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New modeling of the stray light noise in the main arms of the Einstein Telescope

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper simulates stray-light noise in the Einstein Telescope main arms with explicitly modeled serrated baffles, and finds it stays safely below sensitivity only when beam offsets stay under 4–7 cm, tilts under about $8\times10^{-6}$…

desk verdict A solid, quantitative update to ET stray-light noise modeling that deserves serious refereeing, but the quoted tolerances hinge on a baffle-to-ground transfer function taken to be unity without a mechanical model. read the letter →

arxiv 2506.18083 v1 pith:EG2ZE7D4 submitted 2025-06-22 physics.ins-det gr-qc

M. Andrés-Carcasona , J. Grandes Umbert , D. González-Lociga , M. Martínez , Ll. M. Mir , H. Yamamoto This is my paper
classification physics.ins-detgr-qc
keywords EinsteinTelescopestraylightscatterednoisebafflesdiffractionbackscatterbeamalignmenttolerancesgravitationalwavedetector
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 presents an updated simulation of stray-light (scattered-light) noise in the main arms of the Einstein Telescope, the planned underground gravitational-wave observatory, and asks whether the proposed baffle system is sufficient. The new model explicitly includes the baffles and their serrated edges in the optical propagation, and it computes diffraction noise numerically instead of with the analytical approximations used in the previous study. Under ideal alignment, the predicted noise stays at least two orders of magnitude below the target sensitivity at 2–5 Hz, so stray light is not a limiting factor for a perfectly centered beam. The paper then derives operational tolerances: transverse offsets above about 4 cm (ET-HF) or 7 cm (ET-LF), tilts above about $8\times10^{-6}$ rad, or point absorbers absorbing more than about 100 mW within 0.1 m of the mirror center would push the noise above the one-tenth safety margin at 2–6 Hz. The bottom line is that the baffle design works, but only if the beam is kept well aligned and the mirrors are kept clean.

What carries the argument

The carrying mechanism is the FFT-based Stationary Interferometer Simulations (SIS) code, now able to include baffles explicitly in the cavity propagation. For each baffle along the arm, the field from the input test mass is propagated to the baffle plane, clipped by the serrated inner aperture, and propagated to the end test mass, where it recombines with the main beam; this replaces the earlier solid-angle shielding approximation and lets diffraction at each edge feed power to downstream baffles. Two noise channels are assembled from these fields: diffraction noise, which in the frequency domain is $\tilde h_{\mathrm{df}}(f) = \sqrt{\lambda^2 + (8\Gamma P_{\mathrm{circ}}/cM\pi f^2)^2}\, X(f)/(\pi L)\, C$, with $C$ the sum over baffles of the overlap of the propagated fields integrated over each baffle surface; and backscatter noise, $\tilde h^2_{\mathrm{bs}}(f) = (1/L^2)[\lambda^2 + (8\Gamma P_{\mathrm{circ}}/cM\pi f^2)^2]\,(dP/d\Omega)_{\mathrm{bs}}\, X^2(f) K$, with $K = \sum_i z_i^{-2}(dP_i/d\Omega_{\mathrm{ms}})^2\,\delta\Omega_i^{\mathrm{ms}}$ encoding how much mirror-scattered light each baffle intercepts and sends back. The ground-motion input is an envelope of the 90% confidence seismic spectra measured at the two candidate sites, and the baffle displacement $X(f)$ is taken equal to the ground displacement at all frequencies (unit mechanical transfer), then upconverted into the 1–50 Hz band by phase wrapping. The quoted tolerances come from scanning offset, tilt, and absorber power and tracking $\min_f[\mathrm{SM}(f)/h(f)]$, the smallest distance between the one-tenth sensitivity safety margin and the predicted noise.

What would settle it

Measure the mechanical transfer function from ground motion to the baffle edge in a representative 50 m vacuum-tube section over 0.1–10 Hz; if the transfer magnitude exceeds unity enough to lift the predicted diffraction or backscatter noise above the 1/10 sensitivity margin at 2–6 Hz, the central conclusion fails. A complementary check would be a laboratory measurement of the serrated-edge diffraction pattern to validate the SIS clipping model, since diffraction is the dominant noise channel.

Watch

Extended reading notes

Core claim

The central claim is that the proposed baffle configuration keeps scattered-light noise subdominant in the Einstein Telescope main arms under nominal, ideal conditions, for both the triangular 10 km and L-shaped 15 km designs, and for both the high-frequency (ET-HF) and low-frequency (ET-LF) configurations. Using the FFT-based Stationary Interferometer Simulations (SIS) code, the field is now propagated through the actual baffle sequence, clipped at serrated apertures, and diffraction noise is computed numerically via the overlap integral $C = \sum_i \int E_{\mathrm{ITM}\to B_i} E_{B_i\to \mathrm{ETM}}\,dS$ over each baffle surface. Relative to the previous study, the predicted noise rises about 50% for ET-HF and falls about 30% for ET-LF, reflecting the corrected diffraction contribution, and in all nominal cases remains more than two orders of magnitude below the design sensitivity in the band where it is closest (2–5 Hz). The same machinery is then used to map what breaks this conclusion: radial beam offsets of $\Delta r \gtrsim 4$ cm (ET-HF) or $\gtrsim 7$ cm (ET-LF), tilts $\Delta\theta \gtrsim 8\times10^{-6}$ rad, or a single point absorber with $P_{\mathrm{abs}} > 100$ mW located at $r < 0.1$ m on the mirror all bring the noise up to the one-tenth safety margin at low frequencies. The paper's stated conclusion is that stray light does not limit ET in the ideal cavity, but beam alignment and mirror cleanliness are tight operational constraints.

Load-bearing premise

The calculation assumes the baffles move exactly as the ground at every frequency (unit mechanical transfer factor), so any real amplification or filtering by the baffle supports in the 0.1–10 Hz band would shift every quoted noise curve and every tolerance.

Editorial extensions

If this is right

  • In the ideal, perfectly aligned cavity, the proposed baffle layout keeps scattered-light noise at least two orders of magnitude below the ET sensitivity at 2–5 Hz, for both the triangular 10 km and L-shaped 15 km layouts and for both ET-HF and ET-LF.
  • The noise budget is dominated by diffraction at baffle edges, with backscatter roughly a factor 10 (ET-HF) or 4 (ET-LF) smaller, so edge diffraction is the channel to control first.
  • The L-shaped 15 km arms carry about 100 more baffles per arm, lifting the noise; increasing the asymptotic baffle separation (e.g., from 50 m) would reduce both diffraction and backscatter noise, provided the vacuum pumping structures remain hidden from the mirrors.
  • Beam offsets above 4 cm (ET-HF) or 7 cm (ET-LF) already meet the one-tenth safety margin near 5 Hz (ET-HF) or 3 Hz (ET-LF), so these are hard alignment tolerances for operation.
  • Tilts at or above $8\times10^{-6}$ rad, or point absorbers with $P_{\mathrm{abs}} > 100$ mW inside $r < 0.1$ m, would compromise sensitivity at 2–6 Hz, meaning mirror cleanliness and alignment control are as important as baffle design.

Reading between the lines

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

  • Because every noise curve is linear in the baffle displacement spectrum, the quoted tolerances scale inversely with the actual mechanical transfer of the baffle supports: a factor-two amplification of ground motion at 1–5 Hz would approximately halve the allowed offset and tilt before violating the safety margin.
  • The study explicitly excludes stray light from the cryotrap regions and vacuum towers near the main mirrors; if those contributions are comparable to the arm noise, the total stray-light budget could be tighter than the paper's nominal conclusion.
  • The same simulation pipeline could be used to test whether widening the baffle aperture or altering the serration profile relaxes the alignment tolerances, which is the redesign path the authors themselves suggest.
  • The seismic envelope combines 90% confidence spectra from two candidate sites; if the final site's low-frequency ground motion is higher, the safety margin shrinks proportionally, so the 4–7 cm offset tolerances and 8 microradian tilt tolerance are tied to the site assumption.
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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 presents updated simulations of stray-light noise in the main arms of the Einstein Telescope, for both the triangular 10 km and L-shaped 15 km configurations, using the FFT-based code SIS. The authors explicitly include baffles with serrated edges, compute diffraction noise numerically rather than with the earlier analytic formulas, and evaluate backscatter noise using simulated field distributions. Under nominal, perfectly centered beam conditions they find that the scattered-light noise is more than two orders of magnitude below the ET sensitivity in the 2–5 Hz band, and therefore does not limit the design. For the triangular configuration they also study non-ideal conditions: transverse beam offsets, beam tilts, and point absorbers on the mirrors, and derive operational constraints (offsets above about 4 cm for ET-HF and 7 cm for ET-LF, tilts above about 8e-6 rad, and point absorbers with more than 100 mW absorbed power within 0.1 m of the mirror center would compromise the sensitivity at 2–6 Hz). The paper states that the baffle motion is assumed to follow the ground motion with a transfer function equal to one, and that a more realistic mechanical model is deferred to future design work.

Significance. If the results are correct, the paper provides the most detailed stray-light noise estimate for ET to date and, crucially, translates a simulated noise budget into design and operational tolerances for beam alignment and mirror cleanliness. The explicit simulation of baffles, serrations, and numerical diffraction is a clear step beyond the previous analytic treatment, and the use of a measured ground-motion envelope from two candidate sites adds realism. The central qualitative conclusion — that stray light is not limiting in the ideal cavity — has a comfortable margin. However, the quantitative thresholds in Sections 4 and 5 are load-bearing for the design and are derived under assumptions that the authors themselves acknowledge to be uncertain, in particular the baffle-to-ground transfer function. The paper would benefit from a sensitivity analysis and from a validation of the numerical diffraction calculation.

major comments (3)
  1. [Sec. 2.4] The assumption that the baffle motion exactly follows the ground motion, i.e., a mechanical transfer function H(f)=1 at all frequencies, is load-bearing for all noise estimates because both Eq. (2) and Eq. (5) are proportional to |X(f)|^2 and hence to |H(f)|^2. In Sec. 3 the nominal margin is quoted as 'at least two orders of magnitude' below the sensitivity in the 2–5 Hz band; combined with the 1/10 safety margin used in Sec. 4, this leaves only about a factor of 10 in displacement amplitude before the safety margin is touched. Any resonance or amplification in the baffle suspension or vacuum-tube structure in the 0.1–10 Hz band could therefore erase the safety margin and shift all the thresholds quoted in Sec. 4. The paper explicitly notes that a realistic description 'requires a mature implementation of the designs' and that these are 'currently partially unknown' — this is an honest statement, but it makes the central quantitative claims conditional on an unverified assumption. I request a parametric study that varies a low-frequency amplification factor (or a simple single-resonance model) and shows how the nominal margin and the thresholds in Sec. 4 change, or, at minimum, an explicit statement that all quantitative thresholds assume H(f)=1 and could be violated by modest mechanical amplification.
  2. [Sec. 4 and Sec. 5] The quoted operational limits (dr > 4 cm for ET-HF and 7 cm for ET-LF, dtheta >= 8e-6 rad, P_abs > 100 mW within r < 0.1 m) are presented as precise values, but the paper provides no error bars or propagation of input uncertainties. The input parameters — baffle BRDF, mirror roughness maps, the seismic envelope, and the cavity parameters in Tables 1 and 2 — all carry uncertainties, some of which are not quantified. In addition, the thresholds are defined by the min_f(SM(f)/h(f)) crossing of an arbitrary 1/10 safety margin; changing the safety margin from 1/10 to, say, 1/20 or 1/5 would shift the thresholds. The K and C factors in Eqs. (6) and (3) are simulation outputs whose statistical and systematic uncertainties are not reported. I recommend adding a sensitivity analysis or, at least, a discussion of how the quoted thresholds would change under reasonable variations of the dominant inputs (e.g., a factor of two in baffle BRDF or in the seismic envelope). Without this, the thresholds are likely to be over-interpreted by the ET design team.
  3. [Sec. 2.2 and Sec. 3] The new numerical diffraction calculation is a central improvement claimed in the paper, but it is not validated in the manuscript. The authors state that SIS 'does not use any of the analytical relations' and quote results that differ from the previous analytic calculation of Ref. [28] by about +50% (ET-HF) and -30% (ET-LF), yet no comparison is shown against Eq. (1) in a simplified test geometry, and no convergence test or resolution check for the FFT grid is described. Since the C factor in Eq. (3) enters the diffraction noise directly, and since the paper argues that the new numerical treatment is more accurate, the reader cannot tell whether the change in the predicted noise is due to the improved physics (baffle clipping, serrations) or to numerical artifacts. I recommend adding a validation subsection that compares the SIS result with the analytic formula for a simple case (e.g., a single baffle without serrations) and demonstrates convergence with grid size and number of propagated modes.
minor comments (5)
  1. [Abstract and Sec. 1] The abstract and introduction use 'supersede previous studies' without specifying which previous results are changed and by how much; this information appears only later in Sec. 3. A sentence in the introduction summarizing the magnitude of the changes (e.g., +50% / -30%) would help the reader.
  2. [Figures 3 and 4] The legend entries 'Backscattering Ba0es' and 'Di,raction' contain typographical artifacts. The same issue appears in the captions of Figures 5–8 where '7rad' and 'µrad' are inconsistently formatted. These should be corrected before publication.
  3. [Sec. 2.3, Eq. (6)] The definition of K in Eq. (6) uses dP_i/dOmega_ms, which is estimated from the simulation via Eq. (7). This is a reasonable approach, but the finite resolution of the grid and the use of the BRDF tail are not described with enough detail for the reader to reproduce the calculation. A reference to the relevant SIS documentation (Ref. [29]) is good, but the paper could mention the specific angular cutoff where the analytical BRDF tail takes over.
  4. [Sec. 2.4 and Fig. 2] The seismic envelope is described as the 90% confidence level envelope of the two site spectra. It would be helpful to state whether the envelope is the pointwise maximum of the two spectra or the upper bound of the combined set, and to indicate how the 90% confidence is computed (e.g., per frequency bin over time). This is a minor clarity issue but affects the interpretation of 'conservative.'
  5. [Sec. 4.3] The point absorber study assumes a single absorber on the ETM only and uses the same radiative-pressure coupling as for the distributed scattering. The justification for this extension is not explicitly discussed, and the effect of multiple absorbers or absorber location relative to the beam waist is not considered. A brief comment on why the single-absorber scenario captures the essential physics would be useful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the stray-light noise curves are computed from first-principles FFT field propagation with external design and seismic inputs, not from the target sensitivity curves.

full rationale

The paper's derivation chain is self-contained and benchmarked, not circular. The noise estimates in Eqs. (2) and (5) are computed from simulated optical fields (C and K factors) using standard diffraction and backscatter formalisms, with input parameters taken from ET design documents and prior external studies (Tables 1 and 2). The ground-motion input is an envelope of measured seismic data from the two candidate sites, and the mechanical transfer factor of unity is an openly stated assumption, explicitly acknowledged as provisional pending mature designs (Sec. 2.4); this is a modeling limitation, not a circular step, because no target noise level is used to set that assumption. The comparison against the ET sensitivity curve and the 1/10 safety margin is a benchmark, and the offset, tilt, and absorber thresholds in Sec. 4 are derived from the same first-principles simulation, not fitted to the sensitivity curve. The self-citation of Ref. [28] provides the baffle apertures and layout as a design input from prior published work by overlapping authors, but this is not load-bearing in the sense of forbidding alternatives or supplying a uniqueness theorem; the new noise calculations explicitly supersede and improve on that prior study rather than assuming its conclusions. No fitted parameter is renamed as a prediction, and no equation reduces to its own input by construction. Therefore the circularity score is 0.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The noise estimates rest on several domain assumptions inherited from LIGO/Virgo scattered-light theory and on explicit simplifications such as baffle motion equal to ground motion, a fixed baffle BRDF, and Virgo O5 mirror maps. None of these are fitted to the target result, so the processing is not circular, but they set the absolute calibration of the noise curves and therefore the tolerance thresholds.

free parameters (3)
  • Baffle BRDF (dP/dOmega_bs) = 1e-4 sr^-1
    Used in Eq. (5) for all baffles; backscatter noise scales linearly with this value, and no ET-specific baffle BRDF measurement is provided.
  • Mirror surface roughness maps = Virgo O5 mirror maps
    Input for scattering at the mirrors; ET mirrors may differ, and this directly affects the K factor and the backscatter estimate.
  • Asymptotic baffle separation and aperture layout = 50 m separation; apertures inherited from Ref. [28]
    Central to clipping and diffraction noise; the paper states the fixed separation but refers to Ref. [28] for the full geometry, so the exact layout is not self-contained.
assumptions (7)
  • ad hoc to paper Baffle displacement equals ground displacement with transfer factor one at all frequencies.
    Sec. 2.4; no mechanical model for the tube and baffle supports is given, so all noise estimates scale with the assumed baffle motion.
  • domain assumption The reciprocity relation connects light scattering into and out of the main beam.
    Sec. 2.2 invokes Appendix B of Ref. [20] for the reciprocity relation that underlies the backscatter and diffraction formulas.
  • domain assumption The radiation-pressure coupling formula, Eq. (2), from Refs. [28,30] applies to the ET cavities.
    Sec. 2.2; the frequency-domain diffraction noise expression depends on this prior result without re-derivation.
  • domain assumption Baffle surfaces scatter with BRDF 10^-4 sr^-1.
    Used in Eq. (5) and Tables 1-2; no measurement for the proposed ET baffle coating is presented.
  • domain assumption Virgo O5 mirror maps, supplemented by a BRDF tail model, describe ET mirror scattering.
    Sec. 2.3; the scattering properties of ET mirrors are not measured, and the simulation depends on these imported maps.
  • domain assumption The seismic envelope of 90% confidence measured spectra is a conservative worst-case input.
    Sec. 2.4; results are quoted against this envelope, which bounds but does not replace site-specific or mechanical-transfer information.
  • domain assumption The SIS simulation code correctly implements FFT propagation, clipping, and serrated baffle diffraction.
    The entire numerical diffraction calculation rests on this code, but no validation against the analytic expression or independent implementation is shown.

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Pith. "Pith review of New modeling of the stray light noise in the main arms of the Einstein Telescope." pith.science (2026). https://pith.science/paper/EG2ZE7D4

@misc{pith2026250618083,
  author       = {Pith},
  title        = {Pith review of: New modeling of the stray light noise in the main arms of the Einstein Telescope},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EG2ZE7D4}},
  note         = {Machine review of arXiv:2506.18083}
}
read the original abstract

Stray light represents a significant noise source for gravitational wave detectors, requiring an accurate modeling and mitigation to preserve the experiment's sensitivity. In this article, we present an updated and improved analysis of the stray-light induced noise in the Einstein Telescope main arm. The results presented here supersede previous studies taking into account a number of improvements, including baffle clipping effects, new numerical calculations for computing diffraction contributions and the influence of baffle edge serrations. Results are presented for both triangular and L-shaped configurations for the experiment. Furthermore, in the case of the triangular configuration, we examine non-ideal optical cavity conditions, such as beam offsets and misalignments, and the presence of point absorbers in the mirrors, which can increase scattered light noise. This can be translated into future stringent constraints on the design and operating parameters of the interferometer, thus facilitating to achieve its sensitivity targets.

Figures

Figures reproduced from arXiv: 2506.18083 by the authors.

Figure 1
Figure 1. Comparison between the treatment in Ref. [28] (upper half) and the approach adopted in this work (lower half) to simulate the baffles and baffle edges. The red dashed line represents the ray-optics trajectory, while the solid red line illustrates how diffraction enhances the light reaching the baffle. The fact that baffles are serrated introduces further complexity. Baffles not only clip the field via the inner aper… view at source ↗
Figure 2
Figure 2. Measured underground seismic motion as a function of frequency at two ET candidate sites, Euregio Rhein-Maas (ERM) and Sardegna (SAR), and the resulting envelope (see text). of the designs for the vacuum tube, the baffles and the different mechanical supports, which are currently partially unknown. 3. Results in nominal conditions Using the formalism described in the previous section, the scattered light noise can b… view at source ↗
Figure 3
Figure 3. Stray light noise due to diffraction effects (yellow lines), backscattering effects (navy blue lines), and the total noise (cyan lines) as a function of frequency compared to the anticipated (top) ∆-shaped ET-HF and (bottom) ∆-shaped ET-LF sensitivity curves (black lines) and the corresponding 1/10 safety margin (dashed lines). HF, an offset dr ∼ 4 cm already increases the noise such that at frequencies about 5 Hz t… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Stray light noise due to diffraction effects (yellow lines), backscattering effects (navy blue lines), and the total noise (cyan lines) as a function of frequency compared to the anticipated (top) L-shaped ET-HF and (bottom) L-shaped ET-LF sensitivity curves (black lin…
Figure 5
Figure 5. Figure 5: (top) For ∆-shaped ET-HF, the circulating power in the cavity as a function of dr, Pcirc; and the evolution of backscattering, K/K0, and diffraction, C/C0, noise terms as a function of dr, where K0 and C0 denote the corresponding values for dr = 0. Results are presente…
Figure 6
Figure 6. Figure 6: (top) For ∆-shaped ET-LF, the circulating power in the cavity as a function of dr, Pcirc; and the evolution of backscattering, K/K0, and diffraction, C/C0, noise terms as a function of dr, where K0 and C0 denote the corresponding values for dr = 0. Results are presente…
Figure 7
Figure 7. Figure 7: (top) For ∆-shaped ET-HF, the circulating power in the cavity as a function of dθ, Pcirc; and the evolution of backscattering, K/K0, and diffraction, C/C0, noise terms as a function of dθ, where K0 and C0 denote the corresponding values for dθ = 0. Results are presente…
Figure 8
Figure 8. Figure 8: (top) For ∆-shaped ET-LF, the circulating power in the cavity as a function of dθ, Pcirc; and the evolution of backscattering, K/K0, and diffraction, C/C0 noise terms as a function of dθ, where K0 and C0 denote the corresponding values for dθ = 0. Results are presented…
Figure 9
Figure 9. Figure 9: (top) For ∆-shaped ET-HF, the circulating power in the cavity Pcirc as a function of the position dr and the power absorption Pabs of the point defect in the mirror; and the evolution of backscattering, K/K0, and diffraction, C/C0, noise terms as a function of dr and P…
Figure 10
Figure 10. Figure 10: (top) For ∆-shaped ET-LF, the circulating power in the cavity Pcirc as a function of the position dr and the power absorption Pabs of the point defect in the mirror; and the evolution of backscattering, K/K0, and diffraction, C/C0, noise terms as a function of dr and …

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Reviewed August 6, 2026 · model on record in the stance chip above.