外差疊紋干涉術的原理與其應用之研究

Abstract

本論文提出一新穎的外差疊紋(moiré)干涉術，可改良現有moiré條紋的相位解析技術，進而提高傳統疊紋干涉術的量測準確度與解析度。在疊紋干涉術的光學架構中，將光柵以一等速度位移產生外差疊紋信號，此弦波信號可利用最小平方弦波擬合法擬合出最佳化的弦波曲線並獲得其相位值，藉此可分析隱含於moiré條紋的待測資訊，應用於雷射光束的準直測試與校正，以及表面形貌的量測中。 在雷射光束的準直測試與校正方法中，利用外差疊紋干涉術所量測得的相位斜率進行擴束雷射光的準直測試，以及僅藉由量測準直透鏡於光軸上任意兩位置的相位斜率，可以使得光束的準直校正不須沿光軸進行耗時的掃描量測，同時提升定位誤差達7 m，優於現有之技術。在表面形貌的量測中，提出利用外差疊紋干涉術結合投影疊紋法與自成像效應，量測漫射面物體的表面形貌。除簡化投影光柵條紋之光學架構外，並藉由最小平方弦波擬合法分析外差疊紋信號之相位，提升傳統疊紋干涉術量測之解析度與穩定度。亦延伸應用於量測角膜之表面形貌，大幅增加角膜表面的量測點數量，且無一般量測法使用球面假設演算法所可能造成的量測錯誤。此外，為了改良傳統疊紋干涉術的條紋解析技術，提出利用快速傅立葉轉換分析之外差疊紋表面形貌量測術。藉由一維快速傅立葉轉換分別分析相機中每一像素所擷取的外差疊紋信號，可獲得moiré條紋的相位分佈，進而重建待測物體的表面形貌。本方法無以往在每個疊紋相移影像進行濾波時所造成之可能誤差，以及無光學消除疊紋諧波雜訊的繁瑣步驟與於同步控制時所可能造成之誤差，因此具有較優異且快速的條紋解析能力，提高量測的準確度。

A novel heterodyne moiré interferometry has been proposed to advance the moiré phase analysis techniques and increases the accuracy and the resolution of the traditional moiré interferometry. By applying a constant velocity to the grating in the moiré interferometry, the heterodyne moiré signal can be generated and then be fitted by the least square sine fitting algorithm to get the optimized sinusoidal curve and extract the phase data. The tested information within the moiré fringes can subsequently be obtained and applied to the laser light beam collimation testing and calibration and the surface profile measurement. In the laser light beam collimation testing and calibration, the phase slopes can be measured using the heterodyne moiré interferometry to implement the collimation testing of the expanded light beam. Meanwhile, the collimation position of the collimating lens can be determined by only measuring two phase slopes on two different positions along the optical axis. Therefore, the calibration procedure does not need time-consuming scan along the optical axis and can simultaneously improve the positioning error of the previous techniques to 7 m. In the surface profile measurement, a novel method which merges the projection moiré method and the self-image effect has been proposed to measure a diffusive surface. In addition to simplifying the optical configuration of the grating fringe projection, the resolution and the stability of the traditional moiré interferometry can be improved by using the least-squares sine fitting algorithm to analyze the phase of the heterodyne moiré signal. Besides, the extended application has been realized to measure the corneal surface profile. The proposed method dramatically increases the measurement points of the corneal surface and does not produce the probable measurement mistakes from the spherical surface assumption of the common methods. Additionally, to improve the traditional fringe analysis techniques of the moiré interferometry, fast Fourier transform (FFT) heterodyne moiré surface profilometry has been proposed. The precise phase distribution of the moiré fringes can be extracted using a one-dimensional FFT analysis on every pixel to reconstruct the surface profile of the tested object. This method does not have the probable error from the filtering procedure on every phase-shifting image, and does not have the complicated procedure and the error from the synchronous control of the optical elimination method. Therefore, this method has a better and rapid fringe analysis ability and improves the measurement accuracy.