Zhun Wei

Quantitative Theory for Probe-Sample Interaction With Inhomogeneous Perturbation in Near-Field Scanning Microwave Microscopy

A general approach for calculating tip-sample capacitance variation in near-field scanning microwave microscopy is presented. It can be applied to arbitrary tip shapes, thick and thin films, and variation due to inhomogeneous perturbation. The computation domain for the tip-sample interaction problem is reduced to a block perturbation area by applying Greens theorem, and thus it can save substantial time and memory during calculating either electric field or contrast capacitance for three-dimensional models of near-field microwave microscopy. We show that this method can accurately calculate capacitance variation due to inhomogeneous perturbation in insulating or conductive samples, as verified by finite-element analysis results of commercial software and experimental data from microwave impedance microscopy. More importantly, the method in this paper also provides a rigorous framework to solve the inverse problem, which has great potential to improve resolution by deconvolution.

Robust phase retrieval of complex-valued object in phase modulation by hybrid Wirtinger flow method

Abstract. This paper presents a robust iterative algorithm, known as hybrid Wirtinger flow (HWF), for phase retrieval (PR) of complex objects from noisy diffraction intensities. Numerical simulations indicate that the HWF method consistently outperforms conventional PR methods in terms of both accuracy and convergence rate in multiple phase modulations. The proposed algorithm is also more robust to low oversampling ratios, loose constraints, and noisy environments. Furthermore, compared with traditional Wirtinger flow, sample complexity is largely reduced. It is expected that the proposed HWF method will find applications in the rapidly growing coherent diffractive imaging field for high-quality image reconstruction with multiple modulations, as well as other disciplines where PR is needed.

Conjugate gradient method for phase retrieval based on the Wirtinger derivative

A conjugate gradient Wirtinger flow (CG-WF) algorithm for phase retrieval is proposed in this paper. It is shown that, compared with recently reported Wirtinger flow and its modified methods, the proposed CG-WF algorithm is able to dramatically accelerate the convergence rate while keeping the dominant computational cost of each iteration unchanged. We numerically illustrate the effectiveness of our method in recovering 1D Gaussian signals and 2D natural color images under both Gaussian and coded diffraction pattern models.

Two FFT Subspace-Based Optimization Methods for Electrical Impedance Tomography

Two numerical methods are proposed to solve the electric impedance tomography (EIT) problem in a domain with arbitrary boundary shape. The first is the new fast Fourier transform subspace-based optimization method (NFFT-SOM). Instead of implementing optimization within the subspace spanned by smaller singular vectors in subspace-based optimization method (SOM), a space spanned by complete Fourier bases is used in the proposed NFFT-SOM. We discuss the advantages and disadvantages of the proposed method through numerical simulations and comparisons with traditional SOM. The second is the low frequency subspace optimized method (LF-SOM), in which we replace the deterministic current and noise subspace in SOM with low frequency current and space spanned by discrete Fourier bases, respectively. We give a detailed analysis of strengths and weaknesses of LF-SOM through comparisons with mentioned SOM and NFFT-SOM in solving EIT problem in a domain with arbitrary boundary shape.

Analytical Green's function for tip-sample interaction in microwave impedance microscopy

Analysis and evaluation of tip-sample interaction in microwave microscopy are crucial to accurately measure the permittivity and conductivity of nanomaterial. However, even till now, an exact analytical solution for the tip sample interaction has yet to be found due to the complexity of various tips. In this paper, the exact three dimensional solution of Greens function due to an arbitrary dipole is given under bispherical coordinate system, and this solution is verified numerically. Moreover, even though the solution is derived under the spherical model, it turns out that it can be applied to various tip models when sample is close to tip. After obtaining the analytical solution, we can use it to improve the resolution of microwave microscopy and save time and memory in three dimensional simulations.

Analysis of tip-sample interaction in microwave impedance microscopy by lumped element model

We present a detailed analysis of tip-sample interaction in microwave impedance microscopy by applying lumped element method in this paper. A lumped element model is proposed and the value for each lumped element component is optimized. We find that reflection coefficient including both magnitude and phase obtained by simulation using this model matches with experimental data measured by microwave impedance microscopy (MIM) quite well. Also, the effect which both capacitance and resistance variation have on the tip-sample interaction is discussed. After that, sensitivity of this lumped element model to the electrical parameters is analyzed in this paper.

Three dimensional through-wall imaging: Inverse scattering problems with an inhomogeneous background medium

This paper investigates the three dimensional inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. The forward scattering problem is solved using the finite element-boundary integral method (FEM-BI) while the inverse problem is oriented to minimize a cost function using nonlinear conjugate gradient optimization algorithm. The background Greens function at each discrete point on the surface of the computational domain can be numerically obtained using commercial software. Such an approach shrinks the domain of inversion to a much smaller region than the standard finite difference approach. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging.