Gyrator transform: properties and applications.

Optics Express (Impact Factor: 3.55). 04/2007; 15(5):2190-203. DOI: 10.1364/OE.15.002190
Source: PubMed

ABSTRACT 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.

1 Bookmark
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The group‐theoretical structure of the harmonic oscillator appears in many guises. Originally developed by Marcos Moshinsky among several others for applications in nuclear physics, we point out here that the harmonic oscillator structure appears in aberrations of geometric optics, particularly in their classification by rank, symplectic spin and weight. And further, the finite harmonic oscillator appears again in the nonlinear transformations of finite Hamiltonian systems, when applied to the parallel processing of signals.
    AIP Conference Proceedings. 12/2010; 1323(1):313-322.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Hermite-Gauss and Laguerre-Gauss modes of a continuous optical field in two dimensions can be obtained from each other through paraxial optical setups that produce rotations in (four-dimensional) phase space. These transformations build the SU(2) Fourier group that is represented by rigid rotations of the Poincaré sphere. In finite systems, where the emitters and the sensors are in NxN square pixellated arrays, one defines corresponding finite orthonormal and complete sets of two-dimensional Kravchuk modes. Through the importation of symmetry from the continuous case, the transformations of the Fourier group are applied on the finite modes.
    Journal of the Optical Society of America A 03/2008; 25(2):365-70. · 1.67 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: A novel method for color-information security system based on joint-extended gyrator transform correlator is introduced. In this method, the color image is split into three-color channels: red, green, blue. Each color channel bonded to a random phase mask and a random phase key code are gyrator transformed separately. The two obtained information multiplexed to form a joint gyrator power spectrum, which is again gyrator transformed to get a joint-extended gyrator power spectrum. The same phase key code is used in both the data encryption and decryption. The three-color channels are independently encrypted and decrypted to avoid the interference of crosstalks. The decrypted image is obtained without any noise and distortion. The angle parameters of gyrator transform in each channel are additional encryption keys for enhancing the security. The proposed system has resistant against chosen- and known plaintext attacks. The calculated values of mean square error and peak signal-to-noise ratio support the noise-free recovery of original color image. The implementation of opto-electronic setup has been proposed. The validity and feasibility of the proposed method are demonstrated by numerical simulations.
    Optics and Lasers in Engineering 01/2012; · 1.92 Impact Factor


Available from
Jun 5, 2014