一般光學系統的賽德像差可以用澤尼克（Zernike）多項式展開，因為我們所測量到的波面均會出現雜訊，所以利用傳統的最小平方差方法來求得澤尼克係數會產生所謂的數值不穩定（誤差），在此我們提出一個新方法可以解決以上所提到的問題。首先將干涉實驗所得之條紋算出其波面，再將此波面作小波轉換，利用這組新的數據來求賽德像差的大小。從模擬的結果可得知此種新方法所得到的數據比傳統的方法要精確很多，而且所需要的計算時間大約少了十多倍。 另外我們也利用了離散小波轉換來提高影像的對比度。首先我們從螢光顯微鏡取出兩張不同波長的影像，利用影像融合的方法使圖像的對比度提高，藉此可以分辨生物晶片上的不同圖像。 最後用疊紋影像及小波轉換的方法來做微米距離的量測。此方法是藉由光柵及CCD相機之像素的重疊產生影像，然後利用小波轉換來計算兩疊紋間之寬度，並藉由此寬度算出光柵所移動之微小距離，這種測量方法所需之實驗設備簡單又經濟，而且所得到的實驗結果有很高的準確度。 Seidel aberration coefficients can be expressed by Zernike coefficients. The least-squares matrix inversion method of determining the Zernike coefficients from a sampled wave front with measurement noise has been found numerically unstable. We present a new method to estimate the Seidel aberration coefficients by using a two-dimensional discrete wavelet transform and a technique (wavelet transform) for determining the spherical aberration and defocusing of a rotationally symmetric optical system. Compared with the least-squares matrix inversion method, their performance are more stable under input of Gaussian white noise and we obtain not only the more accurate Seidel aberration coefficients but also speed the computation. The simulated wave fronts are fitted, and results are shown for spherical aberration, coma, astigmatism, and defocus. Furthermore, We introduce a contrast and aberration correct image fusion method with the discrete wavelet transform to identify the micro-array biochip. The image fusion method is applied to fuse two images from different microscopes. The results show that the fused image can get better analysis of the details at each original micro spot biochip. Finally, A new approach based on the moiré theory and wavelet transform is proposed for measuring the micro-range distance between a charge-couple-device (CCD) camera and a two-dimensional reference grating. The micro-range distance is determined by measuring the pitch of the moiré pattern image, which is digitized by a CCD camera. A one-dimensional wavelet transform algorithm is applied to estimate the pitch of the moiré pattern. Experimental results prove that this technique is very efficient and highly accuracy, this method evaluates the micro-range distance with a suitable filter (suitable dilation factor ) to obtain a unique value of the average pitch of the moiré image. It is therefore immune to the noise and able to estimate the micro-range distance accurately.
