Abstract

We present a new Fourier-based exact solution for deterministic phase unwrapping from experimental maps of wrapped phase in the presence of noise and phase vortices. This single-step approach has superior performance for images with high phase gradients or insufficient digital sampling approaching 2<i>π</i>/pixel and therefore performs as a fast and practical solution for the phase-unwrapping problem for experimental applications in applied optics, physics, and medicine.

© 2003 Optical Society of America

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  1. A. V. Oppenheim and R. W. Schafer, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).
  2. H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).
  3. L. N. Mertz, Appl. Opt. 18, 611 (1979).
  4. G. H. Kaufmann and G. E. Galizzi, Appl. Opt. 41, 7254 (2002).
  5. D. L. Fried, Opt. Commun. 200, 43 (2001).
  6. P. E. Downing, Y. Jiang, M. Shuman, and N. Kanwisher, Science 293, 2470 (2001).
  7. R. Cusack and N. Papadakis, Neuroimage 16, 754 (2002).
  8. V. Pascazio and G. Schirinzi, IEEE Trans. Image Process. 11, 1478 (2002).
  9. E. Volkl, L. F. Allard, and D. C. Joy, eds., Introduction to Electron Holography (Plenum, New York, 1999).
  10. S. Stramaglia, A. Refice, and L. Guerriero, Physica A 276, 521 (2000).
  11. C. F. Lo, X. Peng, and L. L. Cai, Optik 113, 439 (2002).
  12. P. Soille, Opt. Lasers Eng. 32, 339 (2000).
  13. S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, IEEE Trans. Image Process. 4, 667 (1995).
  14. M. A. Schofield and Y. Zhu, Microsc. Microanal. Microstruct. 8(Suppl. 2), 532 CD (2002).
  15. V. V. Volkov and Y. Zhu, Phys. Rev. Lett. 91, 043904 (2003).
  16. V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).

2003

V. V. Volkov and Y. Zhu, Phys. Rev. Lett. 91, 043904 (2003).

2002

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).

G. H. Kaufmann and G. E. Galizzi, Appl. Opt. 41, 7254 (2002).

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2002).

V. Pascazio and G. Schirinzi, IEEE Trans. Image Process. 11, 1478 (2002).

C. F. Lo, X. Peng, and L. L. Cai, Optik 113, 439 (2002).

M. A. Schofield and Y. Zhu, Microsc. Microanal. Microstruct. 8(Suppl. 2), 532 CD (2002).

2001

D. L. Fried, Opt. Commun. 200, 43 (2001).

P. E. Downing, Y. Jiang, M. Shuman, and N. Kanwisher, Science 293, 2470 (2001).

2000

S. Stramaglia, A. Refice, and L. Guerriero, Physica A 276, 521 (2000).

P. Soille, Opt. Lasers Eng. 32, 339 (2000).

1999

E. Volkl, L. F. Allard, and D. C. Joy, eds., Introduction to Electron Holography (Plenum, New York, 1999).

1995

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, IEEE Trans. Image Process. 4, 667 (1995).

1985

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).

1979

1975

A. V. Oppenheim and R. W. Schafer, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Cai, L. L.

C. F. Lo, X. Peng, and L. L. Cai, Optik 113, 439 (2002).

Cusack, R.

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2002).

De Graef, M.

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).

Downing, P. E.

P. E. Downing, Y. Jiang, M. Shuman, and N. Kanwisher, Science 293, 2470 (2001).

Fried, D. L.

D. L. Fried, Opt. Commun. 200, 43 (2001).

Galizzi, G. E.

Ghiglia, D. C.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).

Glover, G. H.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, IEEE Trans. Image Process. 4, 667 (1995).

Guerriero, L.

S. Stramaglia, A. Refice, and L. Guerriero, Physica A 276, 521 (2000).

Hjalmarson, H. P.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).

Jiang, Y.

P. E. Downing, Y. Jiang, M. Shuman, and N. Kanwisher, Science 293, 2470 (2001).

Jones, E. D.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).

Kanwisher, N.

P. E. Downing, Y. Jiang, M. Shuman, and N. Kanwisher, Science 293, 2470 (2001).

Kaufmann, G. H.

Lo, C. F.

C. F. Lo, X. Peng, and L. L. Cai, Optik 113, 439 (2002).

Mertz, L. N.

Napel, S.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, IEEE Trans. Image Process. 4, 667 (1995).

Norris, C. B.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).

Oppenheim, A. V.

A. V. Oppenheim and R. W. Schafer, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Papadakis, N.

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2002).

Pascazio, V.

V. Pascazio and G. Schirinzi, IEEE Trans. Image Process. 11, 1478 (2002).

Pelc, N. J.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, IEEE Trans. Image Process. 4, 667 (1995).

Peng, X.

C. F. Lo, X. Peng, and L. L. Cai, Optik 113, 439 (2002).

Refice, A.

S. Stramaglia, A. Refice, and L. Guerriero, Physica A 276, 521 (2000).

Romero, L. A.

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).

Schafer, R. W.

A. V. Oppenheim and R. W. Schafer, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

Schirinzi, G.

V. Pascazio and G. Schirinzi, IEEE Trans. Image Process. 11, 1478 (2002).

Schofield, M. A.

M. A. Schofield and Y. Zhu, Microsc. Microanal. Microstruct. 8(Suppl. 2), 532 CD (2002).

Shuman, M.

P. E. Downing, Y. Jiang, M. Shuman, and N. Kanwisher, Science 293, 2470 (2001).

Soille, P.

P. Soille, Opt. Lasers Eng. 32, 339 (2000).

Song, S. M.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, IEEE Trans. Image Process. 4, 667 (1995).

Stramaglia, S.

S. Stramaglia, A. Refice, and L. Guerriero, Physica A 276, 521 (2000).

Volkov, V. V.

V. V. Volkov and Y. Zhu, Phys. Rev. Lett. 91, 043904 (2003).

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).

Zhu, Y.

V. V. Volkov and Y. Zhu, Phys. Rev. Lett. 91, 043904 (2003).

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).

M. A. Schofield and Y. Zhu, Microsc. Microanal. Microstruct. 8(Suppl. 2), 532 CD (2002).

Appl. Opt.

IEEE Trans. Image Process.

S. M. Song, S. Napel, N. J. Pelc, and G. H. Glover, IEEE Trans. Image Process. 4, 667 (1995).

V. Pascazio and G. Schirinzi, IEEE Trans. Image Process. 11, 1478 (2002).

Micron

V. V. Volkov, Y. Zhu, and M. De Graef, Micron 33, 411 (2002).

Microsc. Microanal. Microstruct.

M. A. Schofield and Y. Zhu, Microsc. Microanal. Microstruct. 8(Suppl. 2), 532 CD (2002).

Neuroimage

R. Cusack and N. Papadakis, Neuroimage 16, 754 (2002).

Opt. Commun.

D. L. Fried, Opt. Commun. 200, 43 (2001).

Opt. Lasers Eng.

P. Soille, Opt. Lasers Eng. 32, 339 (2000).

Optik

C. F. Lo, X. Peng, and L. L. Cai, Optik 113, 439 (2002).

Phys. Rev. B

H. P. Hjalmarson, L. A. Romero, D. C. Ghiglia, E. D. Jones, and C. B. Norris, Phys. Rev. B 32, 4300 (1985).

Phys. Rev. Lett.

V. V. Volkov and Y. Zhu, Phys. Rev. Lett. 91, 043904 (2003).

Physica A

S. Stramaglia, A. Refice, and L. Guerriero, Physica A 276, 521 (2000).

Science

P. E. Downing, Y. Jiang, M. Shuman, and N. Kanwisher, Science 293, 2470 (2001).

Other

E. Volkl, L. F. Allard, and D. C. Joy, eds., Introduction to Electron Holography (Plenum, New York, 1999).

A. V. Oppenheim and R. W. Schafer, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975).

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