光学小波变换的4f系统研究
|
摘要
光学小波变换是光学信息处理与小波理论的结合,具有并行性、超高速、大容量的优点。4f系统是实现光学小波变换的一种重要光路,研究4f系统特点与特性是研究光学小波变换的基础。论文以光学小波变换的4f系统为研究对象,对系统的原理和实现方法、线性和时不变特性、误差特性以及改进方法进行了较深入的分析和研究。
首先,论文从傅立叶光学原理出发,分析了4f系统的基本原理和组成,构建了光学小波变换需要的4f系统光路,提出了一种4f系统自动加载和采集图像的实现方法。其次,通过4f系统的叠加性和零输入响应实验以及输出信号的坐标位置稳定性和能量稳定性实验,表明了在目前的器件工艺和光路调节水平下,4f系统的线性与时不变特性均不理想。再次,根据误差理论将4f系统误差分为系统误差和偶然误差两大类,讨论了各种误差的来源以及减小误差的方法和措施,利用PSNR定量地衡量了系统的误差(目前系统PSNR达到24.33dB);计算得到了4f系统仿真时需要的理想低通滤波器的通带大小,并对典型图像进行了4f系统低通滤波仿真;通过分析图像的高频能量百分比与图像通过4f系统后PSNR,得出了高频能量越丰富的图像通过4f系统后PSNR越低的结论。最后,本文还利用光栅衍射理论和傅立叶变换理论,提出一种测量4f系统输入函数载体与滤波函数载体之间角位移的方法,利用该方法的测量结果可以补偿4f系统滤波函数的角位移,并且利用光学实验证明了该方法的有效性和准确性。
论文创新之一是提出了一种4f系统自动加载和采集图像的方法,该方法可以提高实验的效率、降低实验的劳动强度以及减少实验的出错概率;创新之二是提出一种测量4f系统输入函数载体与滤波函数载体之间角位移的方法,该测量方法具有无需修改光路、无需购买额外设备、操作简单以及精度高等特点。
通过文献参考、理论分析、理论仿真以及光学实验,论文研究得到4f系统部分特点与特性,为4f系统误差进一步减小以及最终实现高精度滤波处理打下了一定的基础。
Optical wavelet transform is the combination of optical information processing and wavelet theory. It integrates many advantages of optical science and wavelet transform such as parallelism, high-speed and large capacity. The 4f system is an important optical path for the realization of optical wavelet transform. Study on the characteristics of the 4f system is a basis of studying optical wavelet transform. The author takes the 4f system of optical wavelet transform as the research object, carries out thorough analysis and study on the system’s principle, realization, linear and time-invariant characteristics, error characteristics and improved method.
First of all, according to the principle of Fourier optics, the 4f system's basic principle and the system structure were analyzed. The optical path of the 4f system needed by optical wavelet transform was constructed. The realization method which could automatically load and acquire images in the 4f system was proposed. Secondly, it is proved by experiments of the addition, zero-input response, stability of the output signal coordinate position and the stability of the output signal energy value that the 4f system’s linear and time-invariant characteristics is not ideal under the condition of the present device technology and optical path adjusting level. Thirdly, the errors of the 4f system were divided into two major categories as systematic error and accidental error according to error theory. A variety of error sources were discussed and the methods of reducing errors were elaborated. Peak-to-peak signal to noise ratio (PSNR) were used to measure quantitatively the system’s error, and the system’s PSNR reached 24.33 dB right now. The size of the ideal low-pass filter’s passband in the 4f system needed by the simulation was achieved by computing. Then, the 4f system’s low-pass filtering simulation to the typical image was carried out. The analysis of the percentage of images’high-frequency energy and the PSNR of images passed through the 4f system proved that the images including more high-frequency energy have lower PSNR. Finally, a method which could measure the angular displacement formed by the 4f system’s input function carrier and filter function carrier according to the theory of grating diffraction and Fourier transform theory. The measurement result of the method can compensate the 4f system’s angular displacement of the filter function, while optical experiments have proved the effectiveness and accuracy of the method.
One of the paper’s innovative points is that a method of automatically loading and acquiring images in the 4f system has been proposed, which could improve the experimental efficiency, reduce experimental labor intensity and reduce the experimental error probability. Another one is that a method measuring the angular displacement formed by the 4f system’s input function carrier and filter function carrier has also been proposed, it features no need to change light path, no need to purchase additional equipment, simple operation and high precision.
Through the literature reference, the theoretical analysis, simulation as well as optics experiments, some characteristics of the 4f system was got. This has lay the foundation for further reducing of the 4f system’s error and high accuracy filtering.
首先,论文从傅立叶光学原理出发,分析了4f系统的基本原理和组成,构建了光学小波变换需要的4f系统光路,提出了一种4f系统自动加载和采集图像的实现方法。其次,通过4f系统的叠加性和零输入响应实验以及输出信号的坐标位置稳定性和能量稳定性实验,表明了在目前的器件工艺和光路调节水平下,4f系统的线性与时不变特性均不理想。再次,根据误差理论将4f系统误差分为系统误差和偶然误差两大类,讨论了各种误差的来源以及减小误差的方法和措施,利用PSNR定量地衡量了系统的误差(目前系统PSNR达到24.33dB);计算得到了4f系统仿真时需要的理想低通滤波器的通带大小,并对典型图像进行了4f系统低通滤波仿真;通过分析图像的高频能量百分比与图像通过4f系统后PSNR,得出了高频能量越丰富的图像通过4f系统后PSNR越低的结论。最后,本文还利用光栅衍射理论和傅立叶变换理论,提出一种测量4f系统输入函数载体与滤波函数载体之间角位移的方法,利用该方法的测量结果可以补偿4f系统滤波函数的角位移,并且利用光学实验证明了该方法的有效性和准确性。
论文创新之一是提出了一种4f系统自动加载和采集图像的方法,该方法可以提高实验的效率、降低实验的劳动强度以及减少实验的出错概率;创新之二是提出一种测量4f系统输入函数载体与滤波函数载体之间角位移的方法,该测量方法具有无需修改光路、无需购买额外设备、操作简单以及精度高等特点。
通过文献参考、理论分析、理论仿真以及光学实验,论文研究得到4f系统部分特点与特性,为4f系统误差进一步减小以及最终实现高精度滤波处理打下了一定的基础。
Optical wavelet transform is the combination of optical information processing and wavelet theory. It integrates many advantages of optical science and wavelet transform such as parallelism, high-speed and large capacity. The 4f system is an important optical path for the realization of optical wavelet transform. Study on the characteristics of the 4f system is a basis of studying optical wavelet transform. The author takes the 4f system of optical wavelet transform as the research object, carries out thorough analysis and study on the system’s principle, realization, linear and time-invariant characteristics, error characteristics and improved method.
First of all, according to the principle of Fourier optics, the 4f system's basic principle and the system structure were analyzed. The optical path of the 4f system needed by optical wavelet transform was constructed. The realization method which could automatically load and acquire images in the 4f system was proposed. Secondly, it is proved by experiments of the addition, zero-input response, stability of the output signal coordinate position and the stability of the output signal energy value that the 4f system’s linear and time-invariant characteristics is not ideal under the condition of the present device technology and optical path adjusting level. Thirdly, the errors of the 4f system were divided into two major categories as systematic error and accidental error according to error theory. A variety of error sources were discussed and the methods of reducing errors were elaborated. Peak-to-peak signal to noise ratio (PSNR) were used to measure quantitatively the system’s error, and the system’s PSNR reached 24.33 dB right now. The size of the ideal low-pass filter’s passband in the 4f system needed by the simulation was achieved by computing. Then, the 4f system’s low-pass filtering simulation to the typical image was carried out. The analysis of the percentage of images’high-frequency energy and the PSNR of images passed through the 4f system proved that the images including more high-frequency energy have lower PSNR. Finally, a method which could measure the angular displacement formed by the 4f system’s input function carrier and filter function carrier according to the theory of grating diffraction and Fourier transform theory. The measurement result of the method can compensate the 4f system’s angular displacement of the filter function, while optical experiments have proved the effectiveness and accuracy of the method.
One of the paper’s innovative points is that a method of automatically loading and acquiring images in the 4f system has been proposed, which could improve the experimental efficiency, reduce experimental labor intensity and reduce the experimental error probability. Another one is that a method measuring the angular displacement formed by the 4f system’s input function carrier and filter function carrier has also been proposed, it features no need to change light path, no need to purchase additional equipment, simple operation and high precision.
Through the literature reference, the theoretical analysis, simulation as well as optics experiments, some characteristics of the 4f system was got. This has lay the foundation for further reducing of the 4f system’s error and high accuracy filtering.
引文
[1]崔河富.数字图像处理与通信[M].太原:山西人民出版杜,2007.
[2]韩亮,田逢春,徐鑫,李立. Mallat算法的光学实现[J].光学精密工程,2008,16(8):1490-1499.
[3]路甬祥.现代科学技术大众百科科学卷[M].杭州:浙江教育出版社,2001.
[4] D.G.Feitelson. Optical computing-a survey for computer scientists[M]. the MIT Press, 1988.
[5]赵建林.高等光学[M].西安:西北工业大学出版社,1999.
[6] A.W.Lohman, what classical optics can do for digital optical computer[J], Applied Optics, 1986,25(10):1543-1549.
[7] Yoshiki Ichioka, Tadao Iwaki, Ka’Sunori Matsuoka. Optical Information Processing And Beyond[J]. Proceedings of the IEEE, 1996,84(5):694-719.
[8] Yan. Zhang, Yao Li. Optical determination of gabor coefficients of transient signals[J]. Opt. Lett. 1991, 16(13): 1031.
[9] C. Hirliman, J. F. Morhange. Wavelet analysis of short light pulses[J]. Applied Optics. 1992, 30(7).
[10] H. Szu, Y. Sheng, J. Chen. Wavelet transform as a bank of matched filters[J]. Applied Optics. 1992, 31: 3267–3277.
[11] J. Caulfield, H. Szu. Parallel discrete and continuous wavelet transforms[J]. Opt. Eng. 1992, 31: 1835–1839.
[12] Xiangyang Yang, Harold H. Szu, Yunlong Sheng, H.John Caulfield. Optical wavelet transform of binary images[J]. Optical Engineering. 1992, 31(9): 1846-1851.
[13] Y. Sheng, D. Roberge, H. Szu and T. Lu. Optical wavelet matched filters for shift-invariant pattern recognition[J]. Optics Letters. 1993, 18: 299-301.
[14] M. O. Freeman. Wavelets: Signal representations with important advantages[J]. Opt. Photon. 1993, 4(8): 8-14.
[15] David mendlovic, Naim Konforti. Optical realization of the wavelet transform for two-dimensional objects[J]. Applied Optics. 1993, 32(32): 6542-6546.
[16] Ouzieli Ido, David Mendlovic. Two-dimensional wavelet processor[J]. Applied Optics. October 1996: 5839-5846.
[17]高春林,虞钢.具有特殊衍射强度分布的二元位相光栅设计[J].中国激光, 2001, 28(4): 365-368.
[18] R.A.Maestre, J.Garcia ,C.Ferreira. Pattern recognition using sequential matched filtering ofwavelet coefficients[J]. Optical Communication,1997,133(1-6): 401-414.
[19] David Mendlovic. Continuous two-dimensional on-axis optical wavelet transformer and wavelet processor with white-light illumination[J]. Applied Optics,1998.3, 37(10).
[20] Samuel P. Kozaitis a,1, Mark A. Getbehead. Optical wavelet feature extraction using a multiple-input phase-only encoded joint-transform correlator[J]. Optics Communications, 1998 ,151:15–20.
[21] H. Zhang, C.M. Cartwright, M.S. Ding, W.A. Gillespie. Optical implementation of a photorefractive joint transform correlator with wavelet filters[J]. Optics Communications , 2000,181:223–230.
[22]隋成华,徐来定.利用子波变换实现多通道复合图像特征提取[J].中国激光, 2000.8, A27(8):79-82.
[23] Linfei Chen, Daomu Zhao. Optical Image Encryption Based On Fractional Wavelet Transform[J]. Optics Communications, 2005,254:361-367.
[24] J. Garc?′a, Z. Zalevsky, D. Mendlovic. Two-dimensional wavelet transform by wavelength multiplexing[J]. Appl. Opt. ,1996, 35:7019–7024.
[25] Zeev Zalevsky. Experimental implementation of a continuous two-dimensional on-axis optical wavelet transformer with white light illumination[J]. Optical engineering, 1998.4, 37(4).
[26] Jose J.Esteve-Taboada, Javier Garcia, Carlos Ferreira. Two-dimensional optical wavelet decomposition with white-light illumination by wavelength multiplexing[J]. J. Opt. Soc.Am.A2001.1,18(1).
[27]孟书苹.基于光学小波变换系统研究[D].重庆大学硕士毕业论文,2005.
[28]游明俊.傅立叶光学[M].北京:兵器工业出版社,2000.
[29]王仕璠.信息光学理论与应用[M].北京:北京邮电大学出版社,2003.
[30]游明俊.傅立叶光学[M].北京:兵器工业出版社,2000.
[31]唐光菊,田逢春,李立,刘伟,刘赛.基于四叉树的光学小波滤波器轴心定位的研究[J].光学技术. 2008.34(4):597-600.
[32]谈欣柏.大学物理实验[M].天津:天津大学出版社,2000.
[33]徐鹏,王玉荣.集成薄膜晶体管液晶空间光调制器光调制特性的实验研究[J].液晶与显示, 2005,20(5):412-416.
[34]杨昱冰,王石语,蔡德芳,文建国,过振.被动调Q激光器输出波动因素的实验研究[J].红外与激光工程, 2006, 35(1): 60～65.
[35]杨齐民,钟丽云,吕晓旭.激光原理与激光器件[M].昆明:云南大学出版社,2003.
[36]周景超,戴汝为,肖柏华.图像质量评价研究综述[J].计算机科学, 2008,35(7):1-5.
[37]时红伟,陈世平.一种基于现代通信理论的图像质量评价技术[J].中国空间科学技术,2005,1:1-6.
[38]叶佳,张建秋,胡波.客观评估彩色图像质量的超复数奇异值分解法[J].电子学报,2006,35:28-33.
[39] DiGesu V,Staravoitov V V. Distance-based functions for image comparison[J]. Pattern Recognition Letters,1999,20(2):207-213.
[40] Starovitov V V,Kose C,Sankur B. Generalized distance based matching of non-binary images[J]. IEEE International Conference on Image Processing.1998.
[41] Avcibas I,Sankur B,Sayood K. Statistical Evaluation of Image Quality Measures[J]. Journal of Electronic Imaging, 2002: 206-223.
[42] Eskicioglu A M,Fisher P S. Image Quality Measures and Their Performance[J]. IEEE Transactions on Communication,1995,43(12):2959-2965.
[43]唐光菊.图像小波变换的光学实现[D].重庆大学硕士毕业论文,2008.
[44]刘伟.光学小波变换系统研究[D].重庆大学硕士毕业论文,2007.
[45]郑君里,应启珩,杨为理.信号与系统(第二版)[M].北京:高等教育出版社,2000
[46]殷纯永.光电精密仪器设计[M].北京:机械工业出版社,1996.
[47]维格特著.侯正信译.数字信号处理基础[M].北京:电子工业出版社,2003.
[48]闫敬文.数字图像处理(MATLAB版)[M].北京:国防工业出版社,2007.
[49]井上诚喜. C语言实用数字图像处理[M].北京:科学出版社,2003.
[50]刘伟,田逢春,唐光菊.利用CCD进行透镜焦平面的定位[J].物理实验,2007,27(5):6-9.
[51]冈萨雷斯.数字图像处理[M].北京:电子工业出版社,2003年.
[2]韩亮,田逢春,徐鑫,李立. Mallat算法的光学实现[J].光学精密工程,2008,16(8):1490-1499.
[3]路甬祥.现代科学技术大众百科科学卷[M].杭州:浙江教育出版社,2001.
[4] D.G.Feitelson. Optical computing-a survey for computer scientists[M]. the MIT Press, 1988.
[5]赵建林.高等光学[M].西安:西北工业大学出版社,1999.
[6] A.W.Lohman, what classical optics can do for digital optical computer[J], Applied Optics, 1986,25(10):1543-1549.
[7] Yoshiki Ichioka, Tadao Iwaki, Ka’Sunori Matsuoka. Optical Information Processing And Beyond[J]. Proceedings of the IEEE, 1996,84(5):694-719.
[8] Yan. Zhang, Yao Li. Optical determination of gabor coefficients of transient signals[J]. Opt. Lett. 1991, 16(13): 1031.
[9] C. Hirliman, J. F. Morhange. Wavelet analysis of short light pulses[J]. Applied Optics. 1992, 30(7).
[10] H. Szu, Y. Sheng, J. Chen. Wavelet transform as a bank of matched filters[J]. Applied Optics. 1992, 31: 3267–3277.
[11] J. Caulfield, H. Szu. Parallel discrete and continuous wavelet transforms[J]. Opt. Eng. 1992, 31: 1835–1839.
[12] Xiangyang Yang, Harold H. Szu, Yunlong Sheng, H.John Caulfield. Optical wavelet transform of binary images[J]. Optical Engineering. 1992, 31(9): 1846-1851.
[13] Y. Sheng, D. Roberge, H. Szu and T. Lu. Optical wavelet matched filters for shift-invariant pattern recognition[J]. Optics Letters. 1993, 18: 299-301.
[14] M. O. Freeman. Wavelets: Signal representations with important advantages[J]. Opt. Photon. 1993, 4(8): 8-14.
[15] David mendlovic, Naim Konforti. Optical realization of the wavelet transform for two-dimensional objects[J]. Applied Optics. 1993, 32(32): 6542-6546.
[16] Ouzieli Ido, David Mendlovic. Two-dimensional wavelet processor[J]. Applied Optics. October 1996: 5839-5846.
[17]高春林,虞钢.具有特殊衍射强度分布的二元位相光栅设计[J].中国激光, 2001, 28(4): 365-368.
[18] R.A.Maestre, J.Garcia ,C.Ferreira. Pattern recognition using sequential matched filtering ofwavelet coefficients[J]. Optical Communication,1997,133(1-6): 401-414.
[19] David Mendlovic. Continuous two-dimensional on-axis optical wavelet transformer and wavelet processor with white-light illumination[J]. Applied Optics,1998.3, 37(10).
[20] Samuel P. Kozaitis a,1, Mark A. Getbehead. Optical wavelet feature extraction using a multiple-input phase-only encoded joint-transform correlator[J]. Optics Communications, 1998 ,151:15–20.
[21] H. Zhang, C.M. Cartwright, M.S. Ding, W.A. Gillespie. Optical implementation of a photorefractive joint transform correlator with wavelet filters[J]. Optics Communications , 2000,181:223–230.
[22]隋成华,徐来定.利用子波变换实现多通道复合图像特征提取[J].中国激光, 2000.8, A27(8):79-82.
[23] Linfei Chen, Daomu Zhao. Optical Image Encryption Based On Fractional Wavelet Transform[J]. Optics Communications, 2005,254:361-367.
[24] J. Garc?′a, Z. Zalevsky, D. Mendlovic. Two-dimensional wavelet transform by wavelength multiplexing[J]. Appl. Opt. ,1996, 35:7019–7024.
[25] Zeev Zalevsky. Experimental implementation of a continuous two-dimensional on-axis optical wavelet transformer with white light illumination[J]. Optical engineering, 1998.4, 37(4).
[26] Jose J.Esteve-Taboada, Javier Garcia, Carlos Ferreira. Two-dimensional optical wavelet decomposition with white-light illumination by wavelength multiplexing[J]. J. Opt. Soc.Am.A2001.1,18(1).
[27]孟书苹.基于光学小波变换系统研究[D].重庆大学硕士毕业论文,2005.
[28]游明俊.傅立叶光学[M].北京:兵器工业出版社,2000.
[29]王仕璠.信息光学理论与应用[M].北京:北京邮电大学出版社,2003.
[30]游明俊.傅立叶光学[M].北京:兵器工业出版社,2000.
[31]唐光菊,田逢春,李立,刘伟,刘赛.基于四叉树的光学小波滤波器轴心定位的研究[J].光学技术. 2008.34(4):597-600.
[32]谈欣柏.大学物理实验[M].天津:天津大学出版社,2000.
[33]徐鹏,王玉荣.集成薄膜晶体管液晶空间光调制器光调制特性的实验研究[J].液晶与显示, 2005,20(5):412-416.
[34]杨昱冰,王石语,蔡德芳,文建国,过振.被动调Q激光器输出波动因素的实验研究[J].红外与激光工程, 2006, 35(1): 60～65.
[35]杨齐民,钟丽云,吕晓旭.激光原理与激光器件[M].昆明:云南大学出版社,2003.
[36]周景超,戴汝为,肖柏华.图像质量评价研究综述[J].计算机科学, 2008,35(7):1-5.
[37]时红伟,陈世平.一种基于现代通信理论的图像质量评价技术[J].中国空间科学技术,2005,1:1-6.
[38]叶佳,张建秋,胡波.客观评估彩色图像质量的超复数奇异值分解法[J].电子学报,2006,35:28-33.
[39] DiGesu V,Staravoitov V V. Distance-based functions for image comparison[J]. Pattern Recognition Letters,1999,20(2):207-213.
[40] Starovitov V V,Kose C,Sankur B. Generalized distance based matching of non-binary images[J]. IEEE International Conference on Image Processing.1998.
[41] Avcibas I,Sankur B,Sayood K. Statistical Evaluation of Image Quality Measures[J]. Journal of Electronic Imaging, 2002: 206-223.
[42] Eskicioglu A M,Fisher P S. Image Quality Measures and Their Performance[J]. IEEE Transactions on Communication,1995,43(12):2959-2965.
[43]唐光菊.图像小波变换的光学实现[D].重庆大学硕士毕业论文,2008.
[44]刘伟.光学小波变换系统研究[D].重庆大学硕士毕业论文,2007.
[45]郑君里,应启珩,杨为理.信号与系统(第二版)[M].北京:高等教育出版社,2000
[46]殷纯永.光电精密仪器设计[M].北京:机械工业出版社,1996.
[47]维格特著.侯正信译.数字信号处理基础[M].北京:电子工业出版社,2003.
[48]闫敬文.数字图像处理(MATLAB版)[M].北京:国防工业出版社,2007.
[49]井上诚喜. C语言实用数字图像处理[M].北京:科学出版社,2003.
[50]刘伟,田逢春,唐光菊.利用CCD进行透镜焦平面的定位[J].物理实验,2007,27(5):6-9.
[51]冈萨雷斯.数字图像处理[M].北京:电子工业出版社,2003年.