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Optical encryption scheme for multiple-image based on spatially angular multiplexing and computer generated hologram
Optics and Lasers in Engineering 127 (2019) 105953
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Optics and Lasers in Engineering journal homepage: www.elsevier.com/locate/optlaseng
Optical encryption scheme for multiple-image based on spatially angular multiplexing and computer generated hologram Sixing Xi a, Nana Yu a, Xiaolei Wang b,∗, Xueguang Wang a,∗, Liying Lang c, Huaying Wang a, Weiwei Liu b, Hongchen Zhai b a
School of Mathematics and Physics, Hebei University of Engineering, Handan, Hebei 056038, China Institute of Modern Optics, College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300350, China c Hebei University of Technology, Tianjin 300401, China b
a r t i c l e
i n f o
Keywords: Multiple-image encryption Optical security and encryption Computer generated hologram
a b s t r a c t We propose an optical encryption scheme for multiple images based on angle multiplexing and computer generated hologram(CGH) in this paper. In the encryption process, the original images are firstly modulated by two random phase keys in Fresnel transform with different diffraction distances. Secondly, the modulated images are coherent superposition with solid angle multiplexed reference beams to generate interference fringes and form a compound image. Finally, the compound image is encoded to a CGH by Roman coding method. In the decrypted process, the corresponding experimental system using SLM is built, in which multiple images can be encrypted synchronously with high efficiency. Except random phase key, the proposed encryption system has multiple kind of keys including diffraction distance and wavelength to improve the security. Due to the characteristics of high storage efficiency and simple calculation, this optical multiple-image encryption scheme has important application prospect in improving the efficiency of information transmission and multi-user authentication.
1. Introduction Optical image encryption technology shows great potential in information security field. After Refregier and Javidi firstly proposed double random phase optical encryption technology with high security and strong robustness in 1995 [1], a series of derived optical image encryption methods were proposed, such as optical XOR encryption [2], phase shift interference encryption [3], joint transform correlator encryption [4], gyrator transform encryption [5], polarization encryption [6] and digital holographic encryption [7]. However, the encryption methods mentioned above are only aimed at a single image with limited encryption capacity. The traditional encryption transmission of single image can no longer meet the growing information demand with the rapid growth of big data and the continuous enhancement of information transmission capability. Therefore, more and more scholars begin to study multiple-image encryption technology [8–10]. The major feature of multiple-image encryption is that the images should be composited and the composite method directly affect the computational efficiency of the whole algorithm and the quality of the final decrypted images. Current multiple-image encryption technology is mainly based on the following methods or principles: Multiplexing, Digital Holography, Compressed Sensing, Chaos and special optical
∗
transformation. For example, Situ introduced wavelength multiplexing to achieve multiple-image encryption [11], Sui proposed a multipleimage encryption algorithm based on phase recovery technology and phase mask multiplexing [12]. Xu proposed a multiple-image encryption method based on random amplitude plate and Fresnel hologram [13], Wan proposed a multiple-image compression holographic algorithm based on improved Mach-Zehnder interferometer [14]. Deepan applied compressed sensing to dual random phase space multiplexing technology for realizing multiple-image encryption [15]. Tang combined bit plane decomposition and chaotic mapping algorithm to encrypt multiple images [16], Zhang combined the hybrid image element algorithm with linear chaotic mapping system to realize encryption of multiple images [17]. Kong used cascaded fractional Fourier transform to superpose multiple images into a single image for encryption [18], Alfalou proposed an algorithm using discrete cosine transform to compound multiple images [19]. At present, the number of encrypted images has been improved in these multiple-image encryption methods, but the complexity of the system is also increased. Meanwhile, the time and complexity of data processing also increase along with the increase of encryption capacity. Moreover, most of these multiple-image encryption methods are based on the combination of various technical means because of the limitation of the single-technology encryption method. In addition, this kind of methods are also limited by the requirement of
Corresponding author. E-mail address: [email protected] (X. Wang).
https://doi.org/10.1016/j.optlaseng.2019.105953 Received 18 September 2019; Received in revised form 8 November 2019; Accepted 18 November 2019 0143-8166/© 2019 Elsevier Ltd. All rights reserved.
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Optics and Lasers in Engineering 127 (2019) 105953
Fig. 1. The optical setup of multiple-image encryption process. BE is beam expander, BS is beam splitter, PC is personal computer, o is object beam and R is reference beam which is in the plane determined by the X-axis and Z-axis, R(𝜃) is the rotation angle of CCD, 𝛼 i is angle between o and R, z is the distance of Fresnel diffraction.
pixel-by-pixel alignment of random phase keys in practical decryption experiments [20]. Therefore, these works mainly are concentrated on digital systems and difficult to achieve optically. In order to overcome these problems discussed above, we propose an optical multiple-image encryption scheme based on spatially angular multiplexing and computer generated hologram(CGH), meanwhile, the corresponding experimental decryption system using Spatial Light Modulator (SLM) is built to verify the optical encryption scheme. In this scheme, all images are encrypted into a binary real-value CGH which has strong anti-noise ability. The spatially angular multiplexing is introduced to superpose the multiple image in space domain but ensure their separation in spectra domain. Due to the characteristics of high storage efficiency and simple calculation, this optical multiple-image encryption scheme has important application prospect in improving the efficiency of information transmission and multi-user authentication.
2. Encryption process The multiple-image encryption process can be divided into two steps, that is, spatially angular multiplexing holographic recording of the original multiple images and the CGH coding process. The optical setup of the first step is shown in Fig. 1 which is Mahzedel interferometric system with two SLM. Firstly, the original image is imaged on the SLM1 by a 4f system and is modulated by first random phase key loaded on SLM1 . Secondly, the modulated image goes through a Fresnel diffraction process and reaches SLM2 which load the second random phase key. Thirdly, the twice modulated image is coherent superposition with spatially angle multiplexed reference beam to generate an interference fringe which is recorded by CCD. Changing the original image and rotating the CCD simultaneously, the multiple holograms with different fringe directions can be obtained. Finally, multiple holograms are superimposed together to form a compound image. In this paper, four original images 𝛼 i and d(x, y) are chosen as characters “A”, “B”, “C” and “D” with 128 × 128 pixels respectively, which are shown in Fig. 2. In the first step as shown in Fig. 1, each original image is perpendicularly illuminated by plane wave and is modulated by the first random phase p1i where i is image sequence number, then is performed by Fresnel transform with distance zi and finally modulated by the second
Fig. 2. (a)–(d) Four images to be encrypted.
random phase p2i . The first random phase p1i can be expressed as [ ] 𝑝11 = exp 1.2jπ rand(𝑥, 𝑦) [ ] 𝑝12 = exp 1.2jπ rand(𝑥, 𝑦) [ ] 𝑝13 = exp 1.2jπ rand(𝑥, 𝑦) [ ] 𝑝14 = exp 1.2jπ rand(𝑥, 𝑦)
(1)
It is verified by theoretical simulation and experiments that the random phase p1i will disperse image information on the spectrum plane [7] where the filter is placed, so the image information will lose, resulting the quality of decrypted image declines. Thus, the value range of random phase p1i is chosen from 0 to 1.2𝜋. Based on this, rand(𝑥, 𝑦) in Eq. (1) denotes white sequences uniformly distributed in [0; 1]. The Fresnel diffraction distance zi are chosen as 𝑧1 = 0.1 m, 𝑧2 = 0.2 m, 𝑧3 = 0.3 m and 𝑧4 = 0.4 m corresponding to the four images respectively, since different diffraction distance keys can improve the security of image encryption. In order to simplify the experimental decrypted process, the second random phase keys are designed as the same and can be described as [ ] (2) 𝑝21 = 𝑝22 = 𝑝23 = 𝑝24 = 𝑝2 = exp 2jπ r and(𝑥, 𝑦) As described above, the twice modulated images can be expressed as [ ] 𝑎1 (𝑥, 𝑦) = FrT𝑍1 𝑎(𝑥, 𝑦)𝑝11 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦), [ ] 𝑏1 (𝑥, 𝑦) = FrT𝑍2 𝑏(𝑥, 𝑦)𝑝12 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦), [ ] 𝑐1 (𝑥, 𝑦) = FrT𝑍3 𝑐 (𝑥, 𝑦)𝑝13 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦), [ ] 𝑑1 (𝑥, 𝑦) = FrT𝑍4 𝑑 (𝑥, 𝑦)𝑝14 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦),
(3)
Where Frt[•] denotes the Fresnel transform with distance of Zi and 𝑖 = 1, 2, 3, 4. Then the modulated images interfere successively with reference beams based on spatially angular multiplexing. In our scheme,
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Optics and Lasers in Engineering 127 (2019) 105953
Fig. 3. (a)–(d) Four interference fringes obtained from four images with solid angle multiplexed reference beams.
multiple images are encrypted by spatial angle multiplexing of reference beams. The spatial angle can be controlled by two parameters 𝛼 i and 𝜃 i which is shown in inset of Fig. 1, where 𝛼 i is the included angle between reference beam and Z-axis while 𝜃 i is the rotation angle of CCD. The angle 𝛼 i determined the period of interference fringe and the angle 𝜃 determined the direction of interference fringe, therefore the multiple holograms are overlapped in a frame of CCD but their Fourier spectra are separated in the spectra domain. In this paper, 0.1 cm and 𝜃𝑖 = 0◦ , 𝜃2 = 45◦ , 𝜃3 = 90◦ , 𝜃4 = 135◦ are chosen, that is, four images are encrypted and the corresponding parameters are (2∘ , 0∘ ), (2∘ , 45∘ ), (2∘ , 90∘ ) and (2∘ , 135∘ ) which can be obtained by only rotating CCD to simplify experimental operation. It is noted that both 𝛼 i and 𝜃 i should be chosen properly when more images are encrypted. The four solid angle reference beams can be expressed as ( ) ( ) sin 𝛼 𝜃 = 0◦ ∶ 𝑅1 = A1 exp j2 πxf = exp j2π𝑥 , 𝜂 ( ) [ ] sin 𝛼 𝜃 = 45◦ ∶ 𝑅2 = A2 exp j2 π (𝑥 + 𝑦)𝑓 = exp j2π(𝑥 + 𝑦) , 𝜂 ( ) ( ) sin 𝛼 𝜃 = 90◦ ∶ 𝑅3 = A3 exp j2 π yf = exp j2π y , 𝜂 [ ] [ ] sin 𝛼 𝜃 = 135◦ ∶ 𝑅4 = A4 exp j2 π (−𝑥 + 𝑦)𝑓 = exp j2π(−𝑥 + 𝑦) , 𝜂
Fig. 4. (a) The final encrypted image; (b) the encoded CGH.
2. 3. Decrypted process (4)
Four solid angle reference beams interfere with four modulated images respectively to form four interference fringe images. These four interference fringes in different directions are shown in Fig. 3. After that, four interference fringe images are superimposed together to form a compound image. It is noted that the original bias component is replaced by uniform field to reduce bandwidth and sampling points, improve the quality of reconstructed image. Therefore, the compound image can be described as ( ) ( ) I(𝑥, 𝑦) = 1 + 𝑎1 (𝑥, 𝑦) exp −j2πxf + 𝑎1 (𝑥, 𝑦) exp j2πxf [ ] [ ] + 1 + 𝑏1 (𝑥, 𝑦) exp −j2π(𝑥 + 𝑦)𝑓 + 𝑏1 (𝑥, 𝑦) exp j2π(𝑥 + 𝑦)𝑓 ( ) ( ) + 1 + 𝑐1 (𝑥, 𝑦) exp −j2πyf + 𝑐1 (𝑥, 𝑦) exp j2πyf [ ] [ ] + 1 + 𝑑1 (𝑥, 𝑦) exp −j2π(−𝑥 + 𝑦)𝑓 + 𝑑1 (𝑥, 𝑦) exp j2π(−𝑥 + 𝑦)𝑓 (5)
The decryption experiment system is shown in Fig. 5, which contains 4f, Fresnel diffraction and spatial filtering system. A transmissive phase only SLM (Meadowlark Optics LC_SLM, 1920 × 1152 pixels, pixel pitch 9.2 × 9.2 𝜇m) and a MINTRON 1881EX Charge Coupled Device (CCD) with pixel size of 8.3 × 8.3 𝜇m and pixel number of 768(H) × 576(V) are used in our experiment. The focal length of all Fourier lenses are 0.3 m and the diameter of circular filter is 1 mm. As shown in Fig. 5, the encrypted CGH image is loaded on the upper part of SLM and illuminated perpendicularly by plane wave, then the light is reflected by a 4f system so the encrypted CGH is imaged on bottom part of the same SLM. Obviously, the SLM is divided into two parts to load the encrypted CGH (upper part) and the decrypted phase key p4 (x, y) (bottom part). The decrypted phase key p4 (x, y) is also encoded into CGH with 896 × 896 pixels. As described in Fig. 5, the encrypted CGH is modulated by p4 (x, y) and then performs Fresnel transform with distance of Zi after spatial filtering. When the correct filters and 𝑍𝑖 = 0.1 m, 0.2 m, 0.3, 0.4 m are applied, the decrypted images can be recorded by CCD. In the decrypted process, the decrypted phase key is described as 𝑝4 (𝑥, 𝑦) = 𝑝2 (𝑥, 𝑦)𝑝3 ∗ (𝑥, 𝑦)
(6)
𝑝4 ′ (𝑥, 𝑦) = 𝑝2 (𝑥, 𝑦)𝑝3 (𝑥, 𝑦),
(7)
∗
In the final CGH coding process, in order to improve the security of decryption in experiment, the intensity of compound image is modulated by another random phase 𝑝3 (𝑥, 𝑦) = exp[j2πrand(𝑥, 𝑦)]. The encrypted image I(x, y)p3 (x, y) is shown in Fig. 4(a) and is encoded into CGH as shown in Fig. 4(b) using Roman coding method, thus the encryption is completed and the binary real value CGH is the final encrypted image. Because that the encrypted image I(x, y)p3 (x, y) is 128 × 128 pixels and each pixel is expanded to an unit with 7 × 7 pixels in the process of Roman CGH encoding, therefore the final CGH have pixels number of 896 × 896, as shown in Fig. 4(b). It is clear that the encrypted image (Fig. 4(a)) and CGH (Fig. 4(b)) do not contain the original image information.
where denotes the conjugate operation. The decryption phase key p4 is encoded into CGH with 896 × 896 pixels to reduce the strict setup alignment requirements [21]. In the frequency spectrum plane shown in Fig. 6, the noise of the higher orders units in spectrum increase quickly, so the good reproduced images can only be obtained at −1 order. As shown in Fig. 6(a), when p4 are used, the complex amplitude of the −1 order beam after the SLM is −1 ∶ 𝑝4 (𝑥, 𝑦)I(𝑥, 𝑦)𝑝3 (𝑥, 𝑦) = 𝑝2 (𝑥, 𝑦)𝑝3 ∗ (𝑥, 𝑦)I(𝑥, 𝑦)𝑝3 , (𝑥, 𝑦) = I(𝑥, 𝑦)𝑝2 (𝑥, 𝑦) (8) Thus, when correct phase key, Fresnel transform distance and matched filter are used, by adjusting the location of CCD, the four
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Optics and Lasers in Engineering 127 (2019) 105953
Fig. 5. The schematic of decryption with Fresnel diffraction and spatial filtering based on SLM.
Fig. 6. The frequency spectrum of the CGH in decrypted process with correct keys p4 , F1~F4 are the four filters, (a) simulation result; (b) experimental result.
decrypted images can be orderly obtained as [ { }] 𝑎∗ (𝑥, 𝑦)𝑝11 ∗ (𝑥, 𝑦) = Fr T𝑧1 F1 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦) , [ { }] 𝑏∗ (𝑥, 𝑦)𝑝12 ∗ (𝑥, 𝑦) = Fr T𝑧2 F2 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦) , [ { }] 𝑐 ∗ (𝑥, 𝑦)𝑝13 ∗ (𝑥, 𝑦) = Fr T𝑧3 F3 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦) , [ { }] 𝑑 ∗ (𝑥, 𝑦)𝑝14 ∗ (𝑥, 𝑦) = Fr T𝑧4 F4 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦)
(9)
Where Fi {•} denotes the filtering process for different images, in which the aperture of self-made filters is 0.3 mm. As shown in Fig. 6(b), when p4 ′ is used, the complex amplitude of the +1 order beam after the SLM is ∑∑ (𝑜(𝑚, 𝑛) − 𝑜)(𝑜′ (𝑚, 𝑛) − 𝑜′ ) 𝑚 𝑛 CC = √( (10) )( ) ∑∑ ∑∑ ′ 2 ′ 2 (𝑜(𝑚, 𝑛) − 𝑜) (𝑜 (𝑚, 𝑛) − 𝑜 ) 𝑚 𝑛
𝑚 𝑛
Compared with Eq. (5), we can find that the I∗ (x, y) is the same as y), so the result in Eq. (10) is also the same as that in Eq. (8). Therefore, the same results can be obtained when either p4 or p4 ′ is used and the amplitude obtained in the CCD will be the conjugate of original images a∗ (x, y), b∗ (x, y), c∗ (x, y) and d∗ (x, y). In this case, the experimental I∗ (x,
results are shown in Fig. 7, in which (a)-(d) are a∗ (x, y), b∗ (x, y), c∗ (x, y) and d∗ (x, y) respectively, while (a’)-(d’) are the corresponding simulation results. In conclusion, when the correct keys including p4 (x, y); p4 ′(x, y), filters, Fresnel diffraction distance zi and wavelength 𝜆 are applied, the conjugate original images can be obtained. Meanwhile, the experimental results show good agreements with the numerical simulations which verify the validity of proposed experimental scheme. 4. Security analysis and discussion In this section, we analyzed the security of the proposed encryption scheme. In general, the encrypted image is transmitted through public communication channels, where there are some strong possibilities for information distortion. We introduced correlation coefficient (CC) to evaluate the similarity between the original image o(x, y) and the decrypted image o′(x, y), the definition of CC is ∑∑ (𝑜(𝑚, 𝑛) − 𝑜)(𝑜′ (𝑚, 𝑛) − 𝑜′ ) 𝑚 𝑛 CC = √( (11) )( ) ∑∑ ∑∑ ′ 2 (𝑜(𝑚, 𝑛) − 𝑜)2 (𝑜 (𝑚, 𝑛) − 𝑜′ ) 𝑚 𝑛
𝑚 𝑛
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Optics and Lasers in Engineering 127 (2019) 105953
Fig. 7. (a)–(d) The decrypted images “A”–“D” with all correct keys, and (a’)–(d’) are the corresponding simulation results.
Fig. 8. (a) The decrypted image “A” with wrong key wavelength(𝑛 = 532 nm) and all other correct keys; (b) The decrypted image with wrong phase key p4 and all other correct keys; (c) The decrypted image with all correct keys but wrong filter.
Where, 𝑜 and 𝑜′ denote the mean value of o(x, y) and o′(x, y) respectively. The proposed scheme’s keys include random phase mask, wavelength 𝜆 and Fresnel transform distance zi . Firstly, according to Eq. (11), the CC have been calculated between the original image and the decrypted result when all the keys are correct (shown in Fig. 7(a)−(d)), and the results are 0.907, 0.875, 0.893, 0.861 respectively, so the decryption is completed very well and the high-quality decryption images are obtained. Then we test the influence of keys p4 , 𝜆 and zi on the decrypted images. When the wavelength key 𝜆 is wrong (𝜆 = 532 nm is chosen for convenience) while other keys are all correct, the decryption result is shown in Fig. 8(a) (here, the case of letter A is chosen as example for demonstration). Fig. 8(b) shows the decryption result with wrong phase keys p4 (x, y) and other correct keys. Fig. 8(c) is the result with wrong filter and other correct keys. As shown in Fig. 8(a), the result of decryption is something like “A” when the key wavelength is wrong(𝜆 = 532nm), in which the CC between the original image and the decrypted result 0.108. It is obvious that the image can not be decrypted at all when p4 is wrong in which the corresponding CC is 0.037, so this decrypted result shown in Fig. 8(b) is irrelevant with the original image. Meanwhile, the CC is 0.116 for the decrypted result shown in Fig. 8(c) with wrong filter. The other important key zi in our scheme is discussed more detailed as bellow. Taking image a(x, y) as an example, the CC dependence on z1 is shown in Fig. 9. As shown in Fig. 9, the exact values zi does CC value very close to 1 and good decrypted result can be obtained. Although the value range of random phase is compressed from 0 to 1.2𝜋 to improve the quality of decrypted image, which reduced the sensitivity of diffraction distance, the CC value still decreases exponentially with deviations of zi and will be less than 0.2 when the error of zi greater than 0.1 cm, at this time,
Fig. 9. The CCdependence on Zi of image 𝛼(x, y, ) .
there is a failure to distinguish the decrypted image as shown in the insets. So the CC around the accurate values of zi is highly sensitive and the distance sensitivity is around 0.1 cm, which shows great difficulty in copying the encryption system. In this paper, four images are encrypted and decrypted to verify the proposed scheme. The most important factors that affect encryption capacity of this scheme are the CGH coding parameters and the phase random range of key pi . According to our theoretical simulation and experiment, the image to be encrypted is 128 × 128 pixels and the single encoding unit in CGH includes 7 × 7 pixels, the phase random range of key pi is [0 − 1.2π] and the focal length of Fourier lenses is 0.3m. under that condition the spectrum size of each encrypted image is about 16 × 16 pixels. Fig. 6 is 896 × 896 pixels and shows 7 × 7 spectrum display units with 128 × 128 pixels, so at most 32 images’ spectra can exist in Fig. 6 at the same time without overlapping when proper spatial angle and quantity of reference beams are applied. At this time, the CC values of the decrypted images can be higher than 0.9, indicating the encryption capacity of this scheme ensures 32 images to be encrypted and decrypted with satisfied quality. But the CC values will decrease when the phase random range of key pi increases, and also will be influenced by the optical modulation performance of the SLM applied in experiment.
S. Xi, N. Yu and X. Wang et al.
5. Conclusions In summary, an optical multiple-image encryption scheme based on spatially angular multiplexing and CGH is proposed. In this scheme, spatial angle multiplexing technology of digital holography and CGH are used. Spatial angle of reference beams are precisely controlled by two parameters 𝛼 i and 𝜃 i , ensuring that the spectrum plane space is fully utilized to improve the image encryption capacity. Besides double random phase, the Fresnel diffraction distance, wavelength, CGH parameters also can be used as image encryption keys to improve the security of the optical image encryption scheme. The multiple gray-scale images are encrypted into a binary real value CGH which has strong anti-noise ability and is convenient to be saved and transferred. The decryption phase keys are encoded into CGH to reduce difficulty in ensuring the accurate alignment of decryption random phase key in traditional methods, so the feasibility of optical implementation is increased which is proved by our experimental results. The simulation and experimental results verify the effectiveness of the scheme. By comparing with the original images visually and digitally, it is concluded that good multiple decrypted images can be obtained without obvious distortion, noise or crosstalk phenomenon. Due to the high storage efficiency and security, we believe this scheme has important potential application in multipleimage encryption. Acknowledgments National Science Foundation of China (NSFC) (11904073, 61875093) Natural Science Foundation of Hebei Province (F2019402351, F2018402285) and the Natural Science Foundation of Tianjin (19JCYBJC16500). References [1] Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 1995;20(7):767–9. [2] Li X, Meng X, Yang X, Wang Y, Yin Y, Peng X, He W, Dong G, Chen H. Multiple-image encryption via lifting wavelet transform and XOR operation based on compressive ghost imaging scheme. Opt Lasers Eng 2018;102:106–11. [3] Toto-Arellano N, Rodriguez-Zurita G, Meneses-Fabian C, Vazquez-Castillo J. Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry. Opt Express 2008;16(23):19330–41.
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Optical encryption scheme for multiple-image based on spatially angular multiplexing and computer generated hologram Sixing Xi a, Nana Yu a, Xiaolei Wang b,∗, Xueguang Wang a,∗, Liying Lang c, Huaying Wang a, Weiwei Liu b, Hongchen Zhai b a
School of Mathematics and Physics, Hebei University of Engineering, Handan, Hebei 056038, China Institute of Modern Optics, College of Electronic Information and Optical Engineering, Nankai University, Tianjin 300350, China c Hebei University of Technology, Tianjin 300401, China b
a r t i c l e
i n f o
Keywords: Multiple-image encryption Optical security and encryption Computer generated hologram
a b s t r a c t We propose an optical encryption scheme for multiple images based on angle multiplexing and computer generated hologram(CGH) in this paper. In the encryption process, the original images are firstly modulated by two random phase keys in Fresnel transform with different diffraction distances. Secondly, the modulated images are coherent superposition with solid angle multiplexed reference beams to generate interference fringes and form a compound image. Finally, the compound image is encoded to a CGH by Roman coding method. In the decrypted process, the corresponding experimental system using SLM is built, in which multiple images can be encrypted synchronously with high efficiency. Except random phase key, the proposed encryption system has multiple kind of keys including diffraction distance and wavelength to improve the security. Due to the characteristics of high storage efficiency and simple calculation, this optical multiple-image encryption scheme has important application prospect in improving the efficiency of information transmission and multi-user authentication.
1. Introduction Optical image encryption technology shows great potential in information security field. After Refregier and Javidi firstly proposed double random phase optical encryption technology with high security and strong robustness in 1995 [1], a series of derived optical image encryption methods were proposed, such as optical XOR encryption [2], phase shift interference encryption [3], joint transform correlator encryption [4], gyrator transform encryption [5], polarization encryption [6] and digital holographic encryption [7]. However, the encryption methods mentioned above are only aimed at a single image with limited encryption capacity. The traditional encryption transmission of single image can no longer meet the growing information demand with the rapid growth of big data and the continuous enhancement of information transmission capability. Therefore, more and more scholars begin to study multiple-image encryption technology [8–10]. The major feature of multiple-image encryption is that the images should be composited and the composite method directly affect the computational efficiency of the whole algorithm and the quality of the final decrypted images. Current multiple-image encryption technology is mainly based on the following methods or principles: Multiplexing, Digital Holography, Compressed Sensing, Chaos and special optical
∗
transformation. For example, Situ introduced wavelength multiplexing to achieve multiple-image encryption [11], Sui proposed a multipleimage encryption algorithm based on phase recovery technology and phase mask multiplexing [12]. Xu proposed a multiple-image encryption method based on random amplitude plate and Fresnel hologram [13], Wan proposed a multiple-image compression holographic algorithm based on improved Mach-Zehnder interferometer [14]. Deepan applied compressed sensing to dual random phase space multiplexing technology for realizing multiple-image encryption [15]. Tang combined bit plane decomposition and chaotic mapping algorithm to encrypt multiple images [16], Zhang combined the hybrid image element algorithm with linear chaotic mapping system to realize encryption of multiple images [17]. Kong used cascaded fractional Fourier transform to superpose multiple images into a single image for encryption [18], Alfalou proposed an algorithm using discrete cosine transform to compound multiple images [19]. At present, the number of encrypted images has been improved in these multiple-image encryption methods, but the complexity of the system is also increased. Meanwhile, the time and complexity of data processing also increase along with the increase of encryption capacity. Moreover, most of these multiple-image encryption methods are based on the combination of various technical means because of the limitation of the single-technology encryption method. In addition, this kind of methods are also limited by the requirement of
Corresponding author. E-mail address: [email protected] (X. Wang).
https://doi.org/10.1016/j.optlaseng.2019.105953 Received 18 September 2019; Received in revised form 8 November 2019; Accepted 18 November 2019 0143-8166/© 2019 Elsevier Ltd. All rights reserved.
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Optics and Lasers in Engineering 127 (2019) 105953
Fig. 1. The optical setup of multiple-image encryption process. BE is beam expander, BS is beam splitter, PC is personal computer, o is object beam and R is reference beam which is in the plane determined by the X-axis and Z-axis, R(𝜃) is the rotation angle of CCD, 𝛼 i is angle between o and R, z is the distance of Fresnel diffraction.
pixel-by-pixel alignment of random phase keys in practical decryption experiments [20]. Therefore, these works mainly are concentrated on digital systems and difficult to achieve optically. In order to overcome these problems discussed above, we propose an optical multiple-image encryption scheme based on spatially angular multiplexing and computer generated hologram(CGH), meanwhile, the corresponding experimental decryption system using Spatial Light Modulator (SLM) is built to verify the optical encryption scheme. In this scheme, all images are encrypted into a binary real-value CGH which has strong anti-noise ability. The spatially angular multiplexing is introduced to superpose the multiple image in space domain but ensure their separation in spectra domain. Due to the characteristics of high storage efficiency and simple calculation, this optical multiple-image encryption scheme has important application prospect in improving the efficiency of information transmission and multi-user authentication.
2. Encryption process The multiple-image encryption process can be divided into two steps, that is, spatially angular multiplexing holographic recording of the original multiple images and the CGH coding process. The optical setup of the first step is shown in Fig. 1 which is Mahzedel interferometric system with two SLM. Firstly, the original image is imaged on the SLM1 by a 4f system and is modulated by first random phase key loaded on SLM1 . Secondly, the modulated image goes through a Fresnel diffraction process and reaches SLM2 which load the second random phase key. Thirdly, the twice modulated image is coherent superposition with spatially angle multiplexed reference beam to generate an interference fringe which is recorded by CCD. Changing the original image and rotating the CCD simultaneously, the multiple holograms with different fringe directions can be obtained. Finally, multiple holograms are superimposed together to form a compound image. In this paper, four original images 𝛼 i and d(x, y) are chosen as characters “A”, “B”, “C” and “D” with 128 × 128 pixels respectively, which are shown in Fig. 2. In the first step as shown in Fig. 1, each original image is perpendicularly illuminated by plane wave and is modulated by the first random phase p1i where i is image sequence number, then is performed by Fresnel transform with distance zi and finally modulated by the second
Fig. 2. (a)–(d) Four images to be encrypted.
random phase p2i . The first random phase p1i can be expressed as [ ] 𝑝11 = exp 1.2jπ rand(𝑥, 𝑦) [ ] 𝑝12 = exp 1.2jπ rand(𝑥, 𝑦) [ ] 𝑝13 = exp 1.2jπ rand(𝑥, 𝑦) [ ] 𝑝14 = exp 1.2jπ rand(𝑥, 𝑦)
(1)
It is verified by theoretical simulation and experiments that the random phase p1i will disperse image information on the spectrum plane [7] where the filter is placed, so the image information will lose, resulting the quality of decrypted image declines. Thus, the value range of random phase p1i is chosen from 0 to 1.2𝜋. Based on this, rand(𝑥, 𝑦) in Eq. (1) denotes white sequences uniformly distributed in [0; 1]. The Fresnel diffraction distance zi are chosen as 𝑧1 = 0.1 m, 𝑧2 = 0.2 m, 𝑧3 = 0.3 m and 𝑧4 = 0.4 m corresponding to the four images respectively, since different diffraction distance keys can improve the security of image encryption. In order to simplify the experimental decrypted process, the second random phase keys are designed as the same and can be described as [ ] (2) 𝑝21 = 𝑝22 = 𝑝23 = 𝑝24 = 𝑝2 = exp 2jπ r and(𝑥, 𝑦) As described above, the twice modulated images can be expressed as [ ] 𝑎1 (𝑥, 𝑦) = FrT𝑍1 𝑎(𝑥, 𝑦)𝑝11 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦), [ ] 𝑏1 (𝑥, 𝑦) = FrT𝑍2 𝑏(𝑥, 𝑦)𝑝12 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦), [ ] 𝑐1 (𝑥, 𝑦) = FrT𝑍3 𝑐 (𝑥, 𝑦)𝑝13 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦), [ ] 𝑑1 (𝑥, 𝑦) = FrT𝑍4 𝑑 (𝑥, 𝑦)𝑝14 (𝑥, 𝑦) 𝑝2 (𝑥, 𝑦),
(3)
Where Frt[•] denotes the Fresnel transform with distance of Zi and 𝑖 = 1, 2, 3, 4. Then the modulated images interfere successively with reference beams based on spatially angular multiplexing. In our scheme,
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Optics and Lasers in Engineering 127 (2019) 105953
Fig. 3. (a)–(d) Four interference fringes obtained from four images with solid angle multiplexed reference beams.
multiple images are encrypted by spatial angle multiplexing of reference beams. The spatial angle can be controlled by two parameters 𝛼 i and 𝜃 i which is shown in inset of Fig. 1, where 𝛼 i is the included angle between reference beam and Z-axis while 𝜃 i is the rotation angle of CCD. The angle 𝛼 i determined the period of interference fringe and the angle 𝜃 determined the direction of interference fringe, therefore the multiple holograms are overlapped in a frame of CCD but their Fourier spectra are separated in the spectra domain. In this paper, 0.1 cm and 𝜃𝑖 = 0◦ , 𝜃2 = 45◦ , 𝜃3 = 90◦ , 𝜃4 = 135◦ are chosen, that is, four images are encrypted and the corresponding parameters are (2∘ , 0∘ ), (2∘ , 45∘ ), (2∘ , 90∘ ) and (2∘ , 135∘ ) which can be obtained by only rotating CCD to simplify experimental operation. It is noted that both 𝛼 i and 𝜃 i should be chosen properly when more images are encrypted. The four solid angle reference beams can be expressed as ( ) ( ) sin 𝛼 𝜃 = 0◦ ∶ 𝑅1 = A1 exp j2 πxf = exp j2π𝑥 , 𝜂 ( ) [ ] sin 𝛼 𝜃 = 45◦ ∶ 𝑅2 = A2 exp j2 π (𝑥 + 𝑦)𝑓 = exp j2π(𝑥 + 𝑦) , 𝜂 ( ) ( ) sin 𝛼 𝜃 = 90◦ ∶ 𝑅3 = A3 exp j2 π yf = exp j2π y , 𝜂 [ ] [ ] sin 𝛼 𝜃 = 135◦ ∶ 𝑅4 = A4 exp j2 π (−𝑥 + 𝑦)𝑓 = exp j2π(−𝑥 + 𝑦) , 𝜂
Fig. 4. (a) The final encrypted image; (b) the encoded CGH.
2. 3. Decrypted process (4)
Four solid angle reference beams interfere with four modulated images respectively to form four interference fringe images. These four interference fringes in different directions are shown in Fig. 3. After that, four interference fringe images are superimposed together to form a compound image. It is noted that the original bias component is replaced by uniform field to reduce bandwidth and sampling points, improve the quality of reconstructed image. Therefore, the compound image can be described as ( ) ( ) I(𝑥, 𝑦) = 1 + 𝑎1 (𝑥, 𝑦) exp −j2πxf + 𝑎1 (𝑥, 𝑦) exp j2πxf [ ] [ ] + 1 + 𝑏1 (𝑥, 𝑦) exp −j2π(𝑥 + 𝑦)𝑓 + 𝑏1 (𝑥, 𝑦) exp j2π(𝑥 + 𝑦)𝑓 ( ) ( ) + 1 + 𝑐1 (𝑥, 𝑦) exp −j2πyf + 𝑐1 (𝑥, 𝑦) exp j2πyf [ ] [ ] + 1 + 𝑑1 (𝑥, 𝑦) exp −j2π(−𝑥 + 𝑦)𝑓 + 𝑑1 (𝑥, 𝑦) exp j2π(−𝑥 + 𝑦)𝑓 (5)
The decryption experiment system is shown in Fig. 5, which contains 4f, Fresnel diffraction and spatial filtering system. A transmissive phase only SLM (Meadowlark Optics LC_SLM, 1920 × 1152 pixels, pixel pitch 9.2 × 9.2 𝜇m) and a MINTRON 1881EX Charge Coupled Device (CCD) with pixel size of 8.3 × 8.3 𝜇m and pixel number of 768(H) × 576(V) are used in our experiment. The focal length of all Fourier lenses are 0.3 m and the diameter of circular filter is 1 mm. As shown in Fig. 5, the encrypted CGH image is loaded on the upper part of SLM and illuminated perpendicularly by plane wave, then the light is reflected by a 4f system so the encrypted CGH is imaged on bottom part of the same SLM. Obviously, the SLM is divided into two parts to load the encrypted CGH (upper part) and the decrypted phase key p4 (x, y) (bottom part). The decrypted phase key p4 (x, y) is also encoded into CGH with 896 × 896 pixels. As described in Fig. 5, the encrypted CGH is modulated by p4 (x, y) and then performs Fresnel transform with distance of Zi after spatial filtering. When the correct filters and 𝑍𝑖 = 0.1 m, 0.2 m, 0.3, 0.4 m are applied, the decrypted images can be recorded by CCD. In the decrypted process, the decrypted phase key is described as 𝑝4 (𝑥, 𝑦) = 𝑝2 (𝑥, 𝑦)𝑝3 ∗ (𝑥, 𝑦)
(6)
𝑝4 ′ (𝑥, 𝑦) = 𝑝2 (𝑥, 𝑦)𝑝3 (𝑥, 𝑦),
(7)
∗
In the final CGH coding process, in order to improve the security of decryption in experiment, the intensity of compound image is modulated by another random phase 𝑝3 (𝑥, 𝑦) = exp[j2πrand(𝑥, 𝑦)]. The encrypted image I(x, y)p3 (x, y) is shown in Fig. 4(a) and is encoded into CGH as shown in Fig. 4(b) using Roman coding method, thus the encryption is completed and the binary real value CGH is the final encrypted image. Because that the encrypted image I(x, y)p3 (x, y) is 128 × 128 pixels and each pixel is expanded to an unit with 7 × 7 pixels in the process of Roman CGH encoding, therefore the final CGH have pixels number of 896 × 896, as shown in Fig. 4(b). It is clear that the encrypted image (Fig. 4(a)) and CGH (Fig. 4(b)) do not contain the original image information.
where denotes the conjugate operation. The decryption phase key p4 is encoded into CGH with 896 × 896 pixels to reduce the strict setup alignment requirements [21]. In the frequency spectrum plane shown in Fig. 6, the noise of the higher orders units in spectrum increase quickly, so the good reproduced images can only be obtained at −1 order. As shown in Fig. 6(a), when p4 are used, the complex amplitude of the −1 order beam after the SLM is −1 ∶ 𝑝4 (𝑥, 𝑦)I(𝑥, 𝑦)𝑝3 (𝑥, 𝑦) = 𝑝2 (𝑥, 𝑦)𝑝3 ∗ (𝑥, 𝑦)I(𝑥, 𝑦)𝑝3 , (𝑥, 𝑦) = I(𝑥, 𝑦)𝑝2 (𝑥, 𝑦) (8) Thus, when correct phase key, Fresnel transform distance and matched filter are used, by adjusting the location of CCD, the four
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Fig. 5. The schematic of decryption with Fresnel diffraction and spatial filtering based on SLM.
Fig. 6. The frequency spectrum of the CGH in decrypted process with correct keys p4 , F1~F4 are the four filters, (a) simulation result; (b) experimental result.
decrypted images can be orderly obtained as [ { }] 𝑎∗ (𝑥, 𝑦)𝑝11 ∗ (𝑥, 𝑦) = Fr T𝑧1 F1 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦) , [ { }] 𝑏∗ (𝑥, 𝑦)𝑝12 ∗ (𝑥, 𝑦) = Fr T𝑧2 F2 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦) , [ { }] 𝑐 ∗ (𝑥, 𝑦)𝑝13 ∗ (𝑥, 𝑦) = Fr T𝑧3 F3 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦) , [ { }] 𝑑 ∗ (𝑥, 𝑦)𝑝14 ∗ (𝑥, 𝑦) = Fr T𝑧4 F4 𝐼 (𝑥, 𝑦)𝑝2 (𝑥, 𝑦)
(9)
Where Fi {•} denotes the filtering process for different images, in which the aperture of self-made filters is 0.3 mm. As shown in Fig. 6(b), when p4 ′ is used, the complex amplitude of the +1 order beam after the SLM is ∑∑ (𝑜(𝑚, 𝑛) − 𝑜)(𝑜′ (𝑚, 𝑛) − 𝑜′ ) 𝑚 𝑛 CC = √( (10) )( ) ∑∑ ∑∑ ′ 2 ′ 2 (𝑜(𝑚, 𝑛) − 𝑜) (𝑜 (𝑚, 𝑛) − 𝑜 ) 𝑚 𝑛
𝑚 𝑛
Compared with Eq. (5), we can find that the I∗ (x, y) is the same as y), so the result in Eq. (10) is also the same as that in Eq. (8). Therefore, the same results can be obtained when either p4 or p4 ′ is used and the amplitude obtained in the CCD will be the conjugate of original images a∗ (x, y), b∗ (x, y), c∗ (x, y) and d∗ (x, y). In this case, the experimental I∗ (x,
results are shown in Fig. 7, in which (a)-(d) are a∗ (x, y), b∗ (x, y), c∗ (x, y) and d∗ (x, y) respectively, while (a’)-(d’) are the corresponding simulation results. In conclusion, when the correct keys including p4 (x, y); p4 ′(x, y), filters, Fresnel diffraction distance zi and wavelength 𝜆 are applied, the conjugate original images can be obtained. Meanwhile, the experimental results show good agreements with the numerical simulations which verify the validity of proposed experimental scheme. 4. Security analysis and discussion In this section, we analyzed the security of the proposed encryption scheme. In general, the encrypted image is transmitted through public communication channels, where there are some strong possibilities for information distortion. We introduced correlation coefficient (CC) to evaluate the similarity between the original image o(x, y) and the decrypted image o′(x, y), the definition of CC is ∑∑ (𝑜(𝑚, 𝑛) − 𝑜)(𝑜′ (𝑚, 𝑛) − 𝑜′ ) 𝑚 𝑛 CC = √( (11) )( ) ∑∑ ∑∑ ′ 2 (𝑜(𝑚, 𝑛) − 𝑜)2 (𝑜 (𝑚, 𝑛) − 𝑜′ ) 𝑚 𝑛
𝑚 𝑛
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Optics and Lasers in Engineering 127 (2019) 105953
Fig. 7. (a)–(d) The decrypted images “A”–“D” with all correct keys, and (a’)–(d’) are the corresponding simulation results.
Fig. 8. (a) The decrypted image “A” with wrong key wavelength(𝑛 = 532 nm) and all other correct keys; (b) The decrypted image with wrong phase key p4 and all other correct keys; (c) The decrypted image with all correct keys but wrong filter.
Where, 𝑜 and 𝑜′ denote the mean value of o(x, y) and o′(x, y) respectively. The proposed scheme’s keys include random phase mask, wavelength 𝜆 and Fresnel transform distance zi . Firstly, according to Eq. (11), the CC have been calculated between the original image and the decrypted result when all the keys are correct (shown in Fig. 7(a)−(d)), and the results are 0.907, 0.875, 0.893, 0.861 respectively, so the decryption is completed very well and the high-quality decryption images are obtained. Then we test the influence of keys p4 , 𝜆 and zi on the decrypted images. When the wavelength key 𝜆 is wrong (𝜆 = 532 nm is chosen for convenience) while other keys are all correct, the decryption result is shown in Fig. 8(a) (here, the case of letter A is chosen as example for demonstration). Fig. 8(b) shows the decryption result with wrong phase keys p4 (x, y) and other correct keys. Fig. 8(c) is the result with wrong filter and other correct keys. As shown in Fig. 8(a), the result of decryption is something like “A” when the key wavelength is wrong(𝜆 = 532nm), in which the CC between the original image and the decrypted result 0.108. It is obvious that the image can not be decrypted at all when p4 is wrong in which the corresponding CC is 0.037, so this decrypted result shown in Fig. 8(b) is irrelevant with the original image. Meanwhile, the CC is 0.116 for the decrypted result shown in Fig. 8(c) with wrong filter. The other important key zi in our scheme is discussed more detailed as bellow. Taking image a(x, y) as an example, the CC dependence on z1 is shown in Fig. 9. As shown in Fig. 9, the exact values zi does CC value very close to 1 and good decrypted result can be obtained. Although the value range of random phase is compressed from 0 to 1.2𝜋 to improve the quality of decrypted image, which reduced the sensitivity of diffraction distance, the CC value still decreases exponentially with deviations of zi and will be less than 0.2 when the error of zi greater than 0.1 cm, at this time,
Fig. 9. The CCdependence on Zi of image 𝛼(x, y, ) .
there is a failure to distinguish the decrypted image as shown in the insets. So the CC around the accurate values of zi is highly sensitive and the distance sensitivity is around 0.1 cm, which shows great difficulty in copying the encryption system. In this paper, four images are encrypted and decrypted to verify the proposed scheme. The most important factors that affect encryption capacity of this scheme are the CGH coding parameters and the phase random range of key pi . According to our theoretical simulation and experiment, the image to be encrypted is 128 × 128 pixels and the single encoding unit in CGH includes 7 × 7 pixels, the phase random range of key pi is [0 − 1.2π] and the focal length of Fourier lenses is 0.3m. under that condition the spectrum size of each encrypted image is about 16 × 16 pixels. Fig. 6 is 896 × 896 pixels and shows 7 × 7 spectrum display units with 128 × 128 pixels, so at most 32 images’ spectra can exist in Fig. 6 at the same time without overlapping when proper spatial angle and quantity of reference beams are applied. At this time, the CC values of the decrypted images can be higher than 0.9, indicating the encryption capacity of this scheme ensures 32 images to be encrypted and decrypted with satisfied quality. But the CC values will decrease when the phase random range of key pi increases, and also will be influenced by the optical modulation performance of the SLM applied in experiment.
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5. Conclusions In summary, an optical multiple-image encryption scheme based on spatially angular multiplexing and CGH is proposed. In this scheme, spatial angle multiplexing technology of digital holography and CGH are used. Spatial angle of reference beams are precisely controlled by two parameters 𝛼 i and 𝜃 i , ensuring that the spectrum plane space is fully utilized to improve the image encryption capacity. Besides double random phase, the Fresnel diffraction distance, wavelength, CGH parameters also can be used as image encryption keys to improve the security of the optical image encryption scheme. The multiple gray-scale images are encrypted into a binary real value CGH which has strong anti-noise ability and is convenient to be saved and transferred. The decryption phase keys are encoded into CGH to reduce difficulty in ensuring the accurate alignment of decryption random phase key in traditional methods, so the feasibility of optical implementation is increased which is proved by our experimental results. The simulation and experimental results verify the effectiveness of the scheme. By comparing with the original images visually and digitally, it is concluded that good multiple decrypted images can be obtained without obvious distortion, noise or crosstalk phenomenon. Due to the high storage efficiency and security, we believe this scheme has important potential application in multipleimage encryption. Acknowledgments National Science Foundation of China (NSFC) (11904073, 61875093) Natural Science Foundation of Hebei Province (F2019402351, F2018402285) and the Natural Science Foundation of Tianjin (19JCYBJC16500). References [1] Refregier P, Javidi B. Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 1995;20(7):767–9. [2] Li X, Meng X, Yang X, Wang Y, Yin Y, Peng X, He W, Dong G, Chen H. Multiple-image encryption via lifting wavelet transform and XOR operation based on compressive ghost imaging scheme. Opt Lasers Eng 2018;102:106–11. [3] Toto-Arellano N, Rodriguez-Zurita G, Meneses-Fabian C, Vazquez-Castillo J. Phase shifts in the Fourier spectra of phase gratings and phase grids: an application for one-shot phase-shifting interferometry. Opt Express 2008;16(23):19330–41.
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