Abstract

We propose a new method called modified optical scanning cryptography using Fresnel telescope imaging technique for encryption and decryption of remote objects. An image or object can be optically encrypted on the fly by Fresnel telescope scanning system together with an encryption key. For image decryption, the encrypted signals are received and processed with an optical coherent heterodyne detection system. The proposed method has strong performance through use of secure Fresnel telescope scanning with orthogonal polarized beams and efficient all-optical information processing. The validity of the proposed method is demonstrated by numerical simulations and experimental results.

© 2015 Optical Society of America

1. Introduction

Currently, optical encryption techniques have significant potential for security applications due to their marked advantages of high parallel processing speed and high flexibility [1–3]. Optical encryption as opposed to electronic or digital encryption can provide many degrees of freedom such as amplitude, phase, polarization and wavelength which can be combined in different ways to make the information more secure. Many optical processing techniques, such as double random phase encoding (DRPE) using Fourier transform [4], Fractional Fourier transform [5], Fresnel transform [6], gyrator transform [7] and Hartley transform [8], have been developed. In conventional DRPE, the original image is encoded into a stationary white noise, and no information about the original image can be observed. Many improved techniques have been developed, such as polarized light encoding [9], asymmetric cryptosystem [10], and digital holography [11] etc. Digital holography is one type of important technologies for optical encryption because of the accurate recording and extraction of the fully complex field [11–14]. Recently, holograms of 2-D images or 3-D objects can be encrypted with phase-shifting digital holography by insertion of a phase mask in the path of the reference or the signal beam [12]. It is, however, difficult to directly obtain the whole field with conventional digital holography because of the limited viewing field. An improved encryption technique-optical scanning cryptography was proposed by Poon [15, 16] based on optical scanning holography. The object can be optically encrypted by optical heterodyne scanning. Based on this scanning method, incoherent objects can be directly processed without the usage of spatial light modulators that convert an incoherent image to a coherent image. But the encrypted information must be converted into a heterodyne electrical signal and extracted to the sine and cosine holograms of the scanned objects. It needs complicated electronic phase-lock and demodulation system that limits the processing speed of encrypted and decrypted information.

In this paper, we propose a new method called modified optical scanning cryptography using Fresnel telescope imaging technique. An object can be optically encrypted on the fly by Fresnel telescope scanning together with an encryption key. The scanning pattern is generated by two laser beams with orthogonal polarization. The encrypted signal can be received and processed by an optical coherent heterodyne detection system. We can obtain the sine and cosine holograms of the encrypted object from 90 degree 2 × 4 optical hybrid. This coherent detection system combines with the Fresnel telescope scanning system into the proposed Fresnel telescope imaging system. In contrast to a recently developed optical cryptography based on optical heterodyne scanning, the proposed encryption method is all-optical cryptography and is suitable for remote objects. It has many advantages, such as high security based on orthogonal polarization scanning and high speed of information processing.

2. Principle of modified optical scanning cryptography

2.1 Encryption

The encryption stage illustrated in Fig. 1 shows the optical setup of Fresnel telescope scanning system. A laser is first polarized by a half-wave plate (HWP) and collimated by the combination of a pinhole and a lens, and then is divided into two beams by a polarized beam splitter (PBS1). Two pupils, p1(x, y) and p2(x, y), located in the front focal planes of the lens L1, are placed in the two beams, respectively. The combined optical beams are then used to two-dimensional (2-D) scanner over the object, which is located at a distance zc away from the back focal plane of the lens L1. If the object is located in remote distance, we can place an optimized transmission telescope (TTS) in the encryption system. For enhancing the security, we can put another random phase plate exp[ jr(x, y)] before the object. Then the encryption system can perform double random phase encoding.

 figure: Fig. 1

Fig. 1 The encryption system of modified optical scanning cryptography.

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The field of scanning pattern Escan(x, y; zc) before the object is

Escan(x,y;zc)=[Ep(x,y;zc)Es(x,y;zc)]exp(jω0t),
where the subscripts p and s denote parallel and perpendicular polarization, respectively, Ei(x, y; zc) = Ϝ{pi(x, y)}h(x, y; zc) with i = p or s, h(x, y; zc) is the free-space spatial impulse response in Fourier optics and denotes the 2-D convolution.

In the optical heterodyne scanning system of Ref [15], the scanning pattern is an actual Fresnel zone plate (FZP) generated by interference of two beams. But in our proposed encryption system, the scanning pattern generated by two beams can’t directly interfere owing to their orthogonal polarizations, except that we put a polarization rotator in the system. We call this Fresnel telescope scanning system. It possesses the advantage of higher security than FZP scanning and can perform encryption of remote objects. The optical field just after the encrypted object can be expressed as

Pa(x',y';zc)=T(x'+x,y'+y;zc)Escan(x',y';zc)
where T(x, y; zc) represents the amplitude transmittance of the object, x = x(t) and y = y(t) represent the instantaneous 2-D position of the object with respect to the light amplitude distribution. So the information of the object is encrypted in the scanning pattern.

2.2 Decryption

Decryption of the encrypted information and reconstruction of the original object are performed optically by optical coherent heterodyne detection system as shown in Fig. 2. First, the encrypted information transmitted from the object is collected by a positive lens or a receiving telescope (RTS). Next, it is split into two beams by a PBS, followed by two HWPs after each beam. After passing through the HWP, the polarization state of the two beams is rotated by 45 degrees, respectively. Then these two beams are called as the signal beam US and the local oscillator beam UL and fed to a free space propagating 90 degree 2?4 optical hybrid after reflected by two mirrors.

 figure: Fig. 2

Fig. 2 The decryption system of modified optical scanning cryptography.

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US=22[11]Ep(x',y';z)T(x'+x,y'+y;z),
UL=22[11]Es(x',y';z)T(x'+x,y'+y;z).

90 degree 2?4 optical hybrid is the key device of the optical coherent detection system and often applied in free-space optical communications [17–19]. The basic principle of a 90 degree 2?4 optical hybrid is shown in Fig. 3. This hybrid is used to split and combine two beams from two inputs, and at last to obtain four mixed output beams U0, U90, U180, U270, with 0, 90, 180 and 270 degree phase differences among them. The four output beams are divided into two pairs 180 phase-shift outputs and one pair has a phase difference of 90 degrees with respect to the other.

 figure: Fig. 3

Fig. 3 The basic principle of a 90 degree 2 × 4 optical hybrid.

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In our experiment, we use the optical hybrid as shown in Fig. 2. It consists of three PBSs, two HWPs, two mirrors and a quarter wave plate (QWP).

U0={22ejτ//[Es(x',y')ejτ//ejπ/4+Ep(x',y')ejρ]}T(x'+x,y'+y;z),
U180={22ejρ[Es(x',y')ejτ//ejπ/4Ep(x',y')ejρ]}T(x'+x,y'+y;z),
U90={22ejτ//[Ep(x',y')ejτ//+Es(x',y')ejρejπ/4]}T(x'+x,y'+y;z),
U270={22ejρ[Ep(x',y')ejτ//Es(x',y')ejρejπ/4]}T(x'+x,y'+y;z),
where τ// and ρ denote the phase shifts introduced by the PBS to parallel and perpendicular polarized beam, respectively. Under ideal conditions, we get the subtracted signals,
I0I180=2|ESEp|cos[ϕ(t)],
I90I270=2|ESEp|cos[ϕ(t)+π2],
where Im = |Um|2, m denotes 0, 90, 180 and 270. Two pairs of signals are detected by two balanced detectors, BD1 and BD2. The currents from BD1 and BD2 can be expressed as,
id(x,y)=i0i180Re[EsEp*ejϕ]|T|2dz=Hsin(x,y),
iq(x,y)=i90i270Im[EsEp*ejϕ]|T|2dz=Hcos(x,y).
where Re[ ]and Im[ ] denote the real and imaginary parts of the quantity within the bracket, denotes 2-D correlation. The output signals id (x, y) and iq (x, y) from balanced detectors can be denoted as the sine-Fresnel zone plate (SFZP) hologram Hsin (x, y) and cosine- Fresnel zone plate (CFZP) hologram Hcos(x, y) of the object, respectively [15]. We construct a complex hologram H (x, y; zc) = Hsin(x, y)眏Hcos (x, y) and store them in digital computer. The decryption image can be reconstructed by convolving the hologram H (x, y; zc) with the free-space impulse response function h(x, y; zd) with the decoding distance zd,

H(x,y;zc)h(x,y;zd).

The proposed coherent detection system based on 90 degree 2?4 optical hybrid doesn’t need the acousto-optic modulator and complicated electronic demodulation system. So it has the distinctive advantages of high optical transmittance and high processing speed of both the encrypted and decrypted information.

3. Simulation results

A numerical simulation is employed to verify robustness of the proposed method. We let the pupil functions for encryption p1(x, y) = exp[jM(x, y)], where M(x, y) is a function of numbers randomly distributed in a range of [0, 2π], and p2(x, y) = δ(x, y) is a pinhole in the encryption stage. Encryption is performed on the fly by the Fresnel scanning system illustrated in Fig. 1. Figure 4(a) shows the original image to be encrypted, Figs. 4(b) and 4(c) show the real part and the imaginary part of the original image multiplied by a random phase plate p1(x, y), respectively. Figure 4(d) shows the intensity of the encrypted image. We can see from Fig. 4(d) that the information is effectively hidden and encrypted using the proposed encryption system.

 figure: Fig. 4

Fig. 4 (a) The original image to be encrypted; (b) real part and (c) imaginary part of the original image multiplied by a random phase plate; (d) intensity of encrypted image.

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In the decryption stage, one pupil is a pinhole and the other pupil is the decryption key of the form of a random phase function, exp[jM(-x, -y)]. When the decryption is performed using the totally correct system parameters such as decryption key and decoding distance, the decrypted image can be completely reconstructed. Figures 5(a) and 5(b) show the intensities of the decrypted images with the decoding distance zd = zc and zd = 2zc, respectively, when the decryption key is matched to the encryption key. The quality of decrypted images degrades with the offset from the decoding distance. Figure 5(c) shows the intensity of decrypted image with the correct decoding distance but with a wrong decryption key. It can be seen that although the decoding distance is matched to the coding distance, a correct decrypted image cannot be obtained using the wrong decryption key. The decoding distance also can be treated as another encryption key in addition to the random phase key. This increases decryption difficulty for the unauthorized receivers.

 figure: Fig. 5

Fig. 5 Intensity of the decrypted image with the correct decryption key with (a) zd = zc and (b) zd = 2zc; (c) the decrypted image with wrong decryption key and the correct decoding distance.

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4. Experimental results

In this section, we perform an experiment to demonstrate the feasibility and effectiveness of the proposed optical scanning cryptography method. In the experiment, an image was first encrypted optically using the Fresnel telescope scanning system in the setup of Fig. 1. A letter “H” was used as a 2-D image with size of 25mm × 22mm. The coding distance zc = 10.8m. The laser emits linear polarization beam with wavelength of 532nm. Magnification of transmission telescope is 20. The encryption key and the decryption key are of the same functional form but randomly distributed in a range of [0, 2π], respectively.

Figure 6(a) shows the original image, and Fig. 6(b) shows the encrypted image by the encryption system of Fig. 1. From Fig. 6(b) we can see that the original image is fully hidden, and no useful information about the original image can be observed. It is more efficient and reliable in security applications. During image decryption stage, when the decryption is performed using the correct system parameters such as decoding distance and correct decryption key, the reconstructed image from the encrypted hologram is shown in Fig. 6(c). It can be seen in Fig. 6(c) that the decrypted image at totally correct conditions is reconstructed fairly well. Although the decrypted image has a little noise, it can still be clearly recognized.

 figure: Fig. 6

Fig. 6 (a) The original image; (b) the encrypted image; and (c) the decrypted image.

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5. Conclusion

In summary, we have proposed a new method called modified optical scanning cryptography using Fresnel telescope imaging technique. The electrical processing of sine and cosine holograms in conventional optical scanning cryptography is replaced by the all-optical coherent detection using 90 degree 2 × 4 optical hybrid. It possesses the distinctive advantages of high optical transmittance and high processing speed of both the encrypted and decrypted information. Numerical simulation results and experimental results demonstrate that the proposed method is feasible and effective. The proposed method provides a new optical encryption strategy instead of the conventional electrical processing, which may open up a new application perspective for optical cryptography.

Acknowledgments

This work is partially supported by the Shanghai City Board of education research and innovation project under Grant No.13YZ063, Shanghai Municipal Natural Science Foundation under Grant No.14ZR1430700, and the National Nature Science Foundation of China under Grant No. 61307008, No. 11174304, and No. 61475168.

References and links

1. O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009). [CrossRef]  

2. B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997). [CrossRef]  

3. J. F. Barrera, A. Mira, and R. Torroba, “Optical encryption and QR codes: secure and noise-free information retrieval,” Opt. Express 21(5), 5373–5378 (2013). [CrossRef]   [PubMed]  

4. 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]  

5. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000). [CrossRef]   [PubMed]  

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

7. Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010). [CrossRef]   [PubMed]  

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

9. X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40(14), 2310–2315 (2001). [CrossRef]   [PubMed]  

10. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010). [CrossRef]   [PubMed]  

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

12. B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000). [CrossRef]   [PubMed]  

13. E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39(14), 2313–2320 (2000). [CrossRef]   [PubMed]  

14. T. Nomura, “Hybrid optical encryption of a 3-D object using a digital holographic technique,” Opt. Eng. 43(10), 2228–2232 (2004). [CrossRef]  

15. T. C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42(32), 6496–6503 (2003). [CrossRef]   [PubMed]  

16. T. C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42(32), 6496–6503 (2003). [CrossRef]   [PubMed]  

17. Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

18. P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011). [CrossRef]  

19. R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).

References

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  1. O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
    [Crossref]
  2. B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
    [Crossref]
  3. J. F. Barrera, A. Mira, and R. Torroba, “Optical encryption and QR codes: secure and noise-free information retrieval,” Opt. Express 21(5), 5373–5378 (2013).
    [Crossref] [PubMed]
  4. 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]
  5. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourier domain,” Opt. Lett. 25(12), 887–889 (2000).
    [Crossref] [PubMed]
  6. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29(14), 1584–1586 (2004).
    [Crossref] [PubMed]
  7. Z. Liu, L. Xu, C. Lin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49(29), 5632–5637 (2010).
    [Crossref] [PubMed]
  8. L. Chen and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31(23), 3438–3440 (2006).
    [Crossref] [PubMed]
  9. X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, and K. Kuroda, “Secure optical memory system with polarization encryption,” Appl. Opt. 40(14), 2310–2315 (2001).
    [Crossref] [PubMed]
  10. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35(2), 118–120 (2010).
    [Crossref] [PubMed]
  11. E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39(35), 6595–6601 (2000).
    [Crossref] [PubMed]
  12. B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
    [Crossref] [PubMed]
  13. E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39(14), 2313–2320 (2000).
    [Crossref] [PubMed]
  14. T. Nomura, “Hybrid optical encryption of a 3-D object using a digital holographic technique,” Opt. Eng. 43(10), 2228–2232 (2004).
    [Crossref]
  15. T. C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42(32), 6496–6503 (2003).
    [Crossref] [PubMed]
  16. T. C. Poon, T. Kim, and K. Doh, “Optical scanning cryptography for secure wireless transmission,” Appl. Opt. 42(32), 6496–6503 (2003).
    [Crossref] [PubMed]
  17. Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).
  18. P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
    [Crossref]
  19. R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).

2013 (1)

2011 (1)

P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
[Crossref]

2010 (3)

2009 (1)

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

2006 (1)

2004 (2)

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

T. Nomura, “Hybrid optical encryption of a 3-D object using a digital holographic technique,” Opt. Eng. 43(10), 2228–2232 (2004).
[Crossref]

2003 (2)

2001 (1)

2000 (4)

1997 (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

1995 (1)

1991 (1)

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).

Barrera, J. F.

Chen, L.

Doh, K.

Garreis, R.

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).

Hou, P.

P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
[Crossref]

Ide, M.

Javidi, B.

Joseph, J.

Kim, T.

Kuroda, K.

Lin, C.

Liu, L.

P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
[Crossref]

Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

Liu, S.

Liu, Z.

Luan, Z.

Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

Matoba, O.

Millan, M. Í. S.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Mira, A.

Nomura, T.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

T. Nomura, “Hybrid optical encryption of a 3-D object using a digital holographic technique,” Opt. Eng. 43(10), 2228–2232 (2004).
[Crossref]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25(1), 28–30 (2000).
[Crossref] [PubMed]

Okada-Shudo, Y.

Peng, X.

Perez-Cabre, E.

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Poon, T. C.

Qin, W.

Refregier, P.

Shimura, T.

Singh, K.

Situ, G.

Sun, J.

P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
[Crossref]

Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

Tajahuerce, E.

Tan, X.

Torroba, R.

Unnikrishnan, G.

Verrall, S. C.

Xu, L.

Yan, A.

Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

Zeiss, C.

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).

Zhang, J.

Zhao, D.

Zhi, Y.

P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
[Crossref]

Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

Zhou, Y.

P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
[Crossref]

Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

Appl. Opt. (6)

Chin. Phys. Lett. (1)

P. Hou, Y. Zhi, Y. Zhou, J. Sun, and L. Liu, “An optical 2×4 90° hybrid based on a birefringent crystal for a coherent receiver in a free-space optical communication system,” Chin. Phys. Lett. 28(7), 074204 (2011).
[Crossref]

Opt. Eng. (1)

T. Nomura, “Hybrid optical encryption of a 3-D object using a digital holographic technique,” Opt. Eng. 43(10), 2228–2232 (2004).
[Crossref]

Opt. Express (1)

Opt. Lett. (6)

Phys. Today (1)

B. Javidi, “Securing information with optical technologies,” Phys. Today 50(3), 27–32 (1997).
[Crossref]

Proc. IEEE (1)

O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97(6), 1128–1148 (2009).
[Crossref]

Proc. SPIE (2)

Y. Zhi, Y. Zhou, J. Sun, A. Yan, Z. Luan, and L. Liu, “Self-homodyne interferometric detection in 2×4 optical hybrid for free-space optical communication,” Proc. SPIE 7814, 781412 (2010).

R. Garreis and C. Zeiss, “90° optical hybrid for coherent receivers,” Proc. SPIE 1522, 210–219 (1991).

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Figures (6)

Fig. 1
Fig. 1 The encryption system of modified optical scanning cryptography.
Fig. 2
Fig. 2 The decryption system of modified optical scanning cryptography.
Fig. 3
Fig. 3 The basic principle of a 90 degree 2 × 4 optical hybrid.
Fig. 4
Fig. 4 (a) The original image to be encrypted; (b) real part and (c) imaginary part of the original image multiplied by a random phase plate; (d) intensity of encrypted image.
Fig. 5
Fig. 5 Intensity of the decrypted image with the correct decryption key with (a) zd = zc and (b) zd = 2zc; (c) the decrypted image with wrong decryption key and the correct decoding distance.
Fig. 6
Fig. 6 (a) The original image; (b) the encrypted image; and (c) the decrypted image.

Equations (13)

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E scan (x,y; z c )=[ E p (x,y; z c ) E s (x,y; z c ) ]exp(j ω 0 t),
P a (x',y'; z c )=T(x'+x,y'+y; z c ) E scan (x',y'; z c )
U S = 2 2 [ 1 1 ] E p ( x ' , y ' ;z)T( x ' +x, y ' +y;z),
U L = 2 2 [ 1 1 ] E s ( x ' , y ' ;z)T( x ' +x, y ' +y;z).
U 0 ={ 2 2 e j τ // [ E s ( x ' , y ' ) e j τ // e jπ/4 + E p ( x ' , y ' ) e j ρ ]}T( x ' +x, y ' +y;z),
U 180 ={ 2 2 e j ρ [ E s ( x ' , y ' ) e j τ // e jπ/4 E p ( x ' , y ' ) e j ρ ]}T( x ' +x, y ' +y;z),
U 90 ={ 2 2 e j τ // [ E p ( x ' , y ' ) e j τ // + E s ( x ' , y ' ) e j ρ e jπ/4 ]}T( x ' +x, y ' +y;z),
U 270 ={ 2 2 e j ρ [ E p ( x ' , y ' ) e j τ // E s ( x ' , y ' ) e j ρ e jπ/4 ]}T( x ' +x, y ' +y;z),
I 0 I 180 =2| E S E p |cos[ϕ(t)],
I 90 I 270 =2| E S E p |cos[ϕ(t)+ π 2 ],
i d (x,y)= i 0 i 180 Re[ E s E p * e jϕ ]|T | 2 dz = H sin (x,y),
i q (x,y)= i 90 i 270 Im[ E s E p * e jϕ ]|T | 2 dz = H cos (x,y).
H(x,y; z c )h(x,y; z d ).

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