Abstract

Theoretical results of the use of a Mueller matrix to characterize a one-dimensional rough perfectly reflecting, single-scattering surface in a conical configuration are presented. The conical Mueller matrix (CMM) is derived from the known Mueller matrix of this kind of surface in the plane of incidence [the plane Mueller matrix (PMM)]. The key argument is that, as the PMM is considered to be a Mueller–Jones matrix, an appropriate rotation of the complex amplitude matrix provides the conic Mueller matrix.

© 1998 Optical Society of America

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1996 (2)

R. A. Depine and D. C. Skigin, J. Mod. Opt. 43, 543 (1996).
[CrossRef]

R. E. Luna, Opt. Lett. 21, 1418 (1996).
[CrossRef] [PubMed]

1995 (1)

1994 (1)

D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. A 8, 2305 (1994).
[CrossRef]

1993 (3)

1992 (1)

N. C. Bruce, A. J. Sant, and J. C. Dainty, Opt. Commun. 88, 471 (1992).
[CrossRef]

1991 (2)

1990 (1)

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (New York) 203, 255 (1990).
[CrossRef]

1989 (1)

1987 (1)

1981 (1)

R. Barakat, Opt. Commun. 38, 159 (1981).
[CrossRef]

1974 (1)

D. Maystre and R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 61 (1974).

1972 (1)

D. Maystre and R. Petit, Opt. Commun. 5, 35 (1972).
[CrossRef]

1941 (1)

Anderson, D. G. M.

D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. A 8, 2305 (1994).
[CrossRef]

Arfken, G.

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1975).

Barakat, R.

D. G. M. Anderson and R. Barakat, J. Opt. Soc. Am. A 8, 2305 (1994).
[CrossRef]

R. Barakat, Opt. Commun. 38, 159 (1981).
[CrossRef]

Bruce, N. C.

N. C. Bruce, A. J. Sant, and J. C. Dainty, Opt. Commun. 88, 471 (1992).
[CrossRef]

Dainty, J. C.

N. C. Bruce, A. J. Sant, and J. C. Dainty, Opt. Commun. 88, 471 (1992).
[CrossRef]

Depine, R. A.

Jones, R. C.

Kim, K.

Knotts, M. E.

Luna, R. E.

Mandel, L.

Maradudin, A. A.

A. R. McGurn and A. A. Maradudin, J. Opt. Soc. Am. B 10, 539 (1993).
[CrossRef]

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (New York) 203, 255 (1990).
[CrossRef]

Maystre, D.

D. Maystre and R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 61 (1974).

D. Maystre and R. Petit, Opt. Commun. 5, 35 (1972).
[CrossRef]

McGurn, A. R.

A. R. McGurn and A. A. Maradudin, J. Opt. Soc. Am. B 10, 539 (1993).
[CrossRef]

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (New York) 203, 255 (1990).
[CrossRef]

Méndez, E. R.

R. E. Luna and E. R. Méndez, Opt. Lett. 20, 657 (1995).
[CrossRef] [PubMed]

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (New York) 203, 255 (1990).
[CrossRef]

Michel, T. R.

M. E. Knotts, T. R. Michel, and K. A. O’Donnell, J. Opt. Soc. Am. A 10, 928 (1993).
[CrossRef]

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (New York) 203, 255 (1990).
[CrossRef]

Nieto-Vesperinas, M.

O’Donnell, K. A.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass.1963), pp. 135–143.

Petit, R.

D. Maystre and R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 61 (1974).

D. Maystre and R. Petit, Opt. Commun. 5, 35 (1972).
[CrossRef]

Sant, A. J.

N. C. Bruce, A. J. Sant, and J. C. Dainty, Opt. Commun. 88, 471 (1992).
[CrossRef]

Skigin, D. C.

R. A. Depine and D. C. Skigin, J. Mod. Opt. 43, 543 (1996).
[CrossRef]

Soto-Crespo, J. M.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

Wolf, E.

Ann. Phys. (New York) (1)

A. A. Maradudin, T. R. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (New York) 203, 255 (1990).
[CrossRef]

J. Mod. Opt. (1)

R. A. Depine and D. C. Skigin, J. Mod. Opt. 43, 543 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

J. Opt. Soc. Am. B (1)

J. Spectrosc. Soc. Jpn. (1)

D. Maystre and R. Petit, J. Spectrosc. Soc. Jpn. 23, Suppl. 61 (1974).

Opt. Commun. (3)

D. Maystre and R. Petit, Opt. Commun. 5, 35 (1972).
[CrossRef]

N. C. Bruce, A. J. Sant, and J. C. Dainty, Opt. Commun. 88, 471 (1992).
[CrossRef]

R. Barakat, Opt. Commun. 38, 159 (1981).
[CrossRef]

Opt. Lett. (3)

Other (4)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981).

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass.1963), pp. 135–143.

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980), p. 31.

G. Arfken, Mathematical Methods for Physicists (Academic, New York, 1975).

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Figures (1)

Fig. 1
Fig. 1

Schematic diagram of the conical scattering geometry.

Equations (19)

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Escr,t=Epscr,tEsscr,t=LEir,t=abcdEpir,tEsir,t,
M=TLL*T-1,
T=1001100-101100-ii0,
T-1=121100001i001-i1-100.
M=S11S1200S12S110000S33S3400-S34S33,
S11=12aa*+dd*,S12=12aa*-dd*,S33=12ad*+da*=Read*,S34=i2ad*-da*=-Imad*.
Vsc=MVi.
Isc=Ep2+Es2,Qsc=Ep2-Es2,Usc=EpEs*+Ep*Es,Vsc=iEp*Es-EpEs*,
TrMtM=i,j=14Sij2=4S112,
TrMctMc=i,j=14mij2=4m112,
Jφ/2=Uxφ/2LUx*φ/2,
L=a00d
Uxφ/2=cosφ/2i sinφ/2i sinφ/2cosφ/2.
Mcθ0,θs;φTJφ/2J*φ/2T-1,
Mcθ0,θs;φ=12m11m12m13m14m21m22m23m24m31m32m33m34m41m42m43m44,
m11=J11J11*+J21J21*+J12J12*+J22J22*,m12=J11J11*+J21J21*-J12J12*-J22J22*,m13=J11J12*+J21J22*+J12J11*+J22J21*,m14=iJ11J12*+J21J22*-J12J11*-J22J21*,m21=J11J11*-J21J21*+J12J12*-J22J22*,m22=J11J11*-J21J21*-J12J12*+J22J22*,m23=J11J12*-J21J22*+J12J11*-J22J21*,m24=iJ11J12*-J21J22*-J12J11*+J22J21*,m31=J11J21*+J21J11*+J12J22*+J22J12*,m32=J11J21*+J21J11*-J12J22*-J22J12*,m33=J11J22*+J21J12*+J12J21*+J22J11*,m34=iJ11J22*+J21J12*-J12J21*-J22J11*,m41=i-J11J21*+J21J11*-J12J22*+J22J12*,m42=i-J11J21*+J21J11*+J12J22*-J22J12*,m43=i-J11J22*+J21J12*-J12J21*+J22J11*,m44=J11J22*-J21J12*-J12J21*+J22J11*;
J11=a cos2φ/2+d sin2φ/2,J12=-ia-dsinφ/2cosφ/2,J21=ia-dsinφ/2cosφ/2,J22=a sin2φ/2+d cos2φ/2.
Mcθ0,θs;φ=S11S12 cos φ0-S12 sin φS12 cos φS11 cos2φ+S33 sin2φ-S34 sin φ-S11-S33sin φ cos φ0-S34 sin φS33S34 cos φ-S12 sin φ-S11-S33sin φ cos φ-S34 cos φS11 sin2φ+S33 cos2φ,
TrMctMc=4m112=4S112=TrMtM,

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