像差係數是用以評估光學元件性能，很重要的參考指標，因此，本論文提出三種由干涉條紋圖像預測像差係數的技術，使用卷積神經網絡(Convolution Neural Network, CNN)方式，取代傳統複雜的數學運算方式。在本文中，使用四種卷積神經網絡，IZ-GNet網絡、IP-GAN網絡、PZ-GNet網絡及IZ-GAN網絡，搭配三種不同方式，IZGNet method、IZ2Net method及IZGAN method，預測澤尼克係數，進行分析及比較。在第一種方法IZGNet method和第三種方法IZGAN method中，干涉條紋的圖像分別輸入至IZ-GNet網絡和IZ-GAN網絡中，直接預測得到澤尼克係數。在第二種方法IZ2Net method中，需要兩個步驟，才能將干涉條紋的圖像，預測得到澤尼克係數。第一步，使用干涉條紋圖像，輸入至IP-GAN網絡預測相位圖像。第二步，使用相位圖輸入至PZ-GNet網絡，進行預測澤尼克係數。使用均方根誤差(Root-Mean-Square Error, RMSE)的方式，做為標準值與預測係數的評估標準。
使用理想的圖像(干涉條紋或相位圖)分別訓練IZ-GNet網絡、IP-GAN網絡、PZ-GNet網絡及IZ-GAN網絡。在完成網絡訓練後，分別使用理想的圖像和類真實圖像，分別輸入四個網絡中，進行評估三種方法預測的澤尼克係數能力。測試結果，在使用理想的圖像的情況下，均方根誤差（RMSE）均小於0.055λ；及在使用類真實圖像的情況下，配合使用遷移式學習的方法，使得均方根誤差（RMSE）從均小於0.101λ到0.0586λ。綜上所述，本論文提出預測的方法應可用於真實干涉條紋圖像，進行預測澤尼克像差係數，以及證明遷移式學習的方法，可以提升網絡的預測準確度。

Aberration coefficients are used to estimate the optical performance and it’s an important reference indicator. The paper proposes three prediction techniques to predict Zernike coefficients using interference fringe. Using Convolutional Neural Networks (CNN) replaces traditional methods that require complex mathematical calculations. In the paper, there are four architectures of CNN, IZ-GNet, IP-GAN, PZ-GNet, and IZ-GAN, and three prediction techniques, IZGNet method, IZ2Net method, and IZGAN method, to predict Zernike coefficients. In the first prediction technique, IZGNet method, and third prediction technique, IZGAN method, IZ-GNet and IZ-GAN can directly predict Zernike coefficients using interference fringe, respectively. In the second prediction technique, IZ2Net method, the interference fringe requires two networks to predict Zernike coefficients. First, IP-GAN predicts the phase difference with interference fringe. Second, the result of IP-GAN is used to predict the Zernike coefficients by PZ-GNet. Root-Mean-Square-Error (RMSE) is our criterion for quantifying the ground truth and prediction coefficients.
There are two kinds of the ideal images: interference fringe or phase difference based on formula to train IZ-GNet, IP-GAN, PZ-GNet, and IZ-GAN, respectively. After the training is done, we use two different ways: the formula, ideal images, and optics simulation, simulated images, to estimate the performance of three prediction techniques. As a result, RMSE are less than 0.055λ with ideal images case and RMSE are less than from 0.101λto 0.0586λwith simulated images case and transfer learning. According to the aforementioned, the predicted techniques can be applied to predict the Zernike coefficients through the actual images of interference fringe. Moreover, we prove that transfer learning method improves the prediction accuracy of the network.

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