Femtosecond frequency comb based distance measurement in air

Enhanced Data-Processing Algorithms for Dispersive Interferometry Using a Femtosecond Laser

Dispersive interferometry based on a femtosecond laser is extensively utilized for achieving absolute distance measurements with high accuracy. However, this method cannot measure arbitrary distances without encountering a dead zone, and deviations in its output results are inevitable due to inherent theory limitations. Therefore, two enhanced data-processing algorithms are proposed to improve the accuracy and reduce the dead zone of dispersive interferometry. The principles of the two proposed algorithms, namely the truncated-spectrum algorithm and the high-order-angle algorithm, are proposed after explaining the limitations of conventional methods. A series of simulations were conducted on these algorithms to show the improved accuracy of measurement results and the elimination of the dead zone. Furthermore, an experimental setup based on a dispersive interferometer was established for the application of these proposed algorithms to the experimental interference spectral signals. The results demonstrated that compared with the conventional algorithm, the proposed truncated-spectrum algorithm could reduce the output distance deviations derived from direct inverse Fourier transforming by eight times to reach as low as 1.3 μm. Moreover, the unmeasurable dead zone close to the zero position of the conventional algorithm, i.e., the minimum working distance of a dispersive interferometer, could be shortened to 22 μm with the implementation of the proposed high-order-angle algorithm.

Improved Algorithms of Data Processing for Dispersive Interferometry Using a Femtosecond Laser

Two algorithms of data processing are proposed to shorten the unmeasurable dead-zone close to the zero-position of measurement, i.e., the minimum working distance of a dispersive interferometer using a femtosecond laser, which is a critical issue in millimeter-order short-range absolute distance measurement. After demonstrating the limitation of the conventional data processing algorithm, the principles of the proposed algorithms, namely the spectral fringe algorithm and the combined algorithm that combines the spectral fringe algorithm with the excess fraction method, are presented, together with simulation results for demonstrating the possibility of the proposed algorithms for shortening the dead-zone with high accuracy. An experimental setup of a dispersive interferometer is also constructed for implementing the proposed data processing algorithms over spectral interference signals. Experimental results demonstrate that the dead-zone using the proposed algorithms can be as small as half of that of the conventional algorithm while measurement accuracy can be further improved using the combined algorithm.

Time delay interferometry with a transfer oscillator

In this work, we experimentally perform time delay interferometry by using a transfer oscillator, which is capable of reducing the laser frequency noise and the clock noise simultaneously in the post processing. The iodine frequency reference is coherently downconverted to the microwave frequency using a laser frequency comb. The residual noise of the downconversion network is 5 × 10^-6Hz/Hz^1/2 at 0.7 mHz, and 4 × 10^-6Hz/Hz^1/2 at 0.1 Hz, indicating high homology between the optical frequency and the microwave frequency. We carry out time delay interferometry with the aid of the electrical delay module, which can introduce large time delays. The results show that the laser frequency noise and the clock noise can be reduced simultaneously by ten and three orders of magnitude, respectively, in the frequency band from 0.1 mHz to 0.1 Hz. The performance of the noise reduction can reach 6 × 10^-8Hz/Hz^1/2 at 0.1 mHz, and 7 × 10^-7Hz/Hz^1/2 at 1 mHz, meeting the requirements of the space-borne gravitational wave detection. Our work will be able to offer an alternative method for the frequency comb-based time delay interferometry in the future space-borne gravitational wave detectors.

Arm locking using laser frequency comb

The space-borne gravitational wave (GW) detectors, e.g., LISA, TaiJi, and TianQin, will open the window in the low-frequency regime (0.1 mHz to 1 Hz) to study the highly energetic cosmic events, such as coalescences and mergers of binary black holes and neutron stars. For the sake of successful observatory of GWs, the required strain sensitivity of the detector is approximately 10^-21/Hz^1/2 in the science band, 7 orders of magnitude better than the state of the art of the ultra-stable laser. Arm locking is therefore proposed to reduce the laser phase noise by a few orders of magnitude to relax the burden of time delay interferometry. During the past two decades, various schemes have been demonstrated by using single or dual arms between the spacecraft, with consideration of the gain, the nulls in the science band, and the frequency pulling characteristics, etc. In this work, we describe an updated version of single arm locking, and the noise amplification due to the nulls can be flexibly restricted with the help of optical frequency comb. We show that the laser phase noise can be divided by a specific factor with optical frequency comb as the bridge. The analytical results indicate that, the peaks in the science band have been greatly reduced. The performance of the noise suppression shows that the total noise after arm locking can well satisfy the requirement of time delay interferometry, even with the free-running laser source. When the laser source is pre-stabilized to a Fabry-Perot cavity or a Mach-Zehnder interferometer, the noise can reach the floor determined by the clock noise, the spacecraft motion, and the shot noise. We also estimate the frequency pulling characteristics of the updated single arm locking, and the results suggest that the pulling rate can be tolerated, without the risk of mode hopping. Arm locking will be a valuable solution for the noise reduction in the space-borne GW detectors. We demonstrate that, with the precise control of the returned laser phase noise, the noise amplification in the science band can be efficiently suppressed based on the updated single arm locking. Not only does our method allow the suppression of the peaks, the high gain, and low pulling rate, it can also serve for full year, without the potential risk of locking failure due to the arm length mismatch. We then discuss the unified demonstration of the updated single arm locking, where both the local and the returned laser phase noises can be tuned to generate the expected arm-locking sensor actually. Finally, the time-series simulations in Simulink have been carried out, and the results indicate a good agreement with the theory, showing that the presented method is reasonable and feasible. Our work could provide a back-up strategy for the arm locking in the future space-borne GW detectors.

Multi-color method for the self-correction of the air refractive index

We propose a multi-color method for the self-correction of the air refractive index based on the dispersive interferometry of an optical frequency comb. This method can be applied to correct the air refractive index for long-distance measurements in moist air. Optical lengths of multiple wavelengths were obtained simultaneously by the dispersive interferometry of an optical frequency comb. Interferometric measurement results and calculations from the empirical equation of air refractive indices were similar, with a standard deviation of 2.0×10^-9 throughout the 2 h continuous measurement period. By applying the multi-color method, correction of the air refractive index with an uncertainty of 3.5×10^-7 was achieved.

Achieving Precise Spectral Analysis and Imaging Simultaneously with a Mode-Resolved Dual-Comb Interferometer

In this paper, we report a scheme providing precise spectral analysis and surface imaging, simultaneously, based on a high-coherence dual-comb interferometer. With two tightly phase-locking frequency combs, we demonstrate a high-coherence dual-comb interferometer (DCI) covering 188 to 195 THz (1538.5 to 1595.7 nm) with comb-tooth resolution and a max spectral signal-to-noise ratio (SNR) of 159.7. The combination of the high-coherence dual-comb spectrometer and a reference arm simultaneously enables gas absorption spectroscopy and for the absolute distance information to be obtained in one measurement. As a demonstration, we measure the spectrum of CO2 and CO. From the same interferograms, we demonstrate that distance measurement, by time-of-flight (TOF), can be resolved with an rms precision of 0.53 μm after averaging 140 images and a measurement time of 1 s. Finally, we demonstrate that non-contact surface imaging, using 2D mechanical scanning, reaches lateral resolution of 40 μm. The longitudinal precision is 0.68 μm with a measurement time of 0.5 s. It verifies that DCS has the potential to be applied in standoff detection, environmental pollution monitors, and remote sensing.

260 kHz mode-spacing optical frequency combs for scan-free high-resolution direct-comb spectroscopy

For scan-free high-resolution direct-comb spectroscopy, mode spacing of an optical frequency comb is reduced down to 260 kHz by phase modulation. It turns out that time-domain signal is degraded by averaging because of slow optical path length fluctuations and fast optical pulse timing jitter. In this study, compensation of these effects is introduced, and signal degradation by averaging is avoided. With demonstrations of direct-comb spectroscopy with the narrow-mode-spacing optical frequency comb, Doppler-limited absorption spectrum of methane and reflection spectrum from an optical ring cavity are observed. As a result, detailed resonance spectral line profile of 8 MHz linewidth for the optical ring cavity is obtained in 50 ms measurement time.

Using femtosecond laser pulses for electronic distance meter calibration

Electronic distance meters (EDMs) are widely used in different applications, such as surveying and civil engineering. In order to calibrate an EDM, different techniques can be used, including displacement interferometers and reference baselines. In this paper, an indoor baseline is designed and then accurately measured using femtosecond laser pulses from an optical frequency comb to be used for EDM calibration. The baseline consists of 13 fixed bases that cover 58 m distance. In order to accurately measure the distances between the bases, autocorrelation between femtosecond laser pulses is employed. The measurement shows a maximum precision of 14 µm over the 13 bases. Although this deviation is dominated mainly by the placement of the target mirror, the system capability is much more sufficient to safely calibrate the best available commercial EDM. The stability of the baseline is also investigated by measuring the interbase distances over long periods of time.

Underwater distance measurement using frequency comb laser

In this paper, we theoretically and experimentally analyze the frequency-comb interferometry at 518 nm in the underwater environment, which we use to measure the underwater distance with high accuracy and precision. In the time domain, we analyze the principle of pulse cross correlation. The interferograms can be obtained in the vicinity of N∙lpp, where N is an integer and lpp is the pulse-to-pulse length. Due to the strong dispersion of water, the pulse can be broadened as the distance increases. The distance can be measured via the peak position of the interferograms. The experimental results show a difference within 100 μm at 8 m range, compared with the reference values. In the frequency domain, we analyze the principle of dispersive interferometry. The spectrograms can be observed near the location of N∙lpp, due to the low resolution of the optical spectrum analyzer. Because of the strong dispersion of water, the modulation frequency of the spectrogram is not constant. A balanced wavelength will exist with the widest fringe, at which the group optical path difference between the reference and measurement arm is equal to N∙lpp. The position of the widest fringe can be used to measure the distance. Compared with the reference values, the experimental results indicate a difference within 100 μm at 8 m range.

Calculating the Effective Center Wavelength for Heterodyne Interferometry of an Optical Frequency Comb

Heterodyne interferometry based on an optical frequency comb (OFC) is a powerful tool for distance measurement. In this paper, a method to calculate the effective center wavelength of wide spectrum heterodyne interference signal was explored though both simulation and experiment. Results showed that the effective center wavelength is a function of the spectra of the two interfered beams and time-delay of the two overlapped pulses. If the product of the spectra from two arms is symmetric, the effective center wavelength does not change with time-delay of the two pulses. The relative difference between the simulation and experiment was less than 0.06%.

Construction of traceable absolute distances network for multilateration with a femtosecond pulse laser

The traceable absolute distances network with multiple global targets for multilateration is developed with a femtosecond pulse laser. It is aiming to enhance the ability and flexibility of the coordinate measurement, especially to monitor the positions of distributed stations in real time for some critical industrial environments. Here, multi-target absolute distances are determined by the temporal coherence method simultaneously with the pulse-to-pulse interferometer. Besides, the performance of the proposed system is evaluated in detail by comparing with a conventional interferometer. The experimental results indicate that the accuracy of distances measurement could all reach the sub-micron level and could be traceable to the length standard. Furthermore, a simple scheme of multilateration is presented based on the developed network. The coordinate of the initial point of multiple beams is measured by cooperation with a laser tracker. The results of coordinate measurement show that these methods have the potential for further industrial applications.

Mode density multiplication of an optical frequency comb by N2 with phase modulation

We introduce a simple scheme for mode-density multiplication of an optical frequency comb (OFC) by a factor of square of an arbitrary integer N using phase modulation. This scheme is employed to multiply the mode density of an erbium-doped fiber laser OFC (repetition rate of 66.87 MHz) by factors of 4², 8², and 3 · 4² using an electro-optic phase modulator. The OFC multiplied by 4² is applied to direct-comb spectroscopy of methane with a spectral resolution of 4.18 MHz.

Frequency accurate coherent electro-optic dual-comb spectroscopy in real-time

Electro-optic dual-comb spectrometers have proved to be a promising technology for sensitive, high-resolution and rapid spectral measurements. Electro-optic combs possess very attractive features like simplicity, reliability, bright optical teeth, and typically moderate but quickly tunable optical spans. Furthermore, in a dual-comb arrangement, narrowband electro-optic combs are generated with a level of mutual coherence that is sufficiently high to enable optical multiheterodyning without inter-comb stabilization or signal processing systems. However, this valuable tool still presents several limitations; for instance, on most systems, absolute frequency accuracy and long-term stability cannot be guaranteed; likewise, interferometer-induced phase noise restricts coherence time and limits the attainable signal-to-noise ratio. In this paper, we address these drawbacks and demonstrate a cost-efficient absolute electro-optic dual-comb instrument based on a frequency stabilization mechanism and a novel adaptive interferogram acquisition approach devised for electro-optic dual-combs capable of operating in real-time. The spectrometer, completely built from commercial components, provides sub-ppm frequency uncertainties and enables a signal-to-noise ratio of 10000 (intensity noise) in 30 seconds of integration time.

Absolute Measurement of the Refractive Index of Water by a Mode-Locked Laser at 518 nm

In this paper, we demonstrate a method using a frequency comb, which can precisely measure the refractive index of water. We have developed a simple system, in which a Michelson interferometer is placed into a quartz-glass container with a low expansion coefficient, and for which compensation of the thermal expansion of the water container is not required. By scanning a mirror on a moving stage, a pair of cross-correlation patterns can be generated. We can obtain the length information via these cross-correlation patterns, with or without water in the container. The refractive index of water can be measured by the resulting lengths. Long-term experimental results show that our method can measure the refractive index of water with a high degree of accuracy—measurement uncertainty at 10⁻⁵ level has been achieved, compared with the values calculated by the empirical formula.

Time-of-flight detection of femtosecond laser pulses for precise measurement of large microelectronic step height

We propose and demonstrate a new method which employs time-of-flight detection of femtosecond laser pulses for precise height measurement of large steps. By using time-of-flight detection with fiber-loop optical-microwave phase detectors, precise measurement of large step height is realized. The proposed method shows uncertainties of 15 nm and 6.5 nm at sampling periods of 40 ms and 800 ms, respectively. This method employs only one free-running femtosecond mode-locked laser and requires no scanning of laser repetition rate, making it easier to operate. Precise measurements of 6 μm and 0.5 mm step heights have been demonstrated, which show good functionality of this method for measurement of step heights.

Synthetic wavelength interferometry of an optical frequency comb for absolute distance measurement

We present a synthetic-wavelength based heterodyne interferometer of optical frequency combs with wide consecutive measurement range for absolute distance measurement. The synthetic wavelength is derived from two wavelengths obtained by two band-pass filters. The interferometric phase of the synthetic wavelength is used as a marker for the pulse-to-pulse alignment, which greatly improves the accuracy of traditional peak finding method. The consecutive measurement range is enlarged by using long fiber to increase the path length difference of the reference and measurement arms. The length of the long fiber is stabilized according to the interferometric phase of a CW laser. The experimental results show the present system can realize an accuracy of 75 nm in 350 mm consecutive measurement range.

Enhancement of the performance of a fiber-based frequency comb by referencing to an acetylene-stabilized fiber laser

We demonstrate a significant improvement in the performance of a fiber-based frequency comb when a GPS-disciplined Rb clock is replaced with an acetylene-stabilized laser as the frequency reference. We have developed a compact, maintenance-free acetylene-stabilized fiber laser with a sub-kHz short-term linewidth and an Allan deviation below 3×10^-13 for integration times above 1 s. Switching the comb reference from the Rb clock to the acetylene-stabilized laser improves both comb tooth linewidth and Allan deviation by about two orders of magnitude. Furthermore, long-term measurements of the acetylene-stabilized laser frequency with reference to the GPS-disciplined clock indicate a potential relative frequency uncertainty of 2 × 10^-12.

Glass thickness and index measurement using optical sampling by cavity tuning

In this paper, we describe a method based on optical sampling by cavity tuning, which is capable of high-accuracy glass thickness and index measurement. By tuning the repetition frequency of the frequency comb, a series of cross-correlation patterns can be obtained that correspond to the front and rear surfaces of the specimen and the co-operation mirror. Both the geometrical thickness and the optical thickness of the specimen can be measured via the cross-correlation patterns, and consequently, the glass refractive index can be determined at the same time. The comparison with the reference value shows an agreement within 1.3 μm for the thickness measurement, and within 5×10^-4 for the refractive index measurement.

Absolute distance measurement with correction of air refractive index by using two-color dispersive interferometry

Two-color interferometry is powerful for the correction of the air refractive index especially in the turbulent air over long distance, since the empirical equations could introduce considerable measurement uncertainty if the environmental parameters cannot be measured with sufficient precision. In this paper, we demonstrate a method for absolute distance measurement with high-accuracy correction of air refractive index using two-color dispersive interferometry. The distances corresponding to the two wavelengths can be measured via the spectrograms captured by a CCD camera pair in real time. In the long-term experiment of the correction of air refractive index, the experimental results show a standard deviation of 3.3 × 10^-8 for 12-h continuous measurement without the precise knowledge of the environmental conditions, while the variation of the air refractive index is about 2 × 10^-6. In the case of absolute distance measurement, the comparison with the fringe counting interferometer shows an agreement within 2.5 μm in 12 m range.

Research Progress on F-P Interference-Based Fiber-Optic Sensors

We review our works on Fabry-Perot (F-P) interferometric fiber-optic sensors with various applications. We give a general model of F-P interferometric optical fiber sensors including diffraction loss caused by the beam divergence and the Gouy phase shift. Based on different structures of an F-P cavity formed on the end of a single-mode fiber, the F-P interferometric optical sensor has been extended to measurements of the refractive index (RI) of liquids and solids, temperature as well as small displacement. The RI of liquids and solids can be obtained by monitoring the fringe contrast related to Fresnel reflections, while the ambient temperature and small displacement can be obtained by monitoring the wavelength shift of the interference fringes. The F-P interferometric fiber-optic sensors can be used for many scientific and technological applications.

Absolute distance measurement by multi-heterodyne interferometry using a frequency comb and a cavity-stabilized tunable laser

In this paper, we develop a multi-heterodyne system capable of absolute distance measurement using a frequency comb and a tunable diode laser locked to a Fabry-Perot cavity. In a series of subsequent measurements, numerous beat components can be obtained by downconverting the optical frequency into the RF region with multi-heterodyne interferometry. The distances can be measured via the mode phases with a series of synthetic wavelengths. The comparison with the reference interferometer shows an agreement within 1.5 μm for the averages of five measurements and 2.5 μm for the single measurement, which is at the 10^-8 relative precision level.

Long distance measurement using optical sampling by cavity tuning

We experimentally demonstrate a method enabling absolute distance measurement based on optical sampling by cavity tuning. The cross-correlation patterns can be obtained by sweeping the repetition frequency of the frequency comb. The 114 m long fiber delay line, working as the reference arm, is actively stabilized by using a feedback servo loop with 10^-10 level stability. The unknown distance can be measured via the instantaneous repetition frequency corresponding to the peak of the fringe packet. We compare the present technique with the reference incremental interferometer, and the experimental results show an agreement within 3 μm over 60 m distance, corresponding to 10^-8 level in relative.

Absolute group refractive index measurement of air by dispersive interferometry using frequency comb

The absolute group refractive index of air at 1563 nm is measured by dispersive interferometry, and a combined uncertainty of 1.2 × 10(-8) is achieved. The group refractive index of air is calculated from the dispersive interferograms of the two beams passing through the inner and outer regions of a vacuum cell by fast-Fourier-transform. Experimental results show that the discrepancies between our method and modified Edlén equation are less than 3.43 × 10(-8) and 4.4 × 10(-8) for short-term and long-term experiments, respectively. The interferogram update rate is 15 ms, which makes it suitable for application of real-time monitoring. Furthermore, it is promising to improve the measurement uncertainty to 3.0 × 10(-9) by changing the material of the vacuum cell and measuring its length more accurately through optical interferometry.

Parameter optimization of a dual-comb ranging system by using a numerical simulation method

Dual-comb system parameters have significant impacts on the ranging accuracy. We present a theoretical model and a numerical simulation method for the parameter optimization of a dual-comb ranging system. With this method we investigate the impacts of repetition rate difference, repetition rate, and carrier-envelope-offset frequency on the ranging accuracy. Firstly, the simulation results suggest a series of discrete zones of repetition rate difference in an optimal range, which are consistent with the experimental results. Secondly, the simulation results of the repetition rate indicate that a higher repetition rate is very favorable to improve the ranging accuracy. Finally, the simulation results suggest a series of discrete optimal ranges of the carrier-envelope-offset frequency for the dual-comb system. The simulated results were verified by our experiments.

Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser

We propose here a method for absolute distance measurement by chirped pulse interferometry using frequency comb. The principle is introduced, and the distance can be measured via the shift of the widest fringe. The experimental results show an agreement within 26 μm in a range up to 65 m, corresponding to a relative precision of 4 × 10^-7, compared with a reference distance meter.

Measurement of displacement and distance with a polarization phase shifting folded Twyman Green interferometer

A Sagnac interferometer (SI), consisting of a polarization beam splitter (PBS), along with two equally spaced plane mirrors that are inclined at 45° to each other, is transformed into a folded Twyman Green interferometer (TGI) by placing a mirrored parallel plate (MPP) into the hypotenuse arm of the SI. The converging input beam produced by a telescope objective (TO) is split into reflected (s-polarized) and transmitted (p-polarized) components by the PBS. The p- and s-polarized focal spots are made to fall on the mirrored end surfaces of the parallel plate (PP). The retroreflected p- and s-polarized beams become collimated after passing through the TO. A linear shift of the PP in either (longitudinal) direction alters the positions of the p- and s-polarized focal spots and results in a set of converging and diverging spherical wavefronts that interfere to form concentric circular fringes. We applied polarization phase-shifting interferometry to obtain the optical path difference (OPD) variation of the interference field. The displacement is calculated from the OPD variation. A validation experiment has been carried out by introducing known shifts to the PP. The setup can be used for displacement as well as distance measurement.

Invited Article: A compact optically coherent fiber frequency comb

We describe the design, fabrication, and performance of a self-referenced, optically coherent frequency comb. The system robustness is derived from a combination of an optics package based on polarization-maintaining fiber, saturable absorbers for mode-locking, high signal-to-noise ratio (SNR) detection of the control signals, and digital feedback control for frequency stabilization. The output is phase-coherent over a 1-2 μm octave-spanning spectrum with a pulse repetition rate of ∼200 MHz and a residual pulse-to-pulse timing jitter <3 fs well within the requirements of most frequency-comb applications. Digital control enables phase coherent operation for over 90 h, critical for phase-sensitive applications such as timekeeping. We show that this phase-slip free operation follows the fundamental limit set by the SNR of the control signals. Performance metrics from three nearly identical combs are presented. This laptop-sized comb should enable a wide-range of applications beyond the laboratory.

Intensity evaluation using a femtosecond pulse laser for absolute distance measurement

In this paper, we propose a method of intensity evaluation based on different pulse models using a femtosecond pulse laser, which enables long-range absolute distance measurement with nanometer precision and large non-ambiguity range. The pulse cross-correlation is analyzed based on different pulse models, including Gaussian, Sech(2), and Lorenz. The DC intensity and the amplitude of the cross-correlation patterns are also demonstrated theoretically. In the experiments, we develop a new combined system and perform the distance measurements on an underground granite rail system. The DC intensity and amplitude of the interference fringes are measured and show a good agreement with the theory, and the distance to be determined can be up to 25 m using intensity evaluation, within 64 nm deviation compared with a He-Ne incremental interferometer, and corresponds to a relative precision of 2.7×10(-9).

Air refractive index measurement using low-coherence interferometry

This paper presents a theoretical analysis and an experimental verification of a direct method for a refractive index of air measurement combining low-coherence interferometry and laser interferometry. The method is based on monitoring optical path changes in a measuring arm of the Michelson interferometer caused by the different optical environment in a double-spaced glass cell. This article presents a set of experimental results in comparison with the results obtained by a couple of reference techniques and proves the ability of the designed method to measure the refractive index of air with accuracy in the order of 10^-8.

Pulse-to-pulse alignment based on interference fringes and the second-order temporal coherence function of optical frequency combs for distance measurement

A pulse-to-pulse alignment method based on interference fringes and the second-order temporal coherence function of optical frequency combs is proposed for absolute distance measurement. The second-order temporal coherence function of the pulse train emitted from optical frequency combs is studied. A numerical model of the function is developed with an assumption of Gaussian pulse and has good agreement with experimental measurements taken by an ordinary Michelson interferometer. The experimental results show an improvement of standard deviation of peak finding results from 27.3 nm to 8.5 nm by the method in ordinary laboratory conditions. The absolute distance measurement with the pulse-to-pulse alignment method is also proposed and experimentally proved.

Heterodyne multi-wavelength absolute interferometry based on a cavity-enhanced electro-optic frequency comb pair

We present a heterodyne absolute distance interferometer with a macroscopic range, based on a promising optical source. The basis of the heterodyne measurement principle, a frequency comb pair with slightly different repetition rates and offset frequencies, is realized coherently by synchronized cavity-enhanced electro-optic frequency comb generators. The unknown distance is determined absolutely from the interferometric phases of distinct comb modes, by a parallel digital lock-in scheme. Comparison experiments with a reference HeNe incremental interferometer show an agreement well within 15 μm, for a range up to 10 m.

Absolute distance measurement by intensity detection using a mode-locked femtosecond pulse laser

We propose an interferometric method that enables to measure a distance by the intensity measurement using the scanning of the interferometer reference arm and the recording of the interference fringes including the brightest fringe. With the consideration of the dispersion and absorption of the pulse laser in a dispersive and absorptive medium, we investigate the cross-correlation function between two femtosecond laser pulses in the time domain. We also introduce the measurement principle. We study the relationship between the position of the brightest fringe and the distance measured, which can contribute to the distance measurement. In the experiments, we measure distances using the method of the intensity detection while the reference arm of Michelson interferometer is scanned and the fringes including the brightest fringe is recorded. Firstly we measure a distance in a range of 10 µm. The experimental results show that the maximum deviation is 45 nm with the method of light intensity detection. Secondly, an interference system using three Michelson interferometers is developed, which combines the methods of light intensity detection and time-of-flight. This system can extend the non-ambiguity range of the method of light intensity detection. We can determine a distance uniquely with a larger non-ambiguity range. It is shown that this method and system can realize absolute distance measurement, and the measurement range is a few micrometers in the vicinity of Nl(pp), where N is an integer, and lpp is the pulse-to-pulse length.

Operation of an optically coherent frequency comb outside the metrology lab

We demonstrate a self-referenced fiber frequency comb that can operate outside the well-controlled optical laboratory. The frequency comb has residual optical linewidths of < 1 Hz, sub-radian residual optical phase noise, and residual pulse-to-pulse timing jitter of 2.4 - 5 fs, when locked to an optical reference. This fully phase-locked frequency comb has been successfully operated in a moving vehicle with 0.5 g peak accelerations and on a shaker table with a sustained 0.5 g rms integrated acceleration, while retaining its optical coherence and 5-fs-level timing jitter. This frequency comb should enable metrological measurements outside the laboratory with the precision and accuracy that are the hallmarks of comb-based systems.

Low-noise parametric frequency comb for continuous C-plus-L-band 16-QAM channels generation

A low phase noise frequency comb generated from a continuous-wave seed is experimentally demonstrated across continuous C- and L-bands. Parametrically generated carriers with optical signal-to-noise ratio in excess of 45 dB were used to generate 16-ary quadrature amplitude modulated signals. We characterize 20 GBaud channels' performance that was varied by only 1.7 dB across the combined C/L band.

Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling

A dual-comb nonlinear asynchronous optical sampling method is proposed to simplify determination of the time interval and extend the non-ambiguity range in absolute length measurements. Type II second harmonic generation facilitates curve fitting in determining the time interval between adjacent pulses. Meanwhile, the non-ambiguity range is extended by adjusting the repetition rate of the signal laser. The performance of the proposed method is compared with a heterodyne interferometer. Results show that the system achieves a maximum residual of 100.6 nm and an uncertainty of 1.48 μm in a 0.5 ms acquisition time. With longer acquisition time, the uncertainty can be reduced to 166.6 nm for 50 ms and 82.9 nm for 500 ms. Moreover, the extension of the non-ambiguity range is demonstrated by measuring an absolute distance beyond the inherent range determined by the fixed repetition rate.

Optical frequency comb interference profilometry using compressive sensing

We describe a new optical system using an ultra-stable mode-locked frequency comb femtosecond laser and compressive sensing to measure an object's surface profile. The ultra-stable frequency comb laser was used to precisely measure an object with a large depth, over a wide dynamic range. The compressive sensing technique was able to obtain the spatial information of the object with two single-pixel fast photo-receivers, with no mechanical scanning and fewer measurements than the number of sampling points. An optical experiment was performed to verify the advantages of the proposed method.

Comb-calibrated frequency-modulated continuous-wave ladar for absolute distance measurements

We demonstrate a comb-calibrated frequency-modulated continuous-wave laser detection and ranging (FMCW ladar) system for absolute distance measurements. The FMCW ladar uses a compact external cavity laser that is swept quasi-sinusoidally over 1 THz at a 1 kHz rate. The system simultaneously records the heterodyne FMCW ladar signal and the instantaneous laser frequency at sweep rates up to 3400 THz/s, as measured against a free-running frequency comb (femtosecond fiber laser). Demodulation of the ladar signal against the instantaneous laser frequency yields the range to the target with 1 ms update rates, bandwidth-limited 130 μm resolution and a ~100 nm accuracy that is directly linked to the counted repetition rate of the comb. The precision is <100 nm at the 1 ms update rate and reaches ~6 nm for a 100 ms average.

Pulse-to-pulse alignment technique based on synthetic-wavelength interferometry of optical frequency combs for distance measurement

A synthetic-wavelength interferometry of optical frequency combs is proposed for the pulse-to-pulse alignment in absolute distance measurement. The synthetic wavelength derived from the virtual second harmonic and the real second harmonic is used to bridge the interference intensity peak-finding method and the heterodyne interferometric phase measurement, so that the pulse-to-pulse alignment can be linked directly to single-wavelength heterodyne interferometry. The experimental results demonstrate that the distance measured by the peak-finding method with micrometer accuracy can be improved to the nanometer level by applying the method proposed.

Multi-wavelength generation by self-seeded four-wave mixing

A cost effective method of generating multi-wavelength based on the cascaded four wave mixing effect is experimentally demonstrated. The proposed scheme is free from external tunable laser sources and pump modulators, resulting from the use of a broadened linewidth tunable dual wavelength erbium-doped fiber laser as intracavity pump. In this configuration, the number of four wave mixing cascades becomes larger in tandem with the increment of erbium-doped fiber amplifier output power. When its output power is set at 20.57 dBm, six waves having optical signal to noise ratio larger than 10 dB are generated. The six waves are stable with peak power fluctuations less than 1 dB within 30 minutes period and tunable with wavelength spacing ranging from 1.03 nm to 11.31 nm.

Dynamic optical sampling by cavity tuning and its application in lidar

Optical sampling by cavity tuning (OSCAT) enables cost-effective realization of fast tunable optical delay using a single femtosecond laser. We report here a dynamic model of OSCAT, taking into account the continuous modulation of laser repetition rates. This allows us to evaluate the delay scan depth under high interferometer imbalance and high scan rates, which cannot be described by the previous static model. We also report the demonstration of remote motion tracking based on fast OSCAT. Target vibration as small as 15 µm peak to peak and as fast as 50 Hz along line-of-sight has been successfully detected at an equivalent free-space distance of more than 2 km.

Frequency comb generation by CW laser injection into a quantum-dot mode-locked laser

We report on frequency comb generation at 1.5 μm by injection of a CW laser in a hybridly mode-locked InAs/InP two-section quantum-dot laser (HMLQDL). The generated comb has > 60 modes spaced by ∼ 4.5 GHz and a -20 dBc width of > 100 GHz (23 modes) at > 30 dB signal to background ratio. Comb generation was observed with the CW laser (red) detuned more than 20 nm outside the HMLQDL spectrum, spanning a large part of the gain spectrum of the quantum dot material. It is shown that the generated comb is fully coherent with the injected CW laser and RF frequency used to drive the hybrid mode-locking. This method of comb generation is of interest for the creation of small and robust frequency combs for use in optical frequency metrology, high-frequency (> 100 GHz) RF generation and telecommunication applications.

Graphene oxide vs. reduced graphene oxide as saturable absorbers for Er-doped passively mode-locked fiber laser

In this work we demonstrate comprehensive studies on graphene oxide (GO) and reduced graphene oxide (rGO) based saturable absorbers (SA) for mode-locking of Er-doped fiber lasers. The paper describes the fabrication process of both saturable absorbers and detailed comparison of their parameters. Our results show, that there is no significant difference in the laser performance between the investigated SA. Both provided stable, mode-locked operation with sub-400 fs soliton pulses and more than 9 nm optical bandwidth at 1560 nm center wavelength. It has been shown that GO might be successfully used as an efficient SA without the need of its reduction to rGO. Taking into account simpler manufacturing technology and the possibility of mass production, GO seems to be a good candidate as a cost-effective material for saturable absorbers for Er-doped fiber lasers.

Many-wavelength interferometry with thousands of lasers for absolute distance measurement

We demonstrate a new technique for absolute distance measurement with a femtosecond frequency comb laser, based on unraveling the output of an interferometer to distinct comb modes with 1 GHz spacing. From the fringe patterns that are captured with a camera, a distance is derived by combining spectral and homodyne interferometry, exploiting about 9000 continuous wave lasers. This results in a measurement accuracy far within an optical fringe (λ/30), combined with a large range of nonambiguity (15 cm). Our technique merges multiwavelength interferometry and spectral interferometry, within a single scheme.

Space position measurement using long-path heterodyne interferometer with optical frequency comb

A heterodyne interference system was developed for position measurement. A stabilized optical-frequency comb is used as the laser source. The preliminary experiment to measure a distance of 22.478 m shows a drift of 1.6 μm in 20 minutes after the temperature compensation. Comparison and frequency shift experiments have been done for a distance of about 7.493 m. The experimental results show that the drift is mainly caused by environmental condition changes and the vibration of the table and floor also has some effects. It was verified that the absolute distance measurement can be realized by fringe scanning and frequency-shifting methods.

Generation of wideband frequency combs by continuous-wave seeding of multistage mixers with synthesized dispersion

We numerically and experimentally demonstrate efficient generation of an equalized optical comb with 150-nm bandwidth. The comb was generated by low-power, continuous-wave seeds, eliminating the need for pulsed laser sources. The new architecture relies on efficient creation of higher-order mixing tones in phase-matched nonlinear fiber stages separated by a linear compressor. Wideband generation was enabled by precise dispersion engineering of multiple-stage parametric mixers.

High-accuracy self-correction of refractive index of air using two-color interferometry of optical frequency combs

Long-path pulse-to-pulse interferometers of two-color frequency combs are developed using fundamental and second harmonics of a mode-locked fiber laser. Interferometric phase difference between two-color frequency combs was precisely measured by stabilizing the fundamental fringe phase by controlling the repetition frequency of the comb, and a stability of 10(-10) for 1000 s was achieved in the measurement of an optical path length difference between two wavelengths. In long-term measurements performed for 10 h, results of phase variation of interferometric measurements were highly consistent with the fluctuations in the calculated difference of refractive indices of air at two wavelengths with an accuracy of 10(-10). The difference between the measured optical distances corresponding to two wavelengths and the optical distance corresponding to the fundamental wavelength were used in the two-color method; high-accuracy self-correction of the fluctuation of refractive index of air was performed with an uncertainty of 5 × 10(-8) for 10-h measurements when the maximum refractive index change was on the order of 10(-6).

Sub-micron absolute distance measurements in sub-millisecond times with dual free-running femtosecond Er fiber-lasers

We demonstrate a simplified dual-comb LIDAR setup for precision absolute ranging that can achieve a ranging precision of 2 μm in 140 μs acquisition time. With averaging, the precision drops below 1 μm at 0.8 ms and below 200 nm at 20 ms. The system can measure the distance to multiple targets with negligible dead zones and a ranging ambiguity of 1 meter. The system is much simpler than a previous coherent dual-comb LIDAR because the two combs are replaced by free-running, saturable-absorber-based femtosecond Er fiber lasers, rather than tightly phase-locked combs, with the entire time base provided by a single 10-digit frequency counter. Despite the simpler design, the system provides a factor of three improved performance over the previous coherent dual comb LIDAR system.

Long distance measurement with femtosecond pulses using a dispersive interferometer

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.

Time-of-flight method using multiple pulse train interference as a time recorder

A unique length measurement method, called the multiple pulse train interference-based time-of-flight (TOF) method, is proposed and demonstrated for the first time. By taking advantage of both the high-accuracy measurement capability of a pulse train interference method and the arbitrary and absolute length measurement capability of a TOF method, the present method is expected to be useful for high-precision length measurement for not only science purposes but also industry requirements. A long gauge block was measured using this optical method to demonstrate the feasibility of the proposed method.