Non-ambiguity Range Research Articles

Broadband phononic frequency comb generation in a parametrically excited capacitive micromachined ultrasonic transducer

Optical frequency combs consisting of evenly spaced discrete frequencies have been used for a number of applications such as frequency metrology, range finding and molecular fingerprinting. Recently, the acoustic equivalent of these frequency combs, known as phononic frequency combs (PFCs), have been demonstrated in micro and nanoscale resonators. However, such demonstrations are restricted to PFC generation in high-Q mechanical resonators under carefully controlled operating conditions with limited practical applications. In this work, we demonstrate a novel method of generating PFCs with a parametrically driven capacitive micromachined ultrasonic transducer (CMUT) operating in a fluid medium. The proposed system consists of an electrically driven CMUT array that forms part of a resonant RLC circuit of frequency w0. By applying two drive tones of frequency w0 and w0+Δ, we are able to generate broadband acoustic frequency combs via a parametric four-wave mixing process. The intensity and number of combs generated is strongly dependent on the relative strength of the two driving tones whereas the comb spacing is determined by the frequency difference Δ between the drive signals. We also briefly discuss a potential application of PFCs in extended non-ambiguous range (NAR) distance metrology with interferometric resolution.

High-precision long-distance measurement with an intensity-modulated frequency comb.

We describe an improved synthetic wavelength method for high-precision long-distance measurement with a repetition-rate-locked femtosecond laser modulated by a fiber Mach-Zehnder electro-optic intensity modulator. Harmonics of the repetition rate accompanied with modulating sidebands will be generated via intermode beating, which will be utilized for high-precision ranging. The nonambiguity range is significantly extended with a relatively low modulation frequency, and the ambiguous distance is unwrapped by synchronous phase-shift measurements of a synthetic wavelength chain without any auxiliary measurement operation. Our experiment shows a precision better than 20 µm at 46 m range, and a high-precision translation stage is applied for preliminary test and proof-of-principle demonstration. The demonstrated system is simple and can be easily integrated, and it will find widespread applications in large-scale metrology such as large-volume manufacturing and precision formation flying.

Ultrafast, sub-nanometre-precision and multifunctional time-of-flight detection

Displacement measurement is a fundamental functionality in modern science and technology. Although there has been remarkable progress in the precision of such measurements with various laser ranging methods1–8, they are incapable of capturing fast and complex mechanical displacements. Here, we have established a displacement measurement method using time-of-flight detection9 with femtosecond optical pulses and frequency-locked electrical waveforms. This method uniquely combines ultrafast measurement speed, sub-nanometre precision and non-ambiguity range of more than several millimetres. The achieved performance features unprecedented detection speed and precision. Starting from 24 nm precision for 4 ns acquisition time, the precision can reach 180 pm for 5 ms acquisition time. Using this method, we show real-time detection of single-event, fast and high-dynamic-range mechanical displacements. This capability can lead to the realization of new measurement and analysis platforms for studying broadband, transient and nonlinear mechanical dynamics in real time, which will be useful for directly probing optomechanics10, the onset of cracks11, dynamic deformations12, nonlinear vibrations13, ultrasonic phenomena14 and cell-generated forces15. Using a femtosecond mode-locked laser and a frequency-locked electric signal, a displacement measurement method that offers a >MHz measurement speed, sub-nanometre precision and a measurement range of more than several millimetres is achieved, facilitating the study of broadband, transient and nonlinear mechanical dynamics in real time.

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.

Method of measuring absolute distance based on spectral interferometry using an electro-optic comb

To explore a new generation of ranging method suitable for industrial applications, in this paper, a spectral interferometry ranging method based on electro-optic (EO) comb is proposed. The mathematical model of EO comb and the principle of spectral expansion are analyzed in detail. Besides, the factors affecting the non-ambiguous range and resolution of the spectral interferometry method are also discussed. According to the theoretical analysis, the resolution of spectral interference ranging is mainly affected by the spectrum width of the optical frequency comb, and the non-ambiguous range is affected by the resolution of the optical spectrum analyzer (equal to the highest sampling rate of the optical spectrum analyzer). In the experiment, triple cascaded EO phase modulator is used to modulate a single frequency laser to generate more than 40 high-power sidebands. Then, the laser spectrum output from the EO modulator is expanded by single mode fiber and high nonlinearity fiber. Owing to the use of erbium doped fiber amplifier between the dispersion compensation fiber (single mode fiber) and the highly nonlinearity fiber, the polarization disturbance does not affect the spectrum width of the optical frequency comb significantly. However, the width of spectrum will be still affected by the phases of light, and the phases of light can be adjusted by the phase shifters in the front of the electro-optic modulators. Finally, the EO comb with a repetition frequency of 10 GHz and spectrum width of 30 nm is obtained. The EO comb can be used as the source of spectral interferometry scheme. Since the repetition frequency of the EO comb is high enough, which can meet the distortion-free sampling of optical spectrum analyzer. Hence, there is no “dead zone” in the measurement range. Besides, the equal frequency interval resampling algorithm and quadratic equation fitting algorithm are used in the data processing. Through the use of these algorithms, we can eliminate the measurement errors caused by non-equal frequency interval sampling of the optical spectrum analyzer and improve the ranging accuracy. The experimental results show that within the range of 1 m, the absolute ranging accuracy of 15 μm can be achieved at arbitrary position.

Photon-counting laser interferometer for absolute distance measurement on rough surface.

We designed a dual-wavelength photon-counting laser interferometer for absolute distance measurement of noncooperative targets. The weak optical interference on the rough surface was measured by a single-photon detector. The range of nonambiguity of the dual-wavelength interferometer was less than 1.2 μm, as the maximum errors of Lg and Lr were 7.8 nm and 9.1 nm caused by the photon-counting measurement and the frequency shift of the two unlocked lasers. We integrated laser triangulation into the interferometer as a coarse measurement, thus increasing the range of nonambiguity to 6.5 mm. As a result, a measurement standard deviation of ∼18 nm was achieved within a range of 1.1 mm in the experiment.

Absolute distance measurement based on spectral interferometry using femtosecond optical frequency comb

We demonstrated an absolute distance measurement method based on the frequency folding effect using the spectral interferometry of femtosecond optical frequency comb. And the investigation was carried out on the ranging accuracy influence of the phase noise in the traditional complicated phase unwrapping method via band-pass filter and Fourier Transform. To reduce the effects of the phase noise, we proposed the non-filtered and differential envelop phase demodulation method, and its robustness was illustrated with a standard deviation of 75 nm for the stability of single point measurements. Further, through the extension of the non-ambiguity range, we achieved a resolution of better than 30 µm in a long distance measurements range of 70 m, yielding a relative precision of 3.1 × 10−7.

Analysis of main parameters of spectral interferometry ranging using optical frequency comb and animproved data processing method

<sec>With the rapid development of modern technology, high-precision absolute distance measurement is playing an important role in many applications, such as scientific research, aviation and industry measurement. Among the above various measurement methods, how to realize higher-accuracy, larger-scale, and faster-speed measurement is particularly important. In the traditional technique for long-distance measurement, the emergence of optical frequency comb (OFC) provides a breakthrough technology for accurately measuring the absolute value of distance. The OFC can be considered as a multi-wavelength source,whose phase and repetition rate are locked. The OFC is a very useful light source that can provide phase-coherent link between microwave and optical domain, which has been used as a source in various distance measurement schemes that can reach an extraordinary measurement precision and accuracy. A variety of laser ranging methods such as dual-comb interferometry and dispersive interferometer based on femtosecond laser have been applied to the measuring of absolute distance.</sec><sec>In this paper, the factors affecting the resolution and the non-ambiguous range of spectral interferometry ranging using OFC are particularly discussed. We also analyze the systematic errors and the limitations of traditional transform methods based on Fourier transform, which can conduce to the subsequent research.</sec><sec>To address the problem caused by low resolution and unequal frequency interval, we propose a data processing method referred to as equal frequency interval resampling. The proposed method is based on cubic spline interpolation and can solve the error caused by the frequency spectrum broadening with the increase of distance. Moreover, we propose a new method based on least square fitting to calibrate the error introduced by the low resolution of interferometry spectrum obtained with fast Fourier transform (FFT). With the proposed method, the simulation results show that the systematic error is less than 0.2 μm in the non-ambiguity range and the system resolution is greatly improved. Finally, anabsolute distance measurement system based on Michelson interferometer is built to verify theproposed method. The measurement results compared with those obtained by using a high-precision commercial He-Ne laser interferometer show that the distance measurement accuracy is lower than 3 μm at any distancewithin the non-ambiguity range. The experimental results demonstrate that our data processing algorithm is able to increase the accuracy of dispersive interferometry ranging with OFC.</sec>

Optical Acceleration Measurement Method with Large Non-ambiguity Range and High Resolution via Synthetic Wavelength and Single Wavelength Superheterodyne Interferometry.

Interferometric optomechanical accelerometers provide superior resolution, but the application is limited due to the non-ambiguity range that is always less than half of the wavelength, which corresponds to the order of mg. This paper proposes a novel acceleration measurement method based on synthetic wavelength and single wavelength superheterodyne interferometry to address this issue. Two acousto-optical modulators and several polarizers are introduced to the two-wavelength interferometry to create four beams with different frequencies and polarization states, and two ultra-narrow bandwidth filters are used to realize the single wavelength measurement simultaneously. This technique offers the possibility to expand the non-ambiguity range without compromising the high resolution. Also, the superheterodyne phase measurement and the corresponding processing algorithm are given to enable real-time measurement. A prototype is built and the preliminary experimental results are compared with the simulation results, showing good agreement. The results prove an estimated acceleration measurement resolution of around 10 μg and a non-ambiguity range of larger than 200 mg, which is more than 100 times that of the single wavelength-based optical accelerometer.

Dual-comb interferometry via repetition rate switching of a single frequency comb.

We experimentally demonstrate a versatile technique for performing dual-comb interferometry using a single frequency comb. By rapid switching of the repetition rate, the output pulse train can be delayed and heterodyned with itself to produce interferograms. The full speed and resolution of standard dual-comb interferometry is preserved while simultaneously offering a significant experimental simplification and cost savings. We show that this approach is particularly suited for absolute distance metrology due to an extension of the nonambiguity range as a result of the continuous repetition rate switching.

Absolute Distance Measurement by Self-Heterodyne EO Comb Interferometry

In this letter, we develop a compact and all-fiber system for absolute distance measurement using self-heterodyne electro-optic (EO) comb interferometry. The repetition frequency is at the level of hundreds of MHz, $\ll$ tens of GHz (typical value of EO comb), and the non-ambiguity range is large. The individual comb mode can be resolved by the self-heterodyne interferometry, and the phases of the resulting beat notes can be used to measure the distances. Compared with the reference distance meter, the experimental results show an agreement within $4~\mu \text{m}$ in 50 m range, corresponding to $8\times 10^{-8}$ in relative.

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 750nm over 80m distance at an update rate of 167μs.

Comb-referenced frequency-sweeping interferometry for precisely measuring large stepped structures.

A precise 3D surface measurement method for large stepped structures without height ambiguity is proposed based on optical-frequency-comb-referenced frequency-sweeping interferometry and Fourier-transformed fractional phase retrieval. Unlike other interferometry that depends on the absolute phase value for several certain wavelengths, this method obtains results from the phase change during frequency sweeping and thus remains free from the confined non-ambiguity range. By reference to an optical frequency comb, the relative uncertainty from the tunable laser frequency was reduced by three orders of magnitude, and the sweeping frequency range can be precisely determined. Besides, the fractional phase can be rapidly retrieved in only one step using a Fourier transform method, with advantages of high accuracy and immunity to light intensity fluctuation and mechanical vibration noise. Samples of step heights from 1μm to 1mm were measured, and the standard uncertainty was 45nm. This permits applications such as quality assurance in microelectronics production and micro-electro-mechanical system (MEMS) manufacture.

Real-Time and Meter-Scale Absolute Distance Measurement by Frequency-Comb-Referenced Multi-Wavelength Interferometry.

We report on a frequency-comb-referenced absolute interferometer which instantly measures long distance by integrating multi-wavelength interferometry with direct synthetic wavelength interferometry. The reported interferometer utilizes four different wavelengths, simultaneously calibrated to the frequency comb of a femtosecond laser, to implement subwavelength distance measurement, while direct synthetic wavelength interferometry is elaborately introduced by launching a fifth wavelength to extend a non-ambiguous range for meter-scale measurement. A linearity test performed comparatively with a He–Ne laser interferometer shows a residual error of less than 70.8 nm in peak-to-valley over a 3 m distance, and a 10 h distance comparison is demonstrated to gain fractional deviations of ~3 × 10−8 versus 3 m distance. Test results reveal that the presented absolute interferometer enables precise, stable, and long-term distance measurements and facilitates absolute positioning applications such as large-scale manufacturing and space missions.

High-accuracy long distance measurements with a mode-filtered frequency comb

Homodyne interferometry with a frequency comb as multi-wavelength source is a powerful method to measure long distances with high accuracy. The measurement principle requires that individual comb modes are spectrally resolved, making hundreds or thousands of accurately known wavelengths available for interferometry. For this reason the method cannot be applied directly to frequency combs with a low repetition rate (e.g. 100 MHz), since the modes are too close to be resolved. In this paper we use cavity mode filtering to increasing the pulse repetition rate of a comb and we apply the filtered comb for mode-resolved absolute distance measurement. Mode-filtering takes place with a single Fabry-Perot cavity in a Vernier configuration, allowing to set mode spacings ranging from 10s of GHz to more than 100 GHz. Large mode-spacings significantly reduce the requirements on the resolution of the spectrometer. We demonstrate absolute long distance measurement with a mode-filtered frequency comb using a simple array spectrometer for mode-resolved detection. Here a 1 GHz comb is used, that is converted into a 56 GHz comb by mode-filtering. A trade-o between non-ambiguity range and spectral resolution needs to be made when choosing a filter ratio. The pulse-to-pulse distance after filtering is 5.3 mm in this case, so to overcome ambiguity a rough measurement with an accuracy of about 2.5 mm is required. We show that in comparison to a conventional counting interferometer an agreement within 0.5 µm for distances up to 50 m is found. The presented method may enable the field application of low-repetition rate frequency comb lasers, like fiber lasers, for multi-wavelength homodyne interferometry. It relaxes the requirements on the spectral resolution, allowing for simple grating spectrometers as detector.

Absolute distance measurement method without a non-measurable range and directional ambiguity based on the spectral-domain interferometer using the optical comb of the femtosecond pulse laser

With the help of the optical comb of a femtosecond pulse laser, a spectral-domain interferometer has been utilized for measuring absolute distances. Even if the technique can measure distances at a high speed and with good precision, it has two fundamental problems: non-measurable range and directional ambiguity. First, the non-measurable range arises due to the sampling limit of the interference spectra at very short distances or the integer multiple of a double non-ambiguity range. Second, the peak corresponding to the desired distance in the Fourier domain has a directional ambiguity owing to the repeated property of the optical comb. Therefore, due to these two fundamental problems, most previous works never measure the absolute distances by itself in a single operation. In this letter, an interferometric method for measuring arbitrary absolute distances based on a spectral-domain interferometer operating with two reference mirrors is proposed and demonstrated. The two reference mirrors generate two distinguishable signals, primary and secondary, with a predetermined offset, thus solving these fundamental problems clearly. More importantly, as a practical advantage, the simple layout of the proposed method makes it readily applicable to most previous studies.

Absolute Distance Measurement Using Frequency Comb and a Single-Frequency Laser

We propose, here, a multi-heterodyne method using frequency comb and a tunable laser for absolute distance measurement. Numerous beat frequency components can be obtained in RF region. The distance can be determined via the phases of the beat signals. We potentially extend the non-ambiguity range up to $10^{5}$ m by adjusting the comb repetition frequency slightly. The experimental results show an agreement within 4.5 $\mu \text{m}$ , corresponding to a relative precision of $1.5\times 10^{-7}$ in a range up to 30 m, compared with an incremental distance meter.

A Fast Three-Dimensional Image Reconstruction With Large Depth of Focus Under the Illumination of Terahertz Gaussian Beams by Using Wavenumber Scaling Algorithm

In this paper, a fast three-dimensional wavenumber scaling algorithm (3-D WSA) was proposed to reconstruct the wideband terahertz (THz) holographic image under the illumination of THz Gaussian beams. By taking the cross-range range coupling term into account, which is usually neglected in some fast algorithm, such as the enhanced phase shift migration (EPSM), the focusing depth for image reconstruction is greatly improved in the proposed fast algorithm. To deal with the cross-range range coupling term, a wavenumber scaling operator (WSO) was developed in the proposed algorithm which only uses chirp multiplications and FFTs with high computation efficiency and free of interpolation. Theoretical analysis on the relationship of the WSO parameters to the resulted maximum non-ambiguous range in holography image reconstruction was carried out with a quantitative criterion derived to appropriately determine the WSO parameters. Simulation results validate the proposed focusing algorithm and indicate that 3D WSA offers almost the same focusing capabilities as the most rigid phase shift migration (PSM) algorithm, meanwhile with computation efficiency greatly improved. Proof-of-principle experiments in 0.2 THz band were also performed based on a monostatic prototype imager. The experimental results demonstrate the effectiveness and the efficiency of the 3D WSA proposed in this paper.

Three-dimensional sparse image reconstruction for terahertz surface layer holography with random step frequency.

In this Letter, a sparse image reconstruction approach is proposed for three-dimensional (3D) terahertz (THz) surface layer holography by a sharply dwindled amount of frequency samples, without reducing the high quality of the final reconstructed 3D THz images. To avoid the range ambiguity resulting from the reduction of frequency samples, a random step frequency method is adopted to evaluate the rough range profile of the 3D surface layer. With the obtained range profile, a de-ambiguity procedure is proposed to demodulate the sparse echoed data to greatly compress the maximum nonambiguous range and recover all the information for 3D holography image reconstruction. Proof-of-state experiments are performed in 0.2-THz band. The results verify the effectiveness and the efficiency of the sparse imaging scheme for THz surface layer 3D holography.

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).