Abstract

Spatial coherence plays a major role in characterizing quasi-monochromatic, partially coherent, optical signals. Here a fairly simple system for synthesizing special cases of spatial coherence is proposed. The special cases, called hybrid, include the case of total coherence in the x direction and, simultaneously, total incoherence in the y direction. The optical setup is based on a quasi-monochromatic, spatially coherent light source, such as a laser, and a simple moving optical element.

© 1999 Optical Society of America

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References

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  1. E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width,” Proc. R. Soc. London 230, 246–265 (1955).
    [CrossRef]
  2. L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
    [CrossRef]
  3. L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976).
    [CrossRef]
  4. M. Born, E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, New York, 1980).
  5. L. Mandel, E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995).
    [CrossRef]
  6. A. W. Lohmann, D. Mendlovic, G. Shabtay, “Coherence waves,” J. Opt. Soc. Am. A 16, 359–363 (1999).
    [CrossRef]
  7. D. Mendlovic, G. Shabtay, A. W. Lohmann, N. Konforti, “Display of spatial coherence,” Opt. Lett. 23, 1084–1086 (1998).
    [CrossRef]
  8. D. Mendlovic, G. Shabtay, A. W. Lohmann, “Synthesis of spatial coherence,” Opt. Lett. 24, 361–363 (1999).
    [CrossRef]

1999 (2)

1998 (1)

1976 (1)

1965 (1)

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

1955 (1)

E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width,” Proc. R. Soc. London 230, 246–265 (1955).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, New York, 1980).

Konforti, N.

Lohmann, A. W.

Mandel, L.

L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976).
[CrossRef]

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

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

Mendlovic, D.

Shabtay, G.

Wolf, E.

L. Mandel, E. Wolf, “Spectral coherence and the concept of cross-spectral purity,” J. Opt. Soc. Am. 66, 529–535 (1976).
[CrossRef]

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width,” Proc. R. Soc. London 230, 246–265 (1955).
[CrossRef]

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

M. Born, E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, New York, 1980).

J. Opt. Soc. Am. (1)

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

Opt. Lett. (2)

Proc. R. Soc. London (1)

E. Wolf, “A macroscopic theory of interference and diffraction of light from finite sources II. Fields with a spectral range of arbitrary width,” Proc. R. Soc. London 230, 246–265 (1955).
[CrossRef]

Rev. Mod. Phys. (1)

L. Mandel, E. Wolf, “Coherence properties of optical fields,” Rev. Mod. Phys. 37, 231–287 (1965).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics, Electromagnetic Theory of Propagation, Interference and Diffraction (Pergamon, New York, 1980).

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

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Figures (1)

Fig. 1
Fig. 1

Cylindrical lens, illuminated by collimated light while moving vertically.

Equations (13)

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ΓR1, R2, t1, t2=uR1, t1u*(R2, t2,
Γx1, y1, x2, y2=ux1, y1, tu*x2, y2, t.
Γx1, y1, x2, y2=δ¯y1-y2,
Γx1, y1, x2, y2=1T-T/2T/2 ux1, y1, tu*x2, y2, tdt.
ux, y, t=exp- iπλfy-Vt2,
Γ1x1, y1, x2, y2=1T-T/2T/2exp- iπλfy1-Vt2× expiπλfy2-Vt2dt=exp- iπλfy12-y221T×-T/2T/2expi2πy1-y2Vtλfdt.
Γ1x1, y1, x2, y2=δ¯y1-y2.
ux, y, t=exp- iπλfx2+y-Vt2.
Γ2x1, y1, x2, y2=exp- iπλfx12-x22δ¯y1-y2.
ur, θ=exp-iθ2  ur, θ, t=exp-iθ-ωt2,
Γ3r1, θ1, r2, θ2=1T-T/2T/2 ur1, θ1, tu*r2, θ2, tdt=δ¯θ1-θ2.
ur, θ=exp-irθ  ur, θ, t=exp-irθ-ωt,
Γ4r1,θ1,r2,θ2=exp-ir1θ1-θ2δ¯r1-r2.

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