Abstract

We describe a phase retrieval approach for intensity point-spread functions of high-numerical-aperture optical systems such as light microscopes. The method calculates a generalized pupil function defined on a spherical shell, using measured images at several defocus levels. The resultant pupil functions reproduce measured point-source images significantly better than does an ideal imaging model. Availability of pupil function information will facilitate new approaches to aberration correction in such systems.

© 2003 Optical Society of America

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References

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2002

D. R. Luke, J. V. Burke, and R. G. Lyon, SIAM Rev. 44, 169 (2002).
[CrossRef]

2001

Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, Proc. Natl. Acad. Sci. USA 98, 3790 (2001).
[CrossRef]

1999

1998

1997

1996

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, J. Microsc. 182, 50 (1996).
[CrossRef] [PubMed]

1990

Y. Hiraoka, J. W. Sedat, and D. A. Agard, Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

J. H. Seldin and J. R. Fienup, J. Opt. Soc. Am. A 7, 428 (1990).
[CrossRef]

1989

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, Methods Cell Biol. 30, 44 (1989).

1988

1982

1972

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

1964

Agard, D. A.

Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, Proc. Natl. Acad. Sci. USA 98, 3790 (2001).
[CrossRef]

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, J. Microsc. 182, 50 (1996).
[CrossRef] [PubMed]

Y. Hiraoka, J. W. Sedat, and D. A. Agard, Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, Methods Cell Biol. 30, 44 (1989).

Booth, M. J.

Burke, J. V.

D. R. Luke, J. V. Burke, and R. G. Lyon, SIAM Rev. 44, 169 (2002).
[CrossRef]

Dorband, J. E.

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Gonsalves, R. A.

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[CrossRef]

Gustafsson, M. G. L.

Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, Proc. Natl. Acad. Sci. USA 98, 3790 (2001).
[CrossRef]

Hanser, B.

Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, Proc. Natl. Acad. Sci. USA 98, 3790 (2001).
[CrossRef]

Hiraoka, Y.

Y. Hiraoka, J. W. Sedat, and D. A. Agard, Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, Methods Cell Biol. 30, 44 (1989).

Hollis, J. M.

Kam, Z.

Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, Proc. Natl. Acad. Sci. USA 98, 3790 (2001).
[CrossRef]

Luke, D. R.

D. R. Luke, J. V. Burke, and R. G. Lyon, SIAM Rev. 44, 169 (2002).
[CrossRef]

Lyon, R. G.

McCutchen, C. W.

Neil, M. A. A.

Paxman, R. G.

Philip, J.

J. Philip, J. Mod. Opt. 46, 1031 (1999).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Scalettar, B. A.

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, J. Microsc. 182, 50 (1996).
[CrossRef] [PubMed]

Sedat, J. W.

Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, Proc. Natl. Acad. Sci. USA 98, 3790 (2001).
[CrossRef]

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, J. Microsc. 182, 50 (1996).
[CrossRef] [PubMed]

Y. Hiraoka, J. W. Sedat, and D. A. Agard, Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, Methods Cell Biol. 30, 44 (1989).

Seldin, J. H.

Shaw, P.

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, Methods Cell Biol. 30, 44 (1989).

Sheppard, C. J. R.

C. J. R. Sheppard and P. Torok, J. Microsc. 185, 366 (1997).
[CrossRef]

Swedlow, J. R.

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, J. Microsc. 182, 50 (1996).
[CrossRef] [PubMed]

Torok, P.

C. J. R. Sheppard and P. Torok, J. Microsc. 185, 366 (1997).
[CrossRef]

Wilson, T.

Appl. Opt.

Biophys. J.

Y. Hiraoka, J. W. Sedat, and D. A. Agard, Biophys. J. 57, 325–333 (1990).
[CrossRef] [PubMed]

J. Microsc.

B. A. Scalettar, J. R. Swedlow, J. W. Sedat, and D. A. Agard, J. Microsc. 182, 50 (1996).
[CrossRef] [PubMed]

C. J. R. Sheppard and P. Torok, J. Microsc. 185, 366 (1997).
[CrossRef]

J. Mod. Opt.

J. Philip, J. Mod. Opt. 46, 1031 (1999).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Methods Cell Biol.

D. A. Agard, Y. Hiraoka, P. Shaw, and J. W. Sedat, Methods Cell Biol. 30, 44 (1989).

Opt. Eng.

R. A. Gonsalves, Opt. Eng. 21, 829 (1982).
[CrossRef]

Opt. Lett.

Optik (Stuttgart)

R. W. Gerchberg and W. O. Saxton, Optik (Stuttgart) 35, 237 (1972).

Proc. Natl. Acad. Sci. USA

Z. Kam, B. Hanser, M. G. L. Gustafsson, D. A. Agard, and J. W. Sedat, Proc. Natl. Acad. Sci. USA 98, 3790 (2001).
[CrossRef]

SIAM Rev.

D. R. Luke, J. V. Burke, and R. G. Lyon, SIAM Rev. 44, 169 (2002).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Relations among four ways to characterize 3D imaging properties: FT, Fourier transform; α, aperture angle; other abbreviations defined in text.

Fig. 2
Fig. 2

Phase-retrieved pupil functions based on three different measured PSFs from the same optical system. The gray-scale range is zero to maximum amplitude, and -π/2 to π/2 rad for the phase.

Fig. 3
Fig. 3

Planar XY sections of (a) the measured PSF, (b) a PSF calculated from the central phase-retrieved pupil function in Fig. 2, and (c) a theoretically calculated PSF. The defocus is -2 µm, 0 µm, and +2 µm for the top, center, and bottom rows, respectively. The gray scale ranges between the minimum and the maximum of each image individually.

Fig. 4
Fig. 4

Axial XY sections comparing (top) measured, (middle) phase-retrieved, and (bottom) ideal PSFs. The image scaling is nonlinear to make the weak PSF features visible.

Equations (3)

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

PSFAx,y,z=OTFAkx,ky,kz×expikxx+kyy+kzzdkxdkydkz,
kzkx,ky=2πn/λ2-kx2+ky21/2,
PSAAx,y,z=Pkx,ky×expikzkx,kyzexpikxx+kyydkxdky.

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