{"id":"c37c0050-b0de-4e4f-bdd6-a2403e174e7d","arxiv_id":"2506.18083","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Stray light noise in Einstein Telescope arms is predicted to stay below the safety margin in ideal conditions, but beam offsets above 4 to 7 cm, tilts above 8 microradians, or strong point absorbers could breach it.","lead":"This paper updates the stray light noise model for the Einstein Telescope's main arms, adding baffles, serrated edges and numerical diffraction to the simulation. It finds the noise stays below the safety margin in nominal conditions, but beam offsets above 4 cm, tilts above 8 microradians, or strong mirror point absorbers could exceed it.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Baffle-to-ground transfer function is the load-bearing unknown: the nominal margin is only about a factor 10 in displacement, so any resonance above unity in the 0.1-10 Hz band can erase it.","rationale":"The reader's weakest assumption identifies exactly the same load-bearing concern: the unit mechanical transfer between ground and baffle. I considered alternative concerns, such as the lack of shipped simulation code or the absence of uncertainty estimates on the quoted thresholds. Those affect reproducibility and precision but do not threaten the central argument as directly. The physics of Eqs. (2) and (5) is standard, the use of a 90% confidence envelope for ground motion is conservative, and the thresholds are explicitly defined relative to a 1/10 sensitivity safety margin. The vulnerability is quantitative: the nominal safety margin is only about two orders of magnitude in strain, or a factor of order 10 in baffle displacement after upconversion, so an unmodeled mechanical amplification in the 0.1-10 Hz band can eliminate the margin and change all tolerance claims. This is not an internal inconsistency or an authorial failure; it is an acknowledged external unknown that must be resolved before the central claim can be considered robust. The appropriate final verdict is therefore CONDITIONAL, matching the reader's verdict, so no change is needed.","tokens_in":13275,"tokens_out":4689,"duration_ms":56582,"concrete_test":"Build a finite-element model of a representative vacuum-tube section with the proposed baffle mount and support geometry and compute the transfer function H(f) from ground motion to baffle motion over 0.1-10 Hz, using measured soil coupling at Sos Enattos and Euregio Rhein-Maas. If max|H(f)| in this band is below about 3, the nominal conclusion and the Sec. 4 thresholds survive. If any resonance gives |H(f)| > 10, the noise curves in Figs. 3-4 and all quoted thresholds must be rescaled by |H|^2, and the central claim is not yet established. A field measurement with accelerometers on a prototype baffle and tube section would be the decisive experimental version of the same check.","verdict_should_be":"UNCHANGED","load_bearing_attack":"In Sec. 2.4 the authors set the baffle displacement X(f) equal to the ground-motion envelope, i.e., a mechanical transfer function H(f)=1 at all frequencies. Both noise terms, Eq. (2) for diffraction and Eq. (5) for backscatter, are linear in X(f), so the noise PSD scales as |H(f)|^2. The paper states that at 2-5 Hz the nominal noise is 'at least two orders of magnitude below' the ET sensitivity; with the adopted 1/10 safety margin, that leaves only a factor of about 10 in displacement amplitude before the safety margin is reached. Baffles mounted on the vacuum tube or its supports can plausibly resonate or amplify ground motion in exactly the 0.1-10 Hz band that dominates after phase-wrapping upconversion. Because the tube, supports, and baffle mounting are not yet mature designs, this unit transfer function is not backed by any mechanical model. The paper explicitly acknowledges this in Sec. 2.4, noting that a realistic description requires designs that are 'currently partially unknown.' The nominal 'not limiting' conclusion and the quantitative thresholds in Sec. 4 (dr > 4 cm or 7 cm, dtheta >= 8e-6 rad, P_abs > 100 mW) all inherit this unknown frequency-dependent factor.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13570,"tokens_out":3911,"duration_ms":49861,"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":[{"comment":"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.","section":"Sec. 2.4"},{"comment":"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.","section":"Sec. 4 and Sec. 5"},{"comment":"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.","section":"Sec. 2.2 and Sec. 3"}],"minor_comments":[{"comment":"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.","section":"Abstract and Sec. 1"},{"comment":"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.","section":"Figures 3 and 4"},{"comment":"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.","section":"Sec. 2.3, Eq. (6)"},{"comment":"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.'","section":"Sec. 2.4 and Fig. 2"},{"comment":"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.","section":"Sec. 4.3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is well within the scope of physics.ins-det and is likely to be of significant interest to the ET collaboration. The main technical weakness is the unverified assumption of a unit mechanical transfer function between the ground and the baffles, which the authors themselves acknowledge. I believe the paper can be made suitable for publication by adding a sensitivity study of the transfer function and by reporting uncertainties on the derived thresholds. The numerical diffraction validation and a convergence check would also substantially strengthen the credibility of the quantitative results. I would not reject the paper; the qualitative conclusion appears robust, but the quantitative operational constraints need to be clearly presented as conditional on the current assumptions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this paper is a genuine step forward for ET stray-light modeling, not a repackaging. The authors put baffles explicitly in the SIS simulation, including serrated edges, and compute diffraction noise numerically instead of using the old analytic approximations. They also give first noise estimates for the L-shaped 15 km geometry and scan beam offsets, tilts, and point absorbers to produce concrete alignment and cleanliness tolerances. That is real content, and the nominal-condition conclusion — stray light well below ET sensitivity with the proposed baffles — is credible and robust to the modeling choices they actually vary.\n\nThe soft spots are real but localized. The stress-test concern is on target: Sec. 2.4 assumes baffles move exactly with the ground, a transfer function of one at all frequencies, for designs that are explicitly \"partially unknown.\" The noise is linear in baffle displacement, and the quoted margins over the 1/10 safety margin are only about a factor of 10 in the 2–5 Hz band. A resonance in the baffle supports or vacuum tube could plausibly wipe that out, which would shift the 4 cm/7 cm offsets and 8 µrad tilt limits. The paper flags this itself, so it is not hidden, but it is load-bearing for the quantitative thresholds, not a minor caveat.\n\nAlso missing: no uncertainty propagation on the input BRDF, mirror maps, or seismic envelope, so the thresholds have no error bars. The numerical diffraction pipeline is not validated against the analytic cases or an independent code, and the simulation code and data are not shipped. For a paper whose main currency is quantitative engineering limits, that hurts reproducibility. None of this undermines the central qualitative message — that the baffle layout is not limiting under ideal conditions — but it does mean the tolerances should be read as order-of-magnitude rather than precise.\n\nThe authors are honest about scope: cryotrap and vacuum tower contributions are explicitly excluded. Citation practice looks fine; self-citations are to their own prior studies, which is appropriate here.\n\nThis paper deserves a serious referee. I would send it out, requesting code/data release or a validation appendix, plus a sensitivity study on the mechanical transfer function. It is useful for anyone designing ET baffles or writing noise budgets, and I would cite it in that context.","headline":"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.","tokens_in":14097,"tokens_out":1337,"would_cite":true,"duration_ms":17638,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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 $8\\times10^{-6}$…","keywords":["Einstein Telescope","stray light","scattered light noise","baffles","diffraction noise","backscatter noise","beam alignment tolerances","gravitational wave detector"],"falsifier":"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.","tokens_in":13114,"feed_emoji":"🔭","tokens_out":12326,"duration_ms":106852,"temperature":0.7,"pith_summary":"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.","feed_headline":"Stray light won't block Einstein Telescope—if alignment holds","feed_subtitle":"Noise stays below safety margin if offsets are under 4 cm, tilts under 8 microradians, absorbers under 100 mW.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Provides the baffle apertures, layout, and previous scattered-light estimate that this work supersedes and extends.","marker":"[28]"},{"why":"The FFT-based Stationary Interferometer Simulations (SIS) code used for all field propagation, baffle clipping, and numerical diffraction calculation.","marker":"[29]"},{"why":"The analytical diffraction-noise relations that the numerical calculation replaces; defines the original formalism.","marker":"[19]"},{"why":"Source of the backscatter-noise formalism adopted for baffle and mirror scattering.","marker":"[15]"},{"why":"Supplies the reciprocity relation connecting light scattered into and out of the main beam, used in the diffraction-noise derivation.","marker":"[20]"},{"why":"Adds the radiation-pressure term to the diffraction-noise expression, giving the frequency-domain form used here.","marker":"[30]"},{"why":"Supplies the cavity parameters (mirror masses, radii, reflectivities, round-trip losses) for both ET configurations.","marker":"[45]"},{"why":"Defines the Einstein Telescope design, sensitivity curves, and arm configurations used as the comparison baseline.","marker":"[22, 23]"},{"why":"Sets the range of point-absorber powers (up to 500 mW) considered in the mirror-defect study.","marker":"[46–48]"}],"fun_headline_variants":["ET stray light noise tamed—if alignment holds","Stray light noise in ET: safe under ideal conditions","Stray light won't limit ET—unless alignment slips","Stray light noise in ET is subdominant—if alignment holds","ET stray light noise: alignment and cleanliness are key"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["ET stray light noise tamed—if alignment holds","Stray light noise in ET: safe under ideal conditions","Stray light won't limit ET—unless alignment slips","Stray light noise in ET is subdominant—if alignment holds","ET stray light noise: alignment and cleanliness are key"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000729,"raw_usage":{"total_tokens":3318,"prompt_tokens":1056,"completion_tokens":2262,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":672,"completion_tokens_details":{"reasoning_tokens":2180}},"tokens_in":672,"tokens_out":2262,"duration_ms":16587,"temperature":1.0,"reasoning_tokens":2180,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T23:22:51.247677+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Study of scattered light in the main arms of the Einstein Telescope gravitational wave detector","cited_arxiv_id":"2307.14104","evidence_quote":"Provides the baffle apertures, layout, and previous scattered-light estimate that this work supersedes and extends."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The FFT-based Stationary Interferometer Simulations (SIS) code used for all field propagation, baffle clipping, and numerical diffraction calculation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"The analytical diffraction-noise relations that the numerical calculation replaces; defines the original formalism."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Source of the backscatter-noise formalism adopted for baffle and mirror scattering."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the reciprocity relation connecting light scattered into and out of the main beam, used in the diffraction-noise derivation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Adds the radiation-pressure term to the diffraction-noise expression, giving the frequency-domain form used here."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the cavity parameters (mirror masses, radii, reflectivities, round-trip losses) for both ET configurations."}],"review_version":1}