**6.1 Optical devices in real optical security systems**

In the previous section, a binary encrypted hologram is used for easiness of optical reading and the degraded decryption image due to the binarization is successfully recovered by the optimization of hologram. In that system, we assume that not only a hologram but also a decryption key are displayed through electronic imaging devices. Even when we use optically addressed spatial light modulators (SLMs) with smart-pixel in optical security systems, we must inevitably use some electronic devices for the projection of images onto the SLMs. For example, a liquid crystal television display panel is frequently used for such purpose either of amplitude or phase modulation device. Such an imaging device has a lattice structure, in which the clear aperture is less than 100 % and only a limited light by the lattice structure passes through each pixel. Fig. 13 shows an example of a microscopic image of a liquid crystal display used as an electronically addressed SLM. The aperture ratio is about 0.55 in this case. In the joint transform system using real electronic devices, the decrypted image is greatly degraded due to the presence of the lattice structure, if we use an encrypted hologram generated from pure numerical calculation without considering the lattice structure. Or at worst case, we could not reconstruct any original image due to the degradation (Ohtsubo & Fujimoto, 2002). In this section, we apply the method of the simulated-annealing like optimization for binary hologram in real optical security systems and demonstrate successful decryptions of original images in the presence of lattice structures. The optical security system we treat here is the joint Fourier transform system. Both for the displays or projections of the hologram and the decryption key, we consider the use of electronically addressed SLMs such as liquid crystal television panels.

Fig. 13. Example of lattice structure of a liquid crystal television display used for electronically addressed spatial light modulator.

#### **6.2 Holographic reconstruction in the presence of lattice structure**

Here, we suppose the use of electronic display devices for the decryption of the encrypted hologram in a real optical security system. We assume that each pixel of an image in the input plane has a clear aperture ratio of 25 %. Actual display devices, for example LCTV panel, may have a rather larger value of the clear aperture, however, we take the value for the easiness of the numerical simulations. Fig. 14 shows the result of the numerical simulation for such a case. Fig. 14(a) is the same hologram as in Fig. 7(b), but it is embedded into the periodic lattice structure. The total size of the pattern in the input plane is expanded to 256x256 due to the presence of the periodic lattice structure. Fig. 14(b) is the same random key pattern as that in Fig. 3(b), but it is also embedded into the periodic lattice structure.

In the previous section, a binary encrypted hologram is used for easiness of optical reading and the degraded decryption image due to the binarization is successfully recovered by the optimization of hologram. In that system, we assume that not only a hologram but also a decryption key are displayed through electronic imaging devices. Even when we use optically addressed spatial light modulators (SLMs) with smart-pixel in optical security systems, we must inevitably use some electronic devices for the projection of images onto the SLMs. For example, a liquid crystal television display panel is frequently used for such purpose either of amplitude or phase modulation device. Such an imaging device has a lattice structure, in which the clear aperture is less than 100 % and only a limited light by the lattice structure passes through each pixel. Fig. 13 shows an example of a microscopic image of a liquid crystal display used as an electronically addressed SLM. The aperture ratio is about 0.55 in this case. In the joint transform system using real electronic devices, the decrypted image is greatly degraded due to the presence of the lattice structure, if we use an encrypted hologram generated from pure numerical calculation without considering the lattice structure. Or at worst case, we could not reconstruct any original image due to the degradation (Ohtsubo & Fujimoto, 2002). In this section, we apply the method of the simulated-annealing like optimization for binary hologram in real optical security systems and demonstrate successful decryptions of original images in the presence of lattice structures. The optical security system we treat here is the joint Fourier transform system. Both for the displays or projections of the hologram and the decryption key, we consider the

use of electronically addressed SLMs such as liquid crystal television panels.

Fig. 13. Example of lattice structure of a liquid crystal television display used for

Here, we suppose the use of electronic display devices for the decryption of the encrypted hologram in a real optical security system. We assume that each pixel of an image in the input plane has a clear aperture ratio of 25 %. Actual display devices, for example LCTV panel, may have a rather larger value of the clear aperture, however, we take the value for the easiness of the numerical simulations. Fig. 14 shows the result of the numerical simulation for such a case. Fig. 14(a) is the same hologram as in Fig. 7(b), but it is embedded into the periodic lattice structure. The total size of the pattern in the input plane is expanded to 256x256 due to the presence of the periodic lattice structure. Fig. 14(b) is the same random key pattern as that in Fig. 3(b), but it is also embedded into the periodic lattice structure.

**6.2 Holographic reconstruction in the presence of lattice structure** 

electronically addressed spatial light modulator.

80 μm

**6. Optimization of hologram in real systems 6.1 Optical devices in real optical security systems**  Using the hologram and the random key pattern in Figs. 14(a) and (b), the decryption was performed. The result is shown in Fig. 14(c). We cannot see any information of the original pattern of the fingerprint image. In the optical security system discussed here, the decryption is not a simple reconstruction of hologram, such as illumination by a plane wave. The hologram is illuminated by the Fourier transform of the random key pattern. Therefore the illumination of the Fourier transform of the periodic lattice structure greatly affects the performance of the reconstruction of hologram. It has less redundancy compared with a simple holographic reconstruction done by a plain wave illumination. Without considering the lattice structure, at worst case, we cannot extract any information from the reconstructed pattern as shown in Fig. 14(c).

Fig. 14. Image decryption in the presence of opaque lattice structures on the hologram and the decryption key pattern. (a) Hologram, (b) decryption key pattern, and (c) decryption of image.

#### **6.3 Optimization of hologram in the presence of lattice structure**

The procedure for optimization of hologram in the presence of a lattice structure is almost the same as discussed in section 3. Starting from a hologram as shown in Fig. 14(a) together with a decryption key in Fig. 14(b) all including the lattice structures, the optimization of hologram to obtain good reconstruction is performed following the step 1~5 as discussed in section 3. Throughout the following optimization, the decryption key pattern, which also has a periodic lattice structure, is not changed and is assumed to be the same pattern as shown in Fig. 14(b). On the other hand, starting from the encryption hologram shown in Fig. 14(a), the value of each pixel of the hologram is modified by flipping from +1 to –1 or vice versa. In each flipping, we test the newly decrypted image as to whether it gives rise to a good reconstruction or not. The flipping is successively repeated for every pixel. If the cost function for the optimization still has a large value, the next iteration is performed. When the value of the cost function is sufficiently lowered, the iteration stops. Then, the image is optimized to reach a good estimation.

 In the numerical simulation for the optimization, the area of the image to be compared with the decrypted pattern is expanded to 64x64 pixels due to the presence of the periodic opaque lattice structure. Therefore, we used the fingerprint image with 64x64 pixels as the ideal target image as shown in Fig. 15(a). Fig. 15(b) is the optimized hologram calculated by the proposed method when it contains the lattice structure. Using the optimized hologram together with the random key pattern in Fig. 14(b), we obtain the decrypted pattern as shown in Fig. 15(c). We can successfully decrypt an image close to the original one, though the periodic multiple images are reconstructed. The multiple images are originated due to

Optimization of Hologram for Security Applications 333

authenticity such as credit cards and passport identifications are usually used with electronic imaging systems. Therefore, diffraction effects induced by array structures of electronic addressed spatial light modulators as input optical devices may also degrade the

We here discuss a simpler method of image encryption and decryption in this section, which is different from one in the previous sections. In this method, an encryption of an image for the identification is done by a digital technique, and the decryption and the identification are assumed to be performed by optical systems. We here focus on the method of encryption and decryption of images. The degree of security for an encryption may not be so high, since the information of an original image is partially obtained from the reconstructed phase from the complex encrypted pattern. Therefore, we further consider the use of real-valued encrypted pattern instead of complex-valued encrypted pattern to enhance the degree of the security. Binarization of a complex-valued encrypted pattern that is obtained from the realvalued data is an another common technique to match optical read-out of images in practical optical security systems. Then, we also perform a binarization of an encrypted pattern and propose the method of the optimization for it to obtain a good quality image of

We here discuss the theoretical background of the phase-coding method. At first we assume that an original image *f*0(*x*,*y*) to be encrypted has binary values. The image is transformed to a phase pattern and the phase-coded pattern is multiplied by a binary random phase mask.

where *r*0(*x*,*y*) is a random function that plays a role for the encryption key and both the functions *f*0(*x*,*y*) and *r*0(*x*,*y*) take values of "0" or "1." The Fourier transform of the coded function *f*(*x*,*y*) is an encrypted pattern. Since the original image is transformed to a phase pattern and it is also scrambled by a random phase, one cannot exactly extract the information of the original image from the encrypted pattern without knowing the random key. It is noted here that the encrypted pattern has a complex-valued function and we need a complex representation of the encrypted pattern for the implementation in optical security systems. However, as discussed later, one can extract the original image with good quality

 In the Fourier space, the amplitudes of the encrypted pattern and the Fourier-transform of the random phase key are simply added together for the decryption. Writing the encrypted pattern defined by the Fourier transform of Eq. (14) as *F*(*u*,*v*), the amplitude distribution of

where *R*(*u*,*v*) is the Fourier transform of the function *r*(*x*,*y*)=exp{iπ*r*0(*x*,*y*)}. The function *R*(*u*,*v*) plays the role for the decryption key. Also it is noted that the decryption key is a complex-valued function. Then, the decryption is simply performed by an inverse-Fourier transform for the added pattern. The intensity of the inverse-Fourier transform *h*(*x*,*y*) of Eq.

0 0 *f* ( , ) exp[ ( , )] exp[ ( , )] *xy if xy ir xy* =π ⋅π (14)

*Huv Fuv Ruv* (,) (,) (,) = + (15)

image quality of the reconstruction of holograms.

The distribution of the total coded image is written by

from the real-valued binarized data of the encrypted pattern.

the decryption.

**7.2 Phase-coding: Theory** 

the addition is given by

(15) is easily calculated and written by

the presence of the periodicity of the lattice structure in the display panels. The value of the cost function rapidly decreases in a few iterations and it reaches almost less than 10 % of the initial cost. At the final iteration number, the cost function is less than 5 % of the initial cost. The cost function of 5 % is considered as an enough criterion for the reconstruction of the original images. Indeed, the correlation between the original and decrypted images over 95 % is obtained at this criterion and the reconstructed image can be used for the identification in the security system (Nakayama & Ohtsubo,2007).

 Flipping each pixel value of the hologram on the SLM through a computer control, we can optically and electronically perform the same optimization as done by the numerical simulation discussed here. In actual situation, a lattice structure to display an image is not only the issue to be overcome. However, based on the same principle proposed here, structures of image acquisition devices, a misalignment between optical acquisition and display devices, and even aberrations though optical elements can be compensated by the optimization of binary hologram. Then we can obtain optically an optimized binary hologram for image decryption for a particular optical system.

Fig. 15. Optimization of hologram to obtain the exact image. (a) Original image to compare the estimate of the decryption, (b) optimized hologram, and (c) result of the decryption from the optimized hologram.

## **7. Phase-coding method and optimization of hologram**

#### **7.1 Method of phase-coding**

A hologram with a reference of a random pattern has been used for security encoding of biometric patterns. The methods have been proved to be useful by numerical simulations. Phase-coding techniques have widely been used due to the suitability for optical encoding and decoding with high degree of security (Neto & Sheng, 1996, Javidi & Ahouzi, 1998, Towghi et al., 1999, Tan et al., 2000, and Mogensen &Gluckstad, 2000 & 2001). However, they have some difficulties due to the lack of efficient optical devices used in the systems. In those methods, an image for authenticity is encrypted as a hologram and the hologram is illuminated and reconstructed by a random decode key that is the same as the encryption key and, thus, the methods have some difficulties for actual optical implementation (Yan & Kim, 1996). For example, the size of each pixel of a decryption key must be exactly matched to the corresponding area of a hologram in the Fourier space. To avoid the difficulty, Park *et al*. (2001) proposed a technique to obtain a decrypted image by a simple joint Fourier transform of an encrypted pattern and a decryption key. Another difficulty is the availability of optical devices with sufficient resolution having a large dynamic range to implement a compact optical security system. Optical security systems to verify the

the presence of the periodicity of the lattice structure in the display panels. The value of the cost function rapidly decreases in a few iterations and it reaches almost less than 10 % of the initial cost. At the final iteration number, the cost function is less than 5 % of the initial cost. The cost function of 5 % is considered as an enough criterion for the reconstruction of the original images. Indeed, the correlation between the original and decrypted images over 95 % is obtained at this criterion and the reconstructed image can be used for the identification

 Flipping each pixel value of the hologram on the SLM through a computer control, we can optically and electronically perform the same optimization as done by the numerical simulation discussed here. In actual situation, a lattice structure to display an image is not only the issue to be overcome. However, based on the same principle proposed here, structures of image acquisition devices, a misalignment between optical acquisition and display devices, and even aberrations though optical elements can be compensated by the optimization of binary hologram. Then we can obtain optically an optimized binary

(a) (b) (c) Fig. 15. Optimization of hologram to obtain the exact image. (a) Original image to compare the estimate of the decryption, (b) optimized hologram, and (c) result of the decryption from

A hologram with a reference of a random pattern has been used for security encoding of biometric patterns. The methods have been proved to be useful by numerical simulations. Phase-coding techniques have widely been used due to the suitability for optical encoding and decoding with high degree of security (Neto & Sheng, 1996, Javidi & Ahouzi, 1998, Towghi et al., 1999, Tan et al., 2000, and Mogensen &Gluckstad, 2000 & 2001). However, they have some difficulties due to the lack of efficient optical devices used in the systems. In those methods, an image for authenticity is encrypted as a hologram and the hologram is illuminated and reconstructed by a random decode key that is the same as the encryption key and, thus, the methods have some difficulties for actual optical implementation (Yan & Kim, 1996). For example, the size of each pixel of a decryption key must be exactly matched to the corresponding area of a hologram in the Fourier space. To avoid the difficulty, Park *et al*. (2001) proposed a technique to obtain a decrypted image by a simple joint Fourier transform of an encrypted pattern and a decryption key. Another difficulty is the availability of optical devices with sufficient resolution having a large dynamic range to implement a compact optical security system. Optical security systems to verify the

in the security system (Nakayama & Ohtsubo,2007).

the optimized hologram.

**7.1 Method of phase-coding** 

hologram for image decryption for a particular optical system.

**7. Phase-coding method and optimization of hologram** 

authenticity such as credit cards and passport identifications are usually used with electronic imaging systems. Therefore, diffraction effects induced by array structures of electronic addressed spatial light modulators as input optical devices may also degrade the image quality of the reconstruction of holograms.

We here discuss a simpler method of image encryption and decryption in this section, which is different from one in the previous sections. In this method, an encryption of an image for the identification is done by a digital technique, and the decryption and the identification are assumed to be performed by optical systems. We here focus on the method of encryption and decryption of images. The degree of security for an encryption may not be so high, since the information of an original image is partially obtained from the reconstructed phase from the complex encrypted pattern. Therefore, we further consider the use of real-valued encrypted pattern instead of complex-valued encrypted pattern to enhance the degree of the security. Binarization of a complex-valued encrypted pattern that is obtained from the realvalued data is an another common technique to match optical read-out of images in practical optical security systems. Then, we also perform a binarization of an encrypted pattern and propose the method of the optimization for it to obtain a good quality image of the decryption.

#### **7.2 Phase-coding: Theory**

We here discuss the theoretical background of the phase-coding method. At first we assume that an original image *f*0(*x*,*y*) to be encrypted has binary values. The image is transformed to a phase pattern and the phase-coded pattern is multiplied by a binary random phase mask. The distribution of the total coded image is written by

$$f(\mathbf{x}, y) = \exp[i\pi f\_o(\mathbf{x}, y)] \cdot \exp[i\pi r\_o(\mathbf{x}, y)] \tag{14}$$

where *r*0(*x*,*y*) is a random function that plays a role for the encryption key and both the functions *f*0(*x*,*y*) and *r*0(*x*,*y*) take values of "0" or "1." The Fourier transform of the coded function *f*(*x*,*y*) is an encrypted pattern. Since the original image is transformed to a phase pattern and it is also scrambled by a random phase, one cannot exactly extract the information of the original image from the encrypted pattern without knowing the random key. It is noted here that the encrypted pattern has a complex-valued function and we need a complex representation of the encrypted pattern for the implementation in optical security systems. However, as discussed later, one can extract the original image with good quality from the real-valued binarized data of the encrypted pattern.

 In the Fourier space, the amplitudes of the encrypted pattern and the Fourier-transform of the random phase key are simply added together for the decryption. Writing the encrypted pattern defined by the Fourier transform of Eq. (14) as *F*(*u*,*v*), the amplitude distribution of the addition is given by

$$H(\mu, \upsilon) = F(\mu, \upsilon) + R(\mu, \upsilon) \tag{15}$$

where *R*(*u*,*v*) is the Fourier transform of the function *r*(*x*,*y*)=exp{iπ*r*0(*x*,*y*)}. The function *R*(*u*,*v*) plays the role for the decryption key. Also it is noted that the decryption key is a complex-valued function. Then, the decryption is simply performed by an inverse-Fourier transform for the added pattern. The intensity of the inverse-Fourier transform *h*(*x*,*y*) of Eq. (15) is easily calculated and written by

Optimization of Hologram for Security Applications 335

The degree of the security to hide an image behind a random mask is usually not so high when a phase function is reconstructed from an encrypted pattern. Furthermore, the representation of complex values of an encrypted pattern may not be suited for the implementation of practical optical security systems, since optical images are usually read out through an electronic interface. Therefore, we consider the use of a real-valued data from a complex encrypted pattern. For that purpose, we consider only real parts of an encrypted pattern and a decryption key. Using the real-valued data, the original image is exactly decrypted as shown in Fig. 17. Fig. 17(a) is an input fingerprint image to be decrypted. Here, we used an inverted gray scale and nonlinearly processed (arccosine transformed) fingerprint image to obtain the exactly expected image (compare it with Fig. 16(a)). The converted image is placed only in the area quarter of the input plane, since a mirror image is reconstructed due to the use of real-valued patterns in the following operation. Therefore, the total pixel size of the patterns used throughout the simulations is 128x128. Fig. 17(b) is a random key corresponding to the function *r*0(*x*,*y*). The encrypted pattern and the decryption key are calculated according to Eq. (14) and the Fourier transform of the random phase function, respectively. Next, we take the real parts of the Fourier transformed patterns. They are shown in Figs. 17(c) and (d). Then, the real-valued functions in Figs. 17(c) and (d) are added together and the result is inversely Fouriertransformed. The decrypted image is shown in Fig. 17(e). We obtain the exact image as a decryption, however a mirror image is also reconstructed due to the lack of the information of the imaginary parts of the encrypted image and the decryption key. From the standpoint of the degree of security, the use of a real-valued data from a complex encrypted image is not secure, since the imaginary part of the complex pattern can be easily reconstructed from its real part. Therefore, the binarization of encrypted image is essential for enhancing the

(a) (b) (c)

(d) (e)

Fig. 17. Decryption using real-valued patterns. (a) Original image. The fingerprint image is inverted and the gray scale of each pixel is nonlinearly transformed by an arccosine function (compare it with Fig. 2(a)). (b) Encryption key, (c) real part of the encrypted pattern, (d) real

part of the decryption key, and (e) decrypted image.

degree of the security.

$$\begin{aligned} |\ln(\mathbf{x}, y)|^2 &= |f(\mathbf{x}, y)|^2 + |r(\mathbf{x}, y)|^2 + f(\mathbf{x}, y)r^\circ(\mathbf{x}, y) + f^\circ(\mathbf{x}, y)r(\mathbf{x}, y) \\ &= 2 + 2\cos[\pi f\_\circ(\mathbf{x}, y)] \end{aligned} \tag{16}$$

Since we assumed that the original image has a binary value either "0" or "1," we obtain a negative binary image as a decryption for the input that has a value "4" or "0." The merit of the method is that the inverse-Fourier transform of Eq. (15) is exactly equal to the original image itself and the decrypted image does not contain a zero-th order diffraction or other components.

 The method is straightforwardly applicable to a gray scale image. For a gray scale image, we need no change of the procedure for encryption and decryption. If analogue values of the function *f*0(*x*,*y*) are normalized by its maximum value and they are distributed between 0 and 1, we can also obtain a negative image of the input as easily understand from Eq. (16), though the decrypted image is nonlinearly transformed with a cosine function. But the nonlinearlity can be easily compensated by a digital method due to one to one correspondence between the intensity distributions of the two images. Alternatively, the original image *f*0(*x*,*y*) may be nonlinearly transformed in advance by an arccosine function to give rise to the exact distribution of the image in the encryption process.

#### **7.3 Decryption of image by phase-coding method**

The method is applied to a gray scale image and the real and imaginary parts of the hologram (not a binary hologram) are used in this subsection. Fig. 16 shows the simulation result. A fingerprint image in Fig. 16(a) has a gray scale distribution between 0 and 1. The image is encrypted with a random phase pattern and, then, decrypted following the theory. Finally, we obtain a negative image of the original one as shown in Fig. 16(b). The nonlinearlity of the image distribution due to a cosine function is not compensated in the figure. The size of the original image is also 64x64 pixels and the original intensity level of 8 bit gray scale is normalized to be unity.

Fig. 16. Encryption (a) and decryption (b) for gray scale fingerprint image based on phasecoding method.

2 2 2 \*\*

=++ +


*h x y f x y r x y f x y r x y f x y r x y*

Since we assumed that the original image has a binary value either "0" or "1," we obtain a negative binary image as a decryption for the input that has a value "4" or "0." The merit of the method is that the inverse-Fourier transform of Eq. (15) is exactly equal to the original image itself and the decrypted image does not contain a zero-th order diffraction or other

 The method is straightforwardly applicable to a gray scale image. For a gray scale image, we need no change of the procedure for encryption and decryption. If analogue values of the function *f*0(*x*,*y*) are normalized by its maximum value and they are distributed between 0 and 1, we can also obtain a negative image of the input as easily understand from Eq. (16), though the decrypted image is nonlinearly transformed with a cosine function. But the nonlinearlity can be easily compensated by a digital method due to one to one correspondence between the intensity distributions of the two images. Alternatively, the original image *f*0(*x*,*y*) may be nonlinearly transformed in advance by an arccosine function to

The method is applied to a gray scale image and the real and imaginary parts of the hologram (not a binary hologram) are used in this subsection. Fig. 16 shows the simulation result. A fingerprint image in Fig. 16(a) has a gray scale distribution between 0 and 1. The image is encrypted with a random phase pattern and, then, decrypted following the theory. Finally, we obtain a negative image of the original one as shown in Fig. 16(b). The nonlinearlity of the image distribution due to a cosine function is not compensated in the figure. The size of the original image is also 64x64 pixels and the original intensity level of 8-

(a) (b)

Fig. 16. Encryption (a) and decryption (b) for gray scale fingerprint image based on phase-

=+ π (16)

0

give rise to the exact distribution of the image in the encryption process.

**7.3 Decryption of image by phase-coding method** 

bit gray scale is normalized to be unity.

coding method.

*f xy*

2 2 cos[ ( , )]

components.

The degree of the security to hide an image behind a random mask is usually not so high when a phase function is reconstructed from an encrypted pattern. Furthermore, the representation of complex values of an encrypted pattern may not be suited for the implementation of practical optical security systems, since optical images are usually read out through an electronic interface. Therefore, we consider the use of a real-valued data from a complex encrypted pattern. For that purpose, we consider only real parts of an encrypted pattern and a decryption key. Using the real-valued data, the original image is exactly decrypted as shown in Fig. 17. Fig. 17(a) is an input fingerprint image to be decrypted. Here, we used an inverted gray scale and nonlinearly processed (arccosine transformed) fingerprint image to obtain the exactly expected image (compare it with Fig. 16(a)). The converted image is placed only in the area quarter of the input plane, since a mirror image is reconstructed due to the use of real-valued patterns in the following operation. Therefore, the total pixel size of the patterns used throughout the simulations is 128x128. Fig. 17(b) is a random key corresponding to the function *r*0(*x*,*y*). The encrypted pattern and the decryption key are calculated according to Eq. (14) and the Fourier transform of the random phase function, respectively. Next, we take the real parts of the Fourier transformed patterns. They are shown in Figs. 17(c) and (d). Then, the real-valued functions in Figs. 17(c) and (d) are added together and the result is inversely Fouriertransformed. The decrypted image is shown in Fig. 17(e). We obtain the exact image as a decryption, however a mirror image is also reconstructed due to the lack of the information of the imaginary parts of the encrypted image and the decryption key. From the standpoint of the degree of security, the use of a real-valued data from a complex encrypted image is not secure, since the imaginary part of the complex pattern can be easily reconstructed from its real part. Therefore, the binarization of encrypted image is essential for enhancing the degree of the security.

Fig. 17. Decryption using real-valued patterns. (a) Original image. The fingerprint image is inverted and the gray scale of each pixel is nonlinearly transformed by an arccosine function (compare it with Fig. 2(a)). (b) Encryption key, (c) real part of the encrypted pattern, (d) real part of the decryption key, and (e) decrypted image.

Optimization of Hologram for Security Applications 337

(a) (b)

Fig. 19. Optimization of encrypted pattern. (a) Optimized binary hologram for Fig. 4(a) and

Beside of the security problems in the proposed method, we must consider the congeniality of the method with optical systems. One of the merits of optics is a complex representation of information. Therefore, encryption and decryption of a complex image is easily performed and a high quality image of the decryption can be obtained in optical security systems. However, real systems include electronic interfaces and a complex image must be replaced by real-valued patterns. Furthermore, analogue write-in and read-out of optical data sometimes cause difficulties, for example a gray scale of a pattern must be faithfully recorded in the write-in process and the analogue gray level must be correctly scaled in read-out process. Reducing such problems, binarization of a complex-valued pattern is used as a common technique. However, the quality of a reconstructed pattern usually results in degraded one. Therefore, the optimization for a binary encrypted pattern is essential in optical security systems. As already discussed, we can obtain an excellent decrypted image based on a statistical optimization technique. In the system, we employed an optical phase encoding method, however we can alternatively consider an amplitude encoding technique. For example, instead of 0 (+1) or π (-1) phase encoding of the pattern, a binary amplitude, i.e. amplitude of 0 or 1, can be used. However, the amplitude encoding in the proposed method leads to the same result as that of the phase encoding except for a zero-th order diffraction spot in the reconstructed plane, since the addition of an encrypted pattern and a decryption key takes only three values, 0, 1, and 2. In the meantime, that for the phase coding has also three values of –2, 0, and 2 and the decrypted image reduces to the same pattern as that of the amplitude encoding. Therefore, we here employed the phase encoding technique. An optical phase modulation device is commercially available. The device can be used as a phase modulation spatial light modulator over 2π modulation depth. Generation and addition of phase images can be optically performed by using phase-controlled SLMs together with electronically addressed liquid crystal display panels as input imaging devices. Thus, optical decryption from encrypted pattern proposed here is easily implemented by using such devices. Fig. 20 is an example of the experimental results using

(b) decryption of it.

#### **7.4 Binarization of encrypted image and its optimization**

In actual applications, the format of an encrypted pattern must be congenial to an electronic interface in decryption process. Fast processing is only required for image decryption and identification. The binarization of a real-valued data also greatly enhances the degree of security for encryption and decryption in optical security systems as have already been discussed. We again employ the method of the binarization for an encrypted pattern. Fig. 18 shows the result of the binarizations both for the encrypted pattern and the decryption key. The binary encrypted pattern is obtained from the signs of the real part values of the original encryption pattern in Fig. 17(c). Namely, when a real part of each pixel of the encrypted pattern is positive, we set the pixel value to be +1 (optical phase is 0), while it is – 1 (optical phase is π) for a negative value. The binary decryption key is made from the pattern in Fig. 17(d) as the same manner. Here we assume the use of optically addressed spatial light modulators (SLMs) with phase modulation in actual optical systems. The binarized patterns still have the original information. Then, adding the two binary patterns of the encrypted pattern and the decryption key shown in Figs. 18(a) and (b), the decryption of the image is performed. The result is shown in Fig. 18(c). Though we can recognize a dim structure of the fingerprint image, the decrypted image is greatly degraded due to the binarizations of the encrypted pattern and the decryption key.

Fig. 18. Decryption using binarized patterns of encryption pattern and decryption key. (a) Binarized encryption pattern, (b) binarized decryption key, and (c) decrypted image. The patterns are binarized according to the signs of the real part values.

Therefore, we consider the optimization of the binary encrypted pattern. In the optimization, the decryption key is not changed and remains the same binary pattern as shown in Fig. 18(b) throughout the iterations. Starting from the binary encrypted pattern shown in Fig. 18(a), the value of each pixel of the pattern is flipped form +1 to –1 or vice versa. In each flipping, we test the newly decrypted image whether it gives rise to a good reconstruction or not. Then, the image is optimized to reach a good estimate. The method is one like a simulated annealing technique and the detail of the method is the same as that in the pervious section. The area to be compared for the optimization in the decryption image plane is only a quarter of the original pattern where the ideal fingerprint image is reconstructed. Figs. 19(a) and (b) show the optimized binary encrypted pattern and the result of the decrypted image, respectively. From the comparison between Figs. 19(b) and 18(c), the optimization goes well and almost the same image as the original fingerprint image is recovered as easily recognized from the comparison with the pattern in Fig. 17(e).

In actual applications, the format of an encrypted pattern must be congenial to an electronic interface in decryption process. Fast processing is only required for image decryption and identification. The binarization of a real-valued data also greatly enhances the degree of security for encryption and decryption in optical security systems as have already been discussed. We again employ the method of the binarization for an encrypted pattern. Fig. 18 shows the result of the binarizations both for the encrypted pattern and the decryption key. The binary encrypted pattern is obtained from the signs of the real part values of the original encryption pattern in Fig. 17(c). Namely, when a real part of each pixel of the encrypted pattern is positive, we set the pixel value to be +1 (optical phase is 0), while it is – 1 (optical phase is π) for a negative value. The binary decryption key is made from the pattern in Fig. 17(d) as the same manner. Here we assume the use of optically addressed spatial light modulators (SLMs) with phase modulation in actual optical systems. The binarized patterns still have the original information. Then, adding the two binary patterns of the encrypted pattern and the decryption key shown in Figs. 18(a) and (b), the decryption of the image is performed. The result is shown in Fig. 18(c). Though we can recognize a dim structure of the fingerprint image, the decrypted image is greatly degraded due to the

(a) (b) (c) Fig. 18. Decryption using binarized patterns of encryption pattern and decryption key. (a) Binarized encryption pattern, (b) binarized decryption key, and (c) decrypted image. The

Therefore, we consider the optimization of the binary encrypted pattern. In the optimization, the decryption key is not changed and remains the same binary pattern as shown in Fig. 18(b) throughout the iterations. Starting from the binary encrypted pattern shown in Fig. 18(a), the value of each pixel of the pattern is flipped form +1 to –1 or vice versa. In each flipping, we test the newly decrypted image whether it gives rise to a good reconstruction or not. Then, the image is optimized to reach a good estimate. The method is one like a simulated annealing technique and the detail of the method is the same as that in the pervious section. The area to be compared for the optimization in the decryption image plane is only a quarter of the original pattern where the ideal fingerprint image is reconstructed. Figs. 19(a) and (b) show the optimized binary encrypted pattern and the result of the decrypted image, respectively. From the comparison between Figs. 19(b) and 18(c), the optimization goes well and almost the same image as the original fingerprint image is recovered as easily recognized from the comparison with the pattern in Fig. 17(e).

**7.4 Binarization of encrypted image and its optimization** 

binarizations of the encrypted pattern and the decryption key.

patterns are binarized according to the signs of the real part values.

Fig. 19. Optimization of encrypted pattern. (a) Optimized binary hologram for Fig. 4(a) and (b) decryption of it.

Beside of the security problems in the proposed method, we must consider the congeniality of the method with optical systems. One of the merits of optics is a complex representation of information. Therefore, encryption and decryption of a complex image is easily performed and a high quality image of the decryption can be obtained in optical security systems. However, real systems include electronic interfaces and a complex image must be replaced by real-valued patterns. Furthermore, analogue write-in and read-out of optical data sometimes cause difficulties, for example a gray scale of a pattern must be faithfully recorded in the write-in process and the analogue gray level must be correctly scaled in read-out process. Reducing such problems, binarization of a complex-valued pattern is used as a common technique. However, the quality of a reconstructed pattern usually results in degraded one. Therefore, the optimization for a binary encrypted pattern is essential in optical security systems. As already discussed, we can obtain an excellent decrypted image based on a statistical optimization technique. In the system, we employed an optical phase encoding method, however we can alternatively consider an amplitude encoding technique. For example, instead of 0 (+1) or π (-1) phase encoding of the pattern, a binary amplitude, i.e. amplitude of 0 or 1, can be used. However, the amplitude encoding in the proposed method leads to the same result as that of the phase encoding except for a zero-th order diffraction spot in the reconstructed plane, since the addition of an encrypted pattern and a decryption key takes only three values, 0, 1, and 2. In the meantime, that for the phase coding has also three values of –2, 0, and 2 and the decrypted image reduces to the same pattern as that of the amplitude encoding. Therefore, we here employed the phase encoding technique. An optical phase modulation device is commercially available. The device can be used as a phase modulation spatial light modulator over 2π modulation depth. Generation and addition of phase images can be optically performed by using phase-controlled SLMs together with electronically addressed liquid crystal display panels as input imaging devices. Thus, optical decryption from encrypted pattern proposed here is easily implemented by using such devices. Fig. 20 is an example of the experimental results using

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LCTV SLM. Fig. 20(a) is the experimentally reconstructed image and the nurerical reconstruction image is shown in Fig. 20(b) for comparison.

(a) (b)

Fig. 20. Experimental result of optical phase-coding method. (a) Optical and (b) simulation results.
