應用特徵值法於半穩定系統之光學設計

將光學系統沿著任意方向旋轉任意角度，若出射光線的方向不會因系統旋轉而改變，稱之為「光學穩定系統」，若出射光的方向某單位向量固定，其他方向向量卻因光學系統旋轉而改變，則稱之為「光學半穩定系統」本文要探討的是由特定方向向量成形的光學反射式光學半穩定系統，讓出射光束不受限於逆反射與反射式兩項。本文提出反射式光學半穩定系統與多重反射系統的分析方式。證明在特殊狀況下，光學系統裡多重反射鏡的光束在入射面跟出射面維持平行，就可以得到穩定光學的稜鏡。本研究提出一個利用特徵值對於穩定圖像方位變化之反射鏡和稜鏡系統的設計方法，在該系統中，擇優函數使用以特徵值為基礎的方法解出。反射系統跟隨圖像方位變化擇優函數特徵向量的旋轉維持圖像方位變化穩定，惟圖像仍可物理進入系統的光圈中。結果顯示，在含有多個反射光線的光學系統中，成像方向變化的稜鏡可藉由條件下在出射光和入射光處增加兩折射邊界平面的而使稜鏡呈現穩定現象。

關鍵字

平面反射鏡；稜鏡；光學半穩定系統；特徵值法

並列摘要

Optically-stable (OP) system is a kind of specific optical system,which can keep the emitted rays at a constant direction. There are two kinds of OPS: Fully optically-stable (FOS) systems and partially-optically-stable (POS) systems. A FOS system is always optically stable for arbitrary rotation axis, but a POS is only optically stable for a specific rotation axis. In a FOS system, the exiting light ray is restricted to preservation or retroreflection, but in a POS system is not. The FOS system have been investigated in our lab’s earlier research. In this one, we introduce the (POS) reflector system. Furthermore, it is shown that a POS prism can be obtained by adding two refracting flat boundary surfaces with specific conditions at the entrance and exit positions of the light ray in an optical system with multiple reflectors. Beside, we also provide an “eigenvalue method” to the solve the reflectors’ poses in a POS system. By the method, the eigenvector is the optically stable axis of the in POS system. Therefore, the eigenvalue method is more convenient for other existing methods.

並列關鍵字

prism ； reflector ； optically stable system ； eigenvalue method

參考文獻

[4]N. Schweitzer, Y. Friedman, and M. Skop, “Stabilityof systems of plane reflecting surfaces,” Appl. Opt. 37, 5190–5192 (1998)

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[8]Y. Friedman and N. Schweitzer, “Classification of stable configurations of plane mirrors,” Appl. Opt. 37, 7229–7234, (1998)

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應用特徵值法於半穩定系統之光學設計

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