共查询到20条相似文献,搜索用时 15 毫秒
1.
Improved discrete fractional Fourier transform 总被引:8,自引:0,他引:8
The fractional Fourier transform is a useful mathematical operation that generalizes the well-known continuous Fourier transform. Several discrete fractional Fourier transforms (DFRFT's) have been developed, but their results do not match those of the continuous case. We propose a new DFRFT. This improved DFRFT provides transforms similar to those of the continuous fractional Fourier transform and also retains the rotation properties. 相似文献
2.
The relationship between optical fractional Fourier transforms (OFRTs) obtained at different wavelengths is derived by use of the ABCD matrix formalism. It is shown that varying the wavelength while retaining the same optical system can be used to control the order of the OFRT. The advantage of this method of varying OFRT order is that no variation in the characteristics of the bulk optics is required. A general experimental verification of the theory is provided by showing the exact equivalence of two OFRT systems of different order when they are replayed using the same input function at different wavelengths. 相似文献
3.
Based on the conventional correlation and fractional correlation, the extended fractional correlation (EFC) is presented. And based on the configuration of the nonconventional joint transform correlator, we propose the joint extended fractional Fourier transform correlator (JEFRTC). The properties of the extended fractional cross correlation peak (EFCCP) in theory are analyzed. A sound conclusion is drawn that the width of EFCCP is narrower than that of fractional correlation peak under some conditions. This JEFRTC can permit lower precision of the systemic parameters when implemented with optical configuration. That will improve correlator’s character discriminability. 相似文献
4.
Real color fractional Fourier transform holography is proposed based on fractional Fourier transform holography. The method of fabrication, the principle of reconstruction and the design of system parameters are discussed in detail. The experiments prove real color fractional Fourier transform holograms possess the better function of anti-counterfeit than common fractional Fourier transform holograms. 相似文献
5.
Beam analysis by fractional Fourier transform 总被引:2,自引:0,他引:2
A method of spatial modal decomposition for optical beams by fractional Fourier transform, and its practical implementation with reduced complexity by use of modal interleavers, are discussed. 相似文献
6.
Based on the coherent optical theory, we extend the fractional Fourier transform of first-order correlation to a fractional Fourier transform of second-order correlation. An optical system for implementing a second-order fractional Fourier transform was designed. As a numerical example, we investigate the second-order fractional Fourier transform for a single slit. 相似文献
7.
分数傅里叶变换计算全息 总被引:1,自引:0,他引:1
在计算全息和分数傅里叶变换的基础上提出了不对称分数傅里叶变换计算全息和双随机相位不对称分数傅里叶变换计算全息。在这种方法中,首先用一随机相位函数乘以输入图像信息,然后沿x方向实施α级次的一维分数傅里叶变换,再乘以第二个随机相位函数,最后,沿y方向实施β级次的一维分数傅里叶变换。采用迂回位相编码法对变换后的结果编码,绘出计算全息图。为了恢复原始图像,需要知道变换级次和随机相位函数。利用这种方法进行图像加密,使加密图像的密钥由原来两重增加到四重,从而提高了系统的保密性能。 相似文献
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Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of reconstructing a fractional bandlimited signal with FRFT. We propose a novel reconstruction method for fractional bandlimited signals using the fractional Fourier series (FRFS). The advantage is that the sampling expansion can be deduced directly not based on the Shannon theorem. By utilizing the generalized form of Parseval’s relation for complex FRFS, we obtain the sampling expansion for fractional bandlimited signals with FRFT. We show that the sampling expansion for fractional bandlimited signals with FRFT is a special case of Parseval’s relation for complex FRFS. 相似文献
10.
Deriving the integral representation of a fractional Hankel transform from a fractional Fourier transform 总被引:1,自引:0,他引:1
We derive the integral representation of a fractional Hankel transform (FRHT) from a fractional Fourier transform. Some basic properties of the FRHT such as Parseval's theorem and its optical implementation are discussed qualitatively. 相似文献
11.
随着通信与网络的快速发展,能够包含大容量信息的影片得到了广泛应用。利用分数阶傅里叶变换的特点,提出了一种全光学加密解密影片的方法。将现有的影片加密密钥从二重变为了四重,显著增加了影片的安全性。通过改变振幅型正弦光栅的作用位置,将影片的加密解密次数由现有的每帧各一次减小为总共一次,优化了算法。仿真结果验证了该方法的有效性。 相似文献
12.
Linfei Chen 《Optik》2006,117(3):107-110
Starting from the relationship between the Wigner transformation and the fractional Fourier transform (FRFT), we apply the FRFT to the spatial filtering. In the process of filtering, the noise can be simulated as the chirp functions or their linear combination, which can be filtered at the corresponding fractional planes, and also the actual positions can be exactly obtained. Some numerical simulations prove its possibility. 相似文献
13.
In this research, we thoroughly investigate the complete generalized fractional Fourier transform (CGFRFT) and draw the following conclusions that are different from the original literature: (1) The CGFRFT is not a generalized version, but a special case that ignores the marginal postulate; (2) If the period parameter is not a multiple of four, the CGFRFT can never perform a Fourier transform regardless of the value of the transform order. The simulation results of a rectangular signal support the above conclusions. 相似文献
14.
In this paper the relations between two spreads, between
two group delays, and between one spread and one group delay in
fractional Fourier transform (FRFT) domains, are presented and three
theorems on the uncertainty principle in FRFT domains are also
developed. Theorem 1 gives the bounds of two spreads in two FRFT
domains. Theorem 2 shows the uncertainty relation between two group
delays in two FRFT domains. Theorem 3 presents the crossed
uncertainty relation between one group delay and one spread in two
FRFT domains. The novelty of their results lies in connecting the
products of different physical measures and giving their physical
interpretations. The existing uncertainty principle in the FRFT domain
is only a special case of theorem 1, and the conventional
uncertainty principle in time-frequency domains is a special case of
their results. Therefore, three theorems develop the relations of
two spreads in time-frequency domains into the relations between two
spreads, between two group delays, and between one spread and one
group delay in FRFT domains. 相似文献
15.
Image encryption and decryption using fractional Fourier transform and radial Hilbert transform 总被引:1,自引:0,他引:1
A technique for image encryption using fractional Fourier transform (FRT) and radial Hilbert transform (RHT) is proposed. The spatial frequency spectrum of the image to be encrypted is first segregated into two parts/channels using RHT, and image subtraction technique. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented. 相似文献
16.
<正>We present a novel method for realizing double-image encryption algorithm by combining the images in different transform domains.Two original images are encrypted into two interim images by fractional Fourier transform and gyrator transform,respectively.The two encrypted images can be obtained by means of the addition and subtraction of the two interim images.This is defined as a double-image sharing scheme,in which the original images are encrypted into two parts.The original images cannot be recovered only with any one of the two interim images.Numerical simulation experiments demonstrate the validity of the algorithm. 相似文献
17.
Zhengjun Liu 《Optics Communications》2007,275(2):324-329
We present an image encryption algorithm to simultaneously encrypt two images into a single one as the amplitudes of fractional Fourier transform with different orders. From the encrypted image we can get two original images independently by fractional Fourier transforms with two different fractional orders. This algorithm can be independent of additional random phases as the encryption/decryption keys. Numerical results are given to analyze the capability of this proposed method. A possible extension to multi-image encryption with a fractional order multiplexing scheme has also been given. 相似文献
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We introduce the Ince-Gaussian series representation of the two-dimensional fractional Fourier transform in elliptical coordinates. A physical interpretation is provided in terms of field propagation in quadratic graded-index media whose eigenmodes in elliptical coordinates are derived for the first time to our knowledge. The kernel of the new series representation is expressed in terms of Ince-Gaussian functions. The equivalence among the Hermite-Gaussian, Laguerre-Gaussian, and Ince-Gaussian series representations is verified by establishing the relation among the three definitions. 相似文献