Image watermarking by use of digital holography embedded in the discrete-cosine-transform domain

Digital holography techniques can be utilized to implement image watermarking schemes. In a previous method proposed by Takai and Mifune [Appl. Opt. 41,865 (2002)], a watermark image is transformed into a digital Fourier hologram, which then is directly superposed onto a content image to perform the embedding process. In the detection stage, the watermark is extracted based on the inverse Fourier transform and optical holography techniques. A method in which the hologram is superposed on the discrete-cosine-transform domain of the content image is proposed to significantly improve Takai and Mifune's method. The proposed method can greatly reduce the degradation on the superposed image, which is the major drawback in Takai and Mifune's method. Simulation results also demonstrate that the watermark can be successfully extracted under different kinds of attack.     

Digital watermarking by a holographic technique

A holographic technique is applied for digital watermarking by a computer. A digital-watermark image to be hidden is phase modulated in a random fashion, and its Fourier-transformed hologram is superposed on a content image. The watermark is reconstructed by means of a holographic-reconstruction technique from the bit-map image that hides it. In the study the processes of constructing and reconstructing a digital hologram are described on the basis of the theory of Fourier optics. The conditions for superposing the hologram onto the content images are investigated in detail. The validity of the present method is verified by changing the weighting of the hologram relative to that of the content image. The effect of image size is also discussed with respect to reconstruction of the watermark, and it is shown that watermark information in a form of a diffuse-type Fourier-transform hologram cannot be removed by cutting it out of the host image.     

Accurate phase-added stereogram to improve the coherent stereogram

We propose an "accurate" phase-added stereogram, which can be defined as an improved phase-added stereogram. Generally, the macroblock size transformed by the fast Fourier transform is the same as the segmentation size of the phase-added stereogram. However, the proposed method uses a lager macroblock size than does the conventional method to reduce quantization error in discrete spatial frequencies in the spatial frequency domain. Therefore, even when the fast Fourier transform is used for calculation, the quality of the reconstructed image can be improved to be as clear as the Fresnel hologram.     

Encryption of digital hologram based on phase-shifting interferometry and virtual optics

A new information encryption system is presented, based on phase-shifting interferometry and virtual optics. Three-step phase-shifting interferometry is used to record a digital hologram of the input data and a virtual optical system based on the scaled optical fractional Fourier transform is used for encryption of the recorded digital hologram. In the virtual optical system, the digital hologram to be encrypted is fractional Fourier transformed two times, and a random phase mask is placed at the output plane of the first fractional Fourier transform. Both the encryption and decryption processes are performed digitally. The encrypted data and the keys for decryption can be stored and transmitted in a conventional communication channel. Numerical simulations are presented to verify validity and efficiency.     

Complex Fresnel hologram display using a single SLM

We propose a novel optical method to display a complex Fresnel hologram using a single spatial light modulator (SLM). The method consists of a standard coherent image processing system with a sinusoidal grating at the Fourier plane. Two or three position-shifted amplitude holograms displayed at the input plane of the processing system can be coupled via the grating and will be precisely overlapped at the system's output plane. As a result, we can synthesize a complex hologram that is free of the twin image and the zero-order light using a single SLM. Because the twin image is not removed via filtering, the full bandwidth of the SLM can be utilized for displaying on-axis holograms. In addition, the degree of freedom of the synthesized complex hologram display can be extended by involving more than three amplitude holograms.     

Image hiding in Fourier domain by use of joint transform correlator architecture and holographic technique

Based on joint transform correlator (JTC) architecture and holographic techniques, a new method for image hiding is presented. A hidden image encrypted by JTC architecture is embedded in the Fourier hologram of the host image. Inverse Fourier transform can be used to obtain the watermarked image, and JTC architecture is used to decode the hidden image from the watermarked hologram. Unlike other watermarking techniques, by prechoosing information, the noise added to the recovered hidden image by the host can be reduced. Unlike other watermarking systems based on double random-phase encoding, no conjugate key is used to recover the hidden image. Theoretical analyses have shown the system's feasibility. Computer simulations are presented to verify the system's validity and efficiency. Numerical simulations also show that the proposed system is robust enough to resist attacks, such as occlusion, noise, and filtering.     

Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position

Introducing a microscope objective in an interferometric setup induces a phase curvature on the resulting wavefront. In digital holography, the compensation of this curvature is often done by introducing an identical curvature in the reference arm and the hologram is then processed using a plane wave in the reconstruction. This physical compensation can be avoided, and several numerical methods exist to retrieve phase contrast images in which the microscope curvature is compensated. Usually, a digital array of complex numbers is introduced in the reconstruction process to perform this curvature correction. Different corrections are discussed in terms of their influence on the reconstructed image size and location in space. The results are presented according to two different expressions of the Fresnel transform, the single Fourier transform and convolution approaches, used to propagate the reconstructed wavefront from the hologram plane to the final image plane.     

Lensless anamorphic Fourier transform hologram recorded with prism systems

A novel configuration for recording a lensless anamorphic Fourier transform hologram of a given object's light distribution is proposed. The method is based on the use of prism anamorphic optical systems coupled with phase cancellation at the hologram plane. Anamorphic systems with cylindrical lenses and prisms are critically evaluated through computer simulations for their suitability in anamorphic Fourier transform holographic configurations. A complete theoretical analysis and experimental demonstration of the recording and reconstruction of a lensless anamorphic Fourier transform hologram are presented.     

Computational reconstruction of images from holograms

The equations to reconstruct an image plane from a hologram are developed. This development is carried out for planes parallel to the hologram, which allows fast computation through the use of fast Fourier transforms. Algorithms for a digital computer are developed so images can be reconstructed, both with and without the Fresnel approximation, from a digitized hologram without the need for three-dimensional optical reconstruction equipment. Examples of holographically recorded images of marine micro-organisms are shown. A computational method for counting the number of micro-organisms in the holographically recorded volume is developed, and an example is provided.     

傅里叶变换同轴数字全息记录余弦变换谱系数

余弦变换广泛应用于图像和视频的压缩编码以及模式识别之中。余弦变换为实偶对称的傅里叶变换,把实偶对称物体传送到位于傅里叶变换透镜前焦面的空间光调制器上,采用单色均匀平面激光光波照射,则在后焦面上为光波复振幅分布为实偶对称物体的傅里叶变换,即为物体的余弦变换。由于余弦变换谱系数既有正实数又有负实数,提出了采用傅里叶变换同轴数字全息方法记录余弦变换谱系数,通过把数字全息图减去参考光光强和物光光强而得到余弦变换系数。理论推导和实验结果表明了该方法的可行性,该方法可应用于图像的快速余弦变换。     

Three types of computer-generated hologram synthesized from multiple angular viewpoints of a three-dimensional scene

We describe various techniques to synthesize three types of computer-generated hologram (CGH): the Fresnel-Fourier CGH, the Fresnel CGH, and the image CGH. These holograms are synthesized by fusing multiple perspective views of a computer-generated scene. An initial hologram is generated in the computer as a Fourier hologram. Then it can be converted to either a Fresnel or an image hologram by computing the desired wave propagation and imitating an interference process of optical holography. By illuminating the CGH, a 3D image of the objects is constructed. Computer simulations and experimental results underline the performance of the suggested techniques.     

Digital holographic reconstruction of a local object field using an adjustable magnification

In the research of digital holography, this paper presents a numerical method using an adjustable magnification for local object field reconstruction together with experiment verification. The method first designs a spherical wave according to the given magnification to illuminate the digital hologram, then through a Fourier transform of diffraction, it calculates the reconstructed image plane. Afterward, a filtering window is set in the image plane to extract the image of the local object field, and then the object field reached hologram plane is formed using diffraction's inverse operation. Finally, the object field is reconstructed through diffraction's angular spectrum theory.     

Reflection volume holographic scanners with field-curvature corrections

A new type of polygonal holographic scanner that combines a reflection volume hologram with a computer-generated hologram (CGH) is described. The scanner is free from the aberration of field curvature. Such a scanning system can allow for a compact folded version of the scanner and Bragg diffraction into only a single order. The equations expressing the spatial-variable image distance are derived and are fit to the phase function designated by polynomials incorporated into a CGH in terms of the least-squares method. A reflection scanner with field-curvature correction is made by interfering a diffracted wave front from this CGH with a spherical wave front having scanning focal power through a second plane hologram. Experiments demonstrating the feasibility of this scanner are presented. Raster-scan patterns using a multifaceted scanner are shown. Helpful data on the diffraction efficiency and the spectrally diffracted intensity of reflection holograms are also presented.     

Direct image transmission through a multimode optical fiber

One-way transmission of a multipixel image through the multimode optical fiber based on the phase-conjugation principle is realized. Adistortion-compensating hologram for each pixel of an image to be transmitted is superposed on a photoplate. Each hologram is recorded with a reference beam of different beam incidence angle to provide proper wave-front correction for each pixel without any interference from other pixels. The reference beams are holographically generated from a photoplate in which small holographic lenslets are aligned in a matrix pattern. Images of up to 25 pixels are transmitted through the fiber experimentally.     

Evaluation of Two-dimensional Quantizers for Fourier Transform Binary Holograms

Quantization formats of four digital holographic codes (Lohmann, Lee, Burckhardt and Hsueh-Sawchuk) are evaluated. A quantitative assessment is made from errors in both the Fourier transform and image domains. In general, small errors in the Fourier amplitude or phase alone do not guarantee high image fidelity. From quantization considerations, the Lee hologram is shown to be the best choice for randomly phase coded objects. When phase coding is not feasible, the Lohmann hologram is preferable as it is easier to plot.     

基于图像校正的抗几何变换全息水印算法

目的提出了一种基于图像校正的抗几何变换全息水印算法。方法在水印嵌入时,将原始二值水印图像,利用共轭对称延拓傅里叶计算全息方法生成全息水印,并嵌入在原始图像小波变换的对角线高频系数中,逆变换得到含水印图像。在含水印图像的DFT域中嵌入模版信息,在水印提取时,首先利用模版信息对图像进行校正,然后提取水印信息。结果该算法保留了全息水印的优良特性,结合了模版匹配校正技术,可以有效抵抗滤波、噪声、裁切、JPEG压缩、旋转、等比例缩放及其组合攻击。结论该算法在实际应用中能有效抵抗几何攻击,可以应用于数字图像的版权保护中。     

Analysis of Fourier synthesis holography for imaging through scattering materials

The technique of Fourier synthesis holography to image through scattering materials is analyzed in detail. A broad spectral source is decomposed into its Fourier components, and a hologram is formed at each wavelength and stored in the computer. Upon synthesis in the computer, a clear image can be formed of the obscured object. Post-data-acquisition processing such as selection of the gating time delay and autocorrelation shaping are also demonstrated.     

Optical correlation of spatial-frequency-shifted images in a photorefractive BSO correlator

The optical cross correlation of an image with another image that was spatial-frequency shifted in one dimension was demonstrated in a photorefractive VanderLugt correlator. The first image was stored as a Fourier-transform hologram in a photorefractive Bi12SiO20 crystal (BSO) and was successively correlated with different spatial-frequency-shifted versions of a second image. We implemented the spatial-frequency shift by rotating a galvanometer mirror in an image plane, causing the Fourier transform to be shifted laterally in the BSO. We verified that the resulting operation in the BSO was an accurate complex multiplication of the shifted and the stored Fourier transforms. As many as 20 successive readouts were conducted without measurable erasure of the stored hologram. The dynamic range, saturation behavior, and other performance parameters were measured and are discussed.     

Digital recording and numerical reconstruction of holograms: an optical diagnostic for combustion

Holographic interferometry (HI) has proved to be a useful tool for nonintrusive temperature measurements in flames (and thereafter for inference of the local composition based on the state relationship approach) with high spatial and temporal resolution. Digital holographic interferometry (DHI) is a relatively new imaging and measurement technique that electronically records a hologram (e.g., on a CCD) and reconstructs it by a numerical method. Cumbersome chemical processing of the hologram is avoided in DHI, which thereby provides greater flexibility, speed, and the potential for real-time processing. In conventional holography, fringes that are neither bright nor dark on a hologram cannot be accurately resolved. The DHI technique has not yet to our knowledge been used for combustion applications. Herein we evaluate its efficacy for making temperature measurements in flames and assess its applicability through a simulation. Each part of a double exposure associated with the holographic technique is considered to be recorded by a hypothetical CCD sensor at a separate time from the other part. We applied the principles of Fourier optics to develop two numerical methods for hologram reconstruction, and we show that both methods provide an accurate reconstruction of the phase image associated with a flame. Because of the periodic nature of the wave function, the reconstructed phase values are limited to the interval [-pi/2, pi/2]. Thus an unwrapping algorithm is provided that produces a continuous phase distribution based on the condition that the reconstructed phase is jumped by a value of -pi or pi. We have also developed an iterative calculation method to adjust the value of the digital reference wave parameters that determines the phase imaging reconstruction in DHI.     

改进的基于 QR 码的数字全息水印

目的提出改进的基于快速响应矩阵码(QR码)的数字全息水印。方法利用加密傅里叶全息技术对QR码进行加密并生成全息图,在标准颜色空间下,抽取彩色载体图像的L分量进行二级小波分解,将全息图嵌入到其分解后的低频系数中,以实现水印信息的隐藏。为提高QR码译码成功率,对提取后的水印进行十字型中值滤波处理。结论 QR码水印能够保存完整的水印信息,比普通图像水印鲁棒性强,且相比于其他基于QR码的数字全息水印算法具有更强的鲁棒性。