{"id":"2a8451b1-aad2-4019-bf65-2ee53a70cdba","arxiv_id":"2505.19811","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"An arbitrary retarder can be described by an elliptical retarder axis and retardance, avoiding the misinterpretation caused by the fixed-order circular-plus-linear retarder model used in standard Mueller matrix decomposition.","lead":"This paper proposes describing any optical retarder, no matter how complex its layered structure, as a single elliptical retarder using three parameters, instead of assuming it is a fixed stack of circular and linear retarders. The authors demonstrate on liquid crystal samples that this avoids misleading interpretations in Mueller matrix polarimetry.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The proposed elliptical-retarder parameters are never checked against ground truth: the layered-sample experiments report measured φ, χ, ρ without comparing to values computed from the known individual retarders, so the central claim remains unvalidated.","rationale":"The reader's weakest_assumption focuses on the non-uniqueness of the ER parameters (2π range and fast/slow-axis ambiguity), which the authors themselves acknowledge in Section 4. That issue is real, but it applies equally to conventional retarder parameters (e.g., fast vs. slow axis, phase wrapping) and is a known limitation of Stokes–Mueller formalism rather than a defect specific to this proposal. The more load-bearing concern is the lack of quantitative validation of the proposed parameters against known ground truth. The paper's experiments are designed to show that conventional decomposition can mislead, and they do show large orientation errors in Section 3a. But the positive claim—that the ER parameters are an appropriate characterization—requires showing that the extracted φ, χ, ρ match the values one would compute from the known constituent retarders. The main text never provides this comparison. This is particularly striking because all the necessary reference values are present (θ, δ, and φ for each layer), so the theoretical ER parameters are easily computable. Without that check, the experimental sections only demonstrate internal consistency of the extraction, not physical validity. The non-layered droplet experiment has no independent ground truth, so it cannot validate the approach either. I do not think this concern overturns the paper's mathematical core: any product of non-depolarizing retarders is indeed equivalent to a single elliptical retarder, and the extraction equations are standard. But the empirical support for the central claim is incomplete. The verdict should remain CONDITIONAL, as the reader recommended, with the condition being that the missing ground-truth comparison must be supplied. This is why I set verdict_should_be to UNCHANGED: my concern strengthens the need for the same conditional acceptance, not a change of verdict.","tokens_in":11141,"tokens_out":6056,"duration_ms":64523,"concrete_test":"For the two-layer sample of Section 3a, compute the product M_R = M_CR(φ = 64.986°) · M_LR(θ = 0.54°, δ = 144.47°) using the measured reference parameters, then extract the equivalent elliptical-retarder axis (φ_ER, χ_ER) and retardance ρ_ER via Eqs. (4)–(7), and compare with the reported values (ρ ≈ 143.83°) and the spatial maps in Fig. 2a. Repeat for Section 3b using θ1 = −14.111°, δ1 = 142.969°, θ2 = 86.776°, δ2 = 142.277°. If the computed and measured values agree within the stated uncertainties, the ER characterization is validated; if not, the proposed metrics have not been shown to be accurate. If Supplementary Material 5 already contains such a theoretical comparison, verify that it uses the independently measured reference parameters and that agreement is within uncertainty.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the elliptical-retarder parameters (φ, χ, ρ) provide an appropriate overall characterization of an unknown retarder, avoiding misinterpretations. The experiments, however, do not quantitatively validate this claim. In Section 3a, the individual retarders are characterized with reference values (θ = 0.54°, δ = 144.47°, φ = 64.986°), and the composite is measured; yet the measured ER parameters (e.g., ρ = 143.830° ± 1.205°) are never compared to the theoretically expected values obtained by multiplying the known retarder matrices and extracting the equivalent axis and angle. The same omission occurs in Section 3b, where the two linear retarders have known θ1, δ1, θ2, δ2, but the expected φ, χ, ρ are not computed. Without this ground-truth comparison, the maps in Fig. 2 demonstrate only that ER parameters can be extracted, not that they are correct or physically plausible. The non-layered droplet (Section 3c) has no independent benchmark at all. The paper references Supplementary Material 5 for comparison of measurement results, but that comparison must include the theoretical ER parameters derived from the known layer properties to support the claim; the main text does not provide this. Thus, the central claim currently rests on plausibility rather than quantitative evidence.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper argues that the conventional MMPD retarder decomposition, which models the retarder as a circular retarder followed by a linear retarder, can lead to misinterpretations when the actual sample structure differs from this fixed order. As an alternative, the authors propose characterizing any retarder as a single elliptical retarder using three parameters: the elliptical axis orientation φ, the degree of ellipticity χ, and the elliptical retardance ρ. These are extracted from the 3×3 rotation submatrix of the retarder Mueller matrix via standard rotation-matrix formulas (Eqs. 4–7). The paper demonstrates that reversing the order of the circular and linear retarders in the conventional decomposition leaves φ and δ unchanged but shifts the linear axis orientation from θ to θ+0.5φ. Experiments on liquid-crystal samples—two layered configurations and one non-layered droplet—are used to support the claims. The paper also acknowledges in Section 4 that the ER representation is not unique due to the 2π phase wrapping and the fast/slow axis ambiguity.","tokens_in":11407,"tokens_out":9343,"duration_ms":92533,"significance":"If the proposed ER parameter set were quantitatively validated, it could provide a useful alternative to the conventional MMPD retarder decomposition for samples with unknown or non-layered structure, which is relevant in biomedical imaging and material analysis. The derivation of the order-reversal shift (θ→θ+0.5φ) is clean and supported by the measurements, and the authors are transparent about the limitations of the approach. However, the central claim—that φ, χ, and ρ provide a correct and physically plausible overall characterization—is not currently backed by a quantitative comparison with ground truth. The paper also openly states the non-uniqueness issues in Section 4, which further weaken the claim as presented. The work is within the scope of the journal and has potential, but the experimental validation needs substantial strengthening.","major_comments":[{"comment":"The reported ER parameters are never compared with the equivalent elliptical retarder computed from the known individual retarder Mueller matrices. For example, in Section 3a the reference values θ=0.54°, δ=144.47°, and φ=64.986° are given, from which the expected ρ of the product M_R=M_CR M_LR can be calculated analytically; the measured value ρ=143.830°±1.205° is reported without such a comparison. The same omission occurs in Section 3b, where the two linear retarders are individually characterized but the expected φ, χ, and ρ of their combination are not provided. Without this ground-truth comparison, the experiments demonstrate only that the ER parameters can be extracted from data, not that they correctly or meaningfully represent the sample's overall retardance. Please include the theoretical ER parameters computed from the known layer properties (in the main text or in the supplementary material) and quantify the agreement with the measured values.","section":"Section 3a, 3b, and Supplementary Material 5"},{"comment":"The non-uniqueness of the ER representation is acknowledged but not resolved. The paper notes that within a 2π range there is a second retarder with the same Mueller matrix (the slow-axis counterpart with retardance 2π-ρ), and that a 2π range is assumed. However, it does not state which representation is used for the values reported in Section 3, nor does it give a criterion for selecting one. Since the claimed advantage of the ER parameters is that they are 'physically plausible' for unknown samples, the choice between equivalent representations is a central part of the method and should be specified. Without such a rule, the parameters are not uniquely defined for the intended use case, and the reported values in Section 3 are ambiguous.","section":"Section 4"},{"comment":"There is an inconsistency between the mathematical definition and the stated range of ρ. Equation (7) defines ρ via cos⁻¹, whose principal value lies in [0, π], yet Section 4 states that a 2π range is assumed for the retardance. The manuscript should clarify whether the reported retardance values are principal values or have been unwrapped to (0, 2π), and if the latter, it should describe the unwrapping procedure. This is load-bearing because the fast/slow-axis ambiguity discussed in Section 4 is directly related to ρ vs 2π-ρ, and the reported numbers in Section 3 cannot be interpreted without knowing which convention was used.","section":"Equation (7) and Section 4"}],"minor_comments":[{"comment":"The claim that the reverse-sequence linear axis orientation (θ=-1.298°) is 'close to the reference value' (θ=0.54°) is not fully supported by the stated standard deviation (0.362°); the difference is more than five standard deviations. Please discuss this discrepancy in the context of the stated error sources.","section":"Section 3a"},{"comment":"The measured circular retardance in the composite (70.614°) differs from the reference value (64.986°) by about 5.6°, which is not addressed in the main text. A comment on this deviation would be helpful for assessing the accuracy of the conventional decomposition results.","section":"Section 3a"},{"comment":"The non-layered droplet experiment has no independent validation. While the ER maps are visually suggestive, the claim that the parameters 'effectively characterize' a non-layered sample should be supported by a quantitative benchmark or a comparison with an independent measurement, or this should be explicitly framed as a qualitative demonstration.","section":"Section 3c"},{"comment":"The matrix entries contain notation like 'cos2 2θ' and 'sin2 2θ', which should be typeset as cos²2θ and sin²2θ for clarity.","section":"Equations (2) and (3)"},{"comment":"The ranges for φ and χ are stated in the text, but it would be helpful to explicitly note the modulo-π and modulo-π/2 ambiguities, as these connect directly to the discussion in Section 4 and to the non-uniqueness of the extracted parameters.","section":"Section 2b"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of physics.optics, and the derivations are mathematically standard. The main concern is the missing ground-truth comparison for the ER parameters, which is load-bearing for the central claim. The authors' own Section 4 limitations on uniqueness further weaken the 'physically plausible' claim as it stands. The supplementary material may contain some comparisons, but they are not presented in the main text; the authors should be asked to make the quantitative validation explicit. I would support publication after a major revision that addresses these points."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper makes a real point: the standard MMPD assumption that a retarder is a circular retarder followed by a linear retarder can mislead when the actual layer order is different. The derivation that reversing the order shifts the retrieved linear axis by 0.5φ is clean, and the liquid-crystal experiments show that shift convincingly. That alone is worth having on record.\n\nThe proposed alternative—characterize any retarder as a single elliptical retarder with axis orientation φ, ellipticity χ, and retardance ρ—is mathematically standard (eigenaxis/eigenangle of the 3×3 rotation submatrix), but the paper's contribution is the explicit recommendation to use this in MMPD imaging. That is a fair and useful suggestion, and the authors are honest that the representation has non-uniqueness issues (2π range, fast/slow ambiguity) that need extra assumptions.\n\nMy main concern is that the central claim is not actually validated. The experiments show that φ, χ, ρ can be extracted from measured Mueller matrices, but they never compare those extracted values to the theoretical values computed from the known individual retarders. In Section 3a you know θ, δ for the linear retarder and φ for the circular retarder; multiplying those matrices gives a predicted equivalent retarder whose axis and retardance are computable. The paper does not report that comparison. Same in Section 3b with two linear retarders. The non-layered droplet has no independent benchmark at all. So the paper demonstrates feasibility of extraction and the inadequacy of the conventional model, but not that the ER parameters are quantitatively correct. The authors mention deviations and cite supplementary comparisons, but the main text stops at plausibility.\n\nThe uniqueness caveats in Section 4 are acknowledged but not resolved. I do not think that kills the paper—the order-ambiguity warning and the proposed parameter set are useful regardless—but it does mean the phrase \"physically plausible\" is doing more work than the data supports.\n\nOverall: a serious methodological suggestion for the MMPD community, with solid math and a real experimental demonstration of the order problem, but the key claim about the ER parameters' correctness needs quantitative ground-truth support. That is exactly what referees should ask for.\n\nVerdict: send to peer review. The paper deserves referee time; the experiments need a revision that includes theoretical ER values for the layered samples and a clearer statement of the assumptions needed for uniqueness.","headline":"Useful warning about conventional MMPD retarder decomposition and a sensible alternative parameterization, but the experiments never check the proposed elliptical-retarder parameters against known ground truth.","tokens_in":11916,"tokens_out":1745,"would_cite":false,"duration_ms":21909,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["42.25.Ja","42.25.Lc"],"model":"deepseek-v4-flash","headline":"The paper argues that conventional Mueller matrix polar decomposition (MMPD) describes a retarder as a circular retarder followed by a linear retarder, a choice that can misrepresent samples whose structure is not that fixed two-layer…","keywords":["Mueller matrix polarimetry","Mueller matrix polar decomposition","retarder characterization","elliptical retarder","liquid crystal","polarization imaging","birefringence","Poincaré sphere"],"falsifier":"Manufacture a two-layer stack with known layer properties, measure its Mueller matrix, and compare the elliptical retarder parameters recovered from Eqs. (4)-(7) with an independent determination of the stack's overall fast axis using dual-wavelength phase unwrapping. If the recovered $\\phi$, $\\chi$, $\\rho$ do not reproduce the measured Mueller matrix, or if the recovered fast axis turns out to be the slow axis for a sample with retardance in $(\\pi, 2\\pi)$, the claimed structure-agnostic characterization fails.","tokens_in":10944,"feed_emoji":"🔬","tokens_out":5660,"duration_ms":60826,"temperature":0.7,"pith_summary":"The paper argues that the standard Mueller matrix polar decomposition (MMPD) description of a retarder as a circular retarder followed by a linear retarder can misrepresent real samples whose internal structure is not that particular two-layer stack. Reversing the multiplication order leaves the two retardance values unchanged but shifts the linear axis orientation by half the circular retardance, so the recovered fiber orientation depends on an arbitrary modeling choice. To avoid this, the authors propose characterizing any retarder by a single elliptical retarder with axis orientation $\\phi$, degree of ellipticity $\\chi$, and elliptical retardance $\\rho$, computed from the retarder's fast-axis vector on the Poincaré sphere. They demonstrate the approach on layered and non-layered liquid crystal samples, including a chiral nematic droplet with spatially varying twist, and show it yields a structure-independent overall description. If accepted, this gives biomedical and materials polarimetry a way to report retarder properties without assuming a layer structure.","feed_headline":"New retarder metrics avoid false structure readings in Mueller polarimetry","feed_subtitle":"Three parameters capture any retarder's full optical effect, no layer model required.","key_machinery":"The load-bearing object is the elliptical retarder as a rotation on the Poincaré sphere: any pure retarder's Mueller matrix has a normalized fast-axis vector $S_R = (1, a_1, a_2, a_3)$ with $a_1 = \\cos 2\\phi \\cos 2\\chi$, $a_2 = \\sin 2\\phi \\cos 2\\chi$, $a_3 = \\sin 2\\chi$, and a retardance $\\rho$ given by the trace of the $3\\times 3$ submatrix. This replaces the conventional product $M_R = M_{LR} M_{CR}$ with a single rotation, so no layer ordering has to be assumed. The same formulas also expose the two ambiguities the paper acknowledges: the $2\\pi$ phase-wrap window and the choice between the fast-axis and slow-axis representation.","core_discovery":"The central claim is that for a retarder of unknown structure, the correct overall characterization is the elliptical retarder, whose rotation axis on the Poincaré sphere is the fast axis and whose rotation angle is the elliptical retardance. Concretely, the paper claims that the parameters $\\phi = 0.5\\,\\mathrm{atan2}(a_2, a_1)$, $\\chi = 0.5\\,\\sin^{-1}(a_3)$, and $\\rho = \\cos^{-1}\\big[(\\mathrm{tr}(m_R)-1)/2\\big]$ extracted from the normalized fast-axis vector $(a_1, a_2, a_3)$ describe the full optical response of any retarder, with no need to decide whether circular or linear retardation comes first. The experiments with liquid crystal retarders are offered as evidence that this parameter set captures the polarization properties of both layered stacks and non-layered twisted media, whereas the conventional parameters produce a spurious circular retarder when two linear retarders with mismatched orientations are stacked. The paper frames this as avoiding misinterpretation rather than as a new physical effect.","pith_inferences":["A natural extension is to use these vectorial metrics as a common reporting standard across polarimetry studies, so that tissue fiber-orientation maps from different groups become comparable even when their decomposition conventions differ.","The fast-axis orientation and ellipticity map should be sensitive to the local twist gradient in chiral samples, suggesting a testable method for non-contact measurement of chiral pitch with polarimetric imaging.","The paper does not test stacks with more than two layers; applying the same metric to a three-layer stack of known composition would quantify how much the single-elliptical-retarder model deviates as complexity grows.","The ambiguity discussion implies that combining ER parameters with dual-wavelength phase unwrapping would pin down both the retardance branch and the fast/slow choice, something the paper leaves as future work."],"forward_implications":["Users of MMPD can report $\\phi$, $\\chi$, and $\\rho$ as the retarder metric and avoid any dependence on whether the circular or linear element is placed first in the model.","For two-layer stacks, the axis-orientation shift of $0.5\\phi$ that occurs when the decomposition order is reversed will no longer contaminate fiber-orientation estimates.","Samples without any layered structure, such as chiral droplets with spatially varying twist, become characterizable by a compact three-parameter map instead of a forced bilayer model.","The residual ambiguities of phase wrapping and fast/slow-axis choice remain, so wavelength or absolute-phase information is still needed for a unique assignment.","Existing MMPD pipelines can adopt the new metrics immediately because they are computed from the same decomposed retarder matrix $M_R$."],"supporting_citations":[{"why":"Defines the MMPD factorization $M = M_\\Delta M_R M_D$ that the paper modifies.","marker":"[35]"},{"why":"Supplies the conventional circular-retarder-times-linear-retarder model whose fixed ordering the paper challenges.","marker":"[71]"},{"why":"Establishes extraction of retarder parameters from complex turbid media, the clinical context the new metrics must serve.","marker":"[16]"},{"why":"Analyzes linear birefringence orientation in multi-layered tissue, the misinterpretation scenario motivating the study.","marker":"[53]"},{"why":"Provides LC-based elliptical retarder design and construction used as the experimental basis for the chiral nematic samples.","marker":"[72]"},{"why":"Dual-wavelength phase unwrapping, cited as a route to resolve the $2\\pi$ retardance ambiguity that limits unique ER parameters.","marker":"[73]"}],"fun_headline_variants":["Three parameters fully describe any retarder, no layer model needed","New vectorial metrics replace sequential retarder model in Mueller analysis","Elliptical retardance parameters avoid spurious circular retarder readings","Fast-axis vector metrics characterize retarders independent of structure","Physically plausible retarder parameters end circular-linear order guesswork"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The parameter set is meaningful only if every retarder's Mueller matrix determines a unique elliptical fast axis and a unique retardance once a $2\\pi$ window and one of the two fast/slow representations are chosen; the paper notes that uniqueness requires extra prior knowledge.","fun_headline_variants_meta":{"raw":{"variants":["Three parameters fully describe any retarder, no layer model needed","New vectorial metrics replace sequential retarder model in Mueller analysis","Elliptical retardance parameters avoid spurious circular retarder readings","Fast-axis vector metrics characterize retarders independent of structure","Physically plausible retarder parameters end circular-linear order guesswork"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000193,"raw_usage":{"total_tokens":1366,"prompt_tokens":975,"completion_tokens":391,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":591,"completion_tokens_details":{"reasoning_tokens":316}},"tokens_in":591,"tokens_out":391,"duration_ms":4969,"temperature":1.0,"reasoning_tokens":316,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T14:05:21.517876+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Manufacture a two-layer stack with known layer properties, measure its Mueller matrix, and compare the elliptical retarder parameters recovered from Eqs. (4)-(7) with an independent determination of the stack's overall fast axis using dual-wavelength phase unwrapping. If the recovered $\\phi$, $\\chi$, $\\rho$ do not reproduce the measured Mueller matrix, or if the recovered fast axis turns out to be the slow axis for a sample with retardance in $(\\pi, 2\\pi)$, the claimed structure-agnostic characterization fails.","supporting_citations":[{"cited_title":"& Chipman, R","cited_arxiv_id":null,"evidence_quote":"Defines the MMPD factorization $M = M_\\Delta M_R M_D$ that the paper modifies."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the conventional circular-retarder-times-linear-retarder model whose fixed ordering the paper challenges."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes extraction of retarder parameters from complex turbid media, the clinical context the new metrics must serve."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Analyzes linear birefringence orientation in multi-layered tissue, the misinterpretation scenario motivating the study."},{"cited_title":"& Pau, S","cited_arxiv_id":null,"evidence_quote":"Provides LC-based elliptical retarder design and construction used as the experimental basis for the chiral nematic samples."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Dual-wavelength phase unwrapping, cited as a route to resolve the $2\\pi$ retardance ambiguity that limits unique ER parameters."}],"review_version":1}