We propose a novel method for image encryption,which is realized by the Collins formula with the random shifting method.The Collins formula can denote different optical transforms by one expression with different ABCD...We propose a novel method for image encryption,which is realized by the Collins formula with the random shifting method.The Collins formula can denote different optical transforms by one expression with different ABCD elements.For a generalized optical system,the ABCD elements can be randomly chosen,so the keys are increased and the security of the system is strengthened.Finally,some computer simulations are given for different encryption systems to prove the possibilities.The encryption effect is good,and people without the correct keys can not obtain the information easily.展开更多
Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured...Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained.Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae,the applicable range and exactness of analytical formulae are confirmed. It is shown that the calculating speed of using the obtained approximate analytical formulae,is several hundred times faster than that of using diffraction integral directly.Meanwhile,by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.展开更多
基金the National Natural Science Foundation of China under Grant No 11147138the Natural Science Foundation Zhejiang Province under Grant Nos LQ12A04001 and R1090168the Natural Science Foundation of Educational Department of Zhejiang Province under Grant No Y200908864.
文摘We propose a novel method for image encryption,which is realized by the Collins formula with the random shifting method.The Collins formula can denote different optical transforms by one expression with different ABCD elements.For a generalized optical system,the ABCD elements can be randomly chosen,so the keys are increased and the security of the system is strengthened.Finally,some computer simulations are given for different encryption systems to prove the possibilities.The encryption effect is good,and people without the correct keys can not obtain the information easily.
基金This work was supported by the National Natural Science Foundation of China (NSAF United Foundation) under Grant No. 10276034 and 60276035.
文摘Based on the principle that a rectangular function can be expanded into a sum of complex Gaussian functions with finite numbers, propagation characteristics of a Gaussian beam or a plane wave passing through apertured fractional Fourier transforming systems are analyzed and corresponding analytical formulae are obtained.Analytical formulae in different fractional orders are numerically simulated and compared with the diffraction integral formulae,the applicable range and exactness of analytical formulae are confirmed. It is shown that the calculating speed of using the obtained approximate analytical formulae,is several hundred times faster than that of using diffraction integral directly.Meanwhile,by using analytical formulae the effect of different aperture sizes on Gaussian beam propagation characteristics is numerically simulated, it is shown that the diffraction effect can be neglected when the aperture size is 5 times larger than the beam waist size.
