Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy

Abstract

An important technique for discovering and characterizing planets beyond our solar system relies upon measurement of weak Doppler shifts in the spectra of host stars induced by the influence of orbiting planets. A recent advance has been the introduction of optical frequency combs as frequency references. Frequency combs produce a series of equally spaced reference frequencies and they offer extreme accuracy and spectral grasp that can potentially revolutionize exoplanet detection. Here we demonstrate a laser frequency comb using an alternate comb generation method based on electro-optical modulation, with the comb centre wavelength stabilized to a molecular or atomic reference. In contrast to mode-locked combs, the line spacing is readily resolvable using typical astronomical grating spectrographs. Built using commercial off-the-shelf components, the instrument is relatively simple and reliable. Proof of concept experiments operated at near-infrared wavelengths were carried out at the NASA Infrared Telescope Facility and the Keck-II telescope.

ARTICLE

Received 27 Aug 2015 | Accepted 10 Dec 2015 | Published 27 Jan 2016

X. Yi1, K. Vahala1, J. Li1, S. Diddams2,3, G. Ycas2,3, P. Plavchan4, S. Leifer5, J. Sandhu5, G. Vasisht5, P. Chen5,P. Gao6, J. Gagne7, E. Furlan8, M. Bottom9, E.C. Martin10, M.P. Fitzgerald10, G. Doppmann11 & C. Beichman8

An important technique for discovering and characterizing planets beyond our solar system relies upon measurement of weak Doppler shifts in the spectra of host stars induced by the inuence of orbiting planets. A recent advance has been the introduction of optical frequency combs as frequency references. Frequency combs produce a series of equally spaced reference frequencies and they offer extreme accuracy and spectral grasp that can potentially revolutionize exoplanet detection. Here we demonstrate a laser frequency comb using an alternate comb generation method based on electro-optical modulation, with the comb centre wavelength stabilized to a molecular or atomic reference. In contrast to mode-locked combs, the line spacing is readily resolvable using typical astronomical grating spectrographs. Built using commercial off-the-shelf components, the instrument is relatively simple and reliable. Proof of concept experiments operated at near-infrared wavelengths were carried out at the NASA Infrared Telescope Facility and the Keck-II telescope.

1 Department of Applied Physics and Materials Science, Pasadena, California 91125, USA. 2 National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305, USA. 3 Department of Physics, University of Colorado, 2000 Colorado Avenue, Boulder, Colorado 80309, USA. 4 Department of Physics, Missouri State University, 901 S National Avenue, Springeld, Missouri 65897, USA. 5 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, California 91109, USA. 6 Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125, USA. 7 Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road, Washington, District of Columbia 20015, USA. 8 NASA Exoplanet Science Institute, California Institute of Technology, Pasadena, California 91125, USA. 9 Department of Astronomy, California Institute of Technology, Pasadena, California 91125, USA. 10 Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095, USA. 11 W.M. Keck Observatory, Kamuela, Hawaii 96743, USA. Correspondence and requests for materials should be addressed to K.V. (email: mailto:[email protected]

Web End [email protected] ) or to C.B. (email: mailto:[email protected]

Web End [email protected] ).

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DOI: 10.1038/ncomms10436 OPEN

Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy

ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10436

The earliest technique for the discovery and characterization of planets orbiting other stars (exoplanets) is the Doppler or radial velocity (RV) method whereby small periodic

changes in the motion of a star orbited by a planet are detected via careful spectroscopic measurements1. The RV technique has identied hundreds of planets ranging in mass from a few times the mass of Jupiter to less than an Earth mass, and in orbital periods from less than a day to over 10 years (ref. 2). However, the detection of Earth-analogues at orbital separations suitable for the presence of liquid water at the planets surface, that is, in the habitable zone3, remains challenging for stars like the Sun with RV signatures o0.1 m s 1 (DV/co3 10 10) and periods

of a year (B108 sec to measure three complete periods). For cooler, lower luminosity stars (spectral class M), however, the habitable zone moves closer to the star which, by application of Keplers laws, implies that a planets RV signature increases, B0.5 m s 1 (DV/co1.5 10 9), and its

orbital period decreases, B30 days (B107 s to measure three periods). Both of these effects make the detection easier. But for M stars, the bulk of the radiation shifts from the visible wavelengths, where most RV measurements have been made to date, into the near-infrared. Thus, there is considerable interest among astronomers in developing precise RV capabilities at longer wavelengths.

Critical to precision RV measurements is a highly stable wavelength reference4. Recently a number of groups have undertaken to provide a broadband calibration standard that consists of a comb of evenly spaced laser lines accurately anchored to a stable frequency standard and injected directly into the spectrometer along with the stellar spectrum59. While this effort has mostly been focused on visible wavelengths, there have been successful efforts at near-IR wavelengths as well1012. In all of these earlier studies, the comb has been based on a femtosecond mode-locked laser that is self-referenced1315, such that the spectral line spacing and common offset frequency of all lines are both locked to a radio frequency standard. Thus, laser combs potentially represent an ideal tool for spectroscopic and RV measurements.

However, in the case of mode-locked laser combs, the line spacing is typically in the range of 0.11 GHz, which is too small to be resolved by most astronomical spectrographs. As a result, the output spectrum of the comb must be spectrally ltered to create a calibration grid spaced by 410 GHz, which is more commensurate with the resolving power of a high-resolution astronomical spectrograph8. While this approach has led to spectrograph characterization at the cm s 1 level16, it nonetheless increases the complexity and cost of the system.

In light of this, there is interest in developing photonic tools that possess many of the benets of mode-locked laser combs, but that might be simpler, less expensive and more amenable to hands-off operation at remote telescope sites. Indeed, in many RV measurements, other system-induced errors and uncertainties can limit the achievable precision, such that a frequency comb of lesser precision could still be equally valuable. For example, one alternative technique recently reported is to use a series of spectroscopic peaks induced in a broad continuum spectrum using a compact FabryPerot interferometer1719. While the technique must account for temperature-induced tuning of the interferometer, it has the advantage of simplicity and low cost. Another interesting alternative is the so-called Kerr comb or microcomb, which has the distinct advantage of directly providing a comb with spacing in the range of 10100 GHz, without the need for ltering20. While this new type of laser comb is still under development, there have been promising demonstrations of full microcomb frequency control21,22 and in the future it could be possible to fully integrate such a microcomb on only a few square centimetres of silicon, making a very robust

and inexpensive calibrator. Another approach that has been proposed is to create a comb through electro-optical modulation of a frequency-stabilized laser23,24.

In the following, we describe a successful effort to implement this approach. We produce a line-referenced, electro-optical modulation frequency comb (LR-EOFC) B1559.9 nm in the astronomical H band (1,5001,800 nm). We discuss the experimental set-up, laboratory results and proof of concept demonstrations at the NASA Infrared Telescope Facility (IRTF) and theW. M. Keck observatory (Keck) 10 m telescope.

ResultsComb generation. A LR-EOFC is a spectrum of lines generated by electro-optical modulation of a continuous-wave laser source2529 which has been stabilized to a molecular or atomic reference (for example, f0 fatom). The position of the comb teeth (fN f0Nfm,

N is an integer) has uncertainty determined by the stabilization of f0 and the microwave source that provides the modulation frequency fm. However, the typical uncertainty of a microwave source can be sub-Hertz when synchronized with a compact Rb clock and moreover can be global positioning system (GPS)-disciplined to provide long-term stability12. Thus, the dominant uncertainty in comb tooth frequency in the LR-EOFC is that of f0.

The schematic layout for LR-EOFC generation is illustrated in Fig. 1 and a detailed layout is shown in Fig. 2. All components are commercially available off-the-shelf telecommunications components. Pictures of the key components are shown in the left column of Fig. 1. The frequency-stabilized laser is rst pre-amplied to 200 mW with an Erbium-Doped Fibre Amplier (EDFA, model: Amonics, AEDFA-PM-23-B-FA) and coupled into two tandem lithium niobate (LiNbO3) phase modulators (Vp 3.9

V at 12 GHz, RF input limit: 33 dBm). The phase modulators are driven by an amplied 12 GHz frequency signal at 32.5 and30.7 dBm, and synchronized by using microwave phase shifters. This initial phase modulation process produces a comb having B40 comb lines (E2p V

drive/Vp), or equivalently 4 nm bandwidth. This comb is then coupled into a LiNbO3 amplitude modulator with 1820 dB distinction ratio, driven at the same microwave frequency by the microwave power recycled from the phase modulator external termination port. The modulation index of p/2 is set by an attenuator and the phase offset of the two amplitude modulator arms is set and locked to p/2. Microwave phase shifters are used to align the drive phase so that the amplitude modulator gates-out only those portions of the phase modulation that are approximately linearly chirped with one sign (that is, parabolic phase variation in time). A nearly transform-limited pulse is then formed when this parabolic phase variation is nullied by a dispersion compensation unit using a chirped bre Bragg grating with 8 ps nm 1 dispersion. A 2 ps full-width at half-maximum pulse is measured after the bre grating using an autocorrelator. Owing to this pulse formation, the duty cycle of the pulse train reaches below 2.5%, boosting the peak intensity of the pulses. These pulses are then amplied in a second EDFA (IPG Photonics, EAR-5 K-C-LP). For an average power of 1 W, peak power (pulse energy) is 40 W (83 pJ). The amplied pulses are then coupled into a 20 m length of highly nonlinear bre with0.250.15 ps nm 1 km 1 dispersion and dispersion slope of0.0060.004 ps nm 2 km 1. Propagation in the highly nonlinear bre causes self-phase modulation and strong spectral broadening of the comb30. Comb spectra span and envelope can be controlled by the pump power launched into the highly nonlinear bre. A typical comb spectrum with 4600 mW pump power from the 1,559.9 nm laser is shown in Fig. 3a, with 4100 nm spectral span. Moreover, by using various nonlinear bre and spectral attening methods, broad combs with level power are possible31.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10436 ARTICLE

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Figure 1 | Conceptual schematics of the line-referenced electro-optical frequency comb for astronomy. Vertically, the rst column contains images of key instruments. (ae) The images are reference laser, Rb clock (left) and phase modulator (right), amplitude modulator, highly nonlinear bre and telescope. A simplied schematic set-up is in the second column. Third and fourth columns present the comb state in the frequency and temporal domains. The frequency of N-th comb tooth is expressed as fN f0 N fm, where f0 and fm are the reference laser frequency and modulation frequency, respectively. N is the number

of comb lines relative to the reference laser (taken as comb line N 0), RV is radial velocity and dfN, df0 and dfm are the variance of fN, f0 and fm. (a) The

reference laser is locked to a molecular transition, acquiring stability of 0.2 MHz, corresponding to 30 cm s 1 RV. (b) Cascaded phase modulation (CPM) comb: the phase of the reference laser is modulated by two phase modulators (PM), creating several tens of sidebands with spacing equal to the modulation frequency. The RF frequency generator is referenced to a Rb clock, providing stability at the sub-Hz level (dfmo0.03 Hz at 100 s). (c) Pulse forming is then performed by an amplitude modulator (AM) and dispersion compensation unit (DCU), which could be a long single mode bre (SMF) or chirped bre Bragg grating (FBG). (d) After amplication by an erbium-doped bre amplier (EDFA), the pulse undergoes optical continuum broadening in a highly nonlinear bre (HNLF), extending its bandwidth 4100 nm. (e) Finally the comb light is combined with stellar light using a bre acquisition unit (FAU) and is sent into the telescope spectrograph. The overall comb stability is primarily determined by the pump laser.

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Figure 2 | Detailed set-up of line-referenced electro-optical frequency comb. (a) The entire LR-EOFC system sits in a 19 inch instrument rack. Optics and microwave components in the rack are denoted in orange and black, respectively. Small components were assembled onto a breadboard. These included the phase modulators (PM), amplitude modulator (AM), bre Bragg grating (FBG), photodetector (PD), variable attenuator (VATT), attenuator (ATT), highly nonlinear bre (HNLF), microwave source, microwave amplier (Amp), phase shifter (PS) and band-pass lter (BPS). The reference laser, erbium-doped ber amplier (EDFA), rubidium (Rb) clock, counter, optical spectrum analyser (OSA) and servo lock box are separately located in the instrument rack. (b) A simplied schematic of the bre acquisition unit (FAU) is also shown. Stellar light is focused and coupled into a multimode bre (MMF). The comb light from a single mode bre (SMF), together with the stellar light in the MMF, are focused on the spectrograph slit and sent into the spectrograph.

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10436

a

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Figure 3 | Comb spectra and stability of the C2H2 and HCN reference lasers. (a) A typical comb spectrum from the 1,559.9 nm laser with 4100 nm span generated with 600 mW pump power. The insets show the resolved line spacing of 12 GHz or B0.1 nm. (b) Experimental set-up: BP, optical band-pass lter; PD, photodiode. All beam paths and beam combiners are in single mode bre. (c) Time series of measured beat frequencies for the two frequency-stabilized lasers with 10 s averaging per measurement. The x axes are the dates in November of 2013 and May/June of 2014, respectively. (d) Allan deviation, which is a measure of the fractional frequency stability, computed from the time series data of c. Right-side scale gives the radial velocity precision.

The LR-EOFC system is mounted on an aluminum breadboard (18" 32", or equivalently 45.7 81.3 cm) in a standard 19-inch

instrument rack (see Fig. 2) for transport and implementation with the spectrograph at the NASA IRTF and at Keck II on Mauna Kea in Hawaii. The system is designed to provide operational robustness matching the requirements of astronomical observation. All optical components before the highly nonlinear bre are polarization maintaining bre-based, so as to eliminate the effect of polarization drift on spectral broadening in the highly nonlinear bre. Moreover, no temperature control is required at the two telescope facilities. As a result, the comb is able to maintain its frequency, bandwidth and intensity without the need to adjust any parameters. During a 5 day run at IRTF, the comb had zero failures and the intensity of individual comb teeth was measured to deviate less than 2 dB, including multiple power-off and on cycling of the optical continuum generation system (see Fig. 4b).

Comb stability. As noted above, the frequency stability of the LR-EOFC is dominated by the stability of the reference laser frequency f0. We explored the use of two different commercially

available lasers (Wavelength References) that were stabilized, respectively, to Doppler- and pressure-broadened transitions in acetylene (C2H2) at 1,542.4 nm, and in hydrogen cyanide (H13C15N) at 1,559.9 nm. We note that the spectroscopy related to the locking of the reference laser to the molecular resonances is done internally to the laser system, so that our experiments only assess the stability of these commercial off-the-shelf lasers. To assess the stability, the stabilized laser frequencies were measured relative to an Er:bre-based self-referenced optical frequency comb11,32. Fibre-coupled light from a reference laser was combined into a common optical bre with light from the Er:bre comb. Then the heterodyne beat between a single-comb line and the line-stabilized reference was ltered, amplied and counted with a 10 s gate time using a frequency counter that was referenced to a hydrogen maser (see Fig. 3b). The Er:bre comb was stabilized relative to the same hydrogen maser, such that the fractional frequency stability of the measurement was o2 10 13 at all averaging times. The drift of the hydrogen

maser frequency is o1 10 15 per day, thereby providing a

stable reference at levels corresponding to a RV uncertainty

1 cm s 1. Thus, the frequency of the counted heterodyne beat

accurately represents the uctuations in the reference laser.

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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10436 ARTICLE

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Figure 4 | Experimental results at IRTF. (a) Comb spectrum produced using 1,559.9 nm reference laser. The insets on top left and right show the resolved comb lines on the optical spectrum analyser. Comb spectra taken by the CSHELL spectrograph at 1,375, 1,400, 1,670 and 1,700 nm are presented as insets in the lower half of the gure. The blue circles mark the estimated comb line power and centre wavelength for these spectra. Comb lines are detectable on CSHELL at fW power levels. (b) Comb spectral line power versus time is shown at ve different wavelengths. During the 5 day test at IRTF, no parameter adjustment was made, and comb intensity was very stable even with multiple power-on and -off cycling of the optical continuum generation system. (c) An image of the echelle spectrum from CSHELL on IRTF showing a 4 nm portion of spectrum B1,670 nm. The top row of dots are the laser comb lines, while the broad spectrum at the bottom is from the bright M2 IIIII giant star b Peg seen through dense cloud cover. (d) Spectra extracted from c. The solid red curve denotes the average of 11 individual spectra of b Peg (without the gas cell) obtained with CSHELL on the IRTF. The regular sine-wave like blue lines show the spectrum from the laser comb obtained simultaneously with the stellar spectrum. The vertical axis is normalized ux units.

The series of 10 s measurements of the heterodyne beat was recorded over 20 days in 2013 for the case of the 1,542.4 nm laser and more than 7 days in 2014 for the case of the 1,559.9 nm laser, as shown in Fig. 3c. Gaps in the measurements near 11/31 and 6/4 are due to unlocking of the Er:bre comb from the hydrogen maser reference. From these time series, we calculate the Allan deviation, which is a measure of the fractional frequency uctuations (instability) of the reference laser as a function of averaging time. As seen in Fig. 3d, the instability of the 1,542.2 nm laser is o10 9 (30 cm s 1 RV, or corresponding to 200 kHz in frequency) at all averaging times greater than B30 s. The 1,559.9 nm laser is less stable, but provides a corresponding RV precision of o60 cm s 1 for averaging times greater than 20 s. This different instability was to be expected because of the difference in relative absorption line strength between the acetylene and HCN-stabilized lasers. In both cases, the stability improves with averaging time, although at a rate slower than predicted for white frequency noise. As an aside, we note that despite the lower stability of the 1,559.9 nm laser, this wavelength ultimately produced wider and atter comb spectra owing to the better gain performance of the bre amplier used in this work. We did not explore the noise mechanisms that lead to the observed Allan deviation, as they arise from details of the spectroscopy internal to the commercial off-the-shelf laser, to which we did not have access.

Additional analysis included an estimate of the drift of the frequencies of the two reference lasers obtained by tting a line to the full multi-day counter time series. From these linear ts, an upper limit of the drift over the given measurement period was determined to be o9 10 12 per day for the

acetylene-referenced laser and o4 10 11 for the hydrogen

cyanide-referenced laser. This corresponds to equivalent RV

drifts of o0.27 and o1.2 cm s 1 per day for the two references.

Finally, we attempted to place a bound on the repeatability of the

1,542.4 nm reference laser during re-locking and power cycling. Although only evaluated for a limited number of power cycles and re-locks, in all cases, we found that the laser frequency returned to its predetermined value within o100 kHz, or equivalently, with a RV precision of o15 cm s 1.

While these calibrations are sufcient for the few-day observations reported below, condence in the longer term stability of the molecularly referenced continuous-wave lasers would be required for observations that could extend over many years. Likewise, frequency uncertainty of the molecular references should be examined. Properly addressing the potential frequency drifts on such a multi-year time scale would require a more thorough investigation of systematic frequency effects due to a variety of physical and operational parameters (for example, laser power, pressure, temperature and electronic offsets). Alternatively, narrower absorption features, as available in nonlinear Doppler-free saturation spectroscopy, could provide improved performance. For example, laboratory experiments have shown fractional frequency instability at the level of 10 12 and reproducibility of 1.5 10 11 for lasers locked to a

Doppler-free transition in acetylene33. Most promising of all, self-referencing of an EOFC comb has been demonstrated recently34, enabling full stabilization of the frequency comb to a GPS-disciplined standard. This would eliminate the need for the reference laser to dene f0, and thereby provide comb stability at the level of the GPS reference (for example, o10 11 or equivalently o0.3 cm s 1) on both long and short timescales.

IRTF telescope demonstration. To demonstrate that the laser comb is portable, robust and easy-to-use as a wavelength calibration standard, we shipped the laser comb to the NASA IRTF. IRTF is a 3 m diameter infrared-optimized telescope located at the summit of Mauna Kea, Hawaii. The telescope is

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10436

equipped with a cryogenic echelle spectrograph (CSHELL) operating from 15.4 mm. CSHELL is a cryogenic, near-infrared traditional slit-fed spectrograph, with a resolution35,36 of RBl/ Dl 46,000 and it images an adjustable single B5-nm-wide

order spectrum on a 256 256 InSb detector. We have modied

the CSHELL spectrograph to permit the addition of a bre acquisition unit for the injection of starlight and laser frequency comb light into a bre array and focusing on the spectrograph entrance slit. A simple schematic of the bre acquisition unit is shown in Fig. 2 and the details are described elsewhere37,38. Before the starlight reaches the CSHELL entrance slit, it can be switched to pass through an isotopic methane absorption gas cell to introduce a common optical path wavelength reference38. A pickoff mirror is next inserted into the beam to re-direct the near-infrared starlight to a bre via a bre-coupling lens. A dichroic window re-directs the visible light to a guide camera to maintain the position of the star on the entrance of the bre tip. For the starlight, we made use of a specialized non-circular core multi-mode bre, with a 50 100 mm rectangular core. These

bres scramble the near-eld spatial modes of the bre, so that the spectrograph is evenly illuminated by the output from the bre, regardless of the alignment, focus or weather conditions of the starlight impinging upon the input to the bre. We additionally made use of a dual-frequency agitator motor to vibrate the 10 m length of the bre to provide additional mode mixing, distributing the starlight evenly between all modes. Finally, a lens and a second pickoff mirror are used to relay the output of the starlight from the bre output back to the spectrograph entrance slit. A single-mode bre carrying the laser comb is added next to the non-circular core bre carrying the starlight. This was accomplished by replacing the output single-bre SMA-bre chuck with a custom three-dimensional printed V-groove array ferrule. This allowed us to send the light from both the star and frequency comb to the entrance slit of the CSHELL spectrograph when rotated in the same orientation as the slit.

Finally, the laser comb and associated electronics rack were setup in the room temperature (B5 C) control room. A 50 m length of single mode bre was run from the control room to the telescope dome oor, and along the telescope mount to the CSHELL spectrograph to connect to the V-groove array and the

bre acquisition unit. The unpacking, set-up and integration of the comb bre with CSHELL were straightforward, and required only 2 days working at an oxygen-deprived elevation of 14,000 feet in preparation for the observing run. Because the CSHELL spectrometer has a spectral window o5 nm, there was no effort made to generate spectrally at combs. Comb lines are well resolved on CSHELL from 1,375 to 1,700 nm (Fig. 4a), with power adjusted by tunable optical attenuators to match the power of starlight and 6.7 pixels per comb line spacing at 1,670 nm wavelength. Also, comb line power was monitored (Fig. 4b) periodically during the observing run and was stable.

Three partial nights of CSHELL telescope time in September 2014 were used for this rst on-sky demonstration of the laser comb. Unfortunately, the observing run was plagued by poor weather conditions, with 510 magnitudes of extinction because of clouds. Consequently, we observed the bright M2 IIIII star b Peg (H 2.1 mag), which is a pulsating variable star

(P 43.3 days). Typical exposure times were 150 s, and multiple

exposures were obtained in sequence.

The star was primarily observed at 1,670 nm, with and without the isotopic methane gas cell to provide a wavelength calibration comparison for the laser comb. Other wavelengths were also observed to demonstrate that the spectral grasp of the comb is much larger than the spectral grasp of the spectrograph itself. Given the low SNR (signal-to-noise ratio) on b Peg from the high extinction because of clouds and CSHELLs limited spectral grasp, the SNR of these data is inadequate to demonstrate that the comb is more stable than the gas cell, as shown above.

One critical aspect of demonstrating the usability of the comb for astrophysical spectrographs is the comb line spacing. As seen in Fig. 4a,c,d, the spectra clearly demonstrate that the individual comb lines are resolved with the CSHELL spectrograph without the need for additional line ltering39. Thus this comb operates at a frequency that is natively well-suited for astronomical applications with signicantly less hardware complexity compared with traditional laser frequency combs.

Keck telescope demonstration. We were able to use daytime access to the near-infrared cryogenic echelle spectrograph

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Figure 5 | Data from testing at Keck II. (a) Reduced NIRSPEC image from echelle order 4653, displaying the stabilized laser comb using the 1,559.9 nm reference laser. Line brightness represents data counts. (b) A portion of the extracted comb spectrum from order 48 is plotted versus wavelength.(c) Comb brightness envelope of orders 4750 and orders 48 and 49 when attened by a waveshaper (ws).

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(NIRSPEC) on the Keck-II telescope40 to demonstrate our laser comb. NIRSPEC is a cross-dispersed echelle capable of covering a large fraction of the entire H-band in a single setting with a spectral resolution of RB25,000. Observations were taken on 18 and 19 May 2015, with the comb set-up in the Keck-II control room in the same conguration as at the IRTF. The apparatus was reassembled after almost 8 months of storage from the time of the IRTF experiment and was fully operational within a few hours. The bre output from the comb was routed through a cable wrap up to the Nasmyth platform where NIRSPEC is located. We injected the comb signal using a bre feed into the integrating sphere at the input to the NIRSPEC calibration subsystem. While this arrangement did not allow for simultaneous stellar and comb observations, we were able to measure the comb lines simultaneously with the arc lamps normally used for wavelength calibration and to make hour-long tests of the stability of the NIRSPEC instrument at the sub-pixel level.

Figure 5a shows the laser comb illuminating more than six orders of the high-resolution echellogram. The echelle data were reduced in standard fashion, correcting for dark current and at-eld variations. Under this comb setting, a spectral grasp of B200 nm is covered, from 1,430 to 1,640 nm. A zoomed-in spectral extraction (Fig. 5b) shows that individual comb lines are well resolved at NIRSPECs resolution and spaced approximately 4 pixels apart (0.1 nm), consistent with the higher resolution IRTF observations described above. The spectral intensity of the comb lines can be made more uniform with a attening lter to allow constant illumination over the entire span. In this demonstration, we were also able to implement a programmable optical lter (Waveshaper 1000s) from 1,530 to 1,600 nm, greatly reducing comb intensity variation (Plots 48ws and 49ws in Fig. 5c). If desired, a customized lter could increase the bandwidth of the attened regime to cover the entire comb span.

We used a series of 600 spectra taken over a B2 h time period to test the instrumental stability of NIRSPEC. Order 48, which had the highest SNR comb lines, was reduced following a standard procedure to correct for dark current and at-eld variations. Due to the quasi-Littrow conguration of the instrument, the slits appear tilted on the detector and the spectra have some curvature. We performed a spatial rectication using a at-eld image taken with a pinhole slit to mimic a bright

compact object on the spectrum in order to account for this curvature. Wavelength calibration and spectral rectication to account for slit tilting were applied using the Ne, Kr, Ar and Xe arc lamps and the rectication procedure in the REDSPEC software written for NIRSPEC.

Instrumental stability was tested by performing a cross-correlation between the rst comb spectrum in the 600 image series and each successive comb spectrum. The peak of the cross-correlation function corresponded to the drift, measured in pixels, between the images. Figure 6a demonstrates the power of the laser comb to provide a wavelength standard for the spectrometer. Over a period of roughly an hour the centroid of each comb line in Order 48 moved by about 0.05 pixel, equivalent to 0.0114 . By examining various internal NIRSPEC temperatures it is possible to show that this drift correlates to changes inside the instrument. Figure 6b shows changes in the temperatures measured at ve different points within the instrument: the grating mechanism motor, an optical mounting plate, the top of the grating rotator mechanism, the base of the (unused) LN2 container and the three mirror anastigmat assembly40. At these locations the temperatures range from 50 to 75 K and have been standardized to t onto a single plot: Yi(t) (Ti(t) oT4)/s(T). Average values of each temperature

are given in Table 1 and show drifts of order 1535 mK over this 1 h period. In its present conguration NIRSPEC is cooled using a closed cycle refrigerator without active temperature controlonly the detector temperature is maintained under closed cycle control to B1 mK.

Examination of the wavelength and temperature drifts in the two gures reveals an obvious correlation. A simple linear t of the wavelength drift to the ve standardized temperatures reduces the temperature-induced wavelength drifts from 0.05 pixel per hour to a near-constant value with a s.d. of s 0.0017 pixel for a

single-comb line (bottom curve in Fig. 6a). While other

Table 1 | Internal NIRSPEC temperatures (K).

Rotator motor 54.9440.015 Optics plate 52.8870.023 Top of rotator 74.7780.035 LN2 Can 53.6630.021

TMA 53.8660.022

NIRSPEC, near-infrared cryogenic echelle spectrograph; TMA, three mirror anastigmat.

a b

0.05

3

0.04

Rot. motor Opt. plate Top of rotator LN2 can

TMA Det1 Det2 Avg

2

Wavelength drift (pixel)

Standardized temperature

0.03

1

0.02 0

0.01

0.00

1

2

3

0.01

0.2 0.4 0.6 0.8 1.0 1.2 Time (h)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Time (h)

Figure 6 | Measurement of wavelength and temperature drift on the Keck II NIRSPEC spectrometer. (a) The blue curve shows the drift in the pixel location of individual comb lines in order 48 as measured with the cross-correlation techniques described in the text. The yellow curve shows the residual shifts after de-correlating the effects of the internal NIRSPEC temperatures. (b) Five internal NIRSPEC temperatures are shown as a function of time. For ease of plotting, the individual temperatures have been standardized with respect to the means and s.d. of each sensor (Table 1). The black dashed curve shows the average of these standardized temperatures. The effect of the quantization of the temperature data at the 10 mK level (as recorded in the available telemetry) is evident in the individual temperature curves.

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ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10436

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Acknowledgements

Three IRTF nights were donated in September 2014 to integrate and test the laser comb with CSHELL. One of these nights came from IRTF engineering time and the other two

mechanical effects may manifest themselves in other or longer time series, this small data set indicates the power of the laser comb to stabilize the wavelength scale of the spectrometer. At the present spectral resolution of NIRSPEC, RB25,000, and with over 240 comb lines in just this one order, we can set a limit on the velocity drift due to drifts within NIRSPEC of

c=R s=

# lines

p o1:5 m s 1 where c is the speed of light. Thus, operation with a laser comb covering over 200 nm with more than 2,000 lines in the H-band would allow much higher RV precision than is presently possible using, for example, atmospheric OH lines, as a wavelength standard. NIRSPECs ultimate RV precision will depend on many factors, including the brightness of the star, NIRSPECs spectral resolution (presently 25,000 but increasing to 37,500 after a planned upgrade) and the ability to stabilize the input stellar light against pointing drifts and line prole variations. We anticipate that in an exposure of 900 s NIRSPEC should be able to achieve an RV precision B1 m s 1 for stars brighter than H 7 mag and o3 m s 1 for a stars

brighter than Ho9 mag. A detailed discussion of the NIRSPEC error budget is beyond the scope of this paper, but a stable wavelength reference, observed simultaneously with the stellar spectrum, is critical to achieving this precision.

DiscussionMany challenges remain to achieving the high precision RV capability needed for the study of exoplanets orbiting late M dwarfs, jitter-prone hotter G and K spectral types, or young stars exhibiting high levels of RV noise in the visible. Achieving adequate signal-to-noise on relatively faint stars requires a large spectral grasp on a high-resolution spectrometer on a large aperture telescope. Injecting both the laser comb and starlight into the spectrograph with a highly stable line spread function demands carefully designed interfaces between the comb light and starlight at the entrance to the spectrograph. Extracting the data from the spectrometer requires careful attention to at-elding and other detector features. Finally, reducing the extracted spectra to produce RV measurements at the required level of precision requires sophisticated modelling of complex stellar atmospheres and telluric atmospheric absorption. The research described here addresses only one of these steps, namely the generation of a highly stable wavelength standard in the near IR suitable for sub m s 1 RV measurements.

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Author contributions

X.Y., K.V., J.L., S.D., P.P., S.L., G.V., P.C. and C.B. conceived the experiments. All co-authors designed and performed experiments. X.Y. and K.V. prepared the manuscript with input from all co-authors.

Additional information

Competing nancial interests: The authors declare no competing nancial interests.

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How to cite this article: Yi, X. et al. Demonstration of a near-IR line-referenced electro-optical laser frequency comb for precision radial velocity measurements in astronomy. Nat. Commun. 7:10436 doi: 10.1038/ncomms10436 (2016).

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came from Peter Plavchans CSHELL program to observe nearby M dwarfs with the absorption gas cell to obtain precise radial velocities. We are grateful to the leadership of the IRTF, Director Alan Tokunaga and Deputy Director John Rayner, as well as to the daytime and night time staff at the summit for their support. We further thank Jeremy Colson at Wavelength References for his assistance with the molecular-stabilized lasers. On-sky observations were obtained at the Infrared Telescope Facility, which is operated by the University of Hawaii under Cooperative Agreement no. NNX-08AE38A with the National Aeronautics and Space Administration, Science Mission Directorate, Planetary Astronomy Program. Daytime operations at the Keck-II telescope were carried out with the assistance of Sean Adkins and Steve Milner. We greatfully acknowledge the support of the entire Keck summit team in making these tests possible. We recognize and acknowledge the very signicant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. The data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientic partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous nancial support of the W.M. Keck Foundation. We also acknowledge support from NIST and the NSF grant AST-1310875. This research was carried out at the Jet Propulsion Laboratory and the California Institute of Technology under a contract with the National Aeronautics and Space Administration and funded through the Presidents and Directors Fund Program. Copyright 2014 California Institute of Technology. All rights reserved.

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