科教用途

Nucleic Acid, DNA)結構的繞射圖樣「相片 51」(攝於 1952)[41][42]，說明 DNA 雙股螺旋的發現以及X 光的發明、繞射等物理章節。但由這副圖像如何得知

另一種方法則是Amand A Lucas 等人使用電腦模擬，嘗試將多種DNA形貌 直接用惠更斯-菲涅耳原理算出繞射圖樣，並找出與「相片51」最相似的一種，

並模擬該DNA形貌的雷射繞射圖樣。[45-47]

圖5.4 選擇 12 種不同 DNA 形貌生成繞射 [47]

前者可以與課綱中雙狹縫章節合併進行，以實驗的方式讓學生對波動光學 的有實感的理解；後者則忠實的呈現DNA形貌與繞射圖的對應關係。本論文的 提議是結合這兩者的好處。Franklin使用X光照在寬度約為3.4 nm的B型DNA 上，仿照這個比例，以紅光雷射製造對應寬對的樣品，能在屏幕上呈現出放大 版的「相片51」給學生們觀察，觀察為隨即放進相位取回演算法去重建，能讓 同學在不用計算複雜數學的情形下，理解並相似的體驗繞射紋如何被取得，被 技術性的重建，並且解出真的來是雙股螺旋。

如第二章所述，繞射圖與樣品並非只是傅立葉轉換的關係，當中還丟失了 相位的資訊，普遍適用的相位取回方法是在1980年才發展出來，在那之前，不 同的繞射圖樣必須要藉由其他的先驗資訊(prior information)，以DNA來說，就 是化學鹼基的排列、鍵結方式 [48]，並且要等到「相片51」這張結構較簡單的 繞射圖，才能將雙股螺旋的結構解出來，因此才是那麼非凡難得的成就。真正 直接拍攝的DNA影像在2012年才問世。[49]

圖5.6 首張直接拍攝的 DNA 雙股螺旋照片 [49]

作者認為這項教案適合作為探究與實作課程的原因分為內容與取材方面，

此教案包含中學的既有內容：DNA雙股螺旋的發現以及X光的發明、狹縫干涉 繞射實驗，能連結並強化對這些章節的學習；又能藉由顯微鏡的演進史、光 源、解析度，使學生對於尺度(Scale)這個物理中的重要概念印象深刻；最終，

還能介紹這種越來越被廣泛應用的顯微術 — CDI。學生能藉由實驗的過程理 解，CDI顯微術所做的工作，正如Watson與Click在電子顯微鏡解析度還未到達 10 nm之前，就解出寬度為3.4 nm的週期性結構。而本篇HIO、PIE演算法，能夠 重建更多樣的樣品，是顯微技術上值得研究、發展的方向。

可見光作為光源的CDI除了方便操作以外，可視化使其更適合作為教學演 示之用，所使用的實驗用品甚至與既有的雙狹縫干涉高度重疊，僅需製作適當 比例的DNA樣品即可。若能選取較適當的樣品、並將數據處理的過程合併於一 個應用程式中，HIO相位取回演算法將很適合這樣的課程設計來使用。

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