Abstract

A necessary and sufficient non-negative definiteness condition for the cross-spectral density (CSD) is provided. It is also shown that any genuine CSD can be expanded in terms of the so-called pseudo-modes of the source, understood as coherent contributions, not orthogonal to one another, that, superposed in an uncorrelated way, give rise to the CSD. Their evaluation is analyzed by means of an illustrative example.

© 2009 Optical Society of America

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References

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    [PubMed]
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  17. A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).

2008

2007

2006

2005

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).

2001

1987

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).

1984

1982

1980

F. Gori, Opt. Commun. 34, 301 (1980).

F. Gori, Opt. Acta 27, 1025 (1980).

1979

R. Martínez-Herrero, Nuovo Cimento 54, 205 (1979).

1978

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).

Berlinet, A.

A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).

Borghi, R.

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and C. F. Li, J. Opt. Soc. Am. A 25, 2826 (2008).

F. Gori and M. Santarsiero, Opt. Lett. 32, 3531 (2007).
[PubMed]

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).

F. Gori, Opt. Commun. 34, 301 (1980).

F. Gori, Opt. Acta 27, 1025 (1980).

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).

Korotkova, O.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).

Li, C. F.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

Martínez-Herrero, R.

R. Martínez-Herrero and P. M. Mejías, J. Opt. Soc. Am. A 1, 556 (1984).

R. Martínez-Herrero, Nuovo Cimento 54, 205 (1979).

Mejías, P. M.

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).

Palma, C.

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).

Ponomarenko, S. A.

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).

Santarsiero, M.

Starikov, A.

Thomas-Agnan, C.

A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).

Tricomi, F. G.

F. G. Tricomi, Integral Equations (Interscience Publishers, 1957).

Turunen, J.

Vahimaa, P.

Wolf, E.

E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).

A. Starikov and E. Wolf, J. Opt. Soc. Am. 72, 923 (1982).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nuovo Cimento

R. Martínez-Herrero, Nuovo Cimento 54, 205 (1979).

Opt. Acta

F. Gori, Opt. Acta 27, 1025 (1980).

Opt. Commun.

F. Gori and C. Palma, Opt. Commun. 27, 185 (1978).

F. Gori, G. Guattari, and C. Padovani, Opt. Commun. 64, 311 (1987).

F. Gori, Opt. Commun. 34, 301 (1980).

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).

Opt. Express

Opt. Lett.

Other

F. G. Tricomi, Integral Equations (Interscience Publishers, 1957).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).

A. Berlinet and C. Thomas-Agnan, Reproducing Kernel Hilbert Spaces in Probability and Statistics (Kluwer Academic, 2004).

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Equations (17)

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W ( ρ 1 , ρ 2 ) = p ( v ) H * ( ρ 1 , v ) H ( ρ 2 , v ) d 2 v ,
L ( ρ , v ) = p ( v ) H ( ρ , v ) ,
W ( ρ 1 , ρ 2 ) = L * ( ρ 1 , v ) L ( ρ 2 , v ) d 2 v .
L ( ρ , v ) = n = 1 c n ( ρ ) Φ n ( v ) ,
c m ( ρ ) = L ( ρ , v ) Φ m * ( v ) d 2 v .
W ( ρ 1 , ρ 2 ) = n = 1 c n * ( ρ 1 ) c n ( ρ 2 ) .
c n * ( ρ ) c m ( ρ ) d 2 ρ = A m δ n m .
W ( ρ 1 , ρ 2 ) Ψ k ( ρ 1 ) d 2 ρ 1 = λ k Ψ k ( ρ 2 ) ,
W ( ρ 1 , ρ 2 ) c k ( ρ 1 ) d 2 ρ 1 = A k c k ( ρ 2 ) ,
c k ( ρ ) = α k Ψ k ( ρ ) .
c k ( ρ ) 2 d 2 ρ = α k 2 = A k λ k .
W ( ρ 1 , ρ 2 ) = n = 1 λ n Ψ n * ( ρ 1 ) Ψ n ( ρ 2 ) .
L ( ρ , v ) = n = 1 λ n Ψ n * ( ρ ) Φ n ( v ) ,
W ( x , y ) = { x ( 1 y ) , 0 x y 1 y ( 1 x ) , 0 y x 1 } .
L ( x , v ) = step ( x v ) x ,
c n ( x ) = 2 0 1 L ( x , v ) cos ( n π v ) d v = 2 sin ( n π x ) n π .
Ψ n ( x ) = 2 sin ( n π x ) , λ n = 1 n 2 π 2 , ( n = 1 , 2 , ) .

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