Location deviation compensation based on maximum cross correlation in optical frequency domain reflectometry.

Photosensitive polymers serve as critical adhesives in optical devices, with their thermal strain coefficient determining the performance of temperature-dependent loss in such devices. To accurately measure the true thermal strain coefficient of the adhesive, we proposed a measurement scheme of internal strain distribution in photosensitive polymers by using an optical frequency domain reflectometry (OFDR) system. In our scheme, a self-referencing approach is used to eliminate the temperature-to-strain crosstalk caused by temperature variations in the tested sample, thereby obtaining the true thermal strain coefficient of the tested sample. In our experiment, a 10 cm single-mode fiber (SMF) is embedded within the 2 mm × 2 mm × 100 mm photosensitive polymer, and we use the high spatial resolution of the OFDR system to realize the distributed strain measurements of the SMF. A thermal strain coefficient of 19.108 μϵ/°C is obtained when the temperature ranges from 30 °C to 120 °C. The temperature-to-strain crosstalk is 9.131 μϵ/°C, and the spatial resolution of the OFDR is 1.28 mm. In addition, we validated the stability of the entire experimental setup by conducting long-term measurements under fixed environmental conditions, during which the system fluctuations remained within approximately ± 3 GHz. The experimental results can provide valuable insights for the selection of adhesives and the determination of optimal curing time of the passive optical devices fabrication in the field of optical fiber communication.

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.

This paper describes an integrated, accurate, and inexpensive semiconductor laser -based optical frequency domain reflectometry (OFDR) system design. The system utilizes the fiber under test for both sensing and frequency sweep linearization functions, allowing the system to mitigate and compensate for phase errors without the need for an auxiliary interferometer, as is the case for traditional OFDR systems. Benefiting from the unique and embedded design, this system reaches the minimal OFDR system with only one optical interferometer and its corresponding optic-electric components without sacrificing accuracy. In addition, conventional design requires an external auxiliary interferometer, which may experience different noises from the main measuring interferometer, deteriorating the overall performance. Experimental results demonstrate the enhanced performance of the compact design as compared with the former methods, as well as the reduced complexity and improved cost-effectiveness.

We present a distributed high sensitivity static strain sensing method based on all grating optical fiber in optical frequency domain reflectometry (OFDR).Through the use of all grating optical fiber, the backscattered light can be greatly improved, which increases the signal-to-noise ratio. A higher signal-to-noise ratio can help to obtain more accurate distance domain information, thereby obtaining better segmented optical frequency domain information for cross-correlation. Therefore, in the same cross-correlation method, our system obtains even larger range of FUT information due to the signal with higher signal-to-noise ratio. Using this system, we measured the change of strain at the end of a total 200 m FUT. The minimum measurable strain variation is 5 με and the spatial resolution of the system is 10cm. It should be noted that we use interpolation zero padding method on the basis of cross-correlation to obtain higher strain accuracy. In addition, we verified the stability of the system by fitting the results of different strains. The linearity of the fitting results is extremely high, and the R-square can reach more than 0.9. Compared with the OFDR system using the single mode fiber, the OFDR system using all grating optical fiber can provide a better sensing performance of measuring a minor strain variation under the same sensing spatial resolution. This is of great significance for the improvement of OFDR measurement applications.

In modern society, the amount of data being transferred is growing at an exponential rate, about 2.5 quintillion bytes data created per day. Such data can be realized in the form of include the audio, video, or text. Furthermore, due to the many advantages of the optical fiber, including the low-cost, immunity to electromagnetic interface, light weight, and high carrier frequency, it is taking over the industry. The question then arises as how to diagnose the inner fault and maintain the integrity becomes the crux for the telecommunication system based on optical fiber. There are two main high-precision measurement methodologies to complete the task mentioned above: one is the optical time-domain reflectometry (OTDR), which has been widely applied in technologies such as light detection and ranging (LiDAR) in faraway situations. The other one is optical frequency-domain reflectometry (OFDR), which is also referred to as optical frequency modulated continuous wave (OFMCW) or chirped frequency measurement. Compared with the OTDR, the OFDR measures distance by comparing the phase change of the chirped incident optical signal and reflected signals to capture the distance information. Even though the OFDR has been proven to have many advantages over OTDR in terms of the high spatial resolution at μm level, low power consumption, and eye-friendliness, both the high complexity and cost significantly limit its applications. To overcome the above shortages in the OFDR system and expand this technology in the various applications, the following research was conducted. Firstly, since the optical tuning source utilized in OFDR is too expensive and complex to be implemented in-situ measurements, there are some researches completed in the tuning laser source control methods proposed to reduce the cost and complexity of this technology and fit the various applications. Additionally, to enhance the accuracy of the OFDR measuring, some tuning rate error compensating algorithms were introduced. Benefiting from the improved spatial resolution, the physical unclonable function (PUF) in the optical fiber can be achieved as its unique identification to sustain the data transferring security. Furthermore, even though the initial optical frequency (IOF) in OFDR has been disregarded in the distance measuring, it does influence the PUF reader precision. To fully analyze such effect, some research and IOF mitigating methods were proposed, in which a fast processing method for the PUF reader has been introduced by decreasing the calculating complexity. From the above research, a low-cost, accurate, and effective OFDR system has been

A distributed optical fiber grating sensing system with large capacity and high spatial resolution is presented. Since highdensity identical weak grating array was utilized as sensing fiber, the multiplexing number was greatly increased, meanwhile, optical frequency domain reflectometry (OFDR) technology was used to implement high resolution distributed sensing system. In order to eliminate the nonlinear effect of tunable light source, a windowed FFT algorithm based on cubic spline interpolation was applied. The feasibility of the algorithm was experimentally testified, ultimately, the spatial resolution of system can reach mm-level. The influence of the crosstalk signal in the grating array on the OFDR system was analyzed. A method that a long enough delay fiber was added before the first FBG to remove crosstalk signal was proposed. The experiment was verified using an optical fiber with 113 uniform Bragg gratings at an interval of 10cm whose reflectivity are less than 1%. It demonstrates that crosstalk signal and measurement signal can be completely separated in the distance domain after adding a long enough delay fiber. Finally, the temperature experiment of distributed grating sensing system was carried out. The results display that each raster's center wavelength in the fiber link is independent of each other and the center wavelength drift has a good linear relationship with the temperature. The sensitivity of linear fitting is equal to 11.1pm/°C.

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.

We use a spectrum interpolation technique to improve the distributed strain measurement accuracy in a Rayleigh-scatter-based optical frequency domain reflectometry sensing system. We demonstrate that strain accuracy is not limited by the "uncertainty principle" that exists in the time-frequency analysis. Different interpolation methods are investigated and used to improve the accuracy of peak position of the cross-correlation and, therefore, improve the accuracy of the strain. Interpolation implemented by padding zeros on one side of the windowed data in the spatial domain, before the inverse fast Fourier transform, is found to have the best accuracy. Using this method, the strain accuracy and resolution are both improved without decreasing the spatial resolution. The strain of 3μϵ within the spatial resolution of 1cm at the position of 21.4m is distinguished, and the measurement uncertainty is 3.3μϵ.

As the security of optical fiber lines in data centers has attracted growing attention, it has become increasingly important to accurately characterize the fiber that is used. Optical frequency domain reflectometry (OFDR) has been demonstrated as a means of identifying specific segments of optical fiber; however, OFDR measurements are limited in length due to initial optical frequency (IOF) variations. This Letter describes a detailed analysis of IOF and introduces a method to mitigate it in an OFDR system constructed using a semiconductor laser (SCL). Additionally, an algorithm is described that minimizes the calculating density necessary for OFDR-based optical fiber verification, reducing the calculating time required by an order of magnitude relative to prior techniques. Experiments demonstrate that the described method can be effectively applied to a range of application areas, ranging from centimeter to meter lengths of optical fiber, with an error equal rate (EER) of less than 1%.

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.

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.

Optical frequency domain reflectometry (OFDR) measurements are performed by recording the interference pattern of light backscattered by density fluctuations or Bragg gratings along the length of an optical fiber. Changes in local temperature or strain in the fiber cause shifts in the backscattered light spectrum, which can be calibrated to the applied temperature or strain. Comparing the backscattered optical spectra from each reflection site with a reference (unstrained) spectrum allows for quantification of local spectral shifts. While mature OFDR-based technologies can provide high-precision spatially distributed measurements over kilometer lengths, the post-processing approaches used to recover spectral shifts from raw optical intensity data can limit the use of OFDR in harsh environments. This paper presents a novel approach to post-processing OFDR data which extends the usability of optical fibers exposed to harsh environments. This approach is the first to use the spectral shift quality, calculated for two OFDR measurements, to identify an appropriate reference scan from which the spectral shift can be determined. Three experimental data sets are used to test the algorithm: (1) an optical fiber heated to >950°C, (2) an aluminum-embedded optical fiber under strain from differential thermal expansion, and (3) an optical fiber exposed to a total neutron flux of $2\times 10^{13}$ n/cm2/s over 40 hours in a nuclear test reactor. Results show that using a metric of quality to select an appropriate reference measurement extends the functional range of OFDR strain and temperature sensors. Furthermore, this algorithm can be applied to existing OFDR data.

We introduce a new optical frequency domain reflectometry (OFDR) system and processing method that utilize negative beat frequencies for the first time. The new approach enables efficient use of the available system bandwidth and facilitates distributed sensing with the maximum allowable update rate for a given fiber length. This is achieved by using a coherent optical-communications-type receiver that detects both the in-phase (I) and quadrature (Q) components of the backscatter field. The I and Q components are digitally combined to produce a complex backscatter signal whose Fourier transform is not necessarily symmetric. Judicious processing of the complex backscatter signal maps the reflection profile of one half of the sensing fiber to positive beat-frequencies and the profile of the other half to negative beat-frequencies. The new approach was tested via comprehensive computer simulations and experiment.

We experimentally analyzed the internal reflection and loss of each component in a Si photonics frequency-modulated continuous-wave light detection and ranging (FMCW LiDAR) device using optical frequency domain reflectometry (OFDR) with a spatial resolution of better than 2.5 µm. Sweeping the incident laser wavelength by 120 nm, the reflections and losses of wire waveguides, widened waveguides, and optical switches on the chip were individually revealed. The slow-light grating (SLG) beam scanner, which has a limited working wavelength range, was evaluated with a spatial resolution of >10 µm by narrowing the wavelength sweep range. Consequently, a strong reflection was observed at the transition between the wire waveguide and the SLG, which can be a noise source in the FMCW LiDAR. Additionally, this study showed that the OFDR can be an important analysis tool for Si photonics integrated circuits. To our knowledge, this is the first demonstration, showing that the OFDR can be an important analysis tool for Si photonic integrated circuits.

We proposed and experimentally demonstrated a high-spatial-resolution distributed acoustic sensor based on time-frequency-multiplexing (TFM) optical frequency domain reflectometry (OFDR). The TFM technique enhances the frequency response of OFDR by multiplexing the time-frequency channels and suppresses the crosstalk in the meantime. Phase demodulation is employed to achieve high sensitivity, and the impact of end effect in OFDR is studied and suppressed by a dedicated linear interpolation. In the results, a 10.5 kHz vibration is measured with 22 cm spatial resolution and 20 dB signal-to-noise ratio on a 1 km fiber. By adjusting the parameters, the system also shows a good DAS performance on a 33 kHz vibration with up to 200 kHz sampling rate.