Commonly, the frequency shift of back-reflection spectra is the key parameter to measure quantitatively local temperature or strain changes in frequency-scanned Rayleigh-based distributed fiber sensors. Cross correlation is the most common method to estimate the frequency shift; however, large errors may take place, particularly when the frequency shift introduced by the temperature or strain change applied to the fiber is beyond the spectral width of the main correlation peak. This fact substantially limits the reliability of the system, and therefore requires careful analysis and possible solutions. In this paper, an analytical model is proposed to thoroughly describe the probability of large errors. This model shows that the cross correlation intrinsically and inevitably leads to large errors when the sampled signal distribution is finite, even under perfect signal-to-noise ratio. As an alternative solution to overcome such a problem, least mean squares is employed to estimate the frequency shift. In addition to reducing the probability of large errors, the proposed method only requires to measure a narrow spectrum, significantly reducing the measurement time compared to state-of-the-art implementations. Both the model and the solution are experimentally verified using a frequency-scanned phase-sensitive optical time-domain reflectometry system, achieving a spatial resolution of 5 cm, with a sensing range of 860 m and an acquisition time below 15 s, over a measurable temperature range of more than 100 K with a repeatability of 20 mK, corresponding to a temperature dynamic range of 5000 resolved points.

Although distributed fiber-optic sensing of axial strain and temperature is a well-established technique, there are almost no demonstrations of distributed hydrostatic pressure sensing. The main obstacle for such measurements is the low sensitivity to pressure of standard optical fibers. Structured fibers, such as photonic crystal fibers, can be made pressure sensitive by means of an optimized arrangement of their internal microstructure. In this paper, we demonstrate-for the first time to our knowledge-distributed birefringence and hydrostatic pressure measurements based on phase-sensitive optical time-domain reflectometry (OTDR) in highly birefringent photonic crystal fibers. We study the response to hydrostatic pressure of two dedicated pressure-sensitive photonic crystal fibers in the range from ∼0.8 to ∼67 bar with a 5-cm spatial resolution using a phase-OTDR approach. We find differential pressure sensitivities between the slow and fast polarization axes of the studied fibers of-219 MHz/bar and 95.4 MHz/bar. These values are ∼3.8 to ∼8.8 times larger than those demonstrated previously in distributed pressure measurements with other photonic crystal fibers.

A distributed and dynamic strain sensing system based on frequency-scanning phase-sensitive optical time domain reflectometry is proposed and demonstrated. By utilizing an RF pulse scheme with a fast arbitrary waveform generator, a train of optical pulses covering a large range of different optical frequencies, short pulse width, and high extinction ratio is generated. Also, a Rayleigh-enhanced fiber is used to eliminate the need for averaging, allowing single-shot operation. Using direct detection and harnessing a dedicated least mean square algorithm, the method exhibits a record high spatial resolution of 20 cm, concurrently with a large measurable strain range (80 µε, 60 demonstrated), a fast sampling rate of 27.8 kHz (almost the maximum possible for a 55 m long fiber and 60 frequency steps), and low strain noise floor (<1.8 nε/ √ Hz for vibrations below 700 Hz and <0.7 nε/ √ Hz for higher frequencies).

The phase change of back-scattered light due to external perturbations is retrieved in coherent Rayleigh-based distributed sensors by estimating the frequency shift (FS) between the traces of different measurements. The uncertainty associated with the estimator, due to the presence of system noises, can lead to an inaccurate evaluation of the FS. Additionally, in coherent Rayleigh-based sensors, the calculation of the signal-to-noise ratio (SNR) from the jagged back-scattered intensity trace using the statistical estimators can cause an erroneous determination of the absolute value of the SNR. In this work, a method to accurately evaluate the non-uniform SNR caused by the stochastic variation of the back-scattered light intensity along the fibre is presented and validated. Furthermore, an analytical expression to evaluate the uncertainty in the FS estimation using one of the standard estimators, namely cross-correlation, is presented. A direct-detection frequency-scanned phase-sensitive optical time-domain reflectometer (φ-OTDR) is employed for the experimental verification of the expression as a function of two crucial system parameters: the SNR and the spatial resolution. The performance of various distributed sensing system configurations utilising cross-correlation for determining the FS occurring due to the external perturbations can be properly predicted hereafter with the aid of the analytical expression presented in this study.

The spectral properties of the Rayleigh backscattered traces measured by a phase-sensitive optical time-domain reflectometer (φOTDR) with direct detection are theoretically and experimentally analyzed. The spectrum of the measured φOTDR signal is found to be strictly dependent on the spectral shape of the probing optical pulse. Furthermore, the visibility, spatial resolution, fading rate, and correlation spectrum of the traces are analyzed using different detection bandwidths. Results point out that the quality of φOTDR traces and target spatial resolution are secured only if the electrical bandwidth of the photodetector is broad enough to cover at least 80% of the total power contained in the electrical spectral density function of the measured trace. This means that in the case of using direct detection of the Rayleigh backscattered light induced by rectangular-shaped optical pulses, the minimum bandwidth required for a proper detection of the traces is equal to the reciprocal of the pulse temporal width (which is larger than the pulse spectral width). Although the theoretical analysis and numerical simulations are here experimentally validated for rectangular and sinc-shaped optical pulses, the results and methodology presented in this article can be applied to optimize the direct-detection bandwidth of φOTDR sensors using any optical pulse shape.