This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th...This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.展开更多
Using the intermediate coordinate-momentum representation {x}s,r, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresne...Using the intermediate coordinate-momentum representation {x}s,r, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresnel operator F （r, s） and the Fourier transform operator F- by decomposing U. We also find that the matrix element s,r 〈x｜U｜f） just corresponds to an optical scaled Presnel Fourier transform.展开更多
In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state its...In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.展开更多
Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent t...Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.展开更多
Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a ...Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a 1 a 2）/√ 2） and the Weyl transformation（for（a 1 ＋ a 2）/√ 2）.Physically,（a 1 a 2）/√ 2 and（a 1 ＋ a 2）/√ 2 could be a symmetric beamsplitter＇s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.展开更多
By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator...By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.展开更多
We present a new method for image encryption on the basis of simplifed fractional Hartley transform （SFRHT）. SFRHT is a real transform as Hartley transform （HT） and furthermore, superior to HT in virtue of the adv...We present a new method for image encryption on the basis of simplifed fractional Hartley transform （SFRHT）. SFRHT is a real transform as Hartley transform （HT） and furthermore, superior to HT in virtue of the advantage that it can also append fractional orders as additional keys for the purpose of improving the system security to some extent. With this method, one can encrypt an image with an intensity-only medium such as a photographic film or a CCD camera by spatially incoherent or coherent illumination. The optical realization is then proposed and computer simulations are also performed to verify the feasibility of this method.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
文摘Using the intermediate coordinate-momentum representation {x}s,r, we introduce a new Hadamard transform. It is found that the operator U corresponding to this transform can be considered as a combination of the Fresnel operator F （r, s） and the Fourier transform operator F- by decomposing U. We also find that the matrix element s,r 〈x｜U｜f） just corresponds to an optical scaled Presnel Fourier transform.
基金supported by the Startup Research Fund for Introducing Talents of Anhui Polytechnic University (Grant No. 2009YQQ006)the Research Foundation of the Education Department of Anhui Province of China (Grant No. KJ2011B031)
文摘In this paper, we propose the so-called continuous Fresnel-wavelet combinatorial transform which means that the mother wavelet undergoes the Fresnel transformation. This motivation can let the mother-wavelet-state itself vary from ｜ψ〉 to Ftr, s ｜ψ〉, except for variation within the family of dilations and translations. The Parseval＇s equality, admissibility condition and inverse transform of this continuous Fresnel-wavelet combinatorial transform are analysed. By taking certain parameters and using the admissibility condition of this continuous Fresnel-wavelet combinatorial transform, we obtain some mother wavelets. A comparison between the newly found mother wavelets is presented.
文摘Two physical interpretations of chirp transform related to Fresnel diffraction and Wigner distribution function are given. The chirp transform can be regarded as a Fresnel diffraction observed on a spherical tangent to the diffraction plane, or a rotation and stretching transformation of the Wigner distribution function space. A general fast algorithm for the numerical calculation of chirp transform is developed by employing two fast Fourier transform algorithms. The algorithm, by which a good evaluation can be achieved, unifies the calculations of Fresnel diffraction, arbitrary fractional- order Fourier transforms and other scalar diffraction systems. The algorithm is used to calculate the Fourier transform of a Gaussian function and the Fourier transform, the Fresnel transform, the Fractional-order Fourier transforms of a rectangle function to evaluate the performance of this algorithm. The calculated results are in good agreement with the analytical results, both in the amplitude and phase.
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University,China (Grant No. 33190059)the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20113401120004)the Open Funds from National Laboratory for Infrared Physics,Chinese Academy of Sciences (Grant No. 201117)
文摘Based on the newly developed coherent-entangled state representation,we propose the so-called Fresnel-Weyl complementary transformation operator.The new operator plays the roles of both Fresnel transformation（for（a 1 a 2）/√ 2） and the Weyl transformation（for（a 1 ＋ a 2）/√ 2）.Physically,（a 1 a 2）/√ 2 and（a 1 ＋ a 2）/√ 2 could be a symmetric beamsplitter＇s two output fields for the incoming fields a 1 and a 2.We show that the two transformations are concisely expressed in the coherent-entangled state representation as a projective operator in the integration form.
基金supported by the University Natural Science Foundation of Anhui Province,China (Grant No. KJ2011Z339)the National Natural Science Foundation of China (Grant No. 10874174)
文摘By virtue of the coherent state representation of the newly introduced Fresnel operator and its group product property we obtain new decomposition of the Fresnel operator as the product of the quadratic phase operator, the squeezing operator, and the fractional Fourier transformation operator, which in turn sheds light on the matrix optics design of ABCD-systems The new decomposition for the two-mode Fresnel operator is also obtained by the use of entangled state representation.
文摘We present a new method for image encryption on the basis of simplifed fractional Hartley transform （SFRHT）. SFRHT is a real transform as Hartley transform （HT） and furthermore, superior to HT in virtue of the advantage that it can also append fractional orders as additional keys for the purpose of improving the system security to some extent. With this method, one can encrypt an image with an intensity-only medium such as a photographic film or a CCD camera by spatially incoherent or coherent illumination. The optical realization is then proposed and computer simulations are also performed to verify the feasibility of this method.
