三片稜鏡玻璃選取利用視圖法與優化方法對色差的校正

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姓名

余盈盈(Ying-Ying Yu) 查詢紙本館藏

畢業系所

光電科學與工程學系

論文名稱

三片稜鏡玻璃選取利用視圖法與優化方法對色差的校正
(Diagram method and optimization of triplet prisms for minimizing the chromatic aberration)

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摘要(中)

本文透過研究玻璃材料的選取方法，來找出色差最小的三片稜鏡組合。由於真實光線的公式較為複雜，故本文先做三波段 F-line (0.4861 μm)、d-line (0.5876 μm)、C-line (0.6563 μm) 近軸色差校正，在總偏向角Dd 固定為3度及校正一次色差?F,C和二次色差 ??,C條件下，可求得三片稜鏡的個別偏向角，而後新增 F-line 至 d-line 間的中間波段 A-line (0.5369 μm)，與 d-line 至 C-line 間的中間波段 B-line (0.6219 μm)，即五段波長之超消色差校正。
經過推導後得出的材料選取方法−視圖法，即比較材料 ?d,C−?A,B 與?d,C−?d 之圖，能快速且有效地獲得色差較小之三片玻璃稜鏡組合。而本研究將以視圖法為基礎所挑選出的三片玻璃稜鏡組合，輔以撰寫優化的MATLAB 程式，對視圖法所選取的三片玻璃稜鏡組合優化，以取得真實光線之最小色差的結果。

摘要(英)

The goal of this research is to obtain a triplet prism combination with least chromatic aberration by selecting glass materials. For the complexity of the real ray chromatic aberration formula, first we corrected the paraxial chromatic aberration of F-line (0.4861 μm), d-line (0.5876 μm) and C-line (0.6563 μm), we obtained each deviation angle of a triplet prism by fixing the total d-line deviation angle at 3 degree and corrected the primary chromatic aberration ?F,C and the secondary chromatic aberration ??,C. Then we defined two wavelengths A-line (0.5369μm) and B-line (0.6219μm), where A-line (0.5369μm) is the wavelength between F-line (0.4861 μm) and d-line (0.5876 μm), and B-line (0.6219μm) is the wavelength between d-line (0.5876 μm) and C-line (0.6563 μm). After that we corrected their chromatic aberration to obtain a super-achromat triplet prism corrected at 5 wavelengths.
Deriving the formula of paraxial chromatic aberration of a triplet prism, we are able to obtain a diagram method which can quickly obtain a triplet prism combination with small chromatic aberration. The method is achieved by comparing the area ratio of the ?d,C-PA,B and Pd,C-Vd figures of the materials. After applied diagram method to select a triplet prism combination, we write an optimization code which is based on damped least square method to minimize the chromatic aberration. Then obtain a triplet prism combination with the least real ray chromatic aberration.

關鍵字(中)

★ 三片稜鏡
★ 超消色差
★ 阻尼最小二乘法
★ 視圖法

關鍵字(英)

★ triplet prisms
★ super-achromat
★ damped least square method
★ diagram method

論文目次

摘要 .. ................................................ I
Abstract ............................................... II
誌謝 .................................................. IV
目錄 ................................................... V
圖目錄 ............................................... IX
表目錄 ............................................... XI
第一章緒論 ............................................. 1
1-1 研究動機 ............................................ 1
1-2 研究目的 ... ........................................ 1
1-3 文獻回顧 ............................................ 1
1-4 論文架構 ............................................ 3
第二章理論 ............................................. 5
2-1 符號定義 ............................................ 5
2-2 玻璃折射率與波長關係 ................................ 5
2-3 偏向角定義 .......................................... 7
2-3-1 真實光線偏向角 .................................... 7
2-3-2 真實光線產生全反射定義 ............................ 8
2-3-3 近軸光線偏向角 .................................... 9
2-4 Schott玻璃 Abbe (nd-Vd)圖 ....................... .. 11
2-5 一片稜鏡近軸色差 ................................... 12
2-5-1 近軸一次色差與二次色差的定義 ..................... 12
2-5-2 在 Schott 玻璃圖選取13種玻璃之近軸色差分析 ....... 13
2-6 一片稜鏡真實色差 ................................... 17
2-6-2 一片稜鏡真實色差曲線 ............................. 17
2-6-3 一片稜鏡設計資料與真實總色差 ..................... 18
第三章三片稜鏡組近軸色差 .............................. 20
3-1 近軸三片稜鏡組的偏向角與色差 ....................... 20
3-2 三片稜鏡組近軸色差校正 ............................. 21
3-3 三片稜鏡玻璃近軸色差校正之視圖法 ................... 23
3-3-1 εA,B 的定義與公式............. .................. 23
3-3-2 Vd-Pd,C 曲線圖 (G圖) ............................. 24
3-3-3 PA,B-Pd,C 曲線圖 (K圖) ........................... 26
3-3-4 視圖法 ........................................... 27
3-4 近軸εA,B最小的5組三片稜鏡 ......................... 40
3-5 近軸總色差最小的5組三片稜鏡 ........................ 41
第四章三片稜鏡真實色差校正與優化....................... 44
4-1 阻尼最小二乘法...................................... 44
4-2 優化程式流程........................................ 46
4-3 由13塊Vd值差5之玻璃組成三片稜鏡之真實色差校正與優化. 48
4-4 三片稜鏡玻璃色差視圖法之真實色差校正與優化 ......... 51
第五章結論與未來展望................................... 53
5-1 結論 ............................................... 53
5-2 未來展望 ........................................... 53
參考資料................................................ 54
附錄一玻璃的編號及重要參數表........................... 57
附錄二計算玻璃性質之程式............................... 61
附錄三 13種Vd差5的一片稜鏡近軸色差曲線圖程式............ 62
附錄四 13種Vd差5的一片稜鏡真實色差曲線圖程式............ 63
附錄五計算所有三片稜鏡組合程式......................... 65
附錄六近軸三片稜鏡的色差圖............................. 68
附錄七優化程式和其色差圖............................... 72

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指導教授

孫文信(Wen-Shing Sun)

審核日期

2020-7-29

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