Absolute Ranging with Time Delay Interferometry for Space-Borne Gravitational Wave Detection.

In future space-borne gravitational wave (GW) detectors, time delay interferometry (TDI) will be utilized to reduce the overwhelming noise, including the laser frequency noise and the clock noise etc., by time shifting and recombining the data streams in post-processing. The successful operation of TDI relies on absolute inter-satellite ranging with meter-level precision. In this work, we numerically and experimentally demonstrate a strategy for inter-satellite distance measurement. The distances can be coarsely determined using the technique of arm-locking ranging with a large non-ambiguity range, and subsequently TDI can be used for precise distance measurement (TDI ranging) by finding the minimum value of the power of the residual noises. The measurement principle is introduced. We carry out the numerical simulations, and the results show millimeter-level precision. Further, we perform the experimental verifications based on the fiber link, and the distances can be measured with better than 0.05 m uncertainty, which can well satisfy the requirement of time delay interferometry.

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/Hz1/2 at 0.7 mHz, and 4 × 10-6Hz/Hz1/2 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/Hz1/2 at 0.1 mHz, and 7 × 10-7Hz/Hz1/2 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.

Weak-Light Phase-Locking Time Delay Interferometry with Optical Frequency Combs.

In the future space-borne gravitational wave (GW) detector, the optical transponder scheme, i.e., the phase-locking scheme, will be utilized so as to maintain the signal-to-noise ratio (SNR). In this case, the whole constellation will share one common laser equivalently, which enables the considerable simplification of time delay interferometry (TDI) combinations. Recently, and remarkably, the unique combination of TDI and optical frequency comb (OFC) has shown a bright prospect for the future space-borne missions. When the laser frequency noise and the clock noise are synchronized using OFC as the bridge, the data streams will be reasonably simplified. However, in the optical transponder scheme, the weak-light phase-locking (WLPL) loops could bring additional noises. In this work, we analyze the phase-locking scheme with OFC and transfer characteristics of the noises including the WLPL noise. We show that the WLPL noise can be efficiently reduced by using the specific TDI combination, and the cooperation of phase-locking and frequency combs can greatly simplify the post-processing.

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/Hz1/2 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.

Three-Dimensional Imaging by Frequency-Comb Spectral Interferometry.

In this paper, we demonstrate a three-dimensional imaging system based on the laser frequency comb. We develop a compact, all-fiber mode-locked laser at 1 µm, whose repetition frequency can be tightly synchronized to the external frequency reference. The mode-locked state is achieved via the saturable absorber mirror in a linear cavity, and the laser output power can be amplified from 4 mW to 150 mW after a Yb-doped fiber amplifier. Three-dimensional imaging is realized via the spectral interferometry with the aid of an equal-arm Michelson interferometer. Compared with the reference values, the measurement results show the difference can be below 4 µm. Our system could provide a pathway to the real industry applications in future.

Long distance measurement by dynamic optical frequency comb.

In this paper, we propose a method aiming to measure the absolute distance via the slope of the inter-mode beat phase by sweeping the repetition frequency of the frequency comb. The presented approach breaks the inertial thinking of the extremely stable comb spacing, and the bulky phase-locking circuit of the repetition frequency is not required. In particular, the non-ambiguity range can be expanded to be infinite. To verify the performance of presented method, a series of distance experiments have been devised in different scenarios. Compared with the reference values, the experimental results show the differences within 25 µm at 65 m range in the laboratory, and within 100 µm at 219 m range out of the lab.

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.

Characterization of pulsed ultrasound using optical detection in Raman-Nath regime.

In this paper, we describe an optical detection method for the characterization of pulsed ultrasound based on acousto-optic interaction. We deduce the relationship between the ultrasound and the diffracted light from the principle of acousto-optic diffraction in the Raman-Nath regime, which is verified experimentally. Five ultrasonic transducers with different central frequencies and different focusing types are measured to show the method's performance regarding linearity, sound pressure measurement, phase measurement, frequency response, and spatial resolution. The experimental results show a good agreement with simulation data by CIVA (ultrasonic simulation software, M2M NDT, Inc.) and the pulse-echo method.

Direct measurement of the sound velocity in seawater based on the pulsed acousto-optic effect between the frequency comb and the ultrasonic pulse.

We present a new method to measure the velocity of sound in pure water and seawater using the Raman-Nath diffraction caused by acousto-optic effect between the optical frequency comb and the ultrasonic pulse. In the Mach-Zehnder interferometry system we established, the measurement and reference arms are tagged with sharp negative pulses caused by the pulsed ultrasound passing through them. The difference in optical path between the two parallel beams is twice the flight distance of the ultrasonic waves. The span between the two negative pulses reflects the time interval. At the same time, the distance between the two arms can be measured precisely using the femtosecond laser interferometry. Consequently, the time interval and the distance can be used to measure the sound velocity. The experimental results show that, the uncertainty of the sound speed measurement can achieve 0.03m/s@1482m/s in pure water and 0.029m/s@1527m/s in seawater, respectively, compared with the commercial sound velocity profiler (SVP). More importantly, benefiting from the faster and cleaner response of the acousto-optic effect than the piezoelectric effect which is widely adopted in direct sound velocity measurement method, our method provides a new idea for the metrology of sound velocity in seawater.

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.

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.

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 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.

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).

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.