Transforming nondepolarizing Mueller matrices into Jones matrices

Ertan Kuntman; Mehmet Ali Kuntman

arxiv: 1906.11198 · v1 · pith:FBG7OYODnew · submitted 2019-06-23 · ⚛️ physics.optics · quant-ph

Transforming nondepolarizing Mueller matrices into Jones matrices

Mehmet Ali Kuntman , Ertan Kuntman This is my paper

Pith reviewed 2026-05-25 17:27 UTC · model grok-4.3

classification ⚛️ physics.optics quant-ph

keywords Mueller matrixJones matrixnondepolarizingpolarizationmatrix transformationoptics

0 comments

The pith

A four-dimensional complex vector isomorphic to the Jones matrix can be recovered from any nondepolarizing Mueller matrix up to an overall phase.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates a direct extraction of a four-dimensional complex vector from a nondepolarizing Mueller matrix. This vector is isomorphic to the Jones matrix that describes the same polarization transformation. The extraction works apart from an overall phase factor. A reader would care because Mueller and Jones matrices are standard tools in polarization optics, and a reliable conversion method between them supports consistent modeling of nondepolarizing systems.

Core claim

It is shown that the four dimensional complex vector associated with a nondepolarizing Mueller matrix, which is isomorphic to the Jones matrix, can be obtained from the nondepolarizing Mueller matrix apart from an overall phase.

What carries the argument

The four-dimensional complex vector associated with the nondepolarizing Mueller matrix, which is isomorphic to the Jones matrix.

If this is right

Nondepolarizing Mueller matrices can be converted to their equivalent Jones representations.
Polarization calculations can move between the two matrix types with information preserved except for the overall phase.
The conversion applies to any Mueller matrix that meets the nondepolarizing condition.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Applications may need an extra rule to fix the phase ambiguity when the vector is used in further calculations.
The method presupposes a prior check that the Mueller matrix is nondepolarizing.

Load-bearing premise

The input Mueller matrix must be nondepolarizing so that it corresponds to a single Jones matrix.

What would settle it

A concrete nondepolarizing Mueller matrix from which no four-dimensional complex vector satisfying the Jones isomorphism can be extracted.

read the original abstract

It is well known that there exists a four dimensional complex vector associated with a nondepolarizing Mueller matrix. In this note it is shown that this complex vector, which is isomorphic to the Jones matrix, can be obtained from the nondepolarizing Mueller matrix apart from an overall phase.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This note gives an explicit extraction of the Jones vector from nondepolarizing Mueller matrices up to phase, but stays incremental and thin on verification.

read the letter

Your colleague should know that the paper offers an explicit method to obtain the four-dimensional complex vector associated with a Jones matrix from its nondepolarizing Mueller matrix counterpart, modulo an overall phase factor. This is presented as a practical extraction rather than a new theoretical insight. The work is solid on its own terms because it relies only on the established isomorphism between the two representations. The authors avoid circularity by treating the nondepolarizing property as given and focusing on the algebraic step. If the derivation in the full text is correct, it provides a reproducible way to perform the conversion. Where it falls short is in the lack of supporting material. There are no worked examples, no comparison to existing methods, and no discussion of numerical stability. The abstract is too terse to allow independent checking of the central formula. These issues are typical for a short note but mean the reader has to trust the construction until they implement it themselves. The paper targets researchers in polarization optics who routinely convert between Mueller and Jones formalisms. It could be of value to that narrow group as a reference, but it will not interest readers outside that area. I would not bring this to a reading group meeting. I would not cite it in my work. The authors engage honestly with the literature by acknowledging the known existence of the vector. It deserves peer review because the claim is mathematically precise and limited in scope, so referees can assess it efficiently without needing extensive new experiments or data.

Referee Report

0 major / 1 minor

Summary. The manuscript shows that a four-dimensional complex vector associated with a nondepolarizing Mueller matrix (isomorphic to the Jones matrix) can be recovered directly from the Mueller matrix up to a global phase factor. The construction is presented as an explicit linear-algebraic mapping internal to the known Mueller–Jones correspondence for nondepolarizing systems.

Significance. If correct, the result supplies a parameter-free, direct extraction procedure that simplifies conversion between the two standard representations of nondepolarizing polarization transformations. This is a modest but useful technical contribution in polarization optics, where such mappings are frequently needed for computation or data reduction.

minor comments (1)

The title refers to transforming into Jones matrices, yet the body correctly emphasizes recovery of the associated 4-component complex vector (up to phase). A brief clarifying sentence in the introduction would avoid any potential misreading.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and the recommendation to accept.

Circularity Check

0 steps flagged

No significant circularity; direct algebraic mapping

full rationale

The paper's central claim is a direct mathematical construction: given a nondepolarizing Mueller matrix, recover the associated 4-component complex vector (isomorphic to the Jones matrix) up to global phase. This is presented as an internal linear-algebra procedure on the known Mueller-Jones correspondence in polarization optics. No data fitting, parameter estimation, self-referential definitions, or load-bearing self-citations appear in the abstract or stated claim. The derivation is therefore self-contained against external benchmarks and does not reduce any prediction or result to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no free parameters, axioms, or invented entities can be identified from the text.

pith-pipeline@v0.9.0 · 5559 in / 927 out tokens · 24911 ms · 2026-05-25T17:27:34.519844+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

If and only if the Mueller matrix of the system is non-depolarizing, the associated H matrix will be of rank 1. In this case it is always possible to define a vector |h⟩ such that H = |h⟩⟨h|

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

10 extracted references · 10 canonical work pages

[1]

Simon, R., ”The Connection Between Mueller and Jones Matrices of Polarization Op- tics,” Opt . Commun . 42, 293-297 (1982)

work page 1982
[2]

Mandel, and E

Kim, K., L. Mandel, and E. Wolf, ”Relationship Between Jones and Mu eller Matrices for Random Media, ” J . Opt . Soc . Amer . A4, 433-437 (1987)

work page 1987
[3]

R. A. Chipman, Handbook of Optics, Vol. 2, 2nd ed. (McGraw-Hill P rofessional, 1994), Chap. 22

work page 1994
[4]

Ali Kuntman, and Oriol Arteaga, ”Vector an d matrix states for Mueller matrices of nondepolarizing optical media,” J

Ertan Kuntman, M. Ali Kuntman, and Oriol Arteaga, ”Vector an d matrix states for Mueller matrices of nondepolarizing optical media,” J. Opt. Soc. Am. A 34, 80-86 (2017)

work page 2017
[5]

Kuntman, M

E. Kuntman, M. A. Kuntman, J. Sancho-Parramon, and O. Arte aga, Formalism of optical coherence and polarization based on material media states , Phys. Rev. A 95, 063819 (2017). 11

work page 2017
[6]

Ertan Kuntman, Mehmet Ali Kuntman, Adolf Canillas, and Oriol Art eaga, ”Quaternion algebra for StokesMueller formalism,” J. Opt. Soc. Am. A 36, 492-49 7 (2019)

work page 2019
[7]

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007)

work page 2007
[8]

J. J. Gil, Journal of Applied Remote Sensing 8, 081599 (2014). 5

work page 2014
[9]

Aiello and J

A. Aiello and J. P. Woerdman, Linear algebra for Mueller calculus, (2 006), arXiv:math- ph/0412061

work page arXiv
[10]

Chipman, Ph.D

R. Chipman, Ph.D. thesis, (University of Arizona, 1987) 6

work page 1987

[1] [1]

Simon, R., ”The Connection Between Mueller and Jones Matrices of Polarization Op- tics,” Opt . Commun . 42, 293-297 (1982)

work page 1982

[2] [2]

Mandel, and E

Kim, K., L. Mandel, and E. Wolf, ”Relationship Between Jones and Mu eller Matrices for Random Media, ” J . Opt . Soc . Amer . A4, 433-437 (1987)

work page 1987

[3] [3]

R. A. Chipman, Handbook of Optics, Vol. 2, 2nd ed. (McGraw-Hill P rofessional, 1994), Chap. 22

work page 1994

[4] [4]

Ali Kuntman, and Oriol Arteaga, ”Vector an d matrix states for Mueller matrices of nondepolarizing optical media,” J

Ertan Kuntman, M. Ali Kuntman, and Oriol Arteaga, ”Vector an d matrix states for Mueller matrices of nondepolarizing optical media,” J. Opt. Soc. Am. A 34, 80-86 (2017)

work page 2017

[5] [5]

Kuntman, M

E. Kuntman, M. A. Kuntman, J. Sancho-Parramon, and O. Arte aga, Formalism of optical coherence and polarization based on material media states , Phys. Rev. A 95, 063819 (2017). 11

work page 2017

[6] [6]

Ertan Kuntman, Mehmet Ali Kuntman, Adolf Canillas, and Oriol Art eaga, ”Quaternion algebra for StokesMueller formalism,” J. Opt. Soc. Am. A 36, 492-49 7 (2019)

work page 2019

[7] [7]

J. J. Gil, Eur. Phys. J. Appl. Phys. 40, 1 (2007)

work page 2007

[8] [8]

J. J. Gil, Journal of Applied Remote Sensing 8, 081599 (2014). 5

work page 2014

[9] [9]

Aiello and J

A. Aiello and J. P. Woerdman, Linear algebra for Mueller calculus, (2 006), arXiv:math- ph/0412061

work page arXiv

[10] [10]

Chipman, Ph.D

R. Chipman, Ph.D. thesis, (University of Arizona, 1987) 6

work page 1987