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REVIEW 5 major objections 6 minor 15 references

Quantum Noise Limited Temperature-Change Estimation for Phase-OTDR Employing Coherent Detection

T0 review · 5 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Coherent phase-OTDR temperature-change estimation is bounded by a quantum limit: $\sigma_{\Delta T} = \sqrt{2}/(C_f \Delta L)\,\sigma_\varphi$.

desk verdict Useful framing for a phase-OTDR quantum limit, but Eq. (1) is asserted without derivation and appears to have a factor-of-two error under the stated assumptions. read the letter →

arxiv 2505.06007 v1 pith:LOJXT43J submitted 2025-05-09 eess.SP

Huwei Wang , Roman Ermakov , Francesco Da Ros , Darko Zibar This is my paper · ORCID
classification eess.SP
keywords phase-sensitiveopticaltime-domainreflectometryΦ-OTDRquantumlimitcoherentdetectionphaseestimationtemperature-changeRayleighbackscatteringshot-noise-limitedoperation
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The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper derives and numerically demonstrates a quantum limit for temperature-change estimation in coherent phase-sensitive optical time-domain reflectometry (phase-OTDR). The central result is that the smallest achievable uncertainty in estimating a temperature change between two probe pulses is $\sqrt{2}/(C_f \Delta L)\,\sigma_\varphi$, where $\sigma_\varphi$ is the minimum optical phase uncertainty and $\Delta L$ is the sensing length. The authors simulate a 40 km coherently detected phase-OTDR with a Rayleigh backscattering model and show that the phase uncertainty comes close to the known shot-noise-limited value $1/\sqrt{2\,\mathrm{SNR}}$. If the bound holds, it gives distributed fiber sensors a benchmark: no measurement in this architecture can be more precise, and precision scales linearly with phase noise and inversely with sensing length. This matters for infrastructure monitoring because it tells designers how much SNR and sensing length are needed for a target temperature resolution.

What carries the argument

The machinery is Eq. (1), $\sigma_{\Delta T}^{p\to p+1} = \sqrt{2}/(C_f \Delta L)\,\sigma_\varphi$, which converts a phase uncertainty into a temperature-change uncertainty. The factor $\sqrt{2}$ comes from differencing the phase estimates in two successive frames, $C_f$ collects laser and fiber parameters that relate optical phase to temperature, and $\Delta L$ is the length of fiber over which the temperature change is integrated. The phase floor $\sigma_\varphi$ is supplied by the shot-noise-limited coherent detection result $\sigma_\varphi = 1/\sqrt{2\,\mathrm{SNR}}$, which the numerical Rayleigh-backscattering simulation reproduces with a small gap. The assumption that consecutive-frame phase samples are uncorrelated is what allows the single-frame phase variance to propagate directly as $\sqrt{2}\,\sigma_\varphi$; without it, cross-correlation terms would enter and the stated bound would need modification.

What would settle it

Set up a coherent phase-OTDR system at shot-noise-limited SNR with a known heating zone, estimate the phase at a monitoring point and at the zone boundary over many frames, and compare the frame-to-frame standard deviation of the temperature-change estimate to Eq. (1) for several values of $\Delta L$. Any measured uncertainty below $\sqrt{2}/(C_f \Delta L)\,\sigma_\varphi$, or a direct measurement of significant nonzero correlation between phase estimates in successive frames, would falsify the claimed bound.

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Extended reading notes

Core claim

The paper's load-bearing claim is Eq. (1): $\sigma_{\Delta T}^{p\to p+1} = \sqrt{2}/(C_f \Delta L)\,\sigma_\varphi$, which it presents as a fundamental quantum limit on temperature-change estimation for coherent phase-OTDR. The derivation assumes that the estimated phase samples of the Rayleigh backscattered signal are uncorrelated from frame to frame, an assumption the authors state holds when optical amplifier noise and receiver shot noise dominate the system noise. Under that condition, a single-frame phase uncertainty $\sigma_\varphi$ propagates through two consecutive frames, producing the factor $\sqrt{2}$, and the conversion from optical phase to temperature is carried by the system-dependent constant $C_f$ and the sensing length $\Delta L$. Numerical simulations using a Rayleigh backscattering model show that the phase uncertainty in the presence of the sensing fiber is only slightly above the ideal shot-noise-limited coherent-detection value, so the temperature-change uncertainty follows the same scaling with SNR and $\Delta L$.

Load-bearing premise

The derivation's factor $\sqrt{2}$, and hence the stated quantum limit, holds only if the estimated phase samples of the Rayleigh backscattered signal are uncorrelated from frame to frame; the paper asserts this is true when optical amplifier noise and receiver shot noise dominate the system noise.

Editorial extensions

If this is right

  • The uncertainty in a temperature-change estimate is directly proportional to the minimum phase uncertainty, so operating the phase measurement at the shot-noise-limited level is what makes the temperature estimate quantum-limited.
  • For fixed phase noise, the temperature-change uncertainty shrinks as the sensing length $\Delta L$ grows; the paper demonstrates this for $\Delta L = 1$ m, 10 m, and 50 m.
  • The Rayleigh backscattering fiber adds only a small excess phase uncertainty over the ideal shot-noise-limited coherent detection, so the quantum limit of the simpler system is nearly reached in the fiber sensing case.
  • Averaging over more frames reduces the temperature-change uncertainty through averaging of random fluctuations.
  • The derived expression provides a benchmark for comparing phase-OTDR temperature sensing systems: measured uncertainty cannot fall below $\sqrt{2}/(C_f \Delta L)\,\sigma_\varphi$ when the stated noise conditions hold.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If Eq. (1) is correct, the bound is a per-frame floor; averaging $N$ frames should reduce the temperature-change uncertainty roughly as $1/\sqrt{N}$, so longer observation windows trade directly against required SNR.
  • The same derivation structure should transfer to strain or pressure sensing, since those measurands also enter through optical path-length phase shifts; only the conversion constant $C_f$ would change.
  • Under noise regimes where phase samples become correlated, such as low-frequency laser phase noise, the $\sqrt{2}$ factor would acquire cross-correlation corrections, so Eq. (1) may be optimistic or pessimistic depending on the sign of the correlation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 6 minor

Summary. This paper proposes a quantum-limit expression for temperature-change estimation in coherent phase-OTDR. The central result, Eq. (1), states that sigma_ΔT^(p→p+1) = sqrt(2)/(C_f * ΔL) * sigma_phi, where sigma_phi is the minimum phase-estimation uncertainty, C_f is a system-dependent conversion constant, and ΔL is the sensing length. The authors simulate a 40-km coherent phase-OTDR setup, compute the phase uncertainty sigma_phi^num as a function of SNR, compare it with the analytic shot-noise-limited phase uncertainty from Eq. (2) (taken from [10]), and then plot the temperature-change uncertainty versus SNR for ΔL = 1 m, 10 m, and 50 m using Eq. (1). The paper concludes that this is the first derivation of a quantum limit for temperature-change estimation in phase-OTDR.

Significance. Should Eq. (1) hold, it would provide a simple benchmark for the ultimate precision of distributed temperature-change sensing and clarify the scaling with sensing length and SNR. The numerical comparison in Fig. 3 is a useful sanity check that the phase-uncertainty behavior in the simulated Rayleigh backscattering setup is close to the shot-noise-limited result of Eq. (2). However, the paper as submitted does not provide a derivation of Eq. (1), leaves C_f undefined, does not validate the temperature-change estimate itself, and relies on the authors' prior work for both inputs to Eq. (1). These gaps currently prevent the central claim from being fully assessed; the paper is a promising sketch rather than an established fundamental limit.

major comments (5)
  1. [Phase and temperate-change estimation (Eq. (1))] The square-root-of-two coefficient in Eq. (1) is not consistent with the assumptions stated in the text. Under the definitions Δφ_{k2−k1}(p) = φ̂^p_{k2} − φ̂^p_{k1} and ΔT^{p→p+1} ∝ Δφ_{k2−k1}(p+1) − Δφ_{k2−k1}(p), if sigma_phi is the standard deviation of a single phase estimate and all four phase estimates are uncorrelated, the variance of the temperature-change numerator is 4*sigma_phi^2, which gives a coefficient of 2 instead of sqrt(2). If sigma_phi instead denotes the standard deviation of the already-subtracted phase difference Δφ_{k2−k1}(p), then sqrt(2) is correct but Fig. 3's sigma_phi becomes a different quantity and the notation of Eq. (1) is misleading. Please state unambiguously which quantity sigma_phi denotes and provide the variance propagation that yields the coefficient.
  2. [Phase and temperate-change estimation (paragraph before Eq. (1))] The derivation of Eq. (1) is omitted with the sentence 'Due to space constraints, we omit the full derivation and present only the final result,' and the constant C_f is only described as 'a constant that depends on the laser source and sensing fiber parameters.' No expression, numerical value, or units for C_f are given. Without C_f, Eq. (1) is a proportionality, not a closed-form quantum limit, and it cannot be checked or reproduced. Provide the full derivation and the explicit definition of C_f, including its dependence on laser wavelength, fiber parameters, and the conversion method of [13], or state that C_f must be calibrated per system.
  3. [Results (Fig. 4)] The numerical results do not demonstrate the temperature-change quantum limit. Figure 3 validates only the phase-uncertainty sub-result sigma_phi^num against Eq. (2); Figure 4 propagates that phase uncertainty through Eq. (1) with assumed values of ΔL and an unstated value of C_f. No simulation introduces a known temperature change into a heating zone, estimates ΔT from the phase differences, and compares the achieved standard deviation with Eq. (1). To support the claim that Eq. (1) is a quantum limit, the full estimation chain should be simulated and the achieved sigma_ΔT should be compared with Eq. (1) over a range of SNRs and ΔL.
  4. [Phase and temperate-change estimation (assumption sentence)] The stated assumption that the estimated phase samples are uncorrelated is load-bearing, because Eq. (1) would acquire cross-correlation terms if the assumption failed. The text justifies this assumption by citing [14], but does not explain why the simulated system satisfies it (e.g., how pulse width, Rayleigh coherence length, and noise bandwidth prevent correlation between the phase samples at k1 and k2 and across frames p and p+1). Please provide a quantitative argument or a numerical check of the correlation matrix of the estimated phases for the simulated parameters.
  5. [Introduction and Conclusions] Both inputs to Eq. (1) come from the authors' prior work: sigma_phi from [10] and the phase-to-temperature conversion from [13]. Since C_f is not re-derived in the present manuscript, Eq. (1) is at present a linear rearrangement of two previously published results. This is not inherently wrong, but the claim of deriving a new quantum limit requires a self-contained derivation of C_f (or a clearly identified equation in [13] that defines it), and the numerical demonstration should use an independently specified C_f rather than an unstated value. Please clarify what is new in this paper relative to [10] and [13].
minor comments (6)
  1. [Section heading] The heading 'Phase and temperate-change estimation' contains a typo; 'temperate' should be 'temperature'.
  2. [Results, first paragraph] The phrase 'computing computing' is duplicated, and 'It the absence' should be 'In the absence'.
  3. [System Setup] The word 'backs-cattered' should be 'backscattered'.
  4. [Fig. 4] The y-axis label reads 'T uncertainty [ ]' with an empty unit bracket; specify the unit (e.g., K) and define ΔT in the caption.
  5. [Eq. (1) and Fig. 3] Eq. (1) uses sigma_phi while Fig. 3 uses sigma_phi^num; clarify the relationship between these and the sigma_phi in Eq. (2) to avoid ambiguity.
  6. [References] Reference [13] is a conference paper; when relying on it for the definition of C_f, please cite the specific equation or section so that a reader can verify the conversion without searching the entire paper.

Circularity Check

2 steps flagged · score 6.0 of 10

Eq. (1) is a linear re-scaling of the authors' own phase limit [10] and phase-to-temperature constant [13], and Fig. 4 demonstrates the formula by computing it from itself.

  1. self citation load bearing [Section 'Phase and temperate-change estimation', Eq. (1), and Refs. [10] and [13]]
    "We then apply the method introduced in our recent work[13] to convert the estimated phase difference ∆φ̂_{k2−k1}(p) into a temperature change estimate ∆T̂_k2(p) at position k2. ... Due to space constraints, we omit the full derivation and present only the final result. ... σ^{p→p+1}_{ΔT} = √2/(C_f ΔL) σφ (1) where σφ is the minimum uncertainty on the phase estimation along the fast time. C_f is a constant that depends on the laser source and sensing fiber parameters. ... Following the approach presented in[10], the analytical phase uncertainty σφ can expressed as: σφ = sqrt(1/(2SNR)) (2)"

    The paper's central claimed limit, Eq. (1), is announced without derivation. Its only temperature-specific physical input, C_f, is imported from the authors' own Ref. [13], while the phase uncertainty σφ is taken from the authors' Ref. [10]. With ΔL a user-chosen length, Eq. (1) is algebraically just √2/(C_f ΔL) times these prior self-authored results. No derivation, numerical value, or independent benchmark for C_f is given in this paper, so the load-bearing prefactor of the 'first time' quantum limit reduces to a self-citation chain rather than a self-contained first-principles result.

  2. other [Results section, Fig. 4]
    "In order to move from phase to temperature uncertainty, we use Eq. (1) to compute the temperature change uncertainty, when moving from one frame to another, for different sensing lengths ∆L. We use the numerically obtained phase uncertainty, σ_num_φ as well as the one from Eq. (2). The results are plotted in Fig. (4)."

    The 'demonstration' curves in Fig. 4 are generated by inserting phase uncertainties into Eq. (1), the very equation being demonstrated. The paper does not run the full temperature-estimation chain on noisy backscattered traces and compare the resulting σΔT with Eq. (1); instead, Fig. 4 is the output of Eq. (1). Hence the agreement between the plotted curves and Eq. (1) is identity by construction, not an independent numerical confirmation of the claimed quantum limit.

full rationale

The phase-uncertainty input σφ = sqrt(1/(2SNR)) is a published, parameter-free CRLB-type result from Ref. [10]; citing it is not itself circular. The circularity burden is narrower. First, Eq. (1) is announced after 'we omit the full derivation', and its only temperature-specific ingredient, C_f, is taken from the authors' own Ref. [13] without derivation, numerical value, or independent benchmark in this paper; the claimed quantum limit is therefore a re-expression of the authors' earlier phase-noise formula and their earlier phase-to-temperature conversion, rather than a self-contained first-principles result. Second, the 'demonstration' in Fig. 4 is computed by inserting phase uncertainties into Eq. (1); it thus verifies Eq. (1) by construction and cannot confirm the derived limit. Separately, the printed coefficient √2 is not compatible with the stated assumption under the paper's own definition of σφ: the two-frame estimate involves four single-phase estimates, so the uncorrelated standard deviation would be 2σφ, while √2σφ would require σφ to be the already-subtracted phase-difference uncertainty, which is not what Eq. (2) or Fig. 3 provides. That is an internal-consistency problem rather than a circularity, but it reinforces that Eq. (1) is asserted rather than derived. Score 6 is warranted because the central scaling law and its numerical illustration reduce to the paper's own inputs; the score is not higher because the phase-limit ingredient is independently published and the Rayleigh-backscattering simulation adds some independent numerical content.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central formula rests on four unproved premises: uncorrelated phase samples, the known coherent-detection phase limit, the Rayleigh model, and the phase-to-temperature conversion constant C_f from prior work. No new entities are introduced.

free parameters (1)
  • C_f
    Conversion constant between phase change and temperature change in Eq. (1). The paper says only that it 'depends on the laser source and sensing fiber parameters'; no value or defining formula is given, and it is inherited from the authors' prior work [13].
assumptions (4)
  • domain assumption Estimated phase samples of the Rayleigh backscattered signal are uncorrelated.
    Stated before Eq. (1) as a key assumption; needed for the simple sqrt(2) propagation of phase uncertainty into temperature uncertainty. The paper cites [14] for when this holds.
  • domain assumption The phase uncertainty in shot-noise-limited coherent detection is sigma_phi = sqrt(1/(2 SNR)).
    Used as the quantum-limited phase uncertainty baseline in Eq. (2) and in Fig. 4. Taken from the authors' earlier paper [10] rather than derived in this manuscript.
  • domain assumption The Rayleigh backscattering model of Liokumovich et al. [12] accurately represents the sensing fiber response.
    The numerical simulation is built on this model; the validity of the demonstration depends on it.
  • domain assumption The phase-to-temperature conversion method of [13] provides a valid and correctly calibrated constant C_f.
    Eq. (1) uses C_f from the authors' prior work; if that conversion is wrong or calibrated differently, the absolute temperature uncertainty values would shift.

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Cite this review

Pith. "Pith review of Quantum Noise Limited Temperature-Change Estimation for Phase-OTDR Employing Coherent Detection." pith.science (2026). https://pith.science/paper/LOJXT43J

@misc{pith2026250506007,
  author       = {Pith},
  title        = {Pith review of: Quantum Noise Limited Temperature-Change Estimation for Phase-OTDR Employing Coherent Detection},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LOJXT43J}},
  note         = {Machine review of arXiv:2505.06007}
}
read the original abstract

The quantum limit is a fundamental lower bound on the uncertainty when estimating a parameter in a system dominated by the minimum amount of noise (quantum noise). For the first time, we derive and demonstrate a quantum limit for temperature-change estimation for coherent phase-OTDR sensing-systems.

Figures

Figures reproduced from arXiv: 2505.06007 by the authors.

Figure 1
Figure 1. Simulation set-up for coherently detected Φ-OTDR system. p (frame number/slow-time) 𝑦! " # 1 2 (length L /fast-time k) k2 ∆L Heating zone Temperature change ∆T k1 kstart [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Backscattered signal in slow time domain and fast time domain. is 23 dBm. The sensing fiber is a 40 km long single￾mode fiber with an attenuation coefficient αatt of 0.2 dB/km. The Rayleigh backscattered signal is returned through the third port of the circulator and it is amplified with an EDFA with a gain of 22 dB and NF of 3 dB. For the simulation of the back-reflected Rayleigh signal we implemented the model rep… view at source ↗
Figure 4
Figure 4. Estimated temperature-change uncertainty as a function of SNR and for different sensing lengths ∆L uncertainty is plotted as a function of SNR. As a reference, we also plot Eq. (2). It is observed that that there is only a slight gap between σ num φ and σφ . This implies that the Rayleigh backscattering introduces only a very limited uncertainty in the estimation. The difference may be attributed to the fact that, t… view at source ↗

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Reference graph

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