Le Shen

Objective. X-ray diffraction (XRD) is a non-destructive technique capable of obtaining molecular structural information of materials and achieving higher sensitivity than transmission tomography (CT) for substances with similar densities. It has great potential in medical and security applications, such as rapid breast cancer screening, calculi composition analysis, and detection of drugs and explosives. Among various XRD tomography (XRDT) systems, snapshot coded aperture XRDT (SCA-XRDT) achieves the fastest scanning speed, making it well-suited for practical medical imaging and security inspection. However, SCA-XRDT suffers from poor data condition and an ill-posed reconstruction problem, leading to significant challenges in accurate image reconstruction. In this work, we explore the inherent characteristics of XRD patterns and incorporate a novel and effective prior accordingly into an iterative reconstruction algorithm, thereby improving the reconstruction performance. Approach. By analyzing the key physical factors that shape XRD patterns, we represent XRD patterns as a linear combination of basis functions, and validate the feasibility and generality of this representation using experimental data. Building upon this, we propose a novel basis-function-decomposition reconstruction (BFD-Recon) method that incorporates the basis function representation as a prior into a model-based SCA-XRDT reconstruction framework. This method transforms the optimization target from entire XRD patterns to parameters of basis functions. We further impose smoothness and sparsity constraints on the parameters to restrict the solution space. We employ the Split Bregman algorithm to iteratively solve the optimization problem. Both simulation and experimental results demonstrate the effectiveness of the proposed BFD-Recon method. Main-results. Compared with a conventional MBIR method for XRDT reconstruction, the proposed BFD-Recon method results in more accurate reconstruction of XRD patterns, especially the sharp peaks that closely match the ground truth. It substantially suppresses the noise and the impact of background signals on the reconstructed XRD patterns. Since the proposed basis function decomposition and the prior align well with the characteristics of XRD patterns, its value is well manifested along the spectral dimension of the reconstructed images. It also reduces blur along the x-ray path in the spatial dimension. Quantitatively, BFD-Recon increases the correlation coefficients between the reconstructed and ground-truth XRD patterns by up to 10% and the average PSNR by 20%. Significance. Through theoretical analysis and experiments, we propose a basis function decomposition method for XRD patterns and demonstrate its effectiveness and general applicability. Incorporating the basis-function-decomposition into the model-based iterative reconstruction can significantly enhance the XRDT reconstruction performance. The method provides prior information on XRD patterns and reduces the number of unknowns by at least one order of magnitude by transforming the optimization target to basis function parameters, which effectively alleviates the ill-posedness of the reconstruction problem.

Photon-counting detector CT (PCD-CT) is a revolutionary technology in decades in the field of CT. Its potential benefits in lowering noise, dose reduction, and material-specific imaging enable completely new clinical applications. Spectral reconstruction of basis material maps requires knowledge of the x-ray spectrum and the spectral response calibration of the detector. However, spectrum estimation errors caused by inaccurate energy threshold calibration will degrade the accuracy of the reconstructions. Existing spectrum estimation methods are not adequately modeled for bias in energy threshold position. Besides, directly solving a big number of variables of the pixel-wise effective spectra for PCD is an ill-conditioned problem so that stable solution is hardly achievable. In this paper, we assumed the effective spectra variation across the detector mainly comes from the calibration error in the energy threshold positions as well as the intrinsic threshold distribution. We propose a joint reconstruction and spectrum refinement algorithm (JoSR) that introduces an innovative spectrum model based on non-negative matrix factorization (NMF) to significantly reduce the dimension of unknowns so that makes the problem well-conditioned. The polychromatic spectral imaging model and the basis material decomposition method together form an optimization objective. The proximal regularized block coordinate descent algorithm is adopted to deal with the non-convex optimization problem to ensure convergence. Simulation studies and experiments on a laboratory PCD-CT system validated the proposed JoSR method. The results demonstrate its advantages on image quality and quantitative accuracy over other state-of-the-art methods in the field.

An ABB IRB6640 industrial robot is used as a processing platform for optical polishing. The relationships of coordinate systems are defined, the algorithm of coordinate transformation, Euler angles and quaternion are provided. M-like removal function and Gaussian-like removal function are used to simulation process an off-axis aspheric surface. The surface error after polishing by M-like removal function is 1.5 to 2.5 times bigger than Gaussian-like removal function. This proves that M-like removal function also has good convergence speed. Then, the pentagram polishing head is used to polish a Φ600mm off-axis paraboloid surface. After 15 cycles, about 120 hours processing, PV converges from 5.8μm to 0.836μm, RMS converges from 1.2μm to 0.054μm, PV and RMS respectively converge 85% and 95%. The experiment shows M-like removal function has good convergence speed.

Zoom mirror is a kind of active optical component that can change its curvature radius dynamically. Normally, zoom mirror is used to correct the defocus and spherical aberration caused by thermal lens effect to improve the beam quality of high power solid-state laser since that component was invented. Recently, the probable application of zoom mirror in realizing non-moving element optical zoom imaging in visible band has been paid much attention. With the help of optical leveraging effect, the slightly changed local optical power caused by curvature variation of zoom mirror could be amplified to generate a great alteration of system focal length without moving elements involved in, but in this application the shorter working wavelength and higher surface figure accuracy requirement make the design and fabrication of such a zoom mirror more difficult. Therefore, the key to realize non-moving element optical zoom imaging in visible band lies in zoom mirror which could provide a large enough saggitus variation while still maintaining a high enough surface figure. Although the annular force based actuation could deform a super-thin mirror having a constant thickness to generate curvature variation, it is quite difficult to maintain a high enough surface figure accuracy and this phenomenon becomes even worse when the diameter and the radius-thickness ratio become bigger. In this manuscript, by combing the pressurization based actuation with a variable thickness mirror design, the purpose of obtaining large saggitus variation and maintaining quite good surface figure accuracy at the same time could be achieved. A prototype zoom mirror with diameter of 120mm and central thickness of 8mm is designed, fabricated and tested. Experimental results demonstrate that the zoom mirror having an initial surface figure accuracy superior to 1/50λ could provide at least 21um saggitus variation and after finishing the curvature variation its surface figure accuracy could still be superior to 1/20λ, which proves that the effectiveness of the theoretical design.

Noise in CT images can be a critical issue which degrade image quality and affect diagnosis and inspection. Dual energy CT posed a promising future in better contrast and material discrimination. However, DECT images, such as electron density and atomic reconstructions, normally have their own noise features and are difficult to describe the noise property. Denoising DECT images without harm any resolution is important for practical applications. In this work, we proposed an edge-preserving total variation based denoising method by incorporating the structural information from a low-noise image available which in DECT imaging case would be low/high energy attenuation reconstruction. The method is evaluated on practical experiments and gain very good performance.