Fresnel Domain Research Articles

Dual-optical-multiplexing-based multi-image invisible visual cryptography

In earlier research, the concept of using diffractive optics to indirectly achieve invisible visual cryptography (VC) was proposed. In this approach, the extraction process does not require complex optical implementations or additional computations. However, the system’s security and the capacity still need to be improved. Correspondingly, this paper introduces a multi-image invisible VC system based on dual optical multiplexing. Under the conditions of diffraction distance multiplexing and wavelength multiplexing, the visual keys of secret images are concealed within a phase key in the Fresnel domain. This method enhances the system’s security through dual optical multiplexing and ensures a certain capacity for information concealment. Optical experiments verify that the easy extraction and the high repeatability are all obtainable in the method.

Structural-color meta-nanoprinting embedding multi-domain spatial light field information

Abstract Recently, multifunctional metasurface has showcased its powerful functionality to integrate nanoprinting and holography, and display ultracompact meta-images in near- and far-field simultaneously. Herein, we propose a tri-channel metasurface which can further extend the meta-imaging ranges, with three independent images located at the interface, Fresnel and Fourier domains, respectively. Specifically, a structural-color nanoprinting image is decoded right at the interface of the metasurface, enabled by varying the dimensions of nanostructures; a Fresnel holographic image and another Fourier holographic image are present at the Fresnel and Fourier (far-field) domains, respectively, enabled by geometric phase. The spectral and phase manipulation capabilities of nanostructures have been maximized, and the spatial multiplexing capabilities for diffraction in metasurfaces have also been fully exploited. By leveraging the design freedom enabled through the tuning of the geometric size and orientation of nanostructures, as well as optimizing the diffraction spatial light wave transformation, the encoding of multiple images on the single-celled metasurface is achieved. More interestingly, due to the spatial separation of images across different channels, crosstalk is virtually eliminated, effectively enhancing imaging quality. The proposed metasurface offers several advantages, including a compact design, easiness of fabrication, minimal crosstalk, and high storage density. Consequently, it holds promising applications in image display, data storage, information encryption, anti-counterfeiting, and various other fields.

Fresnel Domain Sector Modulation LFM Signal for Underwater Integrated Communication and Detection

Fresnel Domain Sector Modulation LFM Signal for Underwater Integrated Communication and Detection

Optical double-image cryptosystem based on phase truncation in the Fresnel domain

Optical double-image cryptosystem based on phase truncation in the Fresnel domain

Modified optical multi-image hiding method with a physics-driven neural network

Optics has been verified to play a significant role in the advancement of multiple-image hiding. However, due to the diversity and unrelatedness of hidden information, the quality and quantity of the secret images extracted cannot be guaranteed at the same time. Although various optimized methods have been proposed to enhance the capacity of the system by reducing the crosstalk between the extracted information, the extraction results still suffer from a low signal-to-noise ratio. Here, we propose the modified optical multi-image hiding method in phase cascade system with a physics-driven neural network (MIHNet). The multiple secret images are the only input to the MIHNet which is a physics-driven deep neural network to generate phase keys. The phase keys can independently reproduce the hidden images with higher quality in the Fresnel domain. Simulation results show that the hiding capacity of the proposed method is not only approximately twice that of our previous optimization algorithm (Shi et al., 2007), but also the signal-to-noise ratio of the extracted images are significantly improved. In addition, the feasibility of the proposed method is also demonstrated in metasurface holography.

Convolution, Correlation and Generalized Shift Operations Based on the Fresnel Transform.

The Fresnel transform (FrT) is commonly used to describe the free-space propagation of optical waves. In this work, we present new definitions for the convolution, correlation and generalized shift operations based on the FrT. The generalized shift operation is defined by using simultaneous space and phase shifts. The generalized shift operation is useful for centred optical systems in the Fresnel domain (FrD) when the data distributions at the input plane of the optical system are shifted. The new convolution and correlation operations defined in terms of the FrT, the wavelength and the propagation distance, can be considered as a generalization of the usual convolution and correlation operations. The sampling theorem for distributions, whose resulting FrT has finite support, is formulated by using the new convolution operation introduced in this work and a new definition of the Dirac comb function. These new definitions and results could be applied to describe, design and implement optical processing systems related to the FrT. Finally, we present a centred optical systems used in holography and optical security systems that can be described or modelled by the new definitions of the operations proposed in this paper.

SDFnT-Based Parameter Estimation for OFDM Radar Systems with Intercarrier Interference

The orthogonal frequency division multiplexing (OFDM) radar suffers from severe performance degradation in range-velocity estimation in high mobility scenarios. In this paper, a novel intercarrier interference (ICI)-free parameter estimation method for OFDM radar is proposed. By employing a scale discrete Fresnel transform (SDFnT), the OFDM radar signals are converted to the scale Fresnel domain, and the orthogonality of subcarriers can be recovered with the optimal scale factor. Furthermore, due to the compatibility of the SDFnT and the discrete Fourier Transform (DFT), the proposed method has low computational complexity and high feasibility for OFDM radar implementation. Simulation results show that the proposed SDFnT-based scheme effectively eliminates the ICI effect for single and multiple targets and achieves high accuracy delay-Doppler estimation for OFDM radar systems in circumstances of high velocity and low SNR with consistency and robustness.

Multiuser optical image authentication platform based on sparse constraint and polar decomposition in Fresnel domain

In this paper, a new multiuser optical image encryption and authentication technique is proposed. Sparse multiplexing and polar decomposition are used in the Fresnel domain to obtain the ciphertext of an input image. To enable the multiuser platform, multiple private keys are obtained through polar decomposition during the encryption process. It will allow multiple authorized users to access the secure information simultaneously without having a key distribution problem among them. The proposed method has a large key space and is robust against several attacks, such as contamination attacks (noise and occlusion), brute force attack, plaintext attacks, and special iterative attack. A comparative analysis of the presented technique is also performed with the similar existing techniques. The numerical simulation results demonstrate the robustness and feasibility of the proposed algorithm.

Asymmetric double-image encryption based on chaotic random phase encoding.

An asymmetric double-image encryption scheme based on chaotic random phase encoding (CRPE) is proposed. In this proposed encryption scheme, two grayscale images to be encrypted are first Fresnel transformed and combined into a complex image. Then, the amplitude and phase components are obtained by conducting phase-amplitude truncation on the complex image. Finally, the amplitude component is again Fresnel transformed and encrypted into a noise-like pattern by the CRPE in the Fresnel domain. Since the initial values and control parameters of the chaotic map can replace the random phase masks to serve as secret keys, the management and transmission of secret keys will become more convenient in the proposed encryption scheme. Furthermore, the Fresnel transform parameters and phase keys derived from the complex image's phase component can also act as secret keys during the decryption process. Numerical simulations have demonstrated the feasibility, security, and robustness of the proposed encryption scheme.

Correlation operation in the Fresnel domain and truncation operations applied to the simultaneous encryption of two images

A new nonlinear encryption-decryption scheme for two images using: double random phase encoding (DRPE), random phase masks (RPMs), amplitude and phase encoding, correlation operation in Fresnel domain (FrD) and truncation operations (amplitude truncation, AT and phase truncation, PT), is proposed. AT and PT are operations that work on complex-valued functions (images) in a nonlinear way, with the purpose of selecting the information contained in a complex-valued image, respectively. The first step of the encryption scheme is encoding two original images in amplitude and phase. The encryption or decryption scheme utilizes the correlation operation in FrD, AT, PT and two RPMs in a specific way to obtain the encrypted or decrypted images. The use of the AT and PT operations allow a better security of the encryption and decryption schemes because the nonlinearities introduced by these operations and the generation of two new encryption keys. The encrypted image of this proposal is real valued and the correlation operation in FrD introduces two new keys improving the security of the encryption and decryption schemes. The keys of the proposed security schemes are six and the right values of these all keys have to be used in the decryption scheme to recover the two initial images used in the input of the encryption scheme.

Joint Channel Estimation and Schmidl & Cox Synchronization for OCDM-Based Systems

This letter proposes a joint channel estimation and Schmidl & Cox synchronization for the orthogonal chirp-division multiplexing (OCDM) scheme. First, it is proven that a symbol composed of two identical halves in the Fresnel domain has two identical halves in the time domain, which is required by the considered synchronization technique. In sequel, a Fresnel-domain pilot symbol that enables joint channel estimation and synchronization is proposed, allowing overhead reduction and hence higher data rates. Finally, measurement and simulation results validate the obtained findings for both passband and baseband OCDM schemes.

An Optical Image Encryption Method Using Hopfield Neural Network.

In this paper, aiming to solve the problem of vital information security as well as neural network application in optical encryption system, we propose an optical image encryption method by using the Hopfield neural network. The algorithm uses a fuzzy single neuronal dynamic system and a chaotic Hopfield neural network for chaotic sequence generation and then obtains chaotic random phase masks. Initially, the original images are decomposed into sub-signals through wavelet packet transform, and the sub-signals are divided into two layers by adaptive classification after scrambling. The double random-phase encoding in 4f system and Fresnel domain is implemented on two layers, respectively. The sub-signals are performed with different conversions according to their standard deviation to assure that the local information’s security is guaranteed. Meanwhile, the parameters such as wavelength and diffraction distance are considered as additional keys, which can enhance the overall security. Then, inverse wavelet packet transform is applied to reconstruct the image, and a second scrambling is implemented. In order to handle and manage the parameters used in the scheme, the public key cryptosystem is applied. Finally, experiments and security analysis are presented to demonstrate the feasibility and robustness of the proposed scheme.

Security-enhanced multiple-image encryption based on modified iterative phase retrieval algorithm with structured phase mask in Fresnel domain

A security-enhanced multiple-image encryption method is proposed based on modified iterative phase retrieval algorithm with structured phase mask in Fresnel domain in this paper, where each plaintext is encoded to only one independent phase-only mask with the help of the used structured phase mask, and a group of phase-only masks retrieved by multiple plaintexts are integrated into the ciphertext with the noise-like distribution by using the phase mask multiplexing technique. In the proposed method, the Fresnel diffraction distances and the wavelength of light as well as the optical parameters of the structured phase mask such as focal length, topological charge number are all used as digital keys to expand the key space. Most importantly, the sensitivities of the digital keys are substantially improved by mapping the digital keys with the initial values of chaotic system thanks to the nonlinear, pseudo-random, high sensitivity of initial value of special phase generated by chaotic system, contributing to an extremely high security of multiple-image encryption method. Moreover, computational simulations are performed to demonstrate the feasibility of the proposed security-enhanced multiple-image encryption method, and the simulation results confirm that the proposed method exhibits high effectiveness and strong robustness.

Imaging Through Random Scatterer with Spatial Coherence Structure Measurement

Optical coherence is becoming an efficient degree of freedom for light field manipulations and applications. In this work, we show that the image information hidden a distance behind a random scattering medium is encoded in the complex spatial coherence structure of a partially coherent light beam that generates after the random scatterer. We validate in experiment that the image information can be well recovered with the spatial coherence measurement and the aid of the iterative phase retrieval algorithm in the Fresnel domain. We find not only the spatial shape but also the position including the lateral shift and longitudinal distances of the image hidden behind the random scatterer can be reconstructed, which indicates the potential uses in three-dimensional optical imaging through random scattering media.

Optical information encryption based on partially-update iterative system with azimuth multiplexing

This paper introduces an optical information encryption method based on partially-update iteration system with azimuth multiplexing. Multiple high-definition pictures are stored in multiple QR codes as amplitude constraints, and then encrypted in Fresnel domain by azimuth multiplexing. Due to the proposal of the enhancement system with partial update of the phase mask, the number of pictures can be encrypted increases. The security of the system is guaranteed by azimuth multiplexing, and the multiplexing capacity is jointly guaranteed by phase partial update system and QR code. The decoded QR code can extract the encrypted information without much quality loss. Simulation results show that the scheme has a large-capacity information storage, high security, robustness and practicability.

Optical encryption using phase modulation generated by thermal lens effect

We present the implementation of an experimental optical encryption configuration in the Fresnel domain using the thermal lens (TL) effect to modulate the phase of the illumination beam. We corroborate the basic performance of our cryptosystem by performing the encryption-decryption procedure of a single object. Then, we test the tolerance of the proposed scheme to decryption with keys registered for different modulations of the illumination beam induced by the phase generated due to TL effect. These different phase modulations are obtained by introducing axial displacements of a sample, where the TL effect is induced by an excitation beam (EB). Considering the phase modulation changes in the illumination due to sample displacements, we propose an undercover procedure to further protect the target information using decoy data. The key associated with the target information is obtained when the probe beam (PB) and EB are focused on the same point of the sample, while the decoy object key is registered when the beams are not focused on the same region of the sample. Finally, we analyzed the resistance of the undercover ciphertext to some of the attacks reported in the literature. All experimental results presented in this work demonstrate the basic capabilities, viability, and versatility of our proposals.

Audio and image encryption scheme based on QR decomposition and random modulus decomposition in Fresnel domain

In this paper, an asymmetric audio and image encryption mechanism using QR decomposition and random modulus decomposition (RD) in the Fresnel domain is proposed. The audio file is recorded as a vector and converted to a two-dimensional array to act as an image or a sound map. This sound map is encrypted using the image encryption algorithm proposed in this paper. The proposed cryptosystem is validated for both audios and grayscale images. Fresnel parameters and the two private keys obtained from QR decomposition and random modulus decomposition (RD) form the key space. Computer-based reproductions have been carried out to prove the validity and authenticity of the scheme. Simulation results authenticate that the scheme is robust and efficient against various attacks and is sensitive to input parameters.

Asymmetric double image encryption, compression and watermarking scheme based on orthogonal-triangular decomposition with column pivoting

A novel asymmetric scheme for double image encryption, compression and watermarking based on QR decomposition in the Fresnel domain has been presented. The QR decomposition provides a permutation matrix as a ciphertext and the product of orthogonal and triangular matrix as a key. The ciphertext obtained through this process is a sparse matrix that is compressed by the CSR method to give compressed encrypted data, which, when combined with a host image, gives a watermarked image. Thus, a cryptosystem that involves compression and watermarking is proposed. The proposed scheme is validated for grayscale images. To check the efficacy of the proposed scheme, histograms, statistical parameters, and key sensitivity are analyzed. The scheme is also tested against various attacks. Numerical simulations are performed to validate the security of the scheme.

Optimized Fresnel phase hologram for ringing artifacts removal in lensless holographic projection.

Ringing artifacts are the main noise sources in holographic projection when the quadratic phase is introduced to suppress speckle noise. In this study, the mechanisms of ringing artifacts on reconstructed images are theoretically analyzed, which illustrates the ringing artifacts are related to the bandwidth properties of the reconstructed wave field. Based on the frequency analysis, a band-limited iterative algorithm is proposed to optimize the phase hologram in the Fresnel domain. The proposed method can effectively suppress the ringing artifacts as well as the speckle noise of the Fresnel hologram by optimizing the phase distribution with bandwidth constraint. Numerical simulations and optical experiments have been performed to validate the proposed method for providing quality reconstructions in lensless holographic projection.

Optical image encryption and authentication using phase-only computer-generated hologram

Optical and photonics techniques such as computer-generated holograms (CGHs) are suggested to be used in security applications. In this paper, we present an approach to generate an authenticable phase-only hologram (APOH) for steganographic optical image encryption with phase optimization. The phase hologram can be calculated by the proposed integrated two-stage optimization method where Fresnel domain optimized random phase (OARP) method and modified two-step iterative Fourier transform algorithm under phase constraints are involved. The computer-generated APOH can be respectively verified and decrypted with an authentication key (A-key) and a decryption key(D-key). Numerical and experiment results prove the validity and security of the proposed approach, which offers a new method of holographic encryption for optical images.