[Paper Review] High-precision wavelength calibration with laser frequency combs

M. T. Murphy, Th. Udem+9 more|arXiv (Cornell University)|Mar 23, 2007

Advanced Fiber Laser Technologies11 citations

TL;DR

This paper proposes using laser frequency combs—generated by femtosecond-pulsed mode-locked lasers locked to atomic clocks—for high-precision wavelength calibration of astronomical spectrographs. The combs provide uniformly spaced, absolutely known frequency lines with sub-10⁻¹² precision, enabling wavelength calibration precision of ~1 cm s⁻¹ over a 4000 Å range, and allowing accurate characterization of spectrograph-induced distortions.

ABSTRACT

Accepted —. Received —; in original form — We describe a possible new technique for precise wavelength calibration of high-resolution astronomical spectrographs using femtosecond-pulsed mode-locked lasers controlled by stable oscillators such as atomic clocks. Such ‘frequency combs ’ provide a series of narrow modes which are uniformly spaced according to the laser’s pulse repetition rate and whose absolute frequencies are known a priori with relative precision better than 10 −12. Simulations of frequency comb spectra show that the photon-limited wavelength calibration precision achievable with existing echelle spectrographs should be∼1 cm s −1 when integrated over a 4000 Å range. Moreover, comb spectra may be used to accurately characterise distortions of the wavelength scale introduced by the spectrograph and detector system. The simulations show that frequency combs with pulse repetition rates of 5–30 GHz are required, given the typical resolving power of existing and possible future echelle spectrographs. Achieving such high repetition rates, together with the desire to produce all comb modes with uniform intensity over the entire optical range, represent the only significant challenges in the design of a practical system. Frequency comb systems may remove wavelength calibration uncertainties from all practical spectroscopic experiments, even those combining data from different telescopes over many decades.

Motivation & Objective

• To address long-term wavelength calibration drift and uncertainty in high-resolution astronomical spectroscopy.
• To overcome limitations of traditional calibration sources, such as arc lamps, which lack absolute frequency reference and degrade over time.
• To enable precise, traceable wavelength calibration across decades of observational data from different telescopes.
• To characterize spectrograph and detector-induced distortions in the wavelength scale using frequency comb spectra.
• To establish practical design requirements for frequency comb systems suitable for astronomical use.

Proposed method

• Employing femtosecond-pulsed mode-locked lasers stabilized by atomic clocks to generate frequency combs with absolute frequency precision better than 10⁻¹².
• Utilizing the comb's uniformly spaced optical modes, each with known absolute frequency, as a precise wavelength reference grid.
• Simulating frequency comb spectra to evaluate achievable calibration precision on existing and future echelle spectrographs.
• Analyzing the photon-limited signal-to-noise performance to determine the theoretical calibration limit of ~1 cm s⁻¹ over a 4000 Å range.
• Assessing the need for pulse repetition rates between 5–30 GHz to match the resolving power of typical echelle spectrographs.
• Evaluating the feasibility of achieving uniform comb mode intensity across the full optical bandwidth for practical calibration.

Experimental results

Research questions

• RQ1 What is the theoretical limit of wavelength calibration precision achievable with frequency combs in high-resolution echelle spectrographs?
• RQ2 Can frequency combs be used to detect and correct for instrumental distortions in the spectrograph and detector wavelength response?
• RQ3 What pulse repetition rate is required to match the resolving power of existing and future echelle spectrographs?
• RQ4 How does the photon-limited signal-to-noise of the comb spectrum affect the achievable calibration precision?
• RQ5 Can frequency comb systems eliminate long-term wavelength calibration uncertainties in multi-decade, multi-telescope spectroscopic surveys?

Key findings

• Frequency combs enable wavelength calibration precision of approximately 1 cm s⁻¹ over a 4000 Å spectral range when integrated over the signal bandwidth.
• The absolute frequency of each comb mode is known a priori with a relative precision better than 10⁻¹², enabling traceable calibration.
• Simulations confirm that frequency combs can accurately characterize distortions in the wavelength scale introduced by spectrograph optics and detectors.
• Pulse repetition rates between 5 and 30 GHz are required to match the resolving power of typical echelle spectrographs.
• The primary technical challenges lie in achieving high repetition rates and uniform intensity across the full optical bandwidth of the comb.
• Frequency comb systems have the potential to eliminate wavelength calibration uncertainties in long-term spectroscopic experiments, even across decades and multiple observatories.