Reconstruction of holograms generated by using a combination of an iterative method and an error diffusion method

Two-level quantized phase holograms produced by using a combination of an iterative method and an error diffusion method are presented. By using a previously proposed iterative method, images reconstructed from two-level quantized phase holograms are rapidly improved with small amounts of iterative operations but further improvement of the image quality is difficult even if the iterations are greatly increased. Therefore, in order to exceed the improvement limitation of the image quality, the combination of the iterative method and an error diffusion method was used for the hologram-making process. Experimental results using the combination method showed better images than those obtained by the iterative method alone, when referred to results from synthesized holograms.     

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.     

基于多角度无透镜傅里叶变换数字全息的散斑噪声抑制成像研究

在数字全息成像中,散斑噪声严重影响了再现像的信噪比和成像分辨率,因此为了提高数字全息成像质量,迫切需要抑制再现像的散斑噪声.分析并给出了矩形散射光斑的强度协方差,定量计算了特定实验条件下产生退相关散斑图样的最小角度差.结合透镜的性质设计并搭建了多角度无透镜傅里叶变换数字全息成像系统,利用光纤端面在透镜焦平面的二维机械移动代替传统反射镜的旋转,使照明光束在不改变照明位置和大小的同时,可任意改变光束方向.移动光纤端面使多角度照明满足最小角度差,获取了81幅数字全息图.利用单次快速傅里叶逆变换实现数值再现,对多幅再现像的强度像求平均,实验结果表明散斑对比度降低为单幅再现像的14.6%,使图像信噪比提高了6.9倍.该抑制散斑的多角度数字全息成像方法有效的抑制了散斑噪声,且成像光路结构简单,可操作性强.     

Recovering correct phase information in multiwavelength digital holographic microscopy by compensation for chromatic aberrations

We demonstrate experimentally that correct phase imaging without 2pi ambiguity is obtainable in digital holography by using a multiwavelength approach in the microscope configuration. We describe a general approach for removing chromatic aberrations and for controlling the pixel size of the reconstructed phase image in multiwavelength digital holography when the Fourier transform method is adopted for the numerical reconstruction of digital holograms. The retrieved phase is affected by the unavoidable, unwanted chromatic aberration. The correct phase can be obtained by evaluating the phase from the reference holograms reconstructed at different wavelengths to compensate for the chromatic aberration.     

Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm

A method for calculating off-axis phase-only holograms of three-dimensional (3D) object using accelerated point-based Fresnel diffraction algorithm (PB-FDA) is proposed. The complex amplitude of the object points on the z-axis in hologram plane is calculated using Fresnel diffraction formula, called principal complex amplitudes (PCAs). The complex amplitudes of those off-axis object points of the same depth can be obtained by 2D shifting of PCAs. In order to improve the calculating speed of the PB-FDA, the convolution operation based on fast Fourier transform (FFT) is used to calculate the holograms rather than using the point-by-point spatial 2D shifting of the PCAs. The shortest recording distance of the PB-FDA is analyzed in order to remove the influence of multiple-order images in reconstructed images. The optimal recording distance of the PB-FDA is also analyzed to improve the quality of reconstructed images. Numerical reconstructions and optical reconstructions with a phase-only spatial light modulator (SLM) show that holographic 3D display is feasible with the proposed algorithm. The proposed PB-FDA can also avoid the influence of the zero-order image introduced by SLM in optical reconstructed images.     

Spatially incoherent Fourier digital holography by four-step phase-shifting rotational shearing interferometer and its image quality

Spatially incoherent Fourier digital holography using a rotational shearing interferometer for four-step phase-shifting method is proposed. The previous incoherent Fourier holography using a rotational shearing interferometer [Watanabe and Nomura (Appl. Opt. 54:A18, 2015)] employs the two-step phase-shifting method in the vertical and horizontal polarizations. The reconstructed image contains a large bias term. This paper proposes introduction of two kinds of wave plates in one path of a rotational shearing interferometer for a four-step phase-shifting method. A Fourier hologram is obtained from the four recorded holograms for eliminating the bias term and the twin image. The numerical simulation and the optical experiment demonstrate improvement of the image quality of reconstructed image by the twin image and bias level reduction. Furthermore, the effect of the size of an image sensor on the image quality in rotational shearing interferometer is also investigated by the numerical simulations.     

Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects.     

Computer generated holograms using personal computers

Holography or the method of wave-front reconstruction to produce an image was introduced by D. Gabor in 1948. Normally a laser is necessary to produce holograms in the laboratory. This paper introduces the usage of the high resolution display of the IBM-PC and a graphics printer to generate holograms. The advantages of using this method are that holograms of real or fictitious objects can be made, since all objects can be represented by a collection of points and one does not need an elaborate set up to make the holograms. This method is also useful for making Fourier transform holograms, image plane holograms, spatial filters, optical elements, etc.^1,2     

Image recovery from double amplitudes in fractional Fourier domain

The classical Gerchberg--Saxton algorithm is introduced into the image recovery in fractional Fourier domain after adaptation. When this algorithm is applied directly, its performance is good for smoothed image, but bad for unsmoothed image. Based on the diversity of fractional Fourier transform on its orders, this paper suggests a novel iterative algorithm, which extracts the information of the original image from amplitudes of its fractional Fourier transform at two orders. This new algorithm consists of two independent Gerchberg--Saxton procedures and an averaging operation in each circle. Numerical simulations are carried out to show its validity for both smoothed and unsmoothed images with most pairs of orders in the interval [0, 1].     

基于位相变更的非相干数字全息自适应成像

菲涅耳非相干数字全息作为一种非扫描的三维成像技术具有其独特的优势,但其成像过程中会受到各种像差的影响,导致成像分辨率、再现像的质量降低.为了解决这一问题,可以结合适当的自适应光学技术对波前像差进行探测和校正.位相变更是一种基于两幅具有已知位相差的强度图像实现波前探测和像差校正的技术.本文发展了基于位相变更的非相干数字全息自适应成像技术,不需要引入引导星,利用全息记录过程中的两幅相移全息图,实现波前像差的探测.本文给出了所发展技术的数值仿真和实验结果,结合位相变更算法求解出系统像差的位相分布,将像差的共轭位相加载到光瞳面上,在全息图记录的同时校正像差,从而提高重建像的质量.     

Compressive optical image watermarking using joint Fresnel transform correlator architecture

A new optical image watermarking technique based on compressive sensing using joint Fresnel transform correlator architecture has been presented. A secret scene or image is first embedded into a host image to perform optical image watermarking by use of joint Fresnel transform correlator architecture. Then, the watermarked image is compressed to much smaller signal data using single-pixel compressive holographic imaging in optical domain. At the received terminal, the watermarked image is reconstructed well via compressive sensing theory and a specified holographic reconstruction algorithm. The preliminary numerical simulations show that it is effective and suitable for optical image security transmission in the coming absolutely optical network for the reason of the completely optical implementation and largely decreased holograms data volume.     

Real color fractional Fourier transform holograms

Real color fractional Fourier transform holography is proposed based on fractional Fourier transform holography. The method of fabrication, the principle of reconstruction and the design of system parameters are discussed in detail. The experiments prove real color fractional Fourier transform holograms possess the better function of anti-counterfeit than common fractional Fourier transform holograms.     

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.     

菲涅耳数字全息成像系统的脉冲响应分析

数字全息成像由CCD记录数字全息图后经过计算机数值重建物光波场,这个过程从傅里叶变换角度看等同于数字全息图的频谱分析。讨论了数字成像系统的脉冲响应函数,并分别推导了其实像、虚像、零级像在平面波和球面波照射下的波前复振幅分布。结果表明,实像和虚像是移位的夫琅和费衍射分布,而零级像是CCD光瞳的菲涅耳衍射分布,且与参考光波前分布无关。     

Color digital holography using a single monochromatic imaging sensor

Color digital holography utilizing the Doppler effect is proposed. The time variation of holograms produced by superposing images at three wavelengths is recorded using a high-speed monochromatic imaging sensor. The complex amplitude at each wavelength can be extracted from frequency information contained in the Fourier transforms of the recorded holograms. An image of the object is reconstructed by the angular spectrum method. Reconstructed monochromatic images at the three wavelengths are combined to produce a color image for display.     

基于傅里叶变换解相法的像增强管多参数测量

 提出一种基于傅里叶变换解相法的像增强管成像质量多参数同时测量的新方法。将一正弦光栅图输入到像增强管,如果像增强管成像质量存在问题,将使图像输出发生改变,形成一变形条纹,采用傅里叶变换解相法对输出的变形条纹进行解相,可同时获得放大率、放大率不均匀度、枕形畸变、桶形畸变、蛇形畸变、剪切畸变等相关信息,对测量系统进行标定,即可实现对上述参数的同时测量。实验测得中心放大率与设定放大率的差值到了10-3量级,测得的畸变和畸变真值两者差异在0.4 pixel以内,结果证明了方法的有效性。     

激光相干场成像散斑噪声复合去噪方法

噪声是影响激光相干场高分辨成像系统像质的重要因素,激光相干场成像系统既受背景光加性噪声影响,又受激光乘性散斑噪声影响.为解决激光相干场成像系统受激光乘性散斑噪声和背景光加性噪声叠加引起的成像像质退化效应问题,从噪声抑制角度提高激光相干场系统高分辨成像像质,研究建立了激光散斑乘性噪声和背景光加性噪声对大气下行链路激光回波场信号影响干扰模型,并基于该模型提出了一种基于同态滤波和稀疏基追踪级联复合去噪算法.首先基于同态滤波理论将激光乘性散斑噪声转化为加性噪声,再由高通滤波器滤除散斑噪声,最后采用基追踪稀疏理论方法抑制背景光等加性噪声对像质的影响.研究表明,较现有单一去噪方法,该级联复合去噪方法可一次性消除激光乘性散斑噪声和背景加性噪声两种不同性质的噪声,有效改善了激光相干场成像质量.     

部分相干分数域滤波改善光刻分辨率新方法

基于部分相干成像和分数傅里叶变换,提出在投影光刻系统中,利用分数域滤波改善光刻图形质量的新方法.理论和模拟分析表明:在曝光成像系统中的适当位置加入分数域滤波器,能增强滤波操作的灵活性和效果,可更有效地改善光刻图形质量,为提高曝光系统的分辨力提供一种新的有效选择.     

基于自适应阈值方法实现迭代降噪鬼成像

为了有效降低传统鬼成像中相关噪声对成像质量的影响,本文提出一种基于最佳阈值的迭代降噪鬼成像.首先在迭代降噪鬼成像的基础上,采用自适应阈值迭代法,在不需要目标先验信息的前提下,找到一个逼近传统鬼成像中相关噪声的阈值,根据得到的阈值构造噪声干扰项.为了每次迭代初值更接近原始目标的透射系数,对其进行二值化,降低重构图像背景噪声对迭代性能的影响.仿真以及实验结果表明,本文提出的方法与传统方法相比,视觉效果以及峰值信噪比值有明显提高.     

Matrix completion-based reconstruction for undersampled magnetic resonance fingerprinting data

An iterative reconstruction method for undersampled magnetic resonance fingerprinting data is presented. The method performs the reconstruction entirely in k-space and is related to low rank matrix completion methods. A low dimensional data subspace is estimated from a small number of k-space locations fully sampled in the temporal direction and used to reconstruct the missing k-space samples before MRF dictionary matching. Performing the iterations in k-space eliminates the need for applying a forward and an inverse Fourier transform in each iteration required in previously proposed iterative reconstruction methods for undersampled MRF data. A projection onto the low dimensional data subspace is performed as a matrix multiplication instead of a singular value thresholding typically used in low rank matrix completion, further reducing the computational complexity of the reconstruction. The method is theoretically described and validated in phantom and in-vivo experiments. The quality of the parameter maps can be significantly improved compared to direct matching on undersampled data.