Abstract

The spatial stationarity of scattered optical fields constitutes a basic premise of coherence holography and photon correlation holography. Nevertheless, spatial stationarity seems to have attracted less attention and still remains a less familiar concept than temporal stationarity because it has been a common practice in statistical optics to assume temporal ergodicity and replace the ensemble average with the time average, rather than the space average. To form the theoretical basis for coherence holography and photon correlation holography, an investigation is made into the spatial stationarity of the statistical optical field, and combinations of a light source and an optical system are identified that can create spatially stationary scattered fields. The result justifies the principles of coherence holography and photon correlation holography, and the previously reported experiments.

© 2013 Optical Society of America

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References

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  2. J. W. Goodman, Statistical Optics (Wiley, 1985).
  3. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012 (1)

2011 (1)

2009 (1)

2005 (1)

Duan, Z.

Ezawa, T.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

Mandel, L.

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

Miyamoto, Y.

Naik, D. N.

Singh, R. K.

Takeda, M.

Wang, W.

Wolf, E.

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

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

Opt. Express (4)

Other (3)

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

J. W. Goodman, Statistical Optics (Wiley, 1985).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (2)

Fig. 1.
Fig. 1.

Geometry of source plane, optical system, and observation plane.

Fig. 2.
Fig. 2.

Geometrical interpretation of anisotropic characteristics of the nonstationary phase factor.

Equations (13)

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u(r)=G(r,r^)u(r^)dr^
u*(r1)u(r2)=G*(r1,r^1)G(r2,r^2)u*(r^1)u(r^2)dr^1dr^2,
u*(r^1+Δr^)u(r^2+Δr^)=u*(r^1)u(r^2)
G(r+Δr,r^+Δr)=G(r,r^),
u*(r1+Δr)u(r2+Δr)=G*(r1+Δr,r^1)G(r2+Δr,r^2)u*(r^1)u(r^2)dr^1dr^2=G*(r1,r^1Δr)G(r2,r^2Δr)u*(r^1Δr)u(r^2Δr)dr^1dr^2=G*(r1,r˜1)G(r2,r˜2)u*(r˜1)u(r˜2)dr˜1dr˜2=u*(r1)u(r2),
u*(r^1)u(r^2)=I(r^1)δ(r^1r^2),
u*(r1)u(r2)=G*(r1,r^1)G(r2,r^2)I(r^1)δ(r^1r^2)dr^1dr^2=G*(r1,r^)G(r2,r^)I(r^)dr^,
G(r,r^)=1iλ·exp(ik|z+rr^|)|z+rr^|exp(ikz)iλzexp(ik|r|22r·r^+|r^|22z),
u*(r1)u(r2)1λ2z2I(r^)exp[ik|r2|2|r1|22(r2r1)·r^2z]dr^.
u*(r1+Δr)u(r2+Δr)1λ2z2I(r^)exp[ik|r2+Δr|2|r1+Δr|22(r2r1)·r^2z]dr^=1λ2z2I(r^)exp[ik|r2|2|r1|22(r2r1)·r^2z]dr^×exp[ik(r2r1)·Δrz]=u*(r1)u(r2)exp[ik(r2r1)·Δrz].
G(r,r^)=exp(ikf)iλfexp(ikr·r^f).
G*(r1,r^)G(r2,r^)=1λ2f2exp[ik(r2r1)·r^f]=G*(r1+Δr,r^)G(r2+Δr,r^).
u*(r1+Δr)u(r2+Δr)=G*(r1+Δr,r^)G(r2+Δr,r^)I(r^)dr^=G*(r1,r^)G(r2,r^)I(r^)dr^=u*(r1)u(r2),

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