Recording Fractional Fourier Transform Hologram Using Holographic Zone Plate

FRTH(fractional Fourier transform hologram) is a new kind of hologram that differs from common Fresnel holograms and Fourier transform holograms. Due to the flexibility of zone plate. A method that uses the -1 order diffraction wave of zone plate as the object wave and the 0 order diffraction wave as the reference wave to record FRTH is presented. It provides a new simple way to record FRTH. In this paper, the theory of achieving FRT and recording FRTH using holographic zone plate is presented and experimental results are given.     

双重分数傅里叶变换计算全息

提出了双重分数傅里叶变换计算全息，在这种方法中，将两个图像的信息分别经不同阶的分数傅里叶变换后，记录在同一张分数傅里叶变换计算全息图上，它需要两个特定的分数傅里叶变换系统才能再现出所记录的图像信息，利用其再现方式的特殊性，可制成一种新的安全认证系统。     

分数傅里叶变换全息图及其在防伪中的应用

提出分数傅里叶变换全息图,讨论了它的性质。拍摄分数傅里叶变换彩虹全息图。基于其再现条件的特殊性,可建立一种新型的伪全息术。     

用全息透镜记录多重分数傅里叶变换全息图

提出一种全息透镜记录多重分数傅里叶变换全息图的新方法，它能在三维空间不同位置和不同方向上分别再现所记录的多个物体的图象，分析了利用全息透镜记录多重分数傅里叶变换全息图的原理及特点，制作了多重分数傅里叶变换全息图，并获得了满意的再现结果。     

Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: Modeling and simulation

A fast holographic wavefront sensor is proposed using a computer-generated hologram (CGH). This CGH is a multiplexed hologram of different Zernike mode–amplitude combinations, and is designed in such a manner as to get the corresponding spots on the detector according to the presence and strength of a particular aberration. Interference between the aberrated wavefront (with a single mode–amplitude combination) and the Fourier transform of an image with single bright pixel (defined as dot image) is numerically calculated for one hologram. Different mode–amplitude combination and corresponding different positions of bright pixels (dots) are taken to compute various holograms and then all the holograms are multiplexed to get the final hologram. When the aberrated wavefront with a particular mode–amplitude combination is incident onto the multiplexed hologram, the corresponding dot is generated in the Fourier plane. A lens performs the Fourier transform in optical domain and provides the instant detection of amplitude of the respective Zernike mode. The main advantage of the scheme is to avoid the need of any computations, which makes it really fast. The simulation results are presented with the cross-talk analysis for few Zernike terms.     

Dual beam encoded extended fractional Fourier transform security hologram with in-built repositioning

This paper describes a simple method for making dual beam encoded extended fractional Fourier transform (EFRT) security holograms. The hologram possesses different stages of encoding so that security features are concealed and remain invisible to the counterfeiter. These concealed and encoded anticounterfeit security features in the security hologram can only be read through a key hologram. Key hologram also facilitates in-built repositioning of security hologram. The method of fabrication, the principle of reconstruction and the experimental results are presented.      

通过保留相位进行全息图信息压缩的方法

从全息图的特点出发,研究了全息图的记录和再现原理,提出了一种对离轴菲涅耳全息图信息压缩的方法。对全息图进行傅里叶变换,滤除零级噪声及物光波的共轭波前,仅仅保留物光波的相位信息,而后以采用较低的采样频率对全息图重新抽样,从而大大减少了数字全息图的信息冗余。压缩后的全息图也可以获得良好像质的再现像。理论和实验均证明了该方法的可行性,为全息图的信息存贮与传输提供一条新的途径。     

不对称离散分数傅里叶变换实现数字图像的加密变换

利用不对称分数傅里叶变换的特性,提出了一种图像加密变换的新方法。对图像的x,y方向分别实施不同级次的一维分数傅里叶变换,得到加密图像。解密方法就是对变换后的图像实施对应级次的分数傅里叶逆变换,只有当x,y方向的逆变换级次分别与原变换级次都相同或者满足周期条件时,才能恢复原图像。加密变换有效地提高了图像加密和防伪力度。数值计算验证了方法的正确性和可行性。     

分数傅里叶变换计算全息

在计算全息和分数傅里叶变换的基础上提出了不对称分数傅里叶变换计算全息和双随机相位不对称分数傅里叶变换计算全息。在这种方法中,首先用一随机相位函数乘以输入图像信息,然后沿x方向实施α级次的一维分数傅里叶变换,再乘以第二个随机相位函数,最后,沿y方向实施β级次的一维分数傅里叶变换。采用迂回位相编码法对变换后的结果编码,绘出计算全息图。为了恢复原始图像,需要知道变换级次和随机相位函数。利用这种方法进行图像加密,使加密图像的密钥由原来两重增加到四重,从而提高了系统的保密性能。     

Improvement of reconstruction in 3D computer-generated holograms using 1D Fourier transform operations

Improvement of images reconstructed from 3D computer-generated holograms using 1D Fourier transform operations is presented. Required computing time for making 3D holograms is decreased when 1D Fourier transform method is used instead of 2D Fourier transform method, but reconstructed images from the holograms created by the 1D Fourier transform method are somewhat inferior in quality to the images by 2D Fourier transform method. In this paper, we propose a method that the disadvantageous properties of the holograms made by 1D Fourier transform are improved. We have performed two step improvements in this experiment. From the numerical experiments, the images that are reconstructed from the holograms created from 1D Fourier transform method show marked improvement.     

High order generalized permutational fractional Fourier transforms

We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite－Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M=+∞, M=4k(k is a natural number), and M=4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.     

数字无透镜傅里叶变换全息术中非傍轴及离焦像差的校正

对数字无透镜傅里叶变换全息图直接采用逆傅里叶变换进行物场的数值重建时.需要满足两个条件:第一,全息图的记录过程必须满足傍轴近似条件,否则再现过程中会产生非傍轴像差;第二,记录全息图时物平面与参考点光源到全息图记录平面的距离必须相等,否则再现过程中会产生离焦像差.理论分析了非傍轴及离焦记录条件下数字无透镜傅里叶变换全息图的灰度分布特点,并提出了相应的非傍轴及离焦像差的数值校正方法.根据实际的非傍轴或离焦记录情况.分别给所记录的数字全息图灰度分布矩阵乘以适当的非傍轴或离焦校正因子,以消除灰度矩阵中非傍轴或离焦因素的影响.然后再对校正后的伞息图灰度矩阵做逆傅里叶变换处理.即可得到准确的数字再现像.实验结果表明.该数值重建方法能够有效地消除无透镜傅里叶变换全息术中数字再现像的非傍轴像差及离焦像差,提高再现像的质量.     

基于分频域和菲涅耳域的光学图像加密方法

结合分数傅里叶变换及菲涅耳变换,在光学图像加密系统中分别具有多密钥性和无透镜性的优点,提出了基于分频域和菲涅耳域的光学图像加密方法。基于分数傅里叶变换的光学加密系统,引入菲涅耳变换及全息技术,使原有的加密系统在不增加光学元件的基础上提高了系统的安全性。理论分析和计算机仿真模拟证明了这种方法的可行性。     

菲涅尔数字全息的脉冲响应

数字全息是用CCD记录全息图并用计算机数值重建全息像的一种全息新方法.在数字全息中,通过对不同记录参数下记录的全息图的数值处理,可以消除零级光和共轭光,从而将数字全息系统看作是一个线性系统.本文依据全息理论和付里叶频谱分析,对菲涅尔数字全息系统的脉冲响应和分辨本领进行了理论分析.结果表明,在矩形等间隔抽样的情形下,菲涅尔数字全息的脉冲响应是由CCD有限大小的孔径衍射斑调制的矩形函数;菲涅尔数字全息的分辨率由CCD的孔径尺寸决定;由于CCD像素具有一定的大小,使得点光源的像发生弥散.     

Propagation and transformation of Bessel beam through the fractional Fourier transform system with two hard-edged apertures

The propagation properties of Bessel beam is a meaningful research. In this paper, based on the expanding the hard-edged circular aperture as a finite sum of complex Gaussian functions and the scalar diffraction theory, an approximate analytical solution for Bessel beam propagating through a fractional Fourier transform system is derived in the cylindrical coordinates. Then, the detailed numerical calculation for Bessel beam is presented. The simulation also shows that the beam parameter and the order of fractional Fourier transform result in the change of field distribution, including location, intensity and width.     

利用分数傅里叶变换设计衍射光学元件

讨论了分数傅里叶变换与菲涅尔衍射的关系,提出球面衍射过程就是一种具有尺度因子的分数傅里叶变换,并应用分数傅里叶变换进行衍射光学元件的设计。     

基于数字全息及离散余弦变换的图像数字水印技术

提出了一种以数字全息和离散余弦变换为基础的数字水印技术,实现了在原始图像中嵌入数字全息水印。考虑到数字全息图的不可撕毁性,使得数字全息水印本身就具有良好的抗剪切能力,并且与传统的二维灰度水印相比嵌入的信息更多。数字全息图通过傅里叶变换全息的方法获得,为了提高抗有损压缩能力,在数字全息水印嵌入过程中采用了基于(JPEG模型和分解离散余弦变换(DCT)系数的方法。实验表明,通过该算法获得的数字全息水印对JPEG有损压缩和剪切等图像处理操作均有很好的稳健性,并且采用密钥加强了水印的安全性。因此该算法能成为数字多媒体产品版权保护的有效方案。     

Image encryption based on extended fractional Fourier transform and digital holography technique

We present a new optical image encryption algorithm that is based on extended fractional Fourier transform (FRT) and digital holography technique. We can perform the encryption and decryption with more parameters compared with earlier similar methods in FRT domain. In the extended FRT encryption system, the input data to be encrypted is extended fractional Fourier transformed two times and random phase mask is placed at the output plane of the first extended FRT. By use of an interference with a wave from another random phase mask, the encrypted data is stored as a digital hologram. The data retrieval is operated by all-digital means. Computer simulations are presented to verify its validity and efficiency.     

Method for eliminating zero-order diffraction in lensless Fourier transform digital holography

A method to induce phase shifting in lensless Fourier of digital holography system is presented. In this method, by computer simulation and theoretical analysis on the technology to eliminate the influence of zero-order diffraction in force, it can be found that, a reference light induced in a random non-2π integral number of phase shifting shooting to get the second hologram, and wave reconstruction can be got by the difference value image of the two holograms. And, the method of different digital holography record system with different phase shifting should be used. In this paper, theoretical analyses have been done in detail to discuss the problems that exist in the unsuitable phase-shifting methods. Furthermore, some experiments have been done to prove the reliability of this method. This method can significantly improve the image quality and give better resolution of the reconstructed image.     

Relations between chirp transform and Fresnel diffraction, Wigner distribution function and a fast algorithm for chirp transform

Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given.The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane,or a rotation and stretching transformation of the Wigner distribution function space.A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms.The algorithm,by which a good evaluation can be achieved,unifies the calculations of Fresnel diffraction,arbitrary fractionalorder Fourier transforms and other scalar diffraction systems.The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform,the Fresnel transform,the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm.The calculated results are in good agreement with the analytical results,both in the amplitude and phase.