Spontaneous Raman anti-Stokes backscattering signals within optical fibers exhibit unique sensitivity to temperature [1–4]. Raman distributed fiber-optic sensing, which is based on the principle of Raman optical time-domain reflection (ROTDR), has garnered considerable attention from researchers, particularly for temperature monitoring applications [5–11]. The sensing spatial resolution, representing the smallest sensing spatial unit in the ROTDR system [12], delineates the minimum length of the measurable fiber under test (FUT) and is a crucial technical indicator for measuring sensing performance [13–16].

However, the sensing spatial resolution of a traditional ROTDR system is limited by the pulse width in the OTDR principle. Presently, pulsed lasers employed in ROTDR systems exhibit pulse widths ranging from 10 to 30 ns [17–19]. This limitation confines the spatial resolution of conventional kilometer-scale ROTDR systems to the meter scale. Moreover, it deteriorates with increasing sensing distance owing to dispersion and other factors. Consequently, these systems fail to satisfy the requirements of long-distance and high-precision temperature detection in small temperature-variable regions [19,20]. This is a key scientific and technical bottleneck that restricts the field of globally distributed optical fiber sensing.

Pulse-width reduction is the most direct method for enhancing the spatial resolution of ROTDR systems. Notably, one approach employing a narrow pulse width technique achieved a spatial resolution of 10 cm over a sensing distance of 3 m [21], whereas another approach integrated a superconducting-nanowire-based single-photon detector and realized a spatial resolution of 2.4 cm over a sensing distance of 5 m [22]. However, pulse-width reduction directly affects the incoming fiber power, thereby limiting the signal-to-noise ratio (SNR) of the sensing system. Additionally, the integration time required for single-photon detectors is longer than that required for traditional photodetectors. These features collectively constrain the long-distance sensing capability of narrow-pulse ROTDR schemes [22,23].

In long-distance sensing applications, spatial resolution deterioration is typically minimized by suppressing dispersion. Few-mode fiber sensing schemes utilize few-mode fibers as laser transmission media to suppress the dispersion of the detection pulse effectively [24,25]. Using this strategy, the spatial resolution at the fiber end can be effectively optimized while ensuring extended sensing distances. In 2017, Tang et al. successfully suppressed fiber dispersion over long sensing distances using second-order few-mode fibers, ultimately achieving a notable spatial resolution of 3.0 m across a 20.0 km sensing range [24]. Similarly, in 2018, He et al. proposed an ROTDR system based on an asymptotic refractive index few-mode fiber with a large-mode-field effective area and low-dispersion characteristics. This innovative system achieved an impressive spatial resolution of 1.13 m over a sensing distance of 25.0 km [25]. However, the intricacy and high costs of few-mode fibers limit their widespread large-scale adoption.

The optical pulse coding scheme, which can achieve a high spatial resolution across extended sensing distances, employs coding modulation to enhance the luminous flux of signals with equal pulse widths. In 2011, Soto et al. achieved a spatial resolution of 1.0 m over a sensing distance of 26.0 km using a low-repetition-rate quasiperiodic pulse coding technique in conjunction with a single-mode fiber [26]. In 2020, Sun et al. experimentally demonstrated a genetically optimized coding scheme for ROTDR systems. This scheme yielded a remarkable spatial resolution of 1.0 m over a 39.0 km long sensing distance [23].

Notably, in these previously reported sensing schemes, the spatial resolution is constrained to the meter scale owing to the pulse width. To address the challenge of the pulse-width dependence of resolution, we previously introduced a slope-assisted Raman sensing technique [27] that successfully detects hotspot regions at the centimeter level over a sensing distance of 500 m. However, it is important to note that the spatial resolution of this technique is inherently constrained by the pulse width. Alternatively, deconvolution theorems can be used to enhance spatial resolution [17,28–30]. Similar to the narrow-pulse scheme, the deconvolution algorithm sacrifices the SNR and cannot be applied to long sensing distances.

To solve the above-mentioned problems, we previously presented a chaotic Raman distributed fiber-optic sensing simulation model [31], which initially integrated chaotic signals [32,33] with an ROTDR system. This integration not only enhanced the localization principle of the ROTDR system, surpassing the technological bottleneck associated with the spatial resolution limits imposed by the pulse width in traditional Raman distributed fiber-optic sensing systems, but also achieved submeter spatial resolution [34,35]. However, with increasing sensing distance, a notable challenge arises: the Raman scattering signal strength experiences rapid attenuation, which causes the signal envelope of the FUT to become submerged in noise. Consequently, the SNR of the system underwent rapid reduction, significantly limiting its detection capability for small temperature-variable regions at the end of the optical fiber. Therefore, we only achieved a sensing distance of 1.4 km.

In this study, we first analyzed and constructed an asymmetric paired-pulse Raman backscattering propagation model to enhance the SNR of a long-distance chaotic Raman scheme. Subsequently, a time-domain differential reconstruction principle and a chaotic asymmetric paired-pulse correlation-enhanced (CAPC) scheme are introduced. The scheme employs a chaotic asymmetric paired-pulse signal as the detection signal and begins by analyzing and reconstructing the Raman anti-Stokes scattering signal excited by a sensing fiber. This reconstruction was based on the stochastic oscillatory characteristics of the detection signal time sequence. The subsequent step involves isolating each position point that carries the chaotic time-domain stochastic oscillatory characteristics and ambient temperature information through differential reconstruction. Finally, leveraging the distinctive correlation between the reference and reconstructed signals, we employed the chaotic correlation-enhanced method to obtain high-spatial-resolution temperature variation information along the sensing fiber. While ensuring that the incoming fiber power is not significantly increased and that nonlinear effects are avoided, the CAPC method achieves a correlation peak-to-peak coefficient multiplication effect. This enhancement improves the signal-to-noise performance of the correlation demodulation system proposed in this paper while simultaneously ensuring high spatial resolution. Notably, it significantly enhances the SNR over long sensing distances, facilitating high-spatial-resolution temperature measurement with a sensing distance of 10 km and achieving a spatial resolution of 30 cm and SNR of 6.67 dB in experimental settings. To the best of our knowledge, this is the highest spatial resolution achieved for Raman distributed fiber sensing at a sensing distance of 10 km.

First, we constructed the intensity trace of the Raman scattering using Eq. (1): $$I(L,T)=K_a{\lambda }^{-4}P·R_{\mathrm{as}}(T)\exp [-({\alpha }_0+{\alpha }_{\text{as}})·L],$$(1)where $R_{\mathrm{as}}(T)$ is $$R_{\mathrm{as}}(T)={[\exp (h\mathrm{\Delta }v/kT)-1]}^{-1}.$$(2)

The definitions of the physical parameters in Eqs. (1) and (2) are listed in Table 1.Table 1.

Physical Meaning of Raman Scattering Signal

Enhancing the input fiber power significantly is challenging owing to nonlinear effects. Therefore, regardless of whether a traditional or a chaotic scheme is employed, the SNR of long-distance sensing in a single-pulse ROTDR system is inherently limited. This study begins by analyzing the excitation of Raman scattering trace envelopes for both single-pulse and paired-pulse scenarios in an optical fiber. Figure 1 illustrates the Raman scattering trace envelope under various pulse detection conditions. Specifically, Figs. 1(a)–1(c) depict the situation under a single pulse with a width of $\tau$, where the spatial length is $\mathrm{\Delta }{L}_{\text{pulse}}$: $$\mathrm{\Delta }{L}_{\text{pulse}}=\frac{\tau \times c}{2n_0},$$(3)where $c$ is the velocity of light in a vacuum, $n_0$ is the refractive index in the medium, and the spatial length of the temperature test region is $\mathrm{\Delta }{L}_{\mathrm{FUT}}$. In Fig. 1(a), $\mathrm{\Delta }{L}_{\mathrm{FUT}}>\mathrm{\Delta }{L}_{\text{pulse}}$. When the pulse advances in FUT, it is divided into four phases: entering FUT, being completely inside FUT, starting to leave FUT, and completely leaving FUT. The Raman scattering trace envelope in the FUT produced points A, B, C, and D at their respective stages. As shown in Fig. 1(b), the pulse enters the FUT completely and starts leaving the FUT simultaneously. Consequently, the Raman scattering FUT envelope generates points A, B, and C.

As shown in Figs. 1(a) and 1(b), the FUT temperature was accurately detected. However, when $\mathrm{\Delta }{L}_{\mathrm{FUT}}<\mathrm{\Delta }{L}_{\text{pulse}}$ in Fig. 1(c), at position B, the pulse starts to leave FUT and enters the non-FUT region before completely entering FUT. Consequently, the FUT signal within the pulse width scale was superimposed with the non-FUT signal, leading to an underestimated FUT temperature compared with the actual temperature value.

Figures 1(d)–1(f) show the Raman scattering trace model based on paired-pulse; the pulse contains a main pulse and an auxiliary pulse, with widths of ${\tau }_A$ and ${\tau }_B$, respectively, and the pulse interval is ${\tau }_0$. The Raman scattering signal excited in the FUT region is more complex when a pulse pair is used as the probe signal. For Fig. 1(d), when the pulse pair enters FUT, it contains the following stages: A→B, the main pulse enters FUT; C→D, the auxiliary pulse enters FUT; and D→E, the main pulse leaves FUT; E→F, the auxiliary pulse leaves FUT; a total of eight feature points of A–H will be generated. In Fig. 1(e), the width of the main pulse is narrow and can fully enter FUT, which is manifested as A→B; the width of the auxiliary pulse is wide and cannot fully enter FUT, which is manifested as C→D→E; E→F is the auxiliary pulse leaving FUT, and the FUT temperature information and the non-FUT temperature information will overlap. In Fig. 1(f), neither the main pulse nor the auxiliary pulse can fully enter the FUT; therefore, two FUT envelopes and eight feature points A–H are generated. Therefore, the light intensity information in the pulse scale is superimposed at that time, and the non-FUT temperature information is cross-modulated with the FUT temperature information; thus, the spatial resolution of the traditional ROTDR scheme is determined by the pulse width of the detection signal. When detecting tiny FUT smaller than the pulse scale, the traditional ROTDR scheme is distorted [manifested as the temperature measurement result being less than the real temperature, as shown in Figs. 1(c) and 1(f)]. However, according to the above analysis, the Raman scattering signal is a composite modulation of the detection signal time-domain waveform and FUT temperature information, and the Raman scattering signal trace envelope has a unique correlation with the detection signal time-domain waveform characteristics. The time-domain oscillation of the chaotic signal has randomness and uniqueness, and its sequence modulation characteristics of paired-pulses will significantly strengthen this correlation, while the unmodulated noise does not have this feature, and it can be greatly suppressed after the correlation operation. Therefore, a CAPC scheme was proposed.

The CAPC scheme uses a chaotic asymmetric paired-pulse laser as the detection signal. Figure 2 illustrates the CAPC system scheme and demodulation principle, employing a chaotic main pulse and chaotic auxiliary pulse signal as detection signals. Due to the anti-Stokes signal’s higher sensitivity to temperature, better temperature demodulation can be achieved. The experimental system in this study employs a dual-channel demodulation scheme using the anti-Stokes signal and the chaotic reference signal. In Fig. 2(a), the probe signal, which serves as the reference signal for the related calculations, passes through the optocoupler. The other beam was directed into the sensing fiber through a wavelength-division multiplexer (WDM), which filtered out the Raman anti-Stokes backscattered signals excited in the sensing fiber. As shown in Fig. 2(b), the Raman anti-Stokes backscattered signal was reconstructed in the time domain. The light intensity information for each data point is separated based on the random amplitude oscillation characteristics of the chaotic signal. Consequently, each data point of the reconstructed signal exclusively contained the light intensity information of a single location point, thereby avoiding the superimposition of the light intensity information within the pulse width, as observed in the traditional OTDR principle. Finally, by employing the time-domain correlation demodulation technology, the differential reconstruction signal and reference signal undergo correlated operations. This process compresses the temperature region information to the beginning (forming a positively correlated peak) and end (forming a negatively correlated peak) of the FUT zone. The FUT information along the sensing fiber can then be demodulated. The subsequent analysis provided a principled examination of the proposed methodology.

First, we need differential reconstruction to strip the chaotic timing feature in the chaotic asymmetric paired-pulse Raman-scattered signal trace. The chaotic asymmetric paired-pulse time domain signal has the characteristics of random amplitude oscillation, the light intensity of each data point of the detection signal is different (it can be regarded as a discrete sub-pulse group with random amplitude), and the Raman backscattered signal intensity excited by each sub-pulse is different; based on the OTDR principle, the backscattered signal collected by the acquisition system at the same moment is the intensity superposition of the Raman scattering signal excited by the discrete sub-pulse group with a unique sequence in a sensing fiber, rather than the superposition of the same amplitude light intensity signal in the traditional pulse width, and therefore, the Raman anti-Stokes light intensity collected at the temperature change region can be expressed as follows: $$\begin{gathered} I(L,T)=K_a{\lambda }^{-4}\sum _{i=1}^{({\tau }_A+{\tau }_B+{\tau }_0)f_s}{P}_i·R_{\mathrm{as}}\left(T_{L-\frac{i\mathrm{\Delta }t·c}{2n_0}}\right) \\ ·\exp [-({\alpha }_0+{\alpha }_{\text{as}})(L-\frac{i\mathrm{\Delta }t·c}{2n_0})], \end{gathered}$$(4)where $f_s$ is the sampling rate. The light intensity information for each data point can be stripped using the time-domain differential reconstruction as follows: $$F(L,i)=I(L+\frac{i\mathrm{\Delta }t·c}{2n_0})-I(L),$$(5)where $i$ is the number of sampling points, and $\mathrm{\Delta }t$ is the unit sampling time. The temperature of the FUT was set to $T_1$, the temperature of the non-FUT to $T_0$, the starting position of the temperature region to $L_1$, the end position to $L_2$, and the system sampling rate to $f_s$, after which the reconstructed Raman anti-Stokes scattering signal $F(L,i)$ was obtained, as shown in Eq. (6): $$F(L,i)=\{\begin{array}{c}{K}_a{\lambda }^{-4}[R_{\mathrm{as}}(T_1)-R_{\mathrm{as}}(T_0)]\\ \times \left[P{}_{L+\frac{i\mathrm{\Delta }t·c}{2n_0}}\phi \right(L+\frac{i\mathrm{\Delta }t·c}{2n_0})-P{}_L\phi (L)]+\mathrm{\Delta }\phi (L),\\ L_1<L<L_1+({\tau }_A+{\tau }_B+{\tau }_0)·f_s,\\ K_a{\lambda }^{-4}[R_{\mathrm{as}}(T_0)-R_{\mathrm{as}}(T_1)]\\ \times \left[P{}_{L+\frac{i\mathrm{\Delta }t·c}{2n_0}}\phi \right(L+\frac{i\mathrm{\Delta }t·c}{2n_0})-P{}_L\phi (L)]+\mathrm{\Delta }\phi (L),\\ L_2-({\tau }_A+{\tau }_B+{\tau }_0)·f_s<L<L_2,\\ \mathrm{\Delta }\phi (L),\text{else},\end{array}$$(6)where $\phi (L)$ and $\mathrm{\Delta }\phi (L)$ can be expressed by $$\phi (L)=\exp [-({\alpha }_0+{\alpha }_{\mathrm{as}})\times L],$$(7)$$\begin{gathered} \mathrm{\Delta }\phi (L)=K_a{\lambda }_a^{-4}P\times R_{\mathrm{as}}(T_0) \\ \times [\phi (L)-\phi (L-\frac{\mathrm{\Delta }t·c}{2n_0}\left)\right]. \end{gathered}$$(8)

Equation (6) shows that the time-domain differential reconstruction method can reconstruct and analyze the Raman backscattered signal to strip out the light intensity superposition information of each position data point in the Raman anti-Stokes backscattered signal; thus, each data point in the reconstruction signal contains only the temperature information of one location point of the sensing fiber. Therefore, the Raman anti-Stokes scattering signal after time-domain differential reconstruction is only modulated by the ambient temperature signal, and the light intensity information at any position collected by the acquisition system will not be affected by the light intensity superposition characteristics within the pulse width length; this avoids the problem of temperature demodulation signal crosstalk caused by the superposition of light intensity data at different positions in the traditional system owing to the principle of optical time-domain reflection. Each data point of the reconstructed signal is a composite modulation function of the temperature information of the corresponding location point and the random amplitude oscillation information of the chaotic asymmetric paired-pulse, which has a unique correlation with the amplitude oscillation characteristics of the chaotic asymmetric paired-pulse. So the temperature information along the optical fiber can be obtained using the correlated temperature demodulation technology.

The proposed correlated positioning demodulation scheme uses the probe signal as a reference signal and performs a correlation demodulation operation with the time-domain differential reconstruction signal. The detailed demodulation scheme is as follows. Based on the uniqueness of random amplitude oscillations in the chaotic time domain, the reconstructed signal has a unique correlation with the reference signal. When the reference signal delay $t_0$ moment correlates with the differential reconstruction signal at the sensing fiber position in the FUT region, the correlation scheme is excited at the start of the FUT to form a positive correlation peak. When the reference signal delay $t_1$ is related to the reconstruction signal at the end of the sudden fiber temperature change, a negative correlation peak is excited, and the length of the detected fiber region can be calculated according to the delay difference between these two correlation peaks, as shown in Eq. (9): $$\mathrm{\Delta }L=\frac{(t_1-t_0)\times c}{2n_0}.$$(9)

In temperature demodulation, the peak-to-peak coefficient of the positive correlation is formed by the excitation of the reference signal and a differential reconstruction signal, which is forward modulated by the temperature change region; the peak coefficient of the relevant peak is modulated by the ambient temperature. Therefore, the specific temperature information of the FUT region can be demodulated based on the peak coefficients of the positively correlated peaks. The expression for the peak coefficient of the positively correlated peak is given in Eq. (10): $$C_{\mathrm{peak}}=\sum _{\mathit{i}=1}^{\mathit{\text{I}}\mathit{-}\mathit{\text{a}}-1}{I}_{\mathrm{ref}}(i+a)F(i,T),$$(10)where $I_{\mathrm{ref}}$ is $$I_{\mathrm{ref}}(i)=P_i,1\le i\le W·f_s.$$(11)

To analyze the influence of the length of the temperature mutation region on the correlation peak, the chaotic correlation coefficient A is introduced in Eq. (12): $$A=\{\begin{array}{cc}\sum _{i=1}^{({\tau }_A+{\tau }_B+{\tau }_0)·f_s}{P}_i·P_i-& \sum _{i=1}^{({\tau }_A+{\tau }_B+{\tau }_0)·f_s}{P}_{i+m·f_s}·P_i,\\ & m<({\tau }_A+{\tau }_B+{\tau }_0)/2,\\ \sum _{i=1}^{({\tau }_A+{\tau }_B+{\tau }_0)·f_s}{P}_i·P_i,& m\ge ({\tau }_A+{\tau }_B+{\tau }_0)/2,\end{array}$$(12)where $m=t_1-t_0$, and $m$ is the delay length of the FUT region. By combining Eqs. (5) and (6), Eq. (9) is expanded and Eq. (3) is combined to demodulate the temperature information of the final temperature-mutation region, as shown in Eq. (13): $$T=\frac{h\mathrm{\Delta }v}{k·\ln \left\{1+{[\frac{C_{\mathrm{peak}}-\sum P_{\mathrm{i}}\mathrm{\Delta }\phi (L)}{K_a{\lambda }_a^{-4}A\phi (L)}+\frac{1}{\exp (h\mathrm{\Delta }v/k{T}_0)-1}]}^{-1}\right\}}.$$(13)

Temperature measurement accuracy is an important performance of the Raman distributed optical fiber sensing system, which the root mean square error (RMSE) ${\sigma }_T$ or the mean square error (MSE) ${\sigma }_T^2$ of measured temperature can express. According to Eq. (13), the ${\sigma }_T^2$ satisfies Eq. (14) with the MSE of the $C_{\mathrm{peak}}$, $P$, $\phi (L)$, $A$, and $T_0$. It can be seen that the measurement accuracy of $A$ and $\phi (L)$ is crucial, and the measurement of $A$ and $\phi (L)$ not only affects themselves, but also affects the weight of other measurement errors, and ultimately affects the ${\sigma }_T^2$. $$\begin{gathered} {\sigma }_T^2\propto \frac{1}{A^2\phi {(L)}^2}{\sigma }_{C_{\mathrm{peak}}}^2+\frac{1}{A^2}{\sigma }_P^2+\frac{C_{\mathrm{peak}}^2}{A^2\phi {(L)}^4}{\sigma }_{\phi }^2 \\ +\frac{{[C_{\mathrm{peak}}-\sum P_{\mathrm{i}}\mathrm{\Delta }\phi (L)]}^2}{A^4\phi {(L)}^2}{\sigma }_A^2+\frac{\exp (2T_0^{-1})}{T_0^4}{\sigma }_{T_0}^2. \end{gathered}$$(14)

Different from other pulse modulation techniques, the CAPC scheme consists of two independent pulses with certain intervals; the chaotic broadband characteristics achieve high spatial resolution, and the asymmetry enhances the SNR of the system. Compared with the chaotic single pulse as the detection signal, the chaotic asymmetric paired-pulse contains more chaotic time-domain peak oscillation information and modulation sequence information, which improves the unique correlation between the detection signal and reconstructed signal and weakens the correlation between the detection signal and noise signal, and asymmetry inhibits the correlation of pulses to internal pulses. As a result, the SNR of the system is improved. When asymmetric paired-pulse detection is performed, the correlation between the reconstructed temperature region signal and the detection signal is multiplied, which is characterized by the multiplying of the chaotic correlation peak in the FUT. Moreover, the paired-pulse increases the luminous flux coupled into the fiber without significantly increasing the input fiber power (suppressing the nonlinear effect) and improves the detection ability of the small FUT of the long-distance temperature-sensing system and the SNR of the system.

As mentioned above, FUT localization was performed based on the positively and negatively correlated peaks formed by the correlation trace between the Raman scattering signal and the reference signal after differential reconstruction. For an ideal chaotic pulse, the pulse energy rise time and fall time are infinitesimal, and the positive and negative correlation peak distance is the FUT length $\mathrm{\Delta }L$. However, the chaotic detection pulse in the experiment had a rising edge $t_1$ and falling edge $t_2$, and the small FUT positioning must be corrected. Figure 3 illustrates the correction principle in detail. The ideal pulse waveform and the experimental results are shown in red, and the experimental pulses and the experimental results are indicated by pink dashed lines. When detecting small FUT (pulse edge scale similar to FUT scale), the extra pulse rise time broadens the rising edge of the envelope of the temperature change region of the backscattered signal, which eventually leads to the forward shift of the positively correlated peak; the additional pulse fall time widens the falling edge of the envelope in the temperature region of the backscattered signal, which will lead to the backward shift of the negative correlation peak, and finally causes the scaling of the positive and negative correlation peak distance $\mathrm{\Delta }{L}^{\prime }=\mathrm{\Delta }L+\mathrm{\Delta }{L}_1+\mathrm{\Delta }{L}_2$; then the FUT length $\mathrm{\Delta }L$ using the positive and negative correlation peak distance $\mathrm{\Delta }{L}^{\prime }$ needs to be corrected as shown in Eq. (15): $$\mathrm{\Delta }L=\mathrm{\Delta }{L}^{\prime }-\mathrm{\Delta }{L}_1-\mathrm{\Delta }{L}_2.$$(15)

We established a CAPC experimental setup for Raman distributed fiber-optic sensing, as shown in Fig. 4. Compared to other light source modulation schemes such as pulse coding, chaotic modulated light sources are self-stabilizing and do not require additional encoding designs to surpass the meter-level spatial resolution of traditional ROTDR systems, achieving a submeter spatial resolution as demonstrated. Initially, an optical feedback method [36,37] was used to generate a chaotic laser. The process involves passing the 1550 nm continuous laser from the semiconductor laser through a circulator, a 50:50 dB OC-1, a polarization controller, and an optical attenuator (OA), and then routing it back to the laser. By adjusting the polarization controller and the OA, broadband stable chaotic states can be generated. Once the chaotic state is generated, it can be maintained by using an isolator (ISO) to prevent reflection interference. A semiconductor optical amplifier (SOA) was modulated by a pulse signal generator (PSG) to convert a continuous chaotic signal into a chaotic asymmetric paired-pulse signal. This signal was then amplified using a pulsed erbium-doped fiber amplifier (EDFA) and injected into a 1:99 OC-2; the 1%-port output was collected as a reference signal with an avalanche photodiode (APD), and the 99%-port output was injected into a 10 km sensing fiber via a wavelength division multiplexer (WDM). An FUT is positioned at the tail end of the sensing fiber, and its temperature is varied using a temperature control chamber (TCC), while the remainder of the fiber is maintained at a room temperature of 25°C. The 1450 nm Raman anti-Stokes signal was filtered from the 1450 nm port of the WDM and captured using an APD. The two optical signals were converted into electrical signals and collected using an analog-to-digital converter (ADC). The sampling parameters determine the positioning accuracy and acquisition time of the system. To reduce the positioning error, the sampling rate is set to 2.5 GS/s, which can control the positioning error to $\pm 2\mathrm{cm}$. Meanwhile, the pulse repetition rate is set to 1 kHz to control the peak power of the chaotic asymmetric paired-pulse and the system sampling time. The signal reconstruction and data demodulation were performed using a personal computer (PC).

Figure 5 illustrates the characteristics of continuous chaos and asymmetric paired-pulse chaotic signals. The continuous chaotic laser signals, along with their spectral, temporal, and autocorrelation features, are displayed individually in Figs. 5(a)–5(d). The chaotic signal exhibits distinctive traits, such as a broad spectrum, a wide frequency spectrum, random undulations in timing, and $\delta$-like function. Notably, the spectral full width at half-maximum (FWHM) is measured at 0.5 nm, which is wider than that of the conventional laser by 0.3 nm (conventional lasers typically have a width of only 0.2 nm). The power spectrum boasts a 3 dB bandwidth of 6.1 GHz, while the timing peak-to-peak undulation reaches 200 mV. Additionally, the timing autocorrelation was characterized by an FWHM of 0.07 ns.

The chaotic asymmetric paired-pulse signal was derived from the continuous chaotic laser signal modulated by the SOA, and its timing and temporal autocorrelation are shown in Figs. 5(e) and 5(f). Figure 5(e) shows a main pulse with a narrower width and an auxiliary pulse with a wider width, both preserving the random amplitude characteristics of the chaotic laser signal. This configuration enhanced the chaotic peak-to-peak oscillation characteristics while maintaining the timing autocorrelation of the main peak FWHM at 0.07 ns.

Leveraging the $\delta$ characteristic of chaotic signals and the correlation scheme principle, the spatial resolution of the chaotic Raman distributed temperature sensing system is determined by the autocorrelation of the peak-to-peak FWHM values of chaotic signals. By enhancing the chaotic time-domain peak-to-peak oscillations while preserving the spatial resolution of the sensing system, the chaotic asymmetric paired-pulse detection signals significantly improved the SNR of the long-distance chaotic Raman time-domain reflective fiber-optic sensing system. This enhancement further enhances the performance of long-distance temperature sensing in a chaotic Raman distributed fiber-optic sensing system.

To assess the efficacy of chaotic asymmetric paired-pulse signals in enhancing the SNR (in this paper, the SNR is defined as the sum of the positively and negatively correlated peaks from the base noise), we employed chaotic asymmetric paired-pulse signals with a main pulse width of 20 ns and an auxiliary pulse width of 200 ns as detection signals. A multimode fiber was used as the sensing fiber in the validation experiments. The spatial resolution of the scheme proposed in this study is independent of the pulse width, mitigating issues related to spatial resolution deterioration caused by pulse broadening due to chromatic dispersion in the optical fiber. Hence, the spatial resolution of this scheme remains unaffected by the type of optical fiber used, and the scheme can be applied to single-mode fibers, few-mode fibers, or other special fibers. In particular, multimode fibers offer higher Raman scattering signal gain and an increased threshold for excited Raman scattering, making them widely suitable for Raman distributed sensing systems. For the validation experiments, a sensing fiber of 8.3 km in length was set up, incorporating an FUT with a length of 30 cm and a temperature of 80°C, while the remaining fiber was maintained at room temperature (25°C). In Fig. 6, the SNR of a single chaotic pulse with a width of 220 ns is compared with that of an experimental system using a chaotic asymmetric paired-pulse of 20 and 200 ns. Relative to the single chaotic pulse system, the positive and negative correlation peaks in the CAPC were enhanced by 3.58 dB and 3.42 dB, respectively, resulting in a 7 dB improvement in the overall system SNR. This observation indicates that the CAPC scheme significantly enhances the SNR compared with a single chaotic pulse system. In the chaotic asymmetric paired-pulse scheme, the main pulse with a narrower width excites Raman backscattering as a superposition of Raman backscattering on a smaller scale. Simultaneously, the auxiliary pulse with a wider width provides ample information about the chaotic peak-to-peak oscillations. Thus, the chaotic asymmetric paired-pulse enhances chaotic time-domain peak-to-peak oscillations and incorporates information regarding the modulation sequence. And asymmetry inhibits the correlation of internal pulses. Moreover, because the system noise remained unmodulated and was somewhat suppressed after the correlation, the overall system SNR was substantially improved.

We performed FUT spatial localization and spatial resolution measurements based on the positive and negative correlation peaks of the chaotic correlation trace. Based on this, we used the minimum recognizable FUT length as the discriminant method of spatial resolution. We first set up a 30 cm FUT-1 and a 50 cm FUT-2 at the same position at the end of a 10 km fiber. The sum of the rising and falling edges of the pulses is detected to be 15 ns, which corresponds to $\mathrm{\Delta }{L}_0$ of 1.5 m. The experimental results are shown in Fig. 7; after the small FUT localization correction described in Eq. (15), both FUT-1 of length 30 cm and FUT-2 of length 50 cm can be accurately localized. In other words, the spatial resolution of the scheme presented in this study was 30 cm.

In this study, temperature demodulation was performed based on the CAPC scheme, using Eqs. (10) and (13). To validate the temperature demodulation capability of the proposed scheme, we positioned a 30 cm long FUT at the tail end of a 10 km sensing fiber. The temperatures of the FUT were set to 60°, 70°, 80°, and 90°C, while the rest of the fibers were maintained at a room temperature of 25°C. The correlation peak-to-peak curves are illustrated in Figs. 8(a)–8(d), where accurate detection of the spatial localization and length measurement of FUTs are achieved after correcting for small FUT localization. The peak-to-peak value of the positive correlation increased linearly with increasing temperature.

Figure 8(e) presents the linear fit of temperature against the positive correlation peak-to-peak value, yielding a fitted linear slope of 0.13 and a fitted correlation coefficient of 0.89. This implies that for every 1°C increase in temperature, the positive correlation peak-to-peak value increased by 0.13. To demodulate the temperature we first need to calibrate as follows: (i) the entire optical fiber is placed in a room-temperature environment to obtain the anti-Stokes signal and reference signal at room temperature $T_0$; (ii) a certain length of the optical fiber is exposed to a temperature $T$, obtaining the anti-Stokes signal and reference signal at temperature $\mathit{T}$. Using Eq. (13), the $\phi (L)$ and $A$ can be calculated. The intensity changes at fiber connection points and bending points also can be eliminated through the calibration process. The intensity changes at fiber connection points and bending points also can be eliminated through the calibration process. Subsequently, the FUT temperature was calculated using the positively correlated peaks in Eq. (13) under different FUT temperature conditions in the experiments, resulting in the results shown in Fig. 8(f). We calculated the temperature demodulation results for a 30 cm FUT at 60°, 70°, 80°, and 90°C, obtaining values of 59.30°, 68.44°, 81.65°, and 89.25°C, respectively. The RMSE is 1.25°C. The error range of the temperature calibration equipment is $\pm 0.5°\mathrm{C}$, so we consider that the temperature measurement accuracy achieved by the proposed method is $1.25°\mathrm{C}\pm 0.5°\mathrm{C}$. At a sensing distance of 8 km, this value is $0.81°\mathrm{C}\pm 0.5°\mathrm{C}$. Notably, only the cumulative average denoising method is used to remove polarization noise and random noise in this paper. Denoising methods such as wavelets can still further optimize the SNR and temperature measurement accuracy. Finally, a temperature measurement accuracy better than 2.0°C was achieved with a sensing distance of over 10 km and a spatial resolution of 30 cm.

The chaotic correlation localization principle in this study exploits the distinctive correlation between chaotic time-ordered peak-to-peak oscillations and their induced Raman backward scattering for FUT spatial localization and temperature demodulation. As discussed in the preceding section, relying on the chaotic $\delta$-like function property and the chaotic correlation localization demodulation principle, the spatial resolution of the scheme proposed in this paper is contingent on the chaotic signal bandwidth. The chaotic optical bandwidth signifies the intensity of the stochastic oscillation feature of the chaotic time-domain peak-to-peak values and concurrently determines the spatial resolution of the asymmetric paired-pulse chaotic Raman distributed-sensing system.

Due to the relatively weak Raman scattering signal strength ($-60\mathrm{dBm}$) and the limited detection bandwidth of APD (200 MHz), which are capable of detecting the Raman scattering signal, chaotic timing signals with frequencies exceeding 200 MHz are filtered out. Consequently, the detected chaotic signals exhibited timing autocorrelation of the main peak with FWHM values of 3 ns [Fig. 9(a)]. Thus, the spatial resolution achieved using this system was 30 cm. In contrast, our chaotic optical 3 dB bandwidth, generated using an optical feedback device, is 6.1 GHz, with a temporal autocorrelation FWHM of 0.07 ns and a theoretical spatial resolution of 7 mm. Figure 9(b) shows the theoretically optimal spatial resolution of the chaotic asymmetric paired-pulse Raman system under chaos with different power spectral bandwidths.

Figures 10(a) and 10(b) illustrate the spatial resolution of the system for different main-pulse and auxiliary-pulse widths, respectively, confirming that the pulse width does not affect the spatial resolution. However, the pulse width still influences the chaotic timing of the peak-to-peak oscillation information within the sequence and incoming fiber power, subsequently affecting the peak value of the sensing system’s correlation curve and, ultimately, the SNR of the system.

We adjusted the widths of the main and auxiliary pulses individually to observe their effects on the SNR, as shown in Figs. 10(c) and 10(d). The results reveal a maximum in SNR of 3.82 dB compared to 6.67 dB when modifying the main-pulse and auxiliary-pulse widths. The system SNR exhibited an initial increase, followed by a decrease in the main-pulse width, reaching a peak at 20–30 ns. However, the gain saturation effect of the pulsed EDFA [23] leads to attenuation of chaotic timing peak-to-peak oscillation information, causing a decrease in SNR as the main-pulse width continues to increase. The SNR increases with the auxiliary-pulse width, but the rate of increase gradually slows down due to the gain saturation effect of the EDFA induced by the pulse envelope attenuation. As a result, the SNR does not increase linearly but gradually slows down as the auxiliary-pulse width increases. Based on these experimental findings, we identified the optical main- and auxiliary-pulse widths, as well as the SNR for the chaotic asymmetric paired-pulse correlated enhancement for the Raman distributed fiber-optic sensing system. Under the experimental conditions described in the previous section, the SNR of CAPC for the Raman distributed fiber-optic sensing system was 6.67 dB when the width of the main pulse was 20–30 ns and the width of the auxiliary pulse was 200 ns.

Furthermore, the spatial resolution of this scheme is not limited by the sensing distance; however, due to the attenuation of the detection signal and the sensing signal, the SNR is still related to the sensing distance. The intuitive result is that the accuracy of the temperature measurement is compromised. At a sensing distance of 8 km, the SNR is 7.0 dB, and temperature measurement is $0.81°\mathrm{C}\pm 0.5°\mathrm{C}$; at 10 km, the SNR and temperature measurement accuracy were 6.67 dB and $1.25°\mathrm{C}\pm 0.5°\mathrm{C}$, respectively. In the CAPC scheme, the theoretical spatial resolution of the scheme will not be limited by the SNR, but the SNR will affect the positioning and judgment of FUT, thus affecting the actual performance of the system.

Raman distributed fiber-optic sensing technology has garnered considerable attention owing to its cost effectiveness, high interference immunity, and unique temperature sensitivity. However, the spatial resolution of traditional Raman distributed systems is tied to the pulse width, leading to a degraded SNR over extended sensing distances. This paper introduces a time-domain differential reconstruction principle and a CAPC scheme that breaks the spatial resolution bottleneck associated with the pulse width for Raman distributed sensing technology. Utilizing chaotic asymmetric paired-pulse signals with lengths of 220–230 ns, the proposed technology achieves long-distance submeter spatial resolution measurements over a 10 km sensing distance, with a spatial resolution of 30 cm and an SNR of 6.67 dB.

The theoretical analysis in this study explored the Raman backscattering envelope under single and asymmetric paired-pulse detection, highlighting the inherent limitation of traditional pulse schemes in identifying and locating small FUTs. By leveraging the chaotic stochastic amplitude oscillatory property and the time-domain differential reconstruction technique, this study peels off the Raman backscattering signal at each data point, preventing signal superposition within the pulse scale. The reconstructed signal combines the chaotic stochastic amplitude modulation with the temperature information for each data point. Subsequent submeter-scale FUT pinpointing and temperature demodulation exploited the unique correlation between chaos and its excited backscattered signal, which was enhanced by the correlated scheme. The asymmetric paired-pulse not only provides rich chaotic amplitude oscillation information without altering the incoming fiber power but also offers modulation sequence information. The noise was effectively suppressed through the correlation process, significantly improving the system SNR over long sensing distances.

Finally, this study demonstrates that the spatial resolution of the CAPC Raman distributed sensing system is solely determined by the bandwidth of the power spectrum of the chaotic laser signals, independent of the pulse width. This resolution was unaffected by reducing the sensing distance. This paper also presents the theoretical spatial resolution with different chaotic bandwidths and SNRs of the system with asymmetric paired-pulse, offering a novel perspective for the study of long-distance, high-spatial-resolution, and high-SNR Raman distributed sensing systems.

Acknowledgment. This work was supported also by the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi and the Shanxi-Zheda Institute of Advanced Materials and Chemical Engineering.