以同心圓梯度折射率透鏡消球差之研究

Eliminating Spherical Aberration by Gradient-Indexed Lenses

徐嘉成(Jia-cherng Hsu)

指導教授 ： 李正中

國立中央大學/理學院/光電科學研究所/博士(2008年)

摘要

球面透鏡製造容易，但會產生球面像差，這是高成像品質要求之
精密光學如光學讀寫頭，積體電路暨微機電投影光學系統，及高度放大顯微透鏡等所不能容許的。非球面透鏡是現今解決此球面像差之主流方法。本論文提出以梯度折射率透鏡來消除球面像差。經計算證明將物體置於梯度折射率圓環的中心，而此透鏡折射率隨不同圓環呈線性改變，就可消除主球差。若是折射率改變開放為任意函數，則可完全消除球差。在此亦提出擴散、植入、固熔液非平衡冷卻法等製造同心圓梯度折射率材料之方法。另外基於以上推導基礎我們可找出阿貝點所在位置以及判斷一般均質透鏡非近軸光線成像位置與近軸光線成像位置之關係。最後，我們提出一些梯度折射率透鏡應用的例子。

關鍵字

球面像差 ； 幾何光學 ； 投影光學系統 ； 顯微物鏡 ； 球差判斷 ； 阿貝點 ； 主球差 ； 固溶體 ； 同心圓梯度折射率透鏡

並列摘要

High quality optical instruments and elements like optical pickup head, projection optics systems used in IC manufacture and/or MEMS products, and microscope high magnification objectives, etc, all can not tolerate the spherical aberration caused by spherical surfaces lenses.
Aspherical surface lenses are popular used as the solution candidates, though they may be harder to produce than spherical surfaces lenses. In this paper, we find that concentric gradient-indexed lenses may be another choice. We suggest some methods to produce concentric gradient-indexed materials. As the object point is located at the center of these concentric gradient-indexed shells, by our calculation, when we choose suitable refractive index gradient, the image of the lens made by our concentric gradient-indexed material have no primary spherical
aberration. If we let the refractive index variation function a little deviate from linear one, we can even eliminate spherical aberration absolutely.
By the results deduced in our calculation, we can find the Abbe points and we can also find the Abbe points are also the turning points of the ordinary spherical homogeneous lens spherical aberrations tendency. Finally, we give some applications of the concentric gradient-indexed lenses to microscope objectives and others.

並列關鍵字

spherical aberration judgment ； solid solutions ； primary spherical aberration ； incongruently melting compounds ； geometric optics ； spherical aberration ； projection optics systems ； microscope objective ； Abbe points ； concentric gradient-indexed lenses ； gradient-indexed lenses

參考文獻

[12] E. Chason, S. T. Picraux, J. M. Poate, J. O. Borland, M. I. Current, T. D. d. l. Rubia, D. J. Eaglesham, O. W. Holland, M. E. Law, C. W. Magee, J. W. Mayer, J. Melngailis, and A. F. Tasch: J. Appl. Phys. 81 (1997) 6513.

[6] G. Andersen: 44 (2005) 1355.

[9] A. R. West: “Basic Solid State Chemistry”, (Wiley, New York, 1999).

[10] S. Franssila: “Introduction to Microfabrication”, (Wiley, New York, 2004).

[13] N. W. Cheung: Mater. Chem. Phys. 46 (1996) 132.