Abstract

We present a novel sensor that measures the entire spatial coherence function within an aperture by use of a variable astigmatic lens. This sensor permits digital capture and processing of partially coherent fields. We demonstrate the sensor by sampling and computing the coherent modes of a three-dimensional incoherent source.

© 2000 Optical Society of America

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References

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  1. A. A. Michelson, Philos. Mag. 30, 1 (1890).
    [CrossRef]
  2. A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
    [CrossRef]
  3. M. Murty, J. Opt. Soc. Am. 54, 1187 (1964).
  4. F. Roddier, in High Angular Resolution Stellar Interferometry, J. Davis and W. J. Tango, eds., Vol. 50 of IAU Colloquia (University of Sydney, Sydney, Australia, 1979), paper 3.
  5. A. Pentland, S. Scherock, T. Darrell, and B. Girod, J. Opt. Soc. Am. A 11, 2925 (1994).
    [CrossRef]
  6. S. K. Nayar, M. Watanabe, and M. Noguchi, IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186 (1996).
    [CrossRef]
  7. R. G. Paxman, T. J. Schulz, and J. R. Fienup, J. Opt. Soc. Am. A 9, 1072 (1992).
    [CrossRef]
  8. E. Wolf, J. Opt. Soc. Am. 72, 343 (1982).
  9. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
    [CrossRef]
  10. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1996).
  11. D. L. Marks, R. A. Stack, and D. J. Brady, Appl. Opt. 38, 1332 (1999).
    [CrossRef]
  12. D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
    [CrossRef] [PubMed]
  13. J. Rosen and A. Yariv, Opt. Lett. 21, 1803 (1996).
    [CrossRef] [PubMed]
  14. E. Ribak, C. Roddier, F. Roddier, and J. Breckinridge, Appl. Opt. 27, 1183 (1988).
    [CrossRef] [PubMed]

1999 (2)

D. L. Marks, R. A. Stack, and D. J. Brady, Appl. Opt. 38, 1332 (1999).
[CrossRef]

D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
[CrossRef] [PubMed]

1996 (2)

J. Rosen and A. Yariv, Opt. Lett. 21, 1803 (1996).
[CrossRef] [PubMed]

S. K. Nayar, M. Watanabe, and M. Noguchi, IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186 (1996).
[CrossRef]

1994 (1)

1992 (1)

1988 (1)

1982 (1)

1964 (1)

1921 (1)

A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[CrossRef]

1890 (1)

A. A. Michelson, Philos. Mag. 30, 1 (1890).
[CrossRef]

Brady, D. J.

D. L. Marks, R. A. Stack, and D. J. Brady, Appl. Opt. 38, 1332 (1999).
[CrossRef]

D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
[CrossRef] [PubMed]

Brady, R. B.

D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
[CrossRef] [PubMed]

Breckinridge, J.

Darrell, T.

Fienup, J. R.

Girod, B.

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1996).

Mandel, L.

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

Marks, D. L.

D. L. Marks, R. A. Stack, and D. J. Brady, Appl. Opt. 38, 1332 (1999).
[CrossRef]

D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
[CrossRef] [PubMed]

Michelson, A.

A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[CrossRef]

Michelson, A. A.

A. A. Michelson, Philos. Mag. 30, 1 (1890).
[CrossRef]

Munson, D.

D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
[CrossRef] [PubMed]

Murty, M.

Nayar, S. K.

S. K. Nayar, M. Watanabe, and M. Noguchi, IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186 (1996).
[CrossRef]

Noguchi, M.

S. K. Nayar, M. Watanabe, and M. Noguchi, IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186 (1996).
[CrossRef]

Paxman, R. G.

Pease, F. G.

A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[CrossRef]

Pentland, A.

Ribak, E.

Roddier, C.

Roddier, F.

E. Ribak, C. Roddier, F. Roddier, and J. Breckinridge, Appl. Opt. 27, 1183 (1988).
[CrossRef] [PubMed]

F. Roddier, in High Angular Resolution Stellar Interferometry, J. Davis and W. J. Tango, eds., Vol. 50 of IAU Colloquia (University of Sydney, Sydney, Australia, 1979), paper 3.

Rosen, J.

Scherock, S.

Schulz, T. J.

Stack, R. A.

D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
[CrossRef] [PubMed]

D. L. Marks, R. A. Stack, and D. J. Brady, Appl. Opt. 38, 1332 (1999).
[CrossRef]

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1996).

Watanabe, M.

S. K. Nayar, M. Watanabe, and M. Noguchi, IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186 (1996).
[CrossRef]

Wolf, E.

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

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

Yariv, A.

Appl. Opt. (2)

Astrophys. J. (1)

A. Michelson and F. G. Pease, Astrophys. J. 53, 249 (1921).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. K. Nayar, M. Watanabe, and M. Noguchi, IEEE Trans. Pattern Anal. Mach. Intell. 18, 1186 (1996).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Opt. Lett. (1)

Philos. Mag. (1)

A. A. Michelson, Philos. Mag. 30, 1 (1890).
[CrossRef]

Science (1)

D. L. Marks, R. A. Stack, D. J. Brady, D. Munson, and R. B. Brady, Science 284, 2164 (1999).
[CrossRef] [PubMed]

Other (3)

F. Roddier, in High Angular Resolution Stellar Interferometry, J. Davis and W. J. Tango, eds., Vol. 50 of IAU Colloquia (University of Sydney, Sydney, Australia, 1979), paper 3.

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

G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1996).

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Figures (3)

Fig. 1
Fig. 1

Portion of coherence space that can be sampled in a two-dimensional square aperture (shown for one dimension only; the other is identical).

Fig. 2
Fig. 2

Diagram of the ACS. Two cylindrical lenses of 300-mm focal length form Axis 1 and focus along one diagonal direction, and one cylindrical lens of 150-mm focal length forms Axis 2. The combination of the two foci, oriented at equal and opposite angles to the vertical axis, effectively forms a single lens of adjustable astigmatic focal ratio.

Fig. 3
Fig. 3

(A)–(C) Three coherent modes computed from the sample coherence data. The image intensity corresponds to the magnitude of the real component of the unpolarized optical field. The dimensions of the images are 3 mm×3 mm. The magnitude, spatial frequency, field curvature, and corresponding positions of each mode is shown in the table.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Ix,y,z,fx,fy=1z2AAJx1,y1,x2,y2×expi2πλx12fx+y12fy-x22fx+y22fy×exp-i2πλzx-x12+y-y12-x-x22-y-y22dx1dy1dx2dy2.
z2Ix,y,z,fx,fy=12AAJΔx,Δy,xˆ,yˆ×expi2πλ4xˆΔx1fx-1z+4yˆΔy1fy-1z×exp-i2πλz-4xΔx-4yΔydxˆdyˆdΔxdΔy.
z2Ixz,yz,1fx-1z,1fy-1z=12AA×JΔx,Δy,qx,qyΔxΔyexpi2πλ4qx1fx-1z+4qy1fy-1zexp-i2πλz-4xΔx-4yΔy×dqxdqydΔxdΔy.
z2Ixz,yz,1fx-1z,1fy-1zJΔxλ,Δyλ,qxλ,qyλΔxΔy.
Er2=λkAEr1Jr1,r2dr1Ej=λkiEiJri-rj,ri+rj2,
exp2πiλxznxd+yznyd+12znx2+ny2d2,

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