Abstract

A refocusing criterion adapted to red–green–blue (RGB) digital holographic microscopy is established. It is applicable for both amplitude and phase objects. This color criterion is based on a monochromatic criterion, using the integrated modulus amplitude. Simulated RGB holograms show the value of having color information, even for colorless samples; in addition, the position of the focus plane along the optical axis is determined more accurately. Simulations take into account both the numerical apertures of lenses and noise during the holographic process. We also implement an algorithm exponentially reducing the computation time required for detecting the focus plane. The method is validated on experimental holograms.

© 2014 Optical Society of America

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[CrossRef]

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, B. Javidi, J. Disp. Technol. 4, 97 (2008).
[CrossRef]

J. Sheng, E. Malkiel, J. Katz, Exp. Fluids 45, 1023 (2008).
[CrossRef]

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
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Allano, D.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
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Anand, A.

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T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, O. Matoba, 3D Res. 1, 1 (2010).
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Bhaduri, B.

Bingham, P. R.

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A. B. Bochdansky, M. H. Jericho, G. J. Herndl, Limnol. Oceanogr. 11, 28 (2013).
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Cai, L.

Callens, N.

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Y.-J. Choo, B.-S. Kang, Meas. Sci. Technol. 17, 761 (2006).
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N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
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Decaestecker, C.

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C. Deng, J. Huang, G. Li, Y. Yang, Opt. Commun. 291, 52 (2013).
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El Mallahi, A.

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Finizio, A.

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J. Gillespie, R. King, Pattern Recogn. Lett. 9, 19 (1989).
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Godard, G.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Grilli, S.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, B. Javidi, J. Disp. Technol. 4, 97 (2008).
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Groot, M. L.

Guo, R.

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A. B. Bochdansky, M. H. Jericho, G. J. Herndl, Limnol. Oceanogr. 11, 28 (2013).
[CrossRef]

Hong, S.-H.

Hoyos, M.

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Huang, J.

C. Deng, J. Huang, G. Li, Y. Yang, Opt. Commun. 291, 52 (2013).
[CrossRef]

Huang, L.

G. Li, C. Lin, L. Tang, L. Huang, Y. Yang, Optik 123, 609 (2012).
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Jericho, M.

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A. B. Bochdansky, M. H. Jericho, G. J. Herndl, Limnol. Oceanogr. 11, 28 (2013).
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Joannes, L.

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Y. Yang, B.-S. Kang, Y.-J. Choo, Appl. Opt. 47, 817 (2008).
[CrossRef]

Y.-J. Choo, B.-S. Kang, Meas. Sci. Technol. 17, 761 (2006).
[CrossRef]

Kato, J.-I.

Katz, J.

J. Sheng, E. Malkiel, J. Katz, Exp. Fluids 45, 1023 (2008).
[CrossRef]

J. Sheng, E. Malkiel, J. Katz, Appl. Opt. 45, 3893 (2006).
[CrossRef]

E. Malkiel, J. Sheng, J. Katz, J. R. Strickler, J. Exp. Biol. 206, 3657 (2003).
[CrossRef]

Kemper, B.

Kim, M.

King, R.

J. Gillespie, R. King, Pattern Recogn. Lett. 9, 19 (1989).
[CrossRef]

Kiss, R.

F. Dubois, C. Yourassowsky, O. Monnom, J.-C. Legros, O. Debeir, P. Van Ham, R. Kiss, C. Decaestecker, J. Biomed. Opt. 11, 054032 (2006).
[CrossRef]

Kolman, P.

Kostencka, J.

J. Kostencka, T. Kozacki, K. Liżewski, Opt. Commun. 297, 20 (2013).
[CrossRef]

Kozacki, T.

J. Kostencka, T. Kozacki, K. Liżewski, Opt. Commun. 297, 20 (2013).
[CrossRef]

Kreuzer, H.

Kubota, T.

T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, O. Matoba, 3D Res. 1, 1 (2010).
[CrossRef]

Kühn, J.

Kurowski, P.

Langehanenberg, P.

Lebrun, D.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Legros, J.-C.

F. Dubois, C. Yourassowsky, O. Monnom, J.-C. Legros, O. Debeir, P. Van Ham, R. Kiss, C. Decaestecker, J. Biomed. Opt. 11, 054032 (2006).
[CrossRef]

F. Dubois, L. Joannes, J.-C. Legros, Appl. Opt. 38, 7085 (1999).
[CrossRef]

Lei, M.

Li, G.

C. Deng, J. Huang, G. Li, Y. Yang, Opt. Commun. 291, 52 (2013).
[CrossRef]

G. Li, C. Lin, L. Tang, L. Huang, Y. Yang, Optik 123, 609 (2012).
[CrossRef]

Li, W.

Liebling, M.

Lin, C.

G. Li, C. Lin, L. Tang, L. Huang, Y. Yang, Optik 123, 609 (2012).
[CrossRef]

Lizewski, K.

J. Kostencka, T. Kozacki, K. Liżewski, Opt. Commun. 297, 20 (2013).
[CrossRef]

Loomis, N. C.

Ma, B.

Magistretti, P. J.

Malkiel, E.

J. Sheng, E. Malkiel, J. Katz, Exp. Fluids 45, 1023 (2008).
[CrossRef]

J. Sheng, E. Malkiel, J. Katz, Appl. Opt. 45, 3893 (2006).
[CrossRef]

E. Malkiel, J. Sheng, J. Katz, J. R. Strickler, J. Exp. Biol. 206, 3657 (2003).
[CrossRef]

Mann, C. J.

Mansvelder, H. D.

Marquet, P.

Mater, M.

Matoba, O.

T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, O. Matoba, 3D Res. 1, 1 (2010).
[CrossRef]

Matsumura, T.

Meinertzhagen, I.

Miccio, L.

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, B. Javidi, J. Disp. Technol. 4, 97 (2008).
[CrossRef]

Min, J.

Monaldi, A.

G. Romero, A. Monaldi, E. Alanís, Opt. Commun. 285, 1613 (2012).
[CrossRef]

Monnom, O.

F. Dubois, N. Callens, C. Yourassowsky, M. Hoyos, P. Kurowski, O. Monnom, Appl. Opt. 45, 864 (2006).
[CrossRef]

F. Dubois, C. Yourassowsky, O. Monnom, J.-C. Legros, O. Debeir, P. Van Ham, R. Kiss, C. Decaestecker, J. Biomed. Opt. 11, 054032 (2006).
[CrossRef]

Montfort, F.

Ni, J.

Nishio, K.

T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, O. Matoba, 3D Res. 1, 1 (2010).
[CrossRef]

Paquit, V. C.

Paranthoën, P.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Pierattini, G.

Plauska, A.

Popescu, G.

Rappaz, B.

Ridder, M. C.

Romero, G.

G. Romero, A. Monaldi, E. Alanís, Opt. Commun. 285, 1613 (2012).
[CrossRef]

Rupp, R.

Salah, N.

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Schockaert, C.

Sheng, J.

J. Sheng, E. Malkiel, J. Katz, Exp. Fluids 45, 1023 (2008).
[CrossRef]

J. Sheng, E. Malkiel, J. Katz, Appl. Opt. 45, 3893 (2006).
[CrossRef]

E. Malkiel, J. Sheng, J. Katz, J. R. Strickler, J. Exp. Biol. 206, 3657 (2003).
[CrossRef]

Shin, D.

Strickler, J. R.

E. Malkiel, J. Sheng, J. Katz, J. R. Strickler, J. Exp. Biol. 206, 3657 (2003).
[CrossRef]

Tahara, T.

T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, O. Matoba, 3D Res. 1, 1 (2010).
[CrossRef]

Tang, L.

G. Li, C. Lin, L. Tang, L. Huang, Y. Yang, Optik 123, 609 (2012).
[CrossRef]

Tangella, K.

Tobin, K. W.

Unser, M.

Ura, S.

T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, O. Matoba, 3D Res. 1, 1 (2010).
[CrossRef]

van Berge, L.

Van Ham, P.

F. Dubois, C. Yourassowsky, O. Monnom, J.-C. Legros, O. Debeir, P. Van Ham, R. Kiss, C. Decaestecker, J. Biomed. Opt. 11, 054032 (2006).
[CrossRef]

von Bally, G.

Weible, K.

Witte, S.

Xu, L.

Xu, W.

Yamaguchi, I.

Yan, S.

Yang, Y.

C. Deng, J. Huang, G. Li, Y. Yang, Opt. Commun. 291, 52 (2013).
[CrossRef]

G. Li, C. Lin, L. Tang, L. Huang, Y. Yang, Optik 123, 609 (2012).
[CrossRef]

Y. Yang, B.-S. Kang, Y.-J. Choo, Appl. Opt. 47, 817 (2008).
[CrossRef]

Yao, B.

Ye, T.

Yourassowsky, C.

Yu, L.

Zhang, T.

Zheng, J.

3D Res. (1)

T. Tahara, T. Kakue, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, O. Matoba, 3D Res. 1, 1 (2010).
[CrossRef]

Appl. Opt. (8)

Biomed. Opt. Express (2)

Exp. Fluids (1)

J. Sheng, E. Malkiel, J. Katz, Exp. Fluids 45, 1023 (2008).
[CrossRef]

J. Biomed. Opt. (1)

F. Dubois, C. Yourassowsky, O. Monnom, J.-C. Legros, O. Debeir, P. Van Ham, R. Kiss, C. Decaestecker, J. Biomed. Opt. 11, 054032 (2006).
[CrossRef]

J. Disp. Technol. (1)

P. Ferraro, S. Grilli, L. Miccio, D. Alfieri, S. De Nicola, A. Finizio, B. Javidi, J. Disp. Technol. 4, 97 (2008).
[CrossRef]

J. Exp. Biol. (1)

E. Malkiel, J. Sheng, J. Katz, J. R. Strickler, J. Exp. Biol. 206, 3657 (2003).
[CrossRef]

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

Limnol. Oceanogr. (1)

A. B. Bochdansky, M. H. Jericho, G. J. Herndl, Limnol. Oceanogr. 11, 28 (2013).
[CrossRef]

Meas. Sci. Technol. (2)

N. Salah, G. Godard, D. Lebrun, P. Paranthoën, D. Allano, S. Coëtmellec, Meas. Sci. Technol. 19, 074001 (2008).
[CrossRef]

Y.-J. Choo, B.-S. Kang, Meas. Sci. Technol. 17, 761 (2006).
[CrossRef]

Opt. Commun. (3)

G. Romero, A. Monaldi, E. Alanís, Opt. Commun. 285, 1613 (2012).
[CrossRef]

J. Kostencka, T. Kozacki, K. Liżewski, Opt. Commun. 297, 20 (2013).
[CrossRef]

C. Deng, J. Huang, G. Li, Y. Yang, Opt. Commun. 291, 52 (2013).
[CrossRef]

Opt. Express (6)

Opt. Lett. (13)

Optik (1)

G. Li, C. Lin, L. Tang, L. Huang, Y. Yang, Optik 123, 609 (2012).
[CrossRef]

Pattern Recogn. Lett. (1)

J. Gillespie, R. King, Pattern Recogn. Lett. 9, 19 (1989).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Simulated pure amplitude object: (a) in its focus plane, (b) with the effect of numerical aperture of microscope lenses (NA=0.3), (c) defocused by 50μm, and (d) with 20% uniformly distributed white noise.

Fig. 2.
Fig. 2.

Color criterion MdRGB for the simulated amplitude object as a function of the reconstruction distance d for the image in Fig. 1(c) (with NA=0.3 and defocused by 50μm, but without noise).

Fig. 3.
Fig. 3.

Criteria MdRGB (bold black line) for the simulated amplitude object MdR (thin red line), MdG (thin green line), and MdB (thin blue line) as a function of the reconstruction distance d for the image in Fig. 1(d) (with NA=0.3, defocused by 50μm and with 20% uniformly distributed white noise).

Fig. 4.
Fig. 4.

Simulated spherical pure phase object with an optical depth of 2λG at the center: (a) combined RGB optical phase image in the focus plane, without the effect of NA or noise, and (b) RGB intensity image in the sensor plane with the effect of numerical apertures of microscope lenses (NA=0.3), defocused by 50μm and with 20% uniformly distributed white noise.

Fig. 5.
Fig. 5.

Algal cell Odontella sp.: (a) RGB hologram and (b) corresponding RGB intensity image (region of interest).

Fig. 6.
Fig. 6.

Algal cell Odontella sp. refocused: (a) RGB intensity image and (b) combined RGB optical phase image.

Fig. 7.
Fig. 7.

Color criterion MdRGB as a function of the reconstruction distance d for the algal cell Odontella sp. of Fig. 5(b). Solid blue line was obtained by uniformly scanning along the optical axis (1 μm steps). Red crosses represent the only points computed using the fast algorithm implemented here.

Tables (2)

Tables Icon

Table 1. Averages (μ) and Standard Deviations (σ) of dmin Distributions at Different Values of Noise (n) for Simulated Holograms of Pure Amplitude Objectsa

Tables Icon

Table 2. Averages (μ) and Standard Deviations (σ) of dmax Distributions at Different Values of Noise (n) for Simulated Holograms of Pure Phase Objectsa

Equations (6)

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Md=++|ud(x,y)|dxdy,
MdRGB=MdRMdGMdB,
uI(x,y)={0ifx2+y2D/2AIotherwise,
p(u,v)={1ifu2+v2NA/(2λI)0otherwise,
1+2log2(baε),
1+baε.

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