Analysis and demonstration of multiplexed phase computer-generated hologram for modal wavefront sensing

We propose to implement a modal wavefront sensor (MWS) using a multiplexed phase computer-generated hologram (MPCGH). Based on general orthogonal aberration modes, the theoretical treatments of the MWS employing a MPCGH are presented with scalar diffraction approximations and Fourier analysis. Under the small aberration approximations, we give the analytical formula for characterizing the relationship between the sensor signal and the amplitude of the aberration mode. We design several MPCGHs with an effective method of modified off-axis reference beam holograms superposition, and code some common orthogonal Zernike aberration modes into the MPCGH. The numerical simulation is carried out to investigate the performance of MWS to detect particular aberration mode(s). The results exhibit the expected responses of the corresponding symmetric spot pair, and indicate that the wavefront distorted by a special Zernike aberration mode, after modulated by the MPCGH, can be transformed into beams with an intensity-normalized differential signal, which can reflect the change trend of the aberration coefficients in the test wavefront. The experimental demonstration with designed MPCGHs in conjunction with two phase-only spatial light modulators was carried out to test the performance of the MWS.     

Multiple information encryption by user-image-based gyrator transform hologram

A novel multiple information encryption by user-image-based gyrator transform hologram is proposed. In encryption process, each channel of the user image is phase encoded, modulated by random phase function and then gyrator transformed to get the gyrator spectrum of user image. Subsequently, each channel of the secret image is normalized, phase encoded, multiplied by modulated user image, and then gyrator transformed to obtain the gyrator spectrum of secret image. The encrypted digital hologram is recorded by the interference between the gyrator spectrum of user image and the spherical wave function. Similarly, the digital hologram for decryption is recorded by the interference between the gyrator spectrum of secret image and the spherical wave function. The multiple encrypted digital holograms are multiplexed into a final encoded hologram and the corresponding digital holograms for decryption are multiplexed into a final hologram for decryption. The wavelength and radius of the spherical wave function, and angle of gyrator transform are all essential keys for decryption. The proposed system has two main features. First, the encrypted hologram has no information about secret image. Second, the hologram for decryption used as identification key. Consequently the two marked security layers of information protection are achieved. The proposal can be realized by optoelectronic system. Numerical simulation results demonstrate the feasibility and security of the proposed technique.     

子孔径合成光学成像系统像质评价研究

由于子孔径合成光学成像系统出瞳波前离散,成像特征有异于常规光学系统.对比了两种子孔径合成光学成像系统的像质评价方法,其一是直接利用干涉仪实测获得的整体出瞳波面参量,拟合成泽尼克多项式,通过快速傅里叶变换获得光学系统的调制传递函数;其二是对子出瞳波面在像面复振幅分布的衍射直接积分叠加计算系统调制传递函数.对于离散出瞳波前,拟合的泽尼克多项式不可避免有较大误差,由此计算获得的调制传递函数与实际测量值有较大区别.设计并制造了一个三子镜合成的成像光学系统,在此基础上用ZYGO GPI干涉仪验证并对比了使用两种方法对像质计算的特点.结果表明,子出瞳波面直接衍射积分叠加法的精度更高,但计算量大,且要获得更高的像质评价精度,应使用更适于表达离散不规则形状子出瞳波前的波函数.     

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。     

三路矩形光束相干合成波像差与光束质量

根据相干合成的原理,建立了三路矩形光束相干合成的数学仿真模型,根据数学模型编写了仿真程序;模拟计算了1～21阶泽尼克像差下,单路矩形光束和三路矩形拼接光束的波像差与光束质量因子关系的拟合系数;建立了波像差与因子关系的计算表达式。分析了影响拟合系数的因素,结果表明:拟合系数总体上随着泽尼克像差系数增大而增加。比较了单路矩形光束与三路矩形拼接光束拟合系数的相似点和不同点,并分析了造成拟合系数不同的原因。     

Fast reconstruction of multiple off-axis holograms based on a combination of complex encoding and digital spatial multiplexing

An algorithm is proposed for the fast reconstruction of off-axis digital holograms based on a combination of complex encoding(CE) and spatial multiplexing(SM). In this algorithm, every two off-axis holograms recorded in sequence are first assembled into a CE hologram using the CE method, and then four of the CE holograms are again encoded into one complex spatial multiplexing(CSM) hologram based on the SM algorithm. It is demonstrated that the eight holograms encoded into such one CSM hologram can be quickly reconstructed by performing a two-dimensional(2D) Fourier transform(FT) on the CSM hologram. Using this method, the eight 2D FTs required for the reconstruction of the eight holograms in the conventional spatial filtering methods can be simplified to a process with only one 2D FT, which can largely improve the computation efficiency with the     

Reflection holographic lens having nonspherical wavefront designed by a microcomputer

A design of a reflection holographic lens with nonspherical wavefront is described, which is based on a ray-tracing program and a simple search algorithm suitable for a microcomputer. The optimized wavefront is encoded into a computer- generated hologram (CGH). The reflection holographic lens with the optimum wavefront produced by CGH reduces the rms spot radius at large field angles, and allows for a compact folded system and for Bragg diffraction into a single order. Experimental results are shown. Helpful data on the diffraction efficiency and the spectrally diffracted intensity of reflection holograms are presented.     

High efficient generation of holographic stereograms based on wavefront recording plane

A computer generated holographic stereogram based on the wavefront recording plane(WRP) is presented. A WRP closed to the parallax image plane is introduced to record the complex amplitude in a small region for each point in the parallax image. By using three times of fast Fourier transform(FFT) to execute the Fresnel diffraction calculation between the WRP and the holographic stereogram plane, the object wave contributing to the hologram pattern can be achieved. The computation complexity of the proposed approach is dramatically reduced. The results show that the calculation time can be decreased by more than one order of magnitude.     

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.     

基于博奇编码离轴全息方法的研究

研究了一种计算全息编码过程中使原始像与共轭像分离的方法。通过对傅里叶变换计算全息图再现过程的分析,采用将原物抽样点镶嵌到比原物大的全零矩阵中的方法代替载频参数的计算,来实现原始像与共轭像的分离。对新矩阵进行离散傅里叶变换,利用博奇编码方式制作出计算全息图,并在图像重构时利用高通滤波器消除背景光干扰对重构视觉效果的影响。采用该方法制作的计算全息图可通过控制全零矩阵的大小来控制再现时原始像与共轭像的分离程度,全零矩阵越大,其分离程度越大。实验结果表明,全零矩阵为原物大小的4倍时可使原始像与共轭像刚好分离。但是为了方便滤除零级光斑,全零矩阵需稍大于原物大小的4倍。     

Coaxial holographic data storage without recording the dc components

A technique of recovering the data pages from Fourier holograms recorded without the dc components is demonstrated theoretically and experimentally by use of a coaxial holographic storage system. A reconstructed image is obtained by adding a phase-modulated dc component of the signal beam on reading. The bit error rate of the reconstructed image is comparable with that for the hologram recorded with the dc component as well. Since high intensities of the dc components are not recorded in this technique, the dynamic range of the recording media can be saved, which potentially contributes to increasing the number of multiplexed holograms.     

Fast phase retrieval in slightly off-axis digital holography

In this study, three efficient algorithms are proposed for fast phase retrieval in slightly off-axis digital holography using spectrum cropping, spatial multiplexing, and complex encoding. In the first algorithm, the real spectral order of the subtracted hologram is filtered and cropped, and the number of pixels is decreased in the subsequent retrieval operations. In the second algorithm, two sequential subtracted holograms are digitally phase shifted and spatial multiplexed into one synthetic hologram, and thus only one inverse Fourier transformation is then required. In the third algorithm, two sequential subtracted holograms are encoded separately into the real part and the imaginary part of a complex hologram. Two cross-correlations can be used to reconstruct the phase, thereby improving the utilization of the spectrum. The three new algorithms speed up our previously proposed retrieval method with the assistance of specimen-free holograms. Our experiments demonstrated the validity and improved time requirements of the proposed methods.     

A comparison of iterative Fourier transform algorithms for image quality estimation

A comparison was established between two iterative Fourier transform algorithms (IFTAs), such as the original Gerchberg–Saxton (GS) and the mixed-region amplitude freedom (MRAF) algorithms, for the hologram reconstruction of different target images through the full reference image quality estimation (IQE) and pixel homogeneity in the Fourier plane presented theoretically and experimentally. The comparison was applied depending upon both algorithms based on a computer-generated hologram (CGH) implemented utilizing a reflective phase-modulated liquid-crystal spatial light modulator (LC-SLM) to obtain the digital kinoform holograms of the desired intensity distributions. These digital holograms were applied to reconstruct the intensity patterns for 852 nm, which represents a laser beam source. The theoretical and experimental results of the reconstructed patterns obtained using the MRAF algorithm were found to be smoother and better than the patterns obtained using the GS algorithm. Unmodulated light beam (dc term) is removed from the reconstructed patterns attributed to digital kinoform holograms of MRAF algorithm as an alternative to the theoretical and experimental results without using any additional optic equipment at the light path. Moreover, this paper discussed the full reference objective quality estimations, such as mean square error (MSE), peak signal-to-noise ratio (PSNR), structural content (SC), normalized absolute error (NAE), normalized cross correlation (NK), and homogeneity of pixels, through the contrast (Cont) and inverse difference moment (IDM) for numerical and experimental results. According to the two desired intensity distributions processed theoretically and experimentally, the results of MRAF algorithm were found to be in the highly accurate recovered phase, the quality of image was enhanced, and the dc term was decreased. Image quality estimation of full reference objective relay on the feedback algorithms experimental attestation has not been implemented yet.     

半色调编码计算全息图的数字水印方法

提出一种新的基于信息光学的数字水印方法。该方法将水印信息隐藏于半色调编码的计算全息图之中。通过相位复原技术将需隐藏的水印信息编码为相位函数嵌入在复波前中,其振幅定义为宿主图像,通过计算全息记录复波前并对全息图进行半色调编码完成水印信息的嵌入。水印的提取过程只需对含有水印信息的半色调图像进行光学或数字的傅里叶变换即可完成。并给出了算法有效性的理论分析和仿真实验结果。结果证明这种水印技术对于各种数字图像处理操作具有很高的稳健性,且半色调编码图的二值特性使嵌入水印具有很强的抗打印、抗复印、抗扫描的能力。     

Synthetic holography in microscopy: opportunities arising from advanced wavefront shaping

The advent of computer-generated or synthetic holography has created a wealth of possibilities for wavefront shaping in optics. We discuss the impact this has had on optical microscopy. Synthetic Holographic Microscopy utilises wavefront shaping by a computer-generated ‘hologram’ (CGH) to modify light on the illumination or the detection side, or both. This enables modifications of the general sample appearance concerning contrast, resolution and other aspects. Multiplexing CGHs can perform several tasks at once, for instance splitting the image into sub-images corresponding to different depths in the sample, or displaying differently contrasted images of the sample, e.g. bright field, darkfield or (spiral) phase contrast, in different sub-images. We give an overview of the options and discuss the advantages and disadvantages of using programmable holographic elements inside an optical microscope.     

共轭对称延拓傅里叶计算全息

提出一种计算全息算法,将物光波进行共轭对称延拓,经快速傅里叶变换直接生成实函数,其中包含物光波的幅度和相位信息,可编码得到灰度全息图.利用此全息图可清晰地再现原物光波.通过共轭延拓生成计算全息图的方法与以往基于干涉的计算全息不同之处在于,这里并不需要模拟物光和参考光的干涉,计算效率很高.利用生成的全息图在数字再现和光电再现实验中均获得了良好的效果.理论推导和实验结果都验证了算法的有效性. 关键词： 计算全息 共轭对称 数字再现 光电再现     

The formation of large scale reconstructed images through the use of holograms

We propose and demonstrate a method which constructs large size multicolor images using a holographic technique in limited spaces, i.e., tunnels. A traffic sign image of the same size and color as an actual traffic sign board is displayed using many comparative small holograms. Each hologram is composed of a single computer generated hologram (CGH). Though it was necessary to make many CGHs, we have shortened the hologram production time by putting a reconstructed image on long distance, and using many reconstruction sources. Moreover, though cross-talk images are caused in a color reconstruction, by adjusting the optical system it is possible to make sure that drivers see only the appropriate image. Many holograms function as one big hologram, and it has been confirmed that a large reconstructed image can be displayed in a limited space.     

Binary computer-generated holograms for security applications from a synthetic double-exposure method by electron-beam lithography

We have developed a new multiplexing method for producing binary computer-generated holograms (CGH's) for security applications. This method is based on double recording of two types of coding method upon binary CGH's. The CGH synthesized by the proposed method can have multiple image planes from the region close to the hologram (image region) to infinity (Fraunhofer region) without severe degradation of reconstructed images in the image region. A CGH containing simultaneous image- and Fourier-type holograms is fabricated by electron-beam lithography. Some experimental results are presented.     

Improvement of images generated reconstructed from computer- holograms using an iterative method

An iterative method is presented which can uniformly distribute the Fourier transformed amplitudes of an original object. The method is effective in making phase quantized holograms whose amplitudes have constant values, and further, it is effective for such imaging systems where the decreased spectral information is desirable for transmission and storage. The hologram is produced by iterations of the Fourier transform and inverse Fourier transform operations. The image quality depends upon the number of iterations, however, a great many iterations will not necessarily lead to a marked improvement in the image quality because a rapid improvement is often achieved by only a few iterative operations. From our experiments, the iterative operations have made remarkable improvements in reconstructed images. The proposed method is also suitable for other types of holograms and for applications in imaging systems.     

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.