We experimentally demonstrate that a femtosecond frequency comb laser can be applied as a tool for longdistance measurement in air. Our method is based on the measurement of cross correlation between individual pulses in a Michelson interferometer. From the position of the correlation functions, distances of up to 50 m have been measured. We have compared this measurement to a counting laser interferometer, showing an agreement with the measured distance within 2 m (4 ϫ 10 −8 at 50 m). © 2009 Optical Society of America OCIS codes: 320.7100, 320.2250, 320.1590 Traditional techniques for long-distance measurements are often based on optical interferometry when the demands on accuracy rise. Most of these interferometric techniques rely on incremental measurements of phase accumulation. A priori knowledge of the distance to be measured is required or a complex multiwavelength system may be needed. In 2004, Ye [1] proposed a simple scheme for measuring long distances in space with a stabilized femtosecond frequency comb. The scheme is based on a Michelsontype interferometry with optical interference between individual pulses. The technique proposed by Ye has been demonstrated for interferometric measurement of short displacement [2,3]. The main advantage of applying a frequency comb for distance measurement is the large range of nonambiguity, which is determined by the cavity length of the pulsed laser, ranging from about 30 cm to 3 m. It is thus not necessary to rely on incremental measurement of the optical phase. The ambiguity is easily overcome by, e.g., a laser distance meter. The stabilized frequency comb has been applied as a source in various distance measurement schemes [4,5]. In this Letter, we demonstrate distance measurements of up to 50 m in air by analyzing the cross correlation between pulses emitted from a stabilized frequency comb source. We have implemented a model of pulse propagation in air to account for the effect of air dispersion on the measured cross-correlation functions. The measurement results obtained with the frequency comb and a conventional counting laser interferometer are compared.A mode-locked Ti:sapphire laser is the frequency comb source, with both the repetition frequency and the carrier-envelop offset (CEO) frequency referenced to a cesium atomic clock (Fig. 1). The pulse duration is 40 fs, and the repetition rate f r is locked at approximately 1 GHz, corresponding to a pulse to pulse distance l pp = c / ͑n g f r ͒ of 30 cm. Here c is the speed of light in vacuum and n g is the group refractive index at the center wavelength. The CEO frequency f 0 is fixed at 180 MHz. The center wavelength of the pulses is 815 nm, with an FWHM of about 20 nm. After collimation the beam is sent to a Michelson interferometer. One part of the beam is reflected by a hollow corner cube mounted on a piezoelectric transducer (PZT) along the short reference arm. The length of the short arm can be scanned by a translation stage. The other part of the beam is reflected by two mirrors and propagates along...

We experimentally demonstrate long distance measurements with a femtosecond frequency comb laser using dispersive interferometry. The distance is derived from the unwrapped spectral phase of the dispersed interferometer output and the repetition frequency of the laser. For an interferometer length of 50 m this approach has been compared to an independent phase counting laser interferometer. The obtained mutual agreement is better than 1.5 μm (3 × 10 −8 ), with a statistical averaging of less than 200 nm. Our experiments demonstrate that dispersive interferometry with a frequency comb laser is a powerful method for accurate and non-incremental measurement of long distances.

We experimentally demonstrate that a stabilized femtosecond frequency comb can be applied as a tool for distance measurement in an interferometric scheme. A proof of principle of this method, as proposed by Ye [5], is provided by measuring a displacement of about 15 cm in air and comparing it to a reference value from a calibrated laser interferometer. The experiment shows that the new scheme easily achieves an accuracy better than one optical fringe.

We have investigated correlation patterns generated by a frequency-comb laser in a dispersive unbalanced Michelson interferometer and apply the developed formalism to the case of distance metrology. Due to group velocity dispersion, the position of the brightest fringe of the correlation pattern, which is used for distance determination, cannot be derived by simply using the definition of group refractive index of the dispersive medium. It is shown that the discrete spectrum of the optical frequency comb gives rise to correlation functions which can be represented by a series, namely a discrete correlation series. We have developed a general formalism, valid for any pulse train, extending the discrete model to a continuous model of cross-correlation functions using the Poisson summation. Our model is relevant for any offset and repetition frequency of the frequency comb. From the continuous cross-correlation model we show that, even for a homogeneous dispersive medium the position of the brightest fringe varies nonlinearly for small delay distances and stabilizes for longer ones. We have compared the theoretical results to measurements of pulse propagation in air for path-lengths up to 200 m.

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