Abstract

Digital holography enables a multifocus quantitative phase microscopy for the investigation of reflective surfaces and for marker-free live cell imaging. For digital holographic long-term investigations of living cells an automated (subsequent) robust and reliable numerical focus adjustment is of particular importance. Four numerical methods for the determination of the optimal focus position in the numerical reconstruction and propagation of the complex object waves of pure phase objects are characterized, compared, and adapted to the requirements of digital holographic microscopy. Results from investigations of an engineered surface and human pancreas tumor cells demonstrate the applicability of Fourier-weighting- and gradient-operator-based methods for robust and reliable automated subsequent numerical digital holographic focusing.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high resolution living cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
    [CrossRef]
  4. B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
    [CrossRef]
  5. Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139-149 (2004).
    [CrossRef] [PubMed]
  6. F. Wolf and S. Geley, “A simple and stable autofocusing protocol for long multidimensional live cell microscopy,” J. Microsc. 221, 72-77 (2006).
    [CrossRef] [PubMed]
  7. M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424-2430 (2004).
    [CrossRef]
  8. B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2007 (1)

2006 (4)

F. Dubois, C. Schockaert, N. Callens, and C. Yourassowsky, “Focus plane detection criteria in digital holography microscopy by amplitude analysis,” Opt. Express 14, 5895-5908(2006).
[CrossRef] [PubMed]

F. Wolf and S. Geley, “A simple and stable autofocusing protocol for long multidimensional live cell microscopy,” J. Microsc. 221, 72-77 (2006).
[CrossRef] [PubMed]

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

2005 (2)

2004 (5)

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424-2430 (2004).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high resolution living cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
[CrossRef]

M. T. Özgen and T. E. Tuncer, “Object reconstruction from in-line Fresnel holograms without explicit depth focusing,” Opt. Eng. 43, 1300-1310 (2004).
[CrossRef]

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139-149 (2004).
[CrossRef] [PubMed]

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J Opt Soc Am A 21, 367-377(2004).
[CrossRef]

2002 (1)

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

2000 (1)

J.-M. Geusebroek, F. Cornelissen, A. W. M. Smeulders, and H. Geerts, “Robust autofocusing in microscopy,” Cytometry 39, 1-9 (2000).
[CrossRef] [PubMed]

1999 (1)

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl.Opt. 38, 6994-7001 (1999).
[CrossRef]

1998 (1)

M. Bravo-Zanoguera, B. v. Massenbach, A. L. Kellner, and J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instrum. 69, 3966-3977 (1998).
[CrossRef]

1992 (1)

H. P. Elsässer, U. Lehr, B. Agricola, and H. F. Kern, “Establishment, and characterization of two cell lines with different grades of differentiation derived from one primary human pancreatic adenocarcinoma,” Virchows Arch. 61,295-306(1992).

1991 (1)

L. Firestone, K. Cook, K. Culp, N. Talsania, and K. Preston Jr, “Comparison of autofocus methods for automated microscopy,” Cytometry 12, 195-206 (1991).
[CrossRef] [PubMed]

1985 (1)

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81-91 (1985).
[CrossRef] [PubMed]

Agricola, B.

H. P. Elsässer, U. Lehr, B. Agricola, and H. F. Kern, “Establishment, and characterization of two cell lines with different grades of differentiation derived from one primary human pancreatic adenocarcinoma,” Virchows Arch. 61,295-306(1992).

Blu, T.

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J Opt Soc Am A 21, 367-377(2004).
[CrossRef]

Bongartz, J.

Bravo-Zanoguera, M.

M. Bravo-Zanoguera, B. v. Massenbach, A. L. Kellner, and J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instrum. 69, 3966-3977 (1998).
[CrossRef]

Bredebusch, I.

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

Callens, N.

Carl, D.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high resolution living cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
[CrossRef]

Colomb, T.

Cook, K.

L. Firestone, K. Cook, K. Culp, N. Talsania, and K. Preston Jr, “Comparison of autofocus methods for automated microscopy,” Cytometry 12, 195-206 (1991).
[CrossRef] [PubMed]

Cornelissen, F.

J.-M. Geusebroek, F. Cornelissen, A. W. M. Smeulders, and H. Geerts, “Robust autofocusing in microscopy,” Cytometry 39, 1-9 (2000).
[CrossRef] [PubMed]

Cuche, E.

P. Marquet, B. Rappaz, P. J. 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]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl.Opt. 38, 6994-7001 (1999).
[CrossRef]

Culp, K.

L. Firestone, K. Cook, K. Culp, N. Talsania, and K. Preston Jr, “Comparison of autofocus methods for automated microscopy,” Cytometry 12, 195-206 (1991).
[CrossRef] [PubMed]

Davis, C. S.

Depeursinge, C.

P. Marquet, B. Rappaz, P. J. 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]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl.Opt. 38, 6994-7001 (1999).
[CrossRef]

Domschke, W.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

Dubois, F.

Duthaler, S.

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139-149 (2004).
[CrossRef] [PubMed]

Elsässer, H. P.

H. P. Elsässer, U. Lehr, B. Agricola, and H. F. Kern, “Establishment, and characterization of two cell lines with different grades of differentiation derived from one primary human pancreatic adenocarcinoma,” Virchows Arch. 61,295-306(1992).

Emery, Y.

Firestone, L.

L. Firestone, K. Cook, K. Culp, N. Talsania, and K. Preston Jr, “Comparison of autofocus methods for automated microscopy,” Cytometry 12, 195-206 (1991).
[CrossRef] [PubMed]

Frey, S.

Geerts, H.

J.-M. Geusebroek, F. Cornelissen, A. W. M. Smeulders, and H. Geerts, “Robust autofocusing in microscopy,” Cytometry 39, 1-9 (2000).
[CrossRef] [PubMed]

Geley, S.

F. Wolf and S. Geley, “A simple and stable autofocusing protocol for long multidimensional live cell microscopy,” J. Microsc. 221, 72-77 (2006).
[CrossRef] [PubMed]

Geusebroek, J.-M.

J.-M. Geusebroek, F. Cornelissen, A. W. M. Smeulders, and H. Geerts, “Robust autofocusing in microscopy,” Cytometry 39, 1-9 (2000).
[CrossRef] [PubMed]

Giel, D.

Groen, F. C.

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81-91 (1985).
[CrossRef] [PubMed]

Hering, P.

Höink, A.

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

Hu, Q.

Jüptner, W.

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Kellner, A. L.

M. Bravo-Zanoguera, B. v. Massenbach, A. L. Kellner, and J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instrum. 69, 3966-3977 (1998).
[CrossRef]

Kemper, B.

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high resolution living cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
[CrossRef]

Kern, H. F.

H. P. Elsässer, U. Lehr, B. Agricola, and H. F. Kern, “Establishment, and characterization of two cell lines with different grades of differentiation derived from one primary human pancreatic adenocarcinoma,” Virchows Arch. 61,295-306(1992).

Kreis, T.

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

Lehr, U.

H. P. Elsässer, U. Lehr, B. Agricola, and H. F. Kern, “Establishment, and characterization of two cell lines with different grades of differentiation derived from one primary human pancreatic adenocarcinoma,” Virchows Arch. 61,295-306(1992).

Li, W.

Liebling, M.

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424-2430 (2004).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J Opt Soc Am A 21, 367-377(2004).
[CrossRef]

Ligthart, G.

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81-91 (1985).
[CrossRef] [PubMed]

Loomis, N. C.

Magistretti, P. J.

Marquet, P.

P. Marquet, B. Rappaz, P. J. 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]

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl.Opt. 38, 6994-7001 (1999).
[CrossRef]

Nelson, B. J.

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139-149 (2004).
[CrossRef] [PubMed]

Özgen, M. T.

M. T. Özgen and T. E. Tuncer, “Object reconstruction from in-line Fresnel holograms without explicit depth focusing,” Opt. Eng. 43, 1300-1310 (2004).
[CrossRef]

Preston, K.

L. Firestone, K. Cook, K. Culp, N. Talsania, and K. Preston Jr, “Comparison of autofocus methods for automated microscopy,” Cytometry 12, 195-206 (1991).
[CrossRef] [PubMed]

Price, J. H.

M. Bravo-Zanoguera, B. v. Massenbach, A. L. Kellner, and J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instrum. 69, 3966-3977 (1998).
[CrossRef]

Rappaz, B.

Schäfer, M.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

Schnars, U.

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Schnekenburger, J.

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

Schockaert, C.

Smeulders, A. W. M.

J.-M. Geusebroek, F. Cornelissen, A. W. M. Smeulders, and H. Geerts, “Robust autofocusing in microscopy,” Cytometry 39, 1-9 (2000).
[CrossRef] [PubMed]

Sun, Y.

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139-149 (2004).
[CrossRef] [PubMed]

Talsania, N.

L. Firestone, K. Cook, K. Culp, N. Talsania, and K. Preston Jr, “Comparison of autofocus methods for automated microscopy,” Cytometry 12, 195-206 (1991).
[CrossRef] [PubMed]

Thelen, A.

Tuncer, T. E.

M. T. Özgen and T. E. Tuncer, “Object reconstruction from in-line Fresnel holograms without explicit depth focusing,” Opt. Eng. 43, 1300-1310 (2004).
[CrossRef]

Unser, M.

M. Liebling and M. Unser, “Autofocus for digital Fresnel holograms by use of a Fresnelet-sparsity criterion,” J. Opt. Soc. Am. A 21, 2424-2430 (2004).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J Opt Soc Am A 21, 367-377(2004).
[CrossRef]

v. Massenbach, B.

M. Bravo-Zanoguera, B. v. Massenbach, A. L. Kellner, and J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instrum. 69, 3966-3977 (1998).
[CrossRef]

von Bally, G.

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

D. Carl, B. Kemper, G. Wernicke, and G. von Bally, “Parameter-optimized digital holographic microscope for high resolution living cell analysis,” Appl. Opt. 43, 6536-6544 (2004).
[CrossRef]

Wernicke, G.

Wolf, F.

F. Wolf and S. Geley, “A simple and stable autofocusing protocol for long multidimensional live cell microscopy,” J. Microsc. 221, 72-77 (2006).
[CrossRef] [PubMed]

Young, I. T.

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81-91 (1985).
[CrossRef] [PubMed]

Yourassowsky, C.

Appl. Opt. (1)

Appl.Opt. (1)

E. Cuche, P. Marquet, and C. Depeursinge, “Simultaneous amplitude-contrast and quantitative phase-contrast microscopy by numerical reconstruction of Fresnel off-axis holograms,” Appl.Opt. 38, 6994-7001 (1999).
[CrossRef]

Cytometry (3)

J.-M. Geusebroek, F. Cornelissen, A. W. M. Smeulders, and H. Geerts, “Robust autofocusing in microscopy,” Cytometry 39, 1-9 (2000).
[CrossRef] [PubMed]

F. C. Groen, I. T. Young, and G. Ligthart, “A comparison of different focus functions for use in autofocus algorithms,” Cytometry 6, 81-91 (1985).
[CrossRef] [PubMed]

L. Firestone, K. Cook, K. Culp, N. Talsania, and K. Preston Jr, “Comparison of autofocus methods for automated microscopy,” Cytometry 12, 195-206 (1991).
[CrossRef] [PubMed]

J Opt Soc Am A (1)

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J Opt Soc Am A 21, 367-377(2004).
[CrossRef]

J. Biomed. Opt. (1)

B. Kemper, D. Carl, J. Schnekenburger, I. Bredebusch, M. Schäfer, W. Domschke, and G. von Bally, “Investigations on living pancreas tumor cells by digital holographic microscopy,” J. Biomed. Opt. 11034005 (2006).
[CrossRef]

J. Microsc. (1)

F. Wolf and S. Geley, “A simple and stable autofocusing protocol for long multidimensional live cell microscopy,” J. Microsc. 221, 72-77 (2006).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

U. Schnars and W. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, R85-R101 (2002).
[CrossRef]

Microsc. Res. Tech. (1)

Y. Sun, S. Duthaler, and B. J. Nelson, “Autofocusing in computer microscopy: selecting the optimal focus algorithm,” Microsc. Res. Tech. 65, 139-149 (2004).
[CrossRef] [PubMed]

Opt. Eng. (1)

M. T. Özgen and T. E. Tuncer, “Object reconstruction from in-line Fresnel holograms without explicit depth focusing,” Opt. Eng. 43, 1300-1310 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (1)

B. Kemper, D. Carl, A. Höink, G. von Bally, I. Bredebusch, and J. Schnekenburger, “Modular digital holographic microscopy system for marker-free quantitative phase contrast imaging of living cells,” Proc. SPIE 6191, 61910T (2006).
[CrossRef]

Rev. Sci. Instrum. (1)

M. Bravo-Zanoguera, B. v. Massenbach, A. L. Kellner, and J. H. Price, “High-performance autofocus circuit for biological microscopy,” Rev. Sci. Instrum. 69, 3966-3977 (1998).
[CrossRef]

Virchows Arch. (1)

H. P. Elsässer, U. Lehr, B. Agricola, and H. F. Kern, “Establishment, and characterization of two cell lines with different grades of differentiation derived from one primary human pancreatic adenocarcinoma,” Virchows Arch. 61,295-306(1992).

Other (1)

T. Kreis, Handbook of Holographic Interferometry: Optical and Digital Methods (Wiley-VCH, 2005).

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Figures (5)

Fig. 1
Fig. 1

Setups for digital off-axis holography in (a) incident light and (b) transmission light arrangements. O, object wave; R, slightly tilted reference wave; C, condenser; OB, object; MO, microscope lens; BS, beam splitter; TL, tube lens; CCD, image sensor; Δ b , propagation distance between the hologram and the image plane; Δ g , distance between the object position and the reconstructed object plane corresponding to the hologram plane.

Fig. 2
Fig. 2

Comparison of (a), (c), (d), (f) defocused and (b), (e) focused (a)–(c) reconstructed amplitude and (d)–(f) unwrapped phase distributions of investigations of a nanostructured surface in the incident light arrangement. (g) Focus value functions for SPEC, VAR, GRA, and LAP.

Fig. 3
Fig. 3

Comparison of (a), (c), (d), (f) defocused and (b), (e) focused (a)–(c) reconstructed amplitude and (d)–(f) unwrapped phase distributions of investigations of PaTu 8988S cells in the transmission light arrangement. (g) Focus value functions for SPEC, VAR, GRA, and LAP.

Fig. 4
Fig. 4

Dependence of axial object position Δ g on autofocus distance Δ b AF (SPEC); squares, PaTu 8988S cells in the transmission light arrangement, linear coefficient ( 0.276 ± 0.002 ) cm / μm ; circles, nanostructured surface in the incident light arrangement, linear coefficient ( 0.214 ± 0.008 ) cm / μm .

Fig. 5
Fig. 5

Digital holographic investigations of spreading keratinocyte cell that has been recorded with a fixed focus in the CCD sensor (image) plane ( 40 × microscope lens, NA = 0.6 ): (a)–(c) reconstructed amplitude and (d)–(f) phase distributions at (a), (d) t = 0 and (b), (e) t = 16 min with fixed focus; (c), (f) t = 16 min with applied numerical digital holographic autofocus. (g) Temporal dependence of the autofocus position z AF on the measurement time t with fixed mechanical focus of the microscope lens.

Tables (2)

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Table 1 Comparison of Autofocus Propagation Distance Δ b AF , Width (FWHM), and Unimodal Range of Four Autofocus Algorithms a

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Table 2 Computation Time for the Sharpness Quantification Algorithms for Each Autofocus Algorithm a

Equations (7)

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O ( x , y , Δ b = Δ b AF ) = F 1 { F [ O ( x , y , 0 ) ] exp [ i π λ Δ b AF ( ν 2 + μ 2 ) ] } .
g ( x , y ) = ^ | O ( x , y ) | .
SPEC = μ , ν log { 1 + [ F F ( g ) ( μ , ν ) ] } .
VAR = 1 N x N y x , y [ g ( x , y ) g ¯ ] 2 .
GRA = g ( g ( x , y ) x ) 2 + ( g ( x , y ) y ) 2 = discrete x = 1 N x 1 y = 1 N y 1 ( g ( x , y ) g ( x 1 , y ) ) 2 + ( g ( x , y ) g ( x , y 1 ) ) 2 .
LAP = x , y ( Δ g ( x , y ) ) 2 d x d y with Δ g = 2 g = 2 g x 2 + 2 g y 2 .
LAP = x = 1 N x 1 y = 1 N y 1 [ g ( x + 1 , y ) + g ( x 1 , y ) + g ( x , y + 1 ) + g ( x , y 1 ) 4 g ( x , y ) ] 2 .

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