應用於三維微波全息影像術之增強型相位補償方法與誤差分析

Enhanced Phase Compensation Method and Error Analysis for 3-D Microwave Holographic Imaging

陳徐麒(Hsu-Chi Chen)

指導教授 ： 陳士元

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202100523

摘要

為改善於微波成像中使用包恩近似法所產生之誤差，本論文提出增強型相位補償方法以將實際由散射體造成的場分布變化納入考量。以本實驗室過去已發展之三維微波全像術演算法[1]為基礎，本論文提出之增強型相位補償方法由光譜域切入分析，並藉平面波展開與簡化之射線模型，以達成精準之相位變化估計。此外，本論文提出之增強型相位補償方法全面地分析了各種可能的物體排列，使得微波成像的應用更加廣泛且不受限於物體的空間分布情形。簡而言之，只要物體之空間分布符合於[1]提出之解析度限制，即便兩散射體完全重疊於距離方向，其空間及介電質分布特性皆可藉由增強型相位補償方法的使用而成功取得。
為使已發展之三維微波全像術演算法[1]更貼近實際應用，本論文亦提出並分析解決兩種嚴重損壞成像結果之誤差項：截斷誤差和失配誤差。截斷誤差之產生是由於實際設置之成像系統僅可能有有限大小的掃描面。因此，本論文首先以定性方式解析截斷誤差帶來的影響，再以定量方式輔以模擬數據，規範出於架設成像系統時所需參照之可接受誤差範圍。失配誤差則是源自於成像過程中為精確計算散射體分布，而採用之模擬獲得的電場分布與量測時實際電場分布情形的差異所致。為改善失配誤差，本論文提出一校準方法，係藉由分別使用兩個校準物體：分布校準物與數值大小校準物，以探測出實際量測中，空間的電場分布資訊。最後，欲能合理地檢驗所提出之相位補償與校準方法之正確性，本論文於光譜域定義了總體成像誤差。所定義之總體成像誤差的概念主要是基於計算採用解成像問題之場分布(可為經增強型相位補償或校準取得之場分布)與實際含有散射體之場分布情形間的差異。因此，總體成像誤差能直接地反映成像結果、甚至所提出之增強型相位補償與校準方法的正確性。
本論文以模擬和實測驗證所提出之增強型相位補償方法和校準方法。使用模擬所得之散射資料，增強型相位補償方法和校準方法均獲得充分的驗證；唯量測過程中，由於量測系統中使用之非理想支撐支架，導致本論文提出之方法無法由量測結果獲得印證。然而，經由分析非理想支撐支架所造成的影響，模擬結果與量測結果之間的不一致性即可被完美闡釋。因此，吾人相信若能製造出影響效應較小的支撐支架，量測之結果即能充分驗證所提出之增強型相位補償方法和校準方法。

關鍵字

三維微波全像術 ； 截斷誤差 ； 包恩近似

並列摘要

An enhanced phase compensation (EPC) method for 3-D microwave holographic imaging is proposed. The associated errors incurred during imaging process are also analyzed. Due to the incorrect phase information stemming from the adoption of Born Approximation, the reconstructed images are accompanied by artifacts. On the basis of the holographic algorithm proposed in [1], the phase variation of waves caused by unknown objects can be estimated more accurately by the proposed approach with the aid of plane wave expansion and a simple ray model. In addition, the proposed EPC method comprehensively considers the practical phase distribution in spectral domain on all designated imaging planes for all potential target arrangements, providing the much more stable imaging results regardless of how the targets are placed. In short, as long as the arrangements of targets meet the restrictions of cross-range resolution and range resolution, the spatial distribution and corresponding dielectric property can be successfully retrieved even if the targets completely overlap with each other in range direction.
By closely inspecting the shortcomings of the exploited imaging algorithm, it is found that the imaging results mainly suffer from two specific types of errors, which are truncation error associating with the finite size of scanning aperture and mismatch error originating from the difference in field distribution between simulation and practical application. In this study, the effect of truncation error is qualitatively discussed and quantified with the simulated results. Referring to the quantified results, the criterion of feasible range which guarantees an acceptable error level is proposed. As for the mismatch error, two calibration objects (CO), distribution CO and magnitude CO, are introduced to gain the actual field information on the desired imaging planes instead of using the simulated field distribution. To fairly realize the correctness of imaging results, the total imaging error is defined in spectral domain. With the defined total imaging error, since it computes the difference between the adopted field distribution, might be acquired by EPC or calibration method, for solving the algorithm and the actual field distribution with the presence of scatterers, the correctness of adopted field information can be truly reflected. In that sense, the correctness of proposed EPC method adjusting the field information or the proposed calibration method measuring the actual field distribution is directly examined rather than blindly checking the imaging results in spatial domain which resulted from multiple effects.
To validate the proposed methods, images of a series of cases are reconstructed from the simulated and measured scattering data. All the proposed methods are verified by the simulations. Owing to the non-ideal supporting fixture utilized in measurement setup, the results acquired through measurement are not consistent to the one obtained via simulation. Yet the effect of supporting fixture is fully studied and shown to agree with the measurement results. Therefore, it is expected that the refinement on measurement system will allow the successful verification in practice.

並列關鍵字

3-D microwave holographic imaging ； truncation error ； Born Approximation

參考文獻

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