An Acoustic Encryption Device and Method Based on Cascade Holography Technology
By introducing cascaded holographic technology and physically driven neural network design method in acoustic encryption technology, the shortcomings of existing acoustic encryption methods in terms of information capacity and security are solved, and the acoustic encryption effect with high information capacity and high security is achieved.
Patent Information
- Application Number
- CN202411753784.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-02
- Publication Date
- 2025-06-17
- Estimated Expiration
- 2044-12-02
AI Technical Summary
The existing acoustic encryption methods have shortcomings in information capacity and security, and it is difficult to meet the high information capacity and high security requirements in practical applications.
The acoustic encryption device based on cascade holographic technology is adopted to realize the multi-channel secret sharing mechanism through multiple acoustic holographic devices and corresponding physical drive neural network design methods, and enhance the carrying capacity and security of encrypted information.
It realizes efficient carrying of multiple verification information and encrypted information, improves the security and accuracy of encrypted information, and is suitable for underwater communication and imaging fields.
Smart Images

Figure CN119603049B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of information encryption, and particularly relates to an acoustic encryption device and method based on cascaded holographic technology. Background Art
[0002] With the rapid development of information technology, the transmission and storage of information have become an indispensable part of daily life and work, and information encryption has become a necessary means to protect information security. For individuals, personal identity information, such as name, address, phone number, etc., often needs to be provided in daily life. If this information is directly transmitted or stored without encryption, hackers or identity thieves may easily obtain it and then use it for illegal activities such as fraud and identity theft. For enterprises, large companies usually have a large amount of confidential information, including financial reports, R & D results, etc.; these information are the core assets of the company, and once leaked to competitors or malicious third parties, it may cause significant losses. For countries, government agencies handle a large amount of sensitive information, involving fields such as national defense, diplomacy, and intelligence, and this information is crucial for national security, and once leaked, it may lead to serious consequences. Through information encryption, it can be ensured that even if the data is intercepted, attackers are difficult to decrypt and utilize this information, thus effectively protecting information security.
[0003] Traditional information encryption methods include encryption technologies based on computer encryption algorithms, electromagnetic encryption technologies, and optical encryption technologies, etc. Among them, the encryption technology based on computer encryption algorithms requires a server with better computing power and has a large power consumption; the electromagnetic encryption technology cannot work in an electromagnetically shielded environment; the optical encryption technology is difficult to achieve long-range transmission due to the large attenuation of light waves in water. In contrast, acoustic encryption technology shows unique advantages in certain specific fields. The acoustic encryption method can not only work effectively under electromagnetic shielding conditions, but also the sound wave has less attenuation in water and is the main carrier for underwater information transmission. Therefore, in recent years, with the continuous development of acoustic technology, acoustic-based encryption methods have gradually attracted the attention of researchers. However, most of the existing acoustic encryption methods have limited information capacity and insufficient security performance, and it is difficult to meet the requirements of high information capacity and high security in practical applications.
[0004] Therefore, we provide an acoustic encryption device and method based on cascaded holographic technology to solve the above problems. Summary of the Invention
[0005] To solve the above technical problems, the present invention is realized through the following technical solutions:
[0006] The present invention is an acoustic encryption device based on cascaded holographic technology, including:
[0007] Sound field generating module, the sound field generating module includes an ultrasonic excitation system and an ultrasonic transducer, wherein the ultrasonic excitation system includes a signal generator and a power amplifier;
[0008] Cascaded acoustic holographic encryption module, the cascaded acoustic holographic encryption module includes a plurality of acoustic holographic devices, a carrier bracket, a moving and rotating platform, and a liquid carrier container. There are pores on the upper and lower layers of the carrier bracket that are close to the size of the acoustic holographic device and are strictly aligned. The distance between the upper and lower layers of the carrier bracket is determined according to the distance between two acoustic holograms in the cascaded acoustic encryption calculation process. The acoustic holographic device placed on the lower layer comes from the main key group, and the acoustic holographic device placed on the upper layer comes from the sub-key group. The two acoustic holographic devices modulate the phase distribution of the plane wave sound field alone or in cooperation through phase modulation, which can not only separately reconstruct their respective reconstructed sound fields as their own identification marks, but also cooperate with each other to produce a reconstructed sound field and encrypted information different from that of a single acoustic holographic device. The moving and rotating platform drives the movement and rotation of the second acoustic holographic device, changing the three-dimensional spatial position of the two acoustic holographic devices, which is used to increase the carrying capacity of the encrypted information;
[0009] Cascaded acoustic holographic decryption module, the cascaded acoustic holographic decryption module includes a full-automatic three-dimensional displacement platform, a hydrophone, an oscilloscope, and a system controller. Among them, the full-automatic three-dimensional displacement platform can receive the movement mode and parameters of the system controller to achieve fine movement in the three-dimensional full space. The hydrophone is placed on the three-dimensional displacement platform and can collect the sound field parameters of points, lines, planes, and three-dimensional full space and convert them into electrical signals. These electrical signals are further collected by the oscilloscope and sent to the system controller, and the system controller analyzes these electrical signals to achieve the decryption of acoustic information.
[0010] The present invention is further configured such that the signal generator emits an electrical signal, which is amplified by the power amplifier, and then the ultrasonic transducer is excited to emit a plane wave sound field with a specific frequency and sufficient energy as the incident sound source.
[0011] The present invention is further configured such that the liquid is carried in the carrier container, and the liquid surrounds the ultrasonic transducer, the acoustic holographic device, and the carrier bracket to provide an environment for sound waves to propagate in the liquid.
[0012] The present invention is further configured such that the shapes of the multiple acoustic holographic devices of the cascaded acoustic holographic encryption module include, but are not limited to, circular, square, and elliptical; the materials for making the acoustic holographic devices include, but are not limited to, resin and silicone rubber, and the manufacturing processes include, but are not limited to, laser etching, 3D printing, and casting molding.
[0013] The present invention is further configured such that the ultrasonic excitation system in the sound field generation module can arbitrarily adjust ultrasonic parameters, including ultrasonic frequency, ultrasonic energy, ultrasonic pulse length, and ultrasonic pulse repetition frequency. The ultrasonic transducer includes, but is not limited to, piezoelectric ultrasonic transducers, capacitive micromachined ultrasonic transducers (cMUT), piezoelectric micromachined ultrasonic transducers (pMUT), and other types of ultrasonic transducers.
[0014] An encryption method for an acoustic encryption device based on cascaded holography technology includes the following steps:
[0015] S100. Use the cascaded acoustic hologram design method of a physical-driven neural network to accurately and efficiently obtain the phase distributions of multiple acoustic holograms carrying their own verification information and physically separated encrypted information.
[0016] S200. Design an acoustic holographic device capable of encoding the phase distribution of the acoustic hologram through different phase modulation principles. The phase modulation principles include propagation phase modulation and amplitude-phase modulation. Among them, the propagation phase modulation is achieved by changing the thickness of different positions on the surface of the transmission material, and the amplitude-phase modulation is achieved by changing the pore size of different positions on the surface of the rigid material or using a microbubble array.
[0017] S300. Place the acoustic holographic device at the corresponding physical space position. Each acoustic holographic device can reconstruct an independent reconstructed sound field at a predetermined position under the separate excitation of the incident sound wave as its own verification information. When two acoustic holographic devices from different groups are accurately placed at the corresponding spatial positions to form a corresponding acoustic encryption channel, the incident sound wave can be modulated by these two acoustic holographic devices and reconstruct a new reconstructed sound field different from the verification information of the two acoustic holographic devices at a predetermined position, that is, the encrypted information physically separated by the two acoustic holographic devices is reconstructed.
[0018] The present invention is further configured such that the cascaded acoustic hologram design method of the physical-driven neural network includes the following steps:
[0019] S101. Obtain an image containing verification information and encrypted information as the input of the method, and use multiple acoustic holograms as the output of the method.
[0020] S102. Construct a deep neural network with an image containing verification information and encrypted information as the input and the phase distribution of the acoustic hologram as the output. The deep neural network can adopt an encoding-decoding structure similar to the Unet network or other network structures for image reconstruction.
[0021] S103. Construct a forward acoustic wave diffraction propagation function for simulating the reconstructed sound field after the incident plane acoustic wave is modulated by the acoustic hologram. The forward acoustic wave diffraction propagation function can adopt the angular spectrum method or other acoustic wave diffraction propagation models.
[0022] S104. Construct a total network loss function, compare the reconstructed sound field with the target image, and calculate the mean square error. The total network loss function can be the average of multiple mean square errors;
[0023] S105. Update the parameters of the deep neural network through the gradient descent optimization algorithm, and the gradient descent optimization algorithm can adopt the Adam algorithm;
[0024] S106. Repeat the above steps until the total network loss function converges to the local optimum, and output the optimized phase distribution of the acoustic hologram.
[0025] The present invention is further configured that the phase modulation principle of the acoustic holographic device includes propagation phase modulation and amplitude-phase modulation. Among them, the propagation phase modulation is realized by changing the thickness of different positions on the surface of the transmission material, and the amplitude-phase modulation is realized by changing the pore size of different positions on the surface of the rigid material or using a microbubble array. The transmission material can be resin, and the rigid material can be metal or ceramic.
[0026] The present invention has the following beneficial effects:
[0027] 1. The present invention introduces a multi-channel secret sharing mechanism through cascaded holography technology to realize the bearing of multiple verification information and encrypted information, meeting the requirements for high-information-capacity encryption in practical applications.
[0028] 2. The present invention introduces a multi-channel secret sharing mechanism through cascaded holography technology. Only when two of the multiple acoustic holographic devices serving as keys are accurately placed at the corresponding spatial positions to form the corresponding encryption channels can the encrypted information be read out in the corresponding acoustic encryption channels. If one of the verification images is missing, the encrypted image cannot be reconstructed, thereby improving the security of encryption; at the same time, a cascaded acoustic hologram design method driven by a physical neural network is designed. By using the interaction between a deep learning network and the multi-channel acoustic wave diffraction propagation process, the acoustic holograms of multiple channels are simultaneously and collaboratively optimized and designed. Compared with the design method of independent optimization of single-channel acoustic holograms, this method enables the acoustic hologram design method to simultaneously optimize and update the information of all holograms in each iteration process, making the optimization and encryption processes complex, thereby enhancing the security and accuracy of encryption.
[0029] 3. The present invention utilizes the advantages of acoustic waves that can work effectively under electromagnetic shielding conditions and are not easily attenuated in water and other applications, and applies this method to fields such as underwater communication and imaging, broadening the application scope of current encryption technologies.
[0030] 4. The present invention realizes information encryption by using an acoustic holographic lens to regulate the phase distribution of a sound source. The acoustic holographic lens can be designed according to user requirements. The lens can be made of various materials such as resin and silicone rubber, and can be fabricated using various processes such as laser etching, 3D printing, and casting molding. The materials are easily accessible and inexpensive, and the fabrication is simple and direct, greatly reducing the fabrication difficulty and equipment cost.
[0031] Of course, it is not necessary for any product implementing the present invention to achieve all the above-mentioned advantages simultaneously. BRIEF DESCRIPTION OF THE DRAWINGS
[0032] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for describing the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.
[0033] Figure 1 Schematic diagram of the device of the present invention;
[0034] Figure 2 Schematic diagram of the process in the present invention;
[0035] Figure 3 Schematic diagram of Embodiment 1 of the present invention;
[0036] Figure 4 Schematic diagram of the cascaded acoustic hologram design method of the physical-driven neural network involved in Embodiment 1 of the present invention;
[0037] Figure 5 Phase distribution results of two acoustic holograms in Embodiment 1 of the present invention;
[0038] Figure 6 Simulation and experimental results in Embodiment 1 of the present invention;
[0039] Figure 7 Schematic diagram of Embodiment 2 of the present invention;
[0040] Figure 8 Phase distribution results of three acoustic holograms in Embodiment 2 of the present invention;
[0041] Figure 9 Simulation and experimental results in Embodiment 2 of the present invention;
[0042] Figure 10 Schematic diagram of Embodiment 3 of the present invention;
[0043] Figure 11 Phase distribution results of three acoustic holograms in Embodiment 3 of the present invention;
[0044] Figure 12 This is the simulation result of the third embodiment of the present invention. Specific implementation manner
[0045] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
[0046] The present invention is an acoustic encryption device based on cascaded holographic technology, including:
[0047] An acoustic field generation module, the acoustic field generation module includes an ultrasonic excitation system and an ultrasonic transducer. The ultrasonic excitation system includes a signal generator and a power amplifier. The signal generator emits an electrical signal, which is amplified by the power amplifier and then excites the ultrasonic transducer to emit a plane wave acoustic field with a specific frequency and sufficient energy as an incident sound source;
[0048] A cascaded acoustic holographic encryption module, the cascaded acoustic holographic encryption module includes a plurality of acoustic holographic devices, a carrier bracket, a mobile rotating platform, and a liquid carrier container. The carrier container contains liquid, and the liquid surrounds the ultrasonic transducer, the acoustic holographic devices, and the carrier bracket to provide an environment for sound waves to propagate in the liquid. There are pores on the upper and lower layers of the carrier bracket that are close to the size of the acoustic holographic devices and are strictly aligned. The distance between the upper and lower layers of the carrier bracket is determined according to the distance between two acoustic holograms in the cascaded acoustic encryption calculation process. The acoustic holographic device placed on the lower layer comes from the main key group, and the acoustic holographic device placed on the upper layer comes from the secondary key group. The two acoustic holographic devices modulate the phase distribution of the plane wave acoustic field alone or cooperatively through phase modulation, which can not only separately reconstruct their respective reconstructed acoustic fields as their own identification marks, but also cooperate with each other to produce a reconstructed acoustic field and encrypted information different from that of a single acoustic holographic device. The mobile rotating platform drives the movement and rotation of the second acoustic holographic device, changing the three-dimensional spatial positions of the two acoustic holographic devices, which is used to increase the carrying capacity of the encrypted information;
[0049] A cascaded acoustic holographic decryption module, the cascaded acoustic holographic decryption module includes a full-automatic three-dimensional displacement platform, a hydrophone, an oscilloscope, and a system controller. Among them, the full-automatic three-dimensional displacement platform can receive the movement mode and parameters of the system controller to achieve fine movement in the three-dimensional full space. The hydrophone is placed on the three-dimensional displacement platform and can collect the acoustic field parameters of points, lines, planes, and three-dimensional full space and convert them into electrical signals. These electrical signals are further collected by the oscilloscope and sent to the system controller, and the system controller analyzes these electrical signals to achieve the decryption of acoustic information.
[0050] Specifically, the shapes of the multiple acoustic holographic devices of the cascaded acoustic holographic encryption module include, but are not limited to, circular, square, and elliptical; the materials for fabricating the acoustic holographic devices include, but are not limited to, resin and silicone rubber, and the fabrication processes include, but are not limited to, laser etching, 3D printing, casting molding, etc.
[0051] Furthermore, the ultrasonic excitation system in the sound field generation module can arbitrarily adjust ultrasonic parameters, including ultrasonic frequency, ultrasonic energy, ultrasonic pulse length, and ultrasonic pulse repetition frequency. The ultrasonic transducers include, but are not limited to, piezoelectric ultrasonic transducers, capacitive micromachined ultrasonic transducers (cMUT), piezoelectric micromachined ultrasonic transducers (pMUT), and other types of ultrasonic transducers.
[0052] The present invention also provides an acoustic encryption method based on cascaded holographic technology, which specifically includes the following steps:
[0053] S100. Use the cascaded acoustic hologram design method of the physical-driven neural network to accurately and efficiently obtain the phase distributions of multiple acoustic holograms carrying their own verification information and physically separated encrypted information.
[0054] S200. Design acoustic holographic devices capable of encoding the phase distributions of acoustic holograms through different phase modulation principles. The phase modulation principles include propagation phase modulation and amplitude-phase modulation. Among them, propagation phase modulation is achieved by changing the thickness of different positions on the surface of the transmission material, and amplitude-phase modulation is achieved by changing the pore sizes of different positions on the surface of the rigid material or using a microbubble array.
[0055] S300. Place the acoustic holographic devices at corresponding physical space positions. Each acoustic holographic device can reconstruct independent reconstructed sound fields at predetermined positions under the separate excitation of incident sound waves as its own verification information. When two acoustic holographic devices from different groups are accurately placed at corresponding space positions to form a corresponding acoustic encryption channel, the incident sound waves can be modulated by these two acoustic holographic devices to reconstruct a new reconstructed sound field different from the verification information of the two acoustic holographic devices at a predetermined position, that is, the encrypted information physically separated by the two acoustic holographic devices is reconstructed.
[0056] Among them, the specific steps included in the cascaded acoustic hologram design method of the physical-driven neural network in step S100 are as follows:
[0057] S101. Obtain m + n images containing verification information and m * n images containing encrypted information as the input of the method, and use m + n acoustic holograms as the output of the method.
[0058] S102. Construct a deep neural network. The structure of the deep neural network can adopt an encoding-decoding structure similar to the Unet network or other network structures for image reconstruction. The input of the network has m + n + m * n channels, and the size is the size of the image for verification or encryption information. The output of the network has m + n channels, and the size is the size of the phase distribution of the acoustic hologram.
[0059] S103. Construct m + n + m * n acoustic forward diffraction propagation functions. Among them, m + n are the incident plane acoustic waves modulated by m + n individual acoustic holograms, and m + n independent reconstructed sound fields are reconstructed at a predetermined position. The other m * n are the incident plane acoustic waves modulated by m * n cascaded acoustic holograms, and m * n reconstructed sound fields different from those reconstructed by a single acoustic hologram are reconstructed at a predetermined position.
[0060] S104. Construct the total network loss function. Compare the m + n independent reconstructed sound fields with m + n images containing verification information, calculate m + n mean square errors, and compare the m * n reconstructed sound fields different from those reconstructed by a single acoustic hologram with m * n images containing encryption information, calculate m * n mean square errors. Finally, average these m + n + m * n mean square errors to obtain the total network loss function.
[0061] S105. Obtain the gradient through the total network loss function obtained in step S104. This gradient is the derivative of the total network loss function with respect to the parameters (weights and biases) of the deep neural network.
[0062] S106. According to the gradient obtained in step S105, use the Adam (adaptive moment estimation) gradient descent optimization algorithm to update the parameters (weights and biases) of the deep neural network.
[0063] S107. Repeat steps S101 to S106 for multiple iterations. Continuously update the parameters (weights and biases) of the deep neural network during the iteration process to ensure that the total network loss function finally converges to a local optimum, find a set of network parameters that minimize the total network loss function. At the same time, the deep neural network outputs m + n optimized phase distributions of the acoustic hologram.
[0064] The specific method of the propagation phase modulation in step S200 is as follows: Use a resin material with a relatively high transmittance. According to the phase distribution of the target acoustic hologram, the sound speed of the resin material, and the sound speed information of the background environment, calculate the thickness of the resin protrusions at each position on the resin surface to ensure that the thickness can cover the phase modulation range from 0 to 2Π.
[0065] The specific method of amplitude-phase modulation is as follows: Use a rigid material with a low transmittance. According to the phase distribution of the target acoustic hologram, the sound velocity of the rigid material, and the sound velocity information of the background environment, calculate the positions and sizes of the pores at each position on the surface of the rigid material to achieve binary phase modulation of 0 and 1; or use a microbubble array, where the position corresponding to the phase of 0 is a microbubble and the position corresponding to the phase of 1 is a propagation medium, to achieve binary phase modulation of 0 and 1.
[0066] In the step S300, an acoustic holographic device is fabricated by processes such as laser etching, 3D printing, and casting molding, and then accurately placed at the corresponding physical space position. Each acoustic holographic device can reconstruct an independent reconstructed sound field at a predetermined position under the individual excitation of the incident sound wave as its own verification information; when two acoustic holographic devices from different groups are accurately placed at the corresponding spatial positions to form a corresponding acoustic encryption channel, the incident sound wave can be modulated by these two acoustic holographic devices to reconstruct a new reconstructed sound field different from the verification information of the two acoustic holographic devices at a predetermined position, that is, the encrypted information physically separated by the two acoustic holographic devices in the physical space is reconstructed, realizing the acoustic encryption technology based on cascaded holographic technology.
[0067] Example 1
[0068] Use the acoustic encryption device and method based on cascaded holographic technology to achieve the cascaded encryption of an encrypted message by two acoustic holographic lenses.
[0069] As Figure 3 shown, assume that the frequency of the ultrasonic transducer is 2 MHz, the input amplitude is 10 Vpp, the input pressure field is a plane sound wave, the phase distribution resolution of both acoustic holograms is 160×160 pixels, the simulated test environment is in water, and the sound velocity is 1500 m / s; design the digital "6" and digital "9" as the verification target images, and the letter "B" as the encrypted target image, and the resolution of the images is 160×160 pixels; when the first acoustic hologram is placed alone on the front surface of the ultrasonic transducer, the verification target image "6" is imaged at a position 4 cm away from the ultrasonic transducer; when the second acoustic hologram is placed alone along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer, the verification target image "9" is imaged at a position 4 cm away from the ultrasonic transducer; when the first acoustic hologram is placed on the front surface of the ultrasonic transducer and the second acoustic hologram is placed along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer to form a cascaded acoustic encryption channel, the encrypted target image "B" is imaged at a position 4 cm away from the ultrasonic transducer.
[0070] This implementation case includes the following steps:
[0071] Step 1: Use the cascade acoustic hologram design method of a physically-driven neural network proposed by the present invention to accurately and efficiently obtain the phase distributions of two acoustic holograms carrying two self-verification information and one physically separated encrypted information.
[0072] For this embodiment, the cascade acoustic hologram design method of the physically-driven neural network is as Figure 4 shown, and the specific steps included are:
[0073] 1) Use two images containing verification information and one image containing encrypted information as the input of the method, and use the phases of the two acoustic holograms as the output of the method;
[0074] 2) Construct a deep neural network. The structure of the deep neural network is intended to adopt a Unet network. This network includes a contracting path that captures context and a symmetric expanding path that supports precise localization. The contracting path and the expanding path are symmetric, forming a U-shaped architecture. The input of the network has three channels and a size of 160×160, and the output of the network has two channels and a size of 160×160. The contracting path first passes through two 3×3 convolutional layers to obtain shallow feature maps. Each convolutional layer is followed by a batch normalization (BN) and a LeakyReLU activation function. Then, use a 2×2 max pooling layer with a stride of 2 to perform downsampling on these feature maps and then pass them to the next block. In the next sampling step, the number of feature channels doubles and the image resolution is halved. The purpose of the expanding path of the U-Net is to map the extracted feature information to the output space. Use a 2×2 transposed convolutional layer, and each transposed convolutional layer is followed by a BN and a LeakyReLU activation function. Then, connect the corresponding cropped feature maps in the contracting path through skip connections. In the following layer, use two 3×3 convolutional layers, and each convolutional layer is followed by a BN and a LeakyReLU activation function to perform convolution on the connected feature maps to achieve learning and assembling more accurate outputs according to these feature information. In the last layer, use a 1×1 convolution to map 32 feature channels to two feature channels and output the phase distributions of the two acoustic holograms;
[0075] 3) Use the angular spectrum propagation theory to construct three forward diffraction propagation functions of sound waves. Two of them are that the incident plane sound waves are modulated by two separate acoustic holograms to reconstruct two independent reconstructed sound fields at a predetermined position, and the other one is that the incident plane sound wave is modulated by the cascade acoustic hologram to reconstruct a reconstructed sound field different from that reconstructed by a single acoustic hologram at a predetermined position;
[0076] 4) Construct the total network loss function. Compare the two independent reconstructed sound fields with two images containing verification information to calculate two mean squared errors. Also, compare a reconstructed sound field that is different from the one reconstructed from a single acoustic hologram with an image containing encrypted information to calculate one mean squared error. Finally, average these three mean squared errors to obtain the total network loss function.
[0077] 5) Obtain the gradient from the total network loss function obtained in step 4): This gradient is the derivative of the total network loss function with respect to the parameters (weights and biases) of the deep neural network.
[0078] 6) According to the gradient obtained in step 5), use the Adam (adaptive moment estimation) gradient descent optimization algorithm to update the parameters (weights and biases) of the deep neural network.
[0079] 7) Repeat steps 1) to 6) for multiple iterations. During the iteration process, continuously update the parameters (weights and biases) of the deep neural network to ensure that the total network loss function finally converges to a local optimum and find a set of network parameters that minimize the total network loss function. At the same time, the deep neural network outputs the phase distributions of two optimized acoustic holograms, as Figure 5 shown.
[0080] Step 2: Obtain the phase distributions of the two acoustic holograms obtained in Step 1 through the thickness map encoding step of the acoustic holographic lens. The specific method is as follows: Use a resin material with a relatively high transmittance. According to the phase distribution of the target acoustic hologram, the sound speed of the resin material, and the sound speed information of the background environment, calculate the thickness map of the resin protrusions at each position on the resin surface to ensure that the thickness can cover the phase modulation range from 0 to 2Π.
[0081] Step 3: After calculating the thickness map, use software for 3D modeling. After completing the modeling, two acoustic holographic lenses can be printed using a white resin material through a 3D printer.
[0082] According to the design, the size of the acoustic holographic lens processed in the embodiment is 55mm × 55mm, which contains 160 × 160 pixels. A relatively large pixel size is selected to facilitate the alignment of the cascaded stacked acoustic holographic lenses in the device as much as possible.
[0083] To experimentally verify the acoustic holographic lens samples processed in the embodiment and the acoustic characteristics of the cascaded acoustic holographic lens encryption channel formed by stacking according to a predetermined position as a secret sharing key, Figure 1The device shown conducts experimental verification on the processed acoustic holographic lens samples. In this implementation case, a self-made transducer with a diameter of 55 mm and a center frequency of 2 MHz is driven by a multifunctional waveform generator. The driving signal is a pulse signal with a frequency of 2 MHz, an amplitude of 10 Vpp, and a cycle number of 5. In the single acoustic holographic phase plate mode, the fabricated phase plate is placed separately on the front surface of the ultrasonic transducer. In the cascaded acoustic holographic phase plate mode, a 3D-printed two-layer resin bracket is used, with a square hole in the middle of each layer to support and fix two acoustic holographic phase plates, enabling them to maintain a preset distance and lateral alignment. In addition, a ring is added to the rear surface of the bottom bracket so that the first phase plate can be tightly connected to the ultrasonic transducer. The acoustic pressure field emitted by the transducer is modulated by a single or cascaded acoustic holographic phase plate and then scanned by a needle hydrophone. All data are recorded in a digital storage oscilloscope and processed with the system controller software. The needle hydrophone is placed at the imaging plane (4 cm) position and driven by a fully automatic three-dimensional moving platform. The scanning area of the target acoustic field is 30 mm × 30 mm, with a step size of 0.3 mm.
[0084] The theoretical simulations and experimental results are as Figure 6 shown. Figure 6 (a) show the theoretical simulations and experimental results of each acoustic holographic lens, where under the separate excitation of the incident acoustic wave, independent reconstructed acoustic fields are reconstructed in the imaging plane as verification information for themselves. Figure 6 (b) show the theoretical simulations and experimental results when two holographic lenses are precisely placed at corresponding spatial positions to form corresponding acoustic encryption channels. When the incident acoustic wave is modulated by these two acoustic holographic lenses, a new reconstructed acoustic field different from the verification information of the two acoustic holographic lenses is reconstructed in the imaging plane, that is, the encrypted information separated by the physical space where the two acoustic holographic lenses are located is reconstructed. These theoretical simulations and experimental results are highly consistent, realizing an acoustic secret sharing encryption technology for encrypted information.
[0085] In summary, this embodiment provides an acoustic encryption device and method based on cascaded holographic technology. The device and method can physically separate and dispersedly store encrypted information in the form of acoustic holograms between two key holders, realizing acoustic secret sharing of two acoustic holographic keys. Each acoustic hologram has an independent reconstructed sound field as its own verification information. When the two acoustic holograms are accurately placed at corresponding spatial positions, the entire cascaded acoustic holographic system can generate a new reconstructed sound field, i.e., the encrypted information. The reconstructed sound field of a single acoustic hologram is independent of the reconstructed sound field key of the cascaded acoustic hologram, so there is no mutual crosstalk and leakage between them. The key holder of any single acoustic hologram cannot crack the encrypted information alone. Only when the correct number of acoustic hologram keys are accurately placed at corresponding spatial positions can the encrypted information be read. Utilizing this feature, this cascaded acoustic holographic lens system and device can be applied to data storage, information security, holographic display, encryption, anti-counterfeiting and other fields that require hiding confidential data.
[0086] Embodiment 2
[0087] Use the acoustic encryption device and method based on cascaded holographic technology to achieve cascaded cross-combination encryption between two groups of acoustic holograms. Use one group containing one acoustic hologram as the main key group and another group containing two acoustic holograms as the secondary key group, and two independent encryption channels can be cross-combined to be used for dispersedly storing and encrypting two encrypted information, enhancing the information capacity and security of encryption.
[0088] In the second embodiment, as Figure 7As shown, assume that the frequency of the ultrasonic transducer is 2 MHz, the input amplitude is 10 Vpp, the input pressure field is a plane sound wave, the phase distribution resolution of the three acoustic holograms is 160×160 pixels, the simulation test environment is in water, and the sound speed is 1500 m / s; the numbers "6", "8" and "9" are designed as the verification target images, and the numbers "3" and the letter "B" are designed as the encrypted target images, and the resolution of the images is 160×160 pixels; when the first acoustic hologram is placed alone on the front surface of the ultrasonic transducer, the verification target image "6" is imaged at a position 4 cm away from the ultrasonic transducer; when the second acoustic hologram is placed alone along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer, the verification target image "9" is imaged at a position 4 cm away from the ultrasonic transducer; when the third acoustic hologram is placed alone along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer, the verification target image "8" is imaged at a position 4 cm away from the ultrasonic transducer; when the first acoustic hologram is placed on the front surface of the ultrasonic transducer and the second acoustic hologram is placed along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer to form a cascaded first acoustic encryption channel, the encrypted target image "B" is imaged at a position 4 cm away from the ultrasonic transducer; when the first acoustic hologram is placed on the front surface of the ultrasonic transducer and the third acoustic hologram is placed along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer to form a cascaded second acoustic encryption channel, the encrypted target image "3" is imaged at a position 4 cm away from the ultrasonic transducer.
[0089] This embodiment includes the following steps:
[0090] Step 1: Use the cascaded acoustic hologram design method of a physically driven neural network proposed by the present invention to accurately and efficiently obtain the phase distributions of three acoustic holograms carrying three self-verification information and two physically separated encrypted information.
[0091] This embodiment requires a total of three holograms, one belonging to the master key group and two belonging to the sub-key group, each corresponding to a verification image independent of each other; combine one hologram in the master key group and two holograms in the sub-key group respectively, and the two combination methods also each correspond to a target image independent of each other, that is, the two shared encrypted information stored separately.
[0092] For this embodiment, the cascaded acoustic hologram design method of the physically driven neural network is similar to Figure 4 and includes the following specific steps:
[0093] 1) Use three images containing verification information and two images containing encrypted information as the input of the method, and use the phases of the three acoustic holograms as the output of the method;
[0094] 2) Construct a deep neural network. The structure of the deep neural network is intended to adopt the Unet network. The specific structure is similar to that of the first embodiment, but the input of the network has five channel numbers and a size of 160×160, and the output of the network has three channel numbers and a size of 160×160;
[0095] 3) Use the angular spectrum propagation theory to construct five acoustic wave forward diffraction propagation functions. Among them, three are incident plane acoustic waves modulated by three separate acoustic holograms, and three independent reconstructed sound fields are reconstructed at a predetermined position. The other two are incident plane acoustic waves modulated by a cascaded acoustic hologram, and two reconstructed sound fields different from those reconstructed by a single acoustic hologram are reconstructed at a predetermined position;
[0096] 4) Construct a total network loss function. Compare the three independent reconstructed sound fields with three images containing verification information, calculate three mean square errors, and compare the two reconstructed sound fields different from those reconstructed by a single acoustic hologram with two images containing encrypted information, calculate two mean square errors. Finally, average these five mean square errors to obtain the total network loss function;
[0097] 5) Obtain the gradient through the total network loss function obtained in step 4). This gradient is the derivative of the total network loss function with respect to the parameters (weights and biases) of the deep neural network;
[0098] 6) According to the gradient obtained in step 5), use the Adam (adaptive moment estimation) gradient descent optimization algorithm to update the parameters (weights and biases) of the deep neural network;
[0099] 7) Repeat steps 1) to 6) for multiple iterations. During the iteration process, continuously update the parameters (weights and biases) of the deep neural network to ensure that the total network loss function converges to the local optimum finally, and find a set of network parameters that minimize the total network loss function. At the same time, the deep neural network outputs the phase distributions of three optimized acoustic holograms, as Figure 8 shown.
[0100] Step 2: Obtain the phase distributions of the three acoustic holograms obtained in step 1 through the thickness map encoding step of the acoustic holographic lens. The encoding is realized by the propagation phase modulation principle, and the specific method is similar to step 2 of the first embodiment.
[0101] Step 3: After calculating the thickness map, use software for 3D modeling. After completing the modeling, it can be printed using white resin material by a 3D printer to fabricate three acoustic holographic lenses.
[0102] According to the design, the size of the acoustic holographic lens processed in the embodiment is 55 mm × 55 mm, which contains 160 × 160 pixels. A relatively large pixel size is selected to facilitate the alignment of the cascaded and stacked acoustic holographic lenses in the device as much as possible.
[0103] To experimentally verify the acoustic holographic lens samples processed in the embodiment, and the acoustic characteristics of multiple cascaded acoustic holographic lens encryption channels formed by cross - combining and stacking according to predetermined positions as secret - sharing keys, Figure 2 the device shown in the figure was used to experimentally verify the processed acoustic holographic lens samples. The experimental device used in this implementation case is similar to that in the first embodiment.
[0104] The theoretical simulation and experimental results are as Figure 9 shown. Figure 9 (a) shows the theoretical simulation and experimental results that when each acoustic holographic lens is separately excited by an incident sound wave, independent reconstructed sound fields are reconstructed on the imaging plane as its own verification information; Figure 9 (b) shows that for a cascaded acoustic lens system composed of two sets of holographic lenses cross - combined, two new reconstructed sound fields different from the verification information of the two acoustic holographic lenses are reconstructed on the imaging plane, that is, two shared encrypted information stored in a cross - dispersed manner.
[0105] In summary, this embodiment provides an acoustic encryption device and method based on cascaded holographic technology, which can realize the cross - enhanced encryption mode of two or more sets of acoustic holograms. Using a set containing one acoustic hologram as the main key group and another set containing two acoustic holograms as the secondary key group, two independent encryption channels can be cross - combined to be used for dispersed storage and encryption of two encrypted information; taking advantage of this feature, this cascaded acoustic holographic lens system and device can carry more encrypted information and further enhance the security.
[0106] Embodiment Three
[0107] Use the acoustic encryption device and method based on cascaded holographic technology to realize three - dimensional space cascaded encryption between two acoustic holograms. By superimposing, moving, and rotating the two acoustic holograms, three different encryption channels are formed for dispersed storage and encryption of three encrypted information, enhancing the encrypted information capacity and security.
[0108] In the first implementation case, as Figure 10As shown, assume that the frequency of the ultrasonic transducer is 2 MHz, the input amplitude is 10 Vpp, the input pressure field is a plane sound wave, the phase distribution resolution of both acoustic holograms is 160×160 pixels, the simulation test environment is in water, and the sound speed is 1500 m / s; the digits "6" and "8" are designed as the verification target images, and the digits "3", the letter "B", and the letter "S" are designed as the encrypted target images, and the resolution of the images is all 160×160 pixels. When the first acoustic hologram is placed alone on the front surface of the ultrasonic transducer, the verification target image "6" is imaged at a position 6 cm away from the ultrasonic transducer; when the second acoustic hologram is placed alone along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer, the verification target image "8" is imaged at a position 6 cm away from the ultrasonic transducer; when the first acoustic hologram is placed on the front surface of the ultrasonic transducer and the second acoustic hologram is placed along the sound source propagation direction at a position 2 cm away from the ultrasonic transducer to form a cascaded first acoustic encryption channel, the encrypted target image "B" is imaged at a position 6 cm away from the ultrasonic transducer; when the first acoustic hologram is placed on the front surface of the ultrasonic transducer and the second acoustic hologram is placed along the sound source propagation direction at a position 3 cm away from the ultrasonic transducer and the second acoustic hologram is rotated counterclockwise by 90° to form a cascaded second acoustic encryption channel, the encrypted target image "3" is imaged at a position 6 cm away from the ultrasonic transducer; when the first acoustic hologram is placed on the front surface of the ultrasonic transducer and the second acoustic hologram is placed along the sound source propagation direction at a position 4 cm away from the ultrasonic transducer and the second acoustic hologram is rotated counterclockwise by 180° to form a cascaded third acoustic encryption channel, the encrypted target image "S" is imaged at a position 6 cm away from the ultrasonic transducer.
[0109] This embodiment includes the following steps:
[0110] Step 1: Use the cascaded acoustic hologram design method of a physically driven neural network proposed by the present invention to accurately and efficiently obtain the phase distributions of two acoustic holograms carrying two self-verification information and three physically separated encrypted information.
[0111] This embodiment requires a total of two holograms, each corresponding to an independent verification image; by changing the spatial position combination of the two holograms, the three combination methods also each correspond to an independent encrypted target image, that is, the three encrypted information to be stored.
[0112] For this embodiment, the cascaded acoustic hologram design method of the physically driven neural network is similar to Figure 3 and includes the following specific steps:
[0113] 1) Use two images containing verification information and three images containing encrypted information as the input of the method, and use the phases of the two acoustic holograms as the output of the method;
[0114] 2) Construct a deep neural network. The structure of the deep neural network is intended to adopt the Unet network. The specific structure is similar to that of the first embodiment, but the input of the network has five channel numbers and the size is 160×160, and the output of the network has two channel numbers and the size is 160×160.
[0115] 3) Use the angular spectrum propagation theory to construct five forward acoustic diffraction propagation functions. Among them, two are that the incident plane acoustic waves are modulated by two separate acoustic holograms, and two independent reconstructed sound fields are reconstructed at a predetermined position. The other three are that the incident plane acoustic waves are modulated by the cascaded acoustic holograms of three different encrypted channels after superposition, movement and rotation, and three reconstructed sound fields different from those reconstructed by a single acoustic hologram are reconstructed at a predetermined position;
[0116] 4) Construct the total network loss function. Compare the two independent reconstructed sound fields with two images containing verification information, calculate two mean square errors, and compare the three reconstructed sound fields different from those reconstructed by a single acoustic hologram with three images containing encrypted information, calculate three mean square errors, and finally average these five mean square errors to obtain the total network loss function;
[0117] 5) Obtain the gradient through the total network loss function obtained in step 4): This gradient is the derivative of the total network loss function with respect to the parameters (weights and biases) of the deep neural network;
[0118] 6) According to the gradient obtained in step 5), use the Adam (adaptive moment estimation) gradient descent optimization algorithm to update the parameters (weights and biases) of the deep neural network;
[0119] 7) Repeat steps 1) to 6) for multiple iterations. During the iteration process, continuously update the parameters (weights and biases) of the deep neural network to ensure that the total network loss function converges to the local optimum finally, and find a set of network parameters that minimize the total network loss function. At the same time, the deep neural network outputs the phase distributions of three optimized acoustic holograms, as Figure 11 shown.
[0120] Step 2: Obtain the phase distributions of the two acoustic holograms obtained in step 1 through the thickness map encoding step of the acoustic holographic lens. The encoding is realized by the propagation phase modulation principle, and the specific method is similar to step 2 of the first embodiment;
[0121] Step 3: After calculating the thickness map, use software for 3D modeling. After completing the modeling, it can be printed using white resin material by a 3D printer to fabricate two acoustic holographic lenses.
[0122] According to the design, the size of the acoustic holographic lens processed in the embodiment is 55 mm × 55 mm, which contains 160 × 160 pixels. A relatively large pixel size is selected to facilitate the alignment of the cascaded acoustic holographic lenses in the device as much as possible.
[0123] To experimentally verify the acoustic holographic lens samples processed in the embodiment, and to use the acoustic characteristics of the acoustic holographic lenses combined, moved, and rotated at predetermined positions in space as keys to form multiple cascaded acoustic holographic lens encryption channels, Figure 2 the device shown in the figure was used to experimentally verify the processed acoustic holographic lens samples. The experimental device used in this embodiment is similar to that in the first embodiment.
[0124] The theoretical simulation results are as Figure 12 shown. Figure 12 (a) shows the theoretical simulation and experimental results of each acoustic holographic lens reconstructing independent reconstructed sound fields in the imaging plane under the separate excitation of incident sound waves as its own verification information; Figure 12 (b)-(d) show that the cascaded acoustic lens system composed of two holographic lenses reconstructs three new reconstructed sound fields different from the verification information of the two acoustic holographic lenses in the imaging plane, that is, three encrypted messages stored.
[0125] In summary, this embodiment provides an acoustic encryption device and method based on cascaded holographic technology, which can realize an enhanced encryption mode with three different spatial combinations of two acoustic holograms. By using three different superpositions, movements, and rotations of the two acoustic holograms, three independent encryption channels can be formed for storing and encrypting three encrypted messages. Utilizing this feature, this cascaded acoustic holographic lens system and device can carry more encrypted messages and further enhance the security.
[0126] In the description of this specification, the descriptions referring to terms such as "one embodiment", "example", "specific example", etc. mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in a suitable manner in any one or more embodiments or examples.
[0127] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific embodiments described. Obviously, many modifications and variations can be made according to the content of this specification. These embodiments are selected and specifically described in this specification to better explain the principles and practical applications of the present invention, so that those skilled in the art can well understand and utilize the present invention. The present invention is only limited by the claims and their full scope and equivalents.
Claims
1. An acoustic encryption device based on cascade holography technology, characterized in that: include: An acoustic field generating module, wherein the acoustic field generating module comprises an ultrasonic excitation system and an ultrasonic transducer, wherein the ultrasonic excitation system comprises a signal generator and a power amplifier; A cascaded acoustic holographic encryption module, the cascaded acoustic holographic encryption module comprises a plurality of acoustic holographic devices, a bearing bracket, a mobile rotating platform and a liquid bearing container, the upper and lower layers of the bearing bracket each have a pore whose size is close to that of the acoustic holographic device and is strictly aligned, the distance between the upper and lower layers of the bearing bracket is determined according to the distance between two acoustic holograms in the cascade acoustic encryption calculation process, the acoustic holographic device placed on the lower layer comes from a primary key group, and the acoustic holographic device placed on the upper layer comes from a secondary key group, the two acoustic holographic devices individually or collaboratively modulate the phase distribution of the plane wave sound field by phase modulation, and can not only individually reconstruct their own reconstructed sound fields as their own identification marks, but also cooperate with each other to produce reconstructed sound fields and encrypted information that are different from those of a single acoustic holographic device, the mobile rotating platform drives the movement and rotation of the second acoustic holographic device, changes the three-dimensional spatial positions of the two acoustic holographic devices, and is used to improve the carrying capacity of encrypted information; The cascade acoustic holographic decryption module includes a fully automatic three-dimensional displacement platform, a hydrophone, an oscilloscope and a system controller, wherein the fully automatic three-dimensional displacement platform can receive the movement mode and parameters of the system controller to achieve fine movement in the three-dimensional space; the hydrophone is placed on the three-dimensional displacement platform, and can collect the sound field parameters of points, lines, planes and the three-dimensional space and convert them into electrical signals; these electrical signals are further collected by the oscilloscope and sent to the system controller; the system controller analyzes these electrical signals to achieve decryption of acoustic information.
2. The acoustic encryption device based on cascade holography technology according to claim 1, characterized in that: The signal generator transmits an electrical signal which is amplified by a power amplifier and then stimulates the ultrasonic transducer to transmit a plane wave sound field with a specific frequency and sufficient energy as an incident sound source.
3. The acoustic encryption device based on cascade holography technology according to claim 1, characterized in that: The carrying container carries liquid, and the liquid surrounds the ultrasonic transducer, the acoustic holographic device and the carrying bracket to provide an environment for sound waves to propagate in the liquid.
4. The acoustic encryption device based on cascade holography technology according to claim 1, characterized in that: The shapes of the multiple acoustic holographic devices of the cascaded acoustic holographic encryption module include but are not limited to circle, square, and ellipse; the materials for making the acoustic holographic devices include but are not limited to resin and silicone rubber; the manufacturing process includes but is not limited to laser etching, 3D printing, and casting molding.
5. The acoustic encryption device based on cascade holography technology according to claim 1, characterized in that: The ultrasonic excitation system in the sound field generating module can arbitrarily adjust ultrasonic parameters, including ultrasonic frequency, ultrasonic energy, ultrasonic pulse length, and ultrasonic pulse repetition frequency. The ultrasonic transducer includes but is not limited to piezoelectric ultrasonic transducers, capacitive micromechanical ultrasonic transducers (cMUT), piezoelectric micromechanical ultrasonic transducers (pMUT) and other types of ultrasonic transducers.
6. The encryption method of the acoustic encryption device based on cascade holography technology according to any one of claims 1 to 5, characterized in that: The following steps are involved: S100, using a cascade acoustic hologram design method of a physically driven neural network to accurately and efficiently obtain the phase distribution of multiple acoustic holograms carrying self-verification information and physically separated encrypted information; S200, designing an acoustic holographic device capable of encoding the phase distribution of an acoustic hologram through different phase modulation principles, wherein the phase modulation principles include propagation phase modulation and amplitude phase modulation, wherein the propagation phase modulation is achieved by changing the thickness at different positions on the surface of a transmission material, and the amplitude phase modulation is achieved by changing the pore size at different positions on the surface of a rigid material or by using a microbubble array; S300, placing the acoustic holographic devices at corresponding physical spatial positions, each acoustic holographic device can reconstruct independent reconstructed sound fields at predetermined positions as its own verification information under the individual excitation of the incident sound wave; when two acoustic holographic devices from different groups are precisely placed at corresponding spatial positions to form corresponding acoustic encryption channels, the incident sound waves are modulated by the two acoustic holographic devices, and a new reconstructed sound field different from the verification information of the two acoustic holographic devices can be reconstructed at the predetermined position, that is, the encrypted information physically separated by the two acoustic holographic devices is reconstructed.
7. The acoustic encryption method based on cascade holography technology according to claim 6 is characterized in that: The physically driven neural network cascade acoustic hologram design method comprises the following steps: S101, obtaining an image containing verification information and encryption information as an input of the method, and taking a plurality of acoustic holograms as an output of the method; S102, constructing a deep neural network, the input of which is an image containing verification information and encryption information, and the output of which is a phase distribution of an acoustic hologram, wherein the deep neural network may adopt a coding and decoding structure similar to a Unet network or other network structures for image reconstruction; S103, constructing a sound wave forward diffraction propagation function for simulating a reconstructed sound field after an incident plane sound wave is modulated by an acoustic hologram, wherein the sound wave forward diffraction propagation function may adopt an angular spectrum method or other sound wave diffraction propagation models; S104, constructing a network total loss function, comparing the reconstructed sound field with the target image, and calculating a mean square error, wherein the network total loss function may be an average value of multiple mean square errors; S105, updating the deep neural network parameters by using a gradient descent optimization algorithm, wherein the gradient descent optimization algorithm may adopt an Adam algorithm; S106. Repeat the above steps until the total loss function of the network converges to the local optimum, and output the optimized acoustic hologram phase distribution.
8. The acoustic encryption method based on cascade holography technology according to claim 6 is characterized in that: The phase modulation principle of the acoustic holographic device includes propagation phase modulation and amplitude phase modulation, wherein the propagation phase modulation is achieved by changing the thickness at different positions on the surface of the transmission material, and the amplitude phase modulation is achieved by changing the pore size at different positions on the surface of the rigid material or using a microbubble array. The transmission material can be a resin, and the rigid material can be a metal or a ceramic.
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