Abstract

We present a theoretical formalism for three dimensional (3D) imaging properties of digital holographic microscopy (DHM). Through frequency analysis and visualization of its 3D optical transfer function, an assessment of the imaging behavior of DHM is given. The results are compared with those from other types of interference microscopy. Digital holographic microscopy does not result in true 3D imaging. The main advantage of holographic microscopy lies in its quick acquisition of a single 2D image. Full 3D imaging can be obtained with DHM using a broad-band source or tomographic reconstruction.

© 2007 Optical Society of America

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  1. D. Gabor, "A new microscope principle," Nature 161,777-778 (1948).
    [CrossRef] [PubMed]
  2. U. Schnars and W. Juptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33,179-181 (1994).
    [CrossRef] [PubMed]
  3. P. Marquet, B. Rappaz, P. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge,"Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy," Opt. Lett. 30,468-470 (2005).
    [CrossRef] [PubMed]
  4. B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
    [CrossRef]
  5. A. Stern and B. Javidi,"Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope," J. Opt. Soc. Am. 24,163-168 (2007).
    [CrossRef]
  6. I. Yamaguchi and T. Zhang,"Phase-shifting digital holography," Opt. Lett. 22,1268-1270 (1997).
    [CrossRef] [PubMed]
  7. P. Ferraro, S. De Nicola, A. Finizio, G. Coppola, S. Grilli, C. Magro, and G. Pierattini,"Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging," Appl. Opt. 42,1938-1946 (2003).
    [CrossRef] [PubMed]
  8. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
    [CrossRef] [PubMed]
  9. T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the Synthetic Aperture Microscope," Proc. SPIE 2566,230-240 (1995).
    [CrossRef]
  10. R. Chmelik, "Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes," J. Mod. Optic. 53,2673-2689 (2006).
    [CrossRef]
  11. C. W. McCutchen, "Generalized aperture and the three-dimensional diffraction image," J. Opt. Soc. Am. 54,240-244 (1964).
    [CrossRef]
  12. C. J. R. Sheppard and K. G. Larkin, "Vectorial pupil functions and vectorial transfer functions," Optik 107,79-87 (1997).
  13. E. Wolf, "Three-dimensional structure determination of semi-transparent objects from holographic data," Opt. Commun. 1,153-156 (1969).
    [CrossRef]
  14. C. J. R. Sheppard, "The spatial frequency cut-off in three-dimensional imaging," Optik 72,131-133 (1986).
  15. B. R. Frieden, "Optical Transfer of the Three-Dimensional Object," J. Opt. Soc. Am. 57,56-66 (1967).
    [CrossRef]
  16. C. J. R. Sheppard and M. Gu, "The significance of 3-D transfer functions in confocal scanning microscopy," J. Microsc. 165,377-390 (1991).
    [CrossRef]
  17. D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
    [CrossRef] [PubMed]
  18. D. K. Hamilton and C. J. R. Sheppard, "A confocal interference microscope," Opt. Acta 29,1573-1577 (1982).
    [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] [PubMed]
  20. M. Davidson, K. Kaufman, and I. Mazor, "The Coherence Probe Microscope," Solid State Technol. 30,57-59 (1987).
  21. C. J. R. Sheppard and T. Wilson, "Fourier imaging of phase information in conventional and scanning microscopes," Philos. Tr. R. Soc. S-A 295,513-536 (1980).
    [CrossRef]
  22. M. Born and E. Wolf, Principles of Optics, Cambridge University Press, 7th ed. 2005.
  23. C. J. R. Sheppard and M. Gu, "Imaging by high-aperture optical system," J. Mod. Optic. 40,1631-1651 (1993).
    [CrossRef]
  24. L. Mart’?nez-Le’on, G. Pedrini, andW. Osten, "Applications of short-coherence digital holography in microscopy," Appl. Opt. 44,3977-3984 (2005).
    [CrossRef] [PubMed]
  25. A. J. Devaney, "A filtered back propagation algorithm for diffraction tomography," Ultrason. Imaging 4,336-350 (1982).
    [CrossRef] [PubMed]
  26. 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]

2007

A. Stern and B. Javidi,"Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope," J. Opt. Soc. Am. 24,163-168 (2007).
[CrossRef]

2006

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

R. Chmelik, "Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes," J. Mod. Optic. 53,2673-2689 (2006).
[CrossRef]

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

2005

2004

2003

2002

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]

1997

I. Yamaguchi and T. Zhang,"Phase-shifting digital holography," Opt. Lett. 22,1268-1270 (1997).
[CrossRef] [PubMed]

C. J. R. Sheppard and K. G. Larkin, "Vectorial pupil functions and vectorial transfer functions," Optik 107,79-87 (1997).

1995

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the Synthetic Aperture Microscope," Proc. SPIE 2566,230-240 (1995).
[CrossRef]

1994

1993

C. J. R. Sheppard and M. Gu, "Imaging by high-aperture optical system," J. Mod. Optic. 40,1631-1651 (1993).
[CrossRef]

1991

C. J. R. Sheppard and M. Gu, "The significance of 3-D transfer functions in confocal scanning microscopy," J. Microsc. 165,377-390 (1991).
[CrossRef]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

1987

M. Davidson, K. Kaufman, and I. Mazor, "The Coherence Probe Microscope," Solid State Technol. 30,57-59 (1987).

1986

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

1982

A. J. Devaney, "A filtered back propagation algorithm for diffraction tomography," Ultrason. Imaging 4,336-350 (1982).
[CrossRef] [PubMed]

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

1969

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

1967

1964

1948

D. Gabor, "A new microscope principle," Nature 161,777-778 (1948).
[CrossRef] [PubMed]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

Bredebusch, I.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

Carl, D.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Chmelik, R.

R. Chmelik, "Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes," J. Mod. Optic. 53,2673-2689 (2006).
[CrossRef]

Colomb, T.

Coppola, G.

Cuche, E.

Davidson, M.

M. Davidson, K. Kaufman, and I. Mazor, "The Coherence Probe Microscope," Solid State Technol. 30,57-59 (1987).

De Nicola, S.

Depeursinge, C.

Devaney, A. J.

A. J. Devaney, "A filtered back propagation algorithm for diffraction tomography," Ultrason. Imaging 4,336-350 (1982).
[CrossRef] [PubMed]

Domschke, W.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

Emery, Y.

Ferraro, P.

Finizio, A.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Frieden, B. R.

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, "A new microscope principle," Nature 161,777-778 (1948).
[CrossRef] [PubMed]

Gesell, L.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the Synthetic Aperture Microscope," Proc. SPIE 2566,230-240 (1995).
[CrossRef]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Grilli, S.

Gu, M.

C. J. R. Sheppard and M. Gu, "Imaging by high-aperture optical system," J. Mod. Optic. 40,1631-1651 (1993).
[CrossRef]

C. J. R. Sheppard and M. Gu, "The significance of 3-D transfer functions in confocal scanning microscopy," J. Microsc. 165,377-390 (1991).
[CrossRef]

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

Hamilton, D. K.

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

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Javidi, B.

A. Stern and B. Javidi,"Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope," J. Opt. Soc. Am. 24,163-168 (2007).
[CrossRef]

Juptner, W.

Kaufman, K.

M. Davidson, K. Kaufman, and I. Mazor, "The Coherence Probe Microscope," Solid State Technol. 30,57-59 (1987).

Kemper, B.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

Lapides, J.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the Synthetic Aperture Microscope," Proc. SPIE 2566,230-240 (1995).
[CrossRef]

Larkin, K. G.

C. J. R. Sheppard and K. G. Larkin, "Vectorial pupil functions and vectorial transfer functions," Optik 107,79-87 (1997).

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]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Magistretti, P.

Magro, C.

Marquet, P.

Mart’inez-Le’on, L.

Mazor, I.

M. Davidson, K. Kaufman, and I. Mazor, "The Coherence Probe Microscope," Solid State Technol. 30,57-59 (1987).

McCutchen, C. W.

Pedrini, G.

Pierattini, G.

Price, C.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the Synthetic Aperture Microscope," Proc. SPIE 2566,230-240 (1995).
[CrossRef]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Rappaz, B.

Roy, M.

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

Schafer, M.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

Schnars, U.

Schnekenburger, J.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Sharma, M. D.

Sheppard, C. J. R.

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] [PubMed]

C. J. R. Sheppard and K. G. Larkin, "Vectorial pupil functions and vectorial transfer functions," Optik 107,79-87 (1997).

C. J. R. Sheppard and M. Gu, "Imaging by high-aperture optical system," J. Mod. Optic. 40,1631-1651 (1993).
[CrossRef]

C. J. R. Sheppard and M. Gu, "The significance of 3-D transfer functions in confocal scanning microscopy," J. Microsc. 165,377-390 (1991).
[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]

Stern, A.

A. Stern and B. Javidi,"Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope," J. Opt. Soc. Am. 24,163-168 (2007).
[CrossRef]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Turpin, T.

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the Synthetic Aperture Microscope," Proc. SPIE 2566,230-240 (1995).
[CrossRef]

von Bally, G.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

Wolf, E.

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

Yamaguchi, I.

Zhang, T.

Appl. Opt.

J. Biomed. Opt.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schafer, W. Domschke, and G. von Bally, "Investigation of living pancreas tumor cells by digital holographic microscopy," J. Biomed. Opt. 11,034005 (2006).
[CrossRef]

J. Microsc.

C. J. R. Sheppard and M. Gu, "The significance of 3-D transfer functions in confocal scanning microscopy," J. Microsc. 165,377-390 (1991).
[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] [PubMed]

J. Mod. Optic.

C. J. R. Sheppard and M. Gu, "Imaging by high-aperture optical system," J. Mod. Optic. 40,1631-1651 (1993).
[CrossRef]

R. Chmelik, "Three-dimensional scalar imaging in high-aperture low-coherence interference and holographic microscopes," J. Mod. Optic. 53,2673-2689 (2006).
[CrossRef]

J. Opt. Soc. Am.

A. Stern and B. Javidi,"Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope," J. Opt. Soc. Am. 24,163-168 (2007).
[CrossRef]

C. W. McCutchen, "Generalized aperture and the three-dimensional diffraction image," J. Opt. Soc. Am. 54,240-244 (1964).
[CrossRef]

B. R. Frieden, "Optical Transfer of the Three-Dimensional Object," J. Opt. Soc. Am. 57,56-66 (1967).
[CrossRef]

Nature

D. Gabor, "A new microscope principle," Nature 161,777-778 (1948).
[CrossRef] [PubMed]

Opt. Acta

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

Opt. Commun.

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

Opt. Lett.

Optik

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

C. J. R. Sheppard and K. G. Larkin, "Vectorial pupil functions and vectorial transfer functions," Optik 107,79-87 (1997).

Phys. Rev. Lett.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, "Synthetic aperture fourier holographic optical microscopy," Phys. Rev. Lett. 97,168102 (2006).
[CrossRef] [PubMed]

Proc. SPIE

T. Turpin, L. Gesell, J. Lapides, and C. Price, "Theory of the Synthetic Aperture Microscope," Proc. SPIE 2566,230-240 (1995).
[CrossRef]

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, "Optical Coherence Tomography," Science 254,1178-1181 (1991).
[CrossRef] [PubMed]

Solid State Technol.

M. Davidson, K. Kaufman, and I. Mazor, "The Coherence Probe Microscope," Solid State Technol. 30,57-59 (1987).

Ultrason. Imaging

A. J. Devaney, "A filtered back propagation algorithm for diffraction tomography," Ultrason. Imaging 4,336-350 (1982).
[CrossRef] [PubMed]

Other

C. J. R. Sheppard and T. Wilson, "Fourier imaging of phase information in conventional and scanning microscopes," Philos. Tr. R. Soc. S-A 295,513-536 (1980).
[CrossRef]

M. Born and E. Wolf, Principles of Optics, Cambridge University Press, 7th ed. 2005.

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Figures (8)

Fig. 1.
Fig. 1.

3D Spatial frequency cutoffs in holographic microscopy for (a) transmission mode, and (b) reflection mode. m and s are normalized spatial frequencies in transverse and axial directions respectively as defined in section 3.2.

Fig. 2.
Fig. 2.

Spatial frequency cutoffs in interference microscopes for (a) conventional interference, and (b) confocal interference.

Fig. 3.
Fig. 3.

Spatial frequency cutoffs in holographic microscope for an on-axis configuration (a) and an off-axis configuration (b).

Fig. 4.
Fig. 4.

Basic configuration of the DHM in (a) transmission or (b) reflection mode. BS1, BS2, beam splitters; M1, M2, mirrors; MO, microscope objective; S, sample.

Fig. 5.
Fig. 5.

CTF for holographic microscope at α 0 = π/3 for (a) transmission and (b) reflection mode.

Fig. 6.
Fig. 6.

Spatial frequency cutoffs of low-coherence holographic microscope with a range of k numbers from k2 to k1 in (a) transmission and (b) reflection mode.

Fig. 7.
Fig. 7.

Low-coherence CTF for holographic reflection microscope with (a) Gaussian gating and (b) gating using the modified spectral distribution at α 0 = π/3.

Fig. 8.
Fig. 8.

Spatial frequency coverage representation through tomography. (a) rotation of illumination (b) rotation of object.

Equations (13)

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t ( r ) = O ( r ) + R ( r ) 2
= O ( r ) 2 + R ( r ) 2 + O ( r ) R * ( r ) + O * ( r ) R ( r ) ,
h ( v , u ) = 0 α 0 P ( θ ) J 0 ( v sin θ sin α 0 ) exp [ iu cos θ 4 sin 2 ( α 0 2 ) ] sin θ ,
v = kr sin α 0 ,
u = 4 kz sin 2 ( α 0 2 ) ,
l = ( m 2 + n 2 ) 1 2 .
c ( l , s ) = 0 0 α 0 P ( θ ) J 0 ( v sin θ sin α 0 ) exp [ iu cos θ 4 sin 2 ( α 0 2 ) ] sin θ
× J 0 ( 2 πlr ) exp ( 2 πizs ) 2 πr d r dz .
c ( l , s ) = δ ( s + k k 2 l 2 ) P ( θ ) .
c ( l , s ) = δ ( s + k k 2 l 2 ) ( 1 l 2 k 2 ) 1 4 ,
c poly ( l , s ) = exp ( A ( k k 0 ) 2 ) c ( l , s ) d k .
c poly ( l , s ) = ( k 2 l 2 k ) 1 2 exp [ A ( s 2 + l 2 2 s + k 0 ) 2 ] .
f ( k ) = 1 β Γ ( ρ ) ( k α β ) ρ 1 exp ( k α β ) ,

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