Abstract

It is shown that the spatial frequencies recorded in interferometric synthetic aperture microscopy do not correspond to exact backscattering [as they do in unistatic synthetic aperture radar (SAR)] and that the reconstruction process based on SAR is therefore based on an approximation. The spatial frequency response is developed based on the three-dimensional coherent transfer function approach and compared with that in optical coherence tomography and digital holographic microscopy.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Inverse scattering for optical coherence tomography,” J. Opt. Soc. Am. A 23, 1027–1037 (2006).
    [CrossRef]
  2. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
    [CrossRef]
  3. D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A 24, 1034–1041 (2007).
    [CrossRef]
  4. B. J. Davis, T. S. Ralston, D. L. Marks, S. A. Boppart, and P. S. Carney, “Autocorrelation artifacts in optical coherence tomography and interferometric synthetic aperture microscopy,” Opt. Lett. 32, 1441–1443 (2007).
    [CrossRef]
  5. B. J. Davis, S. Schlachter, D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Non-paraxial vector-field modeling of optical coherence tomography and interferometric synthetic aperture microscopy,” J. Opt. Soc. Am. A 24, 2527–2542 (2007).
    [CrossRef]
  6. T. S. Ralston, G. L. Charvat, S. G. Adie, B. J. Davis, P. S. Carney, and S. A. Boppart, “Microscopic laser radar,” Opt. Photon. News 21(6), 32–38 (2010).
    [CrossRef]
  7. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
    [CrossRef]
  8. J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
    [CrossRef]
  9. A. Dubois, L. Vabre, A.-C. Boccara, and E. Beaurepaire, “High-resolution full-field optical coherence tomography with a Linnik microscope,” Appl. Opt. 41, 805–812 (2002).
    [CrossRef]
  10. M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
    [CrossRef]
  11. M. Roy, C. J. R. Sheppard, and P. Hariharan, “Low-coherence interference microscopy using a ferro-electric liquid crystal phase-modulator,” Opt. Express 12, 2512–2516 (2004).
    [CrossRef]
  12. D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta 29, 1573–1577 (1982).
    [CrossRef]
  13. E. Cuche, F. Bevilacqua, and C. Depeursinge, “Digital holography for quantitative phase-contrast imaging,” Opt. Lett. 24, 291–293 (1999).
    [CrossRef]
  14. V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
    [CrossRef]
  15. F. Charrière, M. A. F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006).
    [CrossRef]
  16. W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Extended depth of focus in tomographic phase microscopy using a propagation algorithm,” Opt. Lett. 33, 171–173 (2008).
    [CrossRef]
  17. J. Kuehn, F. Montfort, T. Colomb, B. Rappaz, C. Moratal, N. Pavillon, P. Marquet, and C. Depeursinge, “Submicrometer tomography of cells by multiple wavelength digital holographic microscopy in reflection,” Opt. Lett. 34, 653–655 (2009).
    [CrossRef]
  18. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
    [CrossRef]
  19. C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43, 1493–1502 (2004).
    [CrossRef]
  20. S. S. Kou and C. J. R. Sheppard, “Imaging in digital holographic microscopy,” Opt. Express 15, 13640–13648 (2007).
    [CrossRef]
  21. R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323–328 (1970).
    [CrossRef]
  22. C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).
  23. C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
    [CrossRef]
  24. C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional imaging in confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), pp. 143–169.
  25. C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in conventional and scanning microscopes,” Phil. Trans. R. Soc. A 295, 513–536 (1980).
    [CrossRef]
  26. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–244 (1964).
    [CrossRef]
  27. C. J. R. Sheppard, M. Gu, and X. Q. Mao, “Three-dimensional coherent transfer function in a reflection-mode confocal scanning microscope,” Opt. Commun. 81, 281–284 (1991).
    [CrossRef]
  28. C. J. R. Sheppard, M. Gu, Y. Kawata, and S. Kawata, “Three-dimensional transfer functions for high aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
    [CrossRef]
  29. T. Sawatari, “Optical heterodyne scanning microscope,” Appl. Opt. 12, 2768–2772 (1973).
    [CrossRef]
  30. M. Kempe and W. Rudolf, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A 13, 46–52 (1996).
    [CrossRef]
  31. M. Gu, X. Gan, and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in fibre optical confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
    [CrossRef]
  32. M. Villiger and T. Lasser, “Image formation and tomogram reconstruction in optical coherence microscopy,” J. Opt. Soc. Am. A 27, 2216–2228 (2010).
    [CrossRef]
  33. C. J. R. Sheppard and T. Wilson, “The theory of scanning microscopes with Gaussian pupil functions,” J. Microsc. 114, 179–197 (1978).
    [CrossRef]
  34. C. J. R. Sheppard, H. Fatemi, and M. Gu, “The Fourier optics of near-field microscopy,” Scanning 17, 28–40 (1995).
    [CrossRef]
  35. M. Gu and C. J. R. Sheppard, “Fibre-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
    [CrossRef]
  36. G. S. Kino, “Acoustic imaging for nondestructive evaluation,” Proc. IEEE 67, 510–525 (1979).
    [CrossRef]
  37. G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
    [CrossRef]
  38. C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
    [CrossRef]
  39. M. Gu and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in confocal imaging with two unequal annular lenses,” J. Mod. Opt. 40, 1255–1272 (1993).
    [CrossRef]
  40. C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).
  41. C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
    [CrossRef]
  42. C. J. R. Sheppard and T. Wilson, “Imaging properties of annular lenses,” Appl. Opt. 18, 3764–3769 (1979).
    [CrossRef]
  43. R. J. Wombell and J. A. De Santo, “Reconstruction of rough-surface profiles with the Kirchhoff approximation,” J. Opt. Soc. Am. A 8, 1892–1897 (1991).
    [CrossRef]
  44. C. H. Greenewalt, W. Brandt, and D. D. Friel, “Irridescent colors of hummingbird feathers,” J. Opt. Soc. Am. 50, 1005–1013 (1960).
    [CrossRef]
  45. C. J. R. Sheppard, “Approximate calculation of the reflection coefficient from a stratified medium,” Pure Appl. Opt. 4, 665–669(1995).
    [CrossRef]
  46. L. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).
  47. C. J. R. Sheppard, T. J. Connolly, and M. Gu, “The scattering potential for imaging in the reflection geometry,” Opt. Commun. 117, 16–19 (1995).
    [CrossRef]
  48. C. J. R. Sheppard and F. Aguilar, “Fresnel coefficients for weak reflection and the scattering potential for three-dimensional imaging,” Opt. Commun. 162, 182–186 (1999).
    [CrossRef]
  49. C. J. R. Sheppard, “Scattering and the spatial frequency representation,” in Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin, ed. (Springer, 2007), pp. 61–92.
  50. P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
    [CrossRef]
  51. M. Gu and C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
    [CrossRef]

2010 (2)

T. S. Ralston, G. L. Charvat, S. G. Adie, B. J. Davis, P. S. Carney, and S. A. Boppart, “Microscopic laser radar,” Opt. Photon. News 21(6), 32–38 (2010).
[CrossRef]

M. Villiger and T. Lasser, “Image formation and tomogram reconstruction in optical coherence microscopy,” J. Opt. Soc. Am. A 27, 2216–2228 (2010).
[CrossRef]

2009 (1)

2008 (1)

2007 (5)

2006 (2)

2004 (3)

2002 (3)

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef]

M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[CrossRef]

A. Dubois, L. Vabre, A.-C. Boccara, and E. Beaurepaire, “High-resolution full-field optical coherence tomography with a Linnik microscope,” Appl. Opt. 41, 805–812 (2002).
[CrossRef]

1999 (2)

C. J. R. Sheppard and F. Aguilar, “Fresnel coefficients for weak reflection and the scattering potential for three-dimensional imaging,” Opt. Commun. 162, 182–186 (1999).
[CrossRef]

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

1998 (1)

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

1996 (1)

1995 (4)

C. J. R. Sheppard, “Approximate calculation of the reflection coefficient from a stratified medium,” Pure Appl. Opt. 4, 665–669(1995).
[CrossRef]

C. J. R. Sheppard, T. J. Connolly, and M. Gu, “The scattering potential for imaging in the reflection geometry,” Opt. Commun. 117, 16–19 (1995).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

C. J. R. Sheppard, H. Fatemi, and M. Gu, “The Fourier optics of near-field microscopy,” Scanning 17, 28–40 (1995).
[CrossRef]

1994 (2)

1993 (2)

M. Gu and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in confocal imaging with two unequal annular lenses,” J. Mod. Opt. 40, 1255–1272 (1993).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Fibre-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

1991 (4)

C. J. R. Sheppard, M. Gu, and X. Q. Mao, “Three-dimensional coherent transfer function in a reflection-mode confocal scanning microscope,” Opt. Commun. 81, 281–284 (1991).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

M. Gu, X. Gan, and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in fibre optical confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

R. J. Wombell and J. A. De Santo, “Reconstruction of rough-surface profiles with the Kirchhoff approximation,” J. Opt. Soc. Am. A 8, 1892–1897 (1991).
[CrossRef]

1990 (1)

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

1986 (1)

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

1982 (1)

D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta 29, 1573–1577 (1982).
[CrossRef]

1980 (1)

C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in conventional and scanning microscopes,” Phil. Trans. R. Soc. A 295, 513–536 (1980).
[CrossRef]

1979 (2)

G. S. Kino, “Acoustic imaging for nondestructive evaluation,” Proc. IEEE 67, 510–525 (1979).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Imaging properties of annular lenses,” Appl. Opt. 18, 3764–3769 (1979).
[CrossRef]

1978 (1)

C. J. R. Sheppard and T. Wilson, “The theory of scanning microscopes with Gaussian pupil functions,” J. Microsc. 114, 179–197 (1978).
[CrossRef]

1977 (2)

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

1973 (1)

1971 (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

1970 (1)

R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323–328 (1970).
[CrossRef]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

1964 (1)

1960 (1)

Adie, S. G.

T. S. Ralston, G. L. Charvat, S. G. Adie, B. J. Davis, P. S. Carney, and S. A. Boppart, “Microscopic laser radar,” Opt. Photon. News 21(6), 32–38 (2010).
[CrossRef]

Aguilar, F.

C. J. R. Sheppard and F. Aguilar, “Fresnel coefficients for weak reflection and the scattering potential for three-dimensional imaging,” Opt. Commun. 162, 182–186 (1999).
[CrossRef]

Badizadegan, K.

Beaurepaire, E.

Bevilacqua, F.

Boccara, A.-C.

Boppart, S. A.

Brandt, W.

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).

Carney, P. S.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Charrière, F.

Charvat, G. L.

T. S. Ralston, G. L. Charvat, S. G. Adie, B. J. Davis, P. S. Carney, and S. A. Boppart, “Microscopic laser radar,” Opt. Photon. News 21(6), 32–38 (2010).
[CrossRef]

Chaumet, P. C.

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

Choi, W.

Choudhury, A.

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

Cogswell, C. J.

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional imaging in confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), pp. 143–169.

Colomb, T.

Connolly, T. J.

C. J. R. Sheppard, T. J. Connolly, and M. Gu, “The scattering potential for imaging in the reflection geometry,” Opt. Commun. 117, 16–19 (1995).
[CrossRef]

Cuche, E.

Dändliker, R.

R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323–328 (1970).
[CrossRef]

Dasari, R. R.

Davis, B. J.

De Santo, J. A.

Depeursinge, C.

Deschamps, G. A.

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

Dubois, A.

Fang-Yen, C.

Fatemi, H.

C. J. R. Sheppard, H. Fatemi, and M. Gu, “The Fourier optics of near-field microscopy,” Scanning 17, 28–40 (1995).
[CrossRef]

Feld, M. S.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Friel, D. D.

Fujimoto, J. G.

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Gan, X.

Greenewalt, C. H.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Gu, M.

C. J. R. Sheppard, T. J. Connolly, and M. Gu, “The scattering potential for imaging in the reflection geometry,” Opt. Commun. 117, 16–19 (1995).
[CrossRef]

C. J. R. Sheppard, H. Fatemi, and M. Gu, “The Fourier optics of near-field microscopy,” Scanning 17, 28–40 (1995).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

C. J. R. Sheppard, M. Gu, Y. Kawata, and S. Kawata, “Three-dimensional transfer functions for high aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in confocal imaging with two unequal annular lenses,” J. Mod. Opt. 40, 1255–1272 (1993).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Fibre-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

C. J. R. Sheppard, M. Gu, and X. Q. Mao, “Three-dimensional coherent transfer function in a reflection-mode confocal scanning microscope,” Opt. Commun. 81, 281–284 (1991).
[CrossRef]

M. Gu, X. Gan, and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in fibre optical confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

Hamilton, D. K.

D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta 29, 1573–1577 (1982).
[CrossRef]

Hariharan, P.

Hee, M. R.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Izatt, J. A.

Kawata, S.

Kawata, Y.

Kempe, M.

Kino, G. S.

G. S. Kino, “Acoustic imaging for nondestructive evaluation,” Proc. IEEE 67, 510–525 (1979).
[CrossRef]

Kou, S. S.

Kuehn, J.

Kühn, J.

Lasser, T.

Lauer, V.

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef]

Lee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Mao, X. Q.

C. J. R. Sheppard, M. Gu, and X. Q. Mao, “Three-dimensional coherent transfer function in a reflection-mode confocal scanning microscope,” Opt. Commun. 81, 281–284 (1991).
[CrossRef]

Marks, D. L.

Marquet, P.

McCutchen, C. W.

Montfort, F.

Montfort, M. A. F.

Moratal, C.

Owen, G. M.

Pavillon, N.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Rahmani, A.

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

Ralston, T. S.

Rappaz, B.

Roy, M.

Rudolf, W.

Saghafi, S.

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

Sawatari, T.

Schlachter, S.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Sentenac, A.

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

Sharma, M. D.

Sheppard, C. J. R.

S. S. Kou and C. J. R. Sheppard, “Imaging in digital holographic microscopy,” Opt. Express 15, 13640–13648 (2007).
[CrossRef]

M. Roy, C. J. R. Sheppard, and P. Hariharan, “Low-coherence interference microscopy using a ferro-electric liquid crystal phase-modulator,” Opt. Express 12, 2512–2516 (2004).
[CrossRef]

C. J. R. Sheppard, M. Roy, and M. D. Sharma, “Image formation in low-coherence and confocal interference microscopes,” Appl. Opt. 43, 1493–1502 (2004).
[CrossRef]

M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[CrossRef]

C. J. R. Sheppard and F. Aguilar, “Fresnel coefficients for weak reflection and the scattering potential for three-dimensional imaging,” Opt. Commun. 162, 182–186 (1999).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

C. J. R. Sheppard, “Approximate calculation of the reflection coefficient from a stratified medium,” Pure Appl. Opt. 4, 665–669(1995).
[CrossRef]

C. J. R. Sheppard, H. Fatemi, and M. Gu, “The Fourier optics of near-field microscopy,” Scanning 17, 28–40 (1995).
[CrossRef]

C. J. R. Sheppard, T. J. Connolly, and M. Gu, “The scattering potential for imaging in the reflection geometry,” Opt. Commun. 117, 16–19 (1995).
[CrossRef]

C. J. R. Sheppard, M. Gu, Y. Kawata, and S. Kawata, “Three-dimensional transfer functions for high aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in confocal imaging with two unequal annular lenses,” J. Mod. Opt. 40, 1255–1272 (1993).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Fibre-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

C. J. R. Sheppard, M. Gu, and X. Q. Mao, “Three-dimensional coherent transfer function in a reflection-mode confocal scanning microscope,” Opt. Commun. 81, 281–284 (1991).
[CrossRef]

M. Gu, X. Gan, and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in fibre optical confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta 29, 1573–1577 (1982).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in conventional and scanning microscopes,” Phil. Trans. R. Soc. A 295, 513–536 (1980).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Imaging properties of annular lenses,” Appl. Opt. 18, 3764–3769 (1979).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “The theory of scanning microscopes with Gaussian pupil functions,” J. Microsc. 114, 179–197 (1978).
[CrossRef]

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

C. J. R. Sheppard, “Scattering and the spatial frequency representation,” in Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin, ed. (Springer, 2007), pp. 61–92.

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional imaging in confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), pp. 143–169.

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Swanson, E. A.

J. A. Izatt, M. R. Hee, G. M. Owen, E. A. Swanson, and J. G. Fujimoto, “Optical coherence microscopy in scattering media,” Opt. Lett. 19, 590–592 (1994).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Vabre, L.

Villiger, M.

Weiss, K.

R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323–328 (1970).
[CrossRef]

Wilson, T.

C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in conventional and scanning microscopes,” Phil. Trans. R. Soc. A 295, 513–536 (1980).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “Imaging properties of annular lenses,” Appl. Opt. 18, 3764–3769 (1979).
[CrossRef]

C. J. R. Sheppard and T. Wilson, “The theory of scanning microscopes with Gaussian pupil functions,” J. Microsc. 114, 179–197 (1978).
[CrossRef]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

Wombell, R. J.

Appl. Opt. (4)

Electron. Lett. (1)

G. A. Deschamps, “Gaussian beam as a bundle of complex rays,” Electron. Lett. 7, 684–685 (1971).
[CrossRef]

J. Microsc. (3)

C. J. R. Sheppard and T. Wilson, “The theory of scanning microscopes with Gaussian pupil functions,” J. Microsc. 114, 179–197 (1978).
[CrossRef]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef]

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional image formation in confocal microscopy,” J. Microsc. 159, 179–194 (1990).
[CrossRef]

J. Mod. Opt. (2)

M. Gu and C. J. R. Sheppard, “Three-dimensional image formation in confocal microscopy under ultra-short laser-pulse illumination,” J. Mod. Opt. 42, 747–762 (1995).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in confocal imaging with two unequal annular lenses,” J. Mod. Opt. 40, 1255–1272 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (8)

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Inverse scattering for optical coherence tomography,” J. Opt. Soc. Am. A 23, 1027–1037 (2006).
[CrossRef]

D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A 24, 1034–1041 (2007).
[CrossRef]

B. J. Davis, S. Schlachter, D. L. Marks, T. S. Ralston, S. A. Boppart, and P. S. Carney, “Non-paraxial vector-field modeling of optical coherence tomography and interferometric synthetic aperture microscopy,” J. Opt. Soc. Am. A 24, 2527–2542 (2007).
[CrossRef]

M. Villiger and T. Lasser, “Image formation and tomogram reconstruction in optical coherence microscopy,” J. Opt. Soc. Am. A 27, 2216–2228 (2010).
[CrossRef]

C. J. R. Sheppard, M. Gu, Y. Kawata, and S. Kawata, “Three-dimensional transfer functions for high aperture systems,” J. Opt. Soc. Am. A 11, 593–598 (1994).
[CrossRef]

M. Gu, X. Gan, and C. J. R. Sheppard, “Three-dimensional coherent transfer functions in fibre optical confocal scanning microscopes,” J. Opt. Soc. Am. A 8, 1019–1025 (1991).
[CrossRef]

R. J. Wombell and J. A. De Santo, “Reconstruction of rough-surface profiles with the Kirchhoff approximation,” J. Opt. Soc. Am. A 8, 1892–1897 (1991).
[CrossRef]

M. Kempe and W. Rudolf, “Comparative study of confocal and heterodyne microscopy for imaging through scattering media,” J. Opt. Soc. Am. A 13, 46–52 (1996).
[CrossRef]

Nat. Phys. (1)

T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
[CrossRef]

Opt. Acta (2)

D. K. Hamilton and C. J. R. Sheppard, “A confocal interference microscope,” Opt. Acta 29, 1573–1577 (1982).
[CrossRef]

C. J. R. Sheppard and A. Choudhury, “Image formation in the scanning microscope,” Opt. Acta 24, 1051–1073 (1977).
[CrossRef]

Opt. Commun. (6)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[CrossRef]

C. J. R. Sheppard, T. J. Connolly, and M. Gu, “The scattering potential for imaging in the reflection geometry,” Opt. Commun. 117, 16–19 (1995).
[CrossRef]

C. J. R. Sheppard and F. Aguilar, “Fresnel coefficients for weak reflection and the scattering potential for three-dimensional imaging,” Opt. Commun. 162, 182–186 (1999).
[CrossRef]

R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Commun. 1, 323–328 (1970).
[CrossRef]

C. J. R. Sheppard, M. Gu, and X. Q. Mao, “Three-dimensional coherent transfer function in a reflection-mode confocal scanning microscope,” Opt. Commun. 81, 281–284 (1991).
[CrossRef]

M. Gu and C. J. R. Sheppard, “Fibre-optical confocal scanning interference microscopy,” Opt. Commun. 100, 79–86 (1993).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

M. Roy and C. J. R. Sheppard, “Geometric phase-shifting for low-coherence interference microscopy,” Opt. Lasers Eng. 37, 631–641 (2002).
[CrossRef]

Opt. Lett. (6)

Opt. Photon. News (1)

T. S. Ralston, G. L. Charvat, S. G. Adie, B. J. Davis, P. S. Carney, and S. A. Boppart, “Microscopic laser radar,” Opt. Photon. News 21(6), 32–38 (2010).
[CrossRef]

Optik (2)

C. J. R. Sheppard, “The spatial frequency cut-off in three-dimensional imaging,” Optik 72, 131–133 (1986).

C. J. R. Sheppard, “The use of lenses with annular aperture in scanning optical microscopy,” Optik 48, 329–334 (1977).

Phil. Trans. R. Soc. A (1)

C. J. R. Sheppard and T. Wilson, “Fourier imaging of phase information in conventional and scanning microscopes,” Phil. Trans. R. Soc. A 295, 513–536 (1980).
[CrossRef]

Phys. Rev. A (1)

C. J. R. Sheppard and S. Saghafi, “Beam modes beyond the paraxial approximation: a scalar treatment,” Phys. Rev. A 57, 2971–2979 (1998).
[CrossRef]

Phys. Rev. E (1)

P. C. Chaumet, A. Sentenac, and A. Rahmani, “Coupled dipole method for scatterers with large permittivity,” Phys. Rev. E 70, 036606 (2004).
[CrossRef]

Proc. IEEE (1)

G. S. Kino, “Acoustic imaging for nondestructive evaluation,” Proc. IEEE 67, 510–525 (1979).
[CrossRef]

Pure Appl. Opt. (1)

C. J. R. Sheppard, “Approximate calculation of the reflection coefficient from a stratified medium,” Pure Appl. Opt. 4, 665–669(1995).
[CrossRef]

Scanning (1)

C. J. R. Sheppard, H. Fatemi, and M. Gu, “The Fourier optics of near-field microscopy,” Scanning 17, 28–40 (1995).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Lee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178–1181 (1991).
[CrossRef]

Other (3)

C. J. R. Sheppard and C. J. Cogswell, “Three-dimensional imaging in confocal microscopy,” in Confocal Microscopy, T. Wilson, ed. (Academic, 1990), pp. 143–169.

L. M. Brekhovskikh, Waves in Layered Media (Academic, 1960).

C. J. R. Sheppard, “Scattering and the spatial frequency representation,” in Light Scattering and Nanoscale Surface Roughness, A. A. Maradudin, ed. (Springer, 2007), pp. 61–92.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

CTF and its contour plot for a CSP Gaussian beam: (a) B=2, (b) B1=20, B2=2, (c) B1=B2=11.

Fig. 2.
Fig. 2.

Comparison of three different Gaussian beam models for B=2: CSP model, a Gaussian beam focused by an aplanatic lens, and a Gaussian beam focused without aplanatic weighting.

Fig. 3.
Fig. 3.

Cross sections through the CTF for Ky=0 for (a) a Gaussian beam focused by an aplanatic lens, B=2, (b) for CSP Gaussian beams B1=20, B2=2.

Fig. 4.
Fig. 4.

Variation of various functions of refractive index: 12(n1) (linear), 14(n21) (Born), 34(n21)/(n2+2) (Lorentz), (n1)/(n+1) (Fresnel), and 12lnn (Kirchhoff).

Equations (13)

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

Kz=k±k2Kx2Ky2.
Kx2+Ky2+Kz2=K2<4k2,2k<Kz<2kcosα,
c(K)=exp(AKz),Kx2+Ky2+Kz2=K24k2&Kz<0,
Kz=4k2Kx2Ky2.
Kz=1πA4k2Kx2Ky2.
P(K)=exp[B(k+Kz)],K=k,
c(K)=2kKexp[B(2k+Kz)],K2k,
c(Kz)=exp[B(4k2Kz2)/4]
c(K)=2kKI0[(B2B1)Kx2+Ky2K1K24]exp[(B1+B2)(k+Kz2)],K2k,
Kz=kcosαk2cos2α+2kKρKρ2,
F(r)=k02[n2(r)1],
F(r)=k02[n2(r)nB2]=kB2{[n2(r)/nB2]1}.
F(r)122ln(n(r)nB).

Metrics