- 學位論文
大動態範圍與高精準度光波前量測方法之探討
Research on Highly-Dynamic and Accurate Wavefront Measurement
摘要
波前感測器(Shack-Hartmann Wavefront sensor)為一種光程差量測儀器，利用微透鏡陣列(Microlens array)將入射光分割為數道子光束並聚焦為光點，利用影像分析法追蹤聚焦光點的軌跡變化以計算入射光的波前擾動。波前感測器一般認定的缺點是動態範圍(Dynamic range)不足，而限制了感測器量測光程差的最大範圍。 利用類神經網路(Artificial Neural-Network)於圖形識別，並配合霍夫轉換(Hough Transform)提出修正霍夫質心演算法(Modified Hough Spots-Centroiding)，用以計算聚焦光點質心位置。相較於現有質心演算法的差異，本文所提出的方式不需利用拘束子孔徑(subaperture)以計算質心位置，因此具有較高的動態範圍與訊噪比。 對於光波前重建演算法，應用哈爾小波波前重建法(Zonal wavelet wavefront)來增加區域波前重建的精準度，並利用Gram-Schmidt正交化修正離散Zernike多項式之正交性。經由模擬分析結果，修正霍夫質心演算法的絕對誤差為0.007 pixel。使用532 nm雷射光源，哈爾小波波前重建法的計算方均根(RMS)誤差為0.0589 λ。利用Grant矩陣的秩(rank)來分析Gram-Schmidt正交化對於Zernike多項式之正交性的修正效能，以Zrnike多項式階數7階為例，將Grant矩陣的秩修正為滿秩(full rank)。 為分析演算法在實際系統的量測效能，利用光學元件和自動化平台建立一套波前量測實驗設備，並以Thorlabs公司的WFS20波前感測器作為量測參考。實驗結果顯示量測精準度誤差與重現性分別為0.0625 λ和0.00363 λ，而動態量測範圍則是WFS20之1.52倍。本研究所建構之波前感測器配合自行開發的修正霍夫質心演算法，不須外加特殊元件以提高動態量測範圍，並利用哈爾小波波前重建法維持量測精準度。利用高動態量測範圍的特性，進而增加光波前感測器在高階波前擾動的應用。
並列摘要
The Shack-Hartmann wavefront sensor uses the microlens array splitting the incident light into several sub-light beam, and converged into focused-spots. Using the image analysis methods, the orientations of the focused-spots are tracked. The wavefront aberration of the incident light is calculated. However, the common problem of the wavefront sensor is the insufficient dynamic range, which limits the maximum detectable range of the sensor. This research introduces artificial neural-network to pattern recognition, in order to find the best-suit contour. Accompanying with the Hough transform, the modified Hough spots-centroiding algorithm is proposed to locate the position of each focused-spot. The algorithm does not need any subaperture as compared with the present centroiding algorithm to calculate the centroid position, therefore the SNR and the dynamic range can be extensively increased. There are two primary numerical algorithms: zonal and modal wavefront reconstruction. This research proposed the Haar wavelet zonal reconstruction to increase the accuracy. As for the modal reconstruction, Gram-Schmidt process is used to modify the orthogonality of the discrete Zernike polynomials and reduce the error. The accuracy of the algorithms is verified through test data, and the analysis results show that the accuracy of the modified Hough centroiding algorithm is 0.007 pixel. When the wavelength of the laser is 532 nm, the reconstruction mean RMS error of the Haar wavelet algorithm is 0.0589 λ. The rank of the Grant matrix is used to analysis the ability Gram-Schmidt process to the Zernike polynomials. For a 7-th order Zernike polynomial sets, the rank Grant matrix can be fixed to full fank. In order to analysis the performance of the proposed algorithms, optical elements and automation platform are used to build-up wavefront measurement experiment equipment. The wavefront sensor WFS20 from Thorlabs Inc. is introduced as a measurement reference, in order to verify the dynamic range, accuracy and repeatability of the system. The accuracy and repeatability are 0.0625 λ and 0.00363 λ respectively. The measured dynamic range is 1.52 times the range of the WFS20 sensor. This research constructs the SHWS system using the developed modified Hough spots-centroiding algorithm without installing any special element to increase the dynamic range of the sensor, while the Haar wavelet zonal reconstruction algorithm is used to maintain the accuracy. With the property of highly-dynamic range, the application for the wavefront sensor on the high order aberration measurement can be increased.