{"id":"7ae2028b-aae2-4ccb-bd75-0272b815e9e3","arxiv_id":"2607.29047","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Spatial-state tomography recovers a multimode fibre's complete transmission matrix from intensity-only camera frames and enables beam shaping under coherent and emulated broadband illumination.","lead":"This paper shows a way to measure the transmission matrix of a multimode optical fibre using only brightness (intensity) camera images, without a separate reference beam. It then uses that matrix to shape light at the far end of the fibre, including for broad-wavelength sources where standard interferometric approaches struggle.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Phase-locking between pixels (Methods A, Eq. 2–3) assumes neighbouring-pixel focusing states are parallel; this is cited from prior work, not validated here, and a failure would corrupt the recovered complex TM. A direct overlap-magnitude check on the released data would settle it.","rationale":"The reader's weakest_assumption correctly identifies the phase-locking smoothness condition as load-bearing. My independent reading confirms that the central claim—recovery of the full complex TM without an external reference—rests entirely on the validity of Eq. (2)–(3) in Methods A. The paper cites prior work for the M²≥4N condition but does not supply a derivation, a numerical validation, or an experimental check on this system. The concern is sharpened by the broadband experiments: when the input is a short-coherence source, the per-pixel dominant eigenstate is itself a source-averaged quantity, so the 'neighbouring states are parallel' assumption is not at all obvious. The paper does provide substantial supporting evidence—a released code/data repository, a coherent-laser experiment with beam shaping, and singular-value analysis that is physically plausible. These give the method credibility, but they do not isolate the phase-locking step from other possible error sources. The proposed test is concrete and would settle the question using already-released data. Because the reader already set CONDITIONAL and this concern reinforces rather than overturns that verdict, I recommend UNCHANGED: the paper should remain conditional pending direct validation of the phase-locking assumption.","tokens_in":25936,"tokens_out":6493,"duration_ms":69378,"concrete_test":"Using the released dataset/code, for each emulated bandwidth (0, 10, 20, 30 nm) compute the normalized inner-product magnitude |⟨φ'_ref|φ_target⟩| for all adjacent pixel pairs within the same speckle grain before phase correction, and tabulate its distribution (median and tail). If a non-negligible fraction of pairs (e.g., >5%) have magnitude <0.9, Eq. (2) does not define a reliable phase offset and the recovered MTM is suspect; if the distribution is tightly clustered at 1, the concern is resolved. As a secondary check, compare the full 420-mode SST MTM against a short-acquisition DH MTM using complex OI with error bars.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Every recovered complex TM depends on stitching per-pixel eigenstates into a global phase using Methods A: Δϕ_ref|target = arg(⟨φ'_ref|φ_target⟩). This is exact only if the true focusing states for adjacent pixels within one speckle grain are identical up to a global phase. The paper's justification is the single sentence: \"if the pixels on the camera are at least four times smaller than ... speckle grain (M² ≥4N), the input states necessary to focus on neighbouring pixels on the camera must be in phase\", citing [5,21] rather than deriving or verifying it. If the inner products used in Eq. (2) have magnitude less than 1, the arg is a weighted average of different vectors, not a well-defined pixel phase offset, and the iterative phase-locking injects errors that propagate across the camera plane. The assumption is especially non-obvious in the broadband case, where each pixel's dominant eigenstate is the source-averaged optimal input for that pixel; spatial decoherence can destroy the parallelism even if M²≥4N. The paper never reports the distribution of |⟨φ'_ref|φ_target⟩| for adjacent pixels, nor validates the full 420-mode SST MTM against DH in a drift-free measurement; the LCS comparison in Fig. 2 is mixed on complex field overlap, and the authors switch to intensity overlap in Supplementary Note 3. This is load-bearing because both per-pixel tomography and beam-shaping demonstrations inherit whatever phase error the stitching step introduces.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an automatic self-referencing technique, spatial state tomography (SST), to measure the full complex transmission matrix (TM) of a multimode fibre from intensity-only camera frames. The method launches 2N^2−N analyser states based on Gell–Mann matrices, reconstructs a density matrix at each output pixel, and recovers the relative phase between pixels by exploiting the assumption that neighbouring pixels within one speckle grain share the same focusing input state up to a global phase. The authors demonstrate the approach on a 420-mode OM1 graded-index fibre under long-coherence (1300 nm) illumination and under emulated short-coherence/broadband sources obtained by summing monochromatic swept-source frames. They benchmark the recovered TM against off-axis digital holography and demonstrate distal beam shaping for several target fields. Data and processing code are made publicly available.","tokens_in":26300,"tokens_out":3759,"duration_ms":43376,"significance":"If the method is sound, it offers a deterministic, source-matched TM measurement that avoids external references, iterative phase retrieval, and preselected internal references, potentially extending wavefront shaping to broadband or low-coherence sources where holographic references are difficult. The paper is supported by a large experimental dataset, reproducible code (GitHub/Zenodo), and extensive supplementary material, which are strengths. The central idea of using distributed local interference as a phase reference is novel and well-motivated. However, the validity of the phase-locking step and the extent to which the broadband claim is supported by emulated measurements need careful scrutiny. The claims are plausible but not yet fully established by the evidence presented.","major_comments":[{"comment":"The phase-locking step assumes that input states required to focus on neighbouring pixels within one speckle grain are identical up to a global phase. The manuscript justifies this only by citing [5, 21] and does not provide any direct validation, such as the distribution of |⟨φ′_ref|φ_target⟩| for adjacent pixels, nor a sensitivity analysis to the speckle oversampling factor M²≥4N. If the inner products in Eq. (2) have magnitude below 1, the arg operation averages distinct vectors and propagates phase errors across the camera plane. Since every downstream beam-shaping result inherits this stitching step, the authors should validate the assumption explicitly, ideally with a drift-free full-mode comparison against DH.","section":"Methods A, Eqs. (2)–(3)"},{"comment":"The 'broadband' and 'low-coherence' demonstrations are not measurements with a true broadband source: they are emulated by summing monochromatic swept-source intensity frames (Methods D, Eq. 5). The title and abstract claim 'broadband control' and operation 'across coherent, low-coherence, and broadband regimes' without this qualification. While the emulation is physically meaningful under static conditions, the authors should clearly state that the source bandwidth is implemented in post-processing and that the method has not been demonstrated with an actual short-coherence source. Additionally, the 'source-matched optimal' claim is not benchmarked against an independent gold standard; the link to the flux matrix in [44] is only a hypothesis.","section":"Results, 'Short coherence source experimental results'; Methods D, Eq. (5)"},{"comment":"The LCS benchmark is ambiguous. In Fig. 2 the complex overlap of MTM_SST is worse than MTM_DH for most patterns; the authors attribute this to reference-arm aberrations and mechanical drift (Supplementary Note 3) and then switch to an intensity-overlap metric that favours their method. The attribution to drift is asserted rather than demonstrated. A fair comparison requires a drift-controlled or interleaved measurement of both matrices under the same time window, and a report of the complex overlap distribution. Without this, the claim that SST performs 'at the level of off-axis digital holography' is not yet supported.","section":"Fig. 2 and Supplementary Note 3"},{"comment":"The paper relies on the assertion that noise and drift 'predominantly corrupt the eigenvalues... while the eigenvectors remain robust' to justify recovering the primary eigenstate from imperfect measurements. This is load-bearing because the phase-locking step uses these eigenvectors, not the eigenvalues. No empirical or simulated evidence is given for this stability. The authors should provide a quantitative analysis, e.g., by comparing eigenvector overlap between repeated measurements or by injecting simulated drift into the raw data and showing that the recovered phase offsets remain stable.","section":"Supplementary Note 0, 'Non-ideal tomography'"}],"minor_comments":[{"comment":"The text contains several typos and placeholder remnants: 'T omographic' (Supplementary Note 0), 'F or' (Abstract), 'demostrated' (Discussion), 'untagle' and 'constitude' (Supplementary Note 1). The supplementary video link is shown as 'YouTube link' rather than an actual URL. These should be cleaned up.","section":"Global"},{"comment":"The labels in Fig. 2 refer to 'Referenceless Digital holography' while the text also uses 'MTM_DH'; please unify terminology. The intensity-overlap figure (S8) should be referenced in the main text where complex overlap results are discussed, otherwise the switch of metrics can be confusing.","section":"Fig. 2 and Supplementary Note 3"},{"comment":"The condition M²≥4N is cited from [5,21] but not derived for the SST pipeline. Since the phase-locking algorithm is central, a brief explanation or reference to the exact proof would improve the self-containedness of the paper.","section":"Methods A / Discussion"},{"comment":"The authors state that the method could be extended to spectrally resolved TM or time-gated measurements, but these are speculative. It would be helpful to mark such extensions clearly as future work, not as demonstrated capabilities.","section":"Discussion"}],"recommendation":"major_revision","confidential_remarks":"This is a potentially important contribution if the phase-locking assumption is validated. The authors have already made detailed data and code available, which is commendable. The main risks are overclaiming in the abstract/title regarding broadband operation that is only emulated, and the lack of a direct test of the phase-locking overlap. I would like the editor to ensure that the revised manuscript contains a quantitative validation of Eq. (2)–(3) before acceptance. The paper is within the scope of the journal and the experimental work is substantial."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a real and mostly convincing experimental method paper. The genuinely new bit is stitching per-pixel SST density matrices into a full N×N mode transmission matrix via a cross-pixel phase-locking algorithm, and using the result for source-matched beam shaping at several emulated bandwidths. The coherent-laser TM retrieval and the beam-shaping demonstrations are well executed; the singular-value analysis is a physically sensible check; and the code/data release is a credit to the authors.\n\nThe soft spots are real but not fatal. First, the 'broadband' headline is stronger than the evidence. The short-coherence measurements are not made with a short-coherence source; they are sums of swept-laser monochromatic frames. That is a legitimate way to emulate spectral incoherence and it does test the algorithm's response to bandwidth, but it does not demonstrate operation with an actual broadband source with its real temporal-coherence and stability properties. The claim that the retrieved MTM is the source-matched optimum for a true broadband source goes beyond what is shown.\n\nSecond, the phase-locking step is load-bearing and under-validated. The assumption that neighbouring pixels within a speckle grain have parallel focusing states is cited from prior work, but the paper does not report the distribution of the inner products that Eq. (2) relies on. A quick plot of |⟨φ'_ref|φ_target⟩| over the camera plane would settle it. The fact that beam shaping works is indirect evidence it holds, but the broadband case is where the assumption is least obvious, and that is exactly where there is no independent ground truth. The stress-test note is right: this should be reported.\n\nThird, the LCS comparison against digital holography is muddled. The complex-field overlap favours DH for most patterns; the paper switches to intensity overlap, which favours SST, and attributes the discrepancy to drift and reference-arm aberration. That may well be true, and the short-acquisition SST data in the supplement support it, but a cleaner comparison would report both metrics on a drift-controlled run and, ideally, averaged DH measurements over a comparable time window.\n\nThe building blocks are from the same group's earlier SST work, but assembling a complete TM with cross-pixel phase locking is a genuine new step, and the source-matched broadband concept is interesting even in its emulated form. The paper is honest about several limitations, including the scaling of the number of analyser states and the inability to verify the broadest-band MTM for spots beyond the swept range.\n\nI'd send this to peer review. The referee should ask for the inner-product validation, a real broadband-source test or a clear statement that the emulation is the limit of what is claimed, and a less selective metric comparison. These are addressable without changing the core method.","headline":"Sound SST-based transmission-matrix retrieval with real experiments and released code; the 'broadband' claim rests on emulated sources and the phase-locking assumption needs a direct check.","tokens_in":26793,"tokens_out":3183,"would_cite":true,"duration_ms":36050,"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":"The paper claims that the full complex transmission matrix of a multimode fibre can be recovered from camera intensity frames alone, by using every propagating mode as a distributed phase reference rather than relying on an external or pres","keywords":["transmission matrix","multimode fibre","spatial state tomography","self-referencing","broadband light","beam shaping","intensity-only measurement","phase locking"],"falsifier":"Run SST on the same fibre while deliberately coarsening the camera pixels until the speckle grain is sampled by fewer than four pixels (M²<4N); if beam-shaping overlap against the target field stays high, the in-phase condition is not load-bearing, and if it collapses, the condition is confirmed as the critical resource. A second check: on a short acquisition to avoid drift, compare the SST matrix with an off-axis holography matrix; any systematic phase error concentrated in particular mode groups would identify where the assumption fails.","tokens_in":25808,"feed_emoji":"💡","tokens_out":6653,"duration_ms":65030,"temperature":0.7,"pith_summary":"This paper claims that the full complex transmission matrix of a multimode fibre can be recovered from intensity-only camera recordings, with no external reference arm, no preselected internal reference, and no iterative phase retrieval. The method uses spatial state tomography: it launches a complete set of pairwise mode-interference patterns into the fibre, records the intensities on a camera, and at each pixel reconstructs the input modal superposition that focuses light there. Missing phases between pixels are stitched together by exploiting the fact that when the camera resolves each speckle grain with several pixels, neighbouring focusing solutions must be in phase. The authors demonstrate this on a 420-mode fibre with coherent, low-coherence, and broadband sources, and use the recovered matrix for distal beam shaping. If correct, the technique removes the main obstacle to controlling light through complex media with short-coherence or broadband sources.","feed_headline":"Camera frames alone map a fibre's full transmission matrix","feed_subtitle":"Turns every mode into its own phase reference, letting broadband sources shape light at the fibre tip.","key_machinery":"The central mechanism is spatial state tomography (SST), applied to each camera pixel in parallel. SST generalises Stokes polarimetry: the mode space of the fibre is treated as an N-dimensional Hilbert space, and a complete set of analyser states—the eigenvectors of the Gell–Mann matrices, realised experimentally as pairwise mode interferences at four phase offsets plus single-mode launches—is used to measure a high-dimensional Stokes vector at every pixel. Multiplying the measured intensities by a sparse weighting matrix K reconstructs the pixel's density matrix; its leading eigenvector is the focusing solution for that output position. The second ingredient is the phase-locking rule: when","core_discovery":"Stated in the paper's terms: the transmission matrix of a complex medium can be measured without any phase reference by turning the measurement into a high-dimensional Stokes-polarimetry problem at every output pixel. For each of the 2N²−N analyser states launched at the input, the camera records an intensity; at each pixel the stack of intensities is converted, through the Gell–Mann operator basis, into an N×N density matrix. Its dominant eigenstate is the input field that maximises power delivery to that pixel. Because the camera oversamples the speckle grain by at least four pixels, adjacent pixels' focusing solutions must share a phase, so the per-pixel phase offsets can be recovered and","pith_inferences":["The core resource is spatial oversampling of the speckle pattern, not anything specific to optical fibres; the same per-pixel tomography plus phase stitching should transfer to any linear scattering medium whose output speckle can be resolved, such as tissue or multimode waveguides.","Because the phase reference is distributed across all modes, the method's failure mode is not reference blindness but stability: the sequential 2N²−N projections assume the medium is static over the whole acquisition, so fast-moving media would need faster projection hardware or sparse recovery.","Secondary eigenstates, which the paper treats mostly as noise or residual decorrelation, may be a practical resource: they carry information about modes that decorrelate from the main solution, so a target-dependent combination of the per-eigenstate matrices could improve broadband shaping beyond the dominant-eigenstate matrix.","The paper's suggested connection to the broadband flux matrix A=∫S(λ)t†(λ)t(λ)dλ points to a quantitative definition of a 'source-matched transmission matrix' that future work could test by comparing SST against spectrally resolved holography followed by spectral weighting."],"forward_implications":["Point-scanning fibre imaging requires only the per-pixel eigenstates, so the phase-locking stage can be skipped when the goal is focusing or scanning rather than a full complex matrix.","For a broadband source, the matrix measured with that source's own bandwidth outperforms the monochromatic matrix for shaping light over that bandwidth; for full-mode targets the best matrix extends the usable bandwidth by about √2 relative to the monochromatic one.","The measurement does not need a camera array: a scanned single photodiode, a spectrometer, or a nonlinear detector could carry the same self-referencing idea into spectrally resolved or time-gated regimes.","Exploiting the known mode-group structure of graded-index fibre reduces the number of input projections from O(N²) to a sum over mode groups, making per-wavelength acquisition time practical with faster modulators."],"fun_headline_variants":["No phase reference needed: map a fibre's full transmission matrix from camera frames alone","Turns every mode into its own phase reference, enabling broadband light control","Automatic self-referencing: measure complex media's transmission matrix without any refere","Camera frames alone map the full transmission matrix, even for low-coherence sources","Self-referencing via local interference: robust matrix measurement for broadband light"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The result stands or falls on the smoothness condition—taken from earlier work rather than re-derived here—that when the camera samples each speckle grain with at least four pixels (M²≥4N), the input fields needed to focus on neighbouring camera pixels are in phase; if that fails for any mode group, or drift breaks the phase relation during the long sequential acquisition, the cross-pixel stitching and the final matrix are corrupted.","fun_headline_variants_meta":{"raw":{"variants":["No phase reference needed: map a fibre's full transmission matrix from camera frames alone","Turns every mode into its own phase reference, enabling broadband light control","Automatic self-referencing: measure complex media's transmission matrix without any reference","Camera frames alone map the full transmission matrix, even for low-coherence sources","Self-referencing via local interference: robust matrix measurement for broadband light"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000239,"raw_usage":{"total_tokens":1378,"prompt_tokens":800,"completion_tokens":578,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":544,"completion_tokens_details":{"reasoning_tokens":487}},"tokens_in":544,"tokens_out":578,"duration_ms":5787,"temperature":1.0,"reasoning_tokens":487,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T14:37:15.755779+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run SST on the same fibre while deliberately coarsening the camera pixels until the speckle grain is sampled by fewer than four pixels (M²<4N); if beam-shaping overlap against the target field stays high, the in-phase condition is not load-bearing, and if it collapses, the condition is confirmed as the critical resource. A second check: on a short acquisition to avoid drift, compare the SST matrix with an off-axis holography matrix; any systematic phase error concentrated in particular mode groups would identify where the assumption fails.","supporting_citations":[],"review_version":1}