- Email: [email protected]
Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators
Optics Communications 237 (2004) 45–52 www.elsevier.com/locate/optcom
Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators Chau-Jern Cheng *, Mao-Ling Chen Department of Electro-Optical Engineering, National Taipei University of Technology, Taipei 10608, Taiwan ROC Received 5 July 2003; received in revised form 21 March 2004; accepted 23 March 2004
Abstract We propose and demonstrate a polarization-encoded encryption system based on a doubly exclusive OR logic (XOR) operation using cascaded twisted nematic liquid crystal spatial light modulators. The transfer characteristic of the encryption system is analyzed by the Jones matrix method to yield the suitable polarization modulation for optical realization. An experimental demonstration reveals that the binary image encryption/decryption is achieved with fair image quality by selecting the orientation of polarization and the modulation conditions. Both analytical and experimental results are presented and discussed. Ó 2004 Elsevier B.V. All rights reserved. PACS: 42.25; 42.30; 42.70; 42.79 Keywords: Optical encryption; Spatial light modulator; Liquid crystal display
1. Introduction Optical techniques are being increasing applied to information security applications [1–5] because of the flexibility of various methods of encoding using the characteristics of light. Phase encoding is one of the most extensively used techniques for optical encryption, because an intensity-sensing device, like a CCD, cannot detect the phase information of the light carrier [6–9]. The double
*
Corresponding author. Tel.: +886-2-27712171x4671; fax: +886-2-87733216. E-mail address: [email protected] (C.-J. Cheng).
random phase encoding technique proposed by Refregier and Javidi [6] is one of the earliest and most widely studied optical encryption methods for encrypting data. The architecture uses a 4-f imaging system together and a pair of random phase masks to encode information in the spatial and Fourier domains, respectively, to convert the image to be encrypted into stationary white noise data. The encrypted image is an amplitude/phase complex image, so copying the phase ingredients of the complex image using an intensity detector or reproducing it without knowledge of the contents of the primary image and code is impossible. Therefore, this method of encryption can ensure extremely high information security and provide
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.03.060
46
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
advanced anti-counterfeiting technology. However, the use of phase encoding to encrypt information may increase some of the problems that may be encountered in this process, including those related to the detection and conversion of complex encrypted data, speckle noise and the sensitivity of the alignment of the system to phase, for optical implementation [10–12]. The polarization encoding technique has been applied to perform the XOR logic operation and Boolean algebraic operations using liquid crystal devices [13]. It has been presented to realize optical encryption [14–16]. Additionally, ferroelectric spatial light modulators have also been developed to achieve an optical XOR encryption system, based on polarization and bistability properties [17]. Twisted nematic liquid crystal displays (TNLCDs) are currently popular display devices [18] that may be some of the most promising candidate devices for displaying information. The TN-LCD is an inherently polarization-sensitive device, which can be used to encrypt information using the polarization encoding technique [19,20], in a manner that inhibits the detection of the encrypted data by an intensity-sensitive device. This device therefore has the potential to display information while securing data. This work presents a polarization-based encoding scheme that involves cascaded twisted nematic liquid crystal spatial light modulators (LC-SLMs) to perform optical encryption/decryption, based on the XOR operation. Encryption is performed by executing a two-dimensional XOR logical operation under effective pixel-to-pixel coupling between the input binary image and the corresponding key code with random polarization. Decryption is also performed by executing another XOR operation through the same system, and then the image is decoded with the random polarization code from the encrypted binary data for recovery.
2. Polarization-encoding XOR operation using twisted nematic liquid crystals In twisted nematic liquid crystal displays, the liquid crystal molecules are generally aligned in the direction of rubbing of the front glass plate and
then slowly twisted in the direction of rubbing of the rear glass plate of the liquid crystal cell. Accordingly, the Jones matrix of the twisted nematic liquid crystal can be written as [18]
cos U sin U M¼ sin U cos U
U sinXX cos X i C sinX 2X ; U sinXX cos X þ i C sinX 2X
ð1Þ where the parameter X is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 C X ¼ U2 þ ; 2
ð2Þ
where U is the total twisted angle, and C is the phase retardation of the liquid crystal which is given by C¼
2p DnðV Þd: k
ð3Þ
In Eq. (3), DnðV Þ is the birefringence between the ordinary and extraordinary indices of refraction, and is a function of the voltage drop ðV Þ between the cell gap of the liquid crystal, k is the wavelength of light, and d is the thickness of the cell gap. For a specific TN-LCD, the phase retardation depends on the birefringence of the liquid crystal and can be adjusted by the applied graylevel voltage of the video signal. Fig. 1 depicts the basic scheme of an optical XOR operation, using double TN-LCs; two TNLCs are cascaded and biased using two distinct voltages (denoted V0 and V1 ). The light beam propagates in the z-direction. A polarizer ðP1 Þ with a transmission axis parallel to the y-direction is inserted at the input port to ensure an appropriate orientation of the linearly polarized light incidence, and an analyzer ðP2 Þ, in cross arrangement is placed at the output port to decode the light as variations of intensity. For simplicity, 90° TN-LC devices are considered: when no voltage is applied, the total twisting angle of each LC cell is 90°, U ¼ p=2. From Eq. (1), the Jones matrices of TNLC1 and TN-LC2 are rewritten as 0 1 p sinXj C sin X cos Xj i j 2Xj j 2Xj A; Mj ¼ @ C sin X p sinXj cos Xj i j 2Xj j 2Xj j ¼ 1; 2; where
ð4Þ
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
y x V0
C¼ z V0
P1
ð9Þ
0-state
P2
1-state
V0
V1
P1
P2
1-state
V1
V1
P1
P2
0-state
TN-LC1
TN-LC2
Fig. 1. XOR operation using two TN-LCs.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 p2 Ci : þ Xi ¼ 4 2
ð5Þ
The multiplication of M1 and M2 for the cascaded TN-LC system yields a composite Jones matrix A iB ðC þ iDÞ M ¼ M2 M1 ¼ ; ð6Þ C iD A þ iB where A¼ B¼
sin X1 sin X2 2 ðp C1 C2 Þ cos X1 cos X2 ; 4X1 X2
ð7Þ
1 ðX1 C2 sin X2 cos X1 X2 C1 sin X1 cos X2 Þ; 2X1 X2 ð8Þ
ð10Þ
The Jones vector of light before the analyzer can be written as V00 ¼ MP1 Vi ;
V0
P1
p ðX1 cos X1 sin X2 þ X2 cos X2 sin X1 Þ; 2X1 X2
p sin X1 sin X2 D¼ ðC1 þ C2 Þ: 4X1 X2
P2
V1
47
ð11Þ
where Vi is the Jones vector of the incident beam and M is the composite matrix of the cascaded TN-LC system. A linearly polarized incident beam with a normalized amplitude polarized in the ydirection is considered, in which the Jones vector of the incident beam is 0 Vi ¼ ; ð12Þ 1 and the polarizer with transmission axis parallel to y-direction is 0 0 P1 ¼ : ð13Þ 0 1 From Eqs. (11)–(13) and Eq. (6), the normalized Jones vector of light in front of the analyzer is rewritten as ðC þ iDÞ V00 ¼ : ð14Þ A þ iB When an analyzer ðP2 Þ is placed at the output port to decode the light as variations of intensity, the Jones matrix of the analyzer with a transmission axis in the x-direction is 1 0 P2 ¼ : ð15Þ 0 0 Then, the output intensity after the analyzer is written as V0 ¼ P2 V00 :
ð16Þ
From Eqs. (14)–(16), the output light with linear polarization in the x-direction is ðC þ iDÞ V0 ¼ : ð17Þ 0 Therefore, the output intensity of the cascaded TN-LC system can be written as
48
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
Table 1 XOR logic operation of the TN-LC1 and TN-LC2 cascaded system, where the phase retardation C ¼ 0 corresponds to the pffiffiffi low state (0-state) and C ¼ 3p corresponds to the high state (1-state), associated with two distinct applied voltages C1
C2
I0
0 (0) 0 pffiffi(0) ffi pffiffi3ffip (1) 3p (1)
0 ffiffi(0) p ffi 3p (1) 0 ffiffi(0) p ffi 3p (1)
0 1 1 0
(0) (1) (1) (0)
I0 ¼ V0 V0 ¼ C 2 þ D2 ¼
p2 2 ðX1 cos X1 sin X2 þ X2 cos X2 sin X1 Þ 4X12 X22 þ
p2 sin2 X1 sin2 X2 2 ðC1 þ C2 Þ : 16X12 X22
ð18Þ
This equation implies that the maximum output intensity is achieved, ðI0 Þmax ¼ 1, when X1 ¼ p=2, X2 ¼ mp or X1 ¼ mp, X2 ¼ p=2 (where m is a positive integer).pFrom Eq. (5), we have the values of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C1;2 as 0 and 4m2 1p. With m ¼ 1, pthe ffiffiffi values of phase retardation C1;2 are 0 and 3p, and the output light intensity, according to Eq. (18) is as presented in Table 1. In the binary operation, the phase retardation C ¼ 0 is the low state (0-state), pffiffiffi and C ¼ 3p is the high state(1-state), obtained by applying two distinct voltages. Table 1 shows the logical XOR operation. The optical XOR operation is performed using the polarization modulation of TN-LCs with a binary voltage drop applied across the cell gap. The output is high with maximum light intensity when the phase retardations are chosen in different states. Conversely, there is a low state and no light output when both the TNLCs are in the same states of phase retardation.
3. XOR-based optical encryption/decryption As an information display, the twisted nematic liquid crystal display consists of a two-dimensional structure with m n pixels; each pixel is a cell of the liquid crystal display. Accordingly, the twodimensional XOR operation can be performed using the TN-LCD panels, and can be briefly written as,
I0 ðm; nÞ ¼ c1 ðm; nÞ c2 ðm; nÞ;
ð19Þ
where the symbol represents the XOR operation and c1 and c2 represent the binary states of the phase retardation of the pixel cell ðm; nÞ in the LCD1 and LCD2 panels, respectively. The addressing voltage of each pixel applies a potential difference between the cell gaps so as to alter the phase retardation of each pixel cell. For simplicity, linearly polarized incident light is assumed to pass through the 90° TN-LC cell without changing the state of polarization, but the polarization of light follows the orientation of the LC director because the wave-guiding effect pertains when no voltage drop is present. That is to say, the orientation of the polarization of the incident light is changed to horizontal as the light passes the LC cell. When an appropriate voltage drop is applied on the pixel cell, the phase retardation of the LC falls to zero, such that the output light remains in the same state of linear polarization, because the LC cell is isotropic. As shown in Fig. 1, the polarization of the output light is in the x-direction, maximizing the intensity output beyond the analyzer. In contrast, when the polarization of the output light is in the original orientation, no light is output. Next, binary image encryption and decryption using the two-dimensional XOR operation are considered. In the encryption stage, an input binary image ai ðm; nÞ and a random key kðm; nÞ with a specific linearly polarized state are employed to execute the XOR operation. The resultant output image can be simply expressed as ae ðm; nÞ ¼ ai ðm; nÞ kðm; nÞ:
ð20Þ
The key kðm; nÞ is a form of randomness, so the output image ae ðm; nÞ to which the XOR operation in Eq. (20) is applied is also a random image, so that it can be called an encrypted image. In the decryption stage, a random key kðm; nÞ is employed to retrieve the decrypted image, which can thus be expressed as ad ðm; nÞ ¼ ae ðm; nÞ kðm; nÞ ¼ ½ai ðm; nÞ kðm; nÞ kðm; nÞ ¼ ai ðm; nÞ:
ð21Þ
Therefore, the resultant image ad ðm; nÞ can be recovered from the encrypted image, ad ðm; nÞ ¼
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
ai ðm; nÞ, if a random key with correct polarization state is used. Conversely, the decrypting image is still noise-like if a random key with the incorrect polarization state is used.
4. Experimental results and discussion Fig. 2 depicts the polarization encoding encryption/decryption system, in which the two twisted nematic liquid crystal spatial light modulators with diagonal size 0:900 and a resolution of 800 600 pixels were used in two-dimensional polarization encoding. An He–Ne laser source with a wavelength of 632.8 nm was collimated and polarized in the y-direction by a polarizer ðP1 Þ. Lens L1 (with focal length 10 cm) was used to image SLM1 and couple this input image to a key pattern on the SLM2 with unit magnification and to align the pixels appropriately. Lens L2 (with a focal length of 10 cm) condensed the pattern displayed on the SLM2 and imaged it onto the CCD (with sensor area size 1=300 and resolution 795 596 pixels) with a demagnification of about 0.37, such that the encrypted pattern could be captured completely and then displayed on the SLM1 for exact dimensional matching. The transmission axis of the polarizer ðP1 Þ was set in the y-direction and the analyzer ðP2 Þ was crossed with P1 to decode the desired polarization state of the output light. Thus, the information encoded as the polarization states of the image was converted into intensity variations and detected by the CCD
49
camera. In the encryption experiment, a two-dimensional XOR operation was executed using the previous experimental setup, wherein the input image to be encrypted was displayed on the SLM1 and coupled with the random code on the SLM2 pixel-to-pixel. The resultant encrypted image was captured by the CCD camera and sent to a personal computer for further processing. Decryption followed the earlier setup and procedure, except in that the SLM1 displayed the encrypted image, which was converted into binary by thresholding, and the SLM2 displayed a random code pattern (key). Therefore, a second XOR operation was used to decrypt the image. The whole system was computerized to perform an experimental demonstration. In the experiment, the polarization characteristics of the TN-LCD panel of the SLM devices were firstly measured and then compared to the simulated characteristics to determine the suitable modulation conditions in the binary operation before optical realization. The experimental setup (not shown) for analyzing the polarization comprised of an LC-SLM, behind which were a rotating analyzer and a photodetector. A linearly polarized laser beam was incident on the LC-SLM, whose gray-level was controlled by a computer and whose output light was polarized with a specific orientation, determined by the transmission axis of the analyzer. The intensity of the transmitted light was then measured by the photodetector. The gray-level was then increased from 0 to 255 to obtain the distribution of output light
Fig. 2. Experimental setup of polarization-encoded encryption system.
50
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
intensity, and thus the polarization state. The rotating analyzer was adjusted to the crossed- and parallel-configurations to measure the light components along the principal axes of polarization ellipse. Fig. 3 shows the experimental results concerning the angle of rotation of output polarization as a function of the applied gray-level, when linearly polarized light passes through the TNLCD panel. Although the output light is typically in an elliptic polarization state with small ellipticity, it is herein regarded as almost linearly polarized, by neglecting the small ellipticity (0.03). The results reveal that the major axis of polarization rotates from 0° to 86° as the applied gray-level increases from 0 to 255. The relationship between the applied gray-level and the angle of rotation of polarization are non-linear: a gray-value of zero was regarded as the 0-state and a gray-value of 255 was regarded as the 1-state in executing binary logic operations. A 2 2 bit XOR operation was performed, as in the experimental setup (Fig. 2), yielding the results presented in Fig. 4, where (a) and (b) are the two-dimensional inputs and (c) is the output state. Notably, the experimental results imply that the polarization encoding of the cascaded TN-LCDs can be used to execute the twodimensional XOR operation.
Fig. 4. Polarization encoding associated with two-dimensional XOR operation performed using TN-LCDs.
Fig. 5 shows the experimental results concerning optical encryption and decryption of the binary image; Figs. 5(a) and (b) are the input image to be encrypted and the random code pattern de-
Angle o f R otation ( degrees)
90 80 70 60 50 40 30 20 10 0
0
50
100
150
200
250
GrayLevel
Fig. 3. Experimental results concerning the angle of rotation of output polarization as a function of the gray-level applied to the TN-LCD panel, where the horizontal axis represents the gray level associated with the video signal and the vertical axis represents the angle of rotation of major axis.
Fig. 5. Experimental results concerning optical encryption/decryption: (a) input binary image, (b) random code, (c) encrypted image, (d) image decrypted using the correct key and (e) image decrypted using a wrong key.
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
tected by the CCD camera, respectively. Fig. 5(c) shows the partially random encrypted image. As shown in Fig. 5(d), the decrypted image was derived when a key code with the correct polarization was used for recovery. A comparison with the input image shown in (a) indicates that the decrypted image can be recognized as the original, except for some image distortion and possible errors. The decrypted image shown in Fig. 5(e) was obtained when a wrong code was used in a trial; the output image was incorrect and irretrievable. The error in the decryption was quantitatively evaluated. The bit-error rate of the decryption with the correct key, presented in Figs. 5(a) and (d), is 6.5% when no error-correction procedure is implemented. In contrast, the bit-error rate, between Figs. 5(a) and (e), is about 33% when an incorrect key is used to perform the decryption. The quality of the decrypted image is somewhat worse than that of the original image, because of the variation in the polarization caused by the TNLC cell and the geometrical mismatching among devices, which may cause a severe pixel-to-pixel coupling problem and thresholding ambiguity, reducing the contrast of the image and increasing the bit errors during decryption. Additionally, the non-uniform distribution of light, including interference from noise and aberrations, may cause ambiguity in the logical operation and also reduce the quality of the decrypted image and should be considered carefully in practice.
5. Conclusion In summary, we have proposed and demonstrated a polarization encoding technique for performing binary image encryption, using twisted nematic liquid crystal displays. The polarization characteristics of TN-LC were analyzed by applying the Jones matrix method and can be exploited to encode information regarding XORbased pffiffiffi encryption. Notably, the phase retardation of 3p is required only by a TN-LC to execute logic function. Moreover, this analysis may be extended to binary phase encoding using a parallel-aligned liquid crystal spatial light modulator (PAL-SLM) and generalized to other LCD-based
51
XOR encryption systems. An experimental demonstration revealed that the binary image encryption and decryption can be realized by appropriately selecting modulation conditions. Although the format mismatch and bit errors may degrade the quality of the decrypted image, these problems can be reduced by selecting appropriately the format of the devices and the thresholding algorithm for error correction and thus improve system performance. Given the increasing need for information displays, this work provides new possible means of encryption using low-cost, commercially available twisted nematic liquid crystal devices for both security and display applications.
Acknowledgements The authors would like to thank the National Science Council of the Republic of China, Taiwan for financially supporting this research under Contract No. NSC91-2215-E-027-007.
References [1] B. Javidi, Phys. Today 50 (3) (1997) 27. [2] B. Javidi, J.L. Horner, Opt. Eng. 33 (1994) 1752. [3] E.G. Johnson, J.D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrmann, S.H. Lee, W. Daschner, P. Long, Opt. Eng. 37 (1998) 18. [4] S. Zhang, M.A. Karim, Opt. Eng. 38 (1999) 20. [5] C.J. Cheng, Opt. Rev. 8 (2001) 431. [6] P. Refregier, B. Javidi, Opt. Lett. 20 (1995) 767. [7] J.F. Heanue, M.C. Bashaw, L. Hesselink, Appl. Opt. 34 (1995) 6012. [8] R.K. Wang, L.A. Watson, C. Chatwin, Opt. Eng. 35 (1996) 2464. [9] G. Unnikrishnan, K. Singh, Opt. Commun. 193 (2001) 51. [10] B. Javidi, G. Zhang, J. Li, Appl. Opt. 36 (1997) 1054. [11] L.G. Neto, Y. Sheng, Opt. Eng. 35 (1996) 2459. [12] B. Wang, C.C. Sun, W.C. Su, A.E.T. Chiou, Appl. Opt. 39 (2000) 4788. [13] F.T.S. Yu, S. Jutamulia, D.A. Gregory, Appl. Opt. 26 (1987) 2738. [14] P.C. Mogensen, J. Gl€ uckstad, Opt. Commun. 173 (2000) 177. [15] J.A. Davis, D.E. McNamara, D.M. Cottrell, T. Sonehara, Appl. Opt. 39 (2000) 1549. [16] J.W. Han, C.S. Park, D.H. Ryu, E.S. Kin, Opt. Eng. 38 (1999) 47.
52
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
[17] G. Unnikrishnan, M. Pohit, K. Singh, Opt. Commun. 185 (2000) 25. [18] P. Yeh, C. Gu, Optics of Liquid Crystal Displays, John Wiley & Sons, New York, 1999.
[19] B. Javidi, T. Nomura, Opt. Eng. 39 (2000) 2439. [20] X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, K. Kuroda, Appl. Opt. 40 (2001) 2310.
Polarization encoding for optical encryption using twisted nematic liquid crystal spatial light modulators Chau-Jern Cheng *, Mao-Ling Chen Department of Electro-Optical Engineering, National Taipei University of Technology, Taipei 10608, Taiwan ROC Received 5 July 2003; received in revised form 21 March 2004; accepted 23 March 2004
Abstract We propose and demonstrate a polarization-encoded encryption system based on a doubly exclusive OR logic (XOR) operation using cascaded twisted nematic liquid crystal spatial light modulators. The transfer characteristic of the encryption system is analyzed by the Jones matrix method to yield the suitable polarization modulation for optical realization. An experimental demonstration reveals that the binary image encryption/decryption is achieved with fair image quality by selecting the orientation of polarization and the modulation conditions. Both analytical and experimental results are presented and discussed. Ó 2004 Elsevier B.V. All rights reserved. PACS: 42.25; 42.30; 42.70; 42.79 Keywords: Optical encryption; Spatial light modulator; Liquid crystal display
1. Introduction Optical techniques are being increasing applied to information security applications [1–5] because of the flexibility of various methods of encoding using the characteristics of light. Phase encoding is one of the most extensively used techniques for optical encryption, because an intensity-sensing device, like a CCD, cannot detect the phase information of the light carrier [6–9]. The double
*
Corresponding author. Tel.: +886-2-27712171x4671; fax: +886-2-87733216. E-mail address: [email protected] (C.-J. Cheng).
random phase encoding technique proposed by Refregier and Javidi [6] is one of the earliest and most widely studied optical encryption methods for encrypting data. The architecture uses a 4-f imaging system together and a pair of random phase masks to encode information in the spatial and Fourier domains, respectively, to convert the image to be encrypted into stationary white noise data. The encrypted image is an amplitude/phase complex image, so copying the phase ingredients of the complex image using an intensity detector or reproducing it without knowledge of the contents of the primary image and code is impossible. Therefore, this method of encryption can ensure extremely high information security and provide
0030-4018/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2004.03.060
46
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
advanced anti-counterfeiting technology. However, the use of phase encoding to encrypt information may increase some of the problems that may be encountered in this process, including those related to the detection and conversion of complex encrypted data, speckle noise and the sensitivity of the alignment of the system to phase, for optical implementation [10–12]. The polarization encoding technique has been applied to perform the XOR logic operation and Boolean algebraic operations using liquid crystal devices [13]. It has been presented to realize optical encryption [14–16]. Additionally, ferroelectric spatial light modulators have also been developed to achieve an optical XOR encryption system, based on polarization and bistability properties [17]. Twisted nematic liquid crystal displays (TNLCDs) are currently popular display devices [18] that may be some of the most promising candidate devices for displaying information. The TN-LCD is an inherently polarization-sensitive device, which can be used to encrypt information using the polarization encoding technique [19,20], in a manner that inhibits the detection of the encrypted data by an intensity-sensitive device. This device therefore has the potential to display information while securing data. This work presents a polarization-based encoding scheme that involves cascaded twisted nematic liquid crystal spatial light modulators (LC-SLMs) to perform optical encryption/decryption, based on the XOR operation. Encryption is performed by executing a two-dimensional XOR logical operation under effective pixel-to-pixel coupling between the input binary image and the corresponding key code with random polarization. Decryption is also performed by executing another XOR operation through the same system, and then the image is decoded with the random polarization code from the encrypted binary data for recovery.
2. Polarization-encoding XOR operation using twisted nematic liquid crystals In twisted nematic liquid crystal displays, the liquid crystal molecules are generally aligned in the direction of rubbing of the front glass plate and
then slowly twisted in the direction of rubbing of the rear glass plate of the liquid crystal cell. Accordingly, the Jones matrix of the twisted nematic liquid crystal can be written as [18]
cos U sin U M¼ sin U cos U
U sinXX cos X i C sinX 2X ; U sinXX cos X þ i C sinX 2X
ð1Þ where the parameter X is defined as sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 C X ¼ U2 þ ; 2
ð2Þ
where U is the total twisted angle, and C is the phase retardation of the liquid crystal which is given by C¼
2p DnðV Þd: k
ð3Þ
In Eq. (3), DnðV Þ is the birefringence between the ordinary and extraordinary indices of refraction, and is a function of the voltage drop ðV Þ between the cell gap of the liquid crystal, k is the wavelength of light, and d is the thickness of the cell gap. For a specific TN-LCD, the phase retardation depends on the birefringence of the liquid crystal and can be adjusted by the applied graylevel voltage of the video signal. Fig. 1 depicts the basic scheme of an optical XOR operation, using double TN-LCs; two TNLCs are cascaded and biased using two distinct voltages (denoted V0 and V1 ). The light beam propagates in the z-direction. A polarizer ðP1 Þ with a transmission axis parallel to the y-direction is inserted at the input port to ensure an appropriate orientation of the linearly polarized light incidence, and an analyzer ðP2 Þ, in cross arrangement is placed at the output port to decode the light as variations of intensity. For simplicity, 90° TN-LC devices are considered: when no voltage is applied, the total twisting angle of each LC cell is 90°, U ¼ p=2. From Eq. (1), the Jones matrices of TNLC1 and TN-LC2 are rewritten as 0 1 p sinXj C sin X cos Xj i j 2Xj j 2Xj A; Mj ¼ @ C sin X p sinXj cos Xj i j 2Xj j 2Xj j ¼ 1; 2; where
ð4Þ
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
y x V0
C¼ z V0
P1
ð9Þ
0-state
P2
1-state
V0
V1
P1
P2
1-state
V1
V1
P1
P2
0-state
TN-LC1
TN-LC2
Fig. 1. XOR operation using two TN-LCs.
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 p2 Ci : þ Xi ¼ 4 2
ð5Þ
The multiplication of M1 and M2 for the cascaded TN-LC system yields a composite Jones matrix A iB ðC þ iDÞ M ¼ M2 M1 ¼ ; ð6Þ C iD A þ iB where A¼ B¼
sin X1 sin X2 2 ðp C1 C2 Þ cos X1 cos X2 ; 4X1 X2
ð7Þ
1 ðX1 C2 sin X2 cos X1 X2 C1 sin X1 cos X2 Þ; 2X1 X2 ð8Þ
ð10Þ
The Jones vector of light before the analyzer can be written as V00 ¼ MP1 Vi ;
V0
P1
p ðX1 cos X1 sin X2 þ X2 cos X2 sin X1 Þ; 2X1 X2
p sin X1 sin X2 D¼ ðC1 þ C2 Þ: 4X1 X2
P2
V1
47
ð11Þ
where Vi is the Jones vector of the incident beam and M is the composite matrix of the cascaded TN-LC system. A linearly polarized incident beam with a normalized amplitude polarized in the ydirection is considered, in which the Jones vector of the incident beam is 0 Vi ¼ ; ð12Þ 1 and the polarizer with transmission axis parallel to y-direction is 0 0 P1 ¼ : ð13Þ 0 1 From Eqs. (11)–(13) and Eq. (6), the normalized Jones vector of light in front of the analyzer is rewritten as ðC þ iDÞ V00 ¼ : ð14Þ A þ iB When an analyzer ðP2 Þ is placed at the output port to decode the light as variations of intensity, the Jones matrix of the analyzer with a transmission axis in the x-direction is 1 0 P2 ¼ : ð15Þ 0 0 Then, the output intensity after the analyzer is written as V0 ¼ P2 V00 :
ð16Þ
From Eqs. (14)–(16), the output light with linear polarization in the x-direction is ðC þ iDÞ V0 ¼ : ð17Þ 0 Therefore, the output intensity of the cascaded TN-LC system can be written as
48
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
Table 1 XOR logic operation of the TN-LC1 and TN-LC2 cascaded system, where the phase retardation C ¼ 0 corresponds to the pffiffiffi low state (0-state) and C ¼ 3p corresponds to the high state (1-state), associated with two distinct applied voltages C1
C2
I0
0 (0) 0 pffiffi(0) ffi pffiffi3ffip (1) 3p (1)
0 ffiffi(0) p ffi 3p (1) 0 ffiffi(0) p ffi 3p (1)
0 1 1 0
(0) (1) (1) (0)
I0 ¼ V0 V0 ¼ C 2 þ D2 ¼
p2 2 ðX1 cos X1 sin X2 þ X2 cos X2 sin X1 Þ 4X12 X22 þ
p2 sin2 X1 sin2 X2 2 ðC1 þ C2 Þ : 16X12 X22
ð18Þ
This equation implies that the maximum output intensity is achieved, ðI0 Þmax ¼ 1, when X1 ¼ p=2, X2 ¼ mp or X1 ¼ mp, X2 ¼ p=2 (where m is a positive integer).pFrom Eq. (5), we have the values of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi C1;2 as 0 and 4m2 1p. With m ¼ 1, pthe ffiffiffi values of phase retardation C1;2 are 0 and 3p, and the output light intensity, according to Eq. (18) is as presented in Table 1. In the binary operation, the phase retardation C ¼ 0 is the low state (0-state), pffiffiffi and C ¼ 3p is the high state(1-state), obtained by applying two distinct voltages. Table 1 shows the logical XOR operation. The optical XOR operation is performed using the polarization modulation of TN-LCs with a binary voltage drop applied across the cell gap. The output is high with maximum light intensity when the phase retardations are chosen in different states. Conversely, there is a low state and no light output when both the TNLCs are in the same states of phase retardation.
3. XOR-based optical encryption/decryption As an information display, the twisted nematic liquid crystal display consists of a two-dimensional structure with m n pixels; each pixel is a cell of the liquid crystal display. Accordingly, the twodimensional XOR operation can be performed using the TN-LCD panels, and can be briefly written as,
I0 ðm; nÞ ¼ c1 ðm; nÞ c2 ðm; nÞ;
ð19Þ
where the symbol represents the XOR operation and c1 and c2 represent the binary states of the phase retardation of the pixel cell ðm; nÞ in the LCD1 and LCD2 panels, respectively. The addressing voltage of each pixel applies a potential difference between the cell gaps so as to alter the phase retardation of each pixel cell. For simplicity, linearly polarized incident light is assumed to pass through the 90° TN-LC cell without changing the state of polarization, but the polarization of light follows the orientation of the LC director because the wave-guiding effect pertains when no voltage drop is present. That is to say, the orientation of the polarization of the incident light is changed to horizontal as the light passes the LC cell. When an appropriate voltage drop is applied on the pixel cell, the phase retardation of the LC falls to zero, such that the output light remains in the same state of linear polarization, because the LC cell is isotropic. As shown in Fig. 1, the polarization of the output light is in the x-direction, maximizing the intensity output beyond the analyzer. In contrast, when the polarization of the output light is in the original orientation, no light is output. Next, binary image encryption and decryption using the two-dimensional XOR operation are considered. In the encryption stage, an input binary image ai ðm; nÞ and a random key kðm; nÞ with a specific linearly polarized state are employed to execute the XOR operation. The resultant output image can be simply expressed as ae ðm; nÞ ¼ ai ðm; nÞ kðm; nÞ:
ð20Þ
The key kðm; nÞ is a form of randomness, so the output image ae ðm; nÞ to which the XOR operation in Eq. (20) is applied is also a random image, so that it can be called an encrypted image. In the decryption stage, a random key kðm; nÞ is employed to retrieve the decrypted image, which can thus be expressed as ad ðm; nÞ ¼ ae ðm; nÞ kðm; nÞ ¼ ½ai ðm; nÞ kðm; nÞ kðm; nÞ ¼ ai ðm; nÞ:
ð21Þ
Therefore, the resultant image ad ðm; nÞ can be recovered from the encrypted image, ad ðm; nÞ ¼
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
ai ðm; nÞ, if a random key with correct polarization state is used. Conversely, the decrypting image is still noise-like if a random key with the incorrect polarization state is used.
4. Experimental results and discussion Fig. 2 depicts the polarization encoding encryption/decryption system, in which the two twisted nematic liquid crystal spatial light modulators with diagonal size 0:900 and a resolution of 800 600 pixels were used in two-dimensional polarization encoding. An He–Ne laser source with a wavelength of 632.8 nm was collimated and polarized in the y-direction by a polarizer ðP1 Þ. Lens L1 (with focal length 10 cm) was used to image SLM1 and couple this input image to a key pattern on the SLM2 with unit magnification and to align the pixels appropriately. Lens L2 (with a focal length of 10 cm) condensed the pattern displayed on the SLM2 and imaged it onto the CCD (with sensor area size 1=300 and resolution 795 596 pixels) with a demagnification of about 0.37, such that the encrypted pattern could be captured completely and then displayed on the SLM1 for exact dimensional matching. The transmission axis of the polarizer ðP1 Þ was set in the y-direction and the analyzer ðP2 Þ was crossed with P1 to decode the desired polarization state of the output light. Thus, the information encoded as the polarization states of the image was converted into intensity variations and detected by the CCD
49
camera. In the encryption experiment, a two-dimensional XOR operation was executed using the previous experimental setup, wherein the input image to be encrypted was displayed on the SLM1 and coupled with the random code on the SLM2 pixel-to-pixel. The resultant encrypted image was captured by the CCD camera and sent to a personal computer for further processing. Decryption followed the earlier setup and procedure, except in that the SLM1 displayed the encrypted image, which was converted into binary by thresholding, and the SLM2 displayed a random code pattern (key). Therefore, a second XOR operation was used to decrypt the image. The whole system was computerized to perform an experimental demonstration. In the experiment, the polarization characteristics of the TN-LCD panel of the SLM devices were firstly measured and then compared to the simulated characteristics to determine the suitable modulation conditions in the binary operation before optical realization. The experimental setup (not shown) for analyzing the polarization comprised of an LC-SLM, behind which were a rotating analyzer and a photodetector. A linearly polarized laser beam was incident on the LC-SLM, whose gray-level was controlled by a computer and whose output light was polarized with a specific orientation, determined by the transmission axis of the analyzer. The intensity of the transmitted light was then measured by the photodetector. The gray-level was then increased from 0 to 255 to obtain the distribution of output light
Fig. 2. Experimental setup of polarization-encoded encryption system.
50
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
intensity, and thus the polarization state. The rotating analyzer was adjusted to the crossed- and parallel-configurations to measure the light components along the principal axes of polarization ellipse. Fig. 3 shows the experimental results concerning the angle of rotation of output polarization as a function of the applied gray-level, when linearly polarized light passes through the TNLCD panel. Although the output light is typically in an elliptic polarization state with small ellipticity, it is herein regarded as almost linearly polarized, by neglecting the small ellipticity (0.03). The results reveal that the major axis of polarization rotates from 0° to 86° as the applied gray-level increases from 0 to 255. The relationship between the applied gray-level and the angle of rotation of polarization are non-linear: a gray-value of zero was regarded as the 0-state and a gray-value of 255 was regarded as the 1-state in executing binary logic operations. A 2 2 bit XOR operation was performed, as in the experimental setup (Fig. 2), yielding the results presented in Fig. 4, where (a) and (b) are the two-dimensional inputs and (c) is the output state. Notably, the experimental results imply that the polarization encoding of the cascaded TN-LCDs can be used to execute the twodimensional XOR operation.
Fig. 4. Polarization encoding associated with two-dimensional XOR operation performed using TN-LCDs.
Fig. 5 shows the experimental results concerning optical encryption and decryption of the binary image; Figs. 5(a) and (b) are the input image to be encrypted and the random code pattern de-
Angle o f R otation ( degrees)
90 80 70 60 50 40 30 20 10 0
0
50
100
150
200
250
GrayLevel
Fig. 3. Experimental results concerning the angle of rotation of output polarization as a function of the gray-level applied to the TN-LCD panel, where the horizontal axis represents the gray level associated with the video signal and the vertical axis represents the angle of rotation of major axis.
Fig. 5. Experimental results concerning optical encryption/decryption: (a) input binary image, (b) random code, (c) encrypted image, (d) image decrypted using the correct key and (e) image decrypted using a wrong key.
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
tected by the CCD camera, respectively. Fig. 5(c) shows the partially random encrypted image. As shown in Fig. 5(d), the decrypted image was derived when a key code with the correct polarization was used for recovery. A comparison with the input image shown in (a) indicates that the decrypted image can be recognized as the original, except for some image distortion and possible errors. The decrypted image shown in Fig. 5(e) was obtained when a wrong code was used in a trial; the output image was incorrect and irretrievable. The error in the decryption was quantitatively evaluated. The bit-error rate of the decryption with the correct key, presented in Figs. 5(a) and (d), is 6.5% when no error-correction procedure is implemented. In contrast, the bit-error rate, between Figs. 5(a) and (e), is about 33% when an incorrect key is used to perform the decryption. The quality of the decrypted image is somewhat worse than that of the original image, because of the variation in the polarization caused by the TNLC cell and the geometrical mismatching among devices, which may cause a severe pixel-to-pixel coupling problem and thresholding ambiguity, reducing the contrast of the image and increasing the bit errors during decryption. Additionally, the non-uniform distribution of light, including interference from noise and aberrations, may cause ambiguity in the logical operation and also reduce the quality of the decrypted image and should be considered carefully in practice.
5. Conclusion In summary, we have proposed and demonstrated a polarization encoding technique for performing binary image encryption, using twisted nematic liquid crystal displays. The polarization characteristics of TN-LC were analyzed by applying the Jones matrix method and can be exploited to encode information regarding XORbased pffiffiffi encryption. Notably, the phase retardation of 3p is required only by a TN-LC to execute logic function. Moreover, this analysis may be extended to binary phase encoding using a parallel-aligned liquid crystal spatial light modulator (PAL-SLM) and generalized to other LCD-based
51
XOR encryption systems. An experimental demonstration revealed that the binary image encryption and decryption can be realized by appropriately selecting modulation conditions. Although the format mismatch and bit errors may degrade the quality of the decrypted image, these problems can be reduced by selecting appropriately the format of the devices and the thresholding algorithm for error correction and thus improve system performance. Given the increasing need for information displays, this work provides new possible means of encryption using low-cost, commercially available twisted nematic liquid crystal devices for both security and display applications.
Acknowledgements The authors would like to thank the National Science Council of the Republic of China, Taiwan for financially supporting this research under Contract No. NSC91-2215-E-027-007.
References [1] B. Javidi, Phys. Today 50 (3) (1997) 27. [2] B. Javidi, J.L. Horner, Opt. Eng. 33 (1994) 1752. [3] E.G. Johnson, J.D. Brasher, D. Gregory, P. Erbach, M. Duignan, G. Behrmann, S.H. Lee, W. Daschner, P. Long, Opt. Eng. 37 (1998) 18. [4] S. Zhang, M.A. Karim, Opt. Eng. 38 (1999) 20. [5] C.J. Cheng, Opt. Rev. 8 (2001) 431. [6] P. Refregier, B. Javidi, Opt. Lett. 20 (1995) 767. [7] J.F. Heanue, M.C. Bashaw, L. Hesselink, Appl. Opt. 34 (1995) 6012. [8] R.K. Wang, L.A. Watson, C. Chatwin, Opt. Eng. 35 (1996) 2464. [9] G. Unnikrishnan, K. Singh, Opt. Commun. 193 (2001) 51. [10] B. Javidi, G. Zhang, J. Li, Appl. Opt. 36 (1997) 1054. [11] L.G. Neto, Y. Sheng, Opt. Eng. 35 (1996) 2459. [12] B. Wang, C.C. Sun, W.C. Su, A.E.T. Chiou, Appl. Opt. 39 (2000) 4788. [13] F.T.S. Yu, S. Jutamulia, D.A. Gregory, Appl. Opt. 26 (1987) 2738. [14] P.C. Mogensen, J. Gl€ uckstad, Opt. Commun. 173 (2000) 177. [15] J.A. Davis, D.E. McNamara, D.M. Cottrell, T. Sonehara, Appl. Opt. 39 (2000) 1549. [16] J.W. Han, C.S. Park, D.H. Ryu, E.S. Kin, Opt. Eng. 38 (1999) 47.
52
C.-J. Cheng, M.-L. Chen / Optics Communications 237 (2004) 45–52
[17] G. Unnikrishnan, M. Pohit, K. Singh, Opt. Commun. 185 (2000) 25. [18] P. Yeh, C. Gu, Optics of Liquid Crystal Displays, John Wiley & Sons, New York, 1999.
[19] B. Javidi, T. Nomura, Opt. Eng. 39 (2000) 2439. [20] X. Tan, O. Matoba, Y. Okada-Shudo, M. Ide, T. Shimura, K. Kuroda, Appl. Opt. 40 (2001) 2310.