摘要
“對數諧波濾波片”可以偵測不同投影角度的相同物體，而“梅林徑諧濾波片”則具有能力偵測不同尺寸大小的相同物體。另外，對於不同尺寸大小或方向的物體，利用“墨西哥帽子波列函數”則可以擷取出相同寬度的邊。所以，將子波列轉換分別和對數諧波濾波片及梅林徑諧濾波片結合，可以改善這兩種濾波片在圖形識別的辨識能力。這兩種結合子波列轉換的濾波片分別稱之：“對數諧波-子波列” (LHW)濾波片，及“梅林徑諧-子波列” (MRHW) 濾波片。此兩種經過設計的濾波片，同時可以免除在辨識過程中對於待辨識物體的前置處理程序；也就是說，待辨識物體可以直接輸入系統，節省辨識運算的時間。
本論文中所設計出的LHW濾波片，對於投影的角度在-83o~83o的物體具有辨識能力；這個範圍幾乎涵蓋了所有的投影角度，而比對結果的輸出相關峰值強度在此範圍內則有30%的變動。另外，所設計的MRHW濾波片則對於僅有原物體尺寸四分之一的物體仍具有辨識能力；可辨識尺寸範圍為1~0.25。此範圍內，輸出相關峰值的強度有30%變動量。本論文中，先以電腦計算出所設計的濾波片，並模擬計算濾波片的辨識能力。另外，光學結合轉換比對器被用來實驗驗證此濾波片的辨識力；也驗證了此濾波片在白色雜訊下仍舊可以正確的辨識物體。
過去的結合轉換器的相關研究中，通常以準直的雷射光波紀錄和讀取結合轉換頻譜。本論文則提出以收斂的雷射光波來讀取紀錄於厚介質中的結合轉換頻譜。此紀錄結合轉換頻譜的厚介質假設被切割為數層；除此之外，並假設入射的讀取光在介質中僅被一層紀錄的光柵散射一次後，就直接繞射到輸出方向，且過程中光波並未衰減。根據以上假設，提出在低繞射效率限制下的數學理論模型，並以電腦模擬數值分析。以不同收斂半徑的光波讀取結合轉換頻譜的結果顯示，當讀取光波的收斂半徑等於紀錄用的傅氏透鏡焦距，輸出的相關峰值強度達到最大。另外，也計算出有效的介質厚度，大於此厚度的紀錄介質並未提供能量給相關輸出強度。在一般的實驗參數下，不同的讀取光波收斂半徑所得到的輸出相關峰值強度並未有很大的差異量；然而，對於需要高辨識率的相似物體、高精密度偵測物體位置及吵雜環境中的辨識系統，正確的讀取光波收斂半徑將使系統的相關輸出峰值強度達到最大。此效應在需要短焦距紀錄透鏡的輕便系統中猶為明顯。

Abstract
Logarithmic harmonic filter can detect objects at different projection angles, while Mellin radial harmonic filter has the ability to detect objects of different scales. The Mexican-hat wavelet function can extract edges of equal width for objects, regardless of their sizes and orientations. Hence, incorporation of wavelet filtering in the logarithmic harmonic and Mellin radial harmonic filter, the LHW and MRHW filter, which is also modified to eliminate the pre-processing, can improve the pattern recognition performance as compared with the LH and MRHW filter. The theory is presented together with computer simulation.
The LHW filter is capable of identifying the input object, within a wide range of projective angle, , with a variance under 30%. On the other hand, the MRHW filter can distinguish the input object with a wide allowable scale range 1~0.25. The correlation peaks are sharp and the peak intensity is relatively uniform with a variance under 30%. Computer simulation is adopted to investigate the performance of the LHW and the MRHW filter. Experimental results, including those obtained under the white noise, implemented in the Joint-transform correlator are also presented.
In the prior research, generally, collimated wave is used both as the incident wave and as the readout wave in a joint transform correlator. Here, we propose the use of converging wave instead to read out the joint transform spectrum, which is recorded in a thick recording medium. The recording medium is conceptually divided into numerous thin layers. Assume that the incident readout wave is scattered only once by each layer and the directly transmitted wave is not significantly attenuated. We arrive at the theory for low diffraction efficiency limit, which is then numerically tested. The result shows that the correlation peak intensity (CPI) is the maximum when the radius of curvature of the readout wavefront is the same as the focal length of the Fourier transforming lens. However, the CPI is quite independent of the radius of curvature of the readout wave under normal experimental conditions. Minimum thickness for the recording medium beyond which the CPI doesn’t increase significantly is obtained. In the condition that requires good discrimination among similar objects and precise determination of the object position under noisy environment, the CPI depends strongly on the curvature of the readout wavefront, particularly for the portable correlator which requires short focal length for the Fourier transforming lens.

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