Optical design of the NASA-NSF extreme precision Dopplerspectrograph concept “WISDOM”

Stuart I. Barnesa, Gabor Fureszb, Robert A. Simcoeb, Stephen A. Shectmanc, and Deborah F.Woodsd

a Stuart Barnes Optical Design (Germany);b MIT Kavli Institute for Astrophysics and Space Research (United States);

c Carnegie Observatories (United States);d MIT Lincoln Lab. (United States).

ABSTRACT

The WISDOM instrument concept was developed at MIT as part of a NASA-NSF funded study to equip the3.5 m WIYN telescope with an extremely precise radial velocity spectrometer. The spectrograph employs anasymmetric white pupil optical design, where the instrument is split into two nearly identical “Short” (380 to750 nm) and “Long” (750 to 1300 nm) wavelength channels. The echelle grating and beam sizes are R3.75/125 mmand R6/80 mm in the short and long channels respectively. Together with the pupil slicer, and octagonal torectangular fibre coupling, this permits resolving powers over R = 120k with a 1.2′′ diameter fibre on the sky. Afactor of two reduction in the focal length between the main collimator OAP and the transfer collimator ensures avery compact instrument, with a small white pupil footprint, thereby enabling small cross-dispersing and cameraelements. A dichroic is used near the white pupil to split each of the long and short channels into two, so thatthe final spectrograph has 4 channels; namely “Blue”, “Green”, “Red” and “NIR”. Each of these channels hasan anamorphic VPH grism for cross-dispersion, and a fully dioptric all-spherical camera objective. The spectralfootprints cover 4k×4k and 6k×6k CCDs with 15µm pixels in the short “Blue” and “Green” wavelength channels,respectively. A 4k×4k CCD with 15µm pixels is used in the long “Red” channel, with a HgCdTe 1.7µm cutoff4k×4k detector with 10um pixels is to be used in the long “NIR” channel. The white pupil relay includes aMangin mirror very close to the intermediate focus to correct the white pupil relay Petzval curvature before itis swept into a cylinder by the cross-dispersers. This design decision allows each of the dioptric cameras to befully optimised and tested independently of the rest of the spectrograph. The baseline design for the camerasalso ensures that the highest possible (diffraction limited) image quality is achieved across all wavelengths, whilealso ensuring insensitivity of spot centroid locations to variations in the pupil illumination. This insensitivity isproven to remain even in the presence of reasonable manufacturing and alignment tolerances. Fully ray-tracedsimulations of the spectral formats are used to demonstrate the optical performance, as well as to provide pre-first-light data that can be used to optimise the data reduction pipeline.

Keywords: Extreme precision radial velocity spectrograph, asymmetric white pupil echelle spectrograph,anamorphic VPH grisms.

1. INTRODUCTION

The WISDOM instrument concept was developed as part of a NASA-NSF funded study to equip the 3.5 mWIYN telescope with an extremely precise radial velocity spectrometer. A general overview of the instrument ispresented elsewhere in these proceedings by Furesz et. al.1 WISDOM is fed from the telescope using a combinationof octagonal and rectangular core fibres, together with an optical double scrambler. The fibre feed includes anADC and tip-tilt mirror for maximising throughput, as well as a novel pupil slicer. Detailed descriptions of theseaspects of the instrument are also presented elsewhere in these proceedings by Furesz et. al.2 This paper willconcentrate on the spectrograph optical design.

Ground-based and Airborne Instrumentation for Astronomy VI, edited by Christopher J. Evans, Luc Simard, Hideki TakamiProc. of SPIE Vol. 9908, 99086J · © 2016 SPIE · CCC code: 0277-786X/16/$18 · doi: 10.1117/12.2232352

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2. OVERVIEW

The WISDOM spectrograph is split into a “Short” wavelength channel (λλ = 380 to 750 nm) and a “Long”wavelength channel (λλ = 750 to 1300 nm). Both the short wavelength channel (SWC) and long wavelengthchannel (LWC) spectrographs follow very similar asymmetric white pupil optical designs∗. That is, they bothhave primary off-axis parabolic collimators with a focal length f1 = 1000 mm, however the collimated beamsizes are 125 mm and 80 mm in the SWC and LWC channels respectively. The slightly ellipsoidal (k ≈ −0.91)secondary (or transfer) collimator has a focal length of f2 = 500 mm. The asymmetry factor (f1/f2 = 2) is usedto reduce the overall size of the instrument, while also allowing significantly smaller cross-dispersers and cameralenses than would be possible with symmetric designs. An asymmetric design can also be used more efficientlywith VPH cross-dispersing elements. The SWC and LWC spectrographs have echelle gratings with differentblaze angles (θB) and line densities (T ). That is, in the SWC θB = 75.1◦ (R3.75) and T = 31.6 lines/mm whilethe LWC grating has θB = 80.7◦ (R6.11), and T = 13.33 lines/mm. Together with the pupil slicer, and octagonalto rectangular fibre coupling, this permits resolving powers (R = λ/∆λ) over R = 120, 000 with a 1.2′′ fibre onthe sky.

Near the location of the white pupil, a dichroic is used to again divide each of the short and long wavelengthchannels†. This maximizes the (average) spatial order separation, while minimizing the (combined) detectorreal estate required for complete wavelength coverage. This splitting also makes it possible to fully optimizethe efficiency of the VPH cross-disperser given the relatively narrow band-pass, and it also allows the highestperformance antireflection (and reflective) coatings to be applied to all single-channel optics. The final geometryof the WISDOM spectrograph is the result of an optimization of the wavelength distributions across the fouravailable channels, given a limited number of detector choices, with the constraint that each resolution elementmust be sampled by at least 3.5 pixels, and that there also be sufficient (minimum) inter-order separation in allfour channels for the multiple-fibre entrance slit. Some additional effort is made to arrange the reflection angle ofthe dichroic, together with the VPH grism parameters, so that the optical axes of the three shorter wavelengthcameras are parallel to the optical axes of the two collimators. This was done in order to simplify the mechanicalassembly, via an easily identified reference axis (that will also be used optically for additional alignment tasks),and also to minimize the overall instrument volume. This adjustment was not performed on the NIR camera inorder to allow the detector to be raised somewhat closer to the top of the vacuum tank. Further details of theintermediate focus Mangin mirror, the VPH grisms, and the four camera objectives will be given below. Fig. 1shows the layout of the SWC spectrograph. A summary of the spectrograph parameters can be found in Table 1.Image quality details are also given below.

Echelle grating

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collimator (M2)

“Blue” camera “Green” camera

“Green” VPH grism

Intermediate “Mangin” mirror

Dichroic

“Blue” VPH grism“Blue” camera

Entrance slit & input relay

Figure 1. The optical layout of the WISDOM short wavelength channel (SWC) spectrograph. The (z-)distance from theprimary mirror vertex to the detector optical plane is 1575 mm. The echelle dispersion direction is normal to the page.Note that the LWC spectrograph is very similar in form and is placed immediately adjacent to the SWC, but with aflipped echelle dispersion direction. See Furesz et. al1 elsewhere in this proceedings for further details.

∗Existing examples of this design form include SALT HRS (Barnes et al., 20083) and KiwiSpec (Gibson et al., 20124).†Multi-channel designs of this type have been discussed in Barnes et al., 20085 (i.e., the “Q-Spec” concept for the GMT

HROS) and Barnes et al., 20126 (i.e., the “KiwiSpec-GHOST” concept for Gemini).

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Table 1. Summary of the WISDOM spectrograph optical properties.

Short wavelength channel (SWC) Long wavelength channel (LWC)

Channel: “Blue” “Green” “Red” “IR”Wavelength range: 378.7–495.2 nm 483.4–769.2 nm 749.7–952.2 nm 934.2–1316.1 nmOrder numbers: 161–124, (n = 38) 126–80, (n = 47) 197–156, (n = 42) 158–113, (n = 46)Resolving power: R = 120k (n = 3.54 pixels) R = 120k (n = 3.50 pixels)Beam size: B = 125 mm B = 80 mmPrimary collimator: f1 = 1000 mm (f/8 OAP, θ = 6.5◦) f1 = 1000 mm (f/12.5 OAP, θ = 6.5◦)Echelle:

Blaze angle: θB = 75.1◦ (R3.75) θB = 80.7◦ (R6.11)Line density: T = 31.6 mm-1 T = 13.33 mm-1

Ruled area: 130 × 400 mm 100 × 400 mmMangin mirror:

Glass, size: S-FSL5, 25 × 120 mm S-FSL5, 25 × 145 mmThic., off-axis dist.: t = 8.7 mm, ∆y ≈ 21.5 mm t = 8.7 mm, ∆y ≈ 21.5 mm

Secondary collimator: f2 = 500 mm, k ≈ −0.91 f2 = 500 mm, k ≈ −0.91Cross-dispersing grisms:

VPH line density: 1125 mm-1 620 mm-1 945 mm-1 565 mm-1

VPH AOI (cwl): 9.45◦ 7.35◦ 15.62◦ 12.19◦

Prism glass: S-BSL7 S-BSL7 S-BSL7 S-BSL7Prism AOI θi = 45.0◦ θi = 45.0◦ θi = 45.0◦ θi = 50.0◦

Prism apex angle: α = 27.6◦ α = 27.8◦ α = 27.9◦ α = 30.6◦

Anamorphic factor: Bout/Bin = 1.25 Bout/Bin = 1.25 Bout/Bin = 1.08 Bout/Bin = 1.31Cameras:

Focal length: fcam = 425.1 mm fcam = 425.1 mm fcam = 258.2 mm fcam = 172.1 mmFocal ratio (X): f/Dx = 6.8 f/Dx = 6.8 f/Dx = 6.5 f/Dx = 4.3Focal ratio (Y): f/Dy = 5.5 f/Dy = 5.5 f/Dy = 6.0 f/Dy = 3.3

Detector:Type: CCD CCD CCD H4RGFormat (approx.): 4096 × 4096 6144 × 6144 4096 × 4096 4096 × 4096Pixel size: 15µm 15µm 15µm 10µm

3. INTERMEDIATE FOCUS “MANGIN” MIRROR TRADE STUDY

The white pupil relay includes correcting lens with a reflecting internal surface very close to the intermediatefocus. The use of a “Mangin” mirror element is also described in detail by Furesz et al. 2014.7 Its purpose is tocorrect the white pupil relay Petzval curvature present at the intermediate focus before it is swept into a cylinderby the cross-dispersers. This eliminates the requirement to include a cylindrical lens very close to the detector inorder to correct this curvature. Invariably, as is common in most other spectrographs of this form, a cylindrical(or otherwise non-rotationally symmetric) lens cannot provide complete correction, and its placement very closeto the detector surface complicates the design and alignment of the detector assembly. The use of an intermediatefocus Mangin mirror allows each of the dioptric cameras to be fully optimised and tested independently of therest of the spectrograph without placing any constraints on the actual form of the camera lenses.

The Mangin mirror to be used in WISDOM is formed from an off-axis section of a concave/convex singlet lens.This has proven to be possible after a trade-study between (i) spherical and (ii) toroidal designs, in addition to acomparison with (iii) designs without a Mangin mirror element (see Figure 2). For each of the studies (i) & (ii),a spectrograph model was created with a paraxial camera lens and a flat detector plane. However, study (iii)used a paraxial camera together with a cylindrical detector plane. The latter model represents the “classical”form of white pupil spectrograph, such as has been implemented in FEROS,8 UVES,9 HRS10,11 HARPS12 etc,but with a “perfect” field-flattening lens. While the toroidal Mangin lens design gave the best image quality fora single (central) field location, a spherical design ensured the best average image quality over the extent of theWISDOM entrance slit. The uncorrected “classical” design has the worst overall image quality, even though themodel assumes perfect correction of the Petzval curvature by using a cylindrical detector.

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It should also be emphasised that this result remains valid independently of the form of the spectrograph cameraoptics, and therefore the result can be transferred to any scaling of this form of instrument. Furthermore, toclarify, it is possible to ensure that all ghosts (both front surface reflections, and internal double-reflections) canbe fully mitigated by slightly adjusting the “y-axis” offset of the parent lens. This effectively introduces a smallwedge in the lens, thereby allowing the ghosts to be redirected away from any other element, and image qualityis not affected. A high quality anti-reflection coating can be applied to the transmissive surface of the Manginmirror in order to further mitigate against stray light.

(i) Spherical (ii) Toridal (iii) None

Figure 2. Results from the Mangin mirror trade-study for a (i) spherical lens, (ii) a toroidal lens, and (iii) no lens butassuming a cylindrical detector. In each case, the image quality averaged over all wavelengths (within the free spectralrange) is shown as a function of the point of origin at the entrance slit. The format of the nominal entrance slit to be usedfor WISDOM is shown (black lines). A Mangin mirror formed from a section of a fully spherical lens clearly produces thebest and most uniform image quality across an extended entrance slit.

4. ANAMORPHIC VPH GRISMS

The multi-channel design of WISDOM is ideal for the use of volume phase holographic (VPH) gratings cross-dispersers. Based on experience with similar instruments, the peak efficiency of VPH grating cross-disperserscan exceed 85 to 90% for the specified wavelength ranges and line densities. Given the conservative bandwidthsof each channel, the minimum cross-disperser efficiency should also exceed 70 to 75%. In addition, the efficiencyenvelope of the VPH gratings can in principle be tuned to mitigate other aspects of the design.

Each of the four VPH gratings are designed to be used together with an S-BSL7 prism on the entranceface. This provides a spatial anamorphic factor ranging from Bout/Bin = 1.25 in the Blue/Green channels, toBout/Bin = 1.08 and 1.31 in the Red and NIR channels respectively The anamorphism allows a spatial compressionof slit image, which increases the effective inter-order separation, while also slightly reducing the number of pixelsrequired to read out the slit image. As noted above, the orientation and dispersive properties of these gratingscan be tuned in order to position the camera optical axes. Finally, it is also important to introduce a slightLittrow angle at the grating surface in order to avoid VPH recombination ghosts (Burgh et al., 200713).

5. CAMERAS AND DETECTORS

The focal lengths, and fields of view of each of the cameras have been adjusted so that a minimum of 3.5 pixelssample each R ≈ 120 000 resolution element. The baseline design for the camera lenses ensures that the highestpossible (near diffraction limited) image quality is achieved across all wavelengths, while also ensuring insensi-tivity of spot centroids to any variation in the pupil illumination. The preliminary camera design (see Fig. 3) has9 all spherical lenses in 7 groups in addition to a fused silica detector entrance window. Aspheric and off-axisand/or decentred elements have been completely avoided so as to limit the additional risks and costs associated

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with these items. It is emphasised that the number of camera optical elements has a negligible effect on theoverall instrument throughput owing the fact that all surfaces will have excellent anti-reflection coatings thanksto the narrow band-pass of each channel in the 4-channel design. An effort has been made to make all fourcameras as nearly similar to one another as possible, however given the large variation in focal length and fieldof view, the final camera designs differ slightly. It has also been possible to ensure a high degree of telecentricity,as a potential mitigation against any possible defocus induced image drift. This requirement, together with thefact that the entrance pupil is actually smaller than the size of the dectector, results in a somewhat unusualcamera layout. Nevertheless, the preliminary design form has proven to be extremely compact; i.e., the lengthof the green camera is ∼530 mm for a 425 mm focal length. In order to further mitigate against the potential forfar-field illumination variations to also cause centroid drifts, the optical prescriptions of each camera are furthertuned in order to minimize this possibility (see Sec. 7 for further details). The image quality of the green channelcamera is shown in Fig. 4 and 5.

Figure 3. The preliminary camera objective for the WISDOM “Green” channel. This camera has a focal length of 425 mmand is 530 mm in length. The anamorphic VPH grism cross-disperser is also shown on the left. The image quality ofWISDOM with this camera is shown in Fig. 4 and 5. In addition to being near-diffraction limited, the camera focal planeis highly telecentric. The camera has also been optimised to ensure immunity to any pupil illumination variations.

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Figure 4. Image quality of the preliminary WISDOM green channel camera. The spot diagrams uniformly cover thespectral format in this channel (see Fig. 6). Each box is one pixel square. The RMS diameter (φrms) is shown above eachpixel. Note that each pixel maintains 100% ensquared energy. See Fig. 5 for the corresponding PSF images.

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λλ = 760.6 − 768.2 nm

Figure 5. Image quality of the preliminary WISDOM green channel camera. The point source PSF images uniformlycover the spectral format in this channel (see Fig. 6). Each box is one resolution element (3.5 pixels) square. The Strehlratio (S) is shown above each box. See Fig. 4 for the corresponding spot diagrams.

The spectral footprints cover 4k×4k and 6k×6k CCDs with 15µm pixels in the “Blue” and “Green” wave-length channels respectively. A 4k×4k CCD with 15µm pixels is used in the “Red” channel, with a HgCdTe1.7µm cutoff 4k×4k detector with 10µm pixels is to be used in the “NIR” channel. See Fig. 6 for the greenchannel format together with a map of RMS image quality. The formats for the other channels are similar (fortheir respective wavelength ranges) and have identical image quality properties (scaled to the nominal pixel size).

6. SYNTHETIC IMAGES

Synthetic spectral images for each of the WISDOM channels have been created using ray-tracing methods withthe EchMod package (Barnes 201214). This makes it possible to create fully realistic spectra during the initialinstrument design phase and ahead of final construction (see Fig. 7 for an example). The intention of this processis to fully validate the data reduction pipeline well in advance of instrument commissioning. In addition, thesemethods also allow the verification of instrumental stability, given the possibility of updating and adjusting theinstrument optical model according to mechanical, environmental, and illumination perturbations. The issue ofpupil illumination variability is further discussed in Sec. 7 below.

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(a) Full frame (b) Segments

Figure 7. Synthetic spectra for the WISDOM “Green” channel. Left (a) shows a full frame spectrum with a solar-likeinput. Right (b) shows segments of full frame spectra (solar-like and calibration) taken from the top, middle, and bottomof the frame. This makes it possible to see the generous inter-slice and inter-order separations.

7. PUPIL ILLUMINATION STABILITY STUDY

While every effort is taken in order to design the mechanical and environmental mountings and enclosures so asto ensure the absolute stability of the WISDOM spectrograph, in addition to excellent wavelength calibrationaccuracy, the radial velocity precision also relies on having very stable illumination of the spectrograph optics.For the WIYN telescope instrument, this issue is addressed by the design of the pupil slicer and scramblingfibre optic train, details of which can be found elsewhere in these proceedings.2 Nevertheless, the possibilitystill remains that some residual illumination variability will remain, and that this will impart a systematic offsetin any one radial velocity observation. In order to examine and address this concern, a detailed study of thespectrographs performance was made in the presence of a range of pupil illumination variations.

The method follows that of various pervious similar studies (e.g., Furesz et. al, 20147 and Sturmer et al, 201415).That is, first, a set of ray-traces was performed where the inner 50% and the outer 50% of the entrance pupil wasilluminated. These ray-traces use a grid of some 51 wavelength spaced uniformly across all orders. Next, for eachsimulated “observation” a linear combination of these two inner and outer ray traces was made, and the locationof the resulting spot was compared to that of a spot created from a fully (uniformly) illuminated ray-trace. Theassumption behind this approach is that the combination of octagonal and rectangular fibres which are used inWISDOM together with a fibre double-scrambler (see op. cit. above), will ensure complete azimuthal scrambling.However, it remains possible that slight radial illumination variations will remain, and furthermore, that thesevariations will not necessarily be stable in time (e.g., Avila et. al, 201216).

As previous work has demonstrated (see op. cit. above), it is possible to design the spectrograph optics inorder to mitigate these remaining pupil variations. In the WISDOM spectrograph, these concerns are largelyeliminated simply by ensuring the highest possible image quality. However, during the final iteration of thecamera optics, a pupil illumination stability factor was included in the merit function, and by this means the

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ideal optical design could be rendered absolutely impervious to any radial pupil illumination variability. However,this does not necessarily imply that the as-built spectrograph will also be impervious as this immunity can only berealised if the spectrograph optics are built and aligned exactly as specified. For the purposes of illustrating thiseffect, from a pool of 100 randomly generated models with standard manufacturing and alignment tolerances‡, aset of 10 spectrograph models were selected for detailed analysis. It was found that a ±1% illumination variationresults in an RMS velocity shift of 46 cms-1, with a linearly increasing effect as a function of increasing pupilillumination fraction. With somewhat tighter tolerances, a ±1% illumination variation was found to result in anRMS velocity shift of 30 cms-1. The implication is that when the spectrograph has been fully assembled, there isa statistically significant chance that the as-built performance will be sensitive to pupil illumination variations atthe RMS values. Nevertheless, there is also a non-zero probability that the performance will be equal to the idealdesign simply as a matter of chance; that is, that the illumination sensitivity contribution of individual elementsadds to zero. However, it is concluded that that the inclusion of manufacturing and alignment tolerances iscritical to the spectrographs precision radial velocity performance. Furthermore, it is suggested that this effectwill be present at some level in all precision radial velocity spectrographs.

8. SUMMARY

The detailed optical design of an extremely precise radial velocity spectrometer has been presented. This con-cept was developed as part of a NASA-NSF funded study to equip the 3.5 m WIYN telescope with an EPRVinstrument. By using a dual-spectrograph 4-channel design with an asymmetric white pupil form, togetherwith anamorphic VPH cross-dispersing grisms, and simple all-spherical dioptric cameras, an extremely com-pact, highly efficient, low risk concept has been demonstrated. The excellent image quality, high telecentricty,and immunity to pupil illuminations variations all contribute to improving the precision radial velocity perfor-mance. This concept study also introduces the technique of including the effects of manufacturing and alignmenttolerances as part of the pupil illumination stability contribution to the radial velocity error budget.

ACKNOWLEDGMENTS

This work was funded in part through the NASA program NNH14ZDA001N-EPDS. This research has made useof NASA’s Astrophysics Data System.

REFERENCES

[1] Furesz, G., Barnes, S. I., Buchhave, L. A., Egan, M. D., Foster, R., Hellickson, T., Malonis, A., Phillips,D. F., Shectman, S. A., Simcoe, R. A., Walsworth, R. L., Winn, J., and Woods, D. F., “WISDOM: theWIYN spectrograph for doppler monitoring: a NASA-NSF concept for an extreme precision radial velocityinstrument in support of TESS,” in [Ground-based and Airborne Instrumentation for Astronomy VI ], Evans,C. J. and Takami, H., eds., Proc. SPIE 9908 (2016).

[2] Furesz, G., Pawluczyk, R., and Fournier, P., “Fiber link design for the NASA-NSF extreme precision dopplerspectrograph concept “WISDOM”,” in [Ground-based and Airborne Instrumentation for Astronomy VI ],Evans, C. J. and Takami, H., eds., Proc. SPIE 9908 (2016).

[3] Barnes, S. I., Cottrell, P. L., Albrow, M. D., Frost, N., Graham, G., Kershaw, G., Ritchie, R., Jones, D.,Sharples, R., Bramall, D., Schmoll, J., Luke, P., Clark, P., Tyas, L., Buckley, D. A. H., and Brink, J.,“The optical design of the Southern African Large Telescope high resolution spectrograph: SALT HRS,” in[Ground-based and Airborne Instrumentation for Astronomy II ], Proc. SPIE 7014, 70140K (July 2008).

[4] Gibson, S., Barnes, S. I., Hearnshaw, J., Nield, K., Cochrane, D., and Grobler, D., “KiwiSpec - an advancedspectrograph for high resolution spectroscopy: prototype design and performance,” in [Ground-based andAirborne Instrumentation for Astronomy IV ], Proc. SPIE 8446, 844648 (Sept. 2012).

[5] Barnes, S. and MacQueen, P., “Q-Spec: a concept for the Giant Magellan Telescope high resolution opticalspectrograph,” in [Ground-based and Airborne Instrumentation for Astronomy II ], Proc. SPIE 7014, 70141H(July 2008).

‡The centration and tip/tilt of each lens element was found to have the highest sensitivity.

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[6] Barnes, S. I., Gibson, S., Nield, K., and Cochrane, D., “KiwiSpec - an advanced spectrograph for highresolution spectroscopy: optical design and variations,” in [Ground-based and Airborne Instrumentation forAstronomy IV ], Proc. SPIE 8446, 844688 (Sept. 2012).

[7] Furesz, G., Epps, H., Barnes, S., Podgorski, W., Szentgyorgyi, A., Mueller, M., Baldwin, D., Bean, J.,Bergner, H., Chun, M.-Y., Crane, J., Evans, J., Evans, I., Foster, J., Gauron, T., Guzman, D., Hertz,E., Jordan, A., Kim, K.-M., McCracken, K., Norton, T., Ordway, M., Park, C., Park, S., Plummer, D.,Uomoto, A., and Yuk, I.-S., “The G-CLEF spectrograph optical design,” in [Ground-based and AirborneInstrumentation for Astronomy V ], Proc. SPIE 9147, 91479G (July 2014).

[8] Kaufer, A., Wolf, B., Andersen, J., and Pasquini, L., “FEROS, the fiber-fed extended range optical spec-trograph for the ESO 1.52-m telescope.,” The Messenger 89, 1–4 (Sept. 1997).

[9] Dekker, H., D’Odorico, S., Kaufer, A., Delabre, B., and Kotzlowski, H., “Design, construction, and perfor-mance of UVES, the echelle spectrograph for the UT2 Kueyen Telescope at the ESO Paranal Observatory,”in [Optical and IR Telescope Instrumentation and Detectors ], Iye, M. and Moorwood, A. F., eds., Proc.SPIE 4008, 534–545 (Aug. 2000).

[10] Tull, R. G., “High-resolution fiber-coupled spectrograph of the Hobby-Eberly Telescope,” in [Optical Astro-nomical Instrumentation ], D’Odorico, S., ed., Proc. SPIE 3355, 387–398 (July 1998).

[11] MacQueen, P. J., South, B. J., Strubhar, J. L., Wesley, G. L., Odoms, P. S., Edmonston, R. D., and Barnes,S. I., “The Hobby Eberly Telescope High Resolution Spectrograph upgrade,” in [Ground-based and AirborneInstrumentation for Astronomy ], Evans, C. J. and Takami, H., eds., Proc. SPIE 9908 (2016).

[12] Pepe, F., Mayor, M., Rupprecht, G., Avila, G., Ballester, P., Beckers, J.-L., Benz, W., Bertaux, J.-L.,Bouchy, F., Buzzoni, B., Cavadore, C., Deiries, S., Dekker, H., Delabre, B., D’Odorico, S., Eckert, W.,Fischer, J., Fleury, M., George, M., Gilliotte, A., Gojak, D., Guzman, J.-C., Koch, F., Kohler, D., Kot-zlowski, H., Lacroix, D., Le Merrer, J., Lizon, J.-L., Lo Curto, G., Longinotti, A., Megevand, D., Pasquini,L., Petitpas, P., Pichard, M., Queloz, D., Reyes, J., Richaud, P., Sivan, J.-P., Sosnowska, D., Soto, R.,Udry, S., Ureta, E., van Kesteren, A., Weber, L., Weilenmann, U., Wicenec, A., Wieland, G., Christensen-Dalsgaard, J., Dravins, D., Hatzes, A., Kurster, M., Paresce, F., and Penny, A., “HARPS: ESO’s comingplanet searcher. Chasing exoplanets with the La Silla 3.6-m telescope,” The Messenger 110, 9–14 (Dec.2002).

[13] Burgh, E. B., Bershady, M. A., Westfall, K. B., and Nordsieck, K. H., “Recombination Ghosts in LittrowConfiguration: Implications for Spectrographs Using Volume Phase Holographic Gratings,” PASP 119,1069–1082 (Sept. 2007).

[14] Barnes, S. I., “EchMod: a MATLAB toolbox for modeling high resolution echelle spectrographs,” in [OpticalSystems Design ], Proc. SPIE 8550 (2012).

[15] Sturmer, J., Stahl, O., Schwab, C., Seifert, W., Quirrenbach, A., Amado, P. J., Ribas, I., Reiners, A.,and Caballero, J. A., “CARMENES in SPIE 2014. Building a fibre link for CARMENES,” in [Advances inOptical and Mechanical Technologies for Telescopes and Instrumentation ], Proc. SPIE 9151, 915152 (July2014).

[16] Avila, G., “FRD and scrambling properties of recent non-circular fibres,” in [Ground-based and AirborneInstrumentation for Astronomy IV ], Proc. SPIE 8446, 84469L (Sept. 2012).

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