Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling

All-polarization-maintaining dual-comb Er-fiber laser with combined figure-8 and figure-9 architectures

We propose and demonstrate, for the first time to the best of our knowledge, an all-polarization-maintaining (all-PM) dual-comb Er-fiber laser based on combined figure-8 and figure-9 architectures. The opposite signs of the non-reciprocal phase shifts required for figure-8 and figure-9 architectures in the shared nonlinear amplifying loop mirror (NALM) are achieved using a single non-reciprocal phase shifter (NRPS) that operates in two orthogonal polarizations. The capability of common mode noise cancellation, environmental stability, long-term reliability, and the tunable range of the repetition rate difference Δf rep between two combs has been investigated and characterized. In addition, the dual-comb spectroscopy measurement with our dual-comb fiber laser is demonstrated to resolve the transmission spectrum of a flat-top DWDM (dense wavelength division multiplexer) demultiplexer, with a passband of ∼50 GHz at 1564.5 nm. Our experimental results indicate that the combined-architecture all-PM fiber laser, with its large tunable range of 100 kHz in Δf rep , shows significant potential for dual-comb applications in precise and rapid metrology outside the laboratory.

Long-distance and high-precision ranging with dual-comb nonlinear asynchronous optical sampling

Precise distance metrology and measurements play an important role in many fields of scientific research and industrial manufacture. Dual-comb laser ranging combines sub-wavelength ranging precision, large non-ambiguity range, and high update rate, making it the most promising candidate in precise distance metrology and measurements. However, previous demonstrations of dual-comb ranging suffer from short working distances, limited by the decoherence of lasers in interferometric schemes or by the low sensitivity of the photodetectors in response to the sparse echo photons. Here, we propose and demonstrate time-of-flight laser ranging with dual-comb nonlinear asynchronous optical sampling and photon counting by a fractal superconducting nanowire single-photon detector, achieving ranging precision of 6.2 micrometers with an acquisition time of 100 ms and 0.9 micrometers with an acquisition time of 1 s in measuring the distance of an outdoor target approximately 298 m away.

Integer-locking condition for stable dual-comb interferometry in situations with fluctuating frequency-comb repetition rates

To make dual-comb interferometry usable in a wide range of applications, it is important to achieve reproducible measurement results even in non-ideal environments that affect the repetition-rate stability. Here, we consider dual-comb interferometry based on a pair of fully referenced optical frequency combs (OFCs) and investigate the impact of fluctuations in the OFC repetition frequencies on the peak position of the center burst in the interferogram. We identify a phase-locking scheme that minimizes the impact of these fluctuations through choosing a special combination of phase-locked frequencies, and the resulting type of operating condition is termed integer-locking condition. Under the integer-locking condition, the number of sampling points in each interferogram remains constant regardless of repetition-rate variations, and this enables more stable phase-resolved measurements in non-ideal environments. We demonstrate the application of this approach using absolute path-length measurements and discuss the accuracy limit imposed by the integer-locking condition. Our findings offer a strategy for robust dual-comb interferometry outside metrology laboratories.

Open-Air Testing of Dual-Comb Time-of-Flight Measurement

We configured a long-distance ranging apparatus to test the principle of dual-comb time-of-flight measurement using ultrashort lasers. Emphasis was given to the evaluation of open-air performance quantitatively in terms of the measurement resolution and stability. The test results revealed that our dual-comb asynchronous optical pulse sampling permits micrometer-resolved ranging with a repeatability of 2.05 μm over a 648 m distance in dry weather conditions. Further atmospheric effects were evaluated in three different weather conditions with corresponding Allan deviations. Finally, the capability of simultaneous determination of multiple targets was verified with the potential of advanced industrial applications, such as manufacturing, surveying, metrology, and geodesy.

Tunable Optical Frequency Comb Generated Using Periodic Windows in a Laser and Its Application for Distance Measurement

A novel method for the generation of an optical frequency comb (OFC) is presented. The proposed approach uses a laser diode with optical feedback and operating at a specific nonlinear dynamic state named periodic window. In this case, the laser spectrum exhibits a feature with a series of discrete, equally spaced frequency components, and the repetition rate can be flexibly adjusted by varying the system parameters (e.g., external cavity length), which can provide many potential applications. As an application example, a dual-OFC system for distance measurement is presented. The results demonstrate the system's ability to achieve target distance detection, underscoring its potential for real-world applications in this field.

Ranging disambiguation of LiDAR using chirped amplitude-modulated phase-shift method

Ranging ambiguity is the major challenge in most LiDAR techniques with amplitude modulation, which limits the performance of range detection due to the tradeoff between the ranging precision and the unambiguous range. Here we propose a novel disambiguation method using a laser with chirped amplitude modulation (sweeping modulation frequency), which can in theory infinitely expand the unambiguous range and completely solve the ranging ambiguation problem. The usage of the earlier proposed Chirped Amplitude-Modulated Phase-Shift (CAMPS) technique enables us to detect the phase-shift of chirped signals with high precision. Incorporating this technique with the proposed disambiguation method, the absolute distance well beyond the conventional unambiguous range can easily be found with merely <1% frequency sweep range. When certain conditions are met, the Non-Mechanical Spectrally Scanned LiDAR (NMSL) system employing the CAMPS method and the Dispersion-Tuned Swept Laser (DTSL) can also realize disambiguation in non-mechanical line-scanning measurement.

Multi-target two-photon dual-comb LiDAR

By substituting two-photon cross-correlation in a wide-bandgap photodiode for the coherent gating conventionally used in dual-comb ranging, two-photon dual-comb LiDAR exchanges data-intensive interferometric acquisition for a single time-stamp from which an absolute distance can be inferred. Here, we report the application of two-photon dual-comb LiDAR to obtain real-time ranging to three independent targets with only a single silicon-photodiode detector. We show precisions of 197-255 nm (2 seconds averaging time) for static targets, and real-time simultaneous ranging to three dynamic targets driven by independent sinusoidal, saw-tooth and square waveforms. Finally, we demonstrate multi-target ranging to three points on a rigid body to provide simultaneous pitch and yaw angular measurements with precisions of 27.1 arcsec (130 µrad) on a 25 mm baseline.

Two-photon imaging of soliton dynamics

Optical solitary waves (solitons) that interact in a nonlinear system can bind and form a structure similar to a molecule. The rich dynamics of this process have created a demand for rapid spectral characterization to deepen the understanding of soliton physics with many practical implications. Here, we demonstrate stroboscopic, two-photon imaging of soliton molecules (SM) with completely unsynchronized lasers, where the wavelength and bandwidth constraints are considerably eased compared to conventional imaging techniques. Two-photon detection enables the probe and tested oscillator to operate at completely different wavelengths, which permits mature near-infrared laser technology to be leveraged for rapid SM studies of emerging long-wavelength laser sources. As a demonstration, using a 1550 nm probe laser we image the behavior of soliton singlets across the 1800-2100 nm range, and capture the rich dynamics of evolving multiatomic SM. This technique may prove to be an essential, easy-to-implement diagnostic tool for detecting the presence of loosely-bound SM, which often remain unnoticed due to instrumental resolution or bandwidth limitations.

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.

Terahertz Time-of-Flight Ranging with Adaptive Clock Asynchronous Optical Sampling

We propose and implement a terahertz time-of-flight ranging system based on adaptive clock asynchronous optical sampling, where the timing jitter is corrected in real time to recover the depth information in the acquired interferograms after compensating for laser instabilities using electronic signal processing. Consequently, the involved measurement uncertainties caused by the timing jitter during the terahertz sampling process and the noise intensity of the terahertz electric field have been reduced by the utilization of the adaptive clock. The achieved uncertainty range is about 2.5 μm at a 5 cm distance after averaging the acquisition time of 1876 ms 5000 times, showing a significant improvement compared with the asynchronous optical sampling using a constant clock. The implemented terahertz ranging system only uses free-running mode-locked lasers without any phase-locked electronics, and this favors simple and robust operations for subsequent applications that extend beyond the laboratory conditions.

Ultra-rapid dual-comb ranging with an extended non-ambiguity range

In this Letter, we report a scheme that combines time-of-flight (ToF) ranging detection of multi-repetition-rate pulses with asymmetric dual-comb ranging (DCR) measurement. Notably, this combination extends the non-ambiguity range (NAR) of the DCR method without sacrificing its refresh rate and distance precision. With this scheme, we demonstrate absolute distance measurement of moving targets with an NAR of 1.5 km, which is 5× larger than that allowed solely by the DCR method for a given refresh rate at 500 kHz. The ranging precision in a single measurement of 2 µs reaches 10 µm at an effective distance of 571 m (down to 60 nm in 0.1 s). This combined scheme benefits remote sensing of high-speed objects.

Dynamic and precise long-distance ranging using a free-running dual-comb laser

Long-distance ranging is a crucial tool for both industrial and scientific applications. Laser-based distance metrology offers unprecedented precision making it the ideal approach for many deployments. In particular, dual-comb ranging is favorable due to its inherently high precision and sampling rate. To make high-performance long-range dual-comb LiDAR more accessible by reducing both cost and complexity, here we demonstrate a fiber-based dual-comb LiDAR frontend combined with a free-running diode-pumped solid-state dual-comb laser that allows for sub-µm measurement precision while offering a theoretical ambiguity range of more than 200 km. Our system simultaneously measures distance with the role of each comb interchanged, thereby enabling Vernier-based determination of the number of ambiguity ranges. As a proof-of-principle experiment, we measure the distance to a moving target over more than 10 m with sub-µm precision and high update rate, corresponding to a relative precision of 10^-7. For a static target at a similar distance, we achieve an instantaneous precision of 0.29 µm with an update time of 1.50 ms. With a longer averaging time of 200 ms, we reach a precision of around 33 nm, which corresponds to a relative precision of about 3·10^-9 with a time-of-flight-based approach.

Extending Non-Ambiguity Range of Dual-Comb Ranging for a Mobile Target Based on FPGA

Dual-comb ranging (DCR) is an important method in absolute distance ranging because of its high precision, fast acquisition rate, and large measuring range. DCR needs to obtain precise results during distance measurements for a mobile target. However, the non-ambiguity range (NAR) is a challenge when pushing the dual-comb ranging to the industry field. This paper presents a solution for extending NAR by designing an algorithm and realizing it on a field-programmable gate array (FPGA). The algorithm is robust when facing the timing jitter in the optical frequency comb. Without averaging, the Allan deviation of the results in 1 ms is ∼3.89 μm and the Allan deviation of the results is ∼0.37 μm at an averaging time of 100 ms when the target object is standstill near the NAR. In addition, several ranging experiments were conducted on a mobile target whose speed was from ∼5 mm/s to ∼10 mm/s. The experimental results verify the effectiveness and robustness of our design. The implemented design is an online and real-time data processing unit that shows great industrial potential for using the DCR system.

Impact of Laser Intensity Noise on Dual-Comb Absolute Ranging Precision

Noise in mode-locked lasers has been a central issue for dual-comb metrological applications. In this work, we investigate the laser intensity noise on dual-comb absolute ranging precision. Two different dual-comb schemes based on linear optical sampling (LOS) and nonlinear asynchronous optical sampling (ASOPS) have been constructed. In the LOS scheme, the ranging precision deteriorates with the increase in laser relative intensity noise (RIN). This effect can be corrected by implementing a balanced photo-detection (BPD). In the ASOPS scheme, the experiment shows that the conversion from laser RIN to dual-comb ranging precision is negligible, making a balanced detection unnecessary for ranging precision improvement. The different manners of RIN's impact on absolute ranging precision are attributed to the distinct cross-correlation signal patterns and the underlying time-of-flight (TOF) extraction algorithms.

Real-time distance and velocity measurement based on the dual-comb system

With the development of laser metrology, the dual-comb system has natural superiority in the measuring fields. Specifically, distance and velocity represent a basic state for the target in space. We propose an application mode of the dual-comb interferometry integrated into the field programmable gate array. A high-speed parallel processor truly gives full play to the benefit of the data processing rate. The algorithm of the peak extraction and the address matching also bring an efficient working mode into the whole scheme. To verify the performance of this system, we devise a series of experiments for distance and velocity, respectively. The data processing rate of the distance is 425 Hz and that of the corresponding average velocity is 0.425 Hz, which is flexible for different measuring conditions. The experimental results show that the difference can be well within 252.8 µm at 5 m range and 284.9 µm/s over 0.5 m/s.

Fast and high-resolution spectroscopy based on asynchronous optical sampling

Dispersive time stretch has made many ultrafast applications possible owing to its high frame rate, as compared to conventional spectroscopies. By further introducing a converging time lens, this spectroscopy can resolve arbitrary emission spectra within the aperture. However, a spectral resolution of tens of picometers hinders its high-precision application. There are two limitations: the temporal aperture of the acquired signal and the actual acquisition bandwidth. To overcome these restrictions, two approaches were developed. First, a large-aperture time lens, with higher-order dispersion compensation, is used to overcome the fundamental limit of the time-bandwidth product. Second, asynchronous optical sampling, based on two frequency combs, overcomes the technical limit of the acquisition bandwidth. As a result, in this study, time-stretch spectroscopy achieved a 1-pm spectral resolution, 24-nm observation bandwidth, and 1-kHz frame rate. Moreover, it was used to observe some spectral dynamics of the random lasing process and devices with narrow spectral widths. This scheme provides essential improvement for time-stretch spectroscopy to achieve high precision.

Timing jitter characterization of free-running dual-comb laser with sub-attosecond resolution using optical heterodyne detection

Pulse trains emitted from dual-comb systems are designed to have low relative timing jitter, making them useful for many optical measurement techniques such as optical ranging and spectroscopy. However, the characterization of low-jitter dual-comb systems is challenging because it requires measurement techniques with high sensitivity. Motivated by this challenge, we developed a technique based on an optical heterodyne detection approach for measuring the relative timing jitter of two pulse trains. The method is suitable for dual-comb systems with essentially any repetition rate difference. Furthermore, the proposed approach allows for continuous and precise tracking of the sampling rate. To demonstrate the technique, we perform a detailed characterization of a single-mode-diode pumped Yb:CaF₂ dual-comb laser from a free-running polarization-multiplexed cavity. This new laser produces 115-fs pulses at 160 MHz repetition rate, with 130 mW of average power in each comb. The detection noise floor for the relative timing jitter between the two pulse trains reaches 8.0 × 10^-7 fs²/Hz (∼ 896 zs/Hz), and the relative root mean square (rms) timing jitter is 13 fs when integrating from 100 Hz to 1 MHz. This performance indicates that the demonstrated laser is highly compatible with practical dual-comb spectroscopy, ranging, and sampling applications. Furthermore, our results show that the relative timing noise measurement technique can characterize dual-comb systems operating in free-running mode or with finite repetition rate differences while providing a sub-attosecond resolution, which was not feasible with any other approach before.

Modelling two-laser asynchronous optical sampling using a single 2-section semiconductor mode-locked laser diode

We present a theoretical overview and a proposed methodology which demonstrates SLASOPS (single laser asynchronous optical sampling) as a single-laser alternative to the conventional two-laser ASOPS technique. We propose the optical and electronic setup in which SLASOPS may be achieved experimentally with a single 2-section mode-locked laser diode as the pulsed-laser source and simulate how asynchronous optical sampling is generated and detected theoretically. We highlight the technique's ability to provide customizable scan ranges, scan rates and scan resolutions through variation of the imbalance in the interferometer arms and by tuning the repetition rate of the pulsed-laser source, which we present as optical cross-correlations between pulse pairs. We incorporate jitter into the system mathematically to assess the limitations on resolving both intensity and interferometric cross-correlation traces and to investigate the effects of averaging such traces in real-time. Analysis is then carried out on cross-correlation trace amplitude, width, and temporal positioning in order to discuss the technique's ability for deployment in typical optical sampling applications. In particular we note SLASOPS' ability to conduct asynchronous optical sampling using only a single laser, halving both the expense and technical requirements, doing so at megahertz scan rates, and within a spatial precision of just a few microns.

Performance and limitations of dual-comb based ranging systems

Dual-comb LiDARs have the potential to perform high-resolution ranging at high speed. Here, through an implementation involving electro-optic modulators and heterodyne detection, we quantify the ranging systems trade-off between precision and non-ambiguity range (NAR) using a unique performance factor. We highlight the influence of the comb amplitude envelope on the precision with a distance measurement limited by the repetition rate of the optical comb. The influence of the combs repetition rate on the NAR and on the precision is illustrated through a setup allowing distance measurement with a tunable NAR. Finally, we demonstrate the impossibility to resolve different targets, quantify the impact on the measured distance and develop on the conditions in which non-linear effects of the interference make the measurement impossible.

Proof-of-concept study of the virtual optical scale bar by the pulse-to-pulse interferometry

The optical scale bar with calibrated or measured internal point-to-point length has many applications in coordinate measurements. In this paper, the virtual optical scale bar with two retroreflectors is constructed by the absolute distance measurement based on pulse-to-pulse interferometry. The temporal and dispersive coherence could be utilized to determine the adjustable internal length of multiple pulse-to-pulse intervals with high precision. The proposed scheme was combined with a pellicle beamsplitter to minimize systematic error. The influence of its thickness on precision is also discussed and calibrated in detail. Besides, a femtosecond mode-locked pulse laser with 100-MHz repetition rates was employed in our system to develop an optical scale bar and verify the feasibility of the proposed method. The sub-micron precision could be realized by temporal coherence with a piezo-driven stage or a simplified non-polarized scheme of dispersed coherence. It shows that this method could achieve a flexible and high-precision virtual optical scale bar for further practical applications.

Two-photon dual-comb LiDAR

The interferometric signals produced in conventional dual-comb laser ranging require femtosecond lasers with long-term carrier-envelope offset frequency stability, and are limited to an upper sampling rate by radio-frequency aliasing considerations. By using cross-polarized dual combs and two-photon detection, we demonstrate carrier-phase-insensitive cross-correlations at sampling rates of up to 12× the conventional dual-comb aliasing limit, recording these in a digitizer-based acquisition system to implement ranging with sub-100 nm precision. We then extend this concept to show how the high data burden of conventional dual-comb acquisition can be eliminated by using a simple microcontroller as a ns-precision stopwatch to record the time intervals separating the two-photon cross-correlation pulses, providing real-time and continuous LiDAR-like distance metrology capable of sub-100 nm precision and dynamic acquisition for unlimited periods.

Aliasing-free dual-comb ranging system based on free-running fiber lasers

A dual-comb ranging (DCR) system without spectral aliasing based on free-running fiber lasers was proposed. By monitoring the repetition frequency over time, we compensate for the instability of the optical pulse train from the free-running fiber lasers. We demonstrated a double-channel filtering structure that eliminates the aliasing between multiheterodyne beats in radio frequency interferograms. Without any frequency locking, the DCR system implements stable running for at least 60 min. The system realizes a 6-µm repetition precision without averaging and shows good consistency with a commercial interferometer.

Simple approach for extending the ambiguity-free range of dual-comb ranging

Dual-comb (DC) ranging is an established method for high-precision and high-accuracy distance measurements. It is, however, restricted by an inherent length ambiguity and the requirement for complex control loops for comb stabilization. Here, we present a simple approach for expanding the ambiguity-free measurement length of DC ranging by exploiting the intrinsic intensity modulation of a single-cavity dual-color DC for simultaneous time-of-flight and DC distance measurements. This measurement approach enables the measurement of distances up to several hundred kilometers with the precision and accuracy of a DC interferometric setup while providing a high data acquisition rate (≈2kHz) and requiring only the repetition rate of one of the combs to be stabilized.

Compression-coding-based surface measurement using a digital micromirror device and heterodyne interferometry of an optical frequency comb

We propose a compression-coding-based surface measurement method that combines single-pixel imaging and heterodyne interference using an optical frequency comb. The real and imaginary parts of the heterodyne interference signals are used to obtain the depth information rapidly. By optimizing the ordering of the Hadamard measurement basis, we reconstruct a three-step sample with heights of approximately 10, 20, and 30 µm without an iterative operation in 6 ms, with a precision of 5 nm. Compared with the uncompressed measurement, the sampling times reduced to 20%, and the measurement time reduced by five times without measurement accuracy loss. The proposed method is effective for rapid measurements, particularly for objects with a simple surface topography.

Sub-100-nm precision distance measurement by means of all-fiber photonic microwave mixing

The importance of dimensional metrology has gradually emerged from fundamental research to high-technology industries. In the era of the fourth industrial revolution, absolute distance measurements are required to cope with various applications, such as unmanned vehicles, intelligent robots, and positioning sensors for smart factories. In such cases, the size, weight, power, and cost (SWaP-C) should essentially be restricted. In this paper, sub-100 nm precision distance measurements based on an amplitude-modulated continuous-wave laser (AMCW) with an all-fiber photonic microwave mixing technique is proposed and realized potentially to satisfy SWaP-C requirements. Target distances of 0.879 m and 8.198 m were measured by detecting the phase delay of 15 GHz modulation frequencies. According to our measurement results, the repeatability could reach 43 nm at an average time of 1 s, a result not previously achieved by conventional AMCW laser distance measurement methods. Moreover, the performance by the proposed method in terms of Allan deviation is competitive with most frequency-comb-based absolute distance measurement methods, even with a simple configuration. Because the proposed method has a simple configuration such that it can be easily utilized and demonstrated on a chip-scale platform using CMOS-compatible silicon photonics, it is expected to herald new possibilities, leading to the practical realization of a fully integrated chip-scale LIDAR system.

Improved Self-Calibration of a Multilateration System Based on Absolute Distance Measurement

Multilateration tracking systems (MLTSs) are used in industrial three-dimensional (3D) coordinate measuring applications. For high-precision measurement, system parameters must be calibrated properly in advance. For an MLTS using absolute distance measurement (ADM), the conventional self-calibration method significantly reduces estimation efficiency because all system parameters are estimated simultaneously using a complicated residual function. This paper presents a novel self-calibration method that optimizes ADM to reduce the number of system parameters via highly precise and separate estimations of dead paths. Therefore, the residual function to estimate the tracking station locations can be simplified. By applying a suitable mathematical procedure and solving the initial guess problem without the aid of an external device, estimation accuracy of the system parameters is significantly improved. In three self-calibration experiments, with ADM repeatability of approximately 3.4 µm, the maximum deviation of the system parameters estimated by the proposed self-calibration method was 68.6 µm, while the maximum deviation estimated by the conventional self-calibration method was 711.9 µm. Validation of 3D coordinate measurements in a 1000 mm × 1000 mm × 1000 mm volume showed good agreement between the proposed ADM-based MLTS and a commercial laser tracker, where the maximum difference based on the standard deviation was 17.7 µm. Conversely, the maximum difference was 98.8 µm using the conventional self-calibration method. These results confirmed the efficiency and feasibility of the proposed self-calibration method.

Photonic Microwave Distance Interferometry Using a Mode-Locked Laser with Systematic Error Correction

We report an absolute interferometer configured with a 1 GHz microwave source photonically synthesized from a fiber mode-locked laser of a 100 MHz pulse repetition rate. Special attention is paid to the identification of the repeatable systematic error with its subsequent suppression by means of passive compensation as well as active correction. Experimental results show that passive compensation permits the measurement error to be less than 7.8 μm (1 σ) over a 2 m range, which further reduces to 3.5 μm (1 σ) by active correction as it is limited ultimately by the phase-resolving power of the phasemeter employed in this study. With precise absolute distance ranging capability, the proposed scheme of the photonic microwave interferometer is expected to replace conventional incremental-type interferometers in diverse long-distance measurement applications, particularly for large machine axis control, precision geodetic surveying and inter-satellite ranging in space.

Absolute laser ranging by time-of-flight measurement of ultrashort light pulses [Invited]

Ultrashort pulse lasers are emerging as an advanced tool of distance measurement, with their unique temporal and spectral characteristics being extended to diverse principles of absolute ranging and instrumentation. Here, a systematic methodology is presented for absolute ranging by means of the time-of-flight measurement of ultrashort light pulses using dual-comb asynchronous optical sampling. Based on an elaborate uncertainty analysis, influencing system parameters such as the pulse duration, repetition rate, and averaging time are optimized to achieve a sub-µm measurement accuracy. The absolute ranging system developed in this study demonstrates a combined standard uncertainty of 0.986 µm for a 0.5 ms averaging over a distance range of 3.0 m, with a further reduction to 0.056 µm when the averaging time is increased to 0.5 s. The outstanding performance leads to unprecedented multitarget applications: machine feed control with thermal error compensation in real time as well as the nondestructive inspection of multilens assembly in a production line.

Coherent narrow-linewidth optical frequency synthesis across the optical telecommunication band

Broadband, coherent narrow-linewidth optical frequency synthesis is of crucial importance in dual-comb interferometric measurement. Here we present a detailed description of the construction and performance characterization of a hertz-level linewidth coherent optical frequency synthesizer across the optical telecommunication band. A narrow-linewidth cavity-stabilized laser at 1565.00 nm is built and coherently transferred through a fiber link with an additional fractional frequency instability of 2.0×10^-16 at 1 s averaging time. Broadband, coherent optical frequency synthesis is then achieved by steering one mode of a laser frequency comb with the transferred optical frequency oscillation. By beating with a 1542.14 nm ultra-stable cavity-stabilized laser, the evaluated fractional frequency stability and absolute linewidth of the nearest synthesized optical oscillation are 3.5×10^-15 at 1 s averaging time and 1.8 Hz, respectively. According to the ultra-low-noise feature of the utilized laser frequency comb of 4.7×10^-17 at 1 s averaging time, the synthesized optical frequency oscillations could maintain the high coherence across the comb's output bandwidth.

Submicrometric absolute positioning of flat reflective surfaces using Michelson interferometry

We present a Target Positioning Interferometer (TPI), a system that uses variations of the wavefront curvature to position solid reflective surfaces with submicrometric precision. The TPI is a Michelson interferometer into which a lens is inserted in the target arm and the mirror of the reference arm is slightly tilted. The TPI configuration presented in this work allows us to position the surface of a reflective target on a beam focus within an uncertainty of 350 nm (2σ) in a subsecond timeframe, using a lens with a numerical aperture of NA = 0.20. We support our experimental findings with numerical simulations of the interference pattern using the ABCD matrices' method, allowing us to define scaling laws for using the TPI with different optics and environments, as well as suggestions to improve the TPI accuracy and adapt the system to different applications. This system is very well suited for accurate and repeatable target positioning used in laser-driven ion acceleration, where a precise alignment is key to optimize the proton acceleration mechanism.

Simplified phase-stable dual-comb interferometer for short dynamic range distance measurement

A simplified phase-stable dual-comb interferometer for absolute distance measurement within a short dynamic range is proposed in this paper. The experimental results demonstrate that stable phase-difference information and lower timing jitter can be obtained within a time delay of 2000 ns between the reference interference signal and measurement interference signal. Using the proposed technique, the time-of-flight (TOF) result can link directly to the carrier-wave interferometric (CWI) result in an average time of 20 ms and can reach 2 nm precision in 0.5 s averaging time. Millimeter-scale measurement dynamic range and nanometer-level precision can thus be achieved without additional noise suppression. This method can also be applied at different stand-off distances.

Broadband and high-resolution electro-optic dual-comb interferometer with frequency agility

We propose a broadband and high-resolution dual-comb interferometer (DCI) realized with dense electro-optic frequency combs (EOFCs), which are generated with two-stage electro-optic modulation and nonlinear fiber spectral broadening. The broadband coarse comb is generated in the first-stage modulation and the space between neighboring combs is filled with a dense electrical comb in the second-stage modulation. The spectral resolution of the DCI can be flexibly changed from 10 MHz to 1 GHz easily as required, and electro-optic DCIs with 10-MHz, 100-MHz, and 1-GHz frequency resolutions are experimentally realized. Meanwhile, DCI working in the quasi-integer-ratio mode is easily implemented in this system for the increased refresh rate and improved figure of merit especially for high resolution. As a demonstration, 150000 comb lines with 10 MHz frequency interval are resolved in the experiment.

Fast molecular fingerprinting with a coherent, rapidly tunable dual-comb spectrometer near 3 μm

We report the multi-species determination and fast molecular fingerprinting under microseconds by employing a rapidly tunable dual-comb spectrometer based on electro-optic frequency combs near 3 μm.

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.

Reduction of Moving Target Time-of-Flight Measurement Uncertainty in Femtosecond Laser Ranging by Singular Spectrum Analysis Based Filtering

Femtosecond laser ranging has drawn great interest in recent years, particularly based on an asynchronous optical sampling implementation where a pair of femtosecond lasers are used. High precision absolute ranging either relies on tightly-phase-locked optical frequency combs (a dual-comb setup) or multiple averaging of the measurements from two free-running femtosecond lasers. The former technique is too complicated for practical applications, while the latter technique does not apply to moving targets. In this report, we propose a new route to utilizing a powerful singular spectrum analysis (SSA) filtering method to improve femtosecond laser ranging precision for moving targets with acceleration. The SSA method is capable of separating complex patterns in signals without a priori knowledge of the dynamical model. Here, we utilize the basic SSA filter to extract the target trajectory in the presence of measurement noise both in numerical simulation and in the absolute ranging experiment based on a pair of free-running femtosecond lasers. The experimentally-achieved absolute ranging uncertainty of a moving target is well below 110 nm at a 200-Hz update rate by applying the basic SSA filter. This method paves the way to the practical applications of femtosecond absolute ranging for dynamic objects.

Ultrafast time-stretch microscopy based on dual-comb asynchronous optical sampling

The ultrafast time-stretch microscopy based on a single-pixel detector has become a hotspot of the research, owing to its high sensitivity compared to those pixel sensors. However, gigahertz or tens of gigahertz acquisition bandwidth is required for this scheme, resulting in great expense for the whole imaging system and hindering its wide applications. In this Letter, a dual-comb asynchronous optical sampling is applied for the conventional time-stretch microscopy, whose ultrafast temporal axis is magnified by 9200 times. The acquisition bandwidth requirement is thus greatly relaxed, and 320 kHz bandwidth successfully resolves 2.3 μm spatial resolution with tens of kilohertz frame rate.

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.

Line-scan spectrum-encoded imaging by dual-comb interferometry

Herein, the method of spectrum-encoded dual-comb interferometry is introduced to measure a three-dimensional (3-D) profile with absolute distance information. By combining spectral encoding for wavelength-to-space mapping, dual-comb interferometry for decoding and optical reference for calibration, this system can obtain a 3-D profile of an object at a stand-off distance of 114 mm with a depth precision of 12 μm. With the help of the reference arm, the absolute distance, reflectivity distribution, and depth information are simultaneously measured at a 5 kHz line-scan rate with free-running carrier-envelope offset frequencies. To verify the concept, experiments are conducted with multiple objects, including a resolution test chart, a three-stair structure, and a designed "ECNU" letter chain. The results show a horizontal resolution of ∼22  μm and a measurement range of 1.93 mm.

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.

Absolute distance measurement by multi-heterodyne interferometry using an electro-optic triple comb

We experimentally demonstrate a method for absolute distance measurement using a triple-comb-based multi-heterodyne interferometer which has the capacity to simultaneously balance the non-ambiguous range, resolution, update rate, and cost. Three flat-top electro-optic combs generated via cascaded intensity and phase modulators are adopted to form a measurement scheme including rough and fine measurements, and the unknown distance is determined by detecting the phase changes of the consecutive synthetic wavelengths. Experimental results demonstrate an agreement within 750 nm over 80 m distance at an update rate of 167 μs.

Simply-integrated dual-comb spectrometer via tunable repetition rates and avoiding self-referencing

Dual-comb system with simplified integration acts a crucial role in the next stage of field-deployable application. Here we demonstrate a home-made dual-comb spectrometer that meets this requirement based on optically stabilized erbium-fiber frequency combs. The simplified integration and operability are highlighted by the embedded large motion-span automatic optical delay line that resulted in 1.7 MHz of continuous repetition rate tuning range and avoid multiple fiber cutbacks. This relaxes the second similar frequency comb duplication, therefore simplifies dual-comb system integration. The mutual coherence was enhanced by optical phase lock to a common narrow-linewidth reference laser via pump current modulation. We acquired the absorption feature of acetylene ¹²C₂H₂ molecule in 1.5 μm region with an apodized instrument linewidth of 0.076 cm^-1. The mean signal-to-noise ratio within a spectral bandwidth of 90 cm^-1 achieved 280, and the corresponding noise equivalent absorption coefficient was 3.7 × 10^-6 cm^-1·Hz^-1/2 for an absorption path of 7.5 cm and a pressure of 100 Torr. The accuracy of the retrieved spectrum was further confirmed by comparing with HITRAN database.

Quantum-limited timing jitter characterization of mode-locked lasers by asynchronous optical sampling

We demonstrate a novel time domain timing jitter characterization method for ultra-low noise mode-locked lasers. An asynchronous optical sampling (ASOPS) technique is employed, allowing timing jitter statistics on a magnified timescale. As a result, sub femtosecond period jitter of an optical pulse train can be readily accessible to slow detectors and electronics (~100 MHz). The concept is applied to determine the quantum-limited timing jitter for a passively mode-locked Er-fiber laser. Period jitter histogram is acquired following an eye diagram analysis routinely used in electronics. The identified diffusion constant for pulse timing agrees well with analytical solution of perturbed master equation.

Optically stabilized Erbium fiber frequency comb with hybrid mode-locking and a broad tunable range of repetition rate

We present an optically stabilized Erbium fiber frequency comb with a broad repetition rate tuning range based on a hybrid mode-locked oscillator. We lock two comb modes to narrow-linewidth reference lasers in turn to investigate the best performance of control loops. The control bandwidth of fast and slow piezoelectric transducers reaches 70 kHz, while that of pump current modulation with phase-lead compensation is extended to 32 kHz, exceeding laser intrinsic response. Eventually, simultaneous lock of both loops is realized to totally phase-stabilize the comb, which will facilitate precision dual-comb spectroscopy, laser ranging, and timing distribution. In addition, a 1.8-MHz span of the repetition rate is achieved by an automatic optical delay line that is helpful in manufacturing a secondary comb with a similar repetition rate. The oscillator is housed in a homemade temperature-controlled box with an accuracy of ±0.02  K, which not only keeps high signal-to-noise ratio of the beat notes with reference lasers, but also guarantees self-starting at the same mode-locking every time.

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.

Comb-referenced laser distance interferometer for industrial nanotechnology

A prototype laser distance interferometer is demonstrated by incorporating the frequency comb of a femtosecond laser for mass-production of optoelectronic devices such as flat panel displays and solar cell devices. This comb-referenced interferometer uses four different wavelengths simultaneously to enable absolute distance measurement with the capability of comprehensive evaluation of the measurement stability and uncertainty. The measurement result reveals that the stability reaches 3.4 nm for a 3.8 m distance at 1.0 s averaging, which further reduces to 0.57 nm at 100 s averaging with a fractional stability of 1.5 × 10(-10). The uncertainty is estimated to be in a 10(-8) level when distance is measured in air due to the inevitable ambiguity in estimating the refractive index, but it can be enhanced to a 10(-10) level in vacuum.

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.