Novel Fourier-based iterative reconstruction for sparse fan projection using alternating direction total variation minimization

Sparse-view x-ray computed tomography(CT) imaging is an interesting topic in CT field and can efficiently decrease radiation dose. Compared with spatial reconstruction, a Fourier-based algorithm has advantages in reconstruction speed and memory usage. A novel Fourier-based iterative reconstruction technique that utilizes non-uniform fast Fourier transform(NUFFT) is presented in this work along with advanced total variation(TV) regularization for a fan sparse-view CT. The proposition of a selective matrix contributes to improve reconstruction quality. The new method employs the NUFFT and its adjoin to iterate back and forth between the Fourier and image space. The performance of the proposed algorithm is demonstrated through a series of digital simulations and experimental phantom studies. Results of the proposed algorithm are compared with those of existing TV-regularized techniques based on compressed sensing method, as well as basic algebraic reconstruction technique. Compared with the existing TV-regularized techniques, the proposed Fourier-based technique significantly improves convergence rate and reduces memory allocation, respectively.     

Tomographic reconstruction of asymmetric soot structure from multi-angular scanning

A tomographic deconvolution technique using the Fourier transformation has been applied for the reconstruction of asymmetric soot structure. Local soot volume fraction distribution can be identified from line-of-sight integrated data using light extinction measurements with multi-angular scanning. A peak-following interpolation technique was adopted to effectively increase the number of scanning angles. The results showed that the peak-following interpolation has improved the accuracy of reconstruction compared to the arithmetic interpolation in determining the local soot volume fraction. The measurement from a laser-induced incandescence technique substantiated the validity of the reconstruction technique.     

Comparison of results of interferometric phase extraction algorithms for three-dimensional flow-field tomography

A comparison of the results of interferometric phase information retrieval and subsequent tomographic reconstruction from deformed wavefront projections by phase unwrapping is presented. In interferogram processing, conventional fringe tracking and Fourier transform methods have been utilized for comparison. With these methods by injecting carrier fringes, the projection data of any axial cross section can be extracted in all projection directions to implement three-dimensional tomographic reconstruction. The results of experiments of a simulated temperature field prove that the phase extraction based on the Fourier transform method produces tomographic reconstruction much superior to the conventional fringe tracking technique.     

像面滤波技术在无透镜傅里叶变换数字全息中的应用

无透镜傅里叶变换数字全息波前重建主要采用全息图的一次快速傅里叶变换方法,重建图像不能充分占有重建平面.本文基于像平面滤波技术,提出对物体局部区域光波场进行放大重建并让重建图像布满重建平面的方法,给出具有精细结构物体的数字全息波前重建实例.此外,将数字全息光波场重建视为具有方形出射光瞳的光学系统的相干光成像过程,导出了物体放大图像的分辨率与光学系统相关参量的关系,并通过实验给予证明.     

黄氏傅里叶计算全息图的数字再现及零级像的消除

将数字再现技术应用于黄氏(T.S. Huang)傅里叶计算全息图的再现过程, 制作计算全息图,利用数字再现直接在计算机上完成全息图的再现.直接利用数字图像处理的方法对所得计算全息图进行滤波处理,消除了零级像和原始像,使得数字再现时得到了清晰的再现像,并给出了所制作的计算全息图以及数字再现的结果.     

Iterative wave-front reconstruction for open-loop metrology applications: Shack-Hartmann and shearing interferometer wave-front sensing using Fourier or Multigrid reconstructors

Numerous techniques exist to reconstruct the wave-front in Shack-Hartmann and shearing interferometer wave-front sensors. Two of these techniques involve solving the least-squares wave-front reconstruction via Fourier transform or Multigrid methods. These two techniques operate on a square grid and are sensitive to both nonlinearities and to the methods used to extend the gradients beyond the aperture to the edges of the square grid. Both of these sensitivities can lead to large residual wave-front errors when reconstructing large aberrations. In this article we introduce an iterative computational loop in the reconstruction process which is designed to improve the reconstruction variances introduced by these parameters. This technique allows for accurate reconstruction of large phases which can arise in applications such as open-loop compensation of atmospheric turbulence, aberrometers and metrology. In this article, it is demonstrated that large aberrations can be accurately reconstructed utilizing this iterative method with Fourier or Multigrid reconstructors.     

像面滤波技术在无透镜傅里叶变换数字全息中的应用

无透镜傅里叶变换数字全息波前重建主要采用全息图的一次快速傅里叶变换方法,重建图像不能充分占有重建平面.本文基于像平面滤波技术,提出对物体局部区域光波场进行放大重建并让重建图像布满重建平面的方法,给出具有精细结构物体的数字全息波前重建实例.此外,将数字全息光波场重建视为具有方形出射光瞳的光学系统的相干光成像过程,导出了物体放大图像的分辨率与光学系统相关参量的关系,并通过实验给予证明.     

Fast gradational reconstruction for Fourier ptychographic microscopy

We develop an improved global reconstruction method for Fourier ptychographic microscopy,a newly reported technique for wide-field and high-resolution microscopic observation.The gradational strategy and graphic processing unit computing are applied to accelerate the conventional global reconstruction method.Both simulations and experiments are carried out to evaluate the performance of our method,and the results show that this method offers a much faster convergence speed and maintains a good reconstruction quality.     

The recording of digital hologram at short distance and reconstruction using convolution approach

By adopting in-line lensless Fourier setup and phase-shifting technique, we recorded the phase-shifting digital hologram at short distance. As the Fresnel diffraction condition is no longer valid, the convolution approach is chosen for the reconstruction. However, the simulated reference wave for the reconstruction would suffer from severe under-sampling due to the comparatively large pixel size. To solve this problem, sinc-interpolation is introduced to get the pixel-size of the hologram reduced prior to the reconstruction. The experimental results show that an object image of high fidelity is obtained with this method.     

基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换,设置阈值和频率积分范围后,进行二维窗口傅里叶逆变换,然后对包裹相位做去载频和相位展开处理得到相位差分布,最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明,使用该方法最大相位复原误差为0.82%,均方根值为0.020 9 rad,实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数,如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比,基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性,为波前检测提供一种新的处理方法。     

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。     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

精油中挥发性成分GC/FTIR与GC/MS联合分析

采用同时蒸馏萃取(SDE)法获得了香紫苏(Salvia sclarea L.)精油,利用气相色谱/傅里叶变换红外光谱联用(GC/FTIR)和气相色谱/质谱联用(GC/MS)相结合的手段,对其挥发成分进行了定性和定量分析,着重讨论了GC/FTIR在精油分析中的应用研究。通过不同波数官能团(Gram-Schmidt)重建红外光谱图、红外光谱差谱技术及质谱等相互验证的方法,大大提高了香紫苏油挥发成分的定性分析准确性。     

Lens-free coherent modulation imaging with collimated illumination

We propose a lens-free coherent modulation imaging(CMI) method for reconstructing a general complex-valued wave field from a single frame of a diffraction pattern. A numerical Fourier transform is introduced in the iterative reconstruction process to replace the lens or zone plate used in the current CMI technique to adopt the constraint on the Fourier components of the exit wave field of the sample. While the complexity of the experimental setup is remarkably reduced by replacing the zone plate and additional accessories with the numerical processing, the energy fluence loss induced by the undesired diffraction orders of the zone plate can be also avoided. The feasibility of the proposed technique is verified experimentally with visible light.     

Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence

We present a novel fluorescence lifetime tomography system applied to a highly scattering autofluorescent phantom containing live cells expressing the fluorophore enhanced green fluorescent protein (EGFP). The fluorescence signal was excited using a fiber-laser-pumped supercontinuum source and detected using wide-field time gating imaging. To facilitate rapid 3D reconstruction of the fluorescence lifetime distribution, the time-resolved data were Fourier-transformed in time to give complex functions that formed a data set for the Fourier domain reconstruction. Initially the presence of an unspecified background autofluorescence signal impeded reconstruction of the lifetime distribution, but we show that this problem can be addressed using a simple iterative technique.     

Tomographie a l'aide du reseau zone de Fresnel. Simulation numerique de la reconstruction optique

In this paper a new method of emission tomography using coded apertures is analysed. The coded image of a radioactive distribution is created using a single linear Fresnel zone plate. The decoding procedure is performed using a computer algorithm simulating the optical phenomenon. This numerical reconstruction requires bidimensional Fourier transform algorithms. On the contrary, a linear Fresnel zone plate only requires a one dimensional Fourier transform algorithms is workable in most of the available nuclear medicine computers. The experimental results demonstrated the focalisation properties of this code (tomographic effect) and the parameters found after numerical reconstruction were similar to those expected from the optical theory. Practically, this technique should make it possible to perform morphological studies of moving organs, i.e. dynamic tomography which should be for example very helpful in cardiac studies.     

Inversion of acoustic diffraction fields in anisotropic solids

We show that the fast Fourier transform (FFT) technique provides a computationally efficient method of calculating 2D amplitude and phase images of complex wave fields generated and measured in elastically anisotropic solids by phase sensitive acoustic microscopy. Further, we discuss how this technique can be used to treat inverse problems such as source reconstruction, image quality assessment, and the determination of elastic constants.     

自参考光谱相干法的小波变换相位重建

将小波变换法引入光谱相位相干电场重建法的相位重建，从光谱干涉条纹的小波变换中直接 读取条纹相位，消除了传统傅里叶方法滤波过程中产生的相位噪声. 这种方法将有利于超宽 带、单周期超短脉冲的产生，更适用于超短脉冲的评价. 关键词： 超短脉冲 相位重建 小波变换     

一种三维物体相息图的迭代计算方法

在传统迭代傅里叶变换算法的基础上,提出了一种计算三维物体相息图的新方法.基于层析法将三维物体的多个分层物面作为衍射再现图像,在一个输入面(相息图)和多个输出面(再现像)之间进行迭代.通过在傅里叶迭代运算中引入距离相位因子,表示物体不同物面的深度,体现了物体的三维特征.实验结果证明了本文算法良好的收敛特性和再现性能.最后,分析了物面数量和间距对全息再现质量的影响,利用液晶空间光调制器采用时分复用的方法还原了三维物体的多个物面.     

Echo-planar rotating-frame imaging

A new rotating-frame imaging method that produces a complete cross section of an object in a single experiment is reported. The echo planar rotating frame imaging (EPROFI) technique uses two perpendicular RF gradients for two-dimensional spatial encoding and fully exploits the formation of rotary echoes for fast sampling of spatial frequencies. The acquisition scheme yields the Fourier transform of the spin distribution on Cartesian coordinates for straightforward image reconstruction. Implementation of the technique on a low-field portable NMR probe is described and results are presented for test objects with different geometries.