Optics Communications 259 (2006) 532–536 www.elsevier.com/locate/optcom
Multiplexing encryption–decryption via lateral shifting of a random phase mask John Fredy Barrera a, Rodrigo Henao a, Myrian Tebaldi Roberto Torroba b, Ne´stor Bolognini b,c
b,*
,
a ´ ptica y Foto´nica, Instituto de Fı´sica, Universidad de Antioquia A.A. 1226 Medellı´n, Colombia Grupo de O ´ pticas (CONICET-CIC) and UID OPTIMO, Facultad de Ingenierı´a, Universidad Nacional de La Centro de Investigaciones O Plata, P.O. Box 124, La Plata (1900), Argentina ´ pticas (CONICET-CIC), Facultad de Ciencias Exactas, Universidad Nacional de La Plata, and UID OPTIMO, Centro de Investigaciones O Facultad de Ingenı´era, Universidad Nacional de La Plata, La Plata, P.O. Box 124, La Plata (1900), Argentina b
c
Received 11 August 2005; received in revised form 9 September 2005; accepted 9 September 2005
Abstract We present an holographic memory optical arrangement based on the successive shifting of a random pure-phase mask to achieve encrypted images multiplexing. The input images are encrypted to a stationary white noise using the usual double random encoding in the Fresnel domain. The encrypted information is imaged in a photorefractive crystal where also a reference beam impinges. In the holographic memory, a BSO crystal is used to provide both a recording medium and a phase conjugate mirror. The combination of these two features supplies at the same time the necessary exact cancellation of the random pure-phase mask as well as allows a real-time decryption process. Successive images are encrypted and position-encoded by speckle patterns arising from the random pure-phase mask in-plane shifting between exposures. We include experimental results to corroborate the multiplexing capability and the read-out fidelity of the proposed arrangement. 2005 Elsevier B.V. All rights reserved. PACS: 42.30.d; 42.65.Hw; 42.40.i Keywords: Encryption; Photorefractive materials; Volume memories
1. Introduction Optical systems employing photorefractive crystals are attractive because of their potential for high density storage and high speed access rate. There are several photorefractive materials so that for a determined experience they can be properly tailored. In this way, researchers have made an effort to find ways to maximize the storage capacities of such crystals. The storage capabilities associated with the 3-D nature of the medium [1] allow recording of *
Corresponding author. Tel.: +54 221 484 0280; fax: +54 221 471 2771. E-mail address:
[email protected] (M. Tebaldi).
0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.09.027
a page of data at one time and the simultaneous readout of an entire page [2]. Numerous multiplexing techniques to store multitude of images into a single crystal without cross talk have been proposed, including spatial, angular [3,4], wavelength [5] and shift multiplexing [6,7]. Another multiplexing technique involves using deterministic orthogonal phase codes in a reference beam. This arrangement allows retrieving multiple images with high diffraction efficiency without adjustment problems [8–10]. On the other hand, the demand for the information security rapidly increased in order to prevent hacking by unauthorized users. So optical encryption techniques play
J. Fredy Barrera et al. / Optics Communications 259 (2006) 532–536
an important role in optical memory systems and have been studied actively. These techniques provide a high level of security [11–17] because there are many degrees of freedom to encrypt the information, such as amplitude, phase, wavelength and polarization. Several methods have been described to use optical encrypting schemes in order to secure data in holographic memory systems. Some of them are based on protecting the stored information by transforming the original data into stationary white-noise data. Original data may be encrypted optically by using techniques such as double random phase encryption [13]. In [18], an encrypted holographic data-storage system that combines orthogonal phase code multiplexing with the use of a random phase code is proposed. This method maintains the advantage of an orthogonal phase code multiplexing and also protects the access to memory from unauthorized users. Analyses on three-dimensional shifting selectivity of the phase-mask in double random encoding holographic memories have been also addressed [19–22]. In [20], it is demonstrated that the lateral shifting selectivity of the decryption phase mask in the system depends not only on its correlation length but also on the dimensions of the recording medium and on the distance between the phase mask and the hologram. This analysis gives information about the alignment and reposition of the random phase mask in the decryption process. In this context, optical encryption system using phase conjugation in photorefractive crystals has been developed [16,23–25]. The technique is not only an option to the high capacity optical data storage of photorefractive crystal but also secures the stored information against unauthorized users. The stored data thus appear to be buried under the encryption, not being able to be decrypted. In our paper, we report a study on multiplexing encrypted images based on the successive shifting of a random pure-phase mask. The double random pure-phase mask scheme is employed to encrypt each input object. As mentioned above, the principle of double random phase encoding is well established [13] and a number of studies have been carried out in this field concerning the shift selectivity and tolerance properties while shifting the random mask [19–22]. However, the analysis on inplane shifting of the second random pure-phase mask to encrypt–decrypt multiple images is not addressed so far. Our proposal is to experimentally implement such procedure in an optical arrangement using a photorefractive BSO crystal as holographic recording medium. A phase conjugation operation performed with the aid of these crystals allows the encryption–decryption implementation. The key to our conception is that each time the random pure-phase mask is properly moved, is equivalent to introduce a new encryption mask. This approach is employed to store several encrypted images in a single crystal. By an appropriate repositioning of the random pure-phase mask and together with the phase conjugation operation, we recover each original image. A detailed description
533
and experimental results that confirm our proposal are presented in the following section. 2. Description of the method Our optical multiple-image encryption system using a photorefractive crystal is shown in Fig. 1. A mini Nd YAG 50 mW power output laser source provides the setup illumination (k = 532 nm). An amplitude object O is transformed by lens L1 and re-imaged by lens L2 on the photorefractive BSO crystal. R1 and R2 represent the random pure-phase masks used to encrypt the input object. Then, each input object is encrypted to a stationary white noise using a double random pure-phase encoding in the Fresnel domain. Each encrypted information is imaged in the BSO crystal where also a reference beam impinges. This intensity distribution generates a space charge field in the crystal due to charge carrier redistribution. Because of the linear electro-optical effect that the crystal exhibits, the resulting space charge field produces a refractive index perturbation, which replicates and stores the encrypted information. The read-out of the stored data is done by the conjugate of the reference beam reconstructing thereby the conjugate of each encrypted image. Camera CCD captures the encrypted phase conjugated wavefront. If the correct key (random pure-phase mask R2) is properly positioned for decryption, then each original image is recovered and captured by the camera CCD. Note that using other than a random pure-phase mask would not result in phase compensation necessary to recover the original encrypted data. In our experimental arrangement, the dimension of the photorefractive BSO crystal is: 10 mm · 10 mm · 10 mm. The crystal is cut normal to the h110i crystallographic direction (transverse electro-optic configuration). The use of a photorefractive material as an active medium allows obtaining each final decrypted image in real-time. The half
Fig. 1. Experimental set-up. (CS: collimation system; BS1, BS2, BS3: beam splitters; O: input object; R1, first random phase mask; R2: second random phase mask; P: pupil; L1, L2, L3: lenses; M1, M2: mirrors; CCD: camera; BSO: photorefractive crystal; A1, A2, A3, A4: optical beams).
534
J. Fredy Barrera et al. / Optics Communications 259 (2006) 532–536
incident angle between the reference and object beam is 8.03. Then, the average grating period is 4.28 lm at the laser wavelength k = 532 nm. It should be pointed out that for this average grating period the application of an external electric field to the crystal (Eo = 7 kV) contributes to enhance the space charge field and therefore also enhances the phase conjugation reflectivity. Let us denote Ai (i = 1, . . . ,4) the amplitudes of the interfering beams. In the crystal, the bearing image encrypted beam A4 interferes with the reference beam A1 so that the three-dimensional encrypted information is fringe modulated. The transmitted part of beam A1 is retroreflected by mirror M2 as beam A2, so that in the crystal, a beam A3 is generated which is proportional to the conjugate of the image-bearing beam A4. This phase conjugate beam allows the decryption of the input image. As mentioned above, a stationary white noise is obtained after the encryption procedure in the photorefractive crystal. This encrypted information is supported on a three-dimensional speckle pattern. We stress the fact that each time the random pure-phase mask R2 is moved a new speckle pattern is generated in the crystal volume. The situation is similar to introduce a general speckle pattern decorrelation, which occur when the mask displacement reaches the average speckle size. Other important aspect to remark is that in the experiments the encrypted data are recovered through a phase conjugation procedure. It should be mentioned that the performance is dependent on the phase conjugation reflectivity which can be controlled by the speckle dimensions [26]. The pattern that represents the encrypted information is essentially a speckle pattern. In our experimental
arrangement, the average speckle depth is given by hSZi k Æ (ZC/D)2, where ZC is the distance between the imaging lens and the crystal plane, k the wavelength and D the diameter of the aperture lens L2. Therefore, it is possible to control the speckle size of the encrypted information. As also demonstrated in [26], the phase conjugate reflectivity depends on the crystal thickness. Note that in the proposed arrangement, the conjugate procedure is produced inside each speckle. Then, the finite average speckle dimension controls the phase conjugate reflectivity because the speckle depth plays the role of the crystal thickness. Then, in the reflectivity theoretical expressions, the crystal depth must be replaced by the speckle depth if the speckle is shorter than the crystal thickness. From the above-mentioned conditions, the parameter ZC is selected so that a high phase conjugation reflectivity is achievable. We use this fact to increase the intensity of the decrypted image. We now analyze the tolerance to the reconstruction shifting of the random pure-phase mask R2 in our experimental arrangement. In Fig. 2, we present a sequence of decrypted images obtained using our procedure. To illustrate this point a single encrypted object was stored in the crystal. Each image in Fig. 2 is obtained by in-plane moving the second random pure-phase mask R2 (see Fig. 1) to different positions in the reconstruction step. Fig. 2(d) is the reconstruction when the mask R2 is located in the same position as it had in the encryption step, showing that the original information is completely recovered. Fig. 2(a)–(c) display the images obtained when the random pure-phase mask R2 is laterally shifted from the correct position by a amount of 15, 10 and 5 lm, respectively. Fig. 2(e)–(g) show the images when the mask is laterally shifted from the
Fig. 2. The composite images show the reconstruction of a single stored encrypted image by shifting the random pure-phase mask R2 as described in the text.
J. Fredy Barrera et al. / Optics Communications 259 (2006) 532–536
535
Fig. 3. Sequential reconstruction of encrypted images stored in a BSO crystal obtained by shifting the random pure-phase mask R2 as described in the paper.
correct position by 5, 10 and 15 lm, respectively (opposite direction as in Fig. 2(a)–(c)). It is clearly seen that in the sequences (a)–(c) and (e)–(g) the information is gradually lost. In particular, let us observe that in Fig. 2(a) and (g) the information disappears at all. In these cases, the conjugate beam impinging on the displaced mask does not locally compensate the random optical path introduced by the random pure-phase mask in the encryption process. This fact could be considered as a drawback concerning the alignment of the optical system in the decryption process but we take advantage of this idea to introduce the concept of multiplexing encrypted images. The shifting range has to be taken into account due to possible crosstalking between images; provided that this feature would distort the final outputs. When the random pure-phase mask R2 is mispositioned, the conjugate beam is unable to recover the original data. This approach is useful in a multiplexing scheme providing that several successive displacements of the random pure-phase mask R2 are introduced. Therefore, the speckle patterns can be employed to encrypt several objects without cross-talk among them. Another aspect to be taken into account is that the crosstalk depends on the number of the elementary speckles comprising in the pure-phase coding mask. The application of our concept of encrypted images multiplexing is shown in the results of Fig. 3. In this case, three input object are sequentially encrypted with the same random pure-phase mask R2 but placed at different inplane positions (15 lm is the distance between successive random pure-phase mask positions). As a result, in the
O1
O2
O3
R1
Shift R2 1-2-3 E1
E2
E3 Crystal Shift
R2
photorefractive crystal three encrypted input objects are multiplexed. In the decryption step the conjugate wave front of all the encrypted images impinge on the random pure-phase mask. Each input object is selectively recovered (decrypted), provided that the random pure-phase mask R2 is located in the position where such input object was encrypted. Recoding intensities for each record were I1 = 195 lW/ cm2, I2 = 60 lW/cm2 and I4 = 42 lW/cm2. Accordingly, the recording times for the multiplexing case were: s = 1 second for the first exposure, s/2 for the second and s/4 for the third. These exposures times follow a rule to achieve equal conjugation reflectivity in all cases. The experimental reflectivity results 0.008. Fig. 4 summarizes in a block diagram the multiplexed encryption procedure for three input objects and the corresponding decryption process. 3. Conclusions A encrypted images multiplexing procedure based on the lateral shifting of a random pure-phase mask has been presented. This technique is experimentally implemented by using a photorefractive BSO crystal as holographic recording medium. The particular selection of the crystal is based on its real-time and the phase conjugation characteristics that allow the encryption–decryption procedure to be implemented. The validity of our proposal is evident through the experimental results which are presented. Further analysis must be devoted in order to optimize the number of multiple encrypted images to be stored in terms of the average speckle volume so that a high phase conjugation reflectivity can be sustained. Another feature that remains to be explored is the competition between the optimal speckle size (referred to its function within the crystal volume) and the shifting sensitivity of the random pure-phase mask. The bigger the speckle pattern the lesser the sensitivity and consequently the number of different stored encrypted images. With this proposal, we are introduced a novel alternative addressing the problem of security when handling multiple images, a field which has not already been deeply explored with optical techniques.
3-2-1
Acknowledgments O1
O2
O3
Fig. 4. Encryption–decryption multiplexing flow diagram: O1, O2, O3; input images, E1, E2, E3: encrypted images.
This research was performed under the auspicious of COLCIENCIAS (Colombia), CONICET PIP 2417 (Argentina),
536
J. Fredy Barrera et al. / Optics Communications 259 (2006) 532–536
CICPBA (Argentina), ANPCYT PICT 12564 (Argentina) and Facultad Ingenierı´a, Universidad Nacional de La Plata (Argentina). References [1] P.J. van Heerden, Appl. Opt. 2 (1963) 393. [2] P. Yeh, Introduction to Photorefractive Nonlinear Optics, Wiley, New York, 1993. [3] D.L. Staebler, W.J. Burke, W. Phillips, J.J. Amodei, Appl. Phys. Lett. 26 (1975) 182. [4] F.H. Mok, Opt. Lett. 18 (1993) 915. [5] G.A. Rakuljic, V. Leyva, A. Yariv, Opt. Lett. 17 (1992) 1471. [6] D. Psaltis, M. Levene, A. Pu, G. Barbastathis, K. Curtis, Opt. Lett. 20 (1995) 782. [7] G. Barbastathis, M. Levene, D. Psaltis, Appl. Opt. 35 (1996) 2403. [8] C. Denz, G. Pauliat, G. Roosen, T. Tschudi, Opt. Commun. 85 (1991) 171. [9] C. Denz, G. Pauliat, G. Roosen, T. Tschudi, Appl. Opt. 31 (1992) 5700.
[10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]
C. Alves, G. Pauliat, G. Roosen, Opt. Lett. 19 (1994) 1894. B. Wang, C.-C. Sun, Opt. Eng. 40 (2001) 1502. B. Javidi, J.L. Horner, Opt. Eng. 33 (1994) 1752. P. Refregier, B. Javidi, Opt. Lett. 20 (1995) 767. C.L. Wilson, C.I. Watson, E.G. Peak, Proc. SPIE 36 (1997) 373. B. Javidi, G. Zhang, J. Li, Appl. Opt. 36 (1997) 1054. G. Unnikrishnan, J. Joseph, K. Singh, Appl. Opt. 37 (1998) 8181. F. Goudail, F. Bollaro, B. Javidi, P. Refregier, J. Opt. Soc. Am. A 15 (1998) 2629. J.F. Heanue, M.C. Bashaw, L. Hesselink, Appl. Opt. 34 (1995) 6012. C.-C. Sun, W.-C. Su, Appl. Opt. 40 (2001) 1253. W.-C. Su, C.-H. Lin, Opt. Commun. 241 (2004) 29. C.-C. Sun, W.-C. Su, B. Wang, A.E.T. Chiou, Opt. Commun. 191 (2001) 209. B. Wang, C.-C. Sun, W.-C. Su, A.E.T. Chiou, Appl. Opt. 39 (2000) 4788. G. Unnikrishnan, J. Joseph, K. Singh, Opt. Lett. 25 (2000) 887. N. Nishchal, J. Joseph, K. Singh, Opt. Eng. 42 (2003) 1583. O. Matoba, B. Javidi, Opt. Lett. 24 (1999) 762. A. Salazar, M. Tebaldi, N. Bolognini, Opt. Commun. 221 (2003) 249.
