Fresnel Domain Research Articles

Interference probe ptychography for computational amplitude and phase microscopy.

We have developed an approach to Fresnel domain ptychography in which the illumination consists of an interference pattern. This pattern is conveniently created by overlapping two coherent beams at an angle. Only the phase and orientation of the interferometric fringe pattern needs to be scanned to reconstruct a high-fidelity object image, which alleviates the requirements for accurate sample positioning and system stability. As such, the resulting imaging systems can be constructed in an extremely simple and robust way. Object images are reconstructed from recorded Fresnel diffraction data using a modified ptychographical iterative engine. We demonstrate the capabilities of this imaging system by recording images of various biological samples, demonstrating quantitative phase contrast as well as a spatial resolution better than 2.2 μm.

Multi-depth three-dimensional image encryption based on the phase retrieval algorithm in the Fresnel and fractional Fourier transform domains.

We propose a multi-depth three-dimensional (3D) image cryptosystem by employing the phase retrieval algorithm in the Fresnel and fractional Fourier (Fr-FrF) domains. Encryption was realized by applying the phase retrieval algorithm based on the double-random-phase-encoding architecture in which two encryption keys will be incessantly updated in each iteration loop. The phase-only functions (POFs) are generated in two cascaded Fr-FrF transforms (Fr-FrFT), serving as decryption keys to efficiently reduce the speckle noise and crosstalk between encrypted 3D image depths. The use of Fr-FrFT position parameters and fractional order as decryption keys further extended the key space, enhancing the cryptosystem's security level. Numerical simulations demonstrated the feasibility and robustness of our proposed scheme.

Parallel encryption and hierarchical retrieval for multi-channel images using an optical joint Fresnel transform correlator

We propose an optical encryption method allowing the parallel encryption and hierarchical retrieval for multi-channel images based on a joint Fresnel transform correlator. In our designed scheme, the linear phase shift operation for the phase masks is utilized to achieve the aim of ensuring that the center of the complex amplitude distributions from the same group can overlap with each other in Fresnel domain, and the phase retrieval algorithm for designing the phase masks is used to avoid the cross talk between multi-channel images. The optimized phase masks can be flexibly reconfigured on the spatial light modulator without increasing the additional optical hardware and system complexity. Our designed scheme can encrypt multi-channel images simultaneously into a single cipher-text, which can also be used to recover arbitrary original images with corresponding keys. Thus, this method can achieve the aim of the hierarchical retrieval of encrypted images from a single cipher-text. Moreover, because the encryption process does not require any transformative lenses and accurate alignment of optical elements, the encryption scheme is easy to be optically implemented. Furthermore, compared with the previous JTC-based cryptosystems, the Fresnel diffraction distance and the position of the key masks in our proposed scheme can both be utilized as the additional encryption keys, which can enhance the security effectively. The theoretical analysis and numeric simulation results both validate the feasibility and effectiveness of the designed scheme.

Asymmetric encryption of multi-image based on compressed sensing and feature fusion with high quality image reconstruction

In this paper, an asymmetric multi-image encryption method based on compressed sensing (CS) and feature fusion is proposed. The spectrums of four grayscale images are obtained by optical wavelet transform (OWT) respectively. According to the different features of the wavelet spectral coefficient, the high-frequency and low-frequency components of four images are merged into a high-frequency fusion image (HFFI) and a low-frequency fusion image (LFFI) respectively, and then the HFFI is divided into two matrices after being measured by CS. Subsequently, the two matrices and the LFFI are encrypted to a single ciphertext by phase truncation (PT) and phase reservation (PR) in the Fresnel domain. This proposed scheme not only can successfully encrypt multi-image, but also can recover the primary image with high quality because of avoiding the loss of high-frequency information. Numerical simulations have demonstrated the security and effectiveness of the proposed method.

Sampling and Super Resolution of Sparse Signals Beyond the Fourier Domain

Recovering a sparse signal from its low-pass projections in the Fourier domain is a problem of broad interest in science and engineering and is commonly referred to as super-resolution. In many cases, however, Fourier domain may not be the natural choice. For example, in holography, low-pass projections of sparse signals are obtained in the Fresnel domain. Similarly, time-varying system identification relies on low-pass projections on the space of linear frequency modulated signals. In this paper, we study the recovery of sparse signals from low-pass projections in the Special Affine Fourier Transform domain (SAFT). The SAFT parametrically generalizes a number of well known unitary transformations that are used in signal processing and optics. In analogy to the Shannon's sampling framework, we specify sampling theorems for recovery of sparse signals considering three specific cases: (1) sampling with arbitrary, bandlimited kernels, (2) sampling with smooth, time-limited kernels and, (3) recovery from Gabor transform measurements linked with the SAFT domain. Our work offers a unifying perspective on the sparse sampling problem which is compatible with the Fourier, Fresnel and Fractional Fourier domain based results. In deriving our results, we introduce the SAFT series (analogous to the Fourier series) and the short time SAFT, and study convolution theorems that establish a convolution--multiplication property in the SAFT domain.

Two-Step Integral Imaging Coding Based Three-Dimensional Information Encryption Approach

We propose a two-step integral imaging coding based three-dimensional (3D) information encryption approach in this paper. In this approach, a synthetic aperture integral imaging system is applied to acquire a set of parallax images including spatial and angular information of 3D scene. In the encryption process, two-step coding is performed. In the first step, the acquired parallax images are encrypted firstly by double random-phase coding in the Fresnel domain. In the second step, these encrypted parallax images are encoded into a cipher image by mapping algorithm which is used to generate elemental image array of integral imaging. In the decryption process, an inverse operation is performed. The experimental results demonstrate the feasibility, security, and robustness of the proposed approach.

Single-channel optical encryption of color image using chessboard grating and diffraction imaging scheme

A single-channel encryption method for color images is proposed using chessboard grating and a phase-retrieval algorithm in the Fresnel domain. The pixel sampling operation is introduced to convert the color image to be encrypted into a Bayer image. Thereafter, with a single channel, the Bayer image is encoded by the chessboard grating before being sent into a diffractive-imaging-based encryption scheme. The cryptosystem is simple owing to only one single intensity pattern being required during encryption. In the decryption procedure, the phase-retrieval algorithm and the chessboard grating are combined to extract the plaintext from the intensity pattern. This proposal not only can successfully encrypt a color image into a single diffractive intensity pattern but also can recover the primary color image with high quality from the one single diffraction pattern with a compact optical setup. Numerical simulations are carried out to prove the feasibility and validity of the proposal.

Asymmetric optical image encryption using Kolmogorov phase screens and equal modulus decomposition

An asymmetric technique for optical image encryption is proposed using Kolmogorov phase screens (KPSs) and equal modulus decomposition (EMD). The KPSs are generated using the power spectral density of Kolmogorov turbulence. The input image is first randomized and then Fresnel propagated with distance d. Further, the output in the Fresnel domain is modulated with a random phase mask, and the gyrator transform (GT) of the modulated image is obtained with an angle α. The EMD is operated on the GT spectrum to get the complex images, Z1 and Z2. Among these, Z2 is reserved as a private key for decryption and Z1 is propagated through a medium consisting of four KPSs, located at specified distances, to get the final encrypted image. The proposed technique provides a large set of security keys and is robust against various potential attacks. Numerical simulation results validate the effectiveness and security of the proposed technique.

Lensless Fourier transform holography for coherence waves

Coherence functions behave like a wave and follow two–four dimensional wave equations. Utilizing this feature, we propose a lensless Fourier transform holography for coherence waves. Experimental demonstration is carried out by synthesizing the coherence function of a stationary random field as a superposition of two independent coherence functions in the Fresnel domain. Using the connection between two point intensity correlation and coherence function for the Gaussian random field, the application of this technique is demonstrated in imaging through a random scatterer in a lensless geometry from a single measurement of the speckle field.

Asymmetric optical cryptosystem based on modulus decomposition in Fresnel domain

We propose a scheme of attacking the pure phase asymmetric optical cryptosystem based on equal modulus decomposition (EMD) method. The cryptosystem is proven to be vulnerable to our modified iterative algorithm, even though the applying of phase encoding can reduce the constrain conditions. Furthermore, since that the improvement of system space asymmetry and key variety is an effective way to further enhance the security, we have proposed an asymmetric cryptosystem based on modulus decomposition in Fresnel domain. Compared with traditional asymmetric cryptosystem in Fourier domain, the combination with Fresnel transform cannot only simplify the system, but also improve the space asymmetry and introduce the geometric parameters as security keys. Numerical simulations are performed to demonstrate the feasibility and security of the proposed cryptosystem. In addition, several exemplary schemes for security-enhanced asymmetric cryptosystems are presented, which may bring profound illumination to many deeper researches in asymmetric optical cryptosystem.

Optical image encryption using Kronecker product and hybrid phase masks

In this paper, we propose a new technique for security enhancement in optical image encryption system. In this technique we have used the Kronecker product of two random matrices along with the double random phase encoding (DRPE) scheme in the Fresnel domain for optical image encryption. The phase masks used here are different than the random masks used in conventional DRPE scheme. These hybrid phase masks are generated by using the combination of random phase masks and a secondary image. For encryption, the input image is first randomized and then the DRPE in the Fresnel domain is performed using the hybrid phase masks. Secondly, the Kronecker product of two random matrices is multiplied with the DRPE output to get the final encoded image for transmission. The proposed technique consists of more unknown keys for enhanced security and robust against various attacks. The simulation results along with effects under various attacks are presented in support of the proposed technique.

Secret shared multiple-image encryption based on row scanning compressive ghost imaging and phase retrieval in the Fresnel domain

A multiple-image encryption method is proposed that is based on row scanning compressive ghost imaging, (t, n) threshold secret sharing, and phase retrieval in the Fresnel domain. In the encryption process, after wavelet transform and Arnold transform of the target image, the ciphertext matrix can be first detected using a bucket detector. Based on a (t, n) threshold secret sharing algorithm, the measurement key used in the row scanning compressive ghost imaging can be decomposed and shared into two pairs of sub-keys, which are then reconstructed using two phase-only mask (POM) keys with fixed pixel values, placed in the input plane and transform plane 2 of the phase retrieval scheme, respectively; and the other POM key in the transform plane 1 can be generated and updated by the iterative encoding of each plaintext image. In each iteration, the target image acts as the input amplitude constraint in the input plane. During decryption, each plaintext image possessing all the correct keys can be successfully decrypted by measurement key regeneration, compression algorithm reconstruction, inverse wavelet transformation, and Fresnel transformation. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.

Compact, cost-effective and field-portable microscope prototype based on MISHELF microscopy

We report on a reduced cost, portable and compact prototype design of lensless holographic microscope with an illumination/detection scheme based on wavelength multiplexing, working with single hologram acquisition and using a fast convergence algorithm for image processing. All together, MISHELF (initials coming from Multi-Illumination Single-Holographic-Exposure Lensless Fresnel) microscopy allows the recording of three Fresnel domain diffraction patterns in a single camera snap-shot incoming from illuminating the sample with three coherent lights at once. Previous implementations have proposed an illumination/detection procedure based on a tuned (illumination wavelengths centered at the maximum sensitivity of the camera detection channels) configuration but here we report on a detuned (non-centered ones) scheme resulting in prototype miniaturization and cost reduction. Thus, MISHELF microscopy in combination with a novel and fast iterative algorithm allows high-resolution (μm range) phase-retrieved (twin image elimination) quantitative phase imaging of dynamic events (video rate recording speed). The performance of this microscope prototype is validated through experiments using both amplitude (USAF resolution test) and complex (live swine sperm cells and flowing microbeads) samples. The proposed method becomes in an alternative instrument improving some capabilities of existing lensless microscopes.

Synthesis and reconstruction of multi-plane phase-only Fresnel holograms

Multi-plane phase-only Fresnel holograms have been synthesized using iterative phase retrieval algorithm. The combination of modified Gerchberg-Saxton algorithm and compensation iterative algorithm has been used for extracting the phase function from a complex multi-plane object function in the Fresnel domain. The combination helps synthesize phase-only holograms having high diffraction efficiencies. In this study, phase-only Fresnel holograms for three- and four-plane objects have been synthesized by taking object of different sizes and placing them in different planes of varying window sizes. The diffraction efficiency and mean square error of the reconstructed images in different planes of multi-plane objects have been calculated, which confirm the good quality of reconstructed images. Numerical simulation results have been presented. Three-dimensional recognition of multi-plane objects has also been presented using the obtained phase-only hologram. This study would help understand the reconstruction patterns of different planes of a multi-plane object which will be helpful in improving the reconstruction quality for three-dimensional holographic display.

EEG based image encryption via quantum walks.

An electroencephalogram (EEG) based image encryption combined with Quantum walks (QW) is encoded in Fresnel domain. The computational version of EEG randomizes the original plaintext whereas QW can serve as an excellent key generator due to its inherent nonlinear chaotic dynamic behavior. First, a spatially coherent monochromatic laser beam passes through an SLM, which introduces an arbitrary EEG phase-only mask. The modified beam is collected by a CCD. Further, the intensity is multiply with the QW digitally. EEG shows high sensitivity to system parameters and capable of encrypting and transmitting the data whereas QW has unpredictability, stability and non-periodicity. Only applying the correct keys, the original image can be retrieved successfully. Simulations and comparisons show the proposed method to be secure enough for image encryption and outperforms prior works. The proposed method opens the door towards introducing EEG and quantum computation into image encryption and promotes the convergence between our approach and image processing.

Encrypting 2D/3D image using improved lensless integral imaging in Fresnel domain

We propose a new image encryption technique, for the first time to our knowledge, combined Fresnel transform with the improved lensless integral imaging technique. In this work, before image encryption, the input image is first recorded into an elemental image array (EIA) by using the improved lensless integral imaging technique. The recorded EIA is encrypted into random noise by use of two phase masks located in the Fresnel domain. The positions of phase masks and operation wavelength, as well as the integral imaging system parameters are used as encryption keys that can ensure security. Compared with previous works, the main novelty of this proposed method resides in the fact that the elemental images possess distributed memory characteristic, which greatly improved the robustness of the image encryption algorithm. Meanwhile, the proposed pixel averaging algorithm can effectively address the overlapping problem existing in the computational integral imaging reconstruction process. Numerical simulations are presented to demonstrate the feasibility and effectiveness of the proposed method. Results also indicate the high robustness against data loss attacks.

Asymmetric Multiple-Image Encryption Based on Octonion Fresnel Transform and Sine Logistic Modulation Map

A novel asymmetric multiple-image encryption method using an octonion Fresnel transform (OFST) and a two-dimensional Sine Logistic modulation map (2D-SLMM) is presented. First, a new multiple-image information processing tool termed the octonion Fresneltransform is proposed, and then an efficient method to calculate the OFST of an octonion matrix is developed. Subsequently this tool is applied to process multiple plaintext images, which are represented by octonion algebra, holistically in a vector manner. The complex amplitude, formed from the components of the OFST-transformed original images and modulated by a random phase mask (RPM), is used to derive the ciphertext image by employing an amplitude- and phase-truncation approach in the Fresnel domain. To avoid sending whole RPMs to the receiver side for decryption, a random phase mask generation method based on SLMM, in which only the initial parameters of the chaotic function are needed to generate the RPMs, is designed. To enhance security, the ciphertext and two decryption keys produced in the encryption procedure are permuted by the proposed SLMM-based scrambling method. Numerical simulations have been carried out to demonstrate the proposed scheme's validity, high security, and high resistance to various attacks.

Hierarchical multilevel authentication system for multiple-image based on phase retrieval and basic vector operations

A hierarchical multilevel authentication system for multiple-image based on phase retrieval and basic vector operations in the Fresnel domain is proposed, by which more certification images are iteratively encoded into multiple cascaded phase masks according to different hierarchical levels. Based on the secret sharing algorithm by basic vector decomposition and composition operations, the iterated phase distributions are split into n pairs of shadow images keys (SIKs), and then distributed to n different participants (the authenticators). During each level in the high authentication process, any 2 or more participants can be gathered to reconstruct the original meaningful certification images. While in the case of each level in the low authentication process, only one authenticator who possesses a correct pair of SIKs, will gain no significant information of certification image; however, it can result in a remarkable peak output in the nonlinear correlation coefficient of the recovered image and the standard certification image, which can successfully provide an additional authentication layer for the high-level authentication. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.

Hierarchical multiple binary image encryption based on a chaos and phase retrieval algorithm in the Fresnel domain

Based on the chaos and phase retrieval algorithm, a hierarchical multiple binary image encryption is proposed. In the encryption process, each plaintext is encrypted into a diffraction intensity pattern by two chaos-generated random phase masks (RPMs). Thereafter, the captured diffraction intensity patterns are partially selected by different binary masks and then combined together to form a single intensity pattern. The combined intensity pattern is saved as ciphertext. For decryption, an iterative phase retrieval algorithm is performed, in which a support constraint in the output plane and a median filtering operation are utilized to achieve a rapid convergence rate without a stagnation problem. The proposed scheme has a simple optical setup and large encryption capacity. In particular, it is well suited for constructing a hierarchical security system. The security and robustness of the proposal are also investigated.

Incoherent ptychography in Fresnel domain with simultaneous multi-wavelength illumination

Single wavelength illumination is used in the traditional ptychography. Even though using multi-wavelength to improve image quality, it takes the scheme of illuminating in turn due to the requirement of coherence. So far, the addition of incoherent modes has been regarded as a nuisance in diffractive imaging. Here we propose a scheme of incoherent ptychography and an algorithm of information multiplexing that uses the multi-wavelength illumination simultaneously, which are demonstrated in experiment and simulation. Compared with the scheme of traditional ptychography, it can recover not only the object well, but also the spectral response of the object, probes of complex value and spectral weight of each wavelength respectively. This method obtains much information about the object and owns the multichannel and multispectral merits. Meanwhile, by means of color image coding, this method can retrieve true color images and enhance the image quality. The proposed algorithm has strong robustness. Besides, we also investigate how many modes can be recovered by this method. The work may open up possibilities for information multiplexing in ptychography and multispectral microscopy imaging over various applications.