在許多雷射應用中需要特定的照度分佈來達到期待的光學要求，在過去的研究中有許多方法來達到雷射整型的目的，而幾何光學設計方法已經被證實是可行的。對於應用在表面輪廓量測的光束擴束器來說，要求的光場不只需要照度均勻，更希望目標面積可以越大越好；而經過準直的光束可以在使用上不受距離的限制，大大的提升了實用性。
在本篇論文中，我們特別針對大範圍目標面來進行設計優化，產生準直且均勻的大面積光場，當中我們利用費馬原理(Fermat’s Law)和能量守恆的概念來達到我們的需求，最後再使用菲涅爾透鏡的概念讓透鏡做薄化設計，已達到便於生產與攜帶的方便性。與之前的研究相比，我們的照射面積可以達到數百個mm等級，而照度均勻度也可達到90%以上。

In this article, a beam expander is designed to transform a Gaussian laser beam into a collimated and uniform large-area illumination. The system exploits two freeform lenses to reach the goal, and has a solution for the over-thickness of the lenses. To close out, it analyzes any possible errors we may find in the experiment in hopes of matching the numerical values we might get from the actual experiment.

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