Gyrator transform: Properties and applications

Complutense University of Madrid, Madrid, Madrid, Spain
Optics Express (Impact Factor: 3.49). 04/2007; 15(5):2190-203. DOI: 10.1364/OE.15.002190
Source: PubMed


In this work we formulate the main properties of the gyrator operation which produces a rotation in the twisting (position-spatial frequency) phase planes. This transform can be easily performed in paraxial optics that underlines its possible application for image processing, holography, beam characterization, mode conversion and quantum information. As an example, it is demonstrated the application of gyrator transform for the generation of a variety of stable modes. (c) 2007 Optical Society of America.

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Available from: Maria L. Calvo, Apr 23, 2014
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    • "In this case the QPS transformation parameters provide extra keys for the encryption system. The Gyrator transform (GT), which also belongs to the class of the linear canonical transforms, has been used for optical encryption systems [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40], where the rotation angle parameter provides the extra key of the encryption system. The Hartley transform (HT), which is effectively a real Fourier transform without any phase information, has also been proposed for the use in optical DRPE systems [41] [42] [43] [44] [45]. "
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    ABSTRACT: Abstract In this paper we review a number of optical image encryption techniques proposed in the literature inspired by the architecture of the classic optical Double Random Phase Encoding (DRPE) system. The optical DRPE method and its numerical simulation algorithm are first investigated in relation to the sampling considerations at various stages of the system according to the spreading of the input signal in both the space and spatial frequency domains. Then the several well-known optically inspired encryption techniques are examined and categorized into all optical techniques and image scrambling techniques. Each method is numerically implemented and compared with the optical DRPE scheme, in which random phase diffusers (masks) are applied after different transformations. The optical system used for each method is first illustrated and the corresponding unitary numerical algorithm implementation is then investigated in order to retain the properties of the optical counterpart. The simulation results for the sensitivities of the various encryption keys are presented and the robustness of each method is examined. This overview allows the numerical simulations of the corresponding optical encryption systems, and the extra degree of freedom (keys) provided by different techniques that enhance the optical encryption security, to be generally appreciated and briefly compared and contrasted.
    Optics & Laser Technology 01/2013; DOI:10.1016/j.optlastec.2013.05.023 · 1.65 Impact Factor
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    • ", which is the characteristic of GT. The patterns are similar to the result reported in Ref.[16]. The reversibility of numerical algorithm of transform is important to the field of optical information processing, such as image encryption, filtering and correlation. "
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    ABSTRACT: The expression of gyrator transform (GT) is rewritten by using convolution operation, from which GT can be composed of phase-only filtering, Fourier transform and inverse Fourier transform. Therefore, fast Fourier transform (FFT) algorithm can be introduced into the calculation of convolution format of GT in the discrete case. Some simulations are presented in order to demonstrate the validity of the algorithm.
    Optik - International Journal for Light and Electron Optics 05/2011; 122(10):864-867. DOI:10.1016/j.ijleo.2010.06.010 · 0.68 Impact Factor
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    • "Recently, gyrator transform is introduced into the field of optical information processing by Rodrigo et al. [23] [24]. The gyrator transform of a two-dimensional function f(x,y) can be expressed as "
    ZJ Liu · Lie Xu · CA Lin · JM Dai · ST Liu ·
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    ABSTRACT: An image encryption is discussed based on the random phase encoding method in gyrator domains. An iterative structure of image encryption is designed for introducing more random phases to encrypt image. These random phase functions are generated by a two-dimensional chaotic mapping with the help of computer. The random phases are utilized for increasing the security of this encryption algorithm. In the chaotic mapping relation, the initial value and expression can serve as the key of algorithm. The mapping relation is considered secretly for storage and transmission in practical application in comparison to traditional algorithms. The angle parameter of gyrator transform is an additional key. Some numerical simulations have been given to validate the performance of the encryption scheme.
    Optics and Lasers in Engineering 04/2011; 49(4):542-546. DOI:10.1016/j.optlaseng.2010.12.005 · 2.24 Impact Factor
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