本研究旨在探討非軸對稱光學系統之波前像差，但是因為光程是複合函數而非多項式，無法計算所需的第一階至第四階波前像差。因此，首先必須將光程函數對光源的五個獨立變數進行泰勒級數展開至四階，再根據展開的結果整理出第一階至第四階波前像差。本論文將分別對物在有限距離與在無窮遠兩種情況討論。
為了驗證本研究的正確性，本論文選用庫克三分離物鏡(Cooke triplet)作為範例，並以Fortran程式計算軸對稱與非軸對稱兩種情況的像差。軸對稱的波前像差會與Zemax比較，但是Zemax沒有提供非軸對稱波前像差，所以本研究的非軸對稱系統波前像差僅能與範例對照。驗證的結果證明本論文的正確性。最後將探討其他變數對於總波前像差的影響，結果顯示若物在有限距離，能調整變數數值使總波前像差為零。

The purpose of this study is to investigate the wavefront aberrations of non-axially symmetrical optical systems, but since the optical path length is a composite function rather than a polynomial, the required first to fourth-order wavefront aberrations cannot be calculated. Therefore, the five independent variables of the light source must be firstly expanded to the fourth-order by Taylor series, and then the first to fourth-order wavefront aberrations must be sorted out according to the expansion results. In this study, we will discuss the two cases of the object point at a finite distance and at an infinite distance.
In order to verify the correctness of this study, this study selects Cooke triplet as an example, and uses Fortran program to calculate the aberrations in both axis-symmetrical and non-axially symmetrical cases. Axis-symmetrical wavefront aberrations will be compared to Zemax, and wavefront aberrations of non-axially symmetrical systems will be compared to the example. The verification results prove the correctness of this study. Finally, the influence of other variables on the total wavefront aberration will be discussed. The results show that if the object is at a limited distance, the total wavefront aberration can be made zero by adjusting the variable value.

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