Abstract

Hiding image data with a light-scattering medium is effective as a basic data protection technique. The hidden image data can be observed only by using a low-coherence interference technique and is thus protected from unauthorized access. Unlike an intensity-distributed object, a digital relief object has no intensity distribution, making it possible to hide its existence by using a dilute light-scattering medium. To reconstruct the digital relief object through the light-scattering medium, we developed phase-shifting digital holography with a low-coherence light source. The experimental performance, including the spatial resolution and phase error of the reconstructed image, is estimated.

© 2006 Optical Society of America

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2004 (1)

2003 (1)

2001 (3)

2000 (10)

B. Javidi and E. Tajahuerce, "Three-dimensional object recognition by use of digital holography," Opt. Lett. 25, 610-612 (2000).
[CrossRef]

G. Indebetouw and P. Klysubun, "Imaging through scattering media with depth resolution by use of low-coherence gating in spatiotemporal digital holography," Opt. Lett. 25, 212-214 (2000).
[CrossRef]

B. Javidi and T. Nomura, "Securing information by use of digital holography," Opt. Lett. 25, 28-30 (2000).
[CrossRef]

E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, "Optoelectronic information encryption with phase-shifting interferometry," Appl. Opt. 39, 2313-2320 (2000).
[CrossRef]

E. Tajahuerce and B. Javidi, "Encrypting three-dimensional information with digital holography," Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, "Stream cipher based on pseudorandom number generation with optical affine transformation," Appl. Opt. 39, 2340-2346 (2000).
[CrossRef]

T. Nomura and B. Javidi, "Optical encryption system with a binary key code," Appl. Opt. 39, 4783-4787 (2000).
[CrossRef]

P. C. Mogensen and J. Glückstad, "Phase-only optical encryption," Opt. Lett. 25, 566-568 (2000).
[CrossRef]

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

S. Bourquin, V. Monterosso, P. Seitz, and R. P. Salathé, "Video-rate optical low-coherence reflectometry based on a linear smart detector array," Opt. Lett. 25, 102-104 (2000).
[CrossRef]

1999 (4)

G. Indebetouw and P. Klysubun, "Space-time digital holography: a three-dimensional microscopic imaging scheme with an arbitrary degree of spatial coherence," Appl. Phys. Lett. 75, 2017-2019 (1999).
[CrossRef]

N. Towghi, B. Javidi, and Z. Luo, "Fully phase encrypted image processor," J. Opt. Soc. Am. A 16, 1915-1927 (1999).
[CrossRef]

O. Matoba and B. Javidi, "Encrypted optical storage with wavelength-key and random phase codes," Appl. Opt. 38, 6785-6790 (1999).
[CrossRef]

S. Zhang and M. A. Karim, "High-security optical integrated stream ciphers," Opt. Eng. 38, 20-24 (1999).
[CrossRef]

1998 (3)

1997 (3)

1996 (1)

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. 35, 2464-2469 (1996).
[CrossRef]

1995 (4)

1994 (1)

B. Javidi and J. L. Homer, "Optical pattern recognition for validation and security verification," Opt. Eng. 33, 1752-1756 (1994).
[CrossRef]

1993 (1)

1992 (1)

1991 (6)

H. Chen, Y. Chen, D. Dilworth, E. Leith, J. Lopez, and J. Valdmanis, "Two-dimensional imaging through diffusing media using 150-fs gated electronic holography techniques," Opt. Lett. 16, 487-489 (1991).
[CrossRef] [PubMed]

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, "Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate," Science 254, 769-771 (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]

K. M. Yoo, Q. Xing, and R. R. Alfano, "Imaging objects hidden in highly scattering media using femtosecond second-harmonic-generation cross-correlation time gating," Opt. Lett. 16, 1019-1021 (1991).
[CrossRef] [PubMed]

E. N. Leith, C. Chen, H. Chen, Y. Chen, J. Lopez, P.-C. Sun, and D. Dilworth, "Imaging through scattering media using spatial incoherence techniques," Opt. Lett. 16, 1820-1822 (1991).
[CrossRef] [PubMed]

S. Fukushima, T. Kurokawa, and Y. Sakai, "Image encipherment based on optical parallel processing using spatial light modulators," IEEE Trans. Photon. Technol. Lett. 3, 1133-1135 (1991).
[CrossRef]

1990 (1)

1971 (1)

Akiba, M.

Alfano, R. R.

Barry, N. P.

Bashaw, M. C.

Beaurepaire, E.

Birngruber, R.

Blanchot, L.

Boccara, A. C.

Bourquin, S.

Chan, K. P.

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]

Chatwin, C.

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. 35, 2464-2469 (1996).
[CrossRef]

Chen, C.

Chen, H.

Chen, Y.

Danity, J. C.

Demos, S. G.

Dilworth, D.

Duguay, M. A.

Engelhardt, R.

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]

French, P. M. W.

Fujimoto, J. G.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, "High-speed optical coherent domain reflectmetry," Opt. Lett. 17, 151-153 (1992).
[CrossRef] [PubMed]

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]

Fukushima, S.

S. Fukushima, T. Kurokawa, and Y. Sakai, "Image encipherment based on optical parallel processing using spatial light modulators," IEEE Trans. Photon. Technol. Lett. 3, 1133-1135 (1991).
[CrossRef]

Glückstad, J.

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]

Hayasaki, Y.

Heanue, J. F.

Hee, M. R.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, "High-speed optical coherent domain reflectmetry," Opt. Lett. 17, 151-153 (1992).
[CrossRef] [PubMed]

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]

Hesselink, L.

Ho, P. P.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, "Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate," Science 254, 769-771 (1991).
[CrossRef]

Homer, J. L.

B. Javidi and J. L. Homer, "Optical pattern recognition for validation and security verification," Opt. Eng. 33, 1752-1756 (1994).
[CrossRef]

Huang, D.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, "High-speed optical coherent domain reflectmetry," Opt. Lett. 17, 151-153 (1992).
[CrossRef] [PubMed]

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]

Hyde, S. C.

Ichioka, Y.

Indebetouw, G.

Javidi, B.

Jones, R.

Joseph, J.

Karim, M. A.

S. Zhang and M. A. Karim, "High-security optical integrated stream ciphers," Opt. Eng. 38, 20-24 (1999).
[CrossRef]

Kato, J.

I. Yamaguchi, J. Kato, and S. Ohta, "Surface shape measurement by phase-shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

Klysubun, P.

Kurokawa, T.

S. Fukushima, T. Kurokawa, and Y. Sakai, "Image encipherment based on optical parallel processing using spatial light modulators," IEEE Trans. Photon. Technol. Lett. 3, 1133-1135 (1991).
[CrossRef]

Lebec, M.

Leith, E.

Leith, E. N.

Lin, C. P.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, "High-speed optical coherent domain reflectmetry," Opt. Lett. 17, 151-153 (1992).
[CrossRef] [PubMed]

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]

Liu, C.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, "Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate," Science 254, 769-771 (1991).
[CrossRef]

Lopez, J.

Luo, Z.

Matoba, O.

Matsuba, Y.

Mattick, A. T.

Mogensen, P. C.

Monterosso, V.

Nagaoka, A.

Nishida, N.

Nomura, T.

Ohta, S.

I. Yamaguchi, J. Kato, and S. Ohta, "Surface shape measurement by phase-shifting digital holography," Opt. Rev. 8, 85-89 (2001).
[CrossRef]

Pan, Y.

Pohit, M.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

Puliafito, C. A.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, "High-speed optical coherent domain reflectmetry," Opt. Lett. 17, 151-153 (1992).
[CrossRef] [PubMed]

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]

Refregier, P.

Rosperich, J.

Saint-Jalmes, H.

Sakai, Y.

S. Fukushima, T. Kurokawa, and Y. Sakai, "Image encipherment based on optical parallel processing using spatial light modulators," IEEE Trans. Photon. Technol. Lett. 3, 1133-1135 (1991).
[CrossRef]

Salathé, R. P.

Sasaki, T.

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]

Seitz, P.

Shih, M.

Singh, K.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption system that uses phase conjugation in a photorefractive crystal," Appl. Opt. 37, 8181-8186 (1998).
[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]

Sun, P. C.

Sun, P.-C.

Swanson, E. A.

E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, "High-speed optical coherent domain reflectmetry," Opt. Lett. 17, 151-153 (1992).
[CrossRef] [PubMed]

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]

Tajahuerce, E.

Tanida, J.

Tanno, N.

Togo, H.

Towghi, N.

Unnikrishnan, G.

G. Unnikrishnan, M. Pohit, and K. Singh, "A polarization encoded optical encryption system using ferroelectric spatial light modulator," Opt. Commun. 185, 25-31 (2000).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption system that uses phase conjugation in a photorefractive crystal," Appl. Opt. 37, 8181-8186 (1998).
[CrossRef]

Valdmanis, J.

Verrall, S. C.

Vossler, G.

Wang, L.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, "Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate," Science 254, 769-771 (1991).
[CrossRef]

Wang, R. K.

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. 35, 2464-2469 (1996).
[CrossRef]

Watson, I. A.

R. K. Wang, I. A. Watson, and C. Chatwin, "Random phase encoding for optical security," Opt. Eng. 35, 2464-2469 (1996).
[CrossRef]

Xing, Q.

Yamaguchi, I.

Yamamoto, H.

Yoo, K. M.

Zhang, G.

L. Wang, P. P. Ho, C. Liu, G. Zhang, and R. R. Alfano, "Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate," Science 254, 769-771 (1991).
[CrossRef]

Zhang, S.

S. Zhang and M. A. Karim, "High-security optical integrated stream ciphers," Opt. Eng. 38, 20-24 (1999).
[CrossRef]

Zhang, T.

Appl. Opt. (14)

T. Nomura and B. Javidi, "Optical encryption system with a binary key code," Appl. Opt. 39, 4783-4787 (2000).
[CrossRef]

E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, "Optoelectronic information encryption with phase-shifting interferometry," Appl. Opt. 39, 2313-2320 (2000).
[CrossRef]

E. Tajahuerce and B. Javidi, "Encrypting three-dimensional information with digital holography," Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

J. F. Heanue, M. C. Bashaw, and L. Hesselink, "Encrypted holographic data storage based on orthogonal-phase-code multiplexing," Appl. Opt. 34, 6012-6015 (1995).
[CrossRef] [PubMed]

G. Unnikrishnan, J. Joseph, and K. Singh, "Optical encryption system that uses phase conjugation in a photorefractive crystal," Appl. Opt. 37, 8181-8186 (1998).
[CrossRef]

O. Matoba and B. Javidi, "Encrypted optical storage with wavelength-key and random phase codes," Appl. Opt. 38, 6785-6790 (1999).
[CrossRef]

T. Sasaki, H. Togo, J. Tanida, and Y. Ichioka, "Stream cipher based on pseudorandom number generation with optical affine transformation," Appl. Opt. 39, 2340-2346 (2000).
[CrossRef]

Y. Hayasaki, Y. Matsuba, A. Nagaoka, H. Yamamoto, and N. Nishida, "Hiding an image with a light-scattering medium and use of a contrast-discrimination method for readout," Appl. Opt. 43, 1552-1558 (2004).
[CrossRef] [PubMed]

M. A. Duguay and A. T. Mattick, "Ultrahigh speed photography of picosecond light pulses and echoes," Appl. Opt. 10, 2162-2170 (1971).
[CrossRef] [PubMed]

P. C. Mogensen and J. Glückstad, "Phase-only optical decryption of a fixed mask," Appl. Opt. 40, 1226-1235 (2001).
[CrossRef]

Y. Pan, R. Birngruber, J. Rosperich, and R. Engelhardt, "Low-coherence optical tomography in turbid tissue: theoretical analysis," Appl. Opt. 34, 6564-6574 (1995).
[CrossRef] [PubMed]

S. G. Demos and R. R. Alfano, "Optical polarization imaging," Appl. Opt. 36, 150-155 (1997).
[CrossRef] [PubMed]

Y. Pan, R. Birngruber, and R. Engelhardt, "Contrast limits of coherence-gated imaging in scattering media," Appl. Opt. 36, 2979-2983 (1997).
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Figures (7)

Fig. 1
Fig. 1

Experimental setup: SLD, superluminescent diode; LD, laser diode; SMF, single-mode fiber; OL, objective lens; P, polarizer; HWP, half-wave plate; PBS, polarizing beam splitter; QWP, quarter-wave plate; A, analyzer; PZT, piezoelectric transducer.

Fig. 2
Fig. 2

Digital relief object produced on a silicon substrate. The depth of the reentrant with 250 µm × 250 µm is 5.25 µm .

Fig. 3
Fig. 3

Degree of coherence versus the optical path difference. Filled circles indicate the degree of coherence obtained from experiments, and the solid curve indicates the degree of coherence calculated from the power spectrum of the SLD (inset). The dotted curve indicates the relative error of [ V t c ( Δ L 1 ) + V t c ( Δ L 3 ) ] / [ V t c ( Δ L 0 ) + V t c ( Δ L 2 ) ] in Eq. (5) relative to the assumed value of 1.

Fig. 4
Fig. 4

Reconstructed images of the digital relief object through a light-scattering medium: (a) Digital relief object is hidden by a light-scattering medium. (b) Low-coherence interference image when the optical path difference between the object and the reference light is set within the coherence length of the SLD. (c) Amplitude and (d) phase distributions of the hologram produced by the phase-shifting interference technique. (e) Amplitude and (f) phase distributions of the reconstructed image calculated from the Fresnel diffraction of the hologram.

Fig. 5
Fig. 5

(a) Amplitude and (b) phase distributions of the reconstructed image from a hologram recorded with the LD. (c) Amplitude and (d) phase distributions of the reconstructed image from a hologram recorded with the SLD.

Fig. 6
Fig. 6

(a) Spatial resolution and the mean phase error versus OD of the light-scattering medium. Filled triangles and filled circles indicate the spatial resolution without averaging and with averaging, respectively. Filled squares indicate the mean phase error. The reconstructed images (b) without averaging and (c) with averaging are obtained at OD = 2.98 .

Fig. 7
Fig. 7

Interference signal of the reference beam and the object beam through the light-scattering medium. Filled circles indicate the detected light intensity, and the solid curve indicates a cosine curve that fits the results. (a) OD = 2.98 and (b) OD = 3.09 .

Equations (6)

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I [ x , y , τ ( x , y ) ] = U ( S ) [ x , y , t + τ ( S ) ( x , y ) ] + U ( R ) ( t + τ ( R ) ) 2 = I ( S ) ( x , y ) + I ( R ) + 2 [ I ( S ) ( x , y ) I ( R ) ] 1 / 2 ×Re { V m c [ τ ( S ) ( x , y ) + τ ( R ) ] } ,
I [ x , y , Δ L ( x , y ) ] = I ( S ) ( x , y ) + I ( R ) + 2 [ I ( S ) ( x , y ) I ( R ) ] 1 / 2 V t c [ Δ L ( x , y ) ] cos [ k c Δ L ( x , y ) ] ,
ϕ e = tan - 1 { [ I ( Δ L 1 ) - I ( Δ L 3 ) ] / [ I ( Δ L 0 ) - I ( Δ L 2 ) ] } ,
A = A [ V t c ( Δ L 0 ) + V t c ( Δ L 2 ) ] / 2 = [ I ( Δ L 0 ) - I ( Δ L 2 ) ] / 4 A ( R ) cos ϕ e ,
[∣ V t c ( Δ L 1 ) + V t c ( Δ L 3 ) ] [ V t c ( Δ L 0 ) + V t c ( Δ L 2 ) ] = 1.
OD = - log 10 [ ( I 2 - I 2 ) I 1 ] ,

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