Optical encryption of unlimited-size images based on ptychographic scanning digital holography Qiankun Gao,1 Yali Wang,1 Tuo Li,1 and Yishi Shi1,2,* 1

College of Material Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China 2

State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China *Corresponding author: [email protected] Received 11 March 2014; revised 11 June 2014; accepted 11 June 2014; posted 11 June 2014 (Doc. ID 207998); published 17 July 2014

The ptychographic scanning operation is introduced into digital holography to expand the field-of-view (FOV). An optical image encryption method based on this technique is further proposed and analyzed. The plaintext is moved sequentially in the way of ptychographic scanning and corresponding pairs of phase-shifted interferograms are recorded as ciphertexts. Then the holographic processing and the ptychographic iterative reconstruction are both employed to retrieve the plaintext. Numerical experiments demonstrate that the proposed system possesses high security level and wide FOV. The proposed method might also be used for other potential applications, such as three-dimensional information encryption and image hiding. © 2014 Optical Society of America OCIS codes: (060.4785) Optical security and encryption; (100.4998) Pattern recognition, optical security and encryption; (090.1995) Digital holography; (110.1650) Coherence imaging. http://dx.doi.org/10.1364/AO.53.004700

1. Introduction

Optical image encryption has been an increasingly attractive technique in the past two decades because of its intrinsic ability of parallel processing and multiple parameters [1–3]. Since Refregier and Javidi reported their double random phase encoding system (DRPE) first in 1995 [4], this technique has experienced great developments to achieve better applications. The system is enhanced by introducing extra freedoms, such as extending it to the Fresnel and the fractional Fourier-domain [5–10], or using other special transforms [3,11,12]. Recently, some encryption techniques based on imaging have also been widely researched. Those imaging physical factors can be used to improve the system safety [13–16]. Digital holography (DH) was applied to optical encryption 1559-128X/14/214700-08$15.00/0 © 2014 Optical Society of America 4700

APPLIED OPTICS / Vol. 53, No. 21 / 20 July 2014

by Javidi and Nomura [17] in 2000. Then, many variations of this approach were researched to obtain higher security and better realization [18–26]. Among them, the optical architecture with plane-wave illumination and Mach–Zehnder interferometer (PMZDH) is mostly employed in the encryption procedure [24,25]. However, the optical aperture in such systems is usually restricted by the physical limitations of the real optical elements (diameter of the lens and surface size of the optical detector). Therefore, the field-of-view (FOV) of PMZ-DH is limited and, subsequently, it is difficult to encrypt large-sized images. Although we can divide the big image to some smaller regions and encrypt them, respectively, the problem of image fusion will emerge and cause other limitations in real applications [27,28]. Ptychography is a coherent imaging technique that uses a movable aperture to scan a specimen and reconstructs it by a series of recorded diffractive patterns [29–35]. The movement of the aperture

should guarantee the illuminated zone of the specimen overlaps with its neighbors. Ptychographic scanning (P-scanning) creates a reconstruction that is clear and free of artificial splicing traces [30,31]. It also ensures the ptychography inherently holds an unlimited FOV. Actually, we have applied ptychography in the optical image encryption in Ref. [36]. A series of probes are used to generate the ciphertexts and a phase retrieval algorithm is operated for the decryption. It is demonstrated that the illuminating probes of ptychography can serve as a new secret key, and safety is improved to a high degree. Then, this technique is further studied in Ref. [37]. Movable probes are realized by employing an amplitude-only spatial light modulator (SLM), which gives the encryption system high flexibility. In this paper, the PMZ-DH encryption system is combined together with the P-scanning operation. Since the big plaintext is moved in the P-scanning way, more regions of the object plane can be illuminated. Both the holographic processing and the ptychographic iteration are employed to extract the plaintext. This combination has some advantages. First, the P-scanning operation expands the FOV of DH; thus, the system can encrypt unlimited-size images, which benefits the information transmission. Second, the illuminating probes can be used as secret keys, as in Ref. [36], and system security is further improved. At last, the holographic processing avoids some potential safety vulnerabilities of those single ptychographic methods [36,37]. Consequently, the proposed encryption system is difficult to attack. 2. System Description and Theoretical Analysis

Since it is very convenient to introduce the Pscanning to almost any DH architecture, we choose the phase-shifting DH as an example. Figure 1 shows the schematic for the experimental arrangement. The monochromatic plane-wave is obtained by using a laser source and a collimating and beam expanding

system. Then, it is divided into two beams by a beam splitter (BS). One supplies phase shifting to the reference wave by a piezoelectric transducer (PZT) mirror while the other illuminates the object to be encrypted. The object is placed on a motorized translation stage to fulfill the P-scanning, as shown in the purple block of Fig. 1. Actually, we can also use a SLM to load the object, which increases the scanning speed and gives us much flexibility to control the system. The efficiency of the encryption will be improved as well. M 1 , M 2 , and M 3 are random phase-only masks, distributed in 0; 2π; and serve as modulators in the Fresnel domain. The distances of M 1 to M 2 , M 2 to the detector, and M 3 to the detector are d1 , d2 , and d3 , respectively. Especially, the size of M 1, M 2 , and M 3 is equal to the illuminating aperture to save the system cost. The phase-shifted interference patterns (i.e., ciphertexts) are recorded by an optical detector (charge-coupled device, CCD). A remarkable difference between the proposed ptychographic scanning DH (P-scanning DH) and the PMZ-DH is the P-scanning operation on the object plane x; y. In the PMZ-DH, the illumination is restricted to a narrow light beam, as shown in Fig. 2(a). For a big-size object, the illumination only covers a small region, whereas in the proposed system, the object is attached to a motorized translation stage and moved in the x- and y-directions to let the narrow light beam enlighten its needed regions. Figure 2(b) illustrates this operation, where 3 × 3 scanning positions and 50% overlap rate are used. As can be seen from Fig. 2(c), more regions of the object are enlightened and the FOV is expanded after scanning. Therefore, the aforementioned limitations of the PMZ-DH are overcome by the P-scanning operation. One may argue that we can also move the object directly to expand the FOV without the overlap requirement. Actually, it is, indeed, an effective way unless the annoying problem of image fusion is solved appropriately, and this is just what many

Fig. 1. Schematic experimental setup for optical encryption of unlimited-size image based on ptychographic scanning digital holography: BS, beam splitter; d1 , d2 , and d3 , diffraction distance; M 1 , M 2 , and M 3 , phase-only masks. 20 July 2014 / Vol. 53, No. 21 / APPLIED OPTICS

4701

Fig. 2. (a) Illumination on the object plane in the classical DH system and (b) Illustration for the P-scanning operation on the object plane. (c) Effect of the P-scanning.

researchers are still investigating at present [27,28]. However, in the proposed method, such a problem is inherently solved by use of the ptychographic iterative reconstruction [32], which supplies a special alternative way to achieve wide FOV. This will be discussed in detail in the next sections. Let us assume the illuminating probe and the object are Pn and Ox; y, respectively. For a typical scanning position, the object wave Onc ξ; η on the CCD plane intervenes with the reference wave. Two interferograms are recorded as ciphertexts, corresponding to 0 and π phase delays: 

ID0n  jOnc j2  jRj2  Onc R  Onc R ; IDπn  jOnc j2  jRj2 − Onc R − Onc R

(2)

If we move the object sequentially, then we will obtain series pairs of interferograms as ciphertexts. These can then be sent to the receiver via the public transmission channel as a whole encoded image. M 1 , M 2 , and M 3 are principal keys while d1 , d2 , d3 , and λ are supplementary keys. They may be given to the receiver separately by different channels for the sake of safety. In addition, the illuminating probes can also serve as security keys to further enhance the system safety [36,37]. During the decryption, the messages mentioned above are available to the authorized receiver. So the original big image can be recovered digitally from the pairs of small ciphertexts (ID0n , IDπn ) using holographic processing and ptychographic iterative reconstruction. The decryption procedure can be described in the following way. First, we initially guess the original image is Okg x; y and set the index k  1. For the nth scanning position, the probe illuminates Okg x; y in the region of Okgn x; y and propagates forward to the CCD plane: Okgnc  FrTλ;d2 fFrTλ;d1 Pn · Okgn · expiM 1  · expiM 2 g; 4702

APPLIED OPTICS / Vol. 53, No. 21 / 20 July 2014

jOnc j2 

(3)

ID0n  IDπn − jRj2 : 2

(4)

Since ID0n , IDπn , and R are already known, Eq. (4) can be solved for jOnc j2 to begin the ptychographic iterative reconstruction, using as a constraint ˆ kgnc  O

1

where  denotes a complex conjugate and the reference wave R is decided by M 3 : R  FrTλ;d expiM 3 :

where FrT represents the Fresnel transform, p the index λ is the light wavelength, and i  −1 is the imaginary number. Next, the corresponding pair of ciphertexts (i.e., ID0n and IDπn ) are processed to extract jOnc j2 according to the formula below:

q Okgnc jOnc j2 · k : jOgnc j

(5)

Propagate back to the object plane and refresh the illuminated region as −1 ˆk OkgnR  FrT−1 λ;d1 fFrTλ;d2 Ognc  · exp−iM 2 g

· exp−iM 1 ;

(6)

where FrT−1 denotes the inverse Fresnel transform. Then OkgnR x; y is returned to the initial guess OkgR x; y and another constraint with the corresponding illuminating aperture Pn is applied to update the wavefront of the plaintext: ˆ kg  Okg  O

jPn j Pn Ok − Pn · Okg ; jPn;max j jPn j2  δ gR

(7)

ˆ kg x; y represents the updated distribution of where O the plaintext Pn;max is the maximum modulus of Pn, and δ is a constant used to suppress noise. In our ˆ kg x; y is employed study, parameter δ is set to 0.01. O to replace the initial guess Okg x; y and the next neighbor scanning probe [i.e., Pn n  n  1] is used. Equations (3)–(7) are repeated to further refresh the plaintext estimate until n reaches the final scanning position. Now, the entire ptychographic iteration is finished and the correlation coefficient (Co) between the retrieved image and the original plaintext is calculated to judge whether the iteration should be stopped, according to the equation below:

Cof ; f o   covf ; f o σ f · σ f o −1 ;

(8)

where f and f o stand for the retrieved image and the original plaintext, respectively. covf ; f o  is the crosscovariance between f and f o , and σ f is the standard deviation. If the calculated Co value reaches the set threshold (Tr), then the retrieved image is output as the final decrypted image. If not, the retrieved image is used as the new guess for the next iteration (k  k  1) until Co equals Tr. The flow chart in Fig. 3 illustrates the decryption procedure. Compared with single ptychographic techniques [36,37], the P-scanning DH method has a great advantage on the aspect of improving the system security. In the P-scanning procedure, the probes keep a certain overlapped rate. Such a requirement is an essential factor for the decryption; however, it may also be a potential drawback for the information transmission, because the adjacent-scanned ciphertexts at least have some common information (i.e., the overlapped portion). This internal relationship may be utilized to attack the encryption system by unauthorized users. However, in the proposed method, the recorded ciphertexts are interferograms. Because of the interference, such common information existing in the neighbor scanning apertures is disturbed once again. The common relation of the ciphertexts can also be weakened and suppressed to a low level. As a result, the potential vulnerability of single ptychographic encryption method can be technically avoided and eliminated. The above analysis can be clarified further in mathematics. We assume the two adjacent illuminated zones are A  B and B  C, in respect to the common portion of B. Since the discussed encryption systems are all linear, we use the signature “Ψ” to stand for the encryption process, which can be written as below:

( Single ptychographic method: ( P-scanning DH method:

N 1  jΨA  Bj2 N 2  jΨB  Cj2

~ 1  jΨA  B  X 1 j2 N ; ~ 2  jΨB  C  X 2 j2 N (9)

~ 1; N ~ 2 denote ciphertexts, and X 1 and where N 1 ; N 2 ; N X 2 are the disturbances caused by M 3. In contrast to the single ptychographic method, the ciphertexts in the P-scanning DH method are disturbed again by X n n  1; 2; …. The more severe X n is, the more disturbances produced. Actually, X n is the diffraction of the phase-only mask M 3 . Better disturbance can be achieved using multiple diffractive distance d3 , or even changing M 3 in the scanning procedure. Therefore, it will produce more difficulties for the attackers and the security of the encryption system will be improved as well. 3. Numerical Experiments Demonstration and Discussions A. Effectiveness of the FOV Enlargement

Since the P-scanning mode can be easily designed, we choose a typical example to demonstrate the proposed method. In the simulations, the plaintext is a gray scale image “Lena,” which is normalized to [0,1] and shown in Fig. 4(a). The object plane is sampled by a pixel size of 10 μm in a 1024 × 1024 pixels area. Figure 4(b) is the illumination on the object plane. Only a region of 512 × 512 pixels (red rectangle) is enlightened under the limitations of the optical system. To expand the FOV, a P-scanning operation is employed, as shown in Fig. 4(c). Because the

Fig. 3. Flow chart of the decryption procedure. 20 July 2014 / Vol. 53, No. 21 / APPLIED OPTICS

4703

Fig. 4. (a) Secret image, (b) illumination on the object plane, and (c) using P-scanning mode (3 × 3 scanning positions and 50% overlapped rate).

overlapped rate is set to 50%, 3 × 3 scanning positions are sufficient to cover the whole image. The phase masks M 1, M 2 , and M 3 are all statistically independent and randomly distributed in 0; 2π. They are the same with the illuminating aperture (512 × 512 pixels) and are shown, respectively, in Figs. 5(a)–5(c). The other system parameters are λ  632.8 nm, d1  30 mm, and d2  d3  50 mm. A CCD camera with 6.0 μm pixel size and 512 × 512 pixels is used to record the interference patterns. For a certain illuminated position, a pair of interferograms is recorded, corresponding to the 0 and π phase delays of the reference wave. Figures 5(d) and 5(e) present a typical pair. We can see the original image is disturbed to totally random white noise. Using the proposed method, the authorized receiver can retrieve the big-size original image from these small ciphertexts. Figure 5(f) shows the retrieved result after 100 iterations. It can be seen that all the illuminated regions of the original image are decrypted successfully and clearly. Especially, there are basically no splicing traces in the overlapped areas. A curve of Co values is depicted in Fig. 5(g) to illustrate the decryption. With about less than 100 iterations, the Co values are close to 1, which indicates the decryption has a fast convergence performance. Therefore, we can see that the proposed method not only obtains a wide FOV, but also has a fast decryption speed. This means the system is able to encode unlimited-size images, which is an outstanding advantage for communications. Next, the scanning error (Se ) is taken into account and analyzed for the real applications. The practical scan (Sp ) may not equal to the initially designed (Sd ). Their difference is defined as Se :

Se  Sp − Sd :

(10)

The initial simulation settings are the same as the above section, and Sd is set to 2.56 mm (256 pixels) per time. In fact, for each scanning position, Se may be negative or positive. However, we only discuss the case that Se is all negative or positive in the whole scanning procedure for the convenience of discussion. We should also notice that, if Se is negative, then the illuminated regions after scanning cannot cover the whole image; conversely, when Se is positive, some additional backgrounds will be illuminated and decrypted. A group of Se from −1.0 mm to 1.0 mm is employed to test the performance of the proposed method. The Co values between the decrypted results and the original image are also calculated in the decryption. Figure 6 shows its variation trend along with Se changing from −1.0 mm to 1.0 mm. Some typical decrypted images are also presented to illustrate the influence of Se directly. From Fig. 6, we can see that, as Se increases, the Co value declines and the decrypted result degrades. But the decrypted images are still recognizable (see these typical ones in Fig. 6), in spite of some noise and ghost fringes, because of the mismatch of the ciphertexts. The results above demonstrate that the proposed method has a powerful error-correcting ability. B. Security Enhancement

The system security of the proposed method is researched in this section. First, we know the greatest advantage of ptychographic technique is that the illuminating probes can be used as new keys to improve the system safety. This good property has

Fig. 5. (a)–(c) Phase-only masks M 1 , M 2 , and M 3 , (512 × 512 pixels). (d) and (e) Typical pair of ciphertexts (512 × 512 pixels) corresponding to 0 and π phase delays, respectively. (f) Correct decrypted image (1024 × 1024 pixels and the iterations are 100). (g) Co curve of the decryption. 4704

APPLIED OPTICS / Vol. 53, No. 21 / 20 July 2014

Fig. 6. Co values between the decrypted results and the original image when the scanning errors (Se ) change from −1.0 mm to 1.0 mm, and some typical examples are also presented.

already been investigated in our previous work [36], which demonstrated that the probes can be designed into various types to enlarge the key space, such as using multiple shapes and even complex-valued probes. Here, we also analyze and test this property in our proposed method. Since the scanning positions are set to 3 × 3, three complex probes are utilized to enlighten the plaintext in turn. Their phase terms are listed in Figs. 7(a)–7(c), and the blue, green, and red parts stand for −π∕2, 0, and π∕2, respectively. Then, the decryption is conducted and the subsequently decoded output image appears in Fig. 7(d). The Co value is 0.9902 after 100 iterations, which shows the decryption is successful and fast. However, once the probes are unavailable to us, the corresponding decryption will suffer failures, as exemplified in Fig. 7(e). The extracted image becomes random noise and no clues about the plaintext can be read. The Co value drops to 0.0241, which indicates the decryption is defeated as well. Therefore, we can find that the P-scanning DH naturally inherits the good property of Ref. [36], which is a great merit for the optical encryption: using multiple probes not only expands the key space but also supplies extra freedom to control the system safety. We then continued the study from the holographic aspect. An important point of the P-scanning DH is that we place M 3 in the reference beam and record interferograms as our ciphertexts. This eliminates the aforementioned potential vulnerabilities of the single ptychographic method [36,37]. From Eq. (9), ~ 2  can be ~ 1; N the similarity of the sub-ciphertexts N suppressed by the disturbance of X n, which is decided by the diffraction of M 3. We can use multiple

d3 , or even change M 3 in the scanning procedure to achieve better disturbances. Simulations are performed to test the effectiveness of such disturbance and Fig. 8 shows the results. We calculated the Co values between the adjacent sub-ciphertexts (CoN ) of both the single ptychographic method and the P-scanning DH method. Since 3 × 3 positions are used, 8 pairs of sub-ciphertexts are examined. In Fig. 8, the black line with circle labels represents the single ptychographic method while the blue dotted line with rectangle labels stands for the P-scanning DH method, with δd3  0.5 mm. δd3 means the stepvariation of d3 in the scanning procedure. From Fig. 8, we can see the CoN values in the single ptychographic method are all high (around 0.8), whereas

Fig. 7. (a)–(c) Three complex probes (phase term, blue: −π∕2; green: 0; red: π∕2). (d) and (e) Decrypted images when using correct and incorrect probes, respectively. 20 July 2014 / Vol. 53, No. 21 / APPLIED OPTICS

4705

Fig. 10. Robustness of the proposed method against noise attack and occlusion: (a) ciphertext with random noise (SNR  5), (b) decrypted image from (a), (c) ciphertext with 6.25% occlusion, and (d) decrypted image from (c).

Fig. 8. Co curves of adjacent positions in the single ptychographic and the P-scanning DH method, respectively.

the CoN values in the P-scanning DH method are extremely low (nearly 0). The simulation results support our analysis and proves the validity of the disturbances. In fact, based on our further simulations, we also find that at larger δd3, the less similarity of the sub-ciphertexts. In addition, the phase mask M 3 itself is an important system key as well. If we use incorrect M 3 or d3 , then the decryption will encounter collapse. Figures 9(a) and 9(b) are the decrypted images after 1000 iterations when using an incorrect M 3 and a wrong d3 (error is 1 mm), respectively. We can see both of them are unrecognizable noise patterns. The Co values of the two cases are 0.0092 and 0.0102, respectively. The above results indicate a defeated decryption. Besides, the other safety keys (M 1 , M 2 , λ, d1 , d2 ) are also tested, and their effectiveness is guaranteed (for the sake of brevity, we only show a part of

the results). Figures 9(c)–9(e) are the retrieved images after 1000 iterations when using a wrong wavelength λ (error is 5 nm), a wrong phase-only mask M 2 and a wrong diffractive distance d2 (error is 1 mm). All of the simulation results are completely random noise and no details about the plaintext can be recognized from the decrypted images. The Co values are all close to 0. From the above simulation results, we can find that the proposed method has a huge key space. The probes (Pn ), phase masks (M 1 , M 2 , M 3 ), diffractive distances (d1 , d2 , d3 ), and light wavelength (λ) are all serving as safety keys. They supply sufficient freedoms to control the system with a high security level. Besides, due to the combination of the holographic technique, the system also avoids the potential safety vulnerabilities of the single ptychographic techniques [36,37]. Thus, the system security will be further improved. C.

Robustness

In this section, we tested the robustness of the proposed method against noise and occlusion attacks. Figure 10(a) is one of the interference patterns contaminated by additive random noise (signal-to-noise ratio, SNR  5). Random noise is generated by fMeanI n ξ; ηg∕SNR × V, where Mean denotes a mean value of the ciphertext and V represents a 2D variable randomly distributed in a range of −0.5; 0.5 [14]. The corresponding retrieved image with the correct keys is shown in Fig. 10(b). The occlusion on all interferograms is 6.25%, and Fig. 10(c) gives one example. By using the correct keys, the ciphertexts are decrypted and the result is shown in Fig. 10(d). The Co values for the two decrypted images are 0.4381 and 0.2014 after 100 iterations, respectively. It can be seen that, in both cases, the quality of the extracted images degrades, but they can still be recognized and understood without doubt, in spite of the fact that the size of the plaintext is four times larger than the ciphertexts. Therefore, we can find the proposed method has a good robustness. 4. Conclusions

Fig. 9. Decrypted images when using (a) a wrong phase-only mask M 3 and (b) a wrong diffractive distance d3 (error  1 mm), (c) a wrong wavelength λ (error  5 nm), (d) a wrong phase-only mask M 2 , and (e) a wrong diffractive distance d2 (error  1 mm). 4706

APPLIED OPTICS / Vol. 53, No. 21 / 20 July 2014

We have proposed a new system to encrypt an image of unlimited size based on the P-scanning DH. Holographic processing and ptychographic iterative reconstruction are both employed to decrypt high-quality images from the recorded ciphertexts. Numerical experiments demonstrated that the

proposed method possesses some outstanding advantages, such as wide FOV, high security level, and the ability to avoid the natural defects of single ptychographic systems. The robustness has also been analyzed and verified against random noise and occlusion attacks. The P-scanning DH method combines the ptychographic and holographic techniques together and successfully overcomes the physical limitations of PMZ-DH. We believe it will find wide use in practice and may open up some new potential applications, such as 3D information encryption and image hiding. This research was supported by National Natural Science Foundation of China grant 61350014 and 61307018, K. C. Wong Education Foundation, Hong Kong, Scientific Research Funds for Excellent Doctoral Dissertation of Chinese Academy of Sciences, Fusion Foundation of Research and Education, Chinese Academy of Sciences, in part by the President Fund of University of the Chinese Academy of Sciences, and the “Young Eagles” Program of the Academy of Opto-Electronics, Chinese Academy of Sciences. References 1. O. Matoba, T. Nomura, E. Perez-Cabre, M. Í. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009). 2. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009). 3. S. Liu, C. Guo, and J. Sheridan, “A review of optical image encryption techniques,” Opt. Laser Technol. 57, 327–342 (2014). 4. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier-plane random encoding,” Opt. Lett. 20, 767–769 (1995). 5. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004). 6. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double-random phase encoding in the fractional Fourierdomain,” Opt. Lett. 25, 887–889 (2000). 7. S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001). 8. S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier-transforms with random phase filtering,” Opt. Commun. 187, 57–63 (2001). 9. B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier-domains,” Opt. Lett. 28, 269–271 (2003). 10. Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier-transform,” Opt. Commun. 275, 324–329 (2007). 11. L. Chen and D. Zhao, “Optical image encryption with Hartley transforms,” Opt. Lett. 31, 3438–3440 (2006). 12. Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010). 13. W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010). 14. W. Chen and X. Chen, “Structured-illumination-based diffractive imaging and its application to optical image encryption,” Opt. Commun. 285, 2044–2047 (2012).

15. P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35, 2391–2393 (2010). 16. J. Zang, Z. Xie, and Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38, 1289–1291 (2013). 17. B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28–30 (2000). 18. E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595– 6601 (2000). 19. E. Tajahuerce, O. Matoba, S. C. Verrall, and B. Javidi, “Optoelectronic information encryption with phase-shifting interferometry,” Appl. Opt. 39, 2313–2320 (2000). 20. H. Kim, D. H. Kim, and Y. H. Lee, “Encryption of digital hologram of 3D object by virtual optics,” Opt. Express 12, 4912–4921 (2004). 21. L. Yu and L. Cai, “Multidimensional data encryption with digital holography,” Opt. Commun. 215, 271–284 (2003). 22. X. Meng, L. Cai, X. Xu, X. Yang, X. Shen, G. Dong, and Y. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416 (2006). 23. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008). 24. N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhao, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009). 25. Y. Han and Y. Zhang, “Optical image encryption based on two beams’ interference,” Opt. Commun. 283, 1690–1692 (2010). 26. H. Di, K. Zheng, X. Zhang, E. Y. Lam, T. Kim, Y. S. Kim, T. C. Poon, and C. Zhou, “Multiple-image encryption by compressive holography,” Appl. Opt. 51, 1000–1009 (2012). 27. J. Di, J. Zhao, H. Jiang, P. Zhang, Q. Fan, and W. Sun, “High resolution digital holographic microscopy with a wide field of view based on a synthetic aperture technique and use of linear CCD scanning,” Appl. Opt. 47, 5654–5659 (2008). 28. T. R. Hillman, T. Gutzler, S. A. Alexandrov, and D. D. Sampson, “High-resolution, wide-field object reconstruction with synthetic aperture Fourier-holographic optical microscopy,” Opt. Express 17, 7873–7892 (2009). 29. W. Hoppe, “Trace structure analysis, ptychography, phase tomography,” Ultramicroscopy 10, 187–198 (1982). 30. H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004). 31. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98, 034801 (2007). 32. J. M. Rodenburg, “Ptychography and related diffractive imaging methods,” in Advances in Imaging and Electron Physics, P. W. Hawkes, ed. (Academic, 2008), pp. 87–184. 33. Y. Wang, T. Li, Q. Gao, S. Zhang, and Y. Shi, “Application of diffractive optical elements for controlling the light beam in ptychography,” Opt. Eng. 52, 091720 (2013). 34. Y. Shi, Y. Wang, and S. Zhang, “Generalized ptychography with divers’ probes,” Chin. Phys. Lett. 30, 054203 (2013). 35. Y. Shi, Y. Wang, T. Li, Q. Gao, H. Wan, S. Zhang, and Z. Wu, “Ptychographic imaging algorithm with a single random phase encoding,” Chin. Phys. Lett. 30, 074203 (2013). 36. Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38, 1425– 1427 (2013). 37. W. Chen, G. Situ, and X. Chen, “High-flexibility optical encryption via aperture movement,” Opt. Express 21, 24680–24691 (2013).

20 July 2014 / Vol. 53, No. 21 / APPLIED OPTICS

4707

Optical encryption of unlimited-size images based on ptychographic scanning digital holography.

The ptychographic scanning operation is introduced into digital holography to expand the field-of-view (FOV). An optical image encryption method based...
942KB Sizes 0 Downloads 6 Views