, Δϕ’ = ± 0.09°

Le spectrographe a une inclinaison de la fente d’entrée optimale pour annuler la défocalisation des bords de la fente sur le détecteur.Elle est donnée par:• tan(ϕ0) = 4 tan(γ) cos2(β / 2), avec β angle hors-axe parabole, γ angle hors-littrow réseau.

Si on ne fait pas attention à l’orientation du dissecteur d’image, on peut soit partiellement compenser (ϕ0 - ϕ’), soit empirer (ϕ0 + ϕ’) l’inclinaison en défocalisation de l’image de la fente sur le détecteur:• Pour β = 6.466° et γ = 0.6°, ϕ0 = 2.39°, ϕ0 - ϕ’ = -10.64°, ϕ0 + ϕ’ = 15.42°• Pour β = 10° et γ = 1.2°, ϕ0 = 4.75°, ϕ0 - ϕ’ = -8.28°, ϕ0 + ϕ’ = 17.78°• Pour β = 11.6° et γ = 1.7°, ϕ0 = 6.70°, ϕ0 - ϕ’ = -6.33°, ϕ0 + ϕ’ = 19.73°

Les spot diagrammes suivants (sur la meilleure surface image pour une caméra parfaite) montrent l’effet de l’inclinaison en focalisation de la fente (option 1), pour la configuration β = 6.466° et γ = 0.6°, pour une inclinaison de ϕ’ = 0° (pas de dissecteur d’image) et une inclinaison de ϕ’ = -13.03° (dissecteur d’image orienté dans le pire cas).On voit que la tache de défocalisation en bord de fente couvre environ la moitié du pixel.


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Figure 3. Spot diagramme ordre 57, inclinaison fente ϕ’ = 0°(croix = 18 µm, 1 pixel)

Figure 4. Spot diagramme ordre 57, inclinaison fente ϕ’ = -13.03°(croix = 18 µm, 1 pixel)


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1.2Spectrographe

1.2.1Calcul des paramètres du spectrographe

Le nombre d’ouverture d’entrée du spectrographe est de N1 = 8.La résolution du spectrographe doit être > 50000, partagée quadratiquement entre l’image de la largeur de la fente d’entrée sur le détecteur (1 pixel) et la taille de la PSF sur le détecteur (1 pixel).Soit RS = 50000 sqrt(2) = 70710 pour chacun des 2 contributeurs.

Le spectrographe est composé de: • Un collimateur (focale F1)• Une caméra (focale F2)• Un réseau échelle R2: substrat silice, n = 23.2 t/mm, incidence: α = 63.435°, tan(α) = 2• Domaine spectral: > 0.96-2.4 µm (ordres 32-80)• Couverture spectrale complète sur le détecteur pour: λ < 2 µm, ordres 38-80• Un détecteur: HgCdTe , 2048 x 2048 pixels de largeur WPIX = 18 µm (36.864 x 36.864 mm)

• Image de la largeur de la fente d’entrée sur le détecteur: WS’ = WS F2 / F1 = WPIX

• Résolution de la fente: RS = 2 tan(α) F1 / WS = 2 tan(α) F2 / WPIX

Soit:• Focale du collimateur: F1 > RS WS / 4• Diamètre de la pupille sur le réseau: ΦP = F1 / N1

• Grandissement de la fente d’entrée: GS = WPIX / WS

• Focale de la caméra: F2 = F1 GS

• Nombre d’ouverture de la caméra: N2 = F2 / ΦP

Application numérique:Fente option 1:• Focale du collimateur: F1 > 50000 sqrt(2) 66.67e-3 / 4 = 1179 mm

on choisit F1 = 1200 mm, soit RS = 72000• Diamètre de la pupille sur le réseau: ΦP = 150 mm• Grandissement de la fente d’entrée: GS = 0.270• Focale de la caméra: F2 = 324 mm• Nombre d’ouverture de la caméra: N2 = 2.16

Fente option 2:• Focale du collimateur: F1 > 50000 sqrt(2) 68.85e-3 / 4 = 1217 mm

on choisit F1 = 1200 mm, soit RS = 69716• Diamètre de la pupille sur le réseau: ΦP = 150 mm• Grandissement de la fente d’entrée: GS = 0.261• Focale de la caméra: F2 = 313.7 mm• Nombre d’ouverture de la caméra: N2 = 2.09

Les calculs effectués dans les sections suivantes utilisent l’option 1 de la fente d’entrée (plus grande longueur de fente). L’option 2 de la fente d’entrée devrait permettre d’avoir une plus grande séparation des images de fente sur le détecteur.


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1.2.2Collimateur

Le collimateur est un miroir parabolique hors-axe (2 miroirs découpés sur la parabole de base).• Focale de la parabole de base: F0

• Angle de hors-axe: β

Soit:• Focale de la parabole hors-axe: F1 = F0 / cos2(β / 2)• Hauteur de hors-axe: h = 2 F0 tan(β / 2)

Application numérique:• Focale de la parabole de base: F0 = 1200 mm• Angle de hors-axe: β = 6.466°

• Focale de la parabole hors-axe: F1 = 1203.83 mm• Hauteur de hors-axe: h = 135.568 mm

1.2.3Spectrographe échelle

Le spectrographe est composé des éléments suivants:• Le collimateur PM1 (miroir parabolique hors-axe) qui collimate le faisceau issu de la fentre

d’entrée ES sur le réseau échelle.• Le réseau échelle EG est incliné de γ = 0.6° (angle hors-littrow) perpendiculairement à sa

dispersion et renvoie le faisceau dispersé sur le collimateur PM1.• Le collimateur PM1 focalise le faisceau et le renvoie sur un miroir de repli FM• Le miroir de repli FM renvoie le faisceau sur un deuxième collimateur PM2 qui collimate le

faisceau et le renvoie vers le disperseur croisé (pupille blanche WP).Note: Le réseau n’est pas placé au foyer du collimateur, ce qui induit une légère non télécentricité en entrée. Cette position pourra etre ajustée en fonction des encombrements mécaniques (change la position de la pupille blanche).

Figure 5. Spectrographe échelle

Table 1. Données optiques du spectrographe échelleSurface Rayon de

courbureDistance /Surf suiv.

Matériau Diamètre Décentrem. Rotation

0 Fente d’entrée infini 1200 Objet 1.886 x 0.067 -6.466 (x)1 Parabole 1 -2400 -1360 Miroir 220 x 340


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2 Réseau infini 1360 Miroir 306 x 154 135.568 (yS) 0.6 (xS)63.435 (yS)

3 Parabole 1 -2400 -1200 Miroir 220 x 3404 100 Air5 Miroir de repli infini 100 Miroir 20 x 1806 1200.533 Air7 Parabole 2 -2400 -1056.036 Miroir 220 x 3408 Pupille blanche Air 150.332 -135.568 (y) 1.2 (x)9 Caméra -324.9

(focale)-324.9 Lentille

Paraxiale150.332

10 Détecteur -598.22 Image 36.86 x 36.86 0.00708 (y)

Figure 6. Spot diagramme ordre 32(croix = 1.8 µm, 0.1 pixel)


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1.2.4Disperseur croisé (4 prismes)

• minimum de déviation pour l'ordre 57

Prismes 1, 2 et 3:• matériau: ZnSe, apex: 24.2°, incidence: 31.08°

Prisme 4:• matériau: Infrasil, apex: 54°, incidence: 41.04°

Séparation minimum des images de fente sur le détecteur (longueur d’onde centrale):• 87.5 µm (4.86 pixels) (ordres 48-49)Séparation minimum interordre sur le détecteur (longueur d’onde centrale):• 579 µm (ordres 46-47)

Séparation maximum interordre sur le détecteur (longueur d’onde centrale):• 789 µm (ordres 32-33)• 877 µm (ordres 79-80)

Distance ordres 32-80 sur le détecteur (longueur d’onde centrale):• 32.631 mm

A cause de l’anamorphose de la longueur de fente due aux prismes, la séparation minimum des images de fente (ordres 48-49) est différente de la séparation minimum interordre (ordres 46-47).

Figure 7. Dispersion croisée (ordonnée minimum à 4 pixels)


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Table 2. Données optiques du disperseur croiséSurface Rayon de



8 Pupille blanche 195 Air9 0 Air 18.98341 (x)10 Prisme 1 S1 infini -50 ZnSe 200 x 220 12.1 (xS)11 Prisme 1 S2 infini 0 Air 200 x 220 -12.1 (xS)12 -105 Air 18.98341 (x)13 0 Air 18.98341 (x)14 Prisme 2 S1 infini -50 ZnSe 200 x 220 12.1 (xS)15 Prisme 2 S2 infini 0 Air 200 x 220 -12.1 (xS)16 -105 Air 18.98341 (x)17 0 Air 18.98341 (x)18 Prisme 3 S1 infini -50 ZnSe 200 x 220 12.1 (xS)19 Prisme 3 S2 infini 0 Air 200 x 220 -12.1 (xS)20 -125 Air 18.98341 (x)21 0 Air 14.04574 (x)22 Prisme 4 S1 infini -110 Infrasil 232 x 220 27 (xS)23 Prisme 4 S2 infini 0 Air 232 x 220 -27 (xS)24 -80 Air 14.04574 (x)25 Caméra -324.9

(focale)-324.9 Lentille

Paraxiale230 6.2 (y)

26 Détecteur -57944 (y)-653.87 (x)

Image 36.86 x 36.86 -0.00456 (y)-0.01407 (x)

Figure 8. Spot diagramme ordre 32(croix = 32 µm, 1.78 pixel)


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Le disperseur croisé amplifie les aberrations d’astigmatisme du spectrographe échelle de manière linéaire en fonction de la dispersion. Minimiser la dispersion croisée permet donc de minimiser les aberrations globales du spectrographe SPIROU.

Figure 9. Spot diagramme ordre 32, dispersion nulle(croix = 32 µm, 1.78 pixel)

Figure 10. Spot diagramme ordre 32, dispersion moitié(croix = 32 µm, 1.78 pixel)


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1.2.5Caméra:

• focale de la caméra F2 = F1 GS = 1203.83 x 0.27 = 325.03 mm.

• dioptrique, focale 324.9 mm F/2.16, 6 lentilles.• matériaux: CaF2 (lentilles 1, 3 et 5), S-FTM16 (lentille 2), Infrasil (lentilles 4 et 6).• détecteur incliné de 0.1° dans la direction de la dispersion croisée.

Figure 11. Caméra spectrographe

Table 3. Données optiques de la caméraSurface Rayon de


Matériau Diamètre

25 Lentille 1 S1 -556.14 -55 CaF2 22826 Lentille 1 S2 290.72 -8.765 Air 22827 Lentille 2 S1 282.30 -25 S-FTM16 22828 Lentille 2 S2 -2212.3 -1 Air 22829 Lentille 3 S1 -479.66 -35 CaF2 22830 Lentille 3 S2 infini -188.094 Air 22831 Lentille 4 S1 -538.32 -35 Infrasil 22232 Lentille 4 S2 1477.6 -225.914 Air 22233 Lentille 5 S1 -90.464 -50 CaF2 14434 Lentille 5 S2 -1487.9 -27.487 Air 14435 Lentille 6 S1 664.54 -50 Infrasil 10436 Lentille 6 S2 -123.42 -7.318 Air 6637 Détecteur 619.51 Image 52.134

La table suivante donne les concentrations dans le pixel de l’ensemble du spectrographe:• Spot diagramme: pourcentage de rayons• PSF: pourcentage de l’énergie diffractée• PSF / PSF parfaite: pourcentage de l’énergie diffractée PSF aberrante / PSF sans aberrations


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Table 4. Qualité image sur le détecteur (% dans le pixel)Spot Diagramme PSF PSF / PSF parfaite

k λ3 (µm) λ1 λ2 λ3 λ4 λ5 λ1 λ2 λ3 λ4 λ5 λ1 λ2 λ3 λ4 λ5

32 2.40956 80.9 100 100 100 88.7 74.8 89.5 87.6 88.3 78.2 82.4 99.0 97.7 99.0 88.033 2.33654 79.8 100 100 100 87.9 75.0 89.7 87.8 88.9 78.5 82.5 99.0 97.5 99.3 87.934 2.26782 81.7 100 100 100 86.5 77.5 89.6 87.6 89.2 78.4 85.1 98.6 97.0 99.2 87.435 2.20302 83.6 100 100 100 84.4 79.4 89.2 87.2 89.2 77.8 87.0 98.0 96.2 98.9 86.536 2.14183 85.6 100 100 100 81.9 80.8 88.7 86.5 89.0 76.9 88.4 97.3 95.2 98.3 85.137 2.08394 87.6 100 100 100 79.2 81.6 88.0 85.7 88.6 75.4 89.2 96.3 94.0 97.6 83.238 2.02910 89.5 100 100 100 77.4 82.0 87.1 84.7 88.0 74.2 89.6 95.3 92.8 96.7 81.639 1.97707 90.9 100 100 100 79.7 82.3 86.3 83.8 87.3 75.5 89.7 94.3 91.6 95.7 82.840 1.92764 91.5 100 100 100 82.1 82.4 85.6 82.9 86.7 76.5 89.8 93.4 90.6 94.8 83.841 1.88063 91.8 100 100 100 84.4 82.6 85.0 82.4 86.1 77.4 89.9 92.6 89.9 94.1 84.642 1.83585 91.8 100 100 100 86.3 83.0 84.8 82.0 85.7 78.2 90.1 92.3 89.3 93.5 85.443 1.79316 92.0 100 100 100 88.0 83.5 84.8 82.1 85.5 79.2 90.5 92.2 89.4 93.2 86.444 1.75240 92.5 100 100 100 89.2 84.2 85.2 82.6 85.7 80.3 91.0 92.4 89.7 93.2 87.345 1.71346 93.4 100 100 100 90.2 85.1 85.9 83.4 86.1 81.3 91.8 93.0 90.4 93.5 88.446 1.67621 94.8 100 100 100 91.2 86.2 86.8 84.4 86.7 82.7 92.7 93.8 91.4 94.0 89.747 1.64055 96.6 100 100 100 92.5 87.3 87.9 85.7 87.5 84.0 93.8 94.7 92.7 94.7 91.148 1.60637 99.3 100 100 100 94.3 88.5 89.1 87.2 88.5 85.5 94.8 95.8 94.0 95.6 92.549 1.57359 100 100 100 100 96.6 89.6 90.3 88.6 89.5 86.9 95.9 96.9 95.4 96.6 93.950 1.54212 100 100 100 100 99.3 90.7 91.3 90.0 90.5 88.3 96.9 97.8 96.6 97.5 95.351 1.51188 100 100 100 100 100 91.6 92.3 91.2 91.5 89.6 97.7 98.6 97.8 98.3 96.552 1.48280 100 100 100 100 100 92.3 93.0 92.2 92.3 90.7 98.3 99.3 98.7 99.0 97.453 1.45483 100 100 100 100 100 92.8 93.5 92.9 92.9 91.6 98.8 99.7 99.3 99.5 98.254 1.42789 100 100 100 100 100 93.1 93.8 93.5 93.3 92.2 99.0 99.9 99.7 99.8 98.755 1.40192 100 100 100 100 100 93.1 93.9 93.8 93.6 92.6 99.0 99.9 99.9 99.9 99.056 1.37689 100 100 100 100 100 93.1 93.8 93.8 93.7 92.8 98.9 99.8 99.9 99.8 99.157 1.35273 100 100 100 100 100 92.8 93.6 93.8 93.6 92.8 98.6 99.5 99.7 99.7 99.058 1.32941 100 100 100 100 100 92.5 93.3 93.5 93.4 92.7 98.2 99.1 99.4 99.4 98.859 1.30688 99.5 100 100 100 100 92.0 92.8 93.2 93.1 92.5 97.7 98.6 99.0 99.0 98.460 1.28510 98.5 100 100 99.9 99.9 91.4 92.3 92.7 92.7 92.2 97.0 98.0 98.5 98.5 98.061 1.26403 96.9 99.2 99.6 99.5 99.4 90.8 91.7 92.2 92.2 91.8 96.2 97.3 97.8 97.9 97.562 1.24364 94.7 97.7 98.8 98.8 98.8 90.0 91.0 91.5 91.5 91.3 95.4 96.5 97.1 97.1 96.963 1.22390 92.1 95.5 97.4 97.6 97.8 89.2 90.2 90.8 90.8 90.6 94.4 95.6 96.2 96.3 96.264 1.20478 89.3 93.3 95.4 96.2 96.1 88.4 89.4 90.0 90.0 90.0 93.5 94.7 95.4 95.5 95.565 1.18624 86.7 91.1 93.2 94.8 94.0 87.6 88.6 89.2 89.3 89.3 92.5 93.7 94.4 94.6 94.766 1.16827 84.7 88.9 91.3 92.8 91.7 86.8 87.8 88.4 88.5 88.7 91.7 92.9 93.6 93.7 94.067 1.15083 83.1 86.8 89.2 90.8 89.8 86.2 87.2 87.7 87.8 88.1 90.9 92.1 92.8 92.9 93.368 1.13391 82.1 85.2 87.5 89.1 88.1 85.9 86.7 87.2 87.3 87.6 90.4 91.5 92.1 92.3 92.769 1.11748 81.7 84.3 86.3 87.9 87.0 85.7 86.4 86.8 86.9 87.3 90.2 91.1 91.6 91.8 92.370 1.10151 82.0 84.1 85.8 87.3 86.4 85.9 86.4 86.8 86.9 87.2 90.3 91.0 91.5 91.7 92.271 1.08600 83.0 84.7 86.0 87.4 86.4 86.3 86.8 87.0 87.1 87.4 90.6 91.2 91.6 91.8 92.272 1.07091 84.6 86.2 87.2 88.3 87.1 87.2 87.4 87.5 87.5 87.8 91.5 91.8 92.0 92.2 92.6


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73 1.05624 86.7 88.6 89.1 90.1 88.6 88.2 88.3 88.3 88.3 88.4 92.5 92.7 92.8 92.9 93.274 1.04197 89.4 91.8 92.0 92.4 90.7 89.3 89.4 89.3 89.3 89.3 93.6 93.8 93.8 93.9 93.975 1.02808 92.5 95.4 95.4 95.1 93.5 90.6 90.7 90.6 90.4 90.3 95.0 95.1 95.0 94.9 94.976 1.01455 96.1 98.0 98.5 97.9 96.5 91.9 92.0 91.8 91.6 91.3 96.3 96.4 96.3 96.2 95.977 1.00137 98.9 99.5 100 100 98.8 92.9 93.2 93.0 92.8 92.3 97.3 97.6 97.5 97.3 96.978 0.98854 99.9 100 100 100 99.8 93.0 94.2 94.0 93.8 92.9 97.4 98.6 98.5 98.3 97.479 0.97602 96.0 100 100 100 100 90.2 94.6 94.8 94.4 92.4 94.4 99.1 99.3 98.9 96.980 0.96382 79.2 100 100 100 94.2 79.8 92.7 94.5 93.9 88.6 83.5 97.0 98.9 98.3 92.8


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Figure 12. Spectrographe SPIROU


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Figure 13. Répartition des ordres sur le détecteur


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(image de la fente d’entrée)

Figure 14. Spot diagramme ordre 57(croix = 18 µm, 1 pixel)


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2.INDICES DE RÉFRACTION ET CONTRACTION CRYOGÉNIQUES DES MATÉRIAUXLes coefficients de Sellmeier des indices de réfraction absolus (dans le vide) dépendant de la température ont été obtenus par des mesures effectuées à l’aide du réfractomètre cryogénique CHARMS de la NASA, D.B. Leviton & al (2005, 2006).

Table 5. Coefficients de Sellmeier des indices de réfraction absolusCoeffs S1(T) S2(T) S3(T) λ1(T) λ2(T) λ3(T)CaF2 25 K ≤ T ≤ 300 K; 0.4 µm ≤ λ ≤ 5.6 µm (ΔnABS/ΔT = -8.54-6 K-1)T0 1.04834 -3.32723e-3 3.72693 7.94375e-2 0.258039 34.0169T1 -2.21666e-4 2.34683e-4 1.49844e-2 -2.20758e-4 -2.12833e-3 6.26867e-2T2 -6.73446e-6 6.55744e-6 -1.47511e-4 2.07862e-6 1.20393e-5 -6.14541e-4T3 1.50138e-8 -1.47028e-8 5.54293e-7 -9.60254e-9 -3.06973e-8 2.31517e-6T4 -2.77255e-11 2.75023e-11 -7.17298e-10 1.31401e-11 2.79793e-11 -2.99638e-9Infrasil 35 K ≤ T ≤ 300 K; 0.5 µm ≤ λ ≤ 3.6 µm (ΔnABS/ΔT = 5.96e-6 K-1)T0 0.105962 0.995429 0.865120 4.500743e-3 9.383735e-2 9.757183T1 9.359142e-6 -7.973196e-6 3.731950e-4 -2.825065e-4 -1.374171e-6 1.864621e-3T2 4.941067e-8 1.006343e-9 -2.010347e-6 3.136868e-6 1.316037e-8 -1.058414e-5T3 4.890163e-11 -8.694712e-11 2.708606e-9 -1.121499e-8 1.252909e-11 1.730321e-8T4 1.492126e-13 -1.220612e-13 1.679976e-12 1.236514e-11 -4.641280e-14 1.719396e-12ZnSe 20 K ≤ T ≤ 300 K; 0.55 µm ≤ λ ≤ 5.6 µm (ΔnABS/ΔT = 61.69e-6 K-1)T0 4.41367 0.447774 6.70952 0.198555 0.382382 73.3880T1 -1.13389e-3 1.11709e-3 -8.18190e-2 -3.62359e-5 -1.56654e-4 -5.06215e-1T2 2.00829e-5 -1.80101e-5 5.77330e-4 7.20678e-7 2.56481e-6 3.06061e-3T3 -8.77087e-8 8.10837e-8 -1.89210e-6 -3.12380e-9 -1.07544e-8 -8.48293e-6T4 1.26557e-10 -1.18476e-10 2.15956e-9 4.51629e-12 1.53230e-11 6.53366e-9BaF2 50 K ≤ T ≤ 300 K; 0.45 µm ≤ λ ≤ 5.6 µm (ΔnABS/ΔT = -13.29e-6 K-1)T0 0.8285359 0.3315039 4.367314 8.362026e-2 -0.1148764 49.21549T1 -8.986505e-4 9.091254e-4 -1.161161e-2 8.880306e-4 3.381142e-3 -6.672202e-2T2 -1.884197e-6 1.656780e-6 7.204123e-5 -1.277585e-5 -1.897870e-5 4.283633e-4T3 -1.332822e-10 5.257707e-10 -4.302326e-8 5.231437e-8 4.686248e-8 -3.280396e-7T4 3.650068e-12 -3.904140e-12 -1.764139e-10 -7.312824e-11 -4.348650e-11 -8.848551e-10

Le coefficient Δn/ΔT des indices de réfraction absolus (dans le vide) du S-FTM16 a été obtenu par des mesures effectuées à l’aide du réfractomère cryogénique de l’Université de l’Arizona, par W.R. Brown & al (2004).

S-FTM16 ΔnABS/ΔT = -2.4 e-6 ± 0.3 e-6 K-1, pour 77K ≤ T ≤ 298K; 0.6 µm ≤ λ ≤ 2.6 µm


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Table 6. Indice de réfraction absolu (dans le vide) cryogénique293K 80K

k λ3 (µm) ZnSe Infrasil CaF2 S-FTM16 ZnSe Infrasil CaF2 S-FTM1632 2.40956 2.44227 1.43199 1.42202 1.55504 2.43001 1.43075 1.42381 1.5555433 2.33654 2.44294 1.43327 1.42244 1.55627 2.43066 1.43203 1.42423 1.5567734 2.26782 2.44362 1.43443 1.42283 1.55740 2.43131 1.43319 1.42462 1.5579035 2.20302 2.44432 1.43549 1.42318 1.55843 2.43198 1.43425 1.42498 1.5589336 2.14183 2.44502 1.43646 1.42351 1.55939 2.43266 1.43522 1.42531 1.5598937 2.08394 2.44575 1.43736 1.42381 1.56027 2.43335 1.43611 1.42561 1.5607838 2.02910 2.44648 1.43818 1.42410 1.56110 2.43406 1.43693 1.42590 1.5616039 1.97707 2.44723 1.43894 1.42436 1.56186 2.43478 1.43769 1.42616 1.5623740 1.92764 2.44799 1.43964 1.42461 1.56258 2.43551 1.43839 1.42641 1.5630941 1.88063 2.44877 1.44030 1.42484 1.56325 2.43626 1.43904 1.42665 1.5637642 1.83585 2.44957 1.44091 1.42506 1.56389 2.43702 1.43965 1.42687 1.5643943 1.79316 2.45038 1.44148 1.42527 1.56448 2.4378 1.44022 1.42707 1.5649944 1.75240 2.45121 1.44201 1.42546 1.56505 2.43859 1.44075 1.42727 1.5655645 1.71346 2.45206 1.44251 1.42565 1.56559 2.43941 1.44125 1.42746 1.5661046 1.67621 2.45292 1.44298 1.42582 1.56610 2.44023 1.44172 1.42763 1.5666147 1.64055 2.45380 1.44343 1.42599 1.56658 2.44108 1.44217 1.42780 1.5670948 1.60637 2.45470 1.44385 1.42615 1.56705 2.44194 1.44259 1.42796 1.5675649 1.57359 2.45562 1.44424 1.42630 1.56750 2.44282 1.44298 1.42812 1.5680150 1.54212 2.45655 1.44462 1.42645 1.56792 2.44372 1.44336 1.42826 1.5684451 1.51188 2.45751 1.44498 1.42659 1.56834 2.44463 1.44372 1.42841 1.5688552 1.48280 2.45848 1.44532 1.42673 1.56873 2.44556 1.44406 1.42854 1.5692553 1.45483 2.45948 1.44565 1.42686 1.56912 2.44652 1.44438 1.42867 1.5696354 1.42789 2.46049 1.44596 1.42699 1.56949 2.44749 1.44470 1.42880 1.5700055 1.40192 2.46152 1.44626 1.42711 1.56985 2.44848 1.44499 1.42892 1.5703756 1.37689 2.46258 1.44654 1.42723 1.57020 2.44949 1.44528 1.42904 1.5707257 1.35273 2.46365 1.44682 1.42734 1.57055 2.45051 1.44555 1.42916 1.5710658 1.32941 2.46474 1.44708 1.42746 1.57088 2.45156 1.44582 1.42927 1.5714059 1.30688 2.46586 1.44734 1.42757 1.57121 2.45263 1.44607 1.42938 1.5717260 1.28510 2.46699 1.44758 1.42767 1.57153 2.45372 1.44632 1.42949 1.5720461 1.26403 2.46815 1.44782 1.42778 1.57184 2.45482 1.44655 1.42959 1.5723662 1.24364 2.46933 1.44805 1.42788 1.57215 2.45595 1.44678 1.42970 1.5726763 1.22390 2.47052 1.44827 1.42798 1.57245 2.45710 1.44701 1.42980 1.5729764 1.20478 2.47175 1.44849 1.42808 1.57275 2.45827 1.44722 1.42990 1.5732765 1.18624 2.47299 1.44870 1.42818 1.57304 2.45946 1.44743 1.42999 1.5735666 1.16827 2.47425 1.44890 1.42828 1.57334 2.46067 1.44764 1.43009 1.5738567 1.15083 2.47554 1.44910 1.42837 1.57362 2.4619 1.44784 1.43018 1.5741468 1.13391 2.47685 1.44930 1.42846 1.57391 2.46316 1.44803 1.43028 1.5744369 1.11748 2.47819 1.44949 1.42856 1.57419 2.46444 1.44822 1.43037 1.5747170 1.10151 2.47955 1.44968 1.42865 1.57447 2.46573 1.44841 1.43046 1.5749971 1.08600 2.48093 1.44986 1.42874 1.57475 2.46706 1.44859 1.43055 1.5752672 1.07091 2.48233 1.45004 1.42883 1.57502 2.4684 1.44877 1.43064 1.57554


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73 1.05624 2.48376 1.45021 1.42892 1.57530 2.46977 1.44894 1.43073 1.5758174 1.04197 2.48521 1.45039 1.42900 1.57557 2.47116 1.44911 1.43082 1.5760975 1.02808 2.48669 1.45056 1.42909 1.57584 2.47257 1.44928 1.43090 1.5763676 1.01455 2.48819 1.45073 1.42918 1.57611 2.47401 1.44945 1.43099 1.5766377 1.00137 2.48972 1.45089 1.42927 1.57638 2.47547 1.44962 1.43108 1.5769078 0.98854 2.49128 1.45105 1.42935 1.57665 2.47695 1.44978 1.43116 1.5771779 0.97602 2.49286 1.45121 1.42944 1.57692 2.47846 1.44994 1.43125 1.5774480 0.96382 2.49446 1.45137 1.42952 1.57719 2.48000 1.4501 1.43133 1.57771


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Les coefficients d’expansion thermique dépendant de la température ont été obtenus par des mesures effectuées à:• CaF2, ZnSe et BaF2: U.S. National Bureau of Standards, A. Feldman & al (1979).• SiIlice fondue IR: U.S. National Institute of Standards and Technology, N.J. Simon (1994).• S-FTM16: Université de l’Arizona, W.R. Brown & al (2004).• Al 6061: IR / EO Handbook, 3 , 358 (1993).• HgTe, CdTe, ZnTe: Smith & White (1975, 1979).

Table 7. Coefficients d’expansion thermiqueCoeffs CTE(T) (1e6 K-1) ΔL/L293K(T) (%)CaF2 80 K ≤ T ≤ 300 K;T0 -9.3655 -0.284113T1 0.22867 -0.00093655T2 -0.00065748 1.14335e-5T3 6.9599e-7 -2.1916e-8T4 0 1.73998e-11Infrasil 80 K ≤ T ≤ 300 K;T0 -1.479 0.0084842T1 0.010916 -0.0001479T2 -1.4319e-5 5.458e-7T3 0 -4.773e-10ZnSe 60 K ≤ T ≤ 300 K;T0 -5.0557 -0.107688T1 0.11566 -0.00050557T2 -0.00039518 5.783e-6T3 4.9225e-7 -1.31727e-8T4 0 1.23063e-11S-FTM16 77 K ≤ T ≤ 300 K;T0 4.27 -0.201087T1 0.0177 0.000427T2 0 8.85e-07BaF2 80 K ≤ T ≤ 300 K;T0 -6.6823 -0.32439T1 0.23875 -0.00066823T2 -0.000837 1.19375e-5T3 1.07e-6 -2.79e-8T4 0 2.675e-11Al 6061 4 K ≤ T ≤ 350 K;T0 -4.103 -0.416569T1 0.2068 -0.0004103T2 -0.0004845 1.034e-5T3 3.0036e-7 -1.615e-8T4 0 7.509e-12HgCdTe 77 K ≤ T ≤ 300 K;T0 -4.3001 -0.0762474


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T1 0.10068 -0.00043001T2 -0.00038371 5.034e-6T3 4.9824e-7 -1.27903e-8T4 0 1.2456e-11

Table 8. CTE, contraction, variation d’indice du matériau entre 293 K et 80 KZnSe Infrasil CaF2 S-FTM16 BaF2 Al 6061 HgCdTe

CTE(293K) (1e6 K-1) 7.29 0.49 18.70 9.46 18.33 22.45 4.79CTE(80K) (1e6 K-1) 1.92 -0.70 5.08 5.69 7.61 9.49 1.55AvCTE(293-80K) (1e6 K-1) 5.51 0.00 13.91 7.57 14.77 18.37 3.97ΔL/L293K(80K) (%) -0.117 -0.000 -0.296 -0.161 -0.315 -0.391 -0.084Δn (293-80K) -0.01314 -0.00127 0.00182 0.00051 0.00283

Pour éviter la défocalisation due au spectrographe échelle, les miroirs paraboliques hors-axe doivent avoir la même expansion thermique que la structure.On prend une structure et des miroirs en aluminium (Al 6061, contraction 293K-80K = -0.391 %).• Focale de la parabole à 80K: F0 = 1195.306 mm• Focale de la parabole hors-axe à 80K: F1 = 1199.120 mm

Le nombre de traits/mm du réseau échelle reste inchangé grâce à à l’expansion nulle de la silice entre 293 K et 80 K.

La taille du pixel à 80 K est de 17.985 mm, la taille du détecteur à 80 K est de 36.833 mm (HgCdTe, contraction 293K-80K = -0.084 %).

La caméra est optimisée à 80 K (indices de réfraction, rayons de courbure, épaisseurs à 80 K).Les données de fabrication (à 293 K) seront calculées en fonction de l’expansion thermique des matériaux.• Grandissement de la fente d’entrée à 80 K: GS = WPIX / WS = 0.2698• Focale de la caméra à 80 K: F2 = F1 GS = 323.5 mm

La correction image sur le détecteur à 80 K est légèrement meilleure que dans l’étude à 293 K, grâce à une plus faible dispersion des prismes du disperseur croisé (-2.86 %).

Du fait de la baisse de l’indice de réfraction du ZnSe et de l’Infrasil entre 293 K et 80K, l’apex des prismes en ZnSe doit être légèrement augmenté de façon à atteindre un minimum de séparation entre les images de fentes de 4 pixels à 80 K.L’incidence sur les prismes est ajustée au minimum de déviation pour 80 K à l’ordre 57.Prismes 1, 2 et 3:• matériau: ZnSe, apex: 24.44°, incidence à 80 K: 31.24°

Prisme 4:• matériau: Infrasil, apex: 54°, incidence à 80 K: 41.02°


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Déplacement du spectre sur le détecteur entre 293 K et 80K: 6.49 mmSéparation minimum des images de fente sur le détecteur (longueur d’onde centrale):• 71.2 µm (3.96 pixels) (ordres 49-50)

Séparation minimum interordre sur le détecteur (longueur d’onde centrale):• 564 µm (ordres 46-47)

Séparation maximum interordre sur le détecteur (longueur d’onde centrale):• 775 µm (ordres 32-33)• 848 µm (ordres 79-80)Distance ordres 32-80 sur le détecteur (longueur d’onde centrale):• 31.697 mm

Figure 17. Dispersion croisée 80K et 293K (ordonnée minimum à 4 pixels)

Table 9. Données optiques du spectrographe SPIROU à 80 KSurface Rayon de



0 Fente d’entrée infini 1195.306 Objet 1.886 x 0.067 -6.466 (x)1 Parabole 1 -2390.612 -1354.680 Miroir 220 x 3402 Réseau infini 1354.680 Miroir 306 x 154 135.037 (yS) 0.6 (xS)

63.435 (yS)3 Parabole 1 -2390.612 -1195.306 Miroir 220 x 3404 99.609 Air5 Miroir de repli infini 99.609 Miroir 20 x 1806 1195.837 Air


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7 Parabole 2 -2390.612 -1051.905 Miroir 220 x 3408 Pupille blanche 194.237 Air 150 -135.037 (y) 1.2 (x)9 0 Air 19.02445 (x)10 Prisme 1 S1 infini -49.941 ZnSe 200 x 220 12.22 (xS)11 Prisme 1 S2 infini 0 Air 200 x 220 -12.22 (xS)12 -104.589 Air 19.02445 (x)13 0 Air 19.02445 (x)14 Prisme 2 S1 infini -49.941 ZnSe 200 x 220 12.22 (xS)15 Prisme 2 S2 infini 0 Air 200 x 220 -12.22 (xS)16 -104.589 Air 19.02445 (x)17 0 Air 19.02445 (x)18 Prisme 3 S1 infini -49.941 ZnSe 200 x 220 12.22 (xS)19 Prisme 3 S2 infini 0 Air 200 x 220 -12.22 (xS)20 -124.511 Air 19.02445 (x)21 0 Air 14.01579 (x)22 Prisme 4 S1 infini -110 Infrasil 232 x 220 27 (xS)23 Prisme 4 S2 infini 0 Air 232 x 220 -27 (xS)24 -79.687 Air 14.01579 (x)25 Lentille 1 S1 -555.982 -55 CaF2 228 6.2 (y)26 Lentille 1 S2 298.967 -10.023 Air 22827 Lentille 2 S1 288.261 -25 S-FTM16 22828 Lentille 2 S2 -2027.04 -1 Air 22829 Lentille 3 S1 -463.513 -35 CaF2 22830 Lentille 3 S2 infini -190.492 Air 22831 Lentille 4 S1 -508.28 -35 Infrasil 22232 Lentille 4 S2 1865.982 -223.552 Air 22233 Lentille 5 S1 -88.8254 -50 CaF2 14434 Lentille 5 S2 -1926.75 -24.800 Air 14435 Lentille 6 S1 641.505 -50 Infrasil 10436 Lentille 6 S2 -118.77 -7.260 Air 6637 Détecteur infini Image 52.134 0.01316 (x)


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Figure 18. Spot diagramme ordre 57 à 80K(croix = 18 µm, 1 pixel)


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Figure 19. Spot diagramme ordre 32 à 80K


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(croix = 18 µm, 1 pixel)

Figure 20. Spot diagramme ordre 80 à 80K(croix = 18 µm, 1 pixel)


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Table 10. Qualité image sur le détecteur (% dans le pixel) à 80KSpot Diagramme PSF PSF / PSF parfaite


32 2.40956 84.7 100 100 100 92.3 78.5 89.6 88.1 88.4 80.6 86.5 99.2 98.3 99.2 90.733 2.33654 84.2 100 100 100 91.9 78.9 89.9 88.4 89.0 80.9 86.7 99.2 98.2 99.5 90.734 2.26782 86.8 100 100 100 91.0 81.0 89.9 88.4 89.4 81.1 88.9 99.0 97.9 99.5 90.535 2.20302 89.5 100 100 100 89.6 82.7 89.7 88.3 89.6 80.9 90.6 98.6 97.4 99.3 89.936 2.14183 92.2 100 100 100 87.8 83.8 89.4 87.9 89.5 80.3 91.8 98.1 96.7 98.9 89.037 2.08394 94.3 100 100 100 85.7 84.5 88.9 87.3 89.3 79.4 92.4 97.4 95.9 98.4 87.738 2.02910 95.5 100 100 100 84.4 84.9 88.3 86.7 89.0 78.6 92.8 96.6 95.0 97.7 86.639 1.97707 95.4 100 100 100 87.1 85.2 87.7 86.1 88.6 79.8 92.9 95.9 94.2 97.1 87.640 1.92764 95.1 100 100 100 89.4 85.3 87.2 85.5 88.2 80.7 93.0 95.2 93.4 96.5 88.541 1.88063 94.9 100 100 100 91.1 85.5 86.9 85.1 87.8 81.6 93.0 94.7 92.9 95.9 89.242 1.83585 95.1 100 100 100 91.7 85.8 86.7 84.9 87.5 82.3 93.2 94.4 92.5 95.5 89.843 1.79316 95.5 100 100 100 92.1 86.3 86.8 85.1 87.4 83.1 93.5 94.3 92.6 95.3 90.544 1.75240 96.2 100 100 100 92.7 86.8 87.2 85.4 87.6 83.8 93.9 94.5 92.8 95.2 91.345 1.71346 97.3 100 100 100 93.6 87.5 87.7 86.0 87.8 84.8 94.4 94.9 93.3 95.4 92.246 1.67621 99.0 100 100 100 94.8 88.3 88.4 86.9 88.3 85.8 95.1 95.5 94.1 95.8 93.147 1.64055 100 100 100 100 96.4 89.2 89.3 87.8 89.0 86.8 95.8 96.3 95.0 96.3 94.148 1.60637 100 100 100 100 98.4 90.1 90.2 88.9 89.7 87.9 96.6 97.0 95.9 97.0 95.149 1.57359 100 100 100 100 100 91.0 91.1 90.0 90.5 89.0 97.3 97.8 96.9 97.6 96.150 1.54212 100 100 100 100 100 91.8 91.9 91.0 91.3 90.0 98.0 98.5 97.8 98.3 97.151 1.51188 100 100 100 100 100 92.4 92.7 91.9 92.0 90.9 98.6 99.1 98.5 98.8 97.952 1.48280 100 100 100 100 100 92.9 93.2 92.6 92.6 91.7 99.0 99.5 99.1 99.3 98.553 1.45483 100 100 100 100 100 93.2 93.6 93.2 93.0 92.3 99.3 99.8 99.6 99.6 99.054 1.42789 100 100 100 100 100 93.4 93.8 93.6 93.4 92.7 99.4 99.9 99.8 99.8 99.355 1.40192 100 100 100 100 100 93.5 93.9 93.8 93.6 93.0 99.4 99.9 99.9 99.9 99.456 1.37689 100 100 100 100 100 93.4 93.9 93.8 93.7 93.2 99.3 99.8 99.9 99.9 99.557 1.35273 100 100 100 100 100 93.3 93.7 93.8 93.6 93.2 99.1 99.6 99.8 99.7 99.458 1.32941 100 100 100 100 100 93.0 93.5 93.6 93.5 93.1 98.8 99.3 99.5 99.5 99.259 1.30688 100 100 100 100 100 92.7 93.1 93.3 93.3 92.9 98.4 98.9 99.2 99.1 98.960 1.28510 100.0 100 100 100 100 92.3 92.7 92.9 92.9 92.7 97.9 98.4 98.7 98.7 98.561 1.26403 99.4 100 100 100 100 91.8 92.2 92.5 92.5 92.4 97.3 97.8 98.2 98.2 98.162 1.24364 98.6 99.7 99.9 99.7 99.9 91.2 91.6 91.9 92.0 92.0 96.6 97.2 97.6 97.6 97.763 1.22390 97.4 98.7 99.3 99.2 99.5 90.7 91.0 91.4 91.4 91.5 95.9 96.4 96.9 97.0 97.164 1.20478 95.9 97.0 98.3 98.4 99.0 90.1 90.4 90.8 90.8 91.0 95.3 95.8 96.2 96.3 96.665 1.18624 94.5 95.2 96.6 97.3 98.1 89.6 89.8 90.2 90.2 90.6 94.6 95.1 95.5 95.6 96.066 1.16827 92.8 93.5 94.9 96.2 97.2 89.1 89.3 89.6 89.7 90.1 94.0 94.4 94.8 95.0 95.567 1.15083 91.3 92.2 93.4 95.1 95.8 88.7 88.9 89.1 89.2 89.7 93.5 93.9 94.2 94.4 95.068 1.13391 90.5 91.4 92.3 94.2 94.8 88.5 88.6 88.8 88.9 89.4 93.2 93.5 93.8 94.0 94.669 1.11748 90.2 90.9 91.6 93.3 93.9 88.5 88.4 88.5 88.7 89.3 93.1 93.2 93.4 93.7 94.470 1.10151 90.6 91.0 91.5 93.1 93.6 88.7 88.6 88.6 88.7 89.3 93.2 93.3 93.5 93.7 94.471 1.08600 91.4 91.8 91.9 93.4 93.8 89.1 88.9 88.9 89.0 89.6 93.6 93.5 93.6 93.8 94.572 1.07091 92.7 93.2 93.0 94.3 94.5 89.8 89.5 89.4 89.4 89.9 94.2 94.1 94.1 94.2 94.9


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73 1.05624 94.5 94.9 94.6 95.8 95.8 90.5 90.3 90.1 90.1 90.5 95.0 94.8 94.7 94.8 95.474 1.04197 96.4 97.0 96.7 97.4 97.5 91.4 91.2 91.0 90.9 91.2 95.9 95.7 95.6 95.6 96.075 1.02808 97.9 98.5 98.9 99.0 98.8 92.3 92.2 91.9 91.8 91.9 96.8 96.7 96.5 96.4 96.776 1.01455 98.9 99.3 100 99.9 99.8 93.2 93.1 92.9 92.8 92.7 97.7 97.6 97.5 97.4 97.477 1.00137 99.7 100.0 100 100 100 93.9 94.0 93.8 93.7 93.4 98.4 98.5 98.3 98.2 98.078 0.98854 100 100 100 100 100 94.2 94.7 94.5 94.4 93.8 98.6 99.2 99.1 98.9 98.479 0.97602 100 100 100 100 100 92.9 95.0 95.1 94.8 93.7 97.3 99.5 99.6 99.4 98.280 0.96382 88.1 100 100 100 100 86.9 94.3 95.1 94.7 91.8 90.9 98.7 99.5 99.2 96.2


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3.CONCLUSION PRÉLIMINAIRELe concept optique proposé pour le spectrographe de SPIROU atteint toutes les spécifications.Un problème potentiel à résoudre est la dimension des prismes, en particulier ceux en ZnSe, l’épaisseur maximale des substrats étant de l’ordre de 40 mm (voir prismes GIANO).En réduisant au maximum l’épaisseur et la hauteur des prismes, on peut arriver à une épaisseur de base de 80 mm. On peut alors atteindre l’épaisseur maximale de 40 mm en scindant chaque prisme en deux prismes rectangles mis dos à dos, l’assemblage pouvant se faire soit avec un espace entre les 2 prismes, soit par adhérence moléculaire.Le nombre total de prismes ZnSe serait alors de 6, assemblés par paires.

On peut peut-être aussi envisager d’autres matériaux à forte dispersion dans les courtes longueurs d’onde (As2S3, AMTIR-1, …), mais les dimensions possibles des substrats sont à étudier.

Une autre option est de placer les prismes de dispersion croisée en pré-dispersion plutôt qu’en post-dispersion, ils sont alors utilisés en double passage avant et après le réseau échelle.Avantages:• Réduit le nombre et l’apex des prismes.• Les prismes sont dans un faisceau collimaté sans aberrations -> pas d’amplification des

aberrations.• Réduit la taille des optiques de la caméra (dans la pupille blanche).• Réduit les aberrations à corriger par la caméra.Inconvénients:• Nécessite l’augmentation de l’angle hors-axe des paraboles et de l’angle hors-littrow du réseau.• Augmente la taille du miroir de repli et des paraboles hors-axe.• Les prismes ne travaillent plus au minimum de déviation -> grandissement plus important dans

le sens de la fente.• Induit une plus forte rotation et courbure des spectres diffractés par le réseau échelle.• Induit un vignettage par le réseau échelle dans le sens de la dispersion croisée.

Cette option, ainsi qu’une option pré-post dispersion sont étudiées dans les sections suivantes.


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4.PRÉ-DISPERSION CROISÉEParamètres du collimateur parabolique (à 80 K):• Focale de la parabole de base à 80 K: F0 = 1195.306 mm• Angle de hors-axe: β = 11.6°• Focale de la parabole hors-axe à 80 K: F1 = 1207.639 mm• Hauteur de hors-axe à 80 K: h = 242.829 mm

Angle hors-littrow du réseau échelle: γ = 1.7°

Le miroir de repli est positionné sur l’image intermédiaire du spectre.Les séparations entre optiques et faisceau sont réduites au minimum (> 5 mm) de façon à minimiser l’angle hors-littrow.

Paramètres de la caméra (à 80 K):• Grandissement de la fente d’entrée à 80 K: GS = WPIX / WS = 0.2698• Focale de la caméra à 80 K: F2 = F1 GS = 325.8 mm

L’incidence sur les prismes est ajustée au minimum de déviation pour 80 K à l’ordre 57.Prismes 1, 2 et 3 assemblés en un seul prisme:• matériau: ZnSe, apex: 9.8°, apex du groupe: 29.4°, incidence du groupe à 80 K: 38.45°

Prisme 4:• matériau: Infrasil, apex: 43°, incidence à 80 K: 31.99°

Rotation du détecteur autour de son axe: 2.858°

La correction image sur le détecteur est bien meilleure que pour la post-dispersion croisée.


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Séparation minimum des images de fente sur le détecteur (toutes longueurs d’onde):• 66.7 µm (3.70 pixels) (ordres 53-54)


Distance ordres 32-80 incluant les images de fente sur le détecteur (toutes longueurs d’onde):• 37.521 mm

On pourrait faire rentrer complètement les spectres sur le détecteur en diminuant la dispersion croisée, mais ce serait au détriment de la séparation minimum des images de fente sur le détecteur qui est déjà inférieure à 4 pixels.

Figure 21. pré-dispersion croisée (ordonnée minimum à 3 pixels)


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Figure 22. Spectrographe SPIROU (pré-dispersion croisée)


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Figure 23. Répartition des ordres sur le détecteur (pré-dispersion croisée)(image de la fente d’entrée)

Table 11. Qualité image sur le détecteur (% dans le pixel) à 80K (pré-dispersion croisée)Spot Diagramme PSF PSF / PSF parfaite


32 2.40956 100 100 100 100 100 86.8 87.1 86.0 84.9 83.9 97.1 97.8 97.2 96.9 96.533 2.33654 100 100 100 100 100 87.6 87.8 86.2 85.5 84.5 97.5 98.1 96.9 97.0 96.534 2.26782 100 100 100 100 100 88.1 88.0 86.2 86.0 85.0 97.7 97.9 96.3 96.9 96.535 2.20302 100 100 100 100 100 88.6 88.2 86.1 86.4 85.6 97.9 97.7 95.8 96.8 96.736 2.14183 100 100 100 100 100 88.9 88.3 86.1 86.8 86.4 98.0 97.6 95.5 96.8 97.037 2.08394 100 100 100 100 100 89.2 88.6 86.4 87.4 87.1 98.2 97.7 95.5 97.0 97.438 2.02910 100 100 100 100 100 89.5 88.9 86.9 88.0 87.8 98.4 97.9 95.8 97.3 97.739 1.97707 100 100 100 100 100 89.7 89.4 87.5 88.6 88.4 98.5 98.2 96.3 97.7 98.0


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40 1.92764 100 100 100 100 100 90.0 89.8 88.2 89.2 88.9 98.6 98.6 96.9 98.2 98.241 1.88063 100 100 100 100 100 90.2 90.2 88.9 89.7 89.3 98.7 98.9 97.5 98.6 98.442 1.83585 100 100 100 100 100 90.3 90.6 89.5 90.2 89.5 98.8 99.2 98.1 99.0 98.443 1.79316 100 100 100 100 100 90.5 90.9 90.1 90.6 89.7 98.8 99.5 98.6 99.3 98.544 1.75240 100 100 100 100 100 90.6 91.2 90.5 90.9 89.8 98.8 99.6 99.0 99.5 98.445 1.71346 100 100 100 100 100 90.7 91.4 90.9 91.1 89.8 98.7 99.7 99.4 99.7 98.446 1.67621 100 100 100 100 100 90.8 91.6 91.2 91.3 89.8 98.6 99.8 99.6 99.8 98.347 1.64055 100 100 100 100 100 90.8 91.7 91.5 91.4 89.8 98.5 99.8 99.7 99.8 98.248 1.60637 100 100 100 100 100 90.9 91.9 91.7 91.5 89.8 98.4 99.8 99.8 99.8 98.149 1.57359 100 100 100 100 100 90.9 92.1 91.9 91.7 89.8 98.3 99.7 99.8 99.8 97.950 1.54212 100 100 100 100 100 91.0 92.2 92.1 91.8 89.8 98.1 99.7 99.8 99.7 97.851 1.51188 100 100 100 100 100 91.0 92.4 92.3 91.9 89.8 98.0 99.7 99.8 99.7 97.752 1.48280 100 100 100 100 100 91.0 92.5 92.4 92.0 89.9 97.9 99.6 99.8 99.6 97.553 1.45483 100 100 100 100 100 91.0 92.6 92.6 92.2 89.9 97.7 99.6 99.8 99.6 97.454 1.42789 100 100 100 100 100 91.0 92.7 92.8 92.3 90.0 97.6 99.6 99.8 99.5 97.355 1.40192 100 100 100 100 100 91.0 92.8 92.9 92.4 90.1 97.5 99.5 99.7 99.5 97.356 1.37689 100 100 100 100 100 91.0 92.9 93.0 92.6 90.2 97.4 99.5 99.7 99.4 97.257 1.35273 100 100 100 100 100 91.0 93.0 93.1 92.7 90.4 97.3 99.5 99.7 99.4 97.158 1.32941 100 100 100 100 100 91.1 93.1 93.2 92.8 90.5 97.3 99.4 99.7 99.4 97.159 1.30688 100 100 100 100 100 91.1 93.1 93.3 92.9 90.6 97.2 99.4 99.7 99.3 97.060 1.28510 100 100 100 100 100 91.2 93.2 93.3 92.9 90.7 97.3 99.4 99.6 99.3 97.061 1.26403 100 100 100 100 100 91.3 93.2 93.4 93.0 90.8 97.3 99.4 99.6 99.3 97.062 1.24364 100 100 100 100 100 91.4 93.3 93.4 93.0 90.9 97.4 99.4 99.6 99.2 97.063 1.22390 100 100 100 100 100 91.6 93.3 93.5 93.1 91.0 97.4 99.4 99.6 99.2 97.064 1.20478 100 100 100 100 100 91.8 93.4 93.5 93.1 91.1 97.6 99.4 99.6 99.2 97.165 1.18624 100 100 100 100 100 92.0 93.5 93.6 93.2 91.1 97.7 99.4 99.6 99.2 97.166 1.16827 100 100 100 100 100 92.2 93.6 93.7 93.2 91.3 97.8 99.4 99.6 99.2 97.267 1.15083 100 100 100 100 100 92.4 93.7 93.7 93.3 91.4 98.0 99.4 99.6 99.2 97.268 1.13391 100 100 100 100 100 92.6 93.8 93.8 93.3 91.5 98.1 99.5 99.6 99.2 97.469 1.11748 100 100 100 100 100 92.8 93.9 93.9 93.4 91.7 98.2 99.5 99.6 99.2 97.470 1.10151 100 100 100 100 100 93.0 94.0 94.0 93.5 91.8 98.4 99.5 99.6 99.2 97.571 1.08600 100 100 100 100 100 93.1 94.0 94.0 93.6 92.0 98.5 99.5 99.6 99.2 97.672 1.07091 100 100 100 100 100 93.3 94.1 94.1 93.6 92.1 98.6 99.5 99.6 99.2 97.773 1.05624 100 100 100 100 100 93.4 94.2 94.1 93.7 92.2 98.7 99.5 99.6 99.2 97.874 1.04197 100 100 100 100 100 93.5 94.2 94.2 93.7 92.4 98.7 99.5 99.6 99.2 97.975 1.02808 100 100 100 100 100 93.6 94.3 94.2 93.8 92.4 98.8 99.5 99.6 99.2 97.976 1.01455 100 100 100 100 100 93.6 94.2 94.2 93.8 92.5 98.8 99.5 99.5 99.1 97.977 1.00137 100 100 100 100 100 93.6 94.2 94.2 93.7 92.5 98.8 99.4 99.4 99.0 97.878 0.98854 100 100 100 100 100 93.5 94.1 94.1 93.6 92.4 98.7 99.3 99.3 98.9 97.779 0.97602 100 100 100 100 99.9 93.4 94.0 94.0 93.5 92.3 98.5 99.1 99.1 98.7 97.580 0.96382 100 100 100 100 99.7 93.1 93.7 93.7 93.3 92.0 98.2 98.9 98.9 98.4 97.2


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5.PRÉ-POST DISPERSION CROISÉEParamètres du collimateur parabolique (à 80 K):• Focale de la parabole de base à 80 K: F0 = 1195.306 mm• Angle de hors-axe: β = 10°• Focale de la parabole hors-axe à 80 K: F1 = 1204.455 mm• Hauteur de hors-axe à 80 K: h = 209.151 mm

Angle hors-littrow du réseau échelle: γ = 1.2°

Le miroir de repli est positionné sur l’image intermédiaire du spectre.

Paramètres de la caméra (à 80 K):• Grandissement de la fente d’entrée à 80 K: GS = WPIX / WS = 0.2698• Focale de la caméra à 80 K: F2 = F1 GS = 325.0 mm

L’incidence sur les prismes est ajustée au minimum de déviation pour 80 K à l’ordre 58.Prismes 1, 2 et 3 assemblés en un seul prisme (pré-dispersion):• matériau: ZnSe, apex: 10.4°, apex du groupe: 31.2°, incidence du groupe à 80 K: 41.24°

Prisme 4 (post-dispersion):• matériau: Infrasil, apex: 60°, incidence à 80 K: 46.30°

Rotation du détecteur autour de son axe: 1.907°

La correction image sur le détecteur est légèrement moins bonne que pour la pré-dispersion croisée, mais bien meilleure que pour la post-dispersion croisée.


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Séparation minimum des images de fente sur le détecteur (toutes longueurs d’onde):• 70.0 µm (3.89 pixels) (ordres 50-51)


Distance ordres 32-80 incluant les images de fente sur le détecteur (toutes longueurs d’onde):• 35.411 mm

La pré-dispersion pourrait être légèrement augmentée pour une couverture maximale du détecteur et se rapprocher plus de la séparation minimum des images de fente sur le détecteur de 4 pixels.

Figure 24. pré-post-dispersion croisée (ordonnée minimum à 3 pixels)


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Figure 25. Spectrographe SPIROU (pré-post-dispersion croisée)


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Figure 26. Répartition des ordres sur le détecteur (pré-post-dispersion croisée)(image de la fente d’entrée)

Table 12. Qualité image sur le détecteur (% dans le pixel) à 80K (pré-post-dispersion croisée)

Spot Diagramme PSF PSF / PSF parfaitek λ3 (µm) λ1 λ2 λ3 λ4 λ5 λ1 λ2 λ3 λ4 λ5 λ1 λ2 λ3 λ4 λ5

32 2.40956 99.6 100 100 100 100 87.9 87.2 86.5 85.0 84.2 98.1 97.8 97.8 97.1 96.933 2.33654 99.0 100 100 100 100 88.2 88.4 87.6 86.5 85.0 98.1 98.6 98.4 98.0 97.234 2.26782 98.8 100 100 100 100 88.5 88.8 87.8 87.2 85.6 98.1 98.7 98.1 98.2 97.335 2.20302 98.8 99.9 100 100 100 88.8 88.9 87.7 87.7 86.2 98.1 98.5 97.5 98.1 97.436 2.14183 99.0 99.7 100 100 100 89.1 89.0 87.5 88.0 86.8 98.2 98.3 96.9 98.1 97.537 2.08394 99.1 99.7 99.9 100 100 89.4 89.3 87.5 88.4 87.3 98.3 98.3 96.6 98.1 97.638 2.02910 99.4 99.7 99.9 100 100 89.6 89.6 87.7 88.9 87.7 98.5 98.5 96.6 98.3 97.6


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39 1.97707 99.6 99.8 99.9 100 100 89.8 90.0 88.2 89.4 88.1 98.6 98.8 96.9 98.6 97.640 1.92764 99.8 99.9 99.9 100 100 90.0 90.4 88.7 89.9 88.3 98.6 99.2 97.4 98.9 97.541 1.88063 99.9 100 100 100 100 90.0 90.8 89.3 90.4 88.3 98.6 99.5 97.9 99.3 97.342 1.83585 100 100 100 100 100 90.0 91.1 89.8 90.7 88.4 98.4 99.8 98.5 99.6 97.243 1.79316 100 100 100 100 100 90.0 91.4 90.3 91.1 88.3 98.2 100 99.0 99.8 96.944 1.75240 100 100 100 100 100 89.9 91.6 90.8 91.3 88.2 98.0 100 99.4 100 96.745 1.71346 100 100 100 100 100 89.8 91.8 91.2 91.5 88.1 97.7 100 99.7 100 96.546 1.67621 100 100 100 100 100 89.6 91.9 91.5 91.6 87.9 97.4 100 99.9 100 96.347 1.64055 100 100 100 100 100 89.5 92.1 91.7 91.7 87.8 97.2 100 100 100 96.148 1.60637 100 100 100 100 100 89.4 92.2 92.0 91.8 87.7 96.9 100 100 100 95.949 1.57359 100 100 100 100 100 89.3 92.3 92.1 91.9 87.6 96.6 100 100 100 95.750 1.54212 100 100 100 100 100 89.2 92.4 92.3 91.9 87.6 96.3 99.9 100 100 95.551 1.51188 100 100 100 100 100 89.2 92.5 92.5 92.0 87.6 96.2 99.9 100 100 95.452 1.48280 100 100 100 100 100 89.2 92.6 92.6 92.2 87.6 96.0 99.8 100 99.9 95.253 1.45483 100 100 100 100 100 89.2 92.7 92.8 92.3 87.7 95.9 99.8 100 99.8 95.254 1.42789 100 100 100 100 100 89.2 92.8 92.9 92.4 87.8 95.8 99.7 100 99.7 95.155 1.40192 100 100 100 100 100 89.3 92.9 93.0 92.5 88.0 95.7 99.7 100 99.7 95.156 1.37689 100 100 100 100 100 89.4 93.0 93.1 92.6 88.2 95.7 99.6 99.9 99.6 95.157 1.35273 100 100 100 100 100 89.5 93.0 93.2 92.8 88.4 95.8 99.6 99.9 99.6 95.258 1.32941 100 100 100 100 100 89.7 93.1 93.3 92.9 88.7 95.9 99.6 99.9 99.6 95.259 1.30688 100 100 100 100 100 89.9 93.2 93.4 93.0 88.9 96.0 99.6 99.9 99.5 95.460 1.28510 100 100 100 100 100 90.1 93.3 93.4 93.1 89.1 96.1 99.6 99.9 99.5 95.561 1.26403 100 100 100 100 100 90.3 93.3 93.5 93.1 89.4 96.3 99.6 99.9 99.5 95.662 1.24364 100 100 100 100 100 90.6 93.4 93.6 93.2 89.7 96.5 99.6 99.8 99.5 95.863 1.22390 100 100 100 100 100 90.9 93.5 93.7 93.3 89.9 96.7 99.6 99.9 99.5 96.064 1.20478 100 100 100 100 100 91.2 93.6 93.7 93.4 90.1 96.9 99.6 99.9 99.5 96.165 1.18624 100 100 100 100 100 91.4 93.7 93.8 93.4 90.3 97.1 99.7 99.9 99.5 96.366 1.16827 100 100 100 100 100 91.7 93.8 93.9 93.5 90.5 97.3 99.7 99.9 99.6 96.567 1.15083 100 100 100 100 100 91.9 93.9 94.0 93.6 90.7 97.5 99.7 99.9 99.6 96.668 1.13391 100 100 100 100 100 92.1 94.0 94.0 93.7 90.9 97.6 99.7 99.9 99.6 96.869 1.11748 100 100 100 100 100 92.3 94.1 94.1 93.7 91.1 97.7 99.7 99.9 99.6 96.970 1.10151 100 100 100 100 100 92.4 94.2 94.2 93.8 91.2 97.8 99.7 99.9 99.6 97.071 1.08600 100 100 100 100 100 92.5 94.2 94.3 93.8 91.4 97.8 99.7 99.9 99.5 97.072 1.07091 100 100 100 100 100 92.5 94.3 94.3 93.9 91.4 97.8 99.7 99.9 99.5 97.073 1.05624 100 100 100 100 100 92.5 94.3 94.4 93.9 91.4 97.7 99.7 99.8 99.4 96.974 1.04197 100 100 100 100 100 92.4 94.3 94.4 93.9 91.3 97.5 99.6 99.8 99.3 96.875 1.02808 100 100 100 100 100 92.1 94.2 94.3 93.8 91.1 97.2 99.4 99.7 99.2 96.576 1.01455 100 100 100 100 100 91.7 94.0 94.2 93.6 90.7 96.8 99.2 99.5 99.0 96.077 1.00137 100 100 100 100 99.4 91.0 93.7 94.0 93.3 90.1 96.0 98.9 99.3 98.6 95.378 0.98854 100 100 100 100 98.2 89.9 93.1 93.6 92.8 89.1 94.9 98.3 98.8 98.0 94.279 0.97602 100 100 100 100 96.7 88.1 92.2 92.9 91.9 87.5 93.0 97.3 98.1 97.1 92.480 0.96382 99.2 100 100 99.9 94.3 85.2 90.6 91.7 90.5 84.8 90.0 95.7 96.8 95.5 89.6


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6.CONCLUSIONLes options de pré-dispersion (totale ou partielle) sont séduisantes, bien qu’elles s’éloignent du concept optique d'ESPaDOnS (post-dispersion).Elles permettent un design plus compact, des optiques (prismes et lentilles) de plus petite taille et une meilleure correction de l’image sur le détecteur, mais des miroirs (paraboles et miroir de repli) de plus grande taille.Une optimisation plus poussée du poids relatif du ZnSe et de l’Infrasil dans la dispersion croisée devrait permettre d’ajuster au mieux le remplissage du détecteur et la séparation minimum entre les images de fente.


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Appendix B : preliminary estimate of the instrument thermal background

This document is for the thermal background estimation of SPIROU. According to the system specifications, the thermal instrument background in the K band should be smaller than the telescopethermal emission, i.e. K>13.5. To meet this goal, the analysis on the actions to limit the thermal background is reported. The calculation is done at 2.4 µm which is longest wavelength of SPIROU and is expected to have highest thermal background. A bandwidth of 1e-4 micron was used to fit the resolution of SPIROU. In the calculation, standard CFHT parameters and the optics parameters from Espadons were used. Some of the calculation will be refined after the optical design of SPIROU is finalized. It should be noticed that due to the large number of optics, the radiation sources closer to the dewar of SPIROU is more important than the ones that is far from the cooled region. The efficiency for different modules in SPIROU is assumed as: ★ telescope: 0.75 (each mirror 0.866)★ polarimeter: 0.80★ fiber: 0.80★ slicer: 0.85

1. The thermal radiation from the sky and telescope:

The sky background and the radiation from the telescope were firstcalculated assuming the radiation is collected in the (200 µm=1.4") circular pinhole of the Cassegrain module. All radiation collected herewill have the same optical path with the star signal, so these are the unavoidable radiation unless a cold stop is added. The radiation from the sky is calculated assuming a 0.76 emissivity at 250K. The totalradiation intensity collected is about 1.22x10-18 W at the pinhole. (11 ph/s/m2/nm/arcsec2). This value is very close to sky background of the K=13.5 star. However, if we use the spectrum of Gemini’s sky background, the sky level is about 2.0x10-19 W from the lowest flux point in the K band. Here we will use this value as the goal of the thermal background reduction from the other parts of SPIROU. The reflectivity of the mirrors is assumed to be 0.866 in the calculation. The radiation from the primary mirror is 6.1x10-19 W and the radiation from the secondary is 5.39x10-19 W. The number here in calculated assuming the emissivity of the mirrors is 0.027 and the temperature is 275 K. If we could add a cold stop, the radiation from the primary mirror will be 5.29x10-19 W and the radiation from the secondary will be reduced to 4.65x10-19 W.

2. The thermal radiation from the polarimeter:

The radiation will be focused to the fiber pickup head after the polarimeter. Due the complicated optical path of the polarimeter, the thermal radiation from the optical components can hardly reach the fiber. Only the radiation from the last lens will contribute most picked up by the optical fiber. With the parameter of the proposed fiber Heraeus Suprasil 300 (NA ~ 0.22), the effective incident angle is 12.7 degrees and the core diameter is 200 µm. Only the radiation within this angular range will be coupled into the fiber. The thermal radiation from the last lens coupled into the fiber is thus 3.02x10-18 W if the temperature is 275K. The used distance from the last lens to the fiber is 18.41mm and the emissivity is 0.05. This is much higher than the thermal background of the sky and the telescope. Considering the transmission of the whole polarimeter is 80%, the thermal radiation from the last lens should be less than 9.78x10-19 W. The last lens needs be cooled around250 K. At 250 K the radiation generated will be 3.41x10-19 W.


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Schematics of the polarimeter. The part that needs cooling is outlined with the red box.

3. The thermal radiation from the fiber:

The radiation from the fiber itself was also considered. According to Heraeus, the index of refraction of the fiber core is 1.4571 and for the cladding it is 1.4404. A model for the fiber was generated with optical simulation tool ASAP. With such model, the thermal radiation from the cladding and the cover of the fiber is simulated. Due to the small effective cross section of the fiber, the ratio for the radiation to propagate to the fiber core is less than 0.001%. We thus neglect the background from the fiber cladding. Some experiment might be needed to verify this result in the future. However, the radiation from the fiber core to the image slicer is calculated. At 275K, it is about 1.22x10-18 W. Again, this is higher than the sky background, the fiber exit part and the focusing lens for the image slicer needs to be cooled to 250 K. The radiation will then be 1.37 x10-19 W.

4.The thermal radiation from the image slicer and spectrometer:

The spectrometer will be cooled to 77K, so the radiation is negligible for the components inside the dewar. It is more important to investigate the radiation from the components of the image slicer. Fortunately, the complicated optical path of the image slicer also helps to block the unwanted radiation to enter the spectrometer if a suitable slit is design in the dewar. With the optical model of Espandons, a 77K cold entrance slit inside the dewar with a size of 0.12x1.8mm could effectively block the unwanted radiation. However, the thermal radiation along the optical path will still be coupled into the system. The thermal radiation for this part is about 7.02 x10-19 W. The sky background is reduced to 6.65 x10-19 W, if we assume the throughput of the image slicer is 80%. Again, we need to cool this part to 250K or include it in the spectrometer dewar. The thermal radiation will be 7.94 x10-20 W if cooled to 250K.

Schematics of the image slicer. The part that needs cooling are outlined with the blue boxes on both sides.

5. Final summary

If we compare the thermal radiation from different parts, the major radiation source is the last lens of the polarimeter, then the fiber exit, slicer focusing lens, sky background, primary mirror and finally the secondary telescope mirror.

In summary, special treatments are needed to reduce the thermal background in SPIROU including: ★ cool the last lens of the polarimeter with the fiber pickup head to -30°C with TE cooler. A vacuum

or nitrogen contained chamber is needed.★ cool the focusing lenses of the image slicer and fiber exist part to -30°C with TE cooler. A vacuum

or nitrogen contained chamber is needed.


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★ cool the collimator and the focusing lens for the spectrometer to -30°C with TE cooler. A vacuum or nitrogen contained chamber is needed. Or include this part into the dewar.

★ a cooled entrance long slit in the dewar of the spectrometer is needed. The detailed size will be given after the design of SPIROU is settled.

If we further compare the thermal radiation in different cases, we find:★ polarimeter & slicer @ room temperature : 1.01x10-17 W ~ 71 ph/s/m2/nm/arcsec2.★ cooling polarimeter output lens only : 6.25x10-18 W ~ 44 ph/s/m2/nm/arcsec2.★ polarimeter output lens & slicer optics cooled : 2.47 x10-18 W ~ 17 ph/s/m2/nm/arcsec2.

By cooling both the polarimeter output optics and the image-slicer module, we can therefore reduce the instrument thermal emission in the K band by about an order of magnitude and keep it lower than the thermal emission from the telescope.


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Appendix C : preliminary study of nIR Fresnel rhombs for SPIRou

Preliminary study of the feasibility of quarter-wave retardation rhombs for SPIROU

1. Introduction:Fresnel rhombs exhibits the less chromatic effect and larger spectral range than other conventional quarter-wave retardation devices like crystalline plates. Using a thin-film coating of MgF2 on one face were occurs a total reflection, improves the achromacity of the rhombThis solution has been used with success in the two twin spectropolarimetric instruments Espadons at CFHT, Hawaii and Narval at Pic du Midi, France. The two instruments work in the spectral band 0.37 – 1µm.The present document gives the current results about the feasibility of this kind of coated rhombs in the IR bands covering 0.9-2.4 µm

2. Model

Given a material with an index of refraction n(λ) depending of the wavelength λ, the retardation between the two polarizations and // occurring at total reflection in a dielectric can be expressed by (according to Born & Wolf) :

: incidence angle

This relation is valid for a bare substrate (no thin film coating)

The model of a reflection with thin film has been done in an Excel sheet. The details are not included in the document. This Excel sheet has already been used for the Espadons and Narval instruments, only the spectral range has been changed, corresponding refractive index for both the substrate and coating have been updated.

3. Solution with optical glasses and MgF2 coating

The choice of glasses has been restricted to the OHARA glass catalog.


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3.1.Valid range of refractive index:

1. Minimum refractive indexFor non-coated glass, only a glass with an index greater than 1.497 can have a retardation of 45° (quarter-wave retardation).

For n>1.497 there is two solutions giving 45°: small angle (A1) and big angle (A2)

The solution A2 should be preferred than the A1 solution has it gives better results in term of sensitivity to incidence angle.

2. Maximum refractive indexWith an MgF2 coating, the thin film formulas work if the index of refraction of the glass is inferior to 1.61.

3.2.Minimum internal transmission of glassThe total path of light in a rhomb (with two total internal reflection) is equal to 2*h* tan(θ) with θ the angle of the Rhomb and h the aperture size of the rhomb.

The aperture of the rhomb is close to 10 mm and the angle of the rhomb between 53 and 63° (A2 solution), the total path of light in the rhomb is between 26.5 and 39.25 mm.As it is planned to have 1 quarter-wave rhomb and two half-waves rhombs for polarimetric analysis, this means 5 times the total path of a quarter-wave rhomb : at least 130 mm.In the OHARA catalog, the internal transmission is given for 10 mm thickness

3.3.Available glasses for MgF2 coatingUsing the refractive index criteria the choice of glasses in the OHARA catalog are

REFRACTIVE INDICES

Glass Code(d) Code(IR)

n2325 n1970 n1530 n1129 Abbe IR

S-TIL 2 541472 521498 1.511176 1.516261 1.521761 1.5267241 49.864406S-FTM16 593353 567471 1.55603 1.561539 1.567666 1.5735659 47.198934S-TIM 8 596392 572491 1.560749 1.566151 1.572121 1.5777844 49.177923S-TIM 5 603380 579484 1.567531 1.57306 1.579177 1.585003 48.493072S-TIM 3 613370 587479 1.57589 1.58154 1.58781 1.59381 47.906275PBM 3 613370 588533 1.578136 1.583021 1.588539 1.5940509 53.359S-TIM 2 620363 594481 1.582398 1.588056 1.594349 1.6004127 48.10049


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INTERNAL TRANSMISSION (10mm Thick)

Glass 900 1200 1600 1800 2000 2200 2400

S-TIL 2 0.998 0.997 0.995 0.987 0.97 0.942 0.917S-FTM16 0.999 0.999 0.994 0.989 0.987 0.959 0.953S-TIM 8 0.997 0.996 0.993 0.983 0.968 0.935 0.915S-TIM 5 0.998 0.998 0.994 0.982 0.966 0.923 0.902S-TIM 3 0.998 0.996 0.994 0.983 0.971 0.929 0.913PBM 3 0.999 0.998 0.995 0.984 0.969 0.936 0.917S-TIM 2 0.999 0.999 0.995 0.984 0.971 0.93 0.914

Only one glass exhibits an acceptable absorption: S-FTM16 in the 2200-2400 nm band.In the IR, all these glasses have equivalent dispersion (except PBM3 but this is an obsolete glass).

To have a comparison, in the visible (Espadons and Narval), the chosen glass for the rhomb was an equivalent to the S-BSL7 glass: nd=1.516, vd=64.1.The available glasses for SPIROU with an MgF2 coating are much more dispersive in comparison.

3.4.Performances of S-FTM16 rhomb

Thickness = 30.8 mm with an entrance aperture of 10 mm.


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3.5.Performances of S-TIL2 rhomb


3.6.Performances of S-TIM8 rhomb

Thickness = 31 mm with an entrance aperture of 10 mm.


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4. Solution with ZnSEA good IR coating on the entrance and exit face of the rhomb is mandatory due to the high index of ZnSe (n= 2.45 in the IR). The


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ZnSe Calculated Transmission Profiles

Calculated transmission profiles of Zinc Selenide (ZnSe) at 293K for substrate thicknesses between 2.0 and 4.5mm

1µm = 10 000 cm-1 ; 2µm = 5 000 cm-1 ; 2.4 µm = 4166 cm-1

4.1.MgF2 coatingOnly the A1 solution is applicable.



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4.2.Diamond CVDA2 solution is applicable


5. Other possibilitiesA different coating with an index of refraction lower than the index of refraction of the substrate may widen the chose of OHARA glasses. For example : SiO2, Al2O3, HfF4…Other materials for thin films coating are available.An Applied Optics article ( Appl.Opt. 36, N°10 April 1997 p2157, Optical and durability properties of infrared transmitting thin films) gives some index of refraction in the Ir with some durability of the different coatings.

The optical glass catalog is classified by decreasing transmission at 2400 nm.

REFRACTIVE INDICES Glass Code(d) Code(IR) n2325 n1970 n1530 n1129 Abbe IR

S-NPH 2 923189 861385 1.84214 1.85093 1.86146 1.87327 38.561325

S-FTM16 593353 567471 1.55603 1.561539 1.567666 1.573565947.198934

S-TIM28 689311 657477 1.644633 1.650622 1.657451 1.6643807 47.785795S-TIH 4 755275 717476 1.7043 1.710541 1.71784 1.7256073 47.645084S-TIH14 762265 723467 1.709159 1.71554 1.723018 1.7310194 46.708367S-TIH11 785257 743470 1.729984 1.73639 1.74397 1.7522185 47.002786S-TIH 1 717295 683474 1.67018 1.67636 1.68344 1.69075 47.494093S-TIH23 785263 744479 1.731025 1.737316 1.744751 1.7528429 47.965846


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S-TIH 3 740283 704476 1.69065 1.69685 1.70405 1.71162 47.667569S-TIH53 847238 800464 1.785306 1.792048 1.800161 1.8092673 46.469098S-TIM35 699301 666465 1.652825 1.659053 1.66615 1.6733528 46.583583S-TIM25 673321 642476 1.629881 1.635832 1.642578 1.6493303 47.603337S-TIH10 728285 692468 1.679341 1.685617 1.692863 1.7004036 46.856866S-TIH18 722292 687473 1.673842 1.680025 1.68715 1.6945255 47.387687S-TIH 6 805254 763476 1.74917 1.755582 1.763205 1.7715962 47.658016BAH32 670393 644563 1.633958 1.638994 1.64471 1.6504341 56.356711LAM58 720420 694605 1.683741 1.688768 1.694481 1.7002367 60.552847

INTERNAL TRANSMISSION (10mm Thick) Glass Code(d) Code(IR) 900 1200 1600 1800 2000 2200 2400

S-NPH 2 923189 861385 0.996 0.997 0.996 0.992 0.988 0.977 0.961S-FTM16 593353 567471 0.999 0.999 0.994 0.989 0.987 0.959 0.953S-TIM28 689311 657477 0.998 0.998 0.996 0.989 0.983 0.961 0.948S-TIH 4 755275 717476 0.999 0.997 0.994 0.987 0.981 0.961 0.942S-TIH14 762265 723467 0.999 0.999 0.996 0.988 0.982 0.961 0.942S-TIH11 785257 743470 0.998 0.999 0.996 0.989 0.982 0.964 0.942S-TIH 1 717295 683474 0.999 0.998 0.995 0.988 0.981 0.957 0.941S-TIH23 785263 744479 0.998 0.999 0.996 0.988 0.981 0.962 0.937S-TIH 3 740283 704476 0.999 0.999 0.996 0.988 0.98 0.955 0.933S-TIH53 847238 800464 0.999 0.999 0.997 0.989 0.981 0.964 0.933S-TIM35 699301 666465 0.999 0.999 0.995 0.988 0.98 0.942 0.931S-TIM25 673321 642476 0.998 0.998 0.995 0.987 0.977 0.944 0.93S-TIH10 728285 692468 0.998 0.998 0.993 0.985 0.977 0.947 0.929S-TIH18 722292 687473 0.999 0.999 0.995 0.986 0.978 0.948 0.928S-TIH 6 805254 763476 0.998 0.998 0.995 0.986 0.978 0.958 0.928BAH32 670393 644563 0.998 0.997 0.995 0.988 0.98 0.951 0.927LAM58 720420 694605 0.998 0.999 0.998 0.993 0.986 0.966 0.924

New materials arise but as the index of refraction increased, the angle of the rhomb increased with the thickness of the rhomb.

Only the S-NPH2 material seems interesting by comparison with S-FTM16.So-far only NdF3 coating seems available.


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6. Comparison matrixThe internal transmission is calculated with the thickness of the rhomb.For ZnSe transmission , the attenuation coefficient has been taken equal to 0.005 cm-1 (conservative number , data given at 10.6 µm give < 0.005 cm-1)Δδ is the difference between the maximal and minimal retard for a normal incidenceδ+i mean(°) is the mean value of the retardation for a +0.15° incidenceδ-i mean(°) is the mean value of the retardation for a -0.15° incidence

Material Coating RhombAngle(°)

ecoating (nm) rhomb thickness(mm)

Internal transmission2200 nm

Internal transmission 2400 nm

Δδ (°) δ+i

mean(°)δ–i

mean(°)

ZnSe Diamond 65.078 20.417 43 0.9787 0.9787 0.041 89.784 90.22S-NPH2 NdF3 62.2159 26.91 38 0.915 0.86 0.2687 89.196 90.8

S-FTM16 MgF2 56.996 32.13 30.8 0.874 0.8567 0.426 89.826 90.17S-TIL2 MgF2 54.067 39.45 27.6 0.848 0.7873 0.605 89.9 90.09S-TIM8 MgF2 57.203 30.518 31 0.812 0.76 0.41 89.82 90.18S-TIM2 MgF2 57.967 28.77 32 0.793 0.75 0.376 89.807 90.19S-TIM5 MgF2 57.46 30.08 31.4 0.775 0.723 0.402 89.817 90.18

ZnSe MgF2 24.942 83.5 9.3 0.995 0.995 2.824 93.12 86.7

For an optimal transition, the best solution is obviously to use a ZnSe rhomb with a diamond CVD coating. We now have to check that ZnSe is available in low-enough birefringence chunks for our purpose. This will be done in the next design stage


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Appendix D : deriving accurate RVs from nIR spectra - the telluric-line issue

The near infrared 1-2.5 micron wavelength range is known to have numerous telluric features of the Earth's Atmosphere. To obtain accurate radial velocity (RV) measurement it is crucial to mask such telluric line: they are moving on the stellar spectrum in function of the barycentric velocity correction and could blend different stellar line according on the time of the observation. Two procedures exist : (1) eliminate the wavelength bands with telluric lines from the RV computation or (2) subtract the telluric lines (by using telluric standard stars, or models, or the sigma-clipped procedure of Bailey et al 2007, PASP 119, 228). The latter option can be use with confidence only for stable and thin telluric line. The most important features are due to H2O, CO2, O2 and CH4. H2O is inhomogeneously located in the atmosphere and its quantity is strongly variable in time; it is more advisable to reject the wavelength range having water vapor lines. CO2, O2 and CH4 Earth's lines are more easily removable because such species are well mixed in the atmosphere, more stable and produce in general thin lines.

From our experience with HARPS and SOPHIE, we fix the maximum depth of « acceptable » telluric lines at 5% and reject (from the RV computation) all regions where H2O lines are deeper that this limit. CO2, O2 and CH4 lines are tolerable until a relative depth of 40-50%, using contemporaneous spectra of standards stars and a specific correction procedure (eg Bailey et al. 2007) to subtract them down to a level of better than 5%.

The IR telluric spectrum of reference is from Hinkle, Wallace and Linvingston (1995, PASP 107, 1042) and has been completed at the Kitt Peak Observatory. To estimate the ratio between Mauna Kea and Kitt Peak H2O lines we use 15 spectrums of the O9V star 10Lac (V=4.87) observed with EspaDons at CFHT, during 5 nights in Sept 04 and Jun 05. They are divided by an O9V stellar spectra (fig. 1, top) to produce a telluric spectrum. The 0.94 - 1.0 µm wavelength range is used to compare Mauna Kea and Kitt Peak telluric lines (fig. 1, bottom).

In Fig.2 we show the depth of ~110 common lines at Kitt Peak and during three nights at Mauna Kea. The depths of H2O lines at Mauna Kea are between 10% and 60% of them of Kitt Peak. On the five nights only one night (21/06) show a ratio superior at 0.31. We use this value as a reference, then a H2O lines with typical depth of 5% at Mauna Kea, have a depth of ~16% in the Kitt Peak reference spectrum.

The Y, J, H and K-band Kitt Peak telluric spectrum is showed in Fig. 3. The wavelength range usable for RV measurements (with H2O lines no deeper than 5% at Mauna Kea, ie 16% at Kitt Peak) is 0.988-1.075; 1.215-1.30; 1.52-1.75 and 2.08-2.16 µm. In the J band, O2 lines are present with a depth of ~20% and can be subtracted. In the H band, CO2 absorption are visible with a typical depth of ~30%; apart from the very strong CO2 features at ~1.57 and ~1.60 µm, they can be subtracted. In the K band, the situation is more complex with a mix of saturated H2O, CO2 and CH4 lines. A more accurate study should be done to properly estimate which part of the K-band can be used.


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Fig 1 : Top : telluric spectrum at Mauna Kea observatory obtained from EspaDons spectrum of O9V stars. Bottom : details (0.97 – 0.98 µm) on telluric spectrum at Mauna Kea (black) and KittPeak (green) Observatory. Red and blue triangle mark location of line, respectively at Mauna Kea and Kitt Peak, used to estimate the ratio of water between the two observatory.


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Fig 2 : Depth of H2O lines, in the 0.94-1.00 µm range, at Mauna Kea and Kitt Peak observatory.

Below are tables summarizing our estimate of the usable spectral range for deriving accurate RVs: band Range (in µm) with lines no deeper than 5%Y 0.988 – 1.075J 1.215 – 1.252; 1.28 - 1.30H 1.52 – 1.57; 1.585 – 1.60; 1.62 – 1.63K 2.08 – 2.16Total ~ 0.300 µm

band Range (in µm) with H2O lines no deeper than 5%; and CO2, CH4, O2 lines no deeper than 50%

Y 0.988 – 1.075J 1.215 – 1.30H 1.52 – 1.57; 1.585 – 1.60; 1.62 – 1.75K 2.08 – 2.16Total ~ 0.450 µm

Following the option used (retain wavelength range without any telluric lines deeper that 5% or accept the presence of CO2, CH4, O2 lines with depth < 50%) a domain of 0.3 or 0.45 microns is usable to compute accurate RVs. This is 3 to 4.5 times larger than the usable domain of HARPS and SOPHIE, where a wavelength range of only ~0.1 µm (0.5-0.68 µm) is used (the flux of M-dwarfs below 0.5 µm being too low to obtain accurate RVs & rejecting 0.08 µm because of telluric lines) and a RV accuracy of 1m/s is obtained for M-dwarfs.


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Fig 3 : nIR telluric spectrum at Kitt Peak (Hinkle, Wallace and Linvingston, 1995). The dark line mark the depth of 16%.


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Figure 4 illustrates the clear advantage of SPIRou over an instrument working at visible wavelengths like HARPS, thanks to both the intrinsic brightness of M dwarfs in the nIR and the large spectral domain available.

Fig 4 : Synthetic spectrum of a mid-M dwarf (~3000K) and a late-M dwarf (2200K) at visible & nIR wavelengths. The regions available for RV measurements are shown in yellow for SPIRou, and in blue for visible spectrographs such as HARPS.


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Appendix E : crushing down the activity-induced RV jitter with nIR spectropolarimetry

Apparent RV shifts do not always originate in the gravitational pull of a companion: in a rotating star, stellar surface inhomogeneities such as plages and spots can break the exact balance between light emitted in the approaching and receding stellar hemispheres. Of much interest to study the topology of stellar magnetic fields, these structures are a real burden when searching for planets with the radial-velocity method. At best, they may have short life and introduce a RV jitter that averages out on long time-scales (at the cost of more measurements though). Surface structures can however have long lifetimes (especially in late M dwarfs), possibly several years. Then, they act much like red-noise in photometric measurements and are very difficult to average out over time.

At near-IR wavelengths, the spot/photosphere brightness contrast is lower than at visible wavelengths, which decreases the impact on RVs. Assuming a black body spectral distribution for both the spot and the star, we can quantitatively estimate the effect on RV (Fig 1). For a stellar temperature of 3000 K, and a spot 300 K cooler, we found that the RV amplitude measured at 0.5 µm is 2.5 times larger than the radial-velocity measured at 2.2 µm (Fig 2). More generally, we derived the gain as a function of spot temperature, for various stellar temperatures (Fig 3). The results are very encouraging, even though the simplistic black body assumption is pessimistic. Spots should actually be brighter in the nIR (than predicted by the blackbody model).

Recently, Setiawan et al (2007 Nature, 451 38) measured RVs of the young T-Tauri star TW Hya and found RV variations with a 3.6-day period and a semi-amplitude of ~200 m/s. They used the absence of correlation between the radial velocities and the line bisectors as a strong argument in favor of a planet signal and claimed the detection of a hot Jupiter. However, Huelamo et al. (2008 A&A, arXiv:0808.2386) shows that, TW Hya being viewed mostly pole-on, the bisector analysis is mostly insensitive to spots. Furthermore, they used the CRIRES spectrograph and measured RVs of TW Hya in the nIR. They found that the true RV variability of TW Hya is lower than the instrumental RV accuracy of CRIRES (about 30 m/s), rejecting the planet interpretation. For stars as hot as TW Hya (having a large spot/photosphere temperature contrast), the gain in RV accuracy at nIR wavelengths is a factor of at least 6.7. We will carry out observations of spotted stars simultaneously at visible and nIR wavelengths to quantify further the advantage of nIR spectroscopy for estimating RVs of M dwarfs.

Given the data collected so far with HARPS (at visible wavelengths), quiet (resp moderately active) M dwarfs display a jitter of about 1 m/s (resp 5 m/s) only. Our simulation thus suggests that the nIR RV jitter from spots in moderately active M dwarfs should not exceed 2 m/s and should often be < 1m/s. Furthermore, the polarimetric capabilities of SPIRou will offer the option of modeling the activity (from the simultaneously recorded Zeeman polarisation signatures) and thus further filter out the RV jitter, giving access to the more active late M dwarfs.

We therefore conclude that the activity jitter of most M dwarfs in the nIR is below 1 m/s, demonstrating the feasibility of high RV accuracy nIR searches for habitable Earth-like planets around M dwarfs like that we propose for SPIRou.


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Fig 1 : our simulation involves a rotating sphere with a single spot (left). To obtain the integrated RV signal, we add the brightness-weighted contributions of all points at the stellar surface (right).

Fig 2 : Simulation for Tstar=3000K; Tspot=2700K; Rstar=0.3Rsun; Rspot=0.2Rstar; Prot=10d; incl=30°. With such stellar and spot parameters a jitter of K~25m/s could be observed at 0.5 micron (top); it is reduced at K~10 m/s if the observation are done at 2.2 µm (bottom).


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Fig 3 : Ratio between activity jitter in the visible (Kvis at 0.5 µm) and in the nIR (Kir at 2.2 µm) as a function of the spot temperature and for various temperatures of the star.


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spirou @ cfht : a nir échelle spectropolarimeter for ...astrolff/cfht_instruments/spirou.pdf ·...

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