© 2009 OSA/DH/FTS/HISE/NTM/OTA 2009 a357_1.pdf JTuB3.pdf JTuB3.pdf
Optical Image Multiplexing Encryption Using Digital Holography in a JTC Architecture Edgar Rueda1, John F. Barrera1, Rodrigo Henao1, Roberto Torroba2 2.
1. Grupo de Óptica y Fotónica, Instituto de Física, Universidad de Antioquia, A.A. 1226, Medellín, Colombia. Centro de Investigaciones Ópticas (CONICET-CIC) and UID OPTIMO, Facultad de Ingeniería, Universidad de la Plata, P.O. Box (124) 1900, La Plata.
[email protected],
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Abstract: An optical scheme that uses a digital holographic technique in a Joint transform correlator architecture to encrypt and decrypt images is presented. A filtering procedure is implemented to improve the multiplexing capabilities of the system. ©2009 Optical Society of America OCIS codes: (060.4785) Optical security and encryption, (070.0070) Fourier optics, (090.1995) Digital holography, (100.2000) Digital image processing.
1.
Introduction
Encryption and decryption of images using the double random phase encoding (DRPE) technique has arisen as a promising method for securing information. Among the alternative architectures that work with this technique, the Joint Transform Correlator (JTC) architecture [1] is attractive in the sense that it does not require the accurate optical alignment of methods like the 4f architecture [2], although it generates unwanted terms in the output. Digital holographic techniques have been implemented in different optical security systems. In particular, for the 4f architecture Nomura et al. [3] proposed a system for securing information using a digital holographic technique that allows the encrypted image to be stored, transmitted and decrypted digitally. Numerous multiplexing techniques to store multitude of images into a single storing device without cross talk have been proposed [4-6]. In some multiplexing techniques there are restrictions over the number of stored images due to the presence of background noise or limitations in the recording device. In this work we present: a system for securing information using a digital holographic technique in a JTC architecture, a filtering procedure to eliminate the unwanted terms in the output plane, and an increase in the number of recovered images in multiplexing techniques thanks to the elimination of the background noise. 2.
Optodigital procedure for encryption and decryption of images
The setup is basically a Mach-Zender with one arm corresponding to a JTC configuration and the other to a reference plane wave beam (Fig. 1). Plane O is the input plane where the image to be encrypted and the phase key are placed; plane K corresponds to the Fourier plane of the input plane where the recording device (CCD camera) is located.
Fig1. Optical setup (Mach-Zender). B1 and B2 are beamsplitters, Plane O is the input plane, L is a positive lens, plane K is the joint power spectrum plane, f is the lens focal distance, M1 and M2 are mirrors.
The encryption step is done optically. First, blocking the reference arm the Joint Power Spectrum (JPS) intensity pattern is stored using the CCD camera, thus storing the encrypted image; next, unblocking the reference arm the hologram of the Phase Key Fourier Transform (PKFT) is stored; and finally, the intensity of: the original image, the PKFT and the reference plane wave are recorded separately. The decryption step is done digitally. First, using the stored intensities, the noisy terms on the encrypted image and on the hologram of the PKFT are removed. These noise-free images are then multiplied and inverse Fourier transformed. The result will have four spatially differentiated terms, one corresponding to the original image. The spatial position of each term is controlled with the input plane windows separation (Fig. 1) and the angle of incidence of the reference plane wave.
© 2009 OSA/DH/FTS/HISE/NTM/OTA 2009 a357_1.pdf JTuB3.pdf JTuB3.pdf
Fig. 2(a) shows the image of a letter that was encrypted employing the optical setup of Fig. 1 and Fig. 2(b) is the result of the digital recovering. The letter is contained by a 2mm square window, the input plane windows are separated 4mm, the lens used has a focal distance of 200mm, the laser wavelength is 632nm, and the CCD camera pixel size is 9μm.
(a) (b) Fig. 2. (a) Image to be encrypted and (b) experimental result of the image recovered using the digital decryption procedure.
With this method, up to nine terms can appear due to intensity saturation in the CCD camera. This saturation is produced in particular by the reference plane wave and/or by the phase key (Fig. 3).
Fig. 3. Simulation result obtained using the digital decryption procedure with saturation in the CCD. The original image was the letter A. 6, 9, 5 and 8 correspond to the result with no saturation (noise-free); 4 and 7 appear when the saturation in the CCD is produced by the reference wave; 1, 2 and 3 appear when the saturation in the CCD is produced by the phase key.
3.
Filtering procedure to eliminate the unwanted terms in the recovered image
As stated in the previous section, when the resulting recovered image is noise-free it still has four terms, only one of them of interest, the decrypted original image. But because a digital holographic technique has been used it is possible to filter the stored images before the decryption procedure, eliminating the unwanted terms. The digital filtering consist on: performing a Fourier Transform (FT) to the stored images, filtering the FT leaving only the terms need it for a successful image decryption, and performing an inverse FT to obtain the new encrypted image and decryption key, which are now complex. Fig. 4 presents a comparison between filtered and unfiltered results.
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(g) (h) Fig. 4. Numerical simulation of the encryption and decryption of a letter A. (a) unfiltered encrypted image, (b) unfiltered PKFT hologram, (c) amplitude of the filtered encrypted image, (d) phase of the filtered encrypted image, (e) amplitude of the filtered PKFT hologram, (f) phase of the filtered PKFT, (g) unfiltered decrypted noise-free image, and (h) filtered decrypted noise-free image.
© 2009 OSA/DH/FTS/HISE/NTM/OTA 2009 a357_1.pdf JTuB3.pdf JTuB3.pdf
4.
Relocation of the phase key information to improve multiplexing results
Different methods used for the multiplexing of encrypted information are restricted in the number of permissible multiplexed images owing to, for example, the background noise produced by the non-decrypted images. In our digital holographic method a reference plane wave is used to generate a hologram of the PKFT (Fig. 1). The angle of incidence of this wave will affect the position of the decrypted image in the output plane, creating the possibility to change the final position of the decrypted image in the output plane. Thus, in a multiplexing procedure where each image is encrypted using a plane wave with a different angle of incidence, the background noise of the nondecrypted images will not affect the decrypted image. For example, six letters were encrypted separately and stored in a single storing device with and without changing the angle of incidence, using a multiplexing procedure. Then letters A and B were decrypted transforming the non-decrypted letters into background noise (Fig. 5). When the angle of incidence has not changed the decrypted letter is over the background noise, while when the angle has changed the decrypted letter is relocated away from the noise.
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(c) (d) Fig. 5. Experimental results of multiplexed images. Using the configuration of Fig. 1 six letters (A, B, C, D, E, F) were encrypted in a multiplexing procedure. (a) Letter A decrypted when using the same angle of incidence for all letters, and (b) letter A decrypted when using different angles. (c) Letter B decrypted when using the same angle, and (d) letter B decrypted when using different angles.
When performing the FT of the stored images the position of the different terms is control by the angle of incidence of the reference plane wave. These positions can be change digitally. Consequently, instead of using different angles of incidence, the relocation of the decrypted image can be done digitally in the filtering step. 5. Conclusions An optodigital scheme that uses a digital holographic technique in a JTC architecture for encryption and decryption of information was presented. The effects in the recovered image due to intensity saturation of the CCD camera were pointed out. A filtering procedure was suggested to eliminate unwanted terms that appear in the recovered image when working with a JTC architecture. The quality of the recovered images in the multiplexing procedure was improved by means of a relocation of the phase key information in the filtering procedure. References [1] T. Nomura, B. Javidi, “Optical encryption using a joint transform correlator architecture”, Opt. Eng. 39, 2031-2035 (2000). [2] B. Javidi, G. Zhang, J Li, “Experimental demonstration of the random phase encoding technique for image encryption and security verification”, Opt. Eng. 35, 2506-2512 (1996). [3] B. Javidi, T. Nomura, “Securing information by used of digital holography”, Opt. Lett. 25, 28-30 (2000). [4] T. Nomura, S. Mikan, Y. Morimoto, B. Javidi, “Secure optical data storage with random phase key codes by use of a configuration of a joint transform correlator”, Appl. Opt. 42, 1508-1514 (2003). [5] J. Barrera, R. Henao, M. Tebaldi, R. Torroba, N. Bolognini, “Multiple image encryption using an aperture-modulated optical system”, Opt. Comm. 261, 29-33 (2006). [6] E. Rueda, J. F. Barrera, R. Henao, R. Torroba, “Lateral shift multiplexing with a modified random mask in a JTC encrypting architecture”, Opt. Eng. 48, (2009).
