Optical image authentication method based on cascade geometric phase metasurface
By adopting cascading geometric phase metasurface technology in the metasurface optical image authentication system, the problems of low authentication efficiency and lack of security keys in the existing system are solved, and optical image authentication with large key space and high security are achieved, ensuring high confidentiality of plain text information.
Patent Information
- Application Number
- CN202510065403.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-01-15
- Publication Date
- 2025-04-22
AI Technical Summary
The existing metasurface optical image authentication system has problems such as low authentication efficiency, lack of security keys, and low security, making it difficult to achieve authentication with large key space and high security.
The optical image authentication method based on the cascaded geometric phase metasurface is adopted, and the plain text image is encoded into Fourier phase holograms with authenticated amplitude through sparse constraint encoding algorithm and iterative Fourier transform algorithm, and the cipher text image and key phase are decomposed into cipher text phase and key phase. The cipher text metasurface and key phase are constructed through the geometric phase metasurface element structure to realize optical image authentication of the cascaded metasurface.
It effectively overcomes the problem of lack of security keys, improves the security of identity authentication, and realizes supersurface optical image authentication with large key space and high security. The authentication steps are simple and easy to implement, and the clear text information is confidential.
Smart Images
Figure CN119865321A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of information security technology, and in particular to an optical image authentication method based on cascaded geometric phase metasurface. Background Art
[0002] Optical information security technology has attracted widespread attention in the field of information security since it was proposed because of its significant advantages such as multi-dimensionality, large capacity, high parallelism, and high security. However, traditional optical information security systems often inevitably use bulky and complex optical devices such as lenses and spatial light modulators, making it difficult to achieve miniaturization and portability. In recent years, the rise of metasurface technology has provided the possibility of flexible, efficient, and lightweight optical information security systems, and a variety of novel metasurface optical information security systems have emerged. At present, most metasurface optical information security systems are metasurface optical image encryption systems. The basic principle is to hide the encrypted image information in the complex amplitude of the metasurface structure, and then use the specific wavelength, polarization, incident angle, observation angle, diffraction distance, orbital angular momentum and other physical dimensions of the incident light or detection light to realize the encryption and decryption of optical image information. However, the main purpose of the metasurface optical image encryption system is to protect the confidentiality of the plaintext image information and prevent the effective information from being read by attackers. However, with the correct decryption, the plaintext image information will also be clearly reconstructed, resulting in the risk of leakage of the plaintext image information. In order to avoid information leakage, some researchers have proposed a metasurface optical image authentication system in recent years. The system can distinguish the identity of the user, determine whether the user is authorized, and protect the integrity and authenticity of the valid information, and avoid the leakage of plaintext information. Therefore, it has great application potential and research value. The most representative metasurface optical image authentication system at present is an all-medium metasurface proposed by Wang et al., which can realize information authentication under visible light illumination without any information leakage, and has outstanding advantages such as high authentication accuracy, good information confidentiality and concealment. However, this scheme also has problems such as low authentication efficiency, lack of security keys, and low security. In 2024, Xue et al. optimized and improved the problem of low authentication efficiency of this scheme, and proposed a metasurface optical multi-image authentication method. The simultaneous authentication of multiple identities of users was successfully realized using an all-medium metasurface, showing the advantages of large encoding information capacity and high authentication efficiency, but the typical problems of lack of security keys and low security have not been solved. In view of this situation, the present invention proposes an optical image authentication method based on a cascaded geometric phase metasurface, aiming to realize a metasurface optical image authentication with a large key space and high security. Summary of the invention
[0003] The purpose of the present invention is to provide an optical image authentication method based on cascaded geometric phase metasurfaces. During encryption, the present invention first encodes the plaintext image into an authentication amplitude based on a sparse constrained coding algorithm, then uses an iterative Fourier transform algorithm to calculate the Fourier phase hologram of the authentication amplitude, and then decomposes it into a ciphertext phase and a key phase. Finally, the ciphertext phase and the key phase are constructed into a ciphertext metasurface and a key metasurface respectively through a geometric phase metasurface unit structure. In addition, during authentication, the cascaded ciphertext metasurface and the key metasurface are required to realize the authentication of the user's identity, which has the advantages of large key space, high security, and good confidentiality.
[0004] To achieve the above-mentioned invention object, the technical solution provided by the present invention is as follows: an optical image authentication method based on cascaded geometric phase metasurface, characterized in that it includes an encryption step:
[0005] S1: Authentication amplitude generation based on sparse constrained coding: First, the original plaintext image P(x, y) is subjected to double random phase encoding in the Fresnel domain to obtain the amplitude A(ξ, η) on the output surface. Then, the amplitude Q(x, y) on the input surface is subjected to double random phase encoding in the Fresnel domain to obtain the phase The initial value of Q(x,y) is a matrix with the same number of pixels as the original plaintext image and all element values are 1, and Q(x,y) is continuously updated in subsequent iterations. Synthesize a new complex amplitude Then, double random phase decoding is performed in the Fresnel domain to obtain the decoded amplitude on the input surface. Then, the decoded amplitude is calculated The correlation coefficient CC between the original plaintext image P(x,y). When the calculated CC does not exceed the preset threshold σ, the decoded amplitude on the input surface is used Update the amplitude Q(x, y) on the input plane, and then perform the encryption step S1 again; when the calculated CC exceeds the preset threshold σ, the output is used to generate the decoding amplitude The amplitude A(ξ,η) and phase on the output surface of Afterwards, the sparse matrix S(ξ,η) is used to transform the output amplitude A(ξ,η) and phase Perform sparse constraints respectively and obtain the sparse amplitude A Ω (ξ,η) and sparse phase Then, the sparse amplitude A Ω (ξ,η) and sparse phase Synthesize a new complex amplitude Then, double random phase decoding is performed in the Fresnel domain to obtain the authentication amplitude A on the input surface. Δ(x, y). Afterwards, the encryption step S2 is performed.
[0006] S2: Phase calculation based on iterative Fourier transform algorithm: Encrypt the authentication amplitude A obtained in step S1 Δ (x, y) is used as the target amplitude, and then the Fourier phase hologram of the target amplitude is optimized and calculated using the iterative Fourier transform algorithm, and the phase distribution of this Fourier phase hologram is output as the authentication phase Afterwards, the encryption step S3 is performed.
[0007] S3: Phase decomposition: arbitrarily generate a phase with the authentication phase The phase with the same number of elements and whose element values are distributed in the interval [0,2π] is denoted as the ciphertext phase After that, the authentication phase and ciphertext phase Perform phase subtraction operation, and the obtained phase is recorded as the key phase Afterwards, the encryption step S4 is performed.
[0008] S4: Design of geometric phase metasurface unit structure: Design the material selection of the geometric phase metasurface unit structure, construct the nanocolumn model of the geometric phase metasurface unit structure, use electromagnetic simulation software to perform parameter scanning on the nanocolumn structure, obtain the nanocolumn structure whose phase modulation can cover the phase interval [0,2π], and output the relationship curves between the nanocolumn rotation angle and transmittance and the nanocolumn rotation angle and phase modulation respectively, which are the amplitude modulation curve and phase modulation curve of the geometric phase metasurface unit structure. After that, perform encryption step S5.
[0009] S5: Construction of ciphertext metasurface and key metasurface: Based on the geometric phase metasurface unit structure designed in encryption step S4, the authentication phase in encryption step S3 is converted into Decomposed ciphertext phase and key phase They are constructed as ciphertext hypersurface C-MH and key hypersurface K-MH respectively.
[0010] At this point, the encryption step is completed.
[0011] Authentication steps:
[0012] J1: Cascading and diffraction of metasurfaces: The ciphertext metasurface C-MH and the authentication key metasurface AK-MH are placed in cascade to form a set of cascaded metasurfaces. After that, the cascaded metasurface is illuminated by a collimated plane light wave, and the light wave after phase modulation of the cascaded metasurface begins to diffract and propagate forward, and then the amplitude distribution of the far-field diffraction of the cascaded metasurface can be obtained, which is recorded as the diffraction image D(x,y) of the cascaded metasurface. After that, the authentication step J2 is performed.
[0013] J2: Nonlinear correlation authentication of diffraction image: The diffraction image D(x,y) of the cascaded metasurface is authenticated using a nonlinear correlation algorithm, that is, the diffraction image D(x,y) and the original plaintext image P(x,y) are compared and authenticated to obtain the corresponding nonlinear correlation distribution NCD(x,y). Subsequently, the central peak value and the highest peak value other than the central peak in the nonlinear correlation distribution NCD(x,y) are defined as signal and noise, respectively, and the signal-to-noise ratio SNR of the nonlinear correlation distribution NCD(x,y) is calculated. When the calculated SNR exceeds the preset threshold δ, it means that the optical image authentication is successful; when the calculated SNR does not exceed the preset threshold δ, it means that the optical image authentication fails.
[0014] At this point, the authentication process is completed.
[0015] In the above-mentioned optical image authentication method based on cascaded geometric phase metasurface, in the encryption step S1, the wavelength and diffraction distance used for the double random phase encoding and double random phase decoding in the Fresnel domain are the same, and the random phase used for the double random phase decoding in the Fresnel domain is the conjugate phase of the random phase used for the double random phase encoding in the Fresnel domain.
[0016] The above-mentioned optical image authentication method based on cascaded geometric phase metasurface, the authentication step J1 can be completed either digitally or optically, wherein the optical method requires the use of the diffraction imaging device provided by the present invention, specifically a diffraction imaging device based on a cascaded metasurface, comprising a laser light source 1 for providing incident light, a half-wave plate 2 and a quarter-wave plate 3 for modulating the polarization state of the incident light, a convex lens 4 for converging the incident light wave, a pinhole 5 for filtering the converging spherical light wave formed by the convex lens 4, a microscope objective 6 for modulating the divergent spherical light wave after passing through the pinhole 5 into a plane light wave, a cascaded ciphertext metasurface 7 and an authentication key metasurface 8, and a cascaded ciphertext metasurface 7 and an authentication key metasurface 8 for modulating the polarization state of the incident light. A quarter wave plate 9 and a linear polarizer 10 for measuring the polarization state of the diffracted light after the diffraction, a Fourier transform lens 11 for forming Fraunhofer far-field diffraction, and an image sensor device 12 for receiving the diffraction image are characterized in that: the pinhole 5 is placed at the image focus of the convex lens 4, and the image focus of the convex lens 4 coincides with the focus of the microscope objective 6; the ciphertext metasurface 7 and the authentication key metasurface 8 are cascaded and placed closely, and each metasurface unit structure on the ciphertext metasurface 7 and the corresponding metasurface unit structure on the authentication key metasurface 8 are aligned one by one; the distance from the Fourier transform lens 11 to the image sensor device 12 is equal to the focal length of the Fourier transform lens 11; the image sensor device 12 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS).
[0017] The beneficial effects of the present invention are: (1) the ciphertext metasurface and the key metasurface in the present invention are physically completely separated. During authentication, only the user with the key metasurface can cooperate with the ciphertext metasurface to form a correct cascade metasurface to successfully pass the authentication, thereby effectively overcoming the problem of lack of security keys that is prevalent in existing optical image authentication methods based on metasurfaces and improving the security level; (2) the key metasurface as a security key in the present invention records the original plaintext information in the form of phase, which is essentially a phase matrix key with many encoding possibilities and a large key space; (3) since the ciphertext phase in the present invention is arbitrarily generated, the ciphertext metasurface constructed by the ciphertext phase has nothing to do with the plaintext information, thereby further increasing the concealment of the plaintext information; (4) the authentication steps in the present invention are simple and easy, and no information of the original plaintext image will be leaked during the authentication process, thereby ensuring the high confidentiality of the plaintext information. BRIEF DESCRIPTION OF THE DRAWINGS
[0018] Figure 1 Flowchart of encryption steps in an optical image authentication method based on cascaded geometric phase metasurfaces.
[0019] Figure 2 A flowchart is shown to assist in describing the encryption steps, where FD_DRPE, FD_DRPD, AE, PE, AU, and CAS represent dual random phase encoding in the Fresnel domain, dual random phase decoding in the Fresnel domain, amplitude extraction, phase extraction, amplitude update, and complex amplitude synthesis operations, respectively; IFTA represents iterative Fourier transform algorithm; and MU represents the metasurface unit structure.
[0020] Figure 3 Flowchart of authentication steps in an optical image authentication method based on cascaded geometric phase metasurfaces.
[0021] Figure 4 A flowchart to assist in describing the authentication steps, wherein FT and AE represent Fourier transform and amplitude extraction operations, respectively, NCC represents a nonlinear correlation algorithm, and SNR represents a signal-to-noise ratio.
[0022] Figure 5 A diagram of a diffraction imaging device for authentication step J1, wherein 1 represents a laser light source; 2 represents a half-wave plate; 3 represents a quarter-wave plate; 4 represents a convex lens; 5 represents a pinhole; 6 represents a microscope objective lens; 7 represents a ciphertext metasurface; 8 represents an authentication key metasurface; 9 represents a quarter-wave plate; 10 represents a linear polarizer; 11 represents a Fourier transform lens; and 12 represents an image sensor device.
[0023] Figure 6(a) is the original plaintext image (“Surveillance”); (b)-(d) are the conjugate phases of random phase R1(x,y), random phase R2(u,v) and R2(u,v) respectively. (e) is the sparse matrix S(ξ,η) with a sparsity of 10%; (f)-(h) are the sparse amplitudes A Ω (ξ,η), sparse phase and certified amplitude A Δ (x,y); (i) authentication phase (j) Ciphertext phase (k) Key Phase
[0024] Figure 7 (a) is the unit structure model of the geometric phase metasurface; (b) is the amplitude modulation curve and phase modulation curve of the unit structure of the geometric phase metasurface; (c) is the ciphertext metasurface C-MH; (d) is the key metasurface K-MH.
[0025] Figure 8 (a) When the key metasurface K-MH is used as the authentication key metasurface AK-MH and forms a set of cascaded metasurfaces with the ciphertext metasurface C-MH, the diffraction image D1(x,y) of the cascaded metasurface; (b) The nonlinear correlation distribution NCD1(x,y) obtained by comparing and authenticating the diffraction image D1(x,y) and the original plaintext image P(x,y); (c) When only the ciphertext metasurface C-MH is used to perform the authentication step, the diffraction image D2(x,y) of the ciphertext metasurface C-MH; (d) The nonlinear correlation distribution NCD2(x,y) obtained by comparing and authenticating the diffraction image D2(x,y) and the original plaintext image P(x,y); (e) An arbitrarily generated one different from the key phase test phase; (f) test metasurface T-MH; (g) when the test metasurface T-MH is used as the authentication key metasurface AK-MH and forms a set of cascaded metasurfaces with the ciphertext metasurface C-MH, the diffraction image D3(x,y) of the cascaded metasurface; (h) the nonlinear correlation distribution NCD3(x,y) obtained after comparing and authenticating the diffraction image D3(x,y) and the original plaintext image P(x,y). DETAILED DESCRIPTION
[0026] The present invention is further described below in conjunction with the embodiments and drawings, but they are not intended to limit the present invention.
[0027] Embodiment: An optical image authentication method based on cascaded geometric phase metasurface, comprising: Figure 1 The encryption steps shown in FIG. Figure 2 Flowchart shown):
[0028] S1: Authentication amplitude generation based on sparse constrained coding: First, the original plaintext image P(x, y) is subjected to double random phase encoding in the Fresnel domain to obtain the amplitude A(ξ, η) on the output surface, namely:
[0029]
[0030] Where FD_DRPE(·) represents the double random phase encoding operation in the Fresnel domain, Indicates that the wavelength is λ and the diffraction distance is z i The Fresnel diffraction operation is performed, |·| represents the amplitude extraction operation, j is an imaginary unit, R1(x,y) and R2(u,v) are two statistically independent random phase matrices, and their element values are randomly distributed in the interval [0,2π]. Subsequently, the amplitude Q(x,y) on the input surface is double-randomly phase-encoded in the Fresnel domain to obtain the phase on the output surface. Right now:
[0031]
[0032] Among them, arg() represents the phase extraction operation, the initial value of Q(x,y) is a matrix with the same number of pixels as the original plaintext image and all element values are 1, and Q(x,y) is continuously updated in the subsequent iteration process. In addition, the wavelength, two diffraction distances, and two statistically independent random phases used by FD_DRPE(·) in formula (2) are the same as those in formula (1). After that, the amplitude A(ξ,η) and phase Synthesize a new complex amplitude Then, double random phase decoding is performed in the Fresnel domain to obtain the decoded amplitude on the input surface. Right now:
[0033]
[0034] Where FD_DRPD(·) represents the double random phase decoding operation in the Fresnel domain, Indicates that the wavelength is λ and the diffraction distance is z i The inverse Fresnel diffraction operation of is the conjugate phase of the random phase R2(u,v). Then, the decoded amplitude is calculated The correlation coefficient CC between the original plaintext image P(x,y). When the calculated CC does not exceed the preset threshold σ, the decoded amplitude on the input surface is used Update the amplitude Q(x,y) on the input plane, and then execute formula (2) and formula (3) again; when the calculated CC exceeds the preset threshold σ, the output is used to generate the decoding amplitude The amplitude A(ξ,η) and phase on the output surface of Afterwards, the sparse matrix S(ξ,η) is used to transform the output amplitude A(ξ,η) and phase Perform sparse constraints respectively and obtain the sparse amplitude A Ω (ξ,η) and sparse phase They are:
[0035]
[0036] Among them, S(ξ,η) is a binary sparse matrix whose element value can only be 0 or 1, and the ratio of the number of elements with element value 1 to the total number of elements in the matrix is defined as the sparsity. Ω (ξ,η) and sparse phase Synthesize a new complex amplitude Then, double random phase decoding is performed in the Fresnel domain to obtain the authentication amplitude A on the input surface. Δ (x,y), that is:
[0037]
[0038] The wavelength, two diffraction distances, and conjugate phase of the random phase used by FD_DRPD(·) in formula (5) are the same as those in formula (3). Then, the encryption step S2 is performed.
[0039] S2: Phase calculation based on iterative Fourier transform algorithm: Encrypt the authentication amplitude A obtained in step S1 Δ (x, y) is used as the target amplitude, and then the Fourier phase hologram of the target amplitude is optimized and calculated using the iterative Fourier transform algorithm, and the phase distribution of this Fourier phase hologram is output as the authentication phase Afterwards, the encryption step S3 is performed.
[0040] S3: Phase decomposition: arbitrarily generate a phase with the authentication phase The phase with the same number of elements and whose element values are distributed in the interval [0,2π] is denoted as the ciphertext phase After that, the authentication phase and ciphertext phase Perform phase subtraction operation, and the obtained phase is recorded as the key phase Right now:
[0041]
[0042] Afterwards, the encryption step S4 is performed.
[0043] S4: Design of geometric phase metasurface unit structure: Design the material selection of the geometric phase metasurface unit structure, construct the nanocolumn model of the geometric phase metasurface unit structure, use electromagnetic simulation software to perform parameter scanning on the nanocolumn structure, obtain the nanocolumn structure whose phase modulation can cover the phase interval [0,2π], and output the relationship curves between the nanocolumn rotation angle and transmittance and the nanocolumn rotation angle and phase modulation respectively, which are the amplitude modulation curve and phase modulation curve of the geometric phase metasurface unit structure. After that, perform encryption step S5.
[0044] S5: Construction of ciphertext metasurface and key metasurface: Based on the geometric phase metasurface unit structure designed in encryption step S4, the authentication phase in encryption step S3 is converted into Decomposed ciphertext phase and key phase They are constructed as ciphertext hypersurface C-MH and key hypersurface K-MH respectively.
[0045] At this point, the encryption step is completed.
[0046] like Figure 3 The authentication steps shown in the figure (to assist in describing the authentication steps, the following are attached Figure 4 Flowchart shown):
[0047] J1: Cascade and diffraction of metasurfaces: The ciphertext metasurface C-MH and the authentication key metasurface AK-MH are placed in cascade to form a set of cascaded metasurfaces. After that, the cascaded metasurface is illuminated by a collimated plane light wave, and the light wave after phase modulation of the cascaded metasurface begins to diffract and propagate forward, and then the amplitude distribution of the far-field diffraction of the cascaded metasurface can be obtained, which is recorded as the diffraction image D(x,y) of the cascaded metasurface.
[0048] J2: Nonlinear correlation authentication of diffraction image: The diffraction image D(x, y) of the cascaded metasurface is authenticated using a nonlinear correlation algorithm, that is, the diffraction image D(x, y) and the original plaintext image P(x, y) are compared and authenticated to obtain the corresponding nonlinear correlation distribution NCD(x, y), that is:
[0049] NCD(x,y)=|IFT{FT[D(x,y)]·{FT[P(x,y)]} * |FT[D(x,y)]·{FT[P(x,y)]} * | ω-1}| 2 (7)
[0050] Where ω represents the nonlinear intensity coefficient. Subsequently, the central peak value and the highest peak value other than the central peak in the nonlinear correlation distribution NCD(x,y) are defined as the signal and the noise, respectively, and the signal-to-noise ratio SNR of the nonlinear correlation distribution NCD(x,y) is calculated. When the calculated SNR exceeds the preset threshold δ, it means that the optical image authentication is successful; when the calculated SNR does not exceed the preset threshold δ, it means that the optical image authentication fails.
[0051] At this point, the authentication steps are completed, wherein the authentication step J1 can be completed in a digital manner or in an optical manner. The optical method that can be used in the authentication step J1 is specifically described below. The above optical method requires the use of the diffraction imaging device provided by the present invention, specifically a diffraction imaging device based on a cascaded metasurface, such as Figure 5 As shown, it includes a laser light source 1 for providing incident light, a half-wave plate 2 and a quarter-wave plate 3 for modulating the polarization state of the incident light, a convex lens 4 for converging the incident light wave, a pinhole 5 for filtering the converging spherical light wave formed by the convex lens 4, a microscope objective 6 for modulating the divergent spherical light wave after passing through the pinhole 5 into a plane light wave, a cascaded ciphertext metasurface 7 and an authentication key metasurface 8, a quarter-wave plate 9 and a linear polarizer 10 for modulating the polarization state of the diffracted light after passing through the ciphertext metasurface 7 and the authentication key metasurface 8, a Fourier transform lens 11 for forming Fraunhofer far-field diffraction, and a laser beam 20 for transmitting the ciphertext metasurface 7 to the authentication key metasurface 8. The image sensor device 12 for receiving the diffraction image is characterized in that: the pinhole 5 is placed at the image focus of the convex lens 4, and the image focus of the convex lens 4 coincides with the focus of the microscope objective 6; the ciphertext metasurface 7 and the authentication key metasurface 8 are cascaded and placed closely, and each metasurface unit structure on the ciphertext metasurface 7 and the corresponding metasurface unit structure on the authentication key metasurface 8 are aligned one by one; the distance from the Fourier transform lens 11 to the image sensor device 12 is equal to the focal length of the Fourier transform lens 11; the image sensor device 12 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS).
[0052] The specific diffraction imaging process is as follows: the linearly polarized light emitted from the laser light source 1 is sequentially irradiated onto the half-wave plate 2 and the quarter-wave plate 3, thereby generating right-handed circularly polarized light. Subsequently, the right-handed circularly polarized light passes through a beam reduction and collimation system composed of a convex lens 4, a pinhole 5, and a microscope objective 6, thereby achieving beam reduction, filtering, and collimation. After that, the right-handed circularly polarized light after beam reduction and collimation is irradiated onto the cascaded ciphertext metasurface 7 and the authentication key metasurface 8, thereby forming diffracted light modulated by the cascaded metasurface. Subsequently, the diffracted light modulated by the cascaded metasurface passes through the quarter-wave plate 9 and the linear polarizer 10 in turn to complete polarization modulation and polarization analysis, and then irradiates onto the Fourier transform lens 11, and then passes through the Fourier transform lens 11 to reach the image sensor device 12, thereby completing the optical cascade and diffraction of the ciphertext metasurface 7 and the authentication key metasurface 8. Since the image sensor device 12 is located on the back focal plane of the Fourier transform lens 11, the image recorded on the image sensor device 12 is the amplitude distribution of the far-field diffraction of the cascaded metasurface, that is, the diffraction image of the cascaded metasurface.
[0053] The content of the present invention is further explained below in conjunction with specific embodiments and drawings.
[0054] First, a grayscale image (“Surveillance”) is selected as the original plaintext image, such as Figure 6 (a). Subsequently, two random phases are generated and used as R1(x, y) and R2(u, v) in the encryption step, respectively. Figure 6 (b) and 6(c), in addition, the conjugate phase of R2(u,v) like Figure 6 (d) is shown. After that, the wavelength λ of the light used in the encryption step is set to 632.8nm, the diffraction distances z1 and z2 are 30mm and 50mm respectively, and the preset threshold σ of CC is 0.94. In addition, a sparse matrix S(ξ,η) with a sparsity of 10% is generated, as shown in Figure 6 (e) The sparse amplitude A generated after the encryption step S1 Ω (ξ,η), sparse phase and certified amplitude A Δ (x,y) are respectively Figure 6 In addition, in the iterative Fourier transform algorithm of the encryption step S2, the correlation coefficient between the authentication amplitude and the reconstructed amplitude of the Fourier phase type hologram is set as the evaluation function, and the iterative overflow threshold is set to 0.99. like Figure 6 (i) is shown. Afterwards, a phase with the authentication phase is generated Ciphertext phases with the same number of elements like Figure 6(j) As shown in the figure. The key phase generated after the operation in the encryption step S3 is like Figure 6 (k) as shown.
[0055] Afterwards, the unit structure model of the geometric phase metasurface is designed as follows Figure 7 As shown in (a), the substrate is set to silicon dioxide (SiO2), the optical antenna is set to a rectangular silicon (Si) nanocolumn, and the geometric phase is introduced by changing the rotation angle θ of the rectangular silicon nanocolumn. In addition, the period C, nanocolumn length L, nanocolumn width W, and nanocolumn height H of the geometric phase metasurface unit structure are set to 464nm, 200nm, 100nm, and 120nm, respectively. The electromagnetic simulation software is used to perform parameter scanning on the rotation angle θ, so as to obtain the relationship curves between the nanocolumn rotation angle and the transmittance and the nanocolumn rotation angle and the phase modulation amount, that is, the amplitude modulation curve and phase modulation curve of the geometric phase metasurface unit structure, as shown in FIG. Figure 7 As shown in (b), it can be seen that the geometric phase metasurface unit structure has a complete 0-2π phase modulation capability and its transmittance is always maintained at about 60%. Figure 7 The phase modulation curve shown in (b) will be Figure 6 (j) The ciphertext phase shown He Ru Figure 6 (k) shows the key phase They are constructed into ciphertext hypersurface C-MH and key hypersurface K-MH, respectively. Figure 7 (c) and 7(d). At this point, the encryption step is completed.
[0056] Then, using Figure 7 (c) The ciphertext hypersurface C-MH shown in Figure 1 starts the authentication step. First, the key hypersurface K-MH generated in the encryption step is used as the authentication key hypersurface AK-MH, and is placed in cascade with the ciphertext hypersurface C-MH to form a set of cascaded hypersurfaces. After the operation of the authentication step J1, the diffraction image D1(x, y) of the cascaded hypersurface is generated, as shown in Figure 8 (a). Then, a nonlinear correlation algorithm is used to Figure 8 The diffraction image D1(x,y) shown in (a) is authenticated, that is, the diffraction image D1(x,y) and the original plaintext image P(x,y) are compared and authenticated, and the nonlinear correlation distribution NCD1(x,y) is obtained as follows Figure 8(b) is shown. Subsequently, the signal-to-noise ratio SNR1 of the nonlinear correlation distribution NCD1(x, y) is calculated to be 5.04, which exceeds the preset threshold δ=3, indicating that the optical image authentication is successful, thereby verifying the correct identity of the user who owns the key metasurface K-MH. Afterwards, in order to examine the effectiveness of the key metasurface K-MH in the present invention, only the ciphertext metasurface C-MH is used to perform the authentication step. First, the diffraction image D2(x, y) of the ciphertext metasurface C-MH is generated, as shown in Figure 8 (c). Then, a nonlinear correlation algorithm is used to Figure 8 The diffraction image D2(x,y) shown in (c) is authenticated, that is, the diffraction image D2(x,y) and the original plaintext image P(x,y) are compared and authenticated, and the nonlinear correlation distribution NCD2(x,y) is obtained as follows Figure 8 (d) is shown. After that, the signal-to-noise ratio SNR2 of the nonlinear correlation distribution NCD2(x,y) is calculated to be 1.05, which does not exceed the preset threshold δ=3, indicating that the optical image authentication fails. Figure 8 (b) as shown and as Figure 8 The authentication result shown in (d) shows that when the key metasurface K-MH is used as the authentication key metasurface AK-MH and forms a cascade metasurface with the ciphertext metasurface C-MH, the diffraction image can be successfully authenticated with the original plaintext image, but when only the ciphertext metasurface C-MH is used, the diffraction image cannot be successfully authenticated with the original plaintext image, thus proving the effectiveness of the key metasurface K-MH in the present invention. Subsequently, in order to test the security of the key metasurface K-MH in the present invention, an arbitrary phase difference different from the key phase is generated. The test phase is as follows Figure 8 (e), then according to Figure 7 The phase modulation curve shown in (b) will be Figure 8 The test phase shown in (e) is constructed as a test metasurface T-MH, as shown in Figure 8 (f) As shown. Subsequently, the test metasurface T-MH is used as the authentication key metasurface AK-MH, and is placed in cascade with the ciphertext metasurface C-MH to form another set of cascaded metasurfaces. After the operation of the authentication step J1, the diffraction image D3(x, y) of the cascaded metasurface is generated, as shown in Figure 8 (g) is shown. Then, the nonlinear correlation algorithm is used to Figure 8 The diffraction image D3(x,y) shown in (g) is authenticated, that is, the diffraction image D3(x,y) and the original plaintext image P(x,y) are compared and authenticated, and the nonlinear correlation distribution NCD3(x,y) is obtained as follows Figure 8 (h) is shown. Then, the signal-to-noise ratio SNR3 of the nonlinear correlation distribution NCD3(x,y) is calculated to be 1.32, which does not exceed the preset threshold δ=3, indicating that the optical image authentication fails. Figure 8 (b) as shown and as Figure 8 It can be seen from the authentication result shown in (h) that when the key metasurface K-MH is used as the authentication key metasurface AK-MH and forms a cascade metasurface with the ciphertext metasurface C-MH, the diffraction image can be successfully authenticated with the original plaintext image, but when the test metasurface T-MH different from the key metasurface K-MH is used as the authentication key metasurface AK-MH and forms a cascade metasurface with the ciphertext metasurface C-MH, the diffraction image cannot be successfully authenticated with the original plaintext image, thereby proving the security of the key metasurface K-MH in the present invention.
[0057] In summary, the present invention discloses an optical image authentication method based on cascaded geometric phase metasurfaces. In the present invention, the encryption process first uses a sparse constrained coding algorithm and an iterative Fourier transform algorithm to encode the plaintext image into a Fourier phase-type hologram of the authentication amplitude, and then decomposes it into a ciphertext phase and a key phase, and finally constructs a physically separated ciphertext metasurface and a key metasurface through a geometric phase metasurface unit structure. The authentication process first requires the cascaded ciphertext metasurface and the key metasurface, and then the diffraction image of the cascaded metasurface is used to perform nonlinear correlation authentication with the plaintext image to achieve user identity authentication, which overcomes the problem of lack of security keys that is common in existing optical image authentication methods based on metasurfaces and improves the security of identity authentication.
Claims
1. An optical image authentication method based on cascaded geometric phase metasurface, characterized in that: The encryption steps include: S1: Authentication amplitude generation based on sparse constrained coding: First, the original plaintext image P(x, y) is subjected to double random phase encoding in the Fresnel domain to obtain the amplitude A(ξ, η) on the output surface. Then, the amplitude Q(x, y) on the input surface is subjected to double random phase encoding in the Fresnel domain to obtain the phase The initial value of Q(x,y) is a matrix with the same number of pixels as the original plaintext image and all element values are 1, and Q(x,y) is continuously updated in subsequent iterations. Synthesize a new complex amplitude Then, double random phase decoding is performed in the Fresnel domain to obtain the decoded amplitude on the input surface. Then, the decoded amplitude is calculated The correlation coefficient CC between the original plaintext image P(x,y). When the calculated CC does not exceed the preset threshold σ, the decoded amplitude on the input surface is used Update the amplitude Q(x, y) on the input plane, and then perform the encryption step S1 again; when the calculated CC exceeds the preset threshold σ, the output is used to generate the decoding amplitude The amplitude A(ξ,η) and phase on the output surface of Afterwards, the sparse matrix S(ξ,η) is used to transform the output amplitude A(ξ,η) and phase Perform sparse constraints respectively and obtain the sparse amplitude A Ω (ξ,η) and sparse phase Then, the sparse amplitude A Ω (ξ,η) and sparse phase Synthesize a new complex amplitude Then, double random phase decoding is performed in the Fresnel domain to obtain the authentication amplitude A on the input surface. Δ (x, y). Afterwards, the encryption step S2 is performed. S2: Phase calculation based on iterative Fourier transform algorithm: Encrypt the authentication amplitude A obtained in step S1 Δ (x, y) is used as the target amplitude, and then the Fourier phase hologram of the target amplitude is optimized and calculated using the iterative Fourier transform algorithm, and the phase distribution of this Fourier phase hologram is output as the authentication phase Afterwards, the encryption step S3 is performed. S3: Phase decomposition: arbitrarily generate a phase with the authentication phase The phase with the same number of elements and whose element values are distributed in the interval [0,2π] is denoted as the ciphertext phase After that, the authentication phase and ciphertext phase Perform phase subtraction operation, and the obtained phase is recorded as the key phase Afterwards, the encryption step S4 is performed. S4: Design of geometric phase metasurface unit structure: Design the material selection of the geometric phase metasurface unit structure, construct the nanocolumn model of the geometric phase metasurface unit structure, use electromagnetic simulation software to perform parameter scanning on the nanocolumn structure, obtain the nanocolumn structure whose phase modulation can cover the phase interval [0,2π], and output the relationship curves between the nanocolumn rotation angle and transmittance and the nanocolumn rotation angle and phase modulation respectively, which are the amplitude modulation curve and phase modulation curve of the geometric phase metasurface unit structure. After that, perform encryption step S5. S5: Construction of ciphertext metasurface and key metasurface: Based on the geometric phase metasurface unit structure designed in encryption step S4, the authentication phase in encryption step S3 is converted into Decomposed ciphertext phase and key phase They are constructed as ciphertext hypersurface C-MH and key hypersurface K-MH respectively. At this point, the encryption step is completed. Authentication steps: J1: Cascading and diffraction of metasurfaces: The ciphertext metasurface C-MH and the authentication key metasurface AK-MH are placed in cascade to form a set of cascaded metasurfaces. After that, the cascaded metasurface is illuminated by a collimated plane light wave, and the light wave after phase modulation of the cascaded metasurface begins to diffract and propagate forward, and then the amplitude distribution of the far-field diffraction of the cascaded metasurface can be obtained, which is recorded as the diffraction image D(x,y) of the cascaded metasurface. After that, the authentication step J2 is performed. J2: Nonlinear correlation authentication of diffraction image: The diffraction image D(x,y) of the cascaded metasurface is authenticated using a nonlinear correlation algorithm, that is, the diffraction image D(x,y) and the original plaintext image P(x,y) are compared and authenticated to obtain the corresponding nonlinear correlation distribution NCD(x,y). Subsequently, the central peak value and the highest peak value other than the central peak in the nonlinear correlation distribution NCD(x,y) are defined as signal and noise, respectively, and the signal-to-noise ratio SNR of the nonlinear correlation distribution NCD(x,y) is calculated. When the calculated SNR exceeds the preset threshold δ, it means that the optical image authentication is successful; when the calculated SNR does not exceed the preset threshold δ, it means that the optical image authentication fails. At this point, the authentication process is completed.
2. The optical image authentication method based on cascaded geometric phase metasurface according to claim 1, characterized in that: In the encryption step S1, the wavelength and diffraction distance used by the double random phase encoding and double random phase decoding in the Fresnel domain are the same, and the random phase used by the double random phase decoding in the Fresnel domain is the conjugate phase of the random phase used by the double random phase encoding in the Fresnel domain.
3. The optical image authentication method based on cascaded geometric phase metasurface according to claim 1, characterized in that: The authentication step J1 can be completed either digitally or optically.
4. The optical image authentication method based on cascaded geometric phase metasurface according to claim 1, characterized in that: When the authentication step J1 is completed optically, a diffraction imaging device is required, specifically a diffraction imaging device based on a cascaded metasurface, including a laser light source 1 for providing incident light, a half-wave plate 2 and a quarter-wave plate 3 for modulating the polarization state of the incident light, a convex lens 4 for converging the incident light wave, a pinhole 5 for filtering the converging spherical light wave formed by the convex lens 4, a microscope objective 6 for modulating the divergent spherical light wave after passing through the pinhole 5 into a plane light wave, a cascaded ciphertext metasurface 7 and an authentication key metasurface 8, a quarter-wave plate 9 and a linear polarizer 10 for modulating the polarization state of the diffracted light after passing through the ciphertext metasurface 7 and the authentication key metasurface 8, a Fourier transform lens 11 for forming Fraunhofer far-field diffraction, and an image sensor device 12 for receiving a diffraction image.
5. The optical image authentication method based on cascaded geometric phase metasurface according to claim 1 and claim 4, characterized in that: In the diffraction imaging device, the pinhole 5 is placed at the image focus of the convex lens 4, and the image focus of the convex lens 4 coincides with the focus of the microscope objective lens 6.
6. The optical image authentication method based on cascaded geometric phase metasurface according to claim 1 and claim 4, characterized in that: In the diffraction imaging device, the ciphertext metasurface 7 and the authentication key metasurface 8 are cascaded and placed closely together, and each metasurface unit structure on the ciphertext metasurface 7 and the corresponding metasurface unit structure on the authentication key metasurface 8 are aligned one by one.
7. The optical image authentication method based on cascaded geometric phase metasurface according to claim 1 and claim 4, characterized in that: In the diffraction imaging device, the distance between the Fourier transform lens 11 and the image sensor 12 is equal to the focal length of the Fourier transform lens 11 .
8. The optical image authentication method based on cascaded geometric phase metasurface according to claim 1 and claim 4, characterized in that: In the diffraction imaging device, the image sensor 12 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS).