使用方解石稜鏡之白光絕對角度量測干涉儀

本文提出一套創新的白光絕對角度量測干涉儀，它包含起偏器、成對方解石雙折射稜鏡、Fresnel rhomb式二分之一波板、PZT推動之角位移平台、檢偏器及CCD照相機，其中第二個雙折射稜鏡置於角位移平台上。本干涉儀的特性是，當第二雙折射稜鏡在零度位置時會產生最小干涉光強。配合該干涉儀，本文提出兩種量測方法，掃描法與即時補償法。掃描法利用最暗干涉條紋初始位置及偏轉後偵測到的位置做比較得到待測角；即時補償法亦是一方向引導術，它將最暗干涉條紋鎖定至CCD觀測窗的中心位置，藉由分析暗紋周圍光強變化，由電腦演算出角位移大小與方向，並引導角位移平台補回該角度偏移，使暗紋再次回到中心，此法可以進行快速、準確的絕對角位移量測。　　本文實際建構一套干涉儀，它具有42545 rad./rad.之高靈敏度，量測解析度為0.01 arc-sec。透過實驗得知，當使用掃描法時，最大誤差為1.55 arc-sec，系統穩定度為0.34 arc-sec；當使用即時補償法時，最大誤差為1.164 arc-sec，系統穩定度為0.24 arc-sec，證明兩種量測法皆具有高精確度與高穩定度的特性。最後將干涉儀應用於大型線性位移平台，以掃描法與即時補償法對平台的水平擺角做量測，驗證了本文所提干涉儀的可應用性。

關鍵字

白光；干涉儀；角位移；光學量測

並列摘要

This paper proposes a novel white-light interferometer available for measuring absolute angular displacements. It is composed of a polarizer, two identical calcite crystals, a Fresnel rhomb half-wave plate, a PZT angular rotation stage, an analyzer and CCD camera, where the 2nd calcite crystal is fixed on the PZT angular rotation stage. The property of the proposed interferometer is its pattern goes to its minimum as the 2nd calcite crystal approach to the position of zero degree. One can thus rotate the crystal back to the position where the minimum pattern intensity reveals after the crystal is moved, and the reverse of the rotation is the angle the crystal has been moved. Two algorithms, the scanning and real-time compensation, incorporated with the interferometer are also proposed. The scanning algorithm, which possesses a wider range of angle measurement, extracts the rotation by scanning the crystal for a pre-determined range of angle. The real-time compensation algorithm, which is able to detect the angular displacements accurately in a very short time, retrieves the rotation by driving the crystal back right after the crystal is moved. The theory of the interferometer is demonstrated, a setup established to realize the interferometer is then introduced, and the experimental results from the uses of the setup are finally presented. The established sensitivity and resolution of 42545 rad./rad. and 0.01 arc-sec, respectively. The experimental results not only agree the validity but also demonstrate an application of the proposed interferometrer. Besides, maximum measurement error and the stability of the use of the scanning technique are 1.55 arc-sec and 0.34 arc-sec, respectively, and those of the uses of the real-time compensation technique are 1.164 arc-sec and 0.24 arc-sec, respectively.

並列關鍵字

white-light source ； interferometer ； angular displacement ； optical measurement

參考文獻

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使用方解石稜鏡之白光絕對角度量測干涉儀

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