結合探針天線及相位補償之三維微波全像術

Abstract

本論文提出了一個三維微波全像術，此演算法可配合單一探針或雙探針的配置來進行成像。在適當的條件下，即使使用單一探針，本演算法也可得到和其他雙探針演算法差不多的成像品質。所提出來的演算法可分為四個部分：首先，為了補償探針天線在發射或接收時的特性，我們從天線的開路電壓模型出發，經適當的理論推導並應用數值方法可得到一個與天線無關的最小平方法問題。不過，在僅使用一個探針天線的狀況下，此最小平方法問題有很嚴重的非良置傾向（雙探針配置則沒有此問題）。故第二部分，為了改善數值穩定性，吾人提出了輔助方程式（須假設介質無損）。第三部分，為了更精確的探測出物體的位置，吾人利用簡單的光束模型發展出相位補償法，僅需針對最小平方法的核心矩陣元素補償適當的相位。最後，考慮到有限大小的掃描孔徑及天線波束寬，吾人採用了一個數值低通濾波器以篩選出在空間頻率中需要求解的範圍，可減少無意義的計算並抑制高頻的雜訊。為了驗證所提出之演算法，我們分別透過模擬與實驗量測的方式來進行測試。測試物體的幾何形狀、位置、介電常數可以被求得。本論文所提出的方法所能達到橫向解析度與縱向解析度分別約為四分之一波長與十分之一波長。

A Novel 3-D microwave holographic imaging algorithm compatible with both single-probe and dual-probe scanning setups is proposed for imaging dielectric targets. In some cases, even with only one probe antenna, the quality of the images reconstructed using the proposed algorithm is comparable or even superior to those using dual-probe-based methods. The proposed algorithms can be divided into four parts. First, starting from the open-circuit voltage of an antenna, the proposed algorithm compensates for both transmitting and receiving properties of the probe antenna, leading to least squares problems to be determined. However, the problem tends to be ill-conditioned in the single-probe setup (irrelevant to the dual-probe one). Second, an auxiliary equation based on lossless condition of an unknown target is thus derived and exploited to effectively improve the numerical stability. Third, to accurately locate the unknown target in range direction, a phase compensation method that requires only phase correction to the associated entries of the kernel matrices is proposed based on a simple ray model. Last but not least, considering both a finite size of a scanning aperture and beamwidth of the probe antenna, a numerical low-pass filter in the spatial-frequency domain is devised to effectively locate the worth-solving area and thus reduce computational time substantially. For verification, a series of images reconstructed from the simulated and measured scattering data using the proposed algorithm are presented. Thanks to the enhanced image quality, the geometry, location, and dielectric constant of the target can readily be retrieved. The range and cross-range resolutions achieved are about /10 and /4,