Abstract

After discussing the desirability of determining the variation of polarization with frequency in planetary spectra, the possibility of measuring the intensity and state of polarization of optical radiation by means of the high resolution Fourier spectroscopic method is discussed. In the proposed experimental arrangement a two-beam interferometer is used with a polarizer in each beam. After recombination the emergent radiation is analyzed with a linear polarizer. It is shown that the interferograms obtained in this way contain information about the four Stokes parameters of the incident radiation. The polarizers introduce an asymmetry in the interferograms requiring full (exponential) transforms for retrieval of the desired data. The effects of the finite range of path difference and the variation of its zero point with frequency are considered, and evaluation of the corresponding phase error with a proper choice of the polarizer settings is discussed. The formalism also takes into account the residual polarization introduced by the beam splitter, and the differential transmission of the two beams. Generally, three independent interferograms are needed for determining the phase error and the four Stokes parameters. Some simple arrangements are described in which the two beams are either both linearly or both circularly polarized. It is hoped that instruments based on the principle described here will be built by workers in the field.

© 1970 Optical Society of America

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References

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  1. M. H. Cohen, Proc. IRE 46, 178 (1958).
  2. E. Wolf, Nuovo Cimento (Ser. X) 13, 1165 (1959).
    [CrossRef]
  3. H. C. Ko, Proc. IRE 50, 1950 (1962); IEEE Trans. Antennas Propagation 15, 10 (1967).
    [CrossRef]
  4. G. B. Parrent, P. Roman, Nuovo Cimento (Ser. X) 15, 370 (1960).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), p. 542.
  6. J. Connes, Rev. Opt. 40,45, 116, 171, 231 (1961), translated into English as U. S. Naval Ordnance Test Station NAVWEPS Rept. 8099 Nots TP 3157, China Lake, Calif. (1963).
  7. W. H. Steel, Interferometry (Cambridge University Press, Cambridge, 1967), Chap. 10.
  8. M. L. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Amer. 56, 1, 59 (1966).
    [CrossRef]
  9. P. Felgett, thesis, Cambridge University, 1951.
  10. P. Jacquinot, J. Phys. Radium 19, 39 (1958).
    [CrossRef]
  11. E. V. Loewenstein, Appl. Opt. 5, 845 (1966).
    [CrossRef] [PubMed]

1966

M. L. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Amer. 56, 1, 59 (1966).
[CrossRef]

E. V. Loewenstein, Appl. Opt. 5, 845 (1966).
[CrossRef] [PubMed]

1962

H. C. Ko, Proc. IRE 50, 1950 (1962); IEEE Trans. Antennas Propagation 15, 10 (1967).
[CrossRef]

1961

J. Connes, Rev. Opt. 40,45, 116, 171, 231 (1961), translated into English as U. S. Naval Ordnance Test Station NAVWEPS Rept. 8099 Nots TP 3157, China Lake, Calif. (1963).

1960

G. B. Parrent, P. Roman, Nuovo Cimento (Ser. X) 15, 370 (1960).
[CrossRef]

1959

E. Wolf, Nuovo Cimento (Ser. X) 13, 1165 (1959).
[CrossRef]

1958

M. H. Cohen, Proc. IRE 46, 178 (1958).

P. Jacquinot, J. Phys. Radium 19, 39 (1958).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), p. 542.

Cohen, M. H.

M. H. Cohen, Proc. IRE 46, 178 (1958).

Connes, J.

J. Connes, Rev. Opt. 40,45, 116, 171, 231 (1961), translated into English as U. S. Naval Ordnance Test Station NAVWEPS Rept. 8099 Nots TP 3157, China Lake, Calif. (1963).

Felgett, P.

P. Felgett, thesis, Cambridge University, 1951.

Forman, M. L.

M. L. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Amer. 56, 1, 59 (1966).
[CrossRef]

Jacquinot, P.

P. Jacquinot, J. Phys. Radium 19, 39 (1958).
[CrossRef]

Ko, H. C.

H. C. Ko, Proc. IRE 50, 1950 (1962); IEEE Trans. Antennas Propagation 15, 10 (1967).
[CrossRef]

Loewenstein, E. V.

Parrent, G. B.

G. B. Parrent, P. Roman, Nuovo Cimento (Ser. X) 15, 370 (1960).
[CrossRef]

Roman, P.

G. B. Parrent, P. Roman, Nuovo Cimento (Ser. X) 15, 370 (1960).
[CrossRef]

Steel, W. H.

M. L. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Amer. 56, 1, 59 (1966).
[CrossRef]

W. H. Steel, Interferometry (Cambridge University Press, Cambridge, 1967), Chap. 10.

Vanasse, G. A.

M. L. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Amer. 56, 1, 59 (1966).
[CrossRef]

Wolf, E.

E. Wolf, Nuovo Cimento (Ser. X) 13, 1165 (1959).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), p. 542.

Appl. Opt.

J. Opt. Soc. Amer.

M. L. Forman, W. H. Steel, G. A. Vanasse, J. Opt. Soc. Amer. 56, 1, 59 (1966).
[CrossRef]

J. Phys. Radium

P. Jacquinot, J. Phys. Radium 19, 39 (1958).
[CrossRef]

Nuovo Cimento (Ser. X)

E. Wolf, Nuovo Cimento (Ser. X) 13, 1165 (1959).
[CrossRef]

G. B. Parrent, P. Roman, Nuovo Cimento (Ser. X) 15, 370 (1960).
[CrossRef]

Proc. IRE

H. C. Ko, Proc. IRE 50, 1950 (1962); IEEE Trans. Antennas Propagation 15, 10 (1967).
[CrossRef]

M. H. Cohen, Proc. IRE 46, 178 (1958).

Rev. Opt.

J. Connes, Rev. Opt. 40,45, 116, 171, 231 (1961), translated into English as U. S. Naval Ordnance Test Station NAVWEPS Rept. 8099 Nots TP 3157, China Lake, Calif. (1963).

Other

W. H. Steel, Interferometry (Cambridge University Press, Cambridge, 1967), Chap. 10.

P. Felgett, thesis, Cambridge University, 1951.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1959), p. 542.

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Figures (1)

Fig. 1
Fig. 1

Proposed two-beam optical interferometer for measuring polarization.

Tables (2)

Tables Icon

Table I Interferometric Arrangements with Linear Polarizers

Tables Icon

Table II Interferometric Arrangements with Circular Polarizers

Equations (26)

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E = ( E x E y ) ,
J = E × E = ( J x x J x y J y x J y y ) ,
{ I = J x x + J y y = Trace J Q = J x x J y y U = J x y + J y x V = i ( J x y J y x ) .
E = KE .
I ( θ , ) = J x x cos 2 θ + J y y sin 2 θ + 2 | J x y | cos θ sin θ cos ( β x y ) .
R 1 = e i δ / 2 1 , R 2 = e i δ / 2 1 .
I ( τ ) = 0 I τ ( σ ) d σ ;
P i ( σ ) = ( P i 1 P i 2 P i 3 P i 4 ) σ ( i = 1,2,3 ) ,
E ( P ) = ( P 31 P 32 P 33 P 34 ) [ ( P 11 P 12 P 13 P 14 ) e i δ / 2 + ( P 21 P 22 P 23 P 24 ) e i δ / 2 ] ( E x E y ) .
E ( P 3 ) = ( [ α 1 cos ( δ / 2 ) i β i sin ( δ / 2 ) ] E x + [ α 2 cos ( δ / 2 ) i β 2 sin ( δ / 2 ) ] E y [ α 3 cos ( δ / 2 ) i β 3 sin ( δ / 2 ) ] E x + [ α 4 cos ( δ / 2 ) i β 4 sin ( δ / 2 ) ] E y ) ,
I τ ( σ ) = a 1 ( σ ) + a 2 ( σ ) cos δ + a 3 ( σ ) sin δ ,
a i ( σ ) = p i ( σ ) I ( σ ) + q i ( σ ) Q ( σ ) + r i ( σ ) U ( σ ) + s i ( σ ) V ( σ ) ( i = 1,2,3 )
a 2 ( σ ) = ρ ( σ ) cos ψ ( σ ) a 3 ( σ ) = ρ ( σ ) sin ψ ( σ ) } ,
I τ ( σ ) = d ( σ ) { a 1 ( σ ) + ρ ( σ ) cos [ δ ψ ( σ ) ] } .
ψ ( σ ) = tan 1 [ a 3 ( σ ) / a 2 ( σ ) ]
I ( τ ) = 0 d ( σ ) { a 1 ( σ ) + ρ ( σ ) cos [ 2 π σ τ ψ ( σ ) ] } d σ ;
Var [ I ( τ ) ] = 0 d ( σ ) ρ ( σ ) cos [ 2 π σ τ ψ ( σ ) ] d σ .
d ( σ ) = d ( σ ) , ρ ( σ ) = ρ ( σ ) , ψ ( σ ) = ψ ( σ ) ,
Var [ I ( τ ) ] = 1 2 d ( σ ) ρ ( σ ) exp [ i ψ ( σ ) ] e i 2 π σ τ d σ .
Var [ I ( τ ) ] = T ( τ ) 0 d ( σ ) ρ ( σ ) B ( σ τ ) cos [ 2 π σ τ ψ ( σ ) ϕ ( σ ) + γ ( σ τ ) ] d σ .
B ( σ τ ) = B ( σ τ ) , ϕ ( σ ) = ϕ ( σ ) , γ ( σ τ ) = γ ( σ τ ) ,
Var [ I ( τ ) ] = 1 2 T ( τ ) d ( σ ) ρ ( σ ) S * ( σ τ ) × exp { i [ ψ ( σ ) + ϕ ( σ ) ] } e i 2 π σ τ d σ ,
S ( σ τ ) = B ( σ τ ) exp [ i γ ( σ τ ) ] = S * ( σ τ ) .
2 Var [ I ( τ ) ] T ( τ ) S * ( σ 0 τ ) = d ( σ ) ρ ( σ ) exp { i [ ψ ( σ ) + ϕ ( σ ) ] } e i 2 π σ τ d σ .
P ( θ ) = f ( cos 2 θ cos θ sin θ cos θ sin θ sin 2 θ ) ,
f 2 ( 1 i + 1 1 ) r and f 2 ( 1 + i i 1 ) l .

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