Study On The 4f System Of Optical Wavelet Transform

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.