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REVIEW 3 major objections 5 minor 71 references

Approaching the quantum-limited precision in frequency-comb-based spectral interferometry for length measurements

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Frequency-comb spectral interferometry reaches 0.67-nm precision at 40 kHz, close to the shot-noise limit, with intensity noise as the short-range floor.

desk verdict A real precision advance in EO-comb spectral interferometry, but the quantum-limit claim rests on a white-noise calibration the paper itself says is not suitable for actual measurements. read the letter →

arxiv 2501.10044 v1 pith:3HWZ5CSF submitted 2025-01-17 physics.optics physics.ins-det

Yoon-Soo Jang , Heulbi Ahn , Sunghoon Eom , Jungjae Park , Jonghan Jin This is my paper · ORCID
classification physics.opticsphysics.ins-det
keywords frequencycombspectralinterferometryabsolutedistancemeasurementshot-noiselimitelectro-opticAllandeviationlengthmetrologyvibrationsensing
verification ladder T0 review T1 audit T2 compute T3 formal

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 claims that frequency-comb-based spectral interferometry can measure absolute distance with sub-nanometer precision at high speed, and that the precision floor is set by fundamental light-source and detector noise rather than by the fringe-analysis algorithm. Using a spectrally flat electro-optic comb and a 40 kHz spectrometer, the authors report a precision of 0.67 nm at a 25 μs averaging time and a sensitivity of $4.5\times10^{-12}$ m/Hz$^{1/2}$, close to the computed shot-noise floor. They argue that intensity noise is the fundamental limit at short distances and that frequency noise becomes gradually dominant as the target distance grows. If correct, this would make comb-based spectral interferometry a credible replacement for laser displacement interferometry in next-generation length standards, while also enabling real-time sensing of vibrations and sound.

What carries the argument

The load-bearing object is the spectral interferogram produced by a spectrally flat electro-optic frequency comb with an 18 GHz mode spacing and about 10 THz bandwidth. The round-trip delay $\tau_{TOF}=2L/v$ appears as a fringe period $1/\tau_{TOF}$ in the frequency domain, so a Fourier transform followed by peak detection converts the spectrum into a distance readout. The noise analysis is carried by Eq. (3), which splits interferogram fluctuations into an intensity-noise term $(1+V^2/2)(\Delta I_o(f_i,t))^2$ and a frequency-noise term $(4\pi I_o V L/v)^2(\Delta\delta f_i(t))^2/2$. A simulation supplies the conversion factor $G=7\times10^{-13}$ m$^2$ that maps a uniform white relative-intensity-noise power spectral density $S_{white}(f)$ into a distance power spectral density $S_{distance}(f)=G\,S_{white}(f)$, and the shot-noise floor is estimated from the CCD electron count, giving $S_{distance,shot}=1.2\times10^{-23}$ m$^2$/Hz, or $3.4\times10^{-12}$ m/Hz$^{1/2}$. The measurement pipeline uses a tenth-order super-Gaussian window over a 9 THz bandwidth and polynomial fitting of the reconstructed peak.

What would settle it

Re-run the shot-noise-limit calculation using the measured per-pixel relative intensity noise from Appendix E instead of uniform white noise, and compare the predicted distance amplitude spectral density with the measured $4.5\times10^{-12}$ m/Hz$^{1/2}$ at 100 mm; if the prediction departs by more than about 20 percent, the closeness to the quantum limit is an artifact of the uniform-noise conversion factor. A direct experimental check is to place a mirror on a calibrated piezo stage at 100 mm and verify that the white-noise Allan deviation follows $3.2$ pm$\cdot\tau^{-1/2}$ as the detector thermal noise is reduced.

Watch

Extended reading notes

Core claim

The central claim is that intensity noise, not the data-processing algorithm, is the limiting noise source of frequency-comb spectral interferometry at short distances, with frequency noise taking over at longer distances. In the authors' model, the spectral interference signal is $I(f_i,t)=I_o(f_i,t)\{1+V\cos(2\pi(f_i+\delta f_i(t))2L/v)\}$, and its fluctuation separates into an intensity-noise term and a frequency-noise term proportional to $L$. Experimentally, at a target distance of about 100 mm, the measured distance sensitivity was $4.5\times10^{-12}$ m/Hz$^{1/2}$ above 1 kHz, close to the quantum-limited (shot-noise-limited) value, and the Allan deviation was 0.67 nm without averaging and 0.34 nm at 250 μs; with one-second averaging in a stable environment the precision reaches about 3.2 pm. The white-noise sensitivity grows as $\sqrt{(4.5\times10^{-12})^2+(L\cdot1.2\times10^{-11})^2}$ m/Hz$^{1/2}$ for target distances from 100 mm to 1000 mm, confirming the predicted transition from intensity-noise to frequency-noise limitation.

Load-bearing premise

The shot-noise-limited sensitivity is computed with a simulation that assumes uniform white noise across the spectrum and a linear conversion factor $G=7\times10^{-13}$ m$^2$; the paper itself notes in Methods that this uniform-noise model is not suitable for actual distance measurements because real intensity noise varies from comb mode to comb mode. If that conversion factor misrepresents the real non-uniform noise, the claim that the measured $4.5\times10^{-12}$ m/Hz$^{1/2}$ is close to the quantum limit is not established.

Editorial extensions

If this is right

  • At a 40 kHz update rate with 0.67 nm precision without averaging, the method can track fast dynamic motion such as acoustic-wave-induced vibration and laser eavesdropping in real time.
  • In the white-noise-limited regime the Allan deviation follows $3.2$ pm$\cdot\tau^{-1/2}$, so one-second averaging reaches roughly 3.2 pm in a stable environment, comparable to laser displacement interferometry without accumulated displacement.
  • Because the distance comes from the spectral fringe period, the measurement is absolute and free of the $2\pi$ ambiguity that constrains single-wavelength displacement interferometers.
  • Combining this interferometer with AMCW ranging for coarse initialization gives absolute distance measurements beyond the 4.2 mm non-ambiguity range of the comb interferometer itself.
  • At long distances the frequency-noise contribution scales linearly with $L$, so reaching the quantum limit at long range will require reducing the seed-laser frequency noise rather than only improving the detector.

Reading between the lines

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

  • Beyond the paper: if the shot-noise floor is real, further precision gains at short range depend on lowering the relative intensity noise of the comb and the detector in the high-noise spectral regions, not on better peak-fitting algorithms.
  • Beyond the paper: the same two-term intensity and frequency noise model could be used to predict the precision limits of other comb sources, such as mode-locked fiber combs or microcombs, directly from their measured relative intensity noise and frequency noise.
  • Beyond the paper: the demonstrated voice and sound sensing suggests the technique could serve as a traceable optomechanical microphone, converting acoustic pressure into calibrated length measurements.
  • Beyond the paper: the empirical conversion factor $G$ could be cross-checked against an information-theoretic bound on peak-position estimation, which would generalize the quantum-limit prediction to arbitrary comb spectra and noise color.
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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

3 major / 5 minor

Summary. The paper reports a frequency-comb-based spectral interferometry system for absolute distance measurements, using a spectrally flat electro-optic comb and a high-speed spectrometer. The authors demonstrate a measurement precision of 0.67 nm at 25 us averaging time, an amplitude spectral density of 4.5e-12 m/Hz^1/2 above 1 kHz, claim this is close to the shot-noise (quantum) limit, and support this with a noise model that separates intensity-noise and frequency-noise contributions. They validate the model by injecting the measured RIN of the same comb into the interferogram and comparing the predicted and measured distance noise, and by analyzing the distance dependence of the sensitivity. Practical demonstrations include acoustic-wave-induced vibration measurements and voice recording through the interferometer.

Significance. If the central claim is established, the paper represents a significant advance in absolute distance metrology: it combines high update rate (40 kHz) with nanometric precision and provides a quantitative noise budget that identifies intensity noise as the dominant limit at short distances and frequency noise at longer distances. The direct Allan deviation and amplitude spectral density measurements are credible, and the noise-injection simulation reproduces the measured noise spectrum, which is a strong internal consistency check. The acoustic and voice-sensing demonstrations show practical utility. However, the 'close to the quantum limit' claim depends on a simulation-derived conversion factor and on internally inconsistent numerical values for the shot-noise floor, so the quantitative conclusion needs strengthening.

major comments (3)
  1. [Introduction / Results / Methods (shot-noise calculation)] The paper quotes three different values for the shot-noise-limited amplitude spectral density: 3.2e-12 m/Hz^1/2 in the Introduction, 3.7e-12 m/Hz^1/2 in the Results (Fig. 2B and accompanying text), and 3.4e-12 m/Hz^1/2 in the Methods section. Because the central claim is that the measured 4.5e-12 m/Hz^1/2 is close to this limit, the reference value must be unique and consistent; please reconcile these numbers and clarify which value is the final shot-noise floor.
  2. [Methods ('Calculation of the shot-noise-limited distance sensitivity') and Appendix G] The conversion factor G = 7e-13 m^2 is obtained from a simulation that injects uniform white noise into an ideal interference signal with V = 0.6, and no uncertainty or sensitivity analysis is provided. The Methods even notes that the uniform-white-noise model 'is not suitable for actual distance measurements.' Since G is used to convert the shot-noise RIN into the shot-noise-limited distance sensitivity, an error in G propagates directly into the quantum-limit claim. Please provide a robustness analysis (e.g., G as a function of visibility, window order, bandwidth, and noise level) and justify why the uniform-noise calibration is valid for shot noise despite the non-uniform RIN observed in Appendix E.
  3. [Results ('High-precision and rapid distance measurements') and Discussion] The agreement between the measured distance noise and the prediction obtained by injecting the measured RIN of the same comb into the same interferogram is a valuable consistency check, but it shows that the measured intensity noise is the dominant contributor, not that the precision is at a fundamental quantum limit. The paper should explicitly distinguish the technical-noise floor (which includes RIN above shot noise, as in Fig. S5) from the shot-noise floor, and state how far the current technical noise sits above the shot-noise floor.
minor comments (5)
  1. [Fig. 2A and main text] The text refers to the measured distance line as 'blue' while the figure caption and legend describe it as 'black'; please make the colors consistent throughout the figure and text.
  2. [Equation (3)] The second term is typeset as '(4πIoVL/v)2 2⁄', which is ambiguous; the factor of 1/2 is unclear. Please typeset the equation clearly, e.g., (4πIoVL/v)^2 / 2.
  3. [Table S1] The 'Precision (1 σ)' entry for this work is 0.33 nm at τ_avg = 250 μs, while the main text reports 0.34 nm at the same averaging time; please harmonize these values.
  4. [Methods ('Shot-noise calculation')] There is a typo: 'conversion efficient' should be 'conversion efficiency'.
  5. [Data and materials availability] For reproducibility of the G-factor simulation, please consider providing the simulation code or a detailed pseudocode, since the current statement only says additional data may be requested.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the noise-injection and shot-noise-limit predictions are forward-model calculations from independently measured inputs, not fits to the distance data; self-citations are not load-bearing.

full rationale

The paper's central claims are validated by self-contained experiments: measured distance ASD and Allan deviation at 100 mm are compared with a prediction obtained by measuring the EO comb/spectrometer RIN and injecting it into a single interferogram, which is a forward noise-propagation test rather than a fitted 'prediction.' The shot-noise-limited sensitivity is computed from CCD parameters and a simulation-derived conversion factor G=7e-13 m^2 (Appendix G); although G is calibrated only for spectrally uniform white noise and the Methods note that the uniform model 'is not suitable for actual distance measurements,' this is a modeling limitation that could affect accuracy, not a circular reduction to the measured result. The frequency-noise term L·1.2e-11 m/Hz^1/2 is estimated from the separately measured self-homodyne frequency noise, not from the distance-vs-L curve. Prior self-citations ([33], [35]) supply data-processing choices and background, but the core validation does not reduce to them. The internal 3.7 vs 3.4e-12 m/Hz^1/2 shot-noise ASD inconsistency is a correctness/consistency concern, not a circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a few measured inputs (RIN, frequency noise) and two calibration choices: the visibility V and the conversion factor G. The quantum-limit comparison is the most parameter-dependent part, since G is derived from a simulation rather than from an independent physical measurement.

free parameters (3)
  • White-noise-to-distance conversion factor G = 7e-13 m^2
    Derived from a simulation that injects uniform white noise into an ideal interference signal with visibility 0.6 (Appendix G). It converts RIN PSD to distance PSD and is central to the shot-noise-limited sensitivity claim.
  • Visibility V = 0.6
    Assumed value used in Eq. 3 and in the shot-noise calculation; no measurement procedure or uncertainty is reported.
  • Super-Gaussian window order and bandwidth = order 10, 9 THz
    Chosen from prior work (ref 35) and used in all distance processing; it affects the peak shape, the conversion factor G, and the achieved precision.
assumptions (4)
  • domain assumption Intensity noise and frequency noise are independent and their variances add in quadrature.
    Invoked in Results and Methods to separate noise contributions; cross terms and correlations are neglected in Eq. 3.
  • domain assumption The frequency noise of the EO comb is dominated by the seed DFB laser and is captured by self-homodyne measurement.
    Stated in Methods: 'The frequency noise of our EO comb is dominated by the distributed feedback laser used as the seed laser'; Appendix H measures the DFB laser, not the full comb after nonlinear broadening.
  • domain assumption Shot noise is identical for all CCD pixels and sets the quantum-limited RIN floor.
    Methods 'Shot-noise calculation' assumes equal pixel voltage and derives shot noise from total electron count; pixel-to-pixel variation or readout noise would raise the real floor.
  • ad hoc to paper The simulation with uniform white noise yields a constant G that applies to the real, non-uniform RIN spectrum.
    Appendix G simulates uniform white noise to obtain G = 7e-13 m^2; the Methods note that the actual intensity noise differs per mode, yet G is still used for the quantum-limit estimate.

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Cite this review

Pith. "Pith review of Approaching the quantum-limited precision in frequency-comb-based spectral interferometry for length measurements." pith.science (2026). https://pith.science/paper/3HWZ5CSF

@misc{pith2026250110044,
  author       = {Pith},
  title        = {Pith review of: Approaching the quantum-limited precision in frequency-comb-based spectral interferometry for length measurements},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3HWZ5CSF}},
  note         = {Machine review of arXiv:2501.10044}
}
read the original abstract

Over the last two decades, frequency combs have brought breakthroughs in length metrology with traceability to length standards. In particular, frequency-comb-based spectral interferometry is regarded as a promising technology for next-generation length standards. However, to achieve this, the nanometer-level precision inherent in laser interferometer is required. Here, we report distance measurements by a frequency-comb-based spectral interferometry with sub-nm precision close to a standard quantum limit. The measurement precision was confirmed as 0.67 nm at an averaging time of 25 us. The measurement sensitivity was found to be 4.5 10-12m/Hz1/2, close to the quantum-limit. As a practical example of observing precise physical phenomena, we demonstrated measurements of acoustic-wave-induced vibration and laser eavesdropping. Our study will be an important step toward the practical realization of upcoming length standards.

Figures

Figures reproduced from arXiv: 2501.10044 by the authors.

Figure 2
Figure 2. FIG. 2. Experimental demonstration of EO comb [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. M [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗

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    Appendix F: Effect of electrical power line noise Figure S7 explains the electrical power line noise. Peaks were observed in the PSD of the length measurement around 100 Hz to 400 Hz and near 7.5 kHz. To investigate the cause of these peaks, the output of the power supply was ...

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    By injecting random noise (Fig

    Appendix G: Relationship between the white -noise-limited PSD of the RIN and the PSD of the distance Figure S8 presents the results of a simulation conducted to examine the impact on distance - measurement results when there is only white noise with an amplitude identical to t...

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    Appendix H: Frequency noise measurement by self-homodyne detection Figure S9 shows the optical layout used during the self-homodyne measurements of the laser frequency noise (49). During the self-homodyne measurements, the output voltage (V PD) of the balanced photodetector (B...

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    Table S1

    Appendix I: Measure ment performance comparison with the -state-of-the-art absolute distance-measurement methods Table S1 and S2 present a performance comparison with state -of-the-art absolute distance - measurement methods and earlier spectral interferometry methods, respect...

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    Fiber-comb-based dual- comb interferometry 100.021 MHz & 100.016 MHz 1.5 m 40 nm∙τ-1/2 (Peak detection) 1 nm∙τ-1/2 (Interferometric method) 3 nm @ τavg=0.5 s 5 kHz [17] Frequency-comb referenced multi- wavelength interferometry (MWI) 100 MHz 3.8 m 2 nm∙τ-1/2 0.57 nm @ τavg=100...

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    Time-programmable frequency comb ranging 200 MHz 750 mm 200 pm∙τ-1/2 1 nm @ τavg=0.2 s 8.3 kHz [23] Frequency-comb-based electro-optic sampling timing detection 250 MHz 300 mm 50 pm∙τ-1/2 1 nm @ τavg=0.1 s 1 MHz

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    Microcomb dual-comb 95.7 GHz & 95.8 GHz 1.6 mm 29 pm∙τ-1/2 12 nm @ τavg=13 μs 96.4 MHz [46] Amplitude-modulation continuous wavelength (AMCW) 15 GHz 10 mm 22 nm∙τ-1/2 43 nm @ τavg=0.4 s 488 Hz

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    Summary Comparison between Spectral Interferometry and EO Comb Spectral Interferometry Ref

    Integrated comb ranging (dual-comb) 49.7 GHz & 50.2 GHz 3 mm 100 pm∙τ-1/2 23 nm @ τavg=101 μs 495 MHz This work EO comb spectral interferometry 18 GHz 4.2 mm 3.2 pm∙τ-1/2 0.33 nm @ τavg=250 μs 40 kHz Table S2. Summary Comparison between Spectral Interferometry and EO Comb Spec...

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    Solid-state frequency- comb-based SDI 1 GHz 150 mm N/A N/A N/A 35

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    Fiber-frequency-comb- based SDI 250 MHz 600 mm N/A N/A 1 Hz

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    EO comb SDI (our previous work) 17.5 GHz 4.3 mm 10 nm∙τ-1/2 50 nm @ τavg=67 ms 3 kHz

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Reviewed August 10, 2026 · model on record in the stance chip above.