Abstract

We present a method for recording in-line single-shot digital holograms based on the fractional Talbot effect. In our system, an image sensor records the interference between the light field scattered by the object and a properly codified parallel reference beam. A simple binary two-dimensional periodic grating is used to codify the reference beam generating a periodic three-step phase distribution over the sensor plane by fractional Talbot effect. This provides a method to perform single-shot phase-shifting interferometry at frame rates only limited by the sensor capabilities. Our technique is well adapted for dynamic wavefront sensing applications. Images of the object are digitally reconstructed from the digital hologram. Both computer simulations and experimental results are presented.

© 2009 OSA

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2008 (2)

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 1–7 (2008).

2006 (5)

2005 (4)

2004 (3)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[CrossRef]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

S. De Nicola, P. Ferraro, G. Coppola, A. Finizio, G. Pierattini, and S. Grilli, “Talbot self-image effect in digital holography and its application to spectrometry,” Opt. Lett. 29(1), 104–106 (2004).
[CrossRef] [PubMed]

2002 (3)

2001 (4)

2000 (4)

1999 (3)

1997 (2)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[CrossRef] [PubMed]

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 37(8), 2357–2360 (1997).
[CrossRef]

1995 (1)

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1-2), 40–44 (1995).
[CrossRef]

1994 (3)

1990 (2)

1987 (1)

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

1972 (1)

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

1971 (1)

A. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
[CrossRef]

1967 (1)

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

1965 (1)

Arrizón, V.

Asundi, A.

Awatsuji, Y.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[CrossRef]

Bevilacqua, F.

Brock, N.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44(32), 6861–6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Cai, L. Z.

Castro, M.-A.

Coppola, G.

Cuche, E.

De Nicola, S.

De Pasquale, L.

N. H. Salama, D. Patrignani, L. De Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31(4), 269–272 (1999).
[CrossRef]

Depeursinge, C.

Dong, G. Y.

Dubois, F.

Fajst, A.

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 1–7 (2008).

Ferraro, P.

Finizio, A.

Frauel, Y.

Y. Frauel, T. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three Dimensional Imaging and Display Using Computational Holographic Imaging,” Proc. IEEE 94(3), 636–654 (2006).
[CrossRef]

Y. Frauel, E. Tajahuerce, M.-A. Castro, and B. Javidi, “Distortion-tolerant 3D object recognition using digital holography,” Appl. Opt. 40, 3887–3893 (2001).
[CrossRef]

Fujii, A.

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Grilli, S.

Guo, Z.

Hayes, J.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44(32), 6861–6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Hettwer, A.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39(4), 960–966 (2000).
[CrossRef]

Huttunen, J.

Jaroszewicz, Z.

A. Kolodziejczyk, Z. Jaroszewicz, A. Kowalik, and O. Quintero, “Kinoform sampling filter,” Opt. Commun. 200(1-6), 35–42 (2001).
[CrossRef]

Javidi, B.

Joannes, L.

Jüptner, W. P. O.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), 85–101 (2002).
[CrossRef]

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 37(8), 2357–2360 (1997).
[CrossRef]

U. Schnars and W. P. O. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33(2), 179–181 (1994).
[CrossRef] [PubMed]

Kaneko, A.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Kim, D.

Kolodziejczyk, A.

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 1–7 (2008).

A. Kolodziejczyk, Z. Jaroszewicz, A. Kowalik, and O. Quintero, “Kinoform sampling filter,” Opt. Commun. 200(1-6), 35–42 (2001).
[CrossRef]

Kowalik, A.

A. Kolodziejczyk, Z. Jaroszewicz, A. Kowalik, and O. Quintero, “Kinoform sampling filter,” Opt. Commun. 200(1-6), 35–42 (2001).
[CrossRef]

Koyama, T.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Kranz, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39(4), 960–966 (2000).
[CrossRef]

Kreis, T. M.

T. M. Kreis and W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 37(8), 2357–2360 (1997).
[CrossRef]

Kronrod, M. A.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Kubota, T.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[CrossRef]

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, “Digital image formation from electronically detected holograms,” Appl. Phys. Lett. 11(3), 77–79 (1967).
[CrossRef]

Leger, J. R.

Legros, J.-C.

Liu, L.

C. Zhou and L. Liu, “Simple equations for the calculation of a multilevel phase grating for Talbot array illumination,” Opt. Commun. 115(1-2), 40–44 (1995).
[CrossRef]

Lohmann, A.

A. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
[CrossRef]

Lohmann, A. W.

Makowski, M.

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 1–7 (2008).

Martínez-León, L.

Matoba, O.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase-shifting digital holography,” Appl. Opt. 45(13), 2995–3002 (2006).
[CrossRef] [PubMed]

Y. Frauel, T. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three Dimensional Imaging and Display Using Computational Holographic Imaging,” Proc. IEEE 94(3), 636–654 (2006).
[CrossRef]

O. Matoba and B. Javidi, “Optical retrieval of encrypted digital holograms for secure real-time display,” Opt. Lett. 27(5), 321–323 (2002).
[CrossRef]

E. Tajahuerce, O. Matoba, and B. Javidi, “Shift-invariant three-dimensional object recognition by means of digital holography,” Appl. Opt. 40(23), 3877–3886 (2001).
[CrossRef]

Meng, X. F.

Merzlyakov, N. S.

M. A. Kronrod, N. S. Merzlyakov, and L. P. Yaroslavsky, “Reconstruction of holograms with a computer,” Sov. Phys. Tech. Phys. 17, 333–334 (1972).

Miao, J.

Millerd, J.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44(32), 6861–6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Moon, I.

B. Javidi, S. Yeom, and I. Moon, “Real-time 3D sensing, visualization and recognition of biological microorganisms,” Proc. IEEE 94(3), 550–567 (2006).
[CrossRef]

Murata, S.

Naughton, T.

Y. Frauel, T. Naughton, O. Matoba, E. Tajahuerce, and B. Javidi, “Three Dimensional Imaging and Display Using Computational Holographic Imaging,” Proc. IEEE 94(3), 636–654 (2006).
[CrossRef]

Nishio, K.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Nitanai, E.

Nomura, T.

North-Morris, M.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44(32), 6861–6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Novak, M.

M. Novak, J. Millerd, N. Brock, M. North-Morris, J. Hayes, and J. Wyant, “Analysis of a micropolarizer array-based simultaneous phase-shifting interferometer,” Appl. Opt. 44(32), 6861–6868 (2005).
[CrossRef] [PubMed]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304–314 (2004).
[CrossRef]

Numata, T.

Ojeda-Castañeda, J.

Onural, L.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

Osten, W.

Patrignani, D.

N. H. Salama, D. Patrignani, L. De Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31(4), 269–272 (1999).
[CrossRef]

Pedrini, G.

Peng, X.

Pierattini, G.

Quintero, O.

A. Kolodziejczyk, Z. Jaroszewicz, A. Kowalik, and O. Quintero, “Kinoform sampling filter,” Opt. Commun. 200(1-6), 35–42 (2001).
[CrossRef]

Rojo-Velázquez, G.

Salama, N. H.

N. H. Salama, D. Patrignani, L. De Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31(4), 269–272 (1999).
[CrossRef]

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase shifting digital holography,” Appl. Phys. Lett. 85(6), 1069–1071 (2004).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13(9), 85–101 (2002).
[CrossRef]

U. Schnars and W. P. O. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33(2), 179–181 (1994).
[CrossRef] [PubMed]

Schwider, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39(4), 960–966 (2000).
[CrossRef]

Scott, P. D.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).

Shen, X. X.

Sicre, E. E.

N. H. Salama, D. Patrignani, L. De Pasquale, and E. E. Sicre, “Wavefront sensor using the Talbot effect,” Opt. Laser Technol. 31(4), 269–272 (1999).
[CrossRef]

Silva, D. E.

A. Lohmann and D. E. Silva, “An interferometer based on the Talbot effect,” Opt. Commun. 2(9), 413–415 (1971).
[CrossRef]

Suszek, J.

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 1–7 (2008).

Swanson, G. J.

Sypek, M.

A. Fajst, M. Sypek, M. Makowski, J. Suszek, and A. Kolodziejczyk, “Self-imaging phase mask used in digital holography with phase-shifting,” Proc. SPIE 7141, 1–7 (2008).

Tahara, T.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Tajahuerce, E.

Thomas, J. A.

Tiziani, H. J.

Turunen, J.

Ura, S.

Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47(19), 183–189 (2008).
[CrossRef]

Wang, Y. R.

Werterholm, J.

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Figures (7)

Fig. 1
Fig. 1

Optical system for recording digital holograms by fractional Talbot effect.

Fig. 2
Fig. 2

Schematic diagram of the phase distribution at the 1/4 fractional Talbot plane provided by an amplitude 2D grating, and the corresponding irradiance distribution at the 1/2 Talbot plane. The magnified unit cell shows the different phases obtained at the 1/4 Fresnel image.

Fig. 3
Fig. 3

Pictures of the irradiance distribution associated to the input 2D objects located at the object beam of the optical system depicted in Fig. 3. Objects (a) and (b) are assumed to be at a distance z1 = 400mm and z2 = 300 mm from the CCD sensor, respectively.

Fig. 4
Fig. 4

Gray level pictures corresponding to the results of the numerical simulation: (a) Talbot interferogram at the output plane of the optical system in Fig. 1, (b) and (c) reconstructed images at two different distances from the resulting digital hologram. The Fresnel image projected onto the sensor plane corresponds to that obtained at a distance from the grating given by (1 + 3/4)zt.

Fig. 5
Fig. 5

Gray level pictures of a central region of the light distribution generated by the grating at the output plane of the system in Fig. 1: (a) Irradiance distribution of the first self image, (b) uniform irradiance distribution of the Fresnel image with = (1 + 3/4)z t, (c) interference pattern between the same Fresnel image and a parallel object beam showing the periodic three-step phase distribution.

Fig. 6
Fig. 6

Gray-level pictures of a partial region of the interference patterns generated at the output plane of the Talbot holography system in Fig. 1 for different 2D objects located at the object beam: (a) the object in Fig. 3(a) and (b) the object in Fig. 3(b). The grating located at the reference beam generates the Fresnel image corresponding to = (1 + 3/4)z t. Note the pixelated structure.

Fig. 7
Fig. 7

Gray level pictures showing the result of the reconstruction of the different digital holograms recorded experimentally: (a), (b), and (c) show the reconstruction of the objects in Fig. 3(a), Fig. 3(b) and the USAF resolution target, respectively.

Equations (8)

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O(x,y,0)=AO(x,y)eiϕO(x,y),
t(x,y)=tc(x,y)[j=P/2P/21   k=P/2P/21δ(xjd)   δ(ykd)],   
z=2d2λ(q+nm)=zt(q+nm)   ,
R(x,y,0)=A2[t(x,y)+it(x+d2,y)+it(x,y+d2)+i2t(x+d2,y+d2)],
tc(x,y)=rect(xd/2)rect(yd/2).
P>>8nm  and  P+P'<<4dλ(q+nm).
O(x,y,0)=14{I(x,y,0)I(x,y,π)+i[2I(x,y,π/2)I(x,y,0)I(x,y,π)]}.
O(m,n;z)=F1{F[O(m,n,0)]exp[iπλz(u2(ΔxNx)2+v2(ΔyNy)2)]},

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