Abstract

In this Letter, we derive a general criterion for the physical realizability of the differential Mueller matrix m of a depolarizing continuous medium. The criterion is based on checking the positive semidefiniteness of a 3×3 restriction of the coherency matrix of the G-symmetric component of m and turns out be a close analogue of the well-known criterion of Cloude for a Mueller matrix to be physically realizable. The related aspects of local and global, as well as Stokes and physical (or Cloude), realizabilities are discussed comparatively. The practical application of the criterion, in connection with the above types of realizabilities, is illustrated on experimental Mueller matrices from the literature.

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References

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[CrossRef]

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R. Simon, J. Mod. Opt. 34, 569 (1987).
[CrossRef]

1986

S. R. Cloude, Optik (Stuttgart) 75, 26 (1986).

1978

Alex Vitkin, I.

N. Ghosh and I. Alex Vitkin, J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

Arce-Diego, J.-L.

Azzam, R. M. A.

Borghi, R.

Charbois, J.-M.

Cloude, S. R.

S. R. Cloude, Optik (Stuttgart) 75, 26 (1986).

Devlaminck, V.

Germer, T. A.

Ghosh, N.

N. Ghosh and I. Alex Vitkin, J. Biomed. Opt. 16, 110801 (2011).
[CrossRef]

Gori, F.

Luderna, K. C.

D. A. Ramsey and K. C. Luderna, Rev. Sci. Instrum. 65, 2874 (1994).
[CrossRef]

Mukunda, N.

Ortega-Quijano, N.

Ossikovski, R.

Ramsey, D. A.

D. A. Ramsey and K. C. Luderna, Rev. Sci. Instrum. 65, 2874 (1994).
[CrossRef]

Santarsiero, M.

Simon, B. N.

Simon, R.

Simon, S.

Terrier, P.

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Equations (22)

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dM(z)dz=mM(z),
m=[d0p1+d1p2+d2p3+d3p1d1d0d7d6+p6d5p5p2d2d6p6d0d8d4+p4p3d3d5+p5d4p4d0d9],
mm=12(mGmTG)andmu=12(m+GmTG),
M(z+Δz)=(I+mmΔz+muΔz)M(z)=M(Δz,z)M(z),
C(I)=[10⃗T0⃗O3],
C(mmΔz)=ΔzC(mm)=Δz[0p⃗+p⃗O3],
C(muΔz)=ΔzC(mu)=Δz[c00⃗T0⃗C3],
C(I+mmΔz)=C(I)+C(mmΔz)=[1p⃗+ΔzpΔzO3].
λ3,4=12(1±1+4p2Δz2),
C(I+mmΔz)=[1p+Δzp⃗ΔzO3]=[1p⃗Δz][1p⃗+Δz].
C311=14(mu11+mu22mu33mu44)C322=14(mu11mu22+mu33mu44)C333=14(mu11mu22mu33+mu44)C312=C321*=12(mu23+imu14)C313=C331*=12(mu24imu13)C323=C332*=12(mu34+imu12).
mu(1)=[k1+k2+k30000k1k2k30000k2k1k30000k3k1k2]ormu(2)=[k1+k2k200k2k1k20000k10000k1]
C3(mu(1))=diag(k1,k2,k3)andC3(mu(2))=12[2k1000k2ik20ik2k2].
mA=diag(0,0,0,σ)
C3(mA)=14diag(σ,σ,σ)
MA(z)=exp(mAz)=diag(1,1,1,eσz),
C(MA)=14[3+eσz00001eσz00001eσz0000eσz1],
Local realizability(CorS)Global realizability(CorS)Cloude’s (physical)realizabilityStokes’ realizability,
Mt=[10.07070.03480.00600.04800.40990.00770.06500.01620.01840.22430.35800.00210.04650.35710.1783]
Ltu=[00.01790.01460.00700.01790.88760.08540.03790.01460.08540.82740.00150.00700.03790.00150.9516].
Ms=[10.16310.03220.08020.00830.40380.25550.21580.00260.42970.13760.20160.01160.05970.31750.3690]
Lsu=[00.05790.06940.12890.05790.48870.04110.12840.06940.04110.52540.09270.12890.12840.09271.1322].

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