基於干涉條紋之下壓深度分析研究

Abstract

本研究提出一套以干涉條紋觀測為基礎的下壓深度分析技術，結合雙折射材料的光彈效應與數位影像處理，建立具光學高解析與可視化的量測系統，研究重點為分析干涉條紋形貌與材料受力變形間的定量關係，進而推估下壓變形區域的深度與作用力。 傳統的表面輪廓與平整度量測多採用接觸示掃描形貌量測與非接觸干涉技術，而本研究採用光彈材料受到外力作用，因應力場導致局部折射率的變化而產生清晰條紋，其條紋階數與主應力差值依序對應，能精確擷取條紋並建立其級數與幾何變形間的關係，獲得受力變形深度與應力分佈之數學模型，進而一次性快速探索整個平面的深度形貌。本研究設計一實驗系統，將光彈材料以圓形邊界固定邊緣，利用中央尖凸之載具下壓，使光彈應力集中區域產生相應階數的干涉條紋。透過圓偏振片光系統採亮/暗場條件下擷取干涉條紋圖像，控制機構調控下壓深度同時紀錄條紋與載荷變化。圖形處理的流程包括灰階化與雜訊濾波，利用影像相減獲得條紋倍增的資訊，並多方向掃描影像之強度變化接著進行全域細線化以提取條紋位置，可獲得清晰的條紋藉以對比下壓深度建立相互關係。 理論解析則依據圓板理論推導軸對稱彈性材料受集中載荷的變形函數，可與光彈實驗的條紋位置與下壓深度建立相互關係，結果顯示本方法可成功擷取至少四階干涉條紋並準確反推下壓深度與應力分佈，條紋形貌與理論模型具良好對應性，相較於傳統三維形貌輪廓儀與先進的共軛焦量測儀，本研究的量測方法具一次性、即時性與可視化的優勢。總結來說，本研究建立一套基於光學元件受力後經由干涉條紋量測深度形貌的技術，透過數位影像處理與光彈與高等材料力學理論，連結條紋階數、光學應力與受力深度，實現高解析的光測力學幾何形貌反算技術，預期未來導入演算法與自動化分析，可拓展至微尺度之變形與應力分析將具更強大的應用範疇。

This study proposes an indentation depth analysis technique based on interference fringe observation, integrating the photoelastic effect of birefringent materials with digital image processing to establish a high-resolution, optical, and visualized measurement system. The research focuses on quantifying the relationship between fringe patterns and material deformation under stress, enabling the estimation of indentation depth and applied force within the deformation region. While conventional surface profiling and flatness measurements typically rely on contact-based scanning or non-contact interferometric techniques, this study utilizes photoelastic materials that produce distinct interference fringes due to local refractive index variations under external loads. These fringe orders correspond directly to the differences in principal stress, allowing for precise fringe extraction and correlation with geometric deformation. A mathematical model is thus developed to describe the stress distribution and deformation depth, enabling full-field, one-shot surface profiling. An experimental setup is designed in which the photoelastic material is fixed with circular boundaries and indented at the center using a pointed indenter to generate interference fringes in the stress-concentrated region. Fringe patterns are captured under light-field and dark-field conditions using a circular polarizer-based optical system. The indentation depth and corresponding load changes are recorded simultaneously. The image processing workflow involves grayscale conversion and noise filtering, followed by fringe enhancement through image subtraction. Multi-directional intensity scanning and global thinning are then applied to accurately extract fringe positions and enhance fringe clarity for further correlation with indentation depth. Theoretical analysis is conducted using circular plate theory to derive the axisymmetric deformation function of elastic materials under concentrated loading. A strong correlation is established between fringe positions observed in photoelastic experiments and the corresponding indentation depths. Experimental results demonstrate that this method can successfully capture at least four fringe orders and accurately reconstruct both indentation depth and stress distribution. The fringe patterns show good agreement with theoretical models. Compared to traditional 3D profilometers and advanced confocal instruments, the proposed method offers advantages in one-shot, real-time, and visualized measurement. In summary, this research develops a fringe-based optical technique for reconstructing deformation geometry through stress-induced interference in birefringent materials. By linking fringe order, optical stress, and indentation depth through digital image processing and advanced mechanics, a high-resolution optical inverse method is achieved. With future integration of algorithms and automation, the system holds great potential for micro-scale deformation and stress analysis.