Ghost-Peak Suppression for Optical Correlation-Domain Reflectometry by Gigahertz-Order Frequency Shift

Optical correlation-domain reflectometry (OCDR) is an interference-based method for measuring the reflectivity distribution of optical fibers using periodic frequency-modulated light. OCDR yields experimental results that cannot be explained solely by existing theories, such as the appearance of ghost peaks at positions where reflection points are not anticipated, thus indicating insufficient theoretical foundation. To elucidate this behavior, the “beat-spectrum theory” has been proposed. Although this theory suggests that ghost peaks are caused by beat spectrum folding, no conclusive evidence based on measurements of the folded beat spectrum has been provided, and no solutions have been proposed for addressing ghost peaks. In this study, we test this hypothesis by measuring the folded beat spectrum. Additionally, we experimentally demonstrate that by applying gigahertz-order frequency shifts to a reflected light using a double-sideband modulator, beat spectrum folding can be mitigated and ghost peaks can be effectively suppressed.

OTDR detects reflection points based on the round-trip time of a light pulse injected into the fiber under test (FUT).The spatial resolution and measurement range depend on the pulse width and power, respectively.Owing to the tradeoff relationship between them, OTDR is generally used for conducting meter-scale measurements within a measurement range of several tens of kilometers.To address its disadvantages of high signal-processing costs and long measurement times, derivative OTDR techniques have been proposed, including coherent OTDR, which enhances sensitivity using coherent detection, and frequency-division-multiplexing OTDR, which reduces the averaging process [7], [8], [9].
OFDR utilizes frequency-chirped modulated incident light [10], [11].Light reflected from the FUT is heterodyne detected, and the beat frequency, which is proportional to the round-trip time of the reflected light, allows one to identify the reflection points.The measurement range of OFDR is determined by the coherence length of the incident light, whereas the spatial resolution is determined by the swept frequency bandwidth.Therefore, OFDR offers a high resolution over a relatively short measurement range.In fact, researchers have presented measurement results with a micrometer-level spatial resolution over ranges measuring several centimeters [12], [13].
By contrast, OCDR is an interference-based technique that uses periodic frequency-modulated light [14], [15].In this modulation, a periodic interference distribution is formed along the FUT.The peak of this distribution, which is known as the "correlation peak," serves as a measurement point, since only light reflected from those locations is strongly detected.Reflectivity measurements were performed by sweeping the positions of the correlation peaks along the FUT.OCDR successfully performs individual operations beyond coherence-length and millimeter-scale measurements [16], [17], [18], thus suggesting its potential to achieve high-resolution measurements over long distances.Furthermore, it can rapidly measure arbitrary points (termed random accessibility) [19], [20], [21], [22] and can be implemented easily via direct modulation.
However, OCDR is devoid of a sufficiently established theoretical foundation, and its behavior is yet to be elucidated.For example, under specific conditions, its results include the appearance of ghost peaks at positions where reflection points are not anticipated [29].To elucidate such phenomena, the "beat-spectrum theory," which explains OCDR behavior in the frequency domain, has been proposed [29], [30], [31].Although this theory suggests that spectrum folding contributes primarily to ghost peaks, experimental verification based on spectrum measurements has not yet been performed, and solutions for addressing ghost peaks have not been proposed.
In this study, we complement the folded-spectrum hypothesis by conducting OCDR measurements in the frequency domain.Additionally, by applying gigahertz-order frequency shifts to reflected light using a double-sideband modulator (DSBM), we experimentally demonstrate the suppression of spectrum folding and the removal of ghost peaks.Additionally, we discuss the disadvantages of this method.
This paper is organized as follows: Section II briefly reviews the beat-spectrum theory and presents the factor of ghost peaks.Section III presents the experimental results of the conventional OCDR, which confirm the presence of ghost peaks and a folded spectrum.Subsequently, by applying a DSBM to OCDR, the successful removal of ghost peaks is confirmed experimentally.Section IV discusses the disadvantages of the proposed method and directions for future studies.Section V summarizes our findings.

II. PRINCIPLE
The standard OCDR experimental setup is shown in Fig. 1.It involves the injection of laser light modulated by a periodic function into the FUT, followed by heterodyne detection.When the frequency modulation is a sinusoidal wave, the spectrum obtained by the heterodyne detection at each position x [m] of the FUT can be expressed as (1) where J ν is the Bessel function of the ν-th order, Δf the modulation amplitude, c the light velocity in vacuum, f m the modulation frequency, and n the refractive index of the FUT core.Equation ( 1) is expresses the beat spectrum, which is originally used to formalize the behavior of the Brillouin gain spectrum but has recently demonstrated utility in analyzing the behavior of reflected light intensity in OCDR [32], [33], [34], [35].
The three-dimensional plot constructed based on (1) is shown in Fig. 2(a-1), and its approximated plane schematic is depicted in the blue region of Fig. 2(a-2).In OCDR, narrowband filtering around the beat center f z ∼ 0 (zero-span processing) is performed to extract information regarding the reflection points from the beat spectrum.Because filtering is expressed as a multiplication of the spectrum and filter characteristics, a peak representing reflection is expressed theoretically as where The full-width at half-maximum expressed in ( 2) is defined as the theoretical spatial resolution of OCDR and can be approximated as follows (see Appendix) [30]: Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Additionally, ( 2) is a periodic function and its period determines the measurement range in OCDR, which is expressed as Because both (2) and ( 5) depend on f m , an inherent trade-off exists between them.
However, when considering measurements in a practical context, as depicted in the orange portion of Fig. 2(a-2), lowfrequency noise centered around 0 Hz occurs.Thus, tone cannot readily set f z = 0.As an alternative, a frequency shift can be introduced using an acousto-optic modulator (AOM) [29].The beat spectrum, considering the frequency shift f A by the AOM, is expressed as where the symbol " * " denotes convolution along the f -axis.
A schematic illustration of the frequency-shifted beat spectrum is shown in Fig. 2(b-1), which shows the overlapping of the positive and negative (folded) beat signals.In OCDR using an AOM, zero-span processing is applied to the beat spectrum with a center frequency of f z = f A , as shown in Fig. 2(b-1) and (b-2).Therefore, the peak shape is expressed as where The first term of (6) corresponds to the peak shape associated with the reflection point, which is consistent with (2).The second term represents the component shifted to negative frequencies (folded beat spectrum), which contributes to the occurrence of ghost peaks.In previous studies, this term was not identified because either the beat spectrum-based theories were not employed [14], [15], [16], [17], [18], [19], [20], [21], [22], [23] or the effect of the AOM was disregarded [29].Hence, the introduction of the beat-spectrum concept highlights the presence of the second term and is noteworthy.Furthermore, when is satisfied, the beat center is not overlapped by the folded beat spectrum, as shown in Fig. 2(c-1); hence, in (6), the second term can be approximated as zero.The bandwidth of the beat spectrum is determined by Δf , which is typically in the order of several gigahertz [21].Therefore, by replacing the megahertz-order frequency shift by the AOM with a gigahertz-order frequency shift, the ghost peaks caused by beat-spectrum folding can be suppressed, as Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.shown in Fig. 2(c-2).Note that either the DSBM or singlesideband modulator can be used for this frequency shift.

A. Confirmation of Ghost Peaks Based on Conventional Experimental Method
Next, we confirm the occurrence of ghost peaks due to beatspectrum folding using a conventional experimental approach.The experimental setup is identical to that shown in Fig. 1.The light source was a laser diode with a wavelength of 1550 nm.The output was sinusoidally frequency modulated with a modulation amplitude of Δf ∼ 7.5 GHz and was segregated into incident and reference arms via a coupler.In the incident arm, an erbium-doped fiber amplifier (EDFA-1) with an output of ∼11.6 dBm was inserted, whereas a 300 m delay was inserted in the reference arm.The FUT was fabricated using silica singlemode fibers, and a reflection point established intentionally by connecting a physical-contact connector was set 1 km away from the circulator.The light reflected from the FUT was amplified via EDFA-2 with an output of ∼0.9 dBm, followed by a 100-MHz frequency shift using an AOM.Subsequently, the reflected light was heterodyne detected using a photodetector (PD; Koheron, PD-100).By sweeping the modulation frequency f m from 125.7 to 129.43 kHz, the area around the reflection point within 20 m was measured.Finally, the PD output signal was processed using an electrical spectrum analyzer (ESA).
Fig. 3 shows the experimental results normalized to a maximum power of 1. Fig. 3(a) shows the measured beat spectrum, which agrees relatively well with the theoretical spectrum shown in Fig. 3(b), and illustrates the folding of the beat spectrum.To obtain the results, the beat signal was analyzed in the frequency range of 10 to 190 MHz using the ESA with both the resolution bandwidth (RBW) and video bandwidth (VBW) set to 1 MHz.The disturbed symmetry of the beat spectrum is attributed to the effect of unintended intensity modulation due to direct modulation, which is consistent with the findings of previous studies [33].
The results of the reflectivity-distribution measurements are shown in Fig. 3(c).To obtain this result, the zero-span function of the ESA was utilized and the temporal variation in signal intensity in the 100-MH band with 1-MHz VBW, 10-MHz RBW, and 32 times averaging was recorded.The obtained results were consistent with the signal-intensity variation in the 100 MHz band shown in Fig. 3(a), thus confirming the correspondence of the ghost-peak position with the foot of the folded beat spectrum.These results suggest that the megahertz-order frequency shift achieved with the AOM is insufficient for the distributionreflectivity measurement, thus highlighting the necessity for a greater frequency shift.

B. Suppression of Ghost Peaks Using DSBM
We conducted a similar experiment by replacing the AOM with a DSBM and confirmed the suppression of ghost peaks.The experimental setup was the same as that presented in Section III-A; however, the DSBM was used as the frequency shifter and the outputs of EDFA-2 were set to ∼5.3 dBm.The output of EDFA-2 was increased to compensate for losses incurred by the DSBM.To satisfy the condition shown in (8), we used a DSBM to apply a 10-GHz frequency shift, since the modulation amplitude Δf ∼7.5 GHz.Additionally, to detect a 10-GHz signal, the PD was replaced with one with a cutoff frequency of 12 GHz (Optilab, PR-12-B-M).
The results, normalized to a maximum value of 1, are shown in Fig. 4. Fig. 4(a) shows the measured beat spectrum obtained via a frequency analysis of the beat signal within the range of 0 to 20 GHz using an ESA, with the VBW and RBW set to 3 MHz.Notably, Fig. 4(a) shows moderate alignment with the theoretical representation shown in Fig. 4(b).Moreover, it shows the presence of the beat spectrum at approximately 0 GHz due to interference with the carrier of the DSBM; however, the beat spectrum is sufficiently separated from the interference light with the sidebands of the DSBM, thus ensuring no overlap and the absence of beat-spectrum folding.
Subsequently, using the zero-span function of the ESA, the temporal variation of the signal intensity was recorded at the 10-GHz band, with 1-MHz VBW, 10-MHz RBW, and 32 times averaging.The result presented in Fig. 4(c) shows a single reflection peak, as beat-spectrum folding is not indicated in Fig. 4(a).Consequently, the ghost peaks were successfully suppressed using the DSBM.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

A. Disadvantages of Gigahertz Frequency-Shift Method
In the gigahertz frequency-shift method, the effect of electric impedance becomes more pronounced, thus resulting in a lower signal-to-noise ratio and increased circuit-design costs.Additionally, based on ( 4) and ( 9), whereas the spatial resolution improves as the modulation amplitude Δf increases, a greater frequency shift f A is required to avoid spectrum folding.Consequently, the performance of the frequency shifter becomes a limiting factor in improving the spatial resolution of OCDR.

B. Future Studies
To avoid ghost peaks, in addition to the gigahertz-shift method, two other approaches were considered: a) elimination of the frequency shifter and b) suppression of the beat-spectrum foot.Regarding (a), researchers have investigated a simplified version of OCDR [36], [37], [38], [39], [40].Notably, the aim of this study is to simplify the system and reduce costs, whereas the usefulness of ghost peaks is emphasized less.Furthermore, because AOM removal degrades the resolution and causes peak splitting [26], [30], it may not be an ideal solution.
Hence, we considered a more effective method based on the aforementioned considerations, specifically, option (b).In cases where ghost peaks appear due to the folding of the beat-spectrum foot, creating a beat spectrum with a subdued foot is advantageous.Notably, noise modulation generated a beat spectrum with a significantly suppressed foot [42].Further performance improvements can be achieved by combining this with the gigahertz frequency shift used in this study.

V. CONCLUSION
In this study, we revealed the phenomenon of ghost peaks occurring at positions where no reflection points were indicated in the reflectivity-distribution measurements within the FUT in OCDR.Using beat-spectrum theory, we attributed this phenomenon to the folding of the beat spectrum caused by the frequency shifter.
Furthermore, based on experimental demonstrations using a DSBM, we demonstrated that ghost peaks can be suppressed by shifting the frequency of the reflected light to the gigahertz level.
Therefore, in future studies, we plan to investigate a combination of gigahertz-level frequency shifts and improvements to the modulation signal to significantly enhance the performance of OCDR.

APPENDIX
The full-width at half-maximum in ( 2) is defined as the theoretical spatial resolution of the OCDR.
where H −1 N denotes the inverse Hankel function.When the argument of arcsin(z) is sufficiently small, the following approximation can be applied.arcsin (z) ∼ z (11) Furthermore, by performing a linear fitting within the range 0 < N < 25 to minimize the error rate, we obtain the following approximation: Thus, the approximate spatial resolution is derived as

Fig. 4 .
Fig. 4. Experimental results of OCDR using DSBM: (a) Beat spectrum and (b) its theoretical shape; and (c) reflection peak without ghost peaks.