本文關(guān)鍵詞： 光學測量 波面擬合 Zernike多項式 非圓域 正交化系數(shù)矩陣　出處：《光學技術(shù)》2017年03期 　論文類型：期刊論文

【摘要】：針對非圓域波面擬合中Zernike多項式失去正交特性、擬合系數(shù)交叉耦合的問題,提出非圓域Zernike正交基底函數(shù)構(gòu)造方法。以圓Zernike為基底,采用Gram-Schimdt正交組構(gòu)造方法,線性表出單位正交基底。通過構(gòu)造不同遮光比環(huán)形光闌下的正交基底與環(huán)Zernike多項式進行比較,驗證了此方法的正確性。然后采用圓Zernike多項式和構(gòu)造的新基底對矩形光闌下的波面進行了擬合,從擬合殘余誤差、各項基底系數(shù)的穩(wěn)定性、傳遞矩陣的條件數(shù)等分析,結(jié)果表明針對特定的非圓域構(gòu)造的新基底可靠性和抗擾動能力優(yōu)于圓Zernike多項式。此方法不需要具體求出基底的解析表達式,不同非圓域僅是正交化系數(shù)矩陣發(fā)生改變,為非圓域正交基底構(gòu)造提供了一種新途徑。
[Abstract]:In order to solve the problem that Zernike polynomials lose their orthogonality and cross coupling of fitting coefficients in non-circular domain wave surface fitting, a method of constructing Zernike orthogonal base functions in non-circular domain is presented. The method of constructing Gram-Schimdt orthogonal group is used to construct the Zernike orthogonal base in non-circular domain. The orthogonal bases with different shading ratios are constructed and compared with the ring Zernike polynomials. The correctness of the method is verified, and then the wavefront under the rectangular aperture is fitted by using the circular Zernike polynomial and the constructed new substrate. The residual error of fitting, the stability of each base coefficient, the condition number of the transfer matrix, and so on are analyzed. The results show that the reliability and anti-disturbance ability of the new basement constructed in the specific non-circular domain is superior to that of the circular Zernike polynomial. This method does not need to obtain the analytical expression of the basement, and the different non-circular domains are only changed by the orthogonal coefficient matrix. It provides a new way for the construction of non-circular orthonormal basement.
【作者單位】： 北京理工大學精密光電測試儀器及技術(shù)北京市重點實驗室;哈藥集團制藥總廠;
【基金】：國家自然基金儀器�？�(61327010)
【分類號】：O174.14;O436.1

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