Abstract

We present a method of securing multispectral 3D photon-counted integral imaging (PCII) using classical Hartley Transform (HT) based encryption by employing optical interferometry. This method has the simultaneous advantages of minimizing complexity by eliminating the need for holography recording and addresses the phase sensitivity problem encountered when using digital cameras. These together with single-channel multispectral 3D data compactness, the inherent properties of the classical photon counting detection model, i.e. sparse sensing and the capability for nonlinear transformation, permits better authentication of the retrieved 3D scene at various depth cues. Furthermore, the proposed technique works for both spatially and temporally incoherent illumination. To validate the proposed technique simulations were carried out for both the 2D and 3D cases. Experimental data is processed and the results support the feasibility of the encryption method.

© 2015 Optical Society of America

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References

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    [Crossref]
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2015 (1)

S. Liu, B. M. Hennelly, C. Guo, and J. T. Sheridan, “Robustness of double random phase encoding spread-space spread-spectrum watermarking technique,” Sig. Process. 109, 345–361 (2015).
[Crossref]

2014 (2)

F. Yi, I. Moon, and Y. H. Lee, “A Multispectral Photon-Counting Double Random Phase Encoding Scheme for Image Authentication,” Sensors (Basel) 14(5), 8877–8894 (2014).
[Crossref] [PubMed]

I. Muniraj, B. Kim, and B. G. Lee, “Encryption and volumetric 3D object reconstruction using multispectral computational integral imaging,” Appl. Opt. 53(27), G25–G32 (2014).
[Crossref] [PubMed]

2013 (3)

2012 (1)

E. Pérez-Cabré, H. Abril, M. Millán, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[Crossref]

2009 (4)

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47(11), 1273–1281 (2009).
[Crossref]

N. T. Shaked, B. Katz, and J. Rosen, “Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods,” Appl. Opt. 48(34), H120–H136 (2009).
[Crossref] [PubMed]

J. H. Park, K. Hong, and B. Lee, “Recent progress in three-dimensional information processing based on integral imaging,” Appl. Opt. 48(34), H77–H94 (2009).
[Crossref] [PubMed]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multi perspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

2008 (1)

2007 (1)

2006 (4)

2005 (3)

2004 (2)

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
[Crossref] [PubMed]

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE Int. Conf. on Acoustic. Speech, Signal Process. 3, 485–488 (2004).

2001 (2)

E. Tajahuerce, J. Lancis, B. Javidi, and P. Andrés, “Optical security and encryption with totally incoherent light,” Opt. Lett. 26(10), 678–680 (2001).
[Crossref] [PubMed]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193(1-6), 51–67 (2001).
[Crossref]

2000 (3)

1999 (1)

1998 (1)

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. 15(8), 2059–2065 (1998).
[Crossref]

1997 (1)

J. D. Brasher and E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentication,” Opt. Eng. 36(9), 2409–2416 (1997).
[Crossref]

1995 (3)

1994 (1)

J. D. Villasenor, “Optical Hartley transform,” Proc. IEEE 82(3), 391–399 (1994).
[Crossref]

1991 (1)

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[Crossref]

1990 (1)

E. A. Watson and G. M. Morris, “Comparison of infrared up conversion methods for photon-limited imaging,” J. Appl. Phys. 67(10), 6075–6084 (1990).
[Crossref]

1987 (1)

J. D. Villasenor and R. N. Bracewell, “Optical phase obtained by analogue Hartley transformation,” Nature 330(6150), 735–737 (1987).
[Crossref]

1984 (1)

1983 (1)

1968 (1)

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]

1931 (1)

1908 (1)

G. Lippmann, “La photographie integrale,” Comptes-Rendus Acad. Sci. 146, 446–451 (1908).

Abril, H.

E. Pérez-Cabré, H. Abril, M. Millán, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[Crossref]

Andrés, P.

Arcos, S.

Badizadegan, K.

Bashaw, M. C.

Bracewell, R. N.

J. D. Villasenor and R. N. Bracewell, “Optical phase obtained by analogue Hartley transformation,” Nature 330(6150), 735–737 (1987).
[Crossref]

R. N. Bracewell, “Discrete Hartley transform,” J. Opt. Soc. Am. 73(12), 1832–1835 (1983).
[Crossref]

Brasher, J. D.

J. D. Brasher and E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentication,” Opt. Eng. 36(9), 2409–2416 (1997).
[Crossref]

Burckhardt, C.

Callens, N.

Carnicer, A.

Chen, L.

L. Chen and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31(23), 3438–3440 (2006).
[Crossref] [PubMed]

L. Chen and D. Zhao, “Optical image encryption based on fractional wavelet transform,” Opt. Commun. 254(4-6), 361–367 (2005).
[Crossref]

Cho, M.

Cutler, R.

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE Int. Conf. on Acoustic. Speech, Signal Process. 3, 485–488 (2004).

Dasari, R. R.

Dorsch, R. G.

Dubois, F.

Feld, M. S.

Fukushima, S.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[Crossref]

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]

Gopinathan, U.

Guo, C.

S. Liu, B. M. Hennelly, C. Guo, and J. T. Sheridan, “Robustness of double random phase encoding spread-space spread-spectrum watermarking technique,” Sig. Process. 109, 345–361 (2015).
[Crossref]

He, L.

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE Int. Conf. on Acoustic. Speech, Signal Process. 3, 485–488 (2004).

Heanue, J. F.

Hennelly, B. M.

S. Liu, B. M. Hennelly, C. Guo, and J. T. Sheridan, “Robustness of double random phase encoding spread-space spread-spectrum watermarking technique,” Sig. Process. 109, 345–361 (2015).
[Crossref]

Hesselink, L.

Hong, K.

Hoshino, H.

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. 15(8), 2059–2065 (1998).
[Crossref]

Hoyos, M.

Isono, H.

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. 15(8), 2059–2065 (1998).
[Crossref]

Ives, H.

Javidi, B.

I. Moon, I. Muniraj, and B. Javidi, “3D Visualization at Low Light Levels Using Multispectral Photon Counting Integral Imaging,” J. Disp. Technol. 9(1), 51–55 (2013).
[Crossref]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38(17), 3198–3201 (2013).
[Crossref] [PubMed]

E. Pérez-Cabré, H. Abril, M. Millán, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[Crossref]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multi perspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

B. Tavakoli, B. Javidi, and E. Watson, “Three dimensional visualization by photon counting computational integral imaging,” Opt. Express 16(7), 4426–4436 (2008).
[Crossref] [PubMed]

S. Yeom, B. Javidi, and E. Watson, “Photon counting passive 3D image sensing for automatic target recognition,” Opt. Express 13(23), 9310–9330 (2005).
[Crossref] [PubMed]

E. Tajahuerce, J. Lancis, B. Javidi, and P. Andrés, “Optical security and encryption with totally incoherent light,” Opt. Lett. 26(10), 678–680 (2001).
[Crossref] [PubMed]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
[Crossref] [PubMed]

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[Crossref] [PubMed]

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20(7), 767–769 (1995).
[Crossref] [PubMed]

Johnson, E. G.

J. D. Brasher and E. G. Johnson, “Incoherent optical correlators and phase encoding of identification codes for access control or authentication,” Opt. Eng. 36(9), 2409–2416 (1997).
[Crossref]

Joseph, J.

Juvells, I.

Katz, B.

Kim, B.

Kim, E.-S.

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47(11), 1273–1281 (2009).
[Crossref]

Konforti, N.

Kurokawa, T.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[Crossref]

Kurowski, P.

Lancis, J.

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]

Lee, B.

Lee, B. G.

Lee, I. H.

Lee, Y. H.

F. Yi, I. Moon, and Y. H. Lee, “A Multispectral Photon-Counting Double Random Phase Encoding Scheme for Image Authentication,” Sensors (Basel) 14(5), 8877–8894 (2014).
[Crossref] [PubMed]

Lippmann, G.

G. Lippmann, “La photographie integrale,” Comptes-Rendus Acad. Sci. 146, 446–451 (1908).

Liu, S.

S. Liu, B. M. Hennelly, C. Guo, and J. T. Sheridan, “Robustness of double random phase encoding spread-space spread-spectrum watermarking technique,” Sig. Process. 109, 345–361 (2015).
[Crossref]

Lohmann, A. W.

Malvar, H.

H. Malvar, L. He, and R. Cutler, “High-quality linear interpolation for demosaicing of Bayer-patterned color images,” in IEEE Int. Conf. on Acoustic. Speech, Signal Process. 3, 485–488 (2004).

Martinez-Corral, M.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multi perspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multi perspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

Matoba, O.

Mendlovic, D.

Millán, M.

E. Pérez-Cabré, H. Abril, M. Millán, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[Crossref]

Monaghan, D. S.

Monnom, O.

Montes-Usategui, M.

Moon, I.

F. Yi, I. Moon, and Y. H. Lee, “A Multispectral Photon-Counting Double Random Phase Encoding Scheme for Image Authentication,” Sensors (Basel) 14(5), 8877–8894 (2014).
[Crossref] [PubMed]

I. Moon, I. Muniraj, and B. Javidi, “3D Visualization at Low Light Levels Using Multispectral Photon Counting Integral Imaging,” J. Disp. Technol. 9(1), 51–55 (2013).
[Crossref]

Morris, G. M.

E. A. Watson and G. M. Morris, “Comparison of infrared up conversion methods for photon-limited imaging,” J. Appl. Phys. 67(10), 6075–6084 (1990).
[Crossref]

G. M. Morris, “Scene matching using photon-limited images,” J. Opt. Soc. Am. A 1(5), 482–488 (1984).
[Crossref]

Muniraj, I.

I. Muniraj, B. Kim, and B. G. Lee, “Encryption and volumetric 3D object reconstruction using multispectral computational integral imaging,” Appl. Opt. 53(27), G25–G32 (2014).
[Crossref] [PubMed]

I. Moon, I. Muniraj, and B. Javidi, “3D Visualization at Low Light Levels Using Multispectral Photon Counting Integral Imaging,” J. Disp. Technol. 9(1), 51–55 (2013).
[Crossref]

Naughton, T. J.

Ohno, M.

S. Fukushima, T. Kurokawa, and M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light-modulator,” Appl. Phys. Lett. 58(8), 787–789 (1991).
[Crossref]

Ohzu, H.

Okano, F.

H. Hoshino, F. Okano, H. Isono, and I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. 15(8), 2059–2065 (1998).
[Crossref]

Park, J. H.

Park, Y.

Peng, X.

Pérez-Cabré, E.

E. Pérez-Cabré, H. Abril, M. Millán, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14(9), 094001 (2012).
[Crossref]

Piao, Y.-R.

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47(11), 1273–1281 (2009).
[Crossref]

Popescu, G.

Refregier, P.

Rosen, J.

Saavedra, G.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, “Progress in 3-D multi perspective display by integral imaging,” Proc. IEEE 97(6), 1067–1077 (2009).
[Crossref]

Shaked, N. T.

Sheridan, J. T.

S. Liu, B. M. Hennelly, C. Guo, and J. T. Sheridan, “Robustness of double random phase encoding spread-space spread-spectrum watermarking technique,” Sig. Process. 109, 345–361 (2015).
[Crossref]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14(8), 3181–3186 (2006).
[Crossref] [PubMed]

Shin, D.-H.

Y.-R. Piao, D.-H. Shin, and E.-S. Kim, “Robust image encryption by combined use of integral imaging and pixel scrambling techniques,” Opt. Lasers Eng. 47(11), 1273–1281 (2009).
[Crossref]

Singh, K.

Situ, G.

Tajahuerce, E.

Takaki, Y.

Tavakoli, B.

Unnikrishnan, G.

Villasenor, J. D.

J. D. Villasenor, “Optical Hartley transform,” Proc. IEEE 82(3), 391–399 (1994).
[Crossref]

J. D. Villasenor and R. N. Bracewell, “Optical phase obtained by analogue Hartley transformation,” Nature 330(6150), 735–737 (1987).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 3D II Principle: (a) Pick-up (recording) process, and (b) Reconstruction (display) process. A Bayer CCD camera (GRBG pattern) is used in the experiment illustrated.
Fig. 2
Fig. 2 The proposed optical setup for performing the HT and capturing and securing the 3D photon limited scene.
Fig. 3
Fig. 3 Test images used in our experiments: (a) Bayer patterned (“GRGB”) 2D elemental image; (b) Interpolated multispectral image; (c) Photon-counted Bayer image with 1000 photons, and (d) The corresponding multispectral photon-counted image.
Fig. 4
Fig. 4 Multispectral visualization of reconstructed 3D sectional images: PSNR is calculated between the computational integral image and the photon-limited integral image: (a) 3D sectional image with the first object in focus; (b) 3D sectional image with the second object in focus; (c) Photon-limited sectional image with first object is focused (PSNR = 32.95 dB); and (d) Photon-limited sectional image with second object is focused (PSNR = 30.54 dB).
Fig. 5
Fig. 5 Encrypted and decrypted data: (a) HT based encrypted 2D elemental image; (b) Photon-limited HT encrypted EI; (c) Decrypted 2D elemental image; and (d) Decrypted 3D sectional image (np = 1000).
Fig. 6
Fig. 6 False class images: (a) the primary false class 2D image; (b) The decrypted false class 3D sectional image.
Fig. 7
Fig. 7 Nonlinear correlation (NC) values versus number of photons (10x) results using a kth law nonlinear processor (k = 0.3): Highest peak values obtained are marked within each figures using 3D surface plot in MATLAB. (a) NC values for the 2D case; (b) NC values for the 3D case; (c) NC values for 2D false class images, and (d) NC values for 3D false class data set. In Fig (b) and (d) the blue colored lines, (i.e. solid lines), refers to the reconstruction of the first object at d = 540 mm while the orange colored lines (i.e. dashed line) refers to the reconstruction of second object at d = 620 mm. The corresponding peak NC values are indicated in the figures as values inside round brackets, e.g. (0.15) in Fig. 7(c).

Equations (8)

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H( u,v )= g( x,y ) cas[ 2π( ux+vy ) ] dxdy,
H( u,v )= exp( iπ/4 ) 2 { F( u,v )+exp( iπ/2 )F( u,v ) },
ψ( u,v )=r( u,v ) g( x,y )cas[ 2π( ux+vy ) ]dxdy ,
g( x,y )= ψ( u,v ) r 1 ( u,v )cas[ 2π( ux+vy ) ]dudv .
Poisson( L w | λ w )= [ λ w ] L w e λ w L w ! , L w =0,1,2,3,....
P w ( x,y )=Poissrnd( λ w ( x,y )= ψ ¯ w ( x,y )× n p )
MLE( g p z 0 )= 1 n p PQ p=0 P1 q=0 Q1 C pq ( k+Δ k pq ) w ,
c( x )= F 1 { | F[ g p d 0 ( x ) ]F( μ ) | k exp[ i( ϕ g p d 0 ( μ ) ϕ F ( μ ) ) ] },

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