Image encryption using fractional Mellin transform,structured phase filters,and phase retrieval

An image encryption scheme has been presented by using two structured phase masks in the fractional Mellin transform (FrMT) plane of a system, employing a phase retrieval technique. Since FrMT is a non-linear integral transform, its use enhances the system security. We also add further security features by carrying out spatial filtering in the frequency domain by using a combination of two phase masks: a toroidal zone plate (TZP) and a radial Hilbert mask (RHM). These masks together increase the key space making the system more secure. The phase key used in decryption has been obtained by applying an iterative phase retrieval algorithm based on the fractional Fourier transform. The algorithm uses amplitude constraints of secret target image and the ciphertext (encrypted image) obtained from multiplication of fractional Mellin transformed arbitrary input image and the two phase masks (TZP and RHM). The proposed encryption scheme has been validated for a few grayscale images, by numerical simulations. The efficacy of the scheme has been evaluated by computing mean-squared-error (MSE) between the secret target image and the decrypted image. The sensitivity analysis of the decryption process to variations in various encryption parameters has also been carried out.     

波前编码系统相位板视场效应的消除

通过在光学系统的光阑面上加入一个非球面相位板,使得光学系统的成像对离焦不敏感.但当入射视场角较大时,图像的边缘发生变形且难以恢复.针对此问题,提出了两种解决方案,方案一是把相位板移至光路中光线较为平缓的区域,但不是系统的光阑位置;方案二是保持相位板位置不变,优化整个光学系统,使相位板前的光线能够平缓地入射到相位板.实验中对一个EFL=12.5 mm,F/#=1.3,半视场角为13.5°的波前编码实际系统进行仿真比较,得出方案二可以有效地消除波前编码相位板引入的视场效应.     

Optimized phase pupil masks for extended depth of field

By properly designing a phase pupil mask to modulate or encode the optical images and then digitally restoring them, one can greatly extend the depth of field and improve image quality. The original works done by Dowski and Cathey introduce the use of a cubic phase pupil mask to extend the depth of field. The theoretical and experimental researches all verified its effectiveness. In this paper, we suggest the use of an exponential phase pupil mask to extend the depth of field. This phase mask has two variable parameters for designing to control the shape of the mask so as to modulate the wave-front more flexible. We employ an optimization procedure based on the Fisher information metric to obtain the optimum values of the parameters for the exponential and the cubic masks, respectively. A series of performance comparisons between these two optimized phase masks in extending the depth of field are then done. The results show that the exponential phase mask provide slight advantage to the cubic one in several aspects.     

Image encryption and decryption using fractional Fourier transform and radial Hilbert transform

A technique for image encryption using fractional Fourier transform (FRT) and radial Hilbert transform (RHT) is proposed. The spatial frequency spectrum of the image to be encrypted is first segregated into two parts/channels using RHT, and image subtraction technique. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented.     

一种基于OTF稳定性的波前编码相位板优化方法

提出了一种简单的可用于光学系统中子午弧矢方向白光OTF稳定性评价的波前编码相位板参量优化方法.该方法仅以标准偏差来评价OTF在目标景深范围内的稳定性,并且结合自适应模拟退火算法在参量空间内优化得到相位板的最佳参量.使用该方法优化得到的相位板参量,可以大幅度提高光学系统的景深,并且可以获得更为清晰、稳定的成像.对应用波前编码技术前后光学系统的成像性能作了比较,并且考察了优化参量的容差性.     

Fractional Fourier plane image encryption technique using radial hilbert-, and Jigsaw transform

A new method for image encryption using integral order radial Hilbert transform (RHT) filter in the fractional Fourier transform (FRT) domain has been proposed. The technique is implemented using the popular double random phase encoding method in the fractional Fourier domain. The random phase masks (RPMs), integral orders of the RHT, fractional orders of FRT, and indices of the Jigsaw transform (JT) have been used as keys for encryption and decryption. Simulation results have been presented and the schematic representation for optical implementation has been proposed. The mean-square-error and signal-to-noise ratio between the decrypted image and the input image have been calculated for the correct as well as incorrect orders of the RHT. Effect of occlusion and noise on the performance of the proposed scheme has also been studied. The robustness of the technique has been verified against attack using partial windows of the correct random phase masks. Similar investigations have also been carried out for the chosen-, and the known-plain-text attacks.     

Optical image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

基于多混沌系统的双图像光学加密算法

为了扩展双图像光学加密算法的密钥空间,克服双随机相位加密系统中随机相位掩模作为密钥难于存储、传输和重构的问题,突破传统图像加密的研究思路,提出了一种基于多混沌系统的双图像加密算法,构造了光学加密系统。系统增加混沌系统参数作为密钥,利用混沌加密密钥空间大和图像置乱隐藏性好的特点,构建基于Logistic混沌映射的图像置乱算法,利用Kent混沌映射生成的伪随机序列构造出一对随机相位掩模,分别放置在分数傅里叶变换光学装置的两端,图像经加密系统变换后得到密文。数值仿真结果表明,算法的密钥敏感性极高,能够有效地对抗统计攻击,具有较高的安全性。     

可调谐相位板空域频域联合分析

波前编码系统采用在传统光学系统中加入相位板来扩大光学系统的景深而避免传统景深延拓技术的不利影响. 由于相位板的参数不可调, 整个系统的景深延拓扩展率也不能动态可调. 采用两相位板组合的方法可以有效克服这一点. 本文首先从光线差的角度提出了两三次相位板组合下的光线像差分布以及点扩散函数尺寸的具体关系表达式, 直观体现了系统的光线结构, 指出了光线结构和点扩散函数尺寸受两三次相位板的面型和相对位移量的影响. 其次采用稳相法从空间域给出了系统点扩散函数表达式, 依据点扩散函数的振荡性质给出了有效带宽表达式, 提出了点扩散函数在像面的位置会随两相位板面型参数以及相对于光瞳中心的位移量而发生平移. 最后利用菲涅耳积分给出两三次相位板任意面型参数和相对位移组合下的准确光学传递函数. 在得到的调制传递函数中直观体现出了面型参数和相对位移量对调制传递函数和相位传递函数以及有效带宽的影响, 并说明了此系统相位传递函数的非线性性质. 通过空间域与频率域相结合的方法分析验证了传统的两三次相位板组合具有景深可调和带宽可调的性质, 为设计可调谐波前编码系统提供了理论依据.     

波前编码系统景深延拓性能研究

波前编码景深延拓技术是在非相干光学系统的出瞳处加入三次位相板,对成像进行解码处理而获得清晰图像以扩大光学系统景深的技术.文章通过深入研究波前编码光学成像系统的调制传递函数(MTF),分析离焦量和位相板的调制系数对MTF的影响,并通过数值计算和曲线拟合得到位相板调制系数、系统带宽、景深延拓性能之间的关系.该研究成果为位相板的调制系数的选择和景深延拓光学系统的设计提供依据. 关键词： 波前编码 景深延拓 调制传递函数 三次位相板     

Optical transfer function analysis of circular-pupil wavefront coding systems with separable phase masks

This paper proposes a simple method to achieve the optical transfer function of a circular pupil wavefront coding system with a separable phase mask in Cartesian coordinates.Based on the stationary phase method,the optical transfer function of the circular pupil system can be easily obtained from the optical transfer function of the rectangular pupil system by modifying the cut-off frequency and the on-axial modulation transfer function.Finally,a system with a cubic phase mask is used as an example to illustrate the way to achieve the optical transfer function of the circular pupil system from the rectangular pupil system.     

Transverse superresolution and focal shift with rotational tunable phase mask

This paper reports the imaging characteristics of an optical system can be modified by our designed polarization pupil mask. The novel rotational symmetric polarization pupil mask design based on combination of half-wave and quarter-wave plates is introduced for realizing the focal shift and extending focal depth of an optical system and the procedure for designing is presented. Numerical results show when an appropriate rotational symmetric polarization pupil mask is used as an apodizer in the optical imaging system, it not only can effectively achieve the continuously focal shift in a small range and extend focal depth of the optimized system, but also can evidently increase the transverse resolution of the optimized system at the genuine focal plane.     

Focal shift and focusing properties generation by radial cosine phase masks

Focal shift and focusing properties of Gaussian beams induced by radial cosine phase masks are investigated. Results show that focal shift and the energy distribution among intensity peaks are controlled by two different parameters of the radial cosine phase mask. Increasing the value of frequency parameter in the cosine part of the phase mask, focal shift and focal switch may occur, simultaneously, the focal shift direction may change. Moreover, by altering frequency parameter or phase variation parameter of the phase mask will change the energy distributions of maximum intensity peak and other small intensity peaks. And novel focal patterns also evolve considerably, such as from only one peak to six of multiple peaks. The tunable focal shift can be used to construct controllable optical tweezers. In practice, the tunable phase mask can be implemented through liquid crystal spatial light modulator, which can conveniently alter the wavefront phase distribution of the incident laser beam in the control of computer.     

Apodization‐Assisted Subdiffraction Near‐Field Localization in 2D Phase Diffraction Grating

Conventional phase diffraction gratings can be used to localize the incoming optical radiation in the near‐field region. A new design of the binary phase diffraction grating is proposed with embedded pupil opaque mask inside each stripe. By means of numerical simulations, it is shown that with this masked phase grating the spatial resolution of the near‐field localization can be substantially improved and brought even beyond the solid immersion limit (λ/2n). Moreover, due to anomalous apodization effect, the subdiffraction field localization is accompanied by intensity enhancement as compared to the non‐masked design. The pupil mask rearranges the optical fluxes within the stripes and promotes the Fano resonances excitation in the periodic step lattice. This can be important for advancing the phase grating‐based super‐resolution technologies, including subdiffraction imaging, interferometry, and surface fabrication.     

光学图像加密中随机模板的特性比较

为比较光学图像加密中随机模板的特性,分别利用随机相位模板和随机振幅模板对几种典型的光学图像加密系统进行了光学图像加密的数值模拟和加密效果分析。模拟结果表明,将随机振幅模板用于基于光学傅里叶变换的双随机模板图像加密系统时,原始图像和加密图像的相关系数大于0.5,不能有效加密原始图。但将其用于基于菲涅耳变换全息的光学图像加密系统时,原始图像和加密图像的相关系数趋于0,可获得与使用随机相位模板时非常接近的加密效果。     

Image displacement based on phase-encoded reference joint fractional transform correlator

In order to utilize the space of an input plane efficiently and make the optical structure more flexible, an image displacement measurement based on phase-encoded reference joint fractional transform correlator (PER-JFrTC) is proposed. We use a random phase mask to encode the reference image and overlay it with the target image forming the input image. Joint power spectrum (JPS) of the input image is obtained by Fourier transform and the resultant is encoded by the same phase mask. Then a fractional Fourier transform with an order p is applied to the phase-encoded JPS (PJPS), resulting in a correlation output with a sharp cross-correlation peak, which includes the displacement information between the reference and the target image. Contrast to displacement measurement based on traditional joint transform correlator (JTC), PER-JFrTC can use the space of the input plane efficiently and reduces the influence of the auto-correlation. Also the position of cross-correlation peak can be fixed arbitrarily according to the fractional order p as well as the optical set-up can be more flexible and easier to implement. Results based on digital computation show that PER-JFrTC could detect the displacement accurately and verify our proposal. A possible optical set-up is suggested.     

一种优化波前编码系统相位板参数的新方法

根据波前编码系统的设计理论,在兼顾图像恢复能力的基础上,提出利用不同离焦距离的点扩散函数与焦面处的点扩散函数之间的希尔伯特空间角作为成像特性一致性的评价函数,结合遗传算法,对扩大景深的波前编码成像系统的相位板参数进行优化。分别在空间域和频率域上分析应用波前编码技术前后光学系统的成像特性,并利用最小二乘数字滤波器对中间模糊图像进行复原。仿真实验结果表明:在三次相位板上应用此方法获得的最佳相位板参数使波前编码系统焦深扩展了10倍。     

Code retrieval via undercover multiplexing

The purpose of this research is to develop an undercover multiplexing technique to give additional protection for optical information encryption. We employ the double random phase mask as our basic optical encryption system. The holographic storage medium of choice is a photorefractive crystal. To achieve the multiplexing we use the aperture size of the pupil in the optical system, as it governs the speckle size. We introduce such variation in order to produce a decorrelation between two consecutively stored speckle patterns. Each stored speckle pattern is associated to an input encrypted image, thus producing a multiplexing of the encrypted information. We implement this operation without altering the setup architecture and the random phase masks. This multiplexing is our undercover operation to encipher a true code behind a fake code. Under this approach, the user can only recover the bulk information stored in the volume hologram. However, he cannot recover the true code without the additional information on the pupil size key, even if accessed in position of the original decoding mask.     

A New Algorithm for Die-to-Wafer-like Image Mask Inspection in Real Time

The effect of variations in defect printability must be considered in order to correctly evaluate mask defect inspection procedures. Because of nonlinear transfer effects and strong dependence of printability on defect types, it is difficult to define the boundary between real defect and false defect. To overcome this problem we developed a new algorithm for die-to-wafer-like image (D-to-WI) inspection in real time. This inspection method compares the die (wafer image calculated from CAD data) with the wafer-like image (WI) calculated from the mask image detected by the mask inspection system. To precisely calculate WI in real time, we developed a new simulation-based software. Since the phase of a mask inspection image cannot be measured, we introduce some assumptions regarding its phase. Moreover, we introduce some corrections for WI such as adding a DC component and multiplying by a proper value. To calculate the die which realizes the desired image with sufficient accuracy in real time, we also introduce a perturbation approach. We demonstrate numerically the possibility of a new algorithm for D-to-WI inspection. We confirm that this technique of generating WI from a measured mask pattern is well suited for attenuated phase shift masks (PSMs) and Cr binary masks.     

Image encryption based on gyrator transform and two-step phase-shifting interferometry

A novel optical image encryption method is proposed, based on gyrator transform and phase-shifting interferometry. The input two-dimensional image to be encrypted is gyrator transformed two times, and two random phase masks are placed at the input plane and the output plane of the first gyrator transform. Two-step phase-shifting interferometry is used to record the digital holograms of the input image encrypted by use of double-random phase encoding technique in gyrator transform domain. The rotation angles of gyrator transform, the random phase mask in the gyrator plane and the arbitrary phase shift used for recording form the keys for decryption of the input image. Numerical simulations are presented to verify its validity and efficiency.