Absolute Distance Measurement Using Frequency-Scanning Interferometry Based on Hilbert Phase Subdivision

Two different sinusoidal wavelength-scanning (SWS) interferometers with a SWS light source using a superluminescent laser diode are proposed for step-profile measurement and real-time distance measurement, respectively. An optical path difference (OPD) longer than a wavelength is measured from detection of sinusoidal phase- modulation amplitude Zb of the interference signal that is proportional to the OPD and the scanning width 2b. In step-profile measurement, if measurement error in the OPD obtained from Zb is smaller than a half wavelength, this measured value of the OPD is combined with a fractional value of the OPD obtained from the conventional phase of the interference signal. This combination enables us to measure the OPD longer than a wavelength with a high accuracy of a few nm. In real-time distance measurement, the amplitude Zb is kept at a specified constant value for changes of OPD by controlling the scanning width 2b of the wavelength with a feedback system. The amplitude Zb is detected by processing the interference signal with electric circuits in real-time. The value of b is easily controlled in the SWS light source, and an OPD longer than a wavelength is measured from the value of b with an accuracy of about a wavelength.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In frequency-modulated continuous wave (FMCW) light detection and ranging (LIDAR), the nonlinearity of the laser frequency modulation causes an increase in the full width at half maximum (FWHM) of the beat signal. This increase seriously affects the ranging precision. In this Letter, a nonlinear correction method based on superlets transform (SLT) is proposed to build a FMCW LIDAR measurement system with an auxiliary interferometer. The time-frequency relation is extracted from the SLT result of the auxiliary path beat signal, and an interpolation sequence is generated to resample the measurement path beat signal, so as to improve the linearity. Experiment results show that the nonlinearity after resampling reaches 2.60 × 10-10, and when the length of the extended fiber for simulating laser transmission is 13 times to the length of the auxiliary fiber, the spectrum still has obvious peaks. The average standard deviation (SD) and average resolution of the ranging within 2.5 m are 2.3 mm and 4.8 cm, respectively. The average SD of the velocity measurement within 6 cm/s is 7.7 mm/s.

In this paper, an algorithm based on homomorphic deconvolution is proposed to give an accurate estimation of nonlinear phase in the beat signal in optical frequency domain reflectometry (OFDR). Nonlinearities in the beat signal are obtained by using an auxiliary interferometer. After converting to cepstrum domain and filtering, the nonlinearity can be separated from the beat signal. Then, the deskew filter is used to eliminate the nonlinearity. In the proposed algorithm, no approximations are used, so the estimation is theoretically unbiased. Certain simulations are performed to verify the versatility and effectiveness of the proposed algorithm. The nonlinearities are accurately estimated and eliminated by the method, which improves the spatial resolution of the OFDR system.

Frequency-scanning interferometry (FSI) utilizing external cavity diode lasers (ECDL) stands out as a potent technique for absolute distance measurement. Nevertheless, the inherent scanning nonlinearity of ECDL and phase noise pose a challenge, as it can compromise the accuracy of phase extraction from interference signals, thereby reducing the measurement accuracy of FSI. In this study, we propose a composite algorithm aimed at mitigating non-orthogonal errors by integrating the least-squares and Heydemann correction technique. Furthermore, we employ Kalman filtering for precise phase tracking. We introduce a parameter selection strategy based on the statistical distribution of instantaneous frequency to achieve the fusion estimation of phase observation values and theoretical models, which starts a new perspective for the application of multi-dimensional data fusion in FSI measurement. Through simulation and experimental validation, the efficacy of this approach is confirmed. The experimental results show promising outcomes: with an average phase error of 0.12%, a standard deviation of less than 1.7 µm in absolute distance measurement, and an average positioning accuracy error of 0.29 µm.

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.

The nonlinear phase of beat signal in Optical Frequency domain Reflectometry(OFDR) has become a bottleneck to its utilization. In this paper, a method to compensate nonlinear phase based on Match Fourier Transform algorithm(MFT) is presented. The nonlinear phase of beat signal is represented as a polynomial phase function, then the coefficients of the polynomial phase function are obtained from an auxiliary interferometer through the polynomial regression algorithm. Finally, the nonlinear phase in main OFDR interferometer can be compensated by Match Fourier Transform algorithm. The experimental results show that the method can effectively suppress the side lobe of the reflection peak and achieve a spatial resolution of 0.2m at 4.3km. The experiment results verify the effectiveness of the proposed algorithm.

Rotating Fourier transform ultraviolet Raman spectrometer (RFTURS) is an ideal and valuable tool for atmospheric CO₂ detection. However, due to the short excitation wavelength and the nonlinear relationship between the optical path difference (OPD) and the rotating angle, it is difficult for RFTURS to produce linear interference signals. This paper proposes a time sequences trigger (TST) method to realize linear sampling of interference signals. Specifically, time sequences are designed at equidistant OPD intervals as external clocking signals to trigger the data acquisition (DAQ) card to sample interference signals. High angular resolution and precise time sequences are obtained by using a gearbox to work at low speed as well as detecting the OPD zero via a sensor, respectively. By a simulation spectrum and white light, the method was tested and ultimately obtained the expected restored spectrum, which addresses the current drawbacks such as large error of the non-uniform fast Fourier transform (NUFFT) method and the subsampling method, and unsuitable work conditions of the reference laser method performing at the UV. This work provides significant guidance for field measurement of atmospheric CO₂ by RFTURS.

A novel method to double the measurement range of wavelength scanning interferometery (WSI) is described. In WSI the measured optical path difference (OPD) is affected by a sign ambiguity, that is, from an interference signal it is not possible to distinguish whether the OPD is positive or negative. The sign ambiguity can be resolved by measuring an interference signal in quadrature. A method to obtain a quadrature interference signal for WSI is described, and a theoretical analysis of the advantages is reported. Simulations of the advantages of the technique and of signal errors due to nonideal quadrature are discussed. The analysis and simulation are supported by experimental measurements to show the improved performances.

We present accurate signal processing techniques based on the continuous wavelet transform (CWT) for nonstationary optical coherence tomography (OCT) interference signals. OCT is attracting considerable attention in the clinical, scientific, and engineering fields. However, the temporal or spatial period of the detected interference signal is unequal because of the nonlinearity of the scanning device or the inverse proportionality of the phase to the wavelength. If these nonstationary interference signals are acquired at equal sampling intervals and processed using fast Fourier transform (FFT), measurement errors occur. We first propose techniques that compensate for the fringe intervals of the temporal interference signal based on the CWT. The accurate position measurement of a reflective surface is demonstrated. Next, we describe a novel signal processing technique that accurately determines the positions of the fringe peak and reference mirror for TD-OCT. An accurate step-height measurement is demonstrated in this study. Finally, we describe a threedimensional profile measurement method. The optical path difference can be determined through a simple relationship between the wavelength and the corresponding phase obtained by the CWT. Measurements of a step-height configured with a pair of gauge blocks and the thickness distribution of a thin glass plate are performed. In the latter case, we demonstrate that the accuracy is improved in the pulse-driven technique.

A data processing method for correcting the frequency sweeping nonlinearity of a tunable laser in an optical frequency domain reflectometry system is presented. The proposed method calibrates the positions of all the data points by the time-scale factor determined by the zero-crossing points of the auxiliary interferometer. Then, the signal of the main interferometer is interpolated with the calibrated results. In experiments, a spatial resolution of 0.17 mm over a measurable range of 155 m has been obtained even when the optical path difference of the auxiliary interferometer is shorter than that of the main interferometer. This method could resolve the problem that measurable range is limited by the length of delay fiber in the auxiliary interferometer and significantly decrease the requirement of sampling rate.

Method of autocorrelation low coherence interferometry (LCI) is investigated in the work and proposed for diagnostic of layered media inner structure. The autocorrelation LCI is non reference beam method [1–3]. A sample beam directs to the interferometer where optical path difference between the waves reflected from different layers within the sample is compensated. In these methods an object is out of interferometer. So any distance to object is suitable and movements of object do not influence on interference signal. The output signal represents sample field autocorrelation function. Variable component of output signal I(2Δz M ) is: given equation where Δt=2Δz M /c, Δt ij =2d ij n ij /c, d ij n ij - is the optical thickness of layer contained by i-th and j-th boundaries, λ 0 =2πc/ω 0 [4,5]. There is a central pulse which corresponds to zero path difference between two sample fields in the interferometer. The side pulses are located symmetrically about the central. Location of side pulses in interference signal shows optical thicknesses of layers and serial combinations of theirs within the sample. Total number of side pulses is N = 1/2*(m2 − m), where m - is the number of reflecting boundaries. Several technical and biological objects (including skin abruption and nanorods of gold [6]) were investigated using the method. Result of scanning of skin abruption is shown on fig. 1. The scheme of the object (fig. 1a) and interference signal of it (fig. 1b) are presented.

Frequency-scanning nonlinearity fundamentally limits the ranging precision of frequency-scanning interferometry (FSI) systems based on external cavity diode lasers (ECDLs). To address this limitation, a frequency scanning nonlinearity suppression method based on a rate-dependent asymmetric Prandtl-Ishlinskii (RA-PI) model is proposed. By employing, for the first time, a phenomenological modeling approach, the rate-dependent and asymmetric nonlinear optical frequency response of the ECDL is accurately characterized. An inverse RA-PI model is derived and implemented as a feedforward compensator to linearize the frequency scanning. Experimental results show that the frequency-scanning linearity is improved by approximately one order of magnitude. Consequently, the maximum standard deviation of absolute distance measurements is reduced from 58.25 μm to 9.79 μm, and the maximum relative displacement deviation decreases from 42.97 μm to 11.56 μm. Furthermore, the velocity measurement precision for dynamic targets is improved by a factor of 2.61 to 5.75.

A new hardware configuration to correct nonlinear tuning affects in optical frequency domain reflectometry (OFDR) is proposed. Unlike conventional correction methods, the new configuration does not require a separate auxiliary interferometer detection, which may eliminate the need for an extra detection device and an acquisition channel. In the proposed method, an intentional beat signal is introduced at the beginning of the OFDR spectrum, which is treated as an auxiliary interferometer to acquire tunable laser phase information for the nonlinear tuning correction. The proposed method may reduce the overall system cost, reduce the data acquisition time and computational load, and make system configuration simpler by eliminating the need for extra components. In this article, the feasibility of the proposed configuration is demonstrated by correcting nonlinear tuning affects using simulations and experiments in a ∼50 m long optical fiber. Distributed strain and temperature sensing are also performed in a 50 m optical fiber with the proposed new configuration.

As radio communication has progressed, reduction of intersystem interference has become a problem. In a conventional interference canceller, the interference signal as a source of cancellation is obtained at the receiving station and the interference component in the desired signal is canceled based on this interference signal. However, the interference signal for cancellation may not be obtained at the receiving station. As a remedy, an extraction and reinjection‐type interference canceller has already been proposed.In this paper, a pre‐interference canceller is proposed in which, if the transmitting station of the desired signal and that of the interference signal are identical, the interference signal is mixed with the desired signal from the transmitting station beforehand and the interference signal leaking into the desired signal is cancelled at the receiving station.First, the applicable range and the fundamental configuration of the present canceller are presented. Subsequently, the method for determining the amplitude and phase of the interference signal injected into the desired signal of the transmitting station and the method for evaluation of the cancellation effect are presented theoretically.Next, an experiment is carried out with the desired signal of 16 QAM or 256 QAM and the interference signal of 256 QAM. Interference improvement by about 20 dB is obtained for both the 16 and 256 QAM signals. Also, the response speed of control for the fading is 60 ms. In addition to the validity of the theoretical results, effectiveness of the proposed canceller is shown.

A fiber-optic distributed acoustic sensing method based on phase-sensitive optical time domain reflectometry combined with dual-chirped pulse and micro-reflective fiber Bragg grating (FBG) is proposed. The sensing fiber consists of a micro-reflective FBG with uniform spatial interval. The micro-reflective FBG help to gain a high signalto-noise ratio light signal, comparing with the Rayleigh backscattering (RBS) light of optical fiber itself. The dualchirped pulses are generated by a time delay, whose corresponding spatial interval approximately equal to twice the spatial interval of adjacent micro-reflective FBG. A beating signal is generated due to the interference of the two identical chirped pulses reflected by the micro-reflective FBG array. Acoustic disturbance between the microreflective fiber gratings will change the phase of the beating signal and the interference waveform will shift. Quantitative measurement can be achieved by directly demodulating the beating signal through using a crosscorrelation algorithm. By using such a method to perform the sensing for the micro-reflective FBG array, distributed quantitative measurement can be realized with only direct detection scheme and simple demodulation algorithm. Experiment are carried out with 2km fiber and PZT vibration simulation and the results verified the effectiveness of our method.