Arbitrary distance measurement without dead zone by chirped pulse spectrally interferometry using a femtosecond optical frequency comb

Qiong Niu; Jihui Zheng; Xingrui Cheng; Junchen Liu; Linhua Jia; Lingman Ni; Ju Nian; Fumin Zhang; Xinghua Qu

doi:10.1364/OE.469774

1. Introduction

Absolute distance measurement with high-precision is one of the important foundations of modern industry and scientific research [1]. Laser ranging technology based on optical interferometry becomes more critical in precision ranging fields such as global measurement and positioning systems [2], large-scale advanced manufacturing and even micro-chips and aperture processing. However, traditional laser ranging method can only achieve incremental measurement, that is to achieve high-precision distance or length measurement by accumulating the interference phase of the continuous-wavelength laser [3,4]. The non-ambiguous distance value of this single-wavelength interference ranging method is only half the wavelength, and the accumulation of the interferometric phase must be continuous to avoid measurement interruptions [5]. Therefore, it has been the goal of metrology researchers to achieve fast, wide-range, high-precision, and real-time absolute distance measurements.

With the advent of the OFCs, it has opened up a new horizon for the field of length metrology and precision ranging, which bridges the laser ranging to absolute time or frequency standard for absolute distance measurement [6]. OFC behaves as a sequence of equally spaced ultrashort pulses in the time domain and as a series of equally spaced fine spectral lines in the frequency domain [7,8]. Besides, due to the superior characteristics of high repetition rate, large number of fine longitudinal modes and phase coherence of the femtosecond laser, the optical interference ranging technology based on OFC has become a hot spot. Researchers have proposed several ranging schemes, such as time-of-flight method [9], dual-comb asynchronous optical sampling (ASOPS) [10], and optical sampling by cavity tuning (OSCAT) in the time domain [11], as well as synthetic wavelength interferometry (SWI) [12,13], multi-wavelength interferometry (MWI) [14], dispersive interferometry (DPI) [15–17], and the combination of multiple measurement schemes in the frequency domain [18].

Although Each of the above schemes has its own advantages in distance measurement, it still faces great challenges to achieve high accuracy, large range, and real-time ranging at the same time. Researchers have put a lot of efforts into expanding the non-ambiguous range (NAR) of distance measurement, such as improving the SWI method by fine-tuning the repetition frequency of OFC to expand the measurement range [19], while it must guarantee the frequency stability of multiple wavelengths to form a synthetic wavelength chain, and the frequency sweeping limited the characteristics of real-time measurement. The dual-optical comb time-of-flight method ranging method had the advantage of a large NAR, but it mainly focused on the phase locking and cross-correlation of two optical frequencies, which increased the complexity of the system [20]. The NAR of DPI cannot cover the entire measurement period due to the limitation of the spectrometer resolution and femtosecond laser repetition frequency matching, resulting in a long measurement dead zone. Although the DPI method based on electro-optic comb and soliton microcomb with high repetition frequency has been proposed to solve the dead zone problem, the directional ambiguity problem still exists [16,21]. Correspondingly, some methods have been proposed to solve the “dead zone” problem by designing a specific spectroscopic system such as a Fabry-Perot filter or a high-resolution virtual imaged phase array (VIPA) [22,23], but the NAR is only improved to the cm level, which also leaded to a complex system architecture and high calibration and maintenance costs. Furthermore, some studies used dichroic spectral resolved interferometry to overcome the measurement range limitation by introducing an additional reference mirror [24], however, the relative distance of the two reference mirrors needs to be specified to calibrate the distance value, which brought greater uncertainty to the measurement and also introduced the problem of multi-band spectral overlap. Chirped pulse interferometry has also been used to extend the measurement range, which still couldn’t break through the cm-level measurement range [25,26,29].

In this paper, we introduce a chirped pulse spectrally interferometry (CPSI) method for arbitrary distance measurement without dead zone. Based on spectral interference technology, we use time-stretch technology to extend the femtosecond pulse width to nanosecond in the time domain, which performs as a chirped pulse. Next, the reference chirped pulse and the non-chirped pulse of the measurement path interfere asymmetrically in the Mach-Zehnder interference (MZI) optical path, forming a spectrum of the oscillation frequency modulated with the angular frequency, which could be detected by an InGaAs line array image sensor with high acquisition speed, and then we obtain the distance value by the displacement of the widest fringe. Importantly, this method can directly determine the relative position of the measurement pulse and the reference pulse according to the position of the widest fringe relative to the center frequency of pulse for overcoming the problem of direction discrimination. At the same time, the VODL is introduced in the reference path to achieve large-scale ultra-fast ranging without dead zone. The experiment results show that the measurement dead-zone has been eliminated, and the measurement error is controlled within 12µm, as well as the Allen variance is within 52 nm in the long-term experiment. Furthermore, it has good stability in long distance and harsh environment. Therefore, it is feasible to achieve high-precision real-time distance measurements at large scales using single-comb frequency-domain interferometry.

2. Principles

2.1 Limitation of DPI

The traditional DPI ranging system is established on the Michelson interference optical path. OFC is divided into two parts including the reference arm ${E_{ref}}(t )= \alpha E(t )$ and the measurement arm ${E_{mea}}(t )= \beta E({t - \tau } )$ respectively in which α, β represent the spectral ratios, and τ represents the delay time between the reference arm and the measurement arm. The two beams enter the spectrometer, forming an interference spectrum, which could be expressed as the following equation in the frequency domain:

(1)$${I_{DPI}}(\omega )= |{E_{ref}}(\omega )+ {E_{mea}}(\omega )|= {E^2}(\omega )[{{\alpha^2} + {\beta^2} + 2\alpha \beta \cos ({\tau \omega } )} ], $$

where ${E_{ref}}(\omega )$, ${E_{mea}}(\omega )$ and $E(\omega )$ are the form of the fast Fourier transform (FFT) of ${E_{ref}}(t )$, ${E_{mea}}(t )$ and $E(t )$ in the frequency domain respectively. It can be seen from the Eq. (1) that the interference signal contains DC and AC components, however only the AC signal is modulated by the delay time τ, which corresponds to the oscillation frequency of interference spectrum. Thus, we can obtain the delay time by demodulating the AC signal, and then get the distance value by the relation:

(2)$$l = c\tau /({2{n_g}} ), $$

where n_g represents the refractive index of air.

Usually, when it travels in space longer, so that τ is much larger than the sampling frequency of spectrometer, we couldn’t solve it by demodulating the AC term. Thus, combined with Nyquist determination, the maximum measurable unambiguous distance determined by the resolution of the spectrometer can be expressed as:

(3)$${l_{NAR - OSA}} = \frac{c}{{2{n_g}}} \cdot \frac{1}{{2df}} = \frac{{{\lambda ^2}}}{{4{n_g}d\lambda }}, $$

where df represents the frequency sampling interval of spectrometer, which is equal to the inverse of the sampling frequency f_s and the wavelength sampling interval dλ is equal to $- df \cdot {\lambda ^2}/c$.

Based on the above analysis, limited by the resolution of spectrometer, it is difficult to achieve a full range measurement with conventional commercial spectrometers actually, and the measurement range that can be measured in one period is only few millimeters, causing a large dead zone.

In addition, in different measurement periods, the arbitrary distance using DPI method can be determined by:

(4)$${L_{DPI}} = N\frac{{{l_{pp}}}}{2} \pm \frac{{c\tau }}{{2{n_g}}}\textrm{ = }N\frac{c}{{2{f_r}}} \pm \frac{{c\tau }}{{2{n_g}}}, $$

where l_pp represents the pulse-to-pulse length, f_r is the repetition frequency of OFC and N is an integer. When measurement pulse is in front of the reference pulse, the sign is positive, otherwise it is negative. However, we can only get a positive value by demodulation through DPI, that is to say only the absolute value of the optical path difference can be obtained, which results in the problem of direction discrimination in ranging.

2.2 Principle of CPSI

The chirping is produced mainly due to the time-dependent change refractive index caused by the group velocity dispersion (GVD) effect when the ultrashort pulse passes through the dispersive medium, and at the same time it would cause the additional phase of each spectral component of the pulse. Subsequently, different frequency components transmit at different speeds, resulting in pulse broadening. Notably, GVD does not affect the spectrum and the shape of pulse.

Generally, chirped pulses are mainly obtained by time-stretch techniques, using GVD to extend ultrashort pulses into wide pulses with nanosecond width in the time domain. Therefore, it is necessary to introduce high-dispersion devices in our ranging system to achieve pulse broadening. At present, the commonly stretchers (compressors) mainly include grating pairs, single-mode fibers (SMF), chirped volume Bragg grating (CVBG), dispersion compensation fiber (DCF) and other special fibers that can provide high dispersion. With the continuous progress of fiber grating etching technology, CFBG with short etch length is often used for dispersion compensation and pulse compression due to their large dispersion and negligible nonlinear effects [27], which could stretch the pulse beyond nanosecond, as well as is beneficial to integrate ranging system with full fibers. Therefore, CFBG is used in this paper to achieve pulse broadening for obtaining chirped pulses. Specifically, when the pulse is incident on the CFBG, different frequency components of the pulse are reflected by different regions of the grating, thus presenting a large normal or anomalous group velocity dispersion characteristics. The schematic diagram of time-stretch through CFBG is shown in Fig. 1:

Fig. 1. Schematic diagram of time-stretch using CFBG.

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The time-stretch effect of dispersive media such as CFBG on ultrashort pulses can be modeled as a linear constant system transfer function:

(5)$$H(\omega )= {H_0}(\omega )\exp [{ - j\phi (\omega )} ], $$

where H₀(ω) is the attenuation spectrum pertaining to the loss of CFBG, ϕ(ω) is the phase distribution introduced by dispersive media, and the effect of chromatic dispersion can be expressed by a Taylor series expanded into phase at the center frequency of the pulse:

(6)$$\phi (\omega )\textrm{ = }{\phi _0}\textrm{ + }{\phi _1}({\omega \textrm{ - }{\omega_0}} )\textrm{ + }\frac{1}{2}{\phi _2}{({\omega \textrm{ - }{\omega_0}} )^2}\textrm{ + }\frac{1}{6}{\phi _3}{({\omega \textrm{ - }{\omega_0}} )^3} \cdots \textrm{ + }\frac{1}{{n!}}{\phi _k}{({\omega \textrm{ - }{\omega_0}} )^k}$$

(7)$${\phi _k} = {\left( {\frac{{{d^k}\phi }}{{d{\omega^k}}}} \right)_{\omega = {\omega _0}}}\quad\quad\quad\quad ({k = 0,1,2,\ldots } )$$

where ω is the angular frequency corresponding to the center frequency of pulse ω₀, and ϕ₁ is the group velocity delay, ϕ₂ is the group velocity dispersion (GVD), which is related to pulse broadening, ϕ₃ is the third-order dispersion (TOD), which will cause distortion of the pulse transmitted in the fiber, and other high-order dispersion will cause the nonlinearity in the time-frequency mapping relationship. In order to eliminate the influence of high-order dispersion on time-stretch, the dispersion mediums with high group velocity dispersion and low high-order dispersion such as CFBG are selected as far as possible for experiments. Strictly analyzing the propagation of femtosecond spectral-like pulses in higher-order dispersive cells is very complicated, however, the frequency chirp caused by the third-order dispersion is much smaller than that of the linear dispersion after simulation [28]. Thus, to simplify the analysis, a simplified processing method based on linear wavelength-time mapping is adopted in this paper, in which first and second-order dispersions are considered.

Firstly, the group velocity dispersion is defined as the amount of pulse broadening in time domain on the unit spectrum width:

(8)$${\phi _2}\textrm{ = }\frac{{\Delta \tau }}{{\Delta \omega }}. $$

And then, in order to facilitate the analysis, we introduce the parameter chirp factor b, which is equal to the inverse of ϕ₂, so that the instantaneous frequency of the pulse can be expressed as:

(9)$${\omega _{chirp}}(t )\approx {\omega _0} + t/{\phi _2} \approx {\omega _0} + bt. $$

After the reference femtosecond laser pulse (a Fourier-transform limited pulse) passes through the CFBG, the output pulse with chirps can be expressed as the complex spectral function:

(10)$${E_{chirp}}(\omega )\approx \exp \left( {j\frac{{{\phi_2}}}{2}{{({\omega - {\omega_0}} )}^2}} \right){E_{\textrm{ref}}}(\omega ). $$

The dispersive spectrometer is used to detected the interference spectrum, and compared with Eq. (1), the spectral intensity can be expressed as:

(11)$${I_{CPSI}}(\omega )= |{E_{chirp}}(\omega )+ {E_{mea}}(\omega )|= {E^2}(\omega )\left[ {{\alpha^2} + {\beta^2} + 2\alpha \beta \cos \left( {\frac{{{\phi_2}}}{2}{{({\omega - \omega {}_0} )}^2} - \tau \omega } \right)} \right], $$

where α, β represent the spectral ratios. We find that in Eq. (11), when ϕ₂ equals to zero, the spectral phase is exactly same as that of the dispersive interferometry. In CPSI, the spectral phase φ(ω) is a quadratic function with respect to the angular frequency, which means the interfered spectral fringes are not the stable oscillation with a single frequency any more, but with a modulated frequency varying with the angular frequency. The widest fringe appears when the oscillation frequency achieves the extremum, i.e., the lowest frequency. By taking the derivation of the phase function, we get:

(12)$$\varphi (\omega )= \frac{{{\phi _2}}}{2}{({\omega - \omega {}_0} )^2} - \tau \omega, $$

(13)$$\frac{{\partial \varphi (\omega )}}{{\partial \omega }} = {\phi _2}({\omega - {\omega_0}} )- \tau = 0, $$

(14)$${\phi _2}\textrm{ = }\frac{{{\partial ^2}\varphi (\omega )}}{{\partial {\omega ^2}}}. $$

Furthermore, by solving the minimum angular frequency ω_b from the chirped spectral interferogram, the pulse delay interval between the measurement path and the reference path can be expressed as:

(15)$$\tau = \frac{{{\partial ^2}\varphi (\omega )}}{{\partial {\omega ^2}}}({{\omega_b} - {\omega_0}} ). $$

Then combined the expression of (2) and (15), distance can be obtained by:

(16)$${L_{CPSI}} = \frac{c}{{2{n_g}}}\phi {}_2({{\omega_b} - {\omega_0}} )= \frac{c}{{2{n_g}}} \cdot \frac{{{\partial ^2}\varphi (\omega )}}{{\partial {\omega ^2}}} \cdot {\omega _{shift}}, $$

where ω_shift is the shift of the center frequency of the pulse, and ϕ₂ is derived by quadratic derivation of φ(ω) with respect to ω. We find that we can determine distances by the shift amount of the center frequency, i.e., the shift of the widest fringe in the spectrograms, and we can achieve a large measurement range with large GVD and broadband OFC source.

2.3 Filling the dead zone by tuning VODL

It can be seen from the above analysis that the measurement range of CPSI ranging can easily reach hundreds of mm using a laser source with wide spectral width. However, it still cannot cover the theoretical pulse interval, existing a certain dead zone for ranging. When the first measurement pulse meets the n^th reference pulse, and we could solve distance by their interference spectrum. Ideally, tuning the time delay between the two pulses continuously by changing the fiber length of reference arm enables that they could meet, but it is impossible for experiments or practical application. Thus, in this research, we introduce a high-precision, large-range, programmable optical delay line in the reference path of MZI optical path to tune the delay time between the measurement pulse and the reference pulse until the modulated spectral interferogram appears again. The measurement range could be extent with the increase of reference arm optical path, it is expected to fill the “dead zone” with the demodulated distance value and the delay time from OVDL. The operation principle is shown in Fig. 2:

Fig. 2. Operation principle of the VODL used for dead zone filling. L_CPSI-idenotes the distance value solved by the center frequency after each variety of the delay line, L_delay denotes the specific optical path delay value by tuning the VODL, which is 150 mm in our experiment.

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It is worth noting that, in the cases of arbitrary distance with interfering, the distance can be determined by the value L_CPSI modulated with interferogram and delay optical path L_delay from OVDL, which is determined by ${L_{delay}} = c{\tau _{delay}}/2{n_g}$, achieving the arbitrary distance measurement without dead zone, which can be expressed as:

(17)$${L_a} = N\frac{{{l_{pp}}}}{2} + {L_{CPSI}} + {L_{delay}}. $$

2.4 Simulations and analysis of CPSI ranging

To make it more intuitive, we give a brief simulation of CPSI with difference time delays in Fig. 3, we find that due to the chirping, the frequency of the fringes is not a constant, but modulated, and there will be a lowest oscillation frequency in the case of modulation. When changing the time delay between the measurement pulse and the reference pulse, the position of the widest fringe changes accordingly, where a forward time difference corresponds to a left shifted frequency amount relative to center frequency in the direction of decreasing optical frequency, and a backward time delay moves the widest fringe to the right side of center frequency in the direction of increasing optical frequency. Therefore, we could remove the problem of direction ambiguity in a direct and efficient way.

Fig. 3. Simulations of chirped pulse interferometry with difference time delays.

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Furthermore, based on Eq. (16), we could derive that, the measurement range of CPSI L_range and the resolution of CPSI ΔL_CPSI can be expressed as:

(18)$${L_{range}} = \frac{c}{{2{n_g}}}\phi {}_2\Delta \omega, $$

(19)$$\Delta {L_{CPSI}} = \frac{c}{{2{n_g}}} \cdot \frac{{{\partial ^2}\varphi (\omega )}}{{\partial {\omega ^2}}} \cdot \Delta {\omega _{shift}} = \frac{{\pi {c^2}\Delta \lambda }}{{b{n_g}{\lambda _c}({{\lambda_c} + \Delta \lambda } )}}, $$

where Δω is the spectral width of light source, Δω_shift is the minimum amount of the angular frequency shift, and similarly, Δλ is the wavelength resolution of spectrometer, λ_c is the central wavelength of OFC, which is 1550 nm in our simulation and experiments. It is obvious that the range of distance measurement is determined by the amount of dispersion and the spectral width of light source together and the ranging resolution is related to the amount of dispersion and the resolution of spectrometer. Especially, the amount of dispersion is negatively correlated with the width of the widest fringe in the spectral interferogram. Specific simulation is as shown in Fig. 4, in which, with the decreases of chirp factor b, the amount of GVD increases and the width of the widest fringe become narrower.

Fig. 4. Simulations of chirped pulse interferometry with difference dispersion value.

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It is easy to obtain through simulation that the movement of distance has a linear relationship with the movement of the widest stripe. Under the condition of a certain OFC spectrum bandwidth, when increasing the amount of dispersion, the width of the widest stripe is decreasing and the range of distance measurement is extent correspondingly. More importantly, when using CPSI, the distance value is directly related to the shift of the center angular frequency of the widest fringe. Compared with DPI, the expansion of the ranging range is no longer limited by the resolution of spectrometer, which can be extended to more than tens of times.

3. Experiment setup and results

3.1 Experiment setup

In order to verify the performance of the CPSI ranging system in a large dynamic range without ambiguous direction discriminating, we conducted a ranging experiment with continuous large steps. The experimental setup is shown in Fig. 5. The stabilized mode-locked femtosecond laser with a repetition frequency of∼200 MHz, center wavelength of 1550 nm and bandwidth of 100 nm was adopted here, which is well locked to a rubidium clock (SRS FS725), corresponding to the pulse-to-pulse length of 0.75 m. Subsequently, the femtosecond laser from OFC source is split into two beams, where one is detected by a photodetector (Menlo Systems FPD510) to monitor and record the repetition of the source in time via a frequency counter (Aglient 53220A). And the other passes through the non-equal-path Mach-Zehnder interference optical path, in which the reference pulse passes through two CFBGs with dispersion coefficient of 11.5 ps/nm and bandwidth of 50 nm using circulators, generating a chirped pulse with ns width, and then passes through a variable optical delay line, of which the delay accuracy is 5 fs and time delay range is 4 ns. The reference chirped pulse and the reflected measurement pulse from the objective mirror are coupled into the coupler, and they interfere. The interference signal is spatially separated using a reflection grating before lighting to a high-speed InGaAs linear array image sensor with 512-pixels (HAMAMATSU G11620-512DF) for interference signal detection, where the maximum measurement rate can be achieved to 17 kHz at the lowest exposure time. What’s more, the resolution of spectrometer is well designed to be 0.2 nm. Compared with commercial spectrometers, although the spectrometer used in our research has no ability to adjust the resolution, the compact structure of the system is conducive to integration and packaging, and the sampling rate can be much higher than that of commercial spectrometers, which contributes to achieve fast and real-time ranging.

Fig. 5. Optical configuration of CSRI based on CFBG. OFC: optics frequency comb; PD: photodetector; PC: polarization controller; CIR: circulator; COL: collimator lens; CFBG: chirped fiber Bragg grating; VODL: variable optical delay line; TCM: target corner mirror.

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The target corner of the measurement is fixed on the mobile station of the guide rail, together with the measurement corners of the commercial He–Ne interferometer (Renishaw XL-80) with 0.5 × 10⁻⁶L linear measurement accuracy, which is employed as a reference distance meter for verifying the accuracy of the proposed CPSI ranging system. And both the measurement beam of our system and the beam of the reference He-Ne laser were aligned strictly parallel to avoid Abbe error. Besides, the environmental parameters such as temperature, pressure, and humidity are compensated by calculating the air refractive index based on the improved Edlen formula, thereby suppressing the influence of environmental noise.

3.2 Continuous large step measurement

We devise continuous large step absolute distance measurement experiments to appraise measurement performance in a stable experimental environment (temperature 22.4°C, humidity 48.1%, atmospheric pressure 1004.7hPa). At first, we move the guide rail to the zero-point (a position two pulses meet at the center frequency), of which the spectrum is shown in Fig. 6(a). And in Fig. 6(b) we show the spectral interferogram obtained for a path length difference of ±10 mm, it can be seen that the CPSI signal is a non-stationary signal with multiple frequency components, and couldn’t be analyzed comprehensively using FFT. Thus, an algorithm is proposed in this paper to solve the distance value. As show in Fig. 6(c), we normalize the originally collected interference spectrum to remove the modulation effect of the light source on the interference spectrum and DC term. And then self-convolve the normalized spectrum for determining the center angular frequency corresponding to the widest fringe, which is the frequency corresponding to the maximum value of the self-convolution. Furthermore, as shown in Fig. 6(e), we Hilbert transform the AC term of the spectrograms to obtain the wrapped phase, and after unwrapping phase, the phase $\varphi (\omega )$ is a quadratic function just as expressed in Eq. (14), which is shown in Fig. 6(f).

Fig. 6. Data processing procedure for measurement L. (a) The spectral interferogram at the zero position; (b) The spectral interferogram at ±10 mm near the zero position; (c) The normalized spectral interferogram after removing the DC term at zero position; (d) The result after self-convolution; (e) The unwrapped phase obtained by Hilbert transform at zero Position; (f) Unwrapped phase at zero position.

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In this algorithm, we determine the center angular frequency by self-convolution, instead of solving half of the angular frequencies corresponding to the spectral extreme points on the left and right sides of the widest fringe [25,26], which can avoid the difficulty of accurately obtaining the central angular frequency caused by the noise and vibration in the environment. Besides, according to Eq. (16), we obtain the distance by the phase slope with omitting the self-calibration, which contributes to obtain the distance with maintaining good accuracy and precision in real time measurement.

We design a comparative experiment to verify the superiority of CFBG as a time-stretch device in expanding the non-ambiguity range. The comparison results are shown in Fig. 7(a), in which the chirp factor values b of the grating pair, 2 km single-mode fiber with dispersion coefficient of 18 ps/nm/km, single CFBG and two CFBGs in cascade are around 1.96 × 10²⁴rad/s², 3.44 × 10²³rad/s², 6.80 × 10²²rad/s² and 3.40 × 10²²rad/s² respectively, and the corresponding NAR of CPSI is 6 mm, 34 mm, 90 mm and 180 mm, respectively, which is consistent with the theoretical analysis.

Fig. 7. The result of continuous large step measurement at a position of ∼10 m far away the zero position: (a) NAR of CPSI using different dispersive media, which reveals that the NAR increases as the dispersion increases ; (b) Measurement results when the target moves from 0 to 750 mm with a step size of 30 mm, where the standard deviations are labeled with error bars (red lines) and the midpoints of the error bars give the average values of 20 measurements at each position; for the blue axis, fitted linearity with reference distance meter (c) Allan deviation of the distance measurement versus averaging time.

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In our experiments, the commercial interferometer is initialized to zero for the initial target mirror position. Within the dynamic range of the pulse-to-pulse length 0.75 m, the measurement is performed in steps of 30 mm and for every target mirror moving step, the distance is measured by 20 times. Actually, the VODL is a delay mechanism with high precision and low insertion loss. in the experiment, once the target mirror moved outside the measurement range, the widest fringe disappeared, and then we could precisely adjust the optical delay line by driving the controller with RS-232 protocol to make the chirp interference fringe appear again to demodulate the absolute distance by the Eq.17, filling the “dead zone”. The results are shown in Fig. 7(b), where the midpoint is the average of 20 single measurement errors, and the error bar is the standard deviation of ten measurement results. It shows that it is consistent with the continuous reference interferometer in the range 12 µm, and the standard deviation is within 12 µm, and measurement linearity is almost equivalent to measuring repeatability. And then the verification experiment of stability for a single point position is carried out for 6 seconds of with sampling rate of 9 kHz. The Allan deviation of distance measurement can reach 52 nm at 1.76 ms averaging time. It is evident that we achieve the arbitrary distance measurement without dead zone by introducing a variable optical delay line using CPSI method.

3.3 Long distance measurement

In order to evaluate the measurement linearity of the CPSI based on the femtosecond optical frequency comb proposed in the long-distance measurement, a distance measurement experiment was carried out at the distance of 30 m, in which target mirror scans with a constant step length of 7.5 mm during the 15 mm stroke. The comparation with the incremental ranging system of He-Ne interferometer is showed in Fig. 8(a), in which the differences between the measured and reference distance show an agreement of ∼20 µm in 20 measurements at each position. Besides, the long-term ranging repeatability is tested under harsh environment with dominant fast noise sources such as vibration and air fluctuation for 1 hour, of which the sampling rate is 9 Hz. As shown in Fig. 8(b), the minimum Allan deviation is 2.51 µm. It is analyzed that at longer averaging times, random walks and flicker noise sources gradually dominate due to environmental drift and spectral intensity fluctuates, making the repeatability of measurement deteriorative.

Fig. 8. The long-distance measurement at a position of ∼30 m far away the zero position:(a) Measurement results when the target moves from 0 to 150 mm with a step size of 7.5 mm, where the standard deviations are labeled with error bars (red lines) and the midpoints of the error bars give the average values of 20 measurements at each position; for the blue axis, fitted linearity with reference distance meter (b) Allan deviation of the distance measurement versus averaging time.

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4. Discussion and conclusion

In this paper, a time-stretch technique based on CFBG is introduced to generate a chirped pulse with a large chirp amount for CPSI ranging, which is demonstrated in principle and experiments in detail. By distinguishing the relative position of the widest fringe, it overcomes the direction ambiguity problem of traditional DPI ranging. At the same time, we achieve the real-time arbitrary distance measurement with high precision by introducing a high-precision variable optical delay line, eliminating the measurement dead zones. And we use an algorithm based on self-convolution to obtain the central angular frequency and use the phase slope to obtain the distance, which has high measurement accuracy and strong anti-interference ability. The accuracy of proposed CPSI system is demonstrated to reach 12 µm in large-scale experiments and 20 µm in long-distance experiments respectively, and the repeatability reaches 52 nm at 1.76 ms at a small distance, while it increases to 2.51 µm in the long-distance experiment for 1 hour, which is affected by vibration and air fluctuation from the harsh environment.

The proposed CPSI system with an extension of the NAR here could be adopted for large-scale precision engineering, geodetic survey, possibly for three-dimensional measurement, and profile measurement, which can significantly extend the dynamic range and versatility of the real-time measurements, with broad application prospects. Furthermore, as an ultra-fast technology, time-stretch playa an important role in ultra-fast single spectrum, imaging and ultra-fast ranging, which can be further developed.

Funding

National Key Research and Development Program of China.

Acknowledgments

We would like to thank the peer reviewers for their very helpful comments.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. T. Osama and H. H. M. and , and K. Hussein, “Soliton mode-locked fiber laser for distance measurements,” Appl. Opt. 60(12), 3452–3457 (2021). [CrossRef]

2. G. Tang, X. Qu, F. Zhang, X. Zhao, and B. Peng, “Absolute distance measurement based on spectral interferometry using femtosecond optical frequency comb,” Opt. Lasers Eng. 120(10), 71–78 (2019). [CrossRef]

3. W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement technologies for precision positioning,” CIRP Ann. 64(2), 773–796 (2015). [CrossRef]

4. P. Koechert, J. Fluegge, C. Weichert, R. Koening, and E. Manske, “Phase measurement of various commercial heterodyne He-Ne-laser interferometers with stability in the picometer regime,” Meas. Sci. Technol. 23(7), 074005 (2012). [CrossRef]

5. M.-C. Amann, T. M. Bosch, M. Lescure, R. A. Myllylae, and M. Rioux, “Laser ranging: a critical review of unusual techniques for distance measurement,” Opt. Eng. 40(12), 10–19 (2001). [CrossRef]

6. J. Zheng, Y. Wang, X. Wang, F. Zhang, W. Wang, X. Ma, J. Wang, J. Chen, L. Jia, M. Song, M. Yuan, B. Little, S. T. Chu, D. Cheng, X. Qu, W. Zhao, and W. Zhang, “Optical ranging system based on multiple pulse train interference using soliton microcomb,” Appl. Phys. Lett. 118(26), 261106 (2021). [CrossRef]

7. Y. K. Chembo, “Kerr optical frequency combs: theory, applications and perspectives,” Nanophotonics 5(2), 214–230 (2016). [CrossRef]

8. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000). [CrossRef]

9. J. Lee, Y.-J. Kim, K. Lee, S. Lee, and S.-W. Kim, “Time-of-flight measurement with femtosecond light pulses,” Nat. Photonics 4(10), 716–720 (2010). [CrossRef]

10. T.-A. Liu, N. R. Newbury, and I. Coddington, “Sub-micron absolute distance measurements in sub-millisecond times with dual free-running femtosecond Er fiber-lasers,” Opt. Express 19(19), 18501–18509 (2011). [CrossRef]

11. T. Hochrein, R. Wilk, M. Mei, R. Holzwarth, N. Krumbholz, and M. Koch, “Optical sampling by laser cavity tuning,” Opt. Express 18(2), 1613–1617 (2010). [CrossRef]

12. Y. Nakajima and K. Minoshima, “Highly stabilized optical frequency comb interferometer with a long fiber-based reference path towards arbitrary distance measurement,” Opt. Express 23(20), 25979–25987 (2015). [CrossRef]

13. L. Yan, J. Xie, B. Chen, Y. Lou, and S. Zhang, “Absolute distance measurement using laser interferometric wavelength leverage with a dynamic-sideband-locked synthetic wavelength generation,” Opt. Express 29(6), 8344–8357 (2021). [CrossRef]

14. N. Schuhler, Y. Salvade, S. Leveque, R. Daendliker, and R. Holzwarth, “Frequency-comb-referenced two-wavelength source for absolute distance measurement,” Opt. Lett. 31(21), 3101–3103 (2006). [CrossRef]

15. K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006). [CrossRef]

16. J. Wang, Z. Lu, W. Wang, F. Zhang, J. Chen, Y. Wang, J. Zheng, S. T. Chu, W. Zhao, B. E. Little, X. Qu, and W. Zhang, “Long-distance ranging with high precision using a soliton microcomb,” Photonics Res. 8(12), 1964–1972 (2020). [CrossRef]

17. X. Xu, H. Zhao, Y. Bi, Z. Qian, C. Liu, H. Shi, and J. Zhai, “Arbitrary distance and angle measurement by dynamic dispersive interferometry using a frequency comb,” Opt. Lasers Eng. 145(13), 106665 (2021). [CrossRef]

18. H. Wu, F. Zhang, F. Meng, T. Liu, J. Li, L. Pan, and X. Qu, “Absolute distance measurement in a combined-dispersive interferometer using a femtosecond pulse laser,” Meas. Sci. Technol. 27(1), 015202 (2016). [CrossRef]

19. Y.-S. Jang, K. Lee, S. Han, J. Lee, Y.-J. Kim, and S.-W. Kim, “Absolute distance measurement with extension of nonambiguity range using the frequency comb of a femtosecond laser,” Opt. Eng. 53(12), 122403 (2014). [CrossRef]

20. J. Lee, S. Han, K. Lee, E. Bae, S. Kim, S. Lee, S.-W. Kim, and Y.-J. Kim, “Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength,” Meas. Sci. Technol. 24(4), 045201 (2013). [CrossRef]

21. S. Xiong, J. Chen, S. Zhou, Y. Wang, R. Zhang, and G. Wu, “Influence of spectral resolution on dispersive interferometry of optical frequency comb,” Opt. Commun. 503(6), 127464 (2022). [CrossRef]

22. A. Lesundak, D. Voigt, O. Cip, and S. van den Berg, “High-accuracy long distance measurements with a mode-filtered frequency comb,” Opt. Express 25(26), 32570–32580 (2017). [CrossRef]

23. S. A. van den Berg, S. van Eldik, and N. Bhattacharya, “Mode-resolved frequency comb interferometry for high-accuracy long distance measurement,” Sci. Rep. 5(1), 14661 (2015). [CrossRef]

24. K.-N. Joo, “Dichroic spectrally-resolved interferometry to overcome the measuring range limit,” Meas. Sci. Technol. 26(9), 095204 (2015). [CrossRef]

25. J. Wang, Y. Lu, X. Sun, H. Zhao, X. Jin, H. Gao, and L. Yu, “Chirped pulse spectrally resolved interferometry without the direction ambiguity and the dead zone,” Opt. Lasers Eng. 152(11), 106892 (2022). [CrossRef]

26. H. Wu, F. Zhang, T. Liu, F. Meng, J. Li, and X. Qu, “Absolute distance measurement by chirped pulse interferometry using a femtosecond pulse laser,” Opt. Express 23(24), 31582–31593 (2015). [CrossRef]

27. A. Mahjoubfar, D. V. Churkin, S. Barland, N. Broderick, S. K. Turitsyn, and B. Jalali, “Time stretch and its applications,” Nat. Photonics 11(6), 341–351 (2017). [CrossRef]

28. H. Xia and C. Zhang, “Ultrafast ranging lidar based on real-time Fourier transformation,” Opt. Lett. 34(14), 2108–2110 (2009). [CrossRef]

29. T. Kato, M. Uchida, and K. Minoshima, “No-scanning 3D measurement method using ultrafast dimensional conversion with a chirped optical frequency comb,” Sci. Rep. 7(1), 1–8 (2017). [CrossRef]

Arbitrary distance measurement without dead zone by chirped pulse spectrally interferometry using a femtosecond optical frequency comb

Abstract

1. Introduction

2. Principles

2.1 Limitation of DPI

2.2 Principle of CPSI

2.3 Filling the dead zone by tuning VODL

2.4 Simulations and analysis of CPSI ranging

3. Experiment setup and results

3.1 Experiment setup

3.2 Continuous large step measurement

3.3 Long distance measurement

4. Discussion and conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (8)

Equations (19)

Optics Express