Abstract

Three-dimensional optical tomographic imaging plays an important role in biomedical research and clinical applications. We introduce spectral tomographic imaging (STI) via spectral encoding of spatial frequency principle that not only has the capability for visualizing the three-dimensional object at sub-micron resolution but also providing spatially-resolved quantitative characterization of its structure with nanoscale accuracy for any volume of interest within the object. The theoretical basis and the proof-of-concept numerical simulations are presented to demonstrate the feasibility of spectral tomographic imaging.

© 2013 OSA

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  1. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Comm.1, 153–156 (1969).
    [CrossRef]
  2. E. Wolf, “Determination of the amplitude and the phase of scattered fields of holography,” J. Opt. Soc. Am.60, 18–20 (1970).
    [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).
  4. Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17, 266–277 (2009).
    [CrossRef] [PubMed]
  5. O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt.57, 686–699 (2010).
    [CrossRef]
  6. A. F. Fercher, “Ophthalmic interferometry,” in Optics in medicine, biology and environment, G. von Bally and S Khanna, eds. (Elsevier, Amsterdam, 1999), 221–235.
  7. C. K. Hitzenberger, “Optical measurement of the axial eye length by laser Doppler interferometry,” Invest. Ophthalmol. Vis. Sci.32, 616–624 (1991).
    [PubMed]
  8. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
    [CrossRef] [PubMed]
  9. B. E. Bouma and G. J. Tearney, The handbook of optical coherence tomography (Marcel Dekker, New York, 2002).
  10. 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] [PubMed]
  11. F. Montfort, T. Colomb, F. Charrière, J. Kühn, P. Marquet, E. Cuche, S. Herminjard, and C. Depeursinge, “Submicrometer optical tomography by multiple-back-scattered digital holographic microscopy,” Appl. Opt.45, 8209–8217 (2006).
    [CrossRef] [PubMed]
  12. M. Kim, “Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography,” Opt. Express7, 305–310 (2000).
    [CrossRef] [PubMed]
  13. L. Yu and M. Kim, “Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method,” Opt. Lett.30, 2092–2094 (2005).
    [CrossRef] [PubMed]
  14. J. Kühn, 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] [PubMed]
  15. R. Dändliker and K. Weiss, “Reconstruction of the three-dimensional refractive index from scattered waves,” Opt. Comm.1, 323–328 (1970).
    [CrossRef]
  16. 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] [PubMed]
  17. M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett.34, 79–81 (2009).
    [CrossRef]
  18. B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
    [CrossRef]
  19. J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
    [CrossRef]
  20. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry” Opt. Comm.117, 43–48 (1995).
    [CrossRef]
  21. T. S. Ralston, D. L. Marks, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys.3, 129–134 (2007).
    [CrossRef]
  22. T. Ralston, D. Marks, P. Carney, and S. Boppart, “Inverse scattering for optical coherence tomography,” J. Opt. Soc. Am. A23, 1027–1037 (2006).
    [CrossRef]
  23. D. Marks, T. Ralston, S. Boppart, and P. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A24, 1034–1041 (2007).
    [CrossRef]
  24. V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
    [CrossRef] [PubMed]
  25. Y. Liu, X. Li, Y. L. Kim, and V. Backman, “Elastic backscattering spectroscopic microscopy,” Opt. Lett.30, 2445–2447 (2005).
    [CrossRef] [PubMed]
  26. L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
    [CrossRef]
  27. K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res.69, 1199–1204 (2009).
    [CrossRef] [PubMed]
  28. A. Wax, C. H. Yang, and J. A. Izatt, “Fourier-domain low-coherence interferometry for light-scattering spectroscopy,” Opt. Lett.28, 1230–1232 (2003).
    [CrossRef] [PubMed]
  29. T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Three-dimensional depth-resolved and extended-resolution micro-particle characterization by holographic light scattering spectroscopy,” Opt. Express18, 25116–25126 (2010).
    [CrossRef] [PubMed]
  30. H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
    [CrossRef] [PubMed]
  31. I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
    [CrossRef] [PubMed]
  32. N. N. Boustany, S. C. Kuo, and N. V. Thakor, “Optical scatter imaging: subcellular morphometry in situ with Fourier filtering,” Opt. Lett.26, 1063–1065 (2001).
    [CrossRef]
  33. R. M. Pasternack, Z. Qian, J. Y. Zheng, D. N. Metaxas, and N. N. Boustany, “Highly sensitive size discrimination of sub-micron objects using optical Fourier processing based on two-dimensional Gabor filters,” Opt. Express17, 12001–12012 (2009).
    [CrossRef] [PubMed]
  34. S. A. Alexandrov, S. Uttam, R. K. Bista, and Y. Liu, “Spectral encoding of spatial frequency approach for characterization of nanoscale structures,” Appl. Phys. Lett.101033702 (2012).
    [CrossRef]
  35. S. A. Alexandrov, S. Uttam, R. K. Bista, C. Zhao, and Y. Liu, “Real-time quantitative visualization of 3D structural information,” Opt. Express20, 9203–9214 (2012).
    [CrossRef] [PubMed]
  36. J. Goodman, Introduction to Fourier Optics (Roberts & Company, Colorado, 1999).
  37. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).

2012 (2)

S. A. Alexandrov, S. Uttam, R. K. Bista, and Y. Liu, “Spectral encoding of spatial frequency approach for characterization of nanoscale structures,” Appl. Phys. Lett.101033702 (2012).
[CrossRef]

S. A. Alexandrov, S. Uttam, R. K. Bista, C. Zhao, and Y. Liu, “Real-time quantitative visualization of 3D structural information,” Opt. Express20, 9203–9214 (2012).
[CrossRef] [PubMed]

2010 (4)

T. Gutzler, T. R. Hillman, S. A. Alexandrov, and D. D. Sampson, “Three-dimensional depth-resolved and extended-resolution micro-particle characterization by holographic light scattering spectroscopy,” Opt. Express18, 25116–25126 (2010).
[CrossRef] [PubMed]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt.57, 686–699 (2010).
[CrossRef]

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

2009 (5)

2007 (4)

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

D. Marks, T. Ralston, S. Boppart, and P. Carney, “Inverse scattering for frequency-scanned full-field optical coherence tomography,” J. Opt. Soc. Am. A24, 1034–1041 (2007).
[CrossRef]

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

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

2006 (2)

2005 (2)

2003 (1)

2002 (1)

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] [PubMed]

2001 (1)

2000 (2)

M. Kim, “Tomographic three-dimensional imaging of a biological specimen using wavelength-scanning digital interference holography,” Opt. Express7, 305–310 (2000).
[CrossRef] [PubMed]

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

1998 (1)

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

1995 (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry” Opt. Comm.117, 43–48 (1995).
[CrossRef]

1994 (1)

1991 (2)

C. K. Hitzenberger, “Optical measurement of the axial eye length by laser Doppler interferometry,” Invest. Ophthalmol. Vis. Sci.32, 616–624 (1991).
[PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

1970 (2)

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

E. Wolf, “Determination of the amplitude and the phase of scattered fields of holography,” J. Opt. Soc. Am.60, 18–20 (1970).
[CrossRef]

1969 (1)

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

Alexandrov, S. A.

Andersson, C.

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Arendt, J. T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Backman, V.

Y. Liu, X. Li, Y. L. Kim, and V. Backman, “Elastic backscattering spectroscopic microscopy,” Opt. Lett.30, 2445–2447 (2005).
[CrossRef] [PubMed]

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Badizadegan, K.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17, 266–277 (2009).
[CrossRef] [PubMed]

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Bansil, R.

Beghin, A.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
[CrossRef]

Belkebir, K.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt.57, 686–699 (2010).
[CrossRef]

Bigio, I.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

Bista, R. K.

S. A. Alexandrov, S. Uttam, R. K. Bista, and Y. Liu, “Spectral encoding of spatial frequency approach for characterization of nanoscale structures,” Appl. Phys. Lett.101033702 (2012).
[CrossRef]

S. A. Alexandrov, S. Uttam, R. K. Bista, C. Zhao, and Y. Liu, “Real-time quantitative visualization of 3D structural information,” Opt. Express20, 9203–9214 (2012).
[CrossRef] [PubMed]

Boppart, S.

Boppart, S. A.

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

Born, M.

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

Bouma, B. E.

B. E. Bouma and G. J. Tearney, The handbook of optical coherence tomography (Marcel Dekker, New York, 2002).

Boustany, N. N.

Carney, P.

Carney, P. S.

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

Chalut, K. J.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res.69, 1199–1204 (2009).
[CrossRef] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Charrière, F.

Chaumet, P. C.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

Choi, W.

Cipolloni, P.

Cipolloni, P. B.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Colomb, T.

Crawford, J. M.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Cuche, E.

Dändliker, R.

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

Dasari, R. R.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17, 266–277 (2009).
[CrossRef] [PubMed]

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Debailleul, M.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
[CrossRef]

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett.34, 79–81 (2009).
[CrossRef]

Depeursinge, C.

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry” Opt. Comm.117, 43–48 (1995).
[CrossRef]

Fang, H.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

Fang-Yen, C.

Feld, M. S.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express17, 266–277 (2009).
[CrossRef] [PubMed]

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Fercher, A. F.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry” Opt. Comm.117, 43–48 (1995).
[CrossRef]

A. F. Fercher, “Ophthalmic interferometry,” in Optics in medicine, biology and environment, G. von Bally and S Khanna, eds. (Elsevier, Amsterdam, 1999), 221–235.

Fitzmaurice, M.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Flotire, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Freedman, S.

Freedman, S. D.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

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] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Georges, V.

Ghiran, I. C.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Giacomelli, M. G.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res.69, 1199–1204 (2009).
[CrossRef] [PubMed]

Giovaninni, H.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt.57, 686–699 (2010).
[CrossRef]

Giovannini, H.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

Girard, J.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, Colorado, 1999).

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Gurjar, R.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Gutzler, T.

Haeberlé, O.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
[CrossRef]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt.57, 686–699 (2010).
[CrossRef]

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett.34, 79–81 (2009).
[CrossRef]

Hamano, T.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Hanlon, E.

Hanlon, E. B.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Hee, M. R.

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] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Herminjard, S.

Hillman, T. R.

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry” Opt. Comm.117, 43–48 (1995).
[CrossRef]

C. K. Hitzenberger, “Optical measurement of the axial eye length by laser Doppler interferometry,” Invest. Ophthalmol. Vis. Sci.32, 616–624 (1991).
[PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Itzkan, I.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Izatt, J. A.

Kabani, S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry” Opt. Comm.117, 43–48 (1995).
[CrossRef]

Keates, S.

Kim, M.

Kim, Y. L.

Kimerer, L.

Kimerer, L. M.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Kline, E.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Kühn, J.

Kuo, S. C.

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] [PubMed]

Levin, H. S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Li, X.

Lim, K. H.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Lima, C.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Liu, Y.

Maire, G.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).

Manoharan, R.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Marks, D.

Marks, D. L.

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

Marquet, P.

McGilligan, J. A.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Metaxas, D. N.

Mller, M. G.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Modell, M.

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Montfort, F.

Moratal, C.

Morin, R.

Nusrat, A.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Ostrander, J. H.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res.69, 1199–1204 (2009).
[CrossRef] [PubMed]

Owen, G. M.

Pasternack, R. M.

Pavillon, N.

Perelman, L.

Perelman, L. T.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Qian, Z.

Qiu, L.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

Ralston, T.

Ralston, T. S.

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

Rappaz, B.

Sachs, B. P.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Salahuddin, S.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

Sampson, D. D.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Seiler, M.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Sentenac, A.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt.57, 686–699 (2010).
[CrossRef]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

Shapshay, S.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Shields, S.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Simon, B.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
[CrossRef]

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, “High-resolution three-dimensional tomographic diffractive microscopy of transparent inorganic and biological samples,” Opt. Lett.34, 79–81 (2009).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Sung, Y.

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] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Talneau, A.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

Tearney, G. J.

B. E. Bouma and G. J. Tearney, The handbook of optical coherence tomography (Marcel Dekker, New York, 2002).

Thakor, N. V.

Tourneur, Y.

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
[CrossRef]

Turner, B.

Uttam, S.

S. A. Alexandrov, S. Uttam, R. K. Bista, and Y. Liu, “Spectral encoding of spatial frequency approach for characterization of nanoscale structures,” Appl. Phys. Lett.101033702 (2012).
[CrossRef]

S. A. Alexandrov, S. Uttam, R. K. Bista, C. Zhao, and Y. Liu, “Real-time quantitative visualization of 3D structural information,” Opt. Express20, 9203–9214 (2012).
[CrossRef] [PubMed]

Valdez, T.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Van Dam, J.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Vitkin, E.

H. Fang, L. Qiu, E. Vitkin, M. Zaman, C. Andersson, S. Salahuddin, L. Kimerer, P. Cipolloni, M. Modell, B. Turner, S. Keates, I. Bigio, I. Itzkan, S. Freedman, R. Bansil, E. Hanlon, and L. Perelman, “Confocal light absorption and scattering spectroscopic microscopy,” Appl. Opt.46, 1760–1769 (2007).
[CrossRef] [PubMed]

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Wallace, M.

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Wallace, M. B.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Wax, A.

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res.69, 1199–1204 (2009).
[CrossRef] [PubMed]

A. Wax, C. H. Yang, and J. A. Izatt, “Fourier-domain low-coherence interferometry for light-scattering spectroscopy,” Opt. Lett.28, 1230–1232 (2003).
[CrossRef] [PubMed]

Weiss, K.

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

Wolf, E.

E. Wolf, “Determination of the amplitude and the phase of scattered fields of holography,” J. Opt. Soc. Am.60, 18–20 (1970).
[CrossRef]

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

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).

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

Yang, C. H.

Yu, L.

Zaman, M.

Zaman, M. M.

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Zhang, Q.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Zhao, C.

Zheng, J. Y.

Zonios, G.

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

S. A. Alexandrov, S. Uttam, R. K. Bista, and Y. Liu, “Spectral encoding of spatial frequency approach for characterization of nanoscale structures,” Appl. Phys. Lett.101033702 (2012).
[CrossRef]

Cancer Res. (1)

K. J. Chalut, J. H. Ostrander, M. G. Giacomelli, and A. Wax, “Light scattering measurements of subcellular structure provide noninvasive early detection of chemotherapy-induced apoptosis,” Cancer Res.69, 1199–1204 (2009).
[CrossRef] [PubMed]

Invest. Ophthalmol. Vis. Sci. (1)

C. K. Hitzenberger, “Optical measurement of the axial eye length by laser Doppler interferometry,” Invest. Ophthalmol. Vis. Sci.32, 616–624 (1991).
[PubMed]

J. Biophoton. (1)

B. Simon, M. Debailleul, A. Beghin, Y. Tourneur, and O. Haeberlé, “High-resolution tomographic diffractive microscopy of biological samples,” J. Biophoton.3, 462–467 (2010).
[CrossRef]

J. Microsc. (1)

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] [PubMed]

J. Mod. Opt. (1)

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt.57, 686–699 (2010).
[CrossRef]

J. Opt. Soc. Am. (1)

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

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]

Nature (1)

V. Backman, M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Mller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, and M. S. Feld, “Detection of preinvasive cancer cells,” Nature406, 35–36 (2000).
[CrossRef] [PubMed]

Opt. Comm. (3)

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

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

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry” Opt. Comm.117, 43–48 (1995).
[CrossRef]

Opt. Express (5)

Opt. Lett. (7)

Phys. Rev. A (1)

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Nanometric resolution using far-field optical tomographic microscopy in the multiple scattering regime,” Phys. Rev. A82, 061801(R) (2010).
[CrossRef]

Phys. Rev. Lett. (1)

L. T. Perelman, V. Backman, M. Wallace, G. Zonios, R. Manoharan, A. Nusrat, S. Shields, M. Seiler, C. Lima, T. Hamano, I. Itzkan, J. Van Dam, J. M. Crawford, and M. S. Feld, “Observation of periodic fine struct ure in reflectance from biological tissue: A new technique for measuring nuclear size distribution,” Phys. Rev. Lett.80, 627–630 (1998).
[CrossRef]

Proc. Natl. Acad. Sci. (1)

I. Itzkan, L. Qiu, H. Fang, M. M. Zaman, E. Vitkin, I. C. Ghiran, S. Salahuddin, M. Modell, C. Andersson, L. M. Kimerer, P. B. Cipolloni, K. H. Lim, S. D. Freedman, I. Bigio, B. P. Sachs, E. B. Hanlon, and L. T. Perelman, “Confocal light absorption and scattering spectroscopic microscopy monitors organelles in live cells with no exogenous labels,” Proc. Natl. Acad. Sci.10417255–17260 (2007).
[CrossRef] [PubMed]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotire, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science254, 1178–1181 (1991).
[CrossRef] [PubMed]

Other (5)

B. E. Bouma and G. J. Tearney, The handbook of optical coherence tomography (Marcel Dekker, New York, 2002).

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

A. F. Fercher, “Ophthalmic interferometry,” in Optics in medicine, biology and environment, G. von Bally and S Khanna, eds. (Elsevier, Amsterdam, 1999), 221–235.

J. Goodman, Introduction to Fourier Optics (Roberts & Company, Colorado, 1999).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, New York, 1995).

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Figures (14)

Fig. 1
Fig. 1

Construction of the muffin-shaped K-space support for STI-based object reconstruction under the reflection-mode configuration.

Fig. 2
Fig. 2

Fourier plane spectral extension.

Fig. 3
Fig. 3

Axial and lateral resolutions as a function of NA for λ = 550nm and n = 1.

Fig. 4
Fig. 4

Dependence of axial spatial frequencies on scattering angle, for NA = 0.5, λ = 550nm, and n = 1.

Fig. 5
Fig. 5

Lateral resolution of the reconstructed object and accuracy of axial spatial period characterization as a function of NA for n = 1.

Fig. 6
Fig. 6

Flow diagram showing the steps for reconstructing the 3D object, and structural characterization via the axial spatial period profile for a given VOI within the object.

Fig. 7
Fig. 7

Error in quantifying axial spatial period for a spectral sub-band, for NA = 0.5 and n = 1.

Fig. 8
Fig. 8

The simulated 3D object consisting of a mixture of high and low scatterer density. Three VOIs have been indicated along with their corresponding spatial period profiles.

Fig. 9
Fig. 9

(i) Volumetric visualization of the STI-based reconstruction of the object. (ii)–(vii) The cross-sectional view of the reconstructions of the three VOIs identified in (i) and in Fig. 8.

Fig. 10
Fig. 10

Original and reconstructed 1D cross-section profile from within the 3D object.

Fig. 11
Fig. 11

Reconstructed axial spatial period profiles of the three VOIs.

Fig. 12
Fig. 12

Cross-section view of two sections of the reconstructed 3D object consisting of nanospheres of four different sizes.

Fig. 13
Fig. 13

(i) 3D object consisting of nanospheres of four different sizes. The color-coded VOIs indicate the four nanosphere stacks. (ii) The corresponding STI-based axial spatial period profiles shown with the same color code.

Fig. 14
Fig. 14

VOI: nanospheres of size 360nm. (i) Reconstructed VOI with σp = 0.5°. (ii) Reconstructed VOI with σp = 1.5°. (iii) Reconstructed VOI with σp = 3°. (iv) Reconstruction error (relative to the no noise case) and peak position of the dominant structure as function of σp.

Tables (1)

Tables Icon

Table 1 Comparison of peak locations from the actual and reconstructed spatial period profiles of the three VOIs.

Equations (25)

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E i ( r , t ; k ) = A ( k ) e i ( k 0 r ω t ) ,
U i ( r ; k ) = A ( k ) e i ( k 0 x x + k 0 y y k 0 z z ) ,
U b s ( r ) = V F ( r ) U i ( r ; k ) G ( r r ; k ) d r ,
G ( r r ; k ) = e i k | r r | | r r | d r .
U b s ( r ) = A ( k ) V F ( r ) e i k 0 r e i k | r r | | r r | .
e i k | r r | | r r | = i 2 π 1 k z e i [ k x ( x x ) + k y ( y y ) + k z ( z z ) ] d k x d k y ,
U b s ( r ) = i 2 π ( A ( k ) Z 1 k z F ˜ ˜ ( k x , k y ; z , k 0 x , k 0 y ) e i ( k 0 z + k z ) z d z ) e i k r d k x d k y ,
F ˜ ˜ ( k x , k y ; z , k 0 x , k 0 y ) = X Y F ( r ) e i ( ( k x k 0 x ) x + ( k y k 0 y ) y ) d x d y .
F ˜ 1 ( K ) F ˜ 1 ( k x k 0 x , k y k 0 y , k 0 z + k z ) = A ( k ) Z 1 k z F ˜ ˜ ( k x , k y ; z , k 0 x , k 0 y ) e i ( k 0 z + k z ) z d z .
K = k s k i ,
k + k z = k + k 2 k x 2 k y 2 ,
F ( r ) = 1 ( 2 π ) 3 V K F ˜ 1 ( K ) e i K r d K .
Δ V = 3 4 λ 1 2 λ 2 2 π n 3 Δ λ ( ( 1 cos 4 ( arcsinNA 2 ) ) ( ( λ 1 + λ 2 ) 2 λ 1 λ 2 1 ) ) 1 .
Δ r z = λ 1 λ 2 2 n Δ λ ,
Δ r l = λ 1 + λ 2 4 n NA .
Δ V = Δ r a Δ r l 2 .
λ = 2 K z K z 2 + ( K x 2 + K y 2 ) .
Δ K z = 2 π n δ λ λ 1 λ 2 .
Δ K x = Δ K y = 4 π n NA λ 1 N .
Δ H z = λ tan 2 ( arcsinNA 2 ) 2 n .
α m = arccos ( cos 2 ( arcsinNA 2 ) ) ,
H z = λ n ( 1 + cos α m ) ,
E m ( H z ) = V m | F m , ( r ) | 2 d r ,
F m , ( r ) = 1 ( 2 π ) 3 K F ( K ) e i 2 π K r m d K ,
I m ( H z ) = E m 1 / 2 ( H z ) ( E m ( H z ) ) 1 / 2 .

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