Abstract

Phase imaging with a high-resolution wavefront sensor is considered. This is based on a quadriwave lateral shearing interferometer mounted on a non-modified transmission white-light microscope. The measurement technology is explained both in the scope of wave optics and geometrical optics in order to discuss its implementation on a conventional microscope. In particular we consider the effect of a non spatially coherent source on the phase-image signal-to-noise ratio. Precise measurements of the phase-shift introduced by microscopic beads or giant unilamellar vesicles validate the principle and show the accuracy of the methods. Diffraction limited images of living COS-7 cells are then presented, with a particular focus on the membrane and organelle dynamics.

© 2009 Optical Society of America

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  1. F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung”, Z. Tech. Phys.  16, 454–457 (1935).
  2. G. Nomarski, “Nouveau Dispositif Pour l’Observation En Contraste De Phase Differentiel”, J. Phys. Radium  16, S88–S88 (1955).
  3. P. Hariharan, “Achromatic Phase-Shifting for White-Light Interferometry”, Appl. Opt. 35(34), 6823–6824 (1996).
    [Crossref]
  4. C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter”, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, C. J. Cogswell, J. A. Conchello, and T. Wilson, eds. (1997), pp. 72–81.
  5. Y. Xu, Y. x. Xu, M. Hui, and X. Cai, , “Quantitative surface topography determination by differential interference contrast microscopy”, Optics and Precision Engineering  9, 226–229 (2001).
  6. M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
    [Crossref]
  7. S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
    [Crossref]
  8. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging”, Opt. Lett.  24(5), 291–293 (1999).
    [Crossref]
  9. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
    [Crossref]
  10. F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
    [Crossref]
  11. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
    [Crossref] [PubMed]
  12. M. Born and E. Wolf, Principles of Optics, Cambridge University Press (1999).
  13. J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
    [Crossref]
  14. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen”, J. Opt. Soc. Am.  61, 656 (1971).
  15. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy”, Opt. Lett.  23(11), 817–819 (1998).
    [Crossref]
  16. C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
    [Crossref]
  17. C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
    [Crossref] [PubMed]
  18. J. Primot and L. Sogno, “Achromatic three-wave (or more) lateral shearing interferometer”, J. Opt. Soc. Am. A  12(12), 2679 (1995).
    [Crossref]
  19. J. Primot, “Theoretical description of Shack-Hartmann wave-front sensor”, Optics Communications  222, 81–92 (2003).
    [Crossref]
  20. J. Primot and N. Guérineau, “Extended Hartmann Test Based on the Pseudoguiding Property of a Hartmann Mask Completed by a Phase Chessboard”, Appl. Opt.  39(31), 5715–5720 (2000).
    [Crossref]
  21. S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).
  22. M. J. Weber, Handbook of Optical materials, CRC Press (2003).
  23. M. Angelova, S. Soléau, P. Méléard, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields. Kinetics and applications” in Trends in Colloid and Interface Science V Steinkopff Darmstadt, eds., (1992), pp. 127–131.
  24. J. F. Nagle and S. Tristram-Nagle, “Structure of lipid bilayers”, Biochim. Biophys. Acta  1469(3), 159–195 (2000).
  25. C. S. Chong and C. Colbow, “Light scattering and turbidity measurements on lipid vesicles”, Biochim. Biophys. Acta  436, 260–282 (1976).
    [Crossref] [PubMed]
  26. F. C. Jensen, J. Anthony, R. V. G. Girardi, and H. Koprowski (1964), “INFECTION OF HUMAN AND SIMIAN TISSUE CULTURES WITH ROUS SARCOMA VIRUS”, PNAS  52(1), 53–59 (1964).
    [Crossref]
  27. A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes”, Nature Methods  5, 687–695 (2008).
    [Crossref] [PubMed]

2008 (2)

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes”, Nature Methods  5, 687–695 (2008).
[Crossref] [PubMed]

2007 (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

2006 (4)

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
[Crossref]

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

2005 (1)

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

2004 (2)

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
[Crossref]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

2003 (1)

J. Primot, “Theoretical description of Shack-Hartmann wave-front sensor”, Optics Communications  222, 81–92 (2003).
[Crossref]

2001 (1)

Y. Xu, Y. x. Xu, M. Hui, and X. Cai, , “Quantitative surface topography determination by differential interference contrast microscopy”, Optics and Precision Engineering  9, 226–229 (2001).

2000 (2)

J. Primot and N. Guérineau, “Extended Hartmann Test Based on the Pseudoguiding Property of a Hartmann Mask Completed by a Phase Chessboard”, Appl. Opt.  39(31), 5715–5720 (2000).
[Crossref]

J. F. Nagle and S. Tristram-Nagle, “Structure of lipid bilayers”, Biochim. Biophys. Acta  1469(3), 159–195 (2000).

1999 (1)

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging”, Opt. Lett.  24(5), 291–293 (1999).
[Crossref]

1998 (1)

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy”, Opt. Lett.  23(11), 817–819 (1998).
[Crossref]

1996 (1)

P. Hariharan, “Achromatic Phase-Shifting for White-Light Interferometry”, Appl. Opt. 35(34), 6823–6824 (1996).
[Crossref]

1995 (1)

J. Primot and L. Sogno, “Achromatic three-wave (or more) lateral shearing interferometer”, J. Opt. Soc. Am. A  12(12), 2679 (1995).
[Crossref]

1976 (1)

C. S. Chong and C. Colbow, “Light scattering and turbidity measurements on lipid vesicles”, Biochim. Biophys. Acta  436, 260–282 (1976).
[Crossref] [PubMed]

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen”, J. Opt. Soc. Am.  61, 656 (1971).

1964 (1)

F. C. Jensen, J. Anthony, R. V. G. Girardi, and H. Koprowski (1964), “INFECTION OF HUMAN AND SIMIAN TISSUE CULTURES WITH ROUS SARCOMA VIRUS”, PNAS  52(1), 53–59 (1964).
[Crossref]

1955 (1)

G. Nomarski, “Nouveau Dispositif Pour l’Observation En Contraste De Phase Differentiel”, J. Phys. Radium  16, S88–S88 (1955).

1935 (1)

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung”, Z. Tech. Phys.  16, 454–457 (1935).

Abdeli, K.

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

Allman, B. E.

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

Angelova, M.

M. Angelova, S. Soléau, P. Méléard, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields. Kinetics and applications” in Trends in Colloid and Interface Science V Steinkopff Darmstadt, eds., (1992), pp. 127–131.

Anthony, J.

F. C. Jensen, J. Anthony, R. V. G. Girardi, and H. Koprowski (1964), “INFECTION OF HUMAN AND SIMIAN TISSUE CULTURES WITH ROUS SARCOMA VIRUS”, PNAS  52(1), 53–59 (1964).
[Crossref]

Arnison, M. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
[Crossref]

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

Barty, A.

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy”, Opt. Lett.  23(11), 817–819 (1998).
[Crossref]

Bellair, C. J.

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

Bernet, S.

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
[Crossref]

Bertaux, N.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes”, Nature Methods  5, 687–695 (2008).
[Crossref] [PubMed]

Bevilacqua, F.

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging”, Opt. Lett.  24(5), 291–293 (1999).
[Crossref]

Born, M.

M. Born and E. Wolf, Principles of Optics, Cambridge University Press (1999).

Bothorel, P.

M. Angelova, S. Soléau, P. Méléard, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields. Kinetics and applications” in Trends in Colloid and Interface Science V Steinkopff Darmstadt, eds., (1992), pp. 127–131.

Cai, X.

Y. Xu, Y. x. Xu, M. Hui, and X. Cai, , “Quantitative surface topography determination by differential interference contrast microscopy”, Optics and Precision Engineering  9, 226–229 (2001).

Charrière, F.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

Choi, W.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

Chong, C. S.

C. S. Chong and C. Colbow, “Light scattering and turbidity measurements on lipid vesicles”, Biochim. Biophys. Acta  436, 260–282 (1976).
[Crossref] [PubMed]

Cogswell, C. J.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
[Crossref]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter”, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, C. J. Cogswell, J. A. Conchello, and T. Wilson, eds. (1997), pp. 72–81.

Cohen, M.

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

Colbow, C.

C. S. Chong and C. Colbow, “Light scattering and turbidity measurements on lipid vesicles”, Biochim. Biophys. Acta  436, 260–282 (1976).
[Crossref] [PubMed]

Colomb, T.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

Cuche, E.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging”, Opt. Lett.  24(5), 291–293 (1999).
[Crossref]

Curl, C.

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

Curl, C. L.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

Dasari, R. R.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

Delbridge, L. M. D.

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

Demoustier, S.

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

Depeursinge, C.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging”, Opt. Lett.  24(5), 291–293 (1999).
[Crossref]

Emery, Y.

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

Fang-Yen, C.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

Feld, M. S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

Fils, J.

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

Fürhapter, S.

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
[Crossref]

Girardi, R. V. G.

F. C. Jensen, J. Anthony, R. V. G. Girardi, and H. Koprowski (1964), “INFECTION OF HUMAN AND SIMIAN TISSUE CULTURES WITH ROUS SARCOMA VIRUS”, PNAS  52(1), 53–59 (1964).
[Crossref]

Guérineau, N.

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

J. Primot and N. Guérineau, “Extended Hartmann Test Based on the Pseudoguiding Property of a Hartmann Mask Completed by a Phase Chessboard”, Appl. Opt.  39(31), 5715–5720 (2000).
[Crossref]

Haidar, R.

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

Hariharan, P.

P. Hariharan, “Achromatic Phase-Shifting for White-Light Interferometry”, Appl. Opt. 35(34), 6823–6824 (1996).
[Crossref]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter”, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, C. J. Cogswell, J. A. Conchello, and T. Wilson, eds. (1997), pp. 72–81.

Harris, P. J.

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

Hui, M.

Y. Xu, Y. x. Xu, M. Hui, and X. Cai, , “Quantitative surface topography determination by differential interference contrast microscopy”, Optics and Precision Engineering  9, 226–229 (2001).

Jensen, F. C.

F. C. Jensen, J. Anthony, R. V. G. Girardi, and H. Koprowski (1964), “INFECTION OF HUMAN AND SIMIAN TISSUE CULTURES WITH ROUS SARCOMA VIRUS”, PNAS  52(1), 53–59 (1964).
[Crossref]

Jesacher, A.

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
[Crossref]

Koprowski, H.

F. C. Jensen, J. Anthony, R. V. G. Girardi, and H. Koprowski (1964), “INFECTION OF HUMAN AND SIMIAN TISSUE CULTURES WITH ROUS SARCOMA VIRUS”, PNAS  52(1), 53–59 (1964).
[Crossref]

Kuehn, J.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

Larkin, K. G.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
[Crossref]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter”, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, C. J. Cogswell, J. A. Conchello, and T. Wilson, eds. (1997), pp. 72–81.

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

Magistretti, P. J.

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

Marguet, D.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes”, Nature Methods  5, 687–695 (2008).
[Crossref] [PubMed]

Marian, A.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

Marquet, P.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

Martin, L.

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

Maurer, C.

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
[Crossref]

Méléard, P.

M. Angelova, S. Soléau, P. Méléard, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields. Kinetics and applications” in Trends in Colloid and Interface Science V Steinkopff Darmstadt, eds., (1992), pp. 127–131.

Montfort, F.

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

Nagle, J. F.

J. F. Nagle and S. Tristram-Nagle, “Structure of lipid bilayers”, Biochim. Biophys. Acta  1469(3), 159–195 (2000).

Nomarski, G.

G. Nomarski, “Nouveau Dispositif Pour l’Observation En Contraste De Phase Differentiel”, J. Phys. Radium  16, S88–S88 (1955).

Nugent, K. A.

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy”, Opt. Lett.  23(11), 817–819 (1998).
[Crossref]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

Paganin, D.

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy”, Opt. Lett.  23(11), 817–819 (1998).
[Crossref]

Platt, B. C.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen”, J. Opt. Soc. Am.  61, 656 (1971).

Primot, J.

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

J. Primot, “Theoretical description of Shack-Hartmann wave-front sensor”, Optics Communications  222, 81–92 (2003).
[Crossref]

J. Primot and N. Guérineau, “Extended Hartmann Test Based on the Pseudoguiding Property of a Hartmann Mask Completed by a Phase Chessboard”, Appl. Opt.  39(31), 5715–5720 (2000).
[Crossref]

J. Primot and L. Sogno, “Achromatic three-wave (or more) lateral shearing interferometer”, J. Opt. Soc. Am. A  12(12), 2679 (1995).
[Crossref]

Rappaz, B.

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

Rigneault, H.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes”, Nature Methods  5, 687–695 (2008).
[Crossref] [PubMed]

Ritsch-Marte, M.

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
[Crossref]

Roberts, A.

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy”, Opt. Lett.  23(11), 817–819 (1998).
[Crossref]

Sauteret, C.

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

Sautivet, A.

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

Sergé, A.

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes”, Nature Methods  5, 687–695 (2008).
[Crossref] [PubMed]

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen”, J. Opt. Soc. Am.  61, 656 (1971).

Sheppard, C. J. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
[Crossref]

Smith, N. I.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
[Crossref]

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter”, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, C. J. Cogswell, J. A. Conchello, and T. Wilson, eds. (1997), pp. 72–81.

Sogno, L.

J. Primot and L. Sogno, “Achromatic three-wave (or more) lateral shearing interferometer”, J. Opt. Soc. Am. A  12(12), 2679 (1995).
[Crossref]

Soléau, S.

M. Angelova, S. Soléau, P. Méléard, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields. Kinetics and applications” in Trends in Colloid and Interface Science V Steinkopff Darmstadt, eds., (1992), pp. 127–131.

Tristram-Nagle, S.

J. F. Nagle and S. Tristram-Nagle, “Structure of lipid bilayers”, Biochim. Biophys. Acta  1469(3), 159–195 (2000).

Velghe, S.

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

Wattellier, B.

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

Weber, M. J.

M. J. Weber, Handbook of Optical materials, CRC Press (2003).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, Cambridge University Press (1999).

Xu, Y.

Y. Xu, Y. x. Xu, M. Hui, and X. Cai, , “Quantitative surface topography determination by differential interference contrast microscopy”, Optics and Precision Engineering  9, 226–229 (2001).

Xu, Y. x.

Y. Xu, Y. x. Xu, M. Hui, and X. Cai, , “Quantitative surface topography determination by differential interference contrast microscopy”, Optics and Precision Engineering  9, 226–229 (2001).

Zernike, F.

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung”, Z. Tech. Phys.  16, 454–457 (1935).

Zou, J.

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

Appl. Opt. (3)

P. Hariharan, “Achromatic Phase-Shifting for White-Light Interferometry”, Appl. Opt. 35(34), 6823–6824 (1996).
[Crossref]

J. Zou, A. Sautivet, J. Fils, L. Martin, K. Abdeli, C. Sauteret, and B. Wattellier, “Optimization of the dynamic wavefront control of a pulsed kilojoule/nanosecond-petawatt laser facility”, Appl. Opt.  47(5), 704–710 (2008).
[Crossref]

J. Primot and N. Guérineau, “Extended Hartmann Test Based on the Pseudoguiding Property of a Hartmann Mask Completed by a Phase Chessboard”, Appl. Opt.  39(31), 5715–5720 (2000).
[Crossref]

Biochim. Biophys. Acta (2)

J. F. Nagle and S. Tristram-Nagle, “Structure of lipid bilayers”, Biochim. Biophys. Acta  1469(3), 159–195 (2000).

C. S. Chong and C. Colbow, “Light scattering and turbidity measurements on lipid vesicles”, Biochim. Biophys. Acta  436, 260–282 (1976).
[Crossref] [PubMed]

Cellular Physiology and Biochemistry (1)

C. Curl, C. J. Bellair, P. J. Harris, B. E. Allman, A. Roberts, K. A. Nugent, and L. M. D. Delbridge, “Single cell volume measurement by Quantitative Phase Microscopy (QPM): A case study of Erythrocyte Morphology”, Cellular Physiology and Biochemistry  17, 193–200 (2006).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen”, J. Opt. Soc. Am.  61, 656 (1971).

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

J. Primot and L. Sogno, “Achromatic three-wave (or more) lateral shearing interferometer”, J. Opt. Soc. Am. A  12(12), 2679 (1995).
[Crossref]

J. Phys. Radium (1)

G. Nomarski, “Nouveau Dispositif Pour l’Observation En Contraste De Phase Differentiel”, J. Phys. Radium  16, S88–S88 (1955).

Journal of Microscopy (1)

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, , “Linear phase imaging using differential interference contrast microscopy”, Journal of Microscopy  214(1), 7–12 (2004).
[Crossref]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, and L. M. D. Delbridge, “Quantitative phase amplitude microscopy IV: imaging thick specimens”, Journal of microscopy  214(1), 62–68 (2004).
[Crossref]

Nature Methods (2)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy”, Nature Methods  4, 717–719 (2007).
[Crossref] [PubMed]

A. Sergé, N. Bertaux, H. Rigneault, and D. Marguet, “Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes”, Nature Methods  5, 687–695 (2008).
[Crossref] [PubMed]

Opt. Express (1)

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, , “Quantitative imaging of complex samples by spiral phase contrast microscopy”, Opt. Express  14(9), 3792–3805 (2006).
[Crossref]

Opt. Lett. (4)

E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging”, Opt. Lett.  24(5), 291–293 (1999).
[Crossref]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrastimaging technique allowing quantitative visualization ofliving cells with subwavelength axial accuracy”, Opt. Lett.  30(5), 468–470 (2005).
[Crossref]

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy”, Opt. Lett.  31(2), 178–180 (2006).
[Crossref]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy”, Opt. Lett.  23(11), 817–819 (1998).
[Crossref]

Optics and Precision Engineering (1)

Y. Xu, Y. x. Xu, M. Hui, and X. Cai, , “Quantitative surface topography determination by differential interference contrast microscopy”, Optics and Precision Engineering  9, 226–229 (2001).

Optics Communications (1)

J. Primot, “Theoretical description of Shack-Hartmann wave-front sensor”, Optics Communications  222, 81–92 (2003).
[Crossref]

PNAS (1)

F. C. Jensen, J. Anthony, R. V. G. Girardi, and H. Koprowski (1964), “INFECTION OF HUMAN AND SIMIAN TISSUE CULTURES WITH ROUS SARCOMA VIRUS”, PNAS  52(1), 53–59 (1964).
[Crossref]

Proc. SPIE (1)

S. Velghe, J. Primot, N. Guérineau, R. Haidar, S. Demoustier, M. Cohen, and B. Wattellier, “Advanced wave-front sensing by quadri-wave lateral shearing interferometry”, Proc. SPIE (2006).

Z. Tech. Phys. (1)

F. Zernike, “Das Phasenkontrastverfahren bei der mikroskopischen Beobachtung”, Z. Tech. Phys.  16, 454–457 (1935).

Other (4)

C. J. Cogswell, N. I. Smith, K. G. Larkin, and P. Hariharan, “Quantitative DIC microscopy using a geometric phase shifter”, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, C. J. Cogswell, J. A. Conchello, and T. Wilson, eds. (1997), pp. 72–81.

M. Born and E. Wolf, Principles of Optics, Cambridge University Press (1999).

M. J. Weber, Handbook of Optical materials, CRC Press (2003).

M. Angelova, S. Soléau, P. Méléard, and P. Bothorel, “Preparation of giant vesicles by external AC electric fields. Kinetics and applications” in Trends in Colloid and Interface Science V Steinkopff Darmstadt, eds., (1992), pp. 127–131.

Supplementary Material (2)

» Media 1: AVI (14264 KB)     
» Media 2: AVI (3890 KB)     

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Figures (9)

Fig. 1.
Fig. 1.

Schematic layout of the setup.

Fig. 2.
Fig. 2.

(a) Ideal transparency for a 4-wave-only 2D diffraction grating. (b) MHM transparency, approximation of (a). (c) Intensity transmission of (a). (d) 1D interferogram formation by a MHM in the case of a disturbed input wavefront; geometrical approach. (e) 2D interferogram formation by a MHM in the case of a plane input wavefront; visualization of the 4 diffracted waves (arrows).

Fig. 3.
Fig. 3.

(a) Interferogram obtained with an aberrant wavefront. (b) Zoom on a part of (a), visualization of the local frequency modulations. (c) Fourier Transform of (a). (d) Obtaining of 2 OPD orthogonal gradients by Inverse Fourier Transform of 2 sub-images of (b). (e) 2D Integration of the gradients to reconstruct the OPD.

Fig. 4.
Fig. 4.

Principle of the interferogram formation in case of an incoherent illumination.

Fig. 5.
Fig. 5.

Diminution of the sensitivity according to the spatial coherence of the source.

Fig. 6.
Fig. 6.

Contrast comparison of simulated interferograms and acquired interferograms, for different input illumination numerical apertures. Obtained with z=1420mm, p=29.6µm and gy =20.

Fig. 7.
Fig. 7.

(a) Intensity image of a 5µm polystyrene bead, in imaging conditions with SID4-HR, into a n=1.552 transparent liquid hydrocarbon ; (b) Phase measurement (false colors) ; (c) 3D phase visualization (false colors); (d) Phase shift profile along the center of the bead, comparison between measurement and model.

Fig. 8.
Fig. 8.

(a) Intensity image, in imaging conditions, of a DPPC GUV without optical index difference between inside and outside the GUV ; (b) Phase-shift image ; (c) Phase-shift value compared to the distance from the GUV center. Red squares : Azimuthal average of the phase-shift map; the symmetry before and after x=0 is explained by the complete 2π averaging. Vertical red lines : error bars, Azimuthal standard deviation. Solid black line : Theoretical phase-shift profile obtained for D=16.65µm, e=3.85nm and δn=nDPPC -nmedium =0.128.

Fig. 9.
Fig. 9.

Single frame excerpts from (Media 1), (Media 2). (a) Intensity image, in imaging conditions, of COS-7 cells ; (b) Phase image.

Equations (20)

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

A (r)=I(r)exp(i[k·rφ(r)])
φ(r)=2πλOPD+φ(r0)
t (x,y)=cos(πxp) · c o s (πyp)
T(x,y)=t(x,y)2=14{1+[cos(2πpx)+cos(2πpy)]+12[cos(2πp(x+y))+cos(2πp(xy))]}
I(r,z)=I0{1+[cos(2πpx+2πpzOPDx)+cos(2πpy+2πpzOPDy)]+12[cos(2πp(x+y)+2πpzOPD(x+y))+cos(2πp(xy)+2πpzOPD(xy))]}
δ=z·OPD
HxHy=2πpzOPDxOPDy
I(x,y)= Sd2I(x,y,xs,ys)
d2 I(x,y,xs,ys)=Iponc(x+xs,y+ys)S·dxsdys
Iponct(x,y)=I0· [1+cos(Kx)+cos(Ky)+12cos(2Kx+y2)+12cos(2Kxy2)]
I(x,y)=ϕs=02πrs=0RIponct(x+rs·cos(ϕs),y+rs·sin(ϕs))πR2·rsdrsdϕs
I(x,y)=I0[1+M(KR)[cos(Kx)+cos(Ky)]+12M(2KR)[cos(K[x+y])+cos(K[xy])]]
M(X)=2J1(X)X
R(D)=z·tan(θo)gy×11z·DfTL2=Rafocal×11z·DfTL2
SNRrelative(KR)=M(KR)ImaxI0
Imax,minI0 {1+2·M(KR)+M(2KR)1M(2KR)12·M(KR)+M(2KR)
r=0.61×λNAobj
4·a=pr·gy
C=max(I)min(I)max(I)+min(I)=ImaxIminImax+Imin
δ(x)={φmaxcos[arcsin(2xD)]ifx<D20else

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