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

Sub-micron inline thickness measurement of cold-rolled metal strips by multi-wavelength interferometry and laser triangulation

Thin metal foils of thicknesses below 100 µm are finding increasing use in high-tech applications. For such foils it is essential that production be controlled inline with sub-micron accuracy in highly challenging environments. An optical thickness gauge combining laser triangulation with multi-wavelength interferometry has now been developed for this purpose. Modulation-based 2f-3f-interferometry was used to realize a compact and robust sensor. A thorough measurement uncertainty analysis of the complete thickness measurement process yielded an expanded measurement uncertainty of U=(0.30μm)2+4π R a2, which is dependent on the roughness average Ra. The influence of oil remnants on measurement results is significantly weaker in the interference measurement than in geometric optical systems. Verification measurements against tactile reference measurements support the derived measurement uncertainty, and initial measurements in actual rolling mill environments have proven the real-world capability of this measurement technique over relevant process time scales at metal strip speeds of 200 m/min.

Tri-comb generation with a dual-ring structure

By introducing a third measurement comb with different repetition frequencies (Δ f r e p ), the tri-comb spectroscopy technique overcomes the ambiguity problem of the original dual-comb spectroscopy technique and eliminates physical delay stages in multidimensional coherent spectroscopy. Nowadays, tri-comb generation based on three frequency-stabilized comb lasers is overly complicated and costly for many potential applications. Previous research on single-cavity dual-combs inspired research on single-cavity tri-combs. However, the currently reported tri-comb structures cannot achieve independently controllable pulses. This paper shows a dual-ring tri-comb seed-source structure using wavelength-based multiplexing in one of the rings. The wavelength and power of the output pulse are independently controlled by using the dual-ring structure. The Δ f r e p of wavelength multiplexing-based dual-comb output can be tuned by adjusting the intra-ring polarization controller (PC). In the case of single-wavelength mode-locking, the PC can be adjusted to achieve a wavelength tuning range of nearly 20 nm. The tri-comb source could offer an attractive alternative solution as a low-complexity light source for field-deployable multi-comb metrology applications.

Multi-heterodyne interferometric absolute distance measurements based on dual dynamic electro-optic frequency combs

In multi-heterodyne interferometry, the non-ambiguous range (NAR) and measurement accuracy are limited by the generation of synthetic wavelengths. In this paper, we propose a multi-heterodyne interferometric absolute distance measurement based on dual dynamic electro-optic frequency combs (EOCs) to realize high-accuracy distance measurement with large scale. The modulation frequencies of the EOCs are synchronously and quickly controlled to perform dynamic frequency hopping with the same frequency variation. Therefore, variable synthetic wavelengths range from tens of kilometer to millimeter can be flexibly constructed, and traced to an atomic frequency standard. Besides, a phase-parallel demodulation method of multi-heterodyne interference signal is implemented based on FPGA. Experimental setup was constructed and absolute distance measurements were performed. Comparison experiments with He-Ne interferometers demonstrate an agreement within 8.6 µm for a range up to 45 m, with a standard deviation of 0.8 µm and a resolution better than 2 µm at 45 m. The proposed method can provide sufficient precision with large scale for many science and industrial applications, such as precision equipment manufacturing, space mission, length metrology.

Accurate and Comprehensive Spectrum Characterization for Cavity-Enhanced Electro-Optic Comb Generators

Cavity-enhanced electro-optic comb generators (CEEOCGs) can provide optical frequency combs with excellent stability and configurability. The existing methods for CEEOCGs spectrum characterization, however, are based on approximations and have suffered from either iterative calculations or limited applicable conditions. In this paper, we show a spectrum characterization method by accumulating the optical electrical field with respect to the count of the round-trip propagation inside of CEEOCGs. The identity transformation and complete analysis of the intracavity phase delay were conducted to eliminate approximations and be applicable to arbitrary conditions, respectively. The calculation efficiency was improved by the noniterative matrix operations. Setting the maximum propagation count as 1000, the spectrum of the center ±300 comb modes can be characterized with merely the truncation error of floating-point numbers within 1.2 s. More importantly, the effects of all CEEOCG parameters were comprehensively characterized for the first time. Accordingly, not only the exact working condition of CEEOCG can be identified for further optimization, but also the power of each comb mode can be predicted accurately and efficiently for applications in optical communications and waveform synthesis.

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.

Absolute distance measurement using sinusoidal phase modulating frequency sweeping interferometry with a reference interferometer

Frequency sweeping interferometry with reference interferometer based on sinusoidal phase modulating technique is proposed in this paper for absolute distance measurement. With the frequency of the external cavity diode laser (ECDL) swept continuously in sinusoidal, a HeNe laser was employed to monitor the drifts of the target and the reference length, and influences caused by drifts during the measurement were compensated in real time. Sinusoidal phase modulation with non-overlapping frequencies were applied to the two laser lights individually by two electro-optic modulators (EOM), and the interference phases corresponding to the two laser lights were extracted simultaneously using the phase generated carrier (PGC) demodulation based on frequency-division multiplex technique. Performance of the phase detection method has been verified by nanometer displacement measurements. Experimental results show that the measurement uncertainty can be considerably reduced by compensating the influences of drifts and by applying linear regression to get the ratio of interference phase changes between the measurement interferometer and the reference interferometer. Comparison of the absolute distance measurement with an incremental interferometer yields a measurement uncertainty of 10^-5, which is in good agreement with the estimation of the measurement uncertainty.

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.

All-optical coherent pulse compression for dynamic laser ranging using an acousto-optic dual comb

We demonstrate a new and simple dynamic laser ranging platform based on analog all-optical coherent pulse compression of modulated optical waveforms. The technique employs a bidirectional acousto-optic frequency shifting loop, which provides a dual-comb photonic signal with an optical bandwidth in the microwave range. This architecture simply involves a CW laser, standard telecom components and low frequency electronics, both for the dual-comb generation and for the detection. As a laser ranging system, it offers a range resolution of a few millimeters, set by a dual-comb spectral bandwidth of 24 GHz, and a precision of 20 µm for an integration time of 20 ms. The system is also shown to provide dynamic measurements at scanning rates in the acoustic range, including phase-sensitive measurements and Doppler shift velocimetry. In addition, we show that the application of perfect correlation phase sequences to the transmitted waveforms allows the ambiguity range to be extended by a factor of 10 up to ∼20 m. The system generates quasi-continuous waveforms with low peak power, which makes it possible to envision long-range telemetry or reflectometry requiring highly amplified signals.

Electro-optic frequency combs for rapid interrogation in cavity optomechanics

Electro-optic frequency combs were employed to rapidly interrogate an optomechanical sensor, demonstrating spectral resolution substantially exceeding that possible with a mode-locked frequency comb. Frequency combs were generated using an integrated-circuit-based direct digital synthesizer and utilized in a self-heterodyne configuration. Unlike approaches based upon laser locking, the present approach allows rapid, parallel measurements of full optical cavity modes, large dynamic range of sensor displacement, and acquisition across a wide frequency range between DC and 500 kHz. In addition to being well suited to measurements of acceleration, this optical frequency comb-based approach can be utilized for interrogation in a wide range of cavity optomechanical sensors.

A Multidimensional Multiplexing Mode-Locked Laser Based on a Dual-Ring Integrative Structure for Tri-Comb Generation

The tri-comb-based multi-heterodyne detection technique has been proven to be a powerful tool for precision metrology, e.g., laser ranging and spectroscopy. However, in existing tri-comb generation methods, it is difficult to provide a large and variable difference in tri-comb repetition rates. In this paper; we propose a multidimensional multiplexing mode-locked laser based on a dual-ring integrative structure. Combining the dimensions of sub-ring multiplexing and wavelength multiplexing, two modes of tri-comb generation can be achieved with the dual-ring single cavity laser. The generated combs are identified based on the relative intensity of the pulse trains and optical spectrum, and the repetition rates of dual-combs from the same sub-ring are distinguished based on dispersion analysis. With repetition rates of approximately 47 MHz and 49.6 MHz, the minimum and maximum repetition rate difference of the generated tri-comb can be changed from 2.38 kHz and 2.59526 MHz to 2.74 kHz and 2.59720 MHz merely by switching the operation mode of the dual-ring integrated mode-locked laser. The obtained results indicate that our method can offer a powerful scheme for future multi-comb generation and its application in multi-heterodyne detection-based laser ranging and spectroscopy.

Analysis of a highly efficient phase-locking stabilization method for electro-optic comb generation

We theoretically show that a slightly modified Pound-Drever-Hall (PDH) stabilization scheme can lead to the optimum time-domain characteristics for electro-optic comb generators (EOCG). The ideal locking point is located by analyzing the EOCG output pulse width. By summing up the electrical field reflected by the EOCG front mirror, a model of the phase-locking error signal is derived with the Jacobi-Anger identical transformation. The simulation and experiment show that the zero-locking point of the error signal of the modified scheme coincides well with the ideal locking point in contrast with the direct application of the PDH scheme. Finally, a power efficiency of up to 2.9% is achieved with this EOCG stabilization scheme. A relative instability of better than 2.6×10^-8 is demonstrated by a dual comb interferometer with fixed paths. The Allan deviations of the comb mode frequencies are smaller than 2.8×10^-9 and 1.1×10^-10 for average times of 1 and 100 s, respectively.

Real-time dynamic absolute ranging with frequency scanning interferometry using a robust Monte-Carlo-based particle filter

A particle-filter-based data processing for a frequency-scanning interferometry system for dynamic long absolute ranging is presented in this paper. Because the particle filter is not restricted by linearity or noise Gaussianity requirements, the proposed system achieves high robustness and accuracy levels when tracking dynamic objects at long standoff distances. We experimentally demonstrate that the proposed system exhibits a standard deviation below 6 μm for a quasi-static target, and superior tracking performance for a vibrating target with vibration amplitude exceeding 10 μm and frequencies of 1-5 Hz at a 15 m standoff distance.

Bidirectional frequency-shifting loop for dual-comb spectroscopy

We present a bidirectional recirculating frequency-shifting loop, seeded by a continuous-wave (cw) laser, to perform multi-heterodyne interferometry. This fiber-optic system generates two counter-propagating "acousto-optic" frequency combs with a controllable line spacing. Apart from its simple architecture, coherent averaging allows us to reach acquisition times up to the second scale without resorting to any active stabilization mechanism. We also show that the relative phase between the combs is quadratic and can be easily controlled by adjusting the parameters of the loop. The capability of our scheme to perform molecular spectroscopy is proven by dual-comb measurements of a transition of hydrogen cyanide in the near-infrared region (1550 nm).

Dynamic cascade-model-based frequency-scanning interferometry for real-time and rapid absolute optical ranging

A new frequency-scanning interferometry (FSI) scheme using in-phase and quadrature (IQ) detection for real-time and rapid absolute optical ranging is presented. Dynamic measurement with FSI modulates interference signal frequency by both target movement and time-varying optical-frequency scanning rate; hence, a dynamic model is proposed to decouple dynamic absolute distance from the instantaneous frequency of interference signals. The unscented Kalman filter and particle filter algorithms are implemented for the nonlinear first-layer and non-Gaussian second-layer models, respectively. The proposed FSI scheme eliminates nonlinear optical-frequency scanning effects in dynamic measurements and realizes real-time measurement only current observed data are used. Experimental results verify high tracking performance for a vibrating target with approximately 10 μm amplitude and 50-500 Hz frequency.

Coherent multi-heterodyne spectroscopy using acousto-optic frequency combs

We propose and characterize experimentally a new source of optical frequency combs for performing multi-heterodyne spectrometry. This comb modality is based on a frequency-shifting loop seeded with a continuous-wave (CW) monochromatic laser. The comb lines are generated by successive passes of the CW laser through an acousto-optic frequency shifter. We report the generation of frequency combs with more than 1500 mutually coherent lines, without resorting to non-linear broadening phenomena or external electronic modulation. The comb line spacing is easily reconfigurable from tens of MHz down to the kHz region. We first use a single acousto-optic frequency comb to conduct self-heterodyne interferometry with a high frequency resolution (500 kHz). By increasing the line spacing to 80 MHz, we demonstrate molecular spectroscopy on the sub-millisecond time scale. In order to reduce the detection bandwidth, we subsequently implement an acousto-optic dual-comb spectrometer with the aid of two mutually coherent frequency shifting loops. In each architecture, the potentiality of acousto-optic frequency combs for spectroscopy is validated by spectral measurements of hydrogen cyanide in the near-infrared region.

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.

Electro-optic dual-comb interferometer for high-speed vibrometry

Electro-optic frequency comb generators are particularly promising for dual-comb spectroscopy. They provide a high degree of mutual coherence between the combs without resorting to complex feedback stabilization mechanisms. In addition, electro-optic frequency combs can operate at very high repetition rates, thus providing very fast acquisition speeds. Here, we exploit these two features to resolve the rapid movement of a vibrating target. Our electro-optic dual-comb interferometer is capable of combining time-of-fight information with a more precise interferometric measurement based on the carrier phase. This fact, previously demonstrated by stabilized femtosecond frequency combs, allows us to increase the precision of the time-of-flight measurement by several orders of magnitude. As a proof of concept, we implement a fiber-based vibrometer that offers sub-nanometer precision at an effective acquisition speed of 250 kHz. These results expand the application landscape of electro-optic dual-comb spectroscopy to laser ranging and other remote sensing measurements.

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.

Overcoming the refractivity limit in manufacturing environment

We present a tracking interferometer with an intrinsic compensation of the refractive index of air. By using both wavelengths of a frequency doubled Nd:YAG laser the refractive index of air can be determined and compensated by the dispersion. One dimensional benchmark verification experiments in air conditioned and typical harsh, uncontrolled environment show an asymptotic length dependent uncertainty in the order of 0.1 μm/m for distances over 10 m, proofing the potential of this approach for high accuracy measurements in industrial environments.

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.

Simultaneous multi-channel absolute position alignment by multi-order grating interferometry

A simultaneous multi-channel absolute position alignment system is investigated to determine the absolute position of a grating mark. By employing a multi-order grating interferometer and a multi-channel phase extraction method, many equivalent measurement results are generated simultaneously for stable and consistent measurement. By combining measurement results of different orders, low-order signals enabled large unambiguous measurement ranges, and high-order signals enhanced the measurement accuracy. Comparison experiments performed using an incremental HeNe reference interferometer yielded the standard deviations of smaller than 11.48nm under laboratory conditions. The proposed scheme will enable a new class of absolute position alignment system for industrial applications.

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.

Precision distance measurement using a two-photon absorption process in a silicon avalanche photodiode with saw-tooth phase modulation

We present a novel configuration of a precision laser distance measurement based on the two-photon absorption (TPA) photocurrent from a silicon avalanche photodiode (Si-APD). The proposed system uses saw-tooth phase modulation, known as serrodyne modulation, in order to shift the frequency of the reference light from that of the probe light. It suppresses the coherent interference noise between the probe and the reference. The serrodyne modulation also enables lock-in detection of the TPA photocurrent. Furthermore, it contributes to the reduction of the system components. The precision measurement is experimentally demonstrated by measuring a fiber length difference of 2.6 m with a standard deviation of 27 μm under constant temperature. The high-precision displacement measurement is also demonstrated by measuring the temperature-induced change in the optical path length difference of a fiber interferometer.

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).

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.