Abstract

Mobile devices are a ubiquitous technology, and many researchers are trying to implement three-dimensional (3D) displays on mobile devices for a variety of applications. We investigate a method to store compressed and encrypted elemental images (EIs) used for 3D integral imaging displays in multiple quick-response (QR) codes. This approach allows user friendly access, readout, and 3D display with mobile devices. We first compress the EIs and then use double-random-phase encryption to encrypt the compressed image and store this information in multiple QR codes. The QR codes are then scanned using a commercial Smartphone to reveal the encrypted information, which can be decrypted and decompressed. We also introduce an alternative scheme by applying photon counting to each color channel of the EIs prior to the aforementioned compression and encryption scheme to generate sparsity and nonlinearity for improved compression and security. Experimental results are presented to demonstrate both 3D computational reconstruction and optical 3D integral imaging display with a Smartphone using EIs from the QR codes. This work utilizing compressed QR encoded EIs for secure integral imaging displays using mobile devices may enable secure 3D displays with mobile devices.

© 2014 Optical Society of America

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References

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2014 (1)

A. Markman, B. Javidi, M. Tehranipoor, IEEE J. Photonics 6, 1 (2014).

2013 (3)

2011 (1)

2008 (2)

B. Tavakoli, B. Javidi, E. Watson, Opt. Express 16, 4426 (2008).
[Crossref]

X. Liu, D. Doermann, H. Li, IEEE Trans. Multimedia 10, 361 (2008).

2007 (1)

2006 (1)

F. Okano, J. Arai, K. Mitani, M. Okui, Proc. IEEE 94, 490 (2006).
[Crossref]

2005 (1)

2004 (1)

1999 (1)

1997 (1)

1995 (2)

1994 (1)

B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

1993 (1)

1989 (1)

1988 (1)

1952 (1)

D. Huffman, Proc. IRE 40, 1098 (1952).
[Crossref]

1931 (1)

1908 (1)

G. Lippmann, C. R. Acad. Sci. 146, 446 (1908).

Arai, J.

F. Okano, J. Arai, K. Mitani, M. Okui, Proc. IEEE 94, 490 (2006).
[Crossref]

F. Okano, H. Hoshino, J. Arai, I. Yuyama, Appl. Opt. 36, 1598 (1997).
[Crossref]

Arcos, S.

Barrera, J. F.

Bashaw, M. C.

Bose, R.

R. Bose, Information Theory, Coding, and Cryptography (Tata McGraw-Hill, 2002).

Carnicer, A.

Castro, A.

Cho, M.

Davies, N.

Doermann, D.

X. Liu, D. Doermann, H. Li, IEEE Trans. Multimedia 10, 361 (2008).

Dubois, F.

Frauel, Y.

Heanue, J. F.

Hesselink, L.

Hong, S.

Horner, J. L.

B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

Hoshino, H.

Huffman, D.

D. Huffman, Proc. IRE 40, 1098 (1952).
[Crossref]

Ives, H. E.

Jang, J.

Javidi, B.

Juvells, I.

Li, H.

X. Liu, D. Doermann, H. Li, IEEE Trans. Multimedia 10, 361 (2008).

Lippmann, G.

G. Lippmann, C. R. Acad. Sci. 146, 446 (1908).

Liu, X.

X. Liu, D. Doermann, H. Li, IEEE Trans. Multimedia 10, 361 (2008).

Markman, A.

A. Markman, B. Javidi, M. Tehranipoor, IEEE J. Photonics 6, 1 (2014).

Martinez-Corral, M.

Matoba, O.

McCormick, M.

Mira, A.

Mitani, K.

F. Okano, J. Arai, K. Mitani, M. Okui, Proc. IEEE 94, 490 (2006).
[Crossref]

Montes-Usategui, M.

Naughton, T. J.

Okano, F.

F. Okano, J. Arai, K. Mitani, M. Okui, Proc. IEEE 94, 490 (2006).
[Crossref]

F. Okano, H. Hoshino, J. Arai, I. Yuyama, Appl. Opt. 36, 1598 (1997).
[Crossref]

Okui, M.

F. Okano, J. Arai, K. Mitani, M. Okui, Proc. IEEE 94, 490 (2006).
[Crossref]

Pérez-Cabré, E.

Réfrégier, P.

Sadjadi, F.

F. Sadjadi, B. Javidi, Physics of Automatic Target Recognition (Springer, 2007).

Stern, A.

Tavakoli, B.

Tehranipoor, M.

A. Markman, B. Javidi, M. Tehranipoor, IEEE J. Photonics 6, 1 (2014).

Torroba, R.

Watson, E.

Xiao, X.

Yang, L.

Yuyama, I.

Appl. Opt. (6)

C. R. Acad. Sci. (1)

G. Lippmann, C. R. Acad. Sci. 146, 446 (1908).

IEEE J. Photonics (1)

A. Markman, B. Javidi, M. Tehranipoor, IEEE J. Photonics 6, 1 (2014).

IEEE Trans. Multimedia (1)

X. Liu, D. Doermann, H. Li, IEEE Trans. Multimedia 10, 361 (2008).

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

B. Javidi, J. L. Horner, Opt. Eng. 33, 1752 (1994).
[Crossref]

Opt. Express (4)

Opt. Lett. (5)

Proc. IEEE (1)

F. Okano, J. Arai, K. Mitani, M. Okui, Proc. IEEE 94, 490 (2006).
[Crossref]

Proc. IRE (1)

D. Huffman, Proc. IRE 40, 1098 (1952).
[Crossref]

Other (4)

“QR code minimum size,” http://www.qrstuff.com .

http://zxing.appspot.com/generator .

R. Bose, Information Theory, Coding, and Cryptography (Tata McGraw-Hill, 2002).

F. Sadjadi, B. Javidi, Physics of Automatic Target Recognition (Springer, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

(a) Pickup and (b) display stages of an integral imaging system.

Fig. 2.
Fig. 2.

(a) 19×19 pixel RGB image; (b) and (c) display the QR codes containing the real and imaginary information for the red color channel from the compressed and ciphered image shown in (a), respectively; (d) and (e) depict a scanned QR code using the iPhone SCAN application revealing the real and imaginary information from the compressed and ciphered image, respectively, for the red color channel of the image shown in (a); (f) shows the decrypted and decompressed image.

Fig. 3.
Fig. 3.

Storing multiple RGB encrypted EIs inside of multiple QR codes.

Fig. 4.
Fig. 4.

19×19 pixel RGB: (a) EIs that were compressed using RLE and Huffman coding followed by encryption using DRPE; (b), (c) computational 3D integral imaging reconstructions with four EIs at a distance (range) of (b) 65 mm focused on “3” and (c) 115 mm focused on “D.”

Fig. 5.
Fig. 5.

Optical 3D integral imaging display setup using a Smartphone and a lenslet array.

Fig. 6.
Fig. 6.

3D display results using Smartphone. (a) 3D optical reconstruction with integral imaging using the primary EIs. (b) Optical 3D reconstruction using the decrypted and decompressed EIs obtained from the compressed DRPE EIs in QR codes.

Fig. 7.
Fig. 7.

3D photon counting integral imaging compression and security experiments. A 54×96 EI array consisting of 19×19 pixel RGB EIs was used. (a) Shows an EI, while (b) depicts the corresponding photon-limited EI using about eight photons per pixel on each color channel of the EI. 3D optical reconstruction after decryption and decompression is shown (c) using original EIs and (d) when photon counting on the EIs was used.

Tables (1)

Tables Icon

Table 1. Specifications of 3D Display Setup

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

R(x,y,z)=1O(x,y)×k=0K1l=0L1Ekl(xkNx×pcx×M,ylNy×pcy×M),
ψ(x)={f(x)×exp[i2πn(x)]}*h(x),
MSE=1NMn=0N1m=0M1[fdecrypt(xn,ym)f(xn,ym)]2,
P(lj;λj)=[λj]ljeλjlj!,forλj>0,lj{0,1,2,},

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