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研究生:王勺融
研究生(外文):Shao-RongWang
論文名稱:基於漢密爾頓特徵方程像差展開式的光源位置二次相依項的消除法
論文名稱(外文):Correction of the Quadratic Light Source Dependence of the Aberration Polynomial based on the Characteristic Function of Hamilton
指導教授:林昌進
指導教授(外文):Psang-Dain Lin
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:83
中文關鍵詞:像差多項式光源相依像差
外文關鍵詞:aberration polynomiallight source dependent aberration
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現今光學系統的設計方式,對於系統像差的消除,多數以光學模擬軟體建立模型,且在設立系統變數與最佳化目標後,進行最佳化運算加以達成;雖然此設計方式已非常成熟且有效,但其基於光學的基礎理論卻明顯較為微弱,偏向於以系統變數數目與最佳化運算時間,來換取設計結果。
本研究從根本的光學像差理論出發,探討欲消除基於漢密爾頓特徵方程(characteristic function of Hamilton)的像差展開式中,光源變數二次相依項,在系統的數學表達上需滿足的條件為何;並基於此像差項特性建立簡化的物理模型,建構數學模型與物理模型間的關係,以研究此數學條件對應至物理系統所需滿足的條件為何。

Nowadays the way of designing optical systems, most of people use optical design code to insert system model. For correcting aberration people set variables and what they want to optimize for, then optimize the system with the optimization tool of optical design code. It sets many system variables and spends a lot of execution time for design result. Although the design way is very complete and effective, the basis of optical feature is wake.
This thesis takes based on optical aberration theory and discusses how to correct the quadratic light source dependence of the aberration polynomial which is based on the characteristic function of Hamilton. A connection between the mathematical model and the physical model due to the property of the aberration is built. Conditions of correcting the aberration in real physical system are found though the connection.

目錄
摘要 I
ABSTRACT II
致謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
符號說明 X
第1章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 漢密爾頓特徵方程 4
1.4 波前像差、光線像差、像差多項式 9
1.5 主像差(賽德像差)介紹 18
1.6 像差多項式基於漢密爾頓特徵函數 25
第2章 光源相依像差多項式 28
2.1 光源相依像差多項式基於漢密爾頓特徵函數 28
2.2 光源零次相依像差以及消除所需條件 29
2.3 光源一次相依像差以及消除所需條件 32
2.4 光源二階相依像差以及消除所需條件 36
第3章 實際系統成像數學模型 40
3.1 像差多項式與物理模型聯結 40
3.2 光學系統物理模型建立 41
3.3 子午面光線聚焦光程分析 43
3.4 弧矢面光線聚焦光程分析 49
第4章 消除光源二次相依像差所需條件 55
4.1 數學模型、物理模型綜合討論 55
4.2 完全消除光源二次相依像差所需條件 55
4.3 部分消除光源二次相依像差所需條件之一 57
4.4 部分消除光源二次相依像差所需條件之二 57
4.5 部分消除光源二次相依像差所需條件之三 59
4.6 部分消除光源二次相依像差探討 60
第5章 實際系統驗證 62
5.1 子午面、弧矢面聚焦位置 62
5.2 實際透鏡系統模擬驗證 68
第6章 結論與未來展望 76
6.1 結論 76
6.2 未來展望 77
參考文獻 79
英文文獻 79
中文文獻 82
自述 83
英文文獻
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[2]Swerdlow, N. M. (1986). Optical Profusion. Isis, 77(1), 136-140.
[3]Wilkins, D. R. (1833). On a General Method of Expressing the Paths of Light, & of the Planets, by the Coefficients of a Characteristic Function by William Rowan Hamilton. William Rowan Hamilton, 1, 795-826.
[4]Mahajan, V. N. (1981). Zernike annular polynomials for imaging systems with annular pupils. J. Opt. Soc. Am., 71(1), 75-85.
[5]Shannon, R. R., Shack, R., Harvey, J. E., & Hooker, R. B. (2005). Robert Shannon and Roland Shack: legends in applied optics: SPIE Press.
[6]Hopkins, H. H. (1964). Canonical Pupil Coordinates in Geometrical and Diffraction Image Theory. Japanese Journal of Applied Physics, 1(Supplement 1-1), 31-35.
[7]Hopkins, G. W. (1976). Aberrational analysis of optical systems: A proximate ray trace approach. Ph.D Dissertation, University of Arizona.
[8]Wachendorf, F. (1949). Bestimmung der Bildfehler fünfter Ordnung in zentrierten optischen Systemen. Optik (Jena), 5, 80-122.
[9]Cox, A. (1967). A system of optical design : the basics of image assessment and of design techniques with a survey of current lens types (1st ed.). London ; New York: Focal Press.
[10]Hopkins, H. H. (1950). Wave theory of aberrations. Oxford: Clarendon Press.
[11]Rayces, J. L. (1964). Exact Relation between Wave Aberration and Ray Aberration. Optica Acta: International Journal of Optics, 11(2), 85-88. doi: 10.1080/713817854
[12]Seidel, L. (1854). Zur Dioptrik, von Ludwig Seidel. Astronomische Nachrichten, 37(8), 105-119. doi: 10.1002/asna.18540370801
[13]Welford, W. T. (1972). A New Total Aberration Formula. Journal of Modern Optics, 19(9), 719-727.
[14]Focke, J. (1965). Higher Order Aberration Theory. In E. Wolf (Ed.), Progress in optics (pp. 1-36). Amsterdam: North-Holland.
[15]Schwarzschild, K. (1905). Untersuchungen zur geometrischen Optik: Dieterich'schen univ.-buchdruckerei (W.F. Kaestner).
[16]Herzberger, M. (1939). Theory of Image Errors of the Fifth Order in Rotationally Symmetrical Systems. I. J. Opt. Soc. Am., 29(9), 395-395.
[17]Born, M., Wolf, E., & Bhatia, A. B. (2002). Principles of optics : electromagnetic theory of propagation, interference and diffraction of light (7th (expanded) ed.). Cambridge: Cambridge University Press.
[18]Hoffman, J. M. (1993). Induced aberrations in optical systems (PHD). Tucson, Arizona University of Arizona.
[19]O'Shea, D. C. (2004). Diffractive Optics: Design, Fabrication, and Test: SPIE Press.
[20]Zhao, C., & Burge, J. H. (2002). Criteria for correction of quadratic field-dependent aberrations. J. Opt. Soc. Am. A, 19(11), 2313-2321.
[21]Mahajan, V. N. (1994). Zernike Annular Polynomials and Optical Aberrations of Systems with Annular Pupils. Appl. Opt., 33(34), 8125-8127.
[22]Gross, H. (2005). Handbook of optical systems / V. 1, Fundamentals of technical optics / Herbert Gross. Weinheim: Wiley-VCH.
[23]Gross, H. (2007). Handbook of optical systems. V. 3, Aberration theory and correction of optical systems. Weinheim: Wiley-VCH.
[24]Kingslake, R., Johnson, R. B., & Knovel (Firm). (2010). Lens design fundamentals (pp. xix, 549 p.).
[25]Luneburg, R. K., & Herzberger, M. (1964). Mathematical theory of optics. Berkeley,: University of California Press.
[26]Mahajan, V. N. (1998). Optical imaging and aberrations. Part 1, Ray geometrical optics (pp. 1 online resource (xxiii, 470 p.).
[27]Simmons, G. F. (1996). Calculus with analytic geometry (2nd. ed ed.). New York: McGraw-Hill.
[28]Smith, W. J. (2000). Modern optical engineering. The design of optical systems (3rd ed ed.). New York [etc.]: McGraw-Hill.
[29]Welford, W. T. (1986). Aberration of optical systems. Bristol: Adam Hilger.
中文文獻
[1]薛鈞哲. (2011). 光程對光學系統變數之梯度矩陣的建模. 博士, 國立成功大學, 台南市.
[2]魏倫佑. (2011). 軸對稱光學系統的波前像差與光線像差的多項式研究. 碩士, 國立成功大學, 台南市.
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