Three-dimensional image encryption method based on phase wrapping principle

Abstract

The invention discloses a three-dimensional image encryption method based on a phase wrapping principle, and the method comprises the encryption steps: firstly, coding a to-be-encrypted three-dimensional plaintext image into a conversion amplitude based on the phase wrapping principle; encoding the converted amplitude into a visible ciphertext image and a diffraction neural network by using a Fresnel domain iterative phase recovery algorithm under structured light illumination; and a decryption step: generating decryption structured light by using the decryption structured phase mask to illuminate the visible ciphertext image and perform forward diffraction propagation, generating a reconstruction amplitude after phase modulation of the diffraction neural network, and then performing unwrapping processing on the reconstruction amplitude to obtain a decrypted three-dimensional image. The three-dimensional image encryption method provided by the invention has the advantages of large key space, high security, high concealment, small calculation amount and low complexity.

Description

Technical Field

[0001] The present invention relates to the field of information security technology, and in particular to a three-dimensional image encryption method based on the phase wrapping principle. Background Art

[0002] Since Refregier and Javidi first proposed the double random phase encoding method in 1995, optical image encryption technology has received increasing attention in the field of information security. At present, the optical image encryption method based on double random phase encoding has been extended to various transform domains, such as Fresnel transform domain, fractional Fourier transform domain, rotation transform domain, etc. In addition, many other types of optical image encryption methods have also been proposed, such as interference encryption, holographic encryption, quantum encryption, ghost imaging encryption, metasurface encryption, etc. However, the existing optical image encryption technology is mainly aimed at two-dimensional images. Compared with two-dimensional images, three-dimensional images have larger information capacity and richer content, and can more realistically and accurately express the depth, position and spatial relationship of objects. Therefore, three-dimensional image encryption has become one of the research hotspots in the field of optical image encryption in recent years.

[0003] At present, the research on 3D image encryption mainly focuses on diffraction imaging, integrated imaging, digital holography and computational holography. For example, Shi Yishi et al. realized 3D image encryption by using 3D information coding based on phase extraction and Fresnel domain double random phase coding, but the decrypted 3D information has serious distortion and poor decryption quality. In addition, Piao et al. proposed a 3D image encryption method of cascading Fresnel domain and fractional Fourier domain phase recovery algorithms, but the security is insufficient due to the low sensitivity of some keys. In addition, the layered angular spectrum algorithm is widely used in three-dimensional image encryption schemes. For example, Kong et al. proposed a three-dimensional scene layered encryption method based on the layered angular spectrum algorithm and chaotic random phase mask; Han et al. also proposed a three-dimensional image encryption method based on the layered angular spectrum algorithm and iterative phase recovery algorithm; Wang et al. also proposed a three-dimensional image encryption method combining the layered angular spectrum algorithm, the dual phase method and the chaotic random phase mask; Recently, Su et al. proposed a three-dimensional image encryption method based on the layered angular spectrum algorithm and structured light illumination. However, the three-dimensional image encryption based on the layered angular spectrum algorithm requires layered processing of the three-dimensional image according to the depth information, which leads to the increase in the calculation amount and complexity of the encryption algorithm with the increase in the number of layers. In addition, the above encryption methods all directly encrypt the three-dimensional image used as the plaintext image into a ciphertext image with white noise distribution, which leads to poor encryption concealment, and the types and quantities of keys in the above methods are both small, so it will also lead to problems such as limited key space and insufficient security. In view of this situation, the present invention proposes a three-dimensional image encryption method based on the phase wrapping principle, aiming to achieve high-security and high-concealment three-dimensional image encryption. Summary of the invention

[0004] The purpose of the present invention is to provide a three-dimensional image encryption method based on the phase wrapping principle. Based on the phase wrapping principle, the present invention first encodes the three-dimensional image to be encrypted into a conversion amplitude, and then uses the Fresnel domain iterative phase recovery algorithm under structured light illumination to re-encode the conversion amplitude into a visible ciphertext image and a diffraction neural network, thereby realizing the encryption of the three-dimensional image, which has the advantages of large key space, high security and high concealment.

[0005] To achieve the above-mentioned purpose, the present invention provides the following technical solution: a three-dimensional image encryption method based on the phase wrapping principle, characterized in that it includes the following encryption steps:

[0006] S1: 3D image wrapping processing: First, obtain the height distribution of the 3D image to be encrypted, and convert the height distribution into a phase distribution; second, perform a phase wrapping operation on the phase distribution to obtain a wrapped phase; finally, perform a phase-amplitude conversion on the wrapped phase to obtain a converted amplitude. After that, perform encryption step S2.

[0007] S2: Generation and illumination of encrypted structured light: Use a pre-designed encrypted structured phase mask to phase modulate the collimated plane light wave, thereby generating a specific encrypted structured light; the encrypted structured light generated after phase modulation by the encrypted structured phase mask is diffracted forward without constraint to illuminate the preset visible ciphertext image, and the complex amplitude distribution of the front surface of the ciphertext image is calculated according to the Fresnel diffraction formula. After that, the encryption step S3 is executed.

[0008] S3: Unconstrained forward propagation: After the encrypted image amplitude is modulated, the encrypted structured light continues to diffract and propagate forward, passing through the planes where the multiple pure phase masks to be restored are located in turn to reach the reconstructed image plane, and the complex amplitude distribution of each plane is calculated in turn according to the Fresnel diffraction algorithm, and then the amplitude and phase of each plane are extracted and saved. After that, the encryption step S4 is executed.

[0009] S4: Convergence condition judgment: Use the evaluation function to calculate the correlation between the amplitude of the reconstructed image plane and the conversion amplitude. If the correlation exceeds the preset threshold, that is, the convergence condition is met, then the encryption step S7 is performed; if the correlation does not exceed the preset threshold, that is, the convergence condition is not met, then the phase of the reconstructed image plane is kept unchanged, and the conversion amplitude is used to replace the amplitude of the reconstructed image plane to achieve amplitude constraint. After that, the encryption step S5 is performed.

[0010] S5: Backward propagation under phase constraint: After reconstructing the image plane amplitude constraint, a new complex amplitude is formed to start diffracting backwards, and the complex amplitude distribution of the next plane where the pure phase mask is located is calculated according to the inverse Fresnel diffraction algorithm, and then the amplitude and phase of the plane are extracted and saved; the amplitude of the plane saved in the encryption step S5 is kept unchanged, and the phase of the plane saved in the encryption step S3 is used to replace the phase of the plane saved in the encryption step S5 to achieve phase constraint; after the phase constraint, a new complex amplitude is formed to continue diffracting backwards, and the above process is repeated until all planes where the pure phase mask to be restored are located have completed the phase constraint. After that, the encryption step S6 is executed.

[0011] S6: forward propagation under phase constraint: keep the amplitude of the plane where the first pure phase mask in the forward direction is located saved in the encryption step S3 unchanged, and use the phase of the plane saved in the encryption step S5 to replace the phase of the plane saved in the encryption step S3 to realize phase constraint; after the phase constraint, a new complex amplitude is formed to start diffracting forward, and the complex amplitude distribution of the plane where the next pure phase mask is located is calculated according to the Fresnel diffraction algorithm, and then the amplitude and phase of the plane are extracted and saved; keep the amplitude of the plane saved in the encryption step S6 unchanged, and use the phase of the plane saved in the encryption step S5 to replace the phase of the plane saved in the encryption step S6 to realize phase constraint; after the phase constraint, a new complex amplitude is formed to continue to diffract forward, and the above process is repeated until all the planes where the pure phase masks to be restored are located have completed the phase constraint; after the phase constraint of the plane where the last pure phase mask in the forward direction is located, a new complex amplitude is formed to continue to diffract forward to reach the reconstructed image plane, and the complex amplitude distribution of the reconstructed image plane is calculated according to the Fresnel diffraction algorithm, and then the amplitude and phase of the plane are extracted and saved. Afterwards, the encryption step S4 is performed.

[0012] S7: Generation and output of pure phase masks: On the planes where all pure phase masks to be restored are located, a phase subtraction operation is performed on the phases respectively saved in encryption step S5 and encryption step S6, thereby generating and outputting the phase distribution of all pure phase masks to be restored.

[0013] At this point, the encryption step is completed.

[0014] Decryption steps:

[0015] J1: Generation and illumination of decrypted structured light: Use the decrypted structured phase mask to phase modulate the collimated plane light wave to generate decrypted structured light; the decrypted structured light generated after phase modulation by the decrypted structured phase mask is diffracted forward without constraint to illuminate the preset ciphertext image, and the complex amplitude distribution of the front surface of the ciphertext image is calculated according to the Fresnel diffraction algorithm. After that, the decryption step J2 is executed.

[0016] J2: Forward propagation decryption: The decrypted structured light after the ciphertext image amplitude modulation passes through multiple pure phase masks in sequence to reach the reconstructed image plane. The complex amplitude distribution of each plane is calculated in sequence according to the Fresnel diffraction algorithm, and then the amplitude of the reconstructed image plane is extracted and saved, recorded as the reconstructed amplitude. After that, the decryption step J3 is executed.

[0017] J3: Reconstructed amplitude unwrapping processing: First, the reconstructed amplitude is converted into a decrypted phase; second, the phase distribution is subjected to a phase unwrapping operation to obtain an unwrapped phase; finally, the unwrapped phase is converted into a height distribution, and the decrypted three-dimensional image can be obtained based on the height distribution.

[0018] At this point, the decryption step is completed.

[0019] In the above-mentioned three-dimensional image encryption method based on the phase wrapping principle, the phase distribution design formula for encrypting the structured phase mask in the encryption step S2 includes at least one editable optical parameter used as a digital key.

[0020] In the above-mentioned three-dimensional image encryption method based on the phase wrapping principle, the phase distribution of the pure phase mask generated in the encryption step S7 is output as a grayscale phase map, which is used as a phase key.

[0021] In the above-mentioned three-dimensional image encryption method based on the phase wrapping principle, the decryption steps J1-J2 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 an optical decryption device based on structured light illumination and diffraction neural network, comprising a laser light source 1 for providing illumination light, a polarization modulator 2 for modulating the polarization state of light, a microscope objective 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulator 60 for carrying the phase distribution of the decrypted structured phase mask, and an amplitude modulator for carrying the ciphertext image. Device 7, phase modulation devices 61-6N for carrying the phase distribution of a pure phase mask, and image sensor device 8 for receiving and reconstructing the amplitude, characterized in that: the polarization modulation device 2 is a polarizer or a half-wave plate; the pinhole 4 is placed at the image focus of the microscope objective 3, and the image focus of the microscope objective 3 coincides with the object focus of the convex lens 5; the amplitude modulation device 7 is an amplitude mask or an amplitude-type spatial light modulator; the phase modulation devices 61-6N are phase masks or phase-type spatial light modulators; and the image sensor device 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS).

[0022] The beneficial effects of the present invention are as follows: (1) the introduction of the structured phase mask in the present invention increases the types and number of digital keys, expands the key space, and improves the encryption security; (2) the ciphertext in the present invention has the distribution of visible images, thereby realizing highly concealed image encryption, and all the pure phase masks in the present invention are used as phase keys, thereby further increasing the number of keys and expanding the key space, and cooperating with a rich variety of digital keys to realize highly secure image encryption; (3) the three-dimensional image encryption method proposed in the present invention does not need to perform complex layered processing on the three-dimensional image according to the depth information during encryption, but only needs to perform simple wrapping processing on the three-dimensional image using the phase wrapping principle, which is simple to operate and easy to implement. Compared with the three-dimensional image encryption based on the layered angular spectrum algorithm, it can significantly reduce the iterative calculation between the multiple layers of plaintext images, thereby effectively reducing the calculation amount and complexity of the encryption algorithm; (4) the optical decryption device in the present invention has a simple structure and is easy to build. No optical lens needs to be placed between the amplitude modulation device and the phase modulation device. Compared with the decrypted three-dimensional image, the two-dimensional reconstructed amplitude is easier to be received and collected by the image sensor device, which is beneficial to the subsequent unwrapping process. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 The encryption flow chart of a three-dimensional image encryption method based on the phase wrapping principle.

[0024] Figure 2 An iterative flow chart is provided to assist in describing the encryption steps, where AC, PC, AE, PE, and PS represent amplitude constraint, phase constraint, amplitude extraction, phase extraction, and phase subtraction operations, respectively; EM, CA, and POM represent encrypted structured phase mask, converted amplitude, and pure phase mask, respectively.

[0025] Figure 3 The decryption flow chart of a three-dimensional image encryption method based on the phase wrapping principle.

[0026] Figure 4 It is a diffraction imaging device for optical decryption method of decryption steps J1-J2, wherein 1 represents a laser light source; 2 represents a polarization modulation device; 3 represents a microscope objective lens; 4 represents a pinhole; 5 represents a convex lens; 60-6N represents a phase modulation device; 7 represents an amplitude modulation device; and 8 represents an image sensor device.

[0027] Figure 5 (a) is the three-dimensional plaintext image ("Dragon"), (b) is the conversion amplitude, (c) is the ciphertext ("Peppers"), (d) is the phase distribution of the encrypted structured phase mask, (e) is the phase distribution of pure phase mask 1, (f) is the phase distribution of pure phase mask 2, and (g) is the phase distribution of pure phase mask 3.

[0028] Figure 6 (a) is the decryption result when both the decryption digital key and the decryption phase key are correct; (b) is the decryption result when the decryption wavelength key λ deviates by 2nm and the other keys are correct; (c) is the decryption result when the decryption focal length key f deviates by 1mm and the other keys are correct; (d) is the decryption result when the decryption topological charge key L deviates by 1 and the other keys are correct; (e) is the decryption result when the decryption distance key d0 deviates by 1mm and the other keys are correct; (f) is the decryption result when the decryption distance key d1 deviates by 1mm and the other keys are correct; (g) is the decryption result when the decryption distance key d2 deviates by 1mm and the other keys are correct; (h) is the decryption result when the decryption distance key d3 deviates by 1mm and the other keys are correct; (i) is the decryption result when the decryption phase key (pure phase mask 1) is wrong and the other keys are correct; (j) is the decryption result when the decryption phase key (pure phase mask 2) is wrong and the other keys are correct; (k) is the decryption result when the decryption phase key (pure phase mask 3) is wrong and the other keys are correct.

[0029] Figure 7 (a) is the sensitivity curve of wavelength key λ; (b) is the sensitivity curve of focal length key f; (c) is the sensitivity curve of topological charge key L; (d) is the sensitivity curve of diffraction distance key d0; (e) is the sensitivity curve of diffraction distance key d1; (f) is the sensitivity curve of diffraction distance key d2; (g) is the sensitivity curve of diffraction distance key d3. Specific implementation plan

[0030] The present invention is further described below in conjunction with the embodiments and drawings, but they are not intended to limit the present invention.

[0031] Embodiment: A three-dimensional image encryption method based on phase wrapping principle, comprising: Figure 1 The encryption steps shown in FIG. Figure 2 Iterative flow chart shown):

[0032] S1: 3D image wrapping processing: First, obtain the height distribution h(x, y) of the 3D image to be encrypted, and convert this height distribution h(x, y) into a phase distribution Right now:

[0033]

[0034] In the formula, λ is the wavelength of the light used in the encryption step, and n is the refractive index used in the encryption step. Perform phase wrapping operation to obtain wrapped phase Right now:

[0035]

[0036] In the formula, mod(·) represents the remainder operation. Finally, for the wrapped phase Perform phase-amplitude conversion to obtain the conversion amplitude A(x, y). Then, perform encryption step S2.

[0037] S2: Generation and illumination of encrypted structured light: First, the encrypted structured phase mask composed of the Fresnel zone plate and the radial Hilbert mask is used to phase modulate the collimated plane light wave of unit amplitude, thereby generating phase-modulated encrypted structured light. Therefore, the complex amplitude distribution of the encrypted structured light is equal to the phase distribution EM(ξ,η) of the encrypted structured phase mask, that is:

[0038]

[0039] Where arg(·) represents the phase extraction operation, j is the imaginary unit, r is the radius of the Fresnel zone plate, f is the focal length of the Fresnel zone plate, L is the topological charge of the radial Hilbert mask, and θ is the spatial azimuth of the radial Hilbert mask. Subsequently, the encrypted structured light generated after phase modulation of the encrypted structured phase mask is diffracted forward without constraints to reach the preset visible ciphertext image. The complex amplitude U0(x0,y0) of the encrypted structured light transmitted forward to the front surface of the ciphertext image is:

[0040]

[0041] In the formula, represents the Fresnel diffraction operation with wavelength λ and diffraction distance d0, k=2π / λ is the wave number, and d0 is the distance from the encrypted structured phase mask to the ciphertext image. Afterwards, the encryption step S3 is performed.

[0042] S3: Unconstrained forward propagation: The encrypted structured light after amplitude modulation of the ciphertext image continues to diffract and propagate forward, passing through the planes where the N pure phase masks to be restored are located in turn and then reaches the reconstructed image plane. The N pure phase masks to be restored are respectively recorded as pure phase mask 1, pure phase mask 2, ..., pure phase mask N, the front surfaces of the N pure phase masks are respectively recorded as Plane1, Plane2, ..., PlaneN, and the back surfaces of the N pure phase masks are respectively recorded as Plane1*, Plane2*, ..., PlaneN*, then the complex amplitude U1(x1, y1) of the encrypted structured light forward to Plane1 is:

[0043]

[0044] In the formula, A C(x0, y0) is the amplitude of the preset visible ciphertext image, and d1 is the distance from the ciphertext image to Plane1. After that, the encrypted structured light continues to diffract and propagate forward, reaching Plane2, Plane3, ..., PlaneN and PlaneN+1 (reconstructed image plane) in sequence, where the complex amplitude U of the encrypted structured light forward to Planen n (x n ,y n )for:

[0045] U n (x n ,y n )=Frt λ,dn [U n-1 (x n-1 ,y n-1 )](n=2:1:N+1) (6)

[0046] Where, d n is the distance from Planen-1 to Planen, n = 2:1:N+1 means n is taken from 2 to N+1 in steps of 1. Then, the amplitude A of the encrypted structured light forward to Planen is extracted and saved. n (x n ,y n ) and phase They are:

[0047]

[0048] In the formula, |·| represents the amplitude extraction operation, and n=1:1:N+1 represents that n is incremented from 1 to N+1 in steps of 1. Then, the encryption step S4 is performed.

[0049] S4: Convergence condition judgment: After obtaining the amplitude A of the encrypted structured light forward to the reconstructed image plane (PlaneN+1) N+1 (x N+1 ,y N+1 )=|U N+1 (x N+1 ,y N+1 )|, and use it as the reconstructed amplitude B(x,y). Then the correlation coefficient (CC) is selected as the evaluation function to calculate the correlation between the reconstructed amplitude and the converted amplitude, so as to verify the convergence condition. The CC between the converted amplitude A(x,y) and the reconstructed amplitude B(x,y) is:

[0050]

[0051] Where X and Y are the horizontal and vertical pixel numbers of the image, respectively. and are the pixel grayscale averages of the converted amplitude and the reconstructed amplitude, respectively. When the calculated CC exceeds the preset threshold σ, that is, the convergence condition is met, the encryption step S6 is performed; when the calculated CC does not exceed the preset threshold σ, that is, the convergence condition is not met, the phase of the encrypted structured light forward to the reconstructed image plane is retained. The converted amplitude A(x, y) is used to replace the reconstructed amplitude B(x, y) (i.e., the amplitude A transmitted from the encrypted structured light to the reconstructed image plane). N+1 (x N+1 ,y N+1 )) implements amplitude constraint, thereby generating a new complex amplitude U′ on the reconstruction plane N+1 (x N+1 ,y N+1 ),Right now:

[0052]

[0053] Afterwards, the encryption step S5 is performed.

[0054] S5: Backward propagation under phase constraint: The encrypted structured light is constrained by amplitude on the reconstructed image plane to form a new complex amplitude U′ N+1 (x N+1 ,y N+1 ) starts to propagate backward by diffraction, and reaches the back surfaces of N pure phase masks (PlaneN*, PlaneN-1*,..., Plane1*) in sequence, where the complex amplitude of the encrypted structured light propagating backward to Planen* for:

[0055]

[0056] In the formula, Indicates that the wavelength is λ and the diffraction distance is d n+1 The inverse Fresnel diffraction operation, d n+1 is the distance from Planen* to Planen+1*, n=N:-1:1 means n is incremented from N to 1 with a step length of -1. After that, the amplitude of the encrypted structured light transmitted to Planen* is extracted and saved. and Phase They are:

[0057]

[0058] Where n=N:-1:1 means that n is incremented from N to 1 in steps of -1. Then, the amplitude of the encrypted structured light stored in the encryption step S5 and transmitted to Planen* is retained. The encrypted structured light saved in the encryption step S3 is used to forward the phase of Planen Instead of encrypting the encrypted structured light stored in step S5, the phase of Planen* is transmitted backward Implement phase constraints to generate a new complex amplitude U for the next backward propagation n ′(x n ,y n ),Right now:

[0059]

[0060] In the formula, n = N:-1:1 means that n is incremented from N to 1 in steps of -1. * Backward propagation until Plane1 * , each time it is transmitted to the next plane, formulas (10)-(12) are cyclically executed once until the encrypted structured light is transmitted back to Plane1 * After that, the encryption step S6 is performed.

[0061] S6: Forward propagation under phase constraint: keep the amplitude A1(x1,y1) of the encrypted structured light saved in encryption step S3 forward to Plane1 unchanged, and use the encrypted structured light saved in encryption step S5 to propagate backward to Plane1 * Phase Instead of encrypting the phase of the structured light saved in step S3, it is forwarded to Plane1 The phase constraint is implemented to generate a new complex amplitude for the next forward propagation, namely: Subsequently, the encrypted structured light begins to diffract and propagate forward, reaching Plane2, Plane3, …, PlaneN, and PlaneN+1 in sequence, where the complex amplitude U of the encrypted structured light transmitted forward to PlaneN is n (x n ,y n ) is updated to:

[0062]

[0063] In the formula, n = 2:1:N+1 means that n is incremented from 2 to N+1 in steps of 1. Then, the amplitude A of the encrypted structured light transmitted forward to Planen is extracted and saved. n (x n ,y n ) and phase They are:

[0064]

[0065] In the formula, n=2:1:N+1 means that n is incremented from 2 to N+1 in steps of 1. Then, the amplitude A of the encrypted structured light forward transmitted to Planen saved in the encryption step S6 is retained.n (x n ,y n ) remains unchanged, and the encrypted structured light saved in the encryption step S5 is used to propagate back to the phase of Planen* Instead of encrypting the phase of the encrypted structured light stored in step S6 forward to Planen Implement phase constraints to generate a new complex amplitude U for the next forward propagation n ″(x n ,y n ),Right now:

[0066]

[0067] In the formula, n=2:1:N means that n is incremented by 1 from 2 to N. The encrypted structured light propagates forward from Plane2 to PlaneN+1. Each time it propagates to the next plane, formulas (13)-(15) are executed once until the encrypted structured light propagates forward to PlaneN+1. After that, the encryption step S4 is executed.

[0068] S7: Generation and output of pure phase mask: On all planes where the pure phase mask to be restored is located, the encrypted structured light saved in the encryption step S5 is transmitted to the phase of Planen* The phase of the encrypted structured light forwarded to Planen saved in the encryption step S6 Perform a phase subtraction operation to generate and output the phase distribution of all pure phase masks to be restored, where the phase distribution of pure phase mask n is for:

[0069]

[0070] Wherein, n=1:1:N means that n is incremented from 1 to N in steps of 1.

[0071] At this point, the encryption step is completed.

[0072] like Figure 3 Decryption steps shown:

[0073] J1: Generation and illumination of decrypted structured light: The decrypted structured phase mask is used to phase modulate the collimated plane light wave to generate decrypted structured light; the decrypted structured light generated after phase modulation by the decrypted structured phase mask is diffracted forward without constraint to illuminate the preset ciphertext image, and the complex amplitude U of the decrypted structured light transmitted forward to the front surface of the ciphertext image is calculated according to the Fresnel diffraction algorithm. 0D (x0,y0), that is:

[0074]

[0075] Where DM(ξ,η) is the phase distribution of the decrypted structured phase mask, λ D To decipher the wavelength of the incident light, d 0D To decrypt the distance from the structured phase mask to the ciphertext image, the decryption step J2 is performed.

[0076] J2: Forward propagation decryption: After the amplitude modulation of the ciphertext image, the decrypted structured light continues to diffract and propagate forward, and the complex amplitude U of the decrypted structured light transmitted forward to Plane1 is 1D (x1,y1) is:

[0077]

[0078] Where, d 1D is the distance from the ciphertext image to Plane1 during decryption. Afterwards, the decrypted structured light continues to diffract and propagate forward, reaching Plane2, Plane3, ..., PlaneN and PlaneN+1 (reconstructed image plane) in sequence, where the complex amplitude U of the decrypted structured light forward to Plane nD (x n ,y n )for:

[0079]

[0080] Where, d nD is the distance from Planen-1 to Planen during decryption, n=2:1:N+1 means n is incremented by 1 from 2 to N+1. Then, the amplitude A of the decrypted structured light forward to the reconstructed image plane (PlaneN+1) is extracted and saved. (N+1)D (x N+1 ,y N+1 )for:

[0081] A (N+1)D (x N+1 ,y N+1 )=|U (N+1)D (x N+1 ,y N+1 )| (20)

[0082] That is the reconstructed amplitude. Afterwards, the decryption step J3 is performed.

[0083] J3: Reconstructed amplitude unwrapping process: First, the reconstructed amplitude A (N+1)D (x N+1 ,y N+1 ) to convert the amplitude into phase and obtain the decrypted phase Secondly, for this phase distribution Perform phase unwrapping operation to obtain unwrapped phase Right now:

[0084]

[0085] In the formula, unwrap(·) represents the phase unwrapping operation. Finally, the unwrapped phase Convert to height distribution h D (x,y), that is:

[0086]

[0087] Where n D is the refractive index used in the decryption step. Based on this height distribution h D (x,y) can get the decrypted three-dimensional image.

[0088] At this point, the decryption steps are completed, wherein the decryption steps J1-J2 can be completed in a digital manner or in an optical manner. The optical decryption method used in the decryption steps J1-J2 is described in detail below. The above optical decryption requires the use of the diffraction imaging device provided by the present invention, specifically a diffraction imaging device based on structured light illumination and a diffraction neural network, such as Figure 3 As shown, it includes a laser light source 1 for providing illumination light, and on the optical axis, there are arranged in sequence a polarization modulation device 2 for modulating the polarization state of light, a microscope objective lens 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulation device 60 for carrying the phase distribution of the decrypted structured phase mask, an amplitude modulation device 7 for carrying the ciphertext image, phase modulation devices 61-6N for carrying the phase distribution of the pure phase mask, and an image sensor device 8 for receiving the reconstructed amplitude, characterized in that: the polarization modulation device 2 is a polarizer or a half-wave plate; the pinhole 4 is placed on the image focus of the microscope objective lens 3, and the image focus of the microscope objective lens 3 coincides with the object focus of the convex lens 5; the amplitude modulation device 7 is an amplitude mask or an amplitude-type spatial light modulator; the phase modulation devices 60-6N are phase masks or phase-type spatial light modulators; and the image sensor device 8 is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS).

[0089] The specific optical decryption process is as follows: the laser emitted by the laser light source 1 first passes through the polarization modulator 2 to form polarized light, and then the polarized light passes through the beam expansion and collimation system composed of the microscope objective 3, the pinhole 4, and the convex lens 5 to form a collimated plane light wave, and then the plane light wave is phase-modulated by the phase modulator 60 that carries the phase distribution of the decrypted structured phase mask to generate the decrypted structured light, and then the decrypted structured light is diffracted and propagated forward without constraint until it reaches the amplitude modulator 7 that carries the ciphertext image, and then the decrypted structured light after amplitude modulation by the amplitude modulator 7 continues to diffract and propagate forward until it reaches the diffraction neural network composed of the phase modulators 61-6N that carry the phase distribution of the pure phase mask, and then the decrypted structured light after phase modulation by the phase modulators 61-6N in the diffraction neural network continues to diffract and propagate forward without constraint until it reaches the image sensor 8, and the optical decryption is completed. At this time, the image recorded on the image sensor 8 is the reconstructed amplitude.

[0090] The subsequent decryption step J3 is completed digitally. The specific process is: the reconstructed amplitude recorded on the image sensor device 8 is read into the computer, and then the reconstructed amplitude is sequentially subjected to amplitude-to-phase conversion, unwrapping processing and phase-to-height conversion operations in the computer to obtain a decrypted three-dimensional image.

[0091] The content of the present invention is further explained below in conjunction with specific embodiments and drawings.

[0092] First, a 3D model ("Dragon") is selected as the 3D plaintext image to be encrypted, and the length, width, and height of the 3D image are set to 100 mm, 100 mm, and 20 mm respectively. Figure 5 In addition, the wavelength λ and refractive index n used in the encryption process are set to 632.8 nm and 1.5 respectively. Then, after the encryption step S1 is performed on the three-dimensional image and the conversion amplitude is obtained, Figure 5 (b) is shown. Then, a grayscale image with a pixel count of 512×512 (“Peppers”) is selected as the preset visible ciphertext image, as shown in Figure 5 As shown in (c), the encrypted structured phase mask is assumed to consist of a Fresnel zone plate with a focal length f of 20 mm and a radial Hilbert mask with a topological charge number L of 6, and its phase distribution is as follows: Figure 5As shown in (d). In addition, it is assumed that the diffraction neural network to be restored includes three pure phase masks (pure phase mask 1, pure phase mask 2, pure phase mask 3), the distance d0 from the encrypted structured phase mask to the ciphertext image is 40 mm, the distance d1 from the ciphertext image to pure phase mask 1 is 40 mm, the distance d2 from pure phase mask 1 to pure phase mask 2 is 150 mm, the distance d3 from pure phase mask 2 to pure phase mask 3 is 100 mm, the distance d4 from pure phase mask 3 to the reconstructed image plane is 150 mm, and the preset threshold σ of CC is 0.9999. Figure 2 After the iterative process shown in FIG. 1 , the phase distributions of the three pure phase masks (pure phase mask 1, pure phase mask 2, and pure phase mask 3) are respectively as follows: Figure 5 (e)-(g) are shown. At this point, the encryption step is completed, the ciphertext is a preset visible image ("Peppers"), and the key includes a digital key and a phase key, where the digital key includes the wavelength λ of the light wave used in the encryption process, the optical parameters (focal length f and topological charge L) in the encrypted structured phase mask, and the diffraction distance (d0, d1, d2, d3), and the phase key refers to the generated pure phase mask (pure phase mask 1, pure phase mask 2, pure phase mask 3).

[0093] Next, test the validity and security of the key in the present invention. When both the decryption digital key and the decryption phase key are correct, the decryption result is as follows: Figure 6 (a); when the decryption wavelength key λ deviates by 2nm and other keys are correct, the decryption result is as follows: Figure 6 (b) When the decryption focal length key f deviates by 1 mm and other keys are correct, the decryption result is as follows: Figure 6 (c) As shown; when the decryption topological charge key L deviates by 1 and other keys are correct, the decryption result is as follows Figure 6 (d) When the decryption distance key d0 deviates by 1 mm and other keys are correct, the decryption result is as follows: Figure 6 (e) When the decryption distance key d1 deviates by 1 mm and other keys are correct, the decryption result is as follows: Figure 6 (f) When the decryption distance key d2 deviates by 1 mm and other keys are correct, the decryption result is as follows: Figure 6 (g) When the decryption distance key d3 deviates by 1 mm and other keys are correct, the decryption result is as follows: Figure 6 (h) When the decryption phase key (pure phase mask 1) is wrong and other keys are correct, the decryption result is as follows: Figure 6 (i) As shown; when the decryption phase key (pure phase mask 2) is wrong and other keys are correct, the decryption result is as follows Figure 6(j) As shown; when the decryption phase key (pure phase mask 3) is wrong and other keys are correct, the decryption result is as follows Figure 6 (k). Figure 6 It can be seen from the decryption results that when the digital key and the phase key are correct, the original three-dimensional plaintext image can be reconstructed with high quality, but when any digital key or phase key is wrong, the correct three-dimensional plaintext image cannot be restored. At this time, the decryption result shows obvious noise distribution, which illustrates the effectiveness and security of the digital key and phase key in the present invention.

[0094] The sensitivity of the digital key in the present invention is examined below. Figure 7 The relationship between the CC between the reconstruction amplitude and the conversion amplitude and the deviation of each digital key is given when the decryption phase key is correct, that is, the sensitivity curve of each digital key, where Figure 7 (a)-(g) represent the sensitivity curves of wavelength key λ, focal length key f, topological charge key L, diffraction distance key d0, diffraction distance key d1, diffraction distance key d2, and diffraction distance key d3, respectively. Figure 7 It can be seen from the sensitivity curve in that when any digital key has a slight deviation, the CC between the reconstructed amplitude and the converted amplitude drops sharply to close to 0. At this time, the reconstructed amplitude shows obvious noise distribution, resulting in the inability to correctly restore the original three-dimensional plaintext image, which shows that the digital key in the present invention has high sensitivity.

[0095] In summary, the present invention discloses a three-dimensional image encryption method based on the phase wrapping principle. In the present invention, the encryption process first encodes the three-dimensional image to be encrypted into a conversion amplitude based on the phase wrapping principle, and then uses the Fresnel domain iterative phase recovery algorithm under structured light illumination to encode the conversion amplitude into a visible ciphertext image and a diffraction neural network, wherein the ciphertext has a distribution of visible images, thus showing extremely high encryption concealment, and all pure phase masks in the diffraction neural network are used as phase keys, thereby effectively increasing the types and number of keys and greatly expanding the key space. In addition, the optical parameters in the structured phase mask are all used as digital keys, thereby further expanding the key space and improving the security of three-dimensional image encryption; the decryption process can be completed digitally or by a combination of optical and digital methods, wherein the diffraction imaging device used for optical decryption has a simple structure and is easy to build, and compared with decrypting three-dimensional images, the two-dimensional reconstructed amplitude is easier to be received and collected by image sensors.

Claims

1. A three-dimensional image encryption method based on the phase wrapping principle, characterized in that: The encryption steps include: S1: 3D image wrapping processing: First, obtain the height distribution of the 3D image to be encrypted, and convert the height distribution into a phase distribution; second, perform a phase wrapping operation on the phase distribution to obtain a wrapped phase; finally, perform a phase-amplitude conversion on the wrapped phase to obtain a converted amplitude. After that, perform encryption step S2. S2: Generation and illumination of encrypted structured light: using a pre-designed encrypted structured phase mask to phase modulate the collimated plane light wave, thereby generating a specific encrypted structured light; The encrypted structured light generated after phase modulation of the encrypted structured phase mask is diffracted forward without constraint to illuminate the preset visible ciphertext image, and the complex amplitude distribution of the front surface of the ciphertext image is calculated according to the Fresnel diffraction formula. Then, the encryption step S3 is performed. S3: Unconstrained forward propagation: After the encrypted image amplitude is modulated, the encrypted structured light continues to diffract and propagate forward, passing through the planes where the multiple pure phase masks to be restored are located in turn to reach the reconstructed image plane, and the complex amplitude distribution of each plane is calculated in turn according to the Fresnel diffraction algorithm, and then the amplitude and phase of each plane are extracted and saved. After that, the encryption step S4 is executed. S4: Convergence condition judgment: Use the evaluation function to calculate the correlation between the amplitude of the reconstructed image plane and the conversion amplitude. If the correlation exceeds the preset threshold, that is, the convergence condition is met, then the encryption step S7 is performed; if the correlation does not exceed the preset threshold, that is, the convergence condition is not met, then the phase of the reconstructed image plane is kept unchanged, and the conversion amplitude is used to replace the amplitude of the reconstructed image plane to achieve amplitude constraint. After that, the encryption step S5 is performed. S5: Backward propagation under phase constraint: After reconstructing the image plane amplitude constraint, a new complex amplitude is formed to start diffracting backwards, and the complex amplitude distribution of the next plane where the pure phase mask is located is calculated according to the inverse Fresnel diffraction algorithm, and then the amplitude and phase of the plane are extracted and saved; the amplitude of the plane saved in the encryption step S5 is kept unchanged, and the phase of the plane saved in the encryption step S3 is used to replace the phase of the plane saved in the encryption step S5 to achieve phase constraint; after the phase constraint, a new complex amplitude is formed to continue diffracting backwards, and the above process is repeated until all planes where the pure phase mask to be restored are located have completed the phase constraint. After that, the encryption step S6 is executed. S6: forward propagation under phase constraint: keep the amplitude of the plane where the first pure phase mask in the forward direction is located saved in the encryption step S3 unchanged, and use the phase of the plane saved in the encryption step S5 to replace the phase of the plane saved in the encryption step S3 to realize phase constraint; after the phase constraint, a new complex amplitude is formed to start diffracting forward, and the complex amplitude distribution of the plane where the next pure phase mask is located is calculated according to the Fresnel diffraction algorithm, and then the amplitude and phase of the plane are extracted and saved; keep the amplitude of the plane saved in the encryption step S6 unchanged, and use the phase of the plane saved in the encryption step S5 to replace the phase of the plane saved in the encryption step S6 to realize phase constraint; after the phase constraint, a new complex amplitude is formed to continue to diffract forward, and the above process is repeated until all the planes where the pure phase masks to be restored are located have completed the phase constraint; after the phase constraint of the plane where the last pure phase mask in the forward direction is located, a new complex amplitude is formed to continue to diffract forward to reach the reconstructed image plane, and the complex amplitude distribution of the reconstructed image plane is calculated according to the Fresnel diffraction algorithm, and then the amplitude and phase of the plane are extracted and saved. Afterwards, the encryption step S4 is performed. S7: Generation and output of pure phase masks: On the planes where all pure phase masks to be restored are located, a phase subtraction operation is performed on the phases respectively saved in encryption step S5 and encryption step S6, thereby generating and outputting the phase distribution of all pure phase masks to be restored. At this point, the encryption step is completed. Decryption steps: J1: Generation and illumination of decrypted structured light: Use the decrypted structured phase mask to phase modulate the collimated plane light wave to generate decrypted structured light; the decrypted structured light generated after phase modulation by the decrypted structured phase mask is diffracted forward without constraint to illuminate the preset ciphertext image, and the complex amplitude distribution of the front surface of the ciphertext image is calculated according to the Fresnel diffraction algorithm. After that, the decryption step J2 is executed. J2: Forward propagation decryption: The decrypted structured light after the ciphertext image amplitude modulation passes through multiple pure phase masks in sequence to reach the reconstructed image plane. The complex amplitude distribution of each plane is calculated in sequence according to the Fresnel diffraction algorithm, and then the amplitude of the reconstructed image plane is extracted and saved, recorded as the reconstructed amplitude. After that, the decryption step J3 is executed. J3: Reconstructed amplitude unwrapping processing: First, the reconstructed amplitude is converted into a decrypted phase; second, the phase distribution is subjected to a phase unwrapping operation to obtain an unwrapped phase; finally, the unwrapped phase is converted into a height distribution, and the decrypted three-dimensional image can be obtained based on the height distribution. At this point, the decryption step is completed.

2. The three-dimensional image encryption method based on the phase wrapping principle according to claim 1, characterized in that: The phase distribution design formula for encrypting the structured phase mask in the encryption step S2 includes at least one editable optical parameter, which is used as a digital key.

3. The three-dimensional image encryption method based on the phase wrapping principle according to claim 1, characterized in that: The phase distribution of the pure phase mask generated in the encryption step S7 is output as a grayscale phase map, which is used as a phase key.

4. The three-dimensional image encryption method based on the phase wrapping principle according to claim 1, characterized in that: The decryption steps J1-J2 can be completed either digitally or optically.

5. A three-dimensional image encryption method based on the phase wrapping principle according to claim 1 and claim 4, characterized in that: The decryption steps J1-J2 are completed optically and require the use of a diffraction imaging device based on structured light illumination and diffraction neural network, including a laser light source 1 for providing illumination light, and a polarization modulation device 2 for modulating the polarization state of light, a microscope objective 3 for beam expansion, a pinhole 4 for filtering, a convex lens 5 for collimation, a phase modulation device 60 for carrying the phase distribution of the decrypted structured phase mask, an amplitude modulation device 7 for carrying the ciphertext image, a phase modulation device 61-6N for carrying the phase distribution of the pure phase mask, and an image sensor device 8 for receiving the reconstructed amplitude.

6. A three-dimensional image encryption method based on the phase wrapping principle according to claim 1 and claim 5, characterized in that: In the diffraction imaging device based on structured light illumination and diffraction neural network, the pinhole 4 is placed at the image focus of the microscope objective lens 3, and the image focus of the microscope objective lens 3 and the object focus of the convex lens 5 coincide with each other.

7. A three-dimensional image encryption method based on the phase wrapping principle according to claim 1 and claim 5, characterized in that: The polarization modulation device 2 in the diffraction imaging device based on structured light illumination and diffraction neural network is a polarizer or a half-wave plate.

8. A three-dimensional image encryption method based on the phase wrapping principle according to claim 1 and claim 5, characterized in that: The phase modulation device 61-6N in the diffraction imaging device based on structured light illumination and diffraction neural network is a phase mask or a phase-type spatial light modulator.

9. A three-dimensional image encryption method based on the phase wrapping principle according to claim 1 and claim 5, characterized in that: The amplitude modulation device 7 in the diffraction imaging device based on structured light illumination and diffraction neural network is an amplitude mask or an amplitude-type spatial light modulator.

10. A three-dimensional image encryption method based on the phase wrapping principle according to claim 1 and claim 5, characterized in that: The image sensor device 8 in the diffraction imaging device based on structured light illumination and diffraction neural network is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS).

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