Now showing 1 - 10 of 13
  • Publication
    Optical wave propagation simulation, Wigner phase-space diagrams, and wave energy confinement
    (Optical Society of America, 2005-10-16) ; ;
    The number of samples required for efficient numerical simulation of wave propagation can be determined by a combination of Wigner phase-space techniques, wave energy confinement arguments, and a theorem relating energy confinement to accuracy.
  • Publication
    Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms
    (Optical Society of America, 2005-05-01) ;
    By use of matrix-based techniques it is shown how the space–bandwidth product (SBP) of a signal, as indicated by the location of the signal energy in the Wigner distribution function, can be tracked through any quadraticphase optical system whose operation is described by the linear canonical transform. Then, applying the regular uniform sampling criteria imposed by the SBP and linking the criteria explicitly to a decomposition of the optical matrix of the system, it is shown how numerical algorithms (employing interpolation and decimation), which exhibit both invertibility and additivity, can be implemented. Algorithms appearing in the literature for a variety of transforms (Fresnel, fractional Fourier) are shown to be special cases of our general approach. The method is shown to allow the existing algorithms to be optimized and is also shown to permit the invention of many new algorithms.
      599Scopus© Citations 169
  • Publication
    Wavelength-controlled variable-order optical fractional Fourier transform
    (Optical Society of America, 2004-03-01) ; ;
    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.
      277Scopus© Citations 8
  • Publication
    Additional sampling criterion for the linear canonical transform
    (Optical Society of America, 2008-11-15) ; ;
    The linear canonical transform describes the effect of first-order quadratic phase optical systems on a wave field. Several recent papers have developed sampling rules for the numerical approximation of the transform. However, sampling an analog function according to existing rules will not generally permit the reconstruction of the analog linear canonical transform of that function from its samples. To achieve this, an additional sampling criterion has been developed for sampling both the input and the output wave fields.
      376Scopus© Citations 43
  • Publication
    Speckle photography : mixed domain fractional Fourier motion detection
    A reflection-based optical implementation of two simultaneous scale-invariant fractional Fourier transforms (FRTs) is used to develop a novel compact speckle photographic system. The system allows the independent determination of both surface tilting and in-plane translational motion from two sequential mixed domain images captured using a single camera
      350Scopus© Citations 26
  • Publication
    Magnitude and direction of motion with speckle correlation and the optical fractional Fourier transform
    (Optical Society of America, 2005-05-10) ; ;
    The optical fractional Fourier transform (OFRT) in combination with speckle photography has previously been used to measure the magnitude of surface tilting and translation. Previous OFRT techniques used to determine motion have not been able to discern the direction of the tilt and translation. A simple new approach involving use of correlation is presented to overcome this limitation. Controlled variation of the minimum resolution and dynamical range of measurement is demonstrated. It is then experimentally confirmed that if a rigid body’s motion is captured by two OFRT systems of different orders, the direction and magnitude of both the tilting and the in-plane translation motion of the body can be independently determined without a priori knowledge. The experimental results confirm the validity of previous theoretical predictions
      391Scopus© Citations 28
  • Publication
    Generalized Yamaguchi correlation factor for coherent quadratic phase speckle metrology systems with an aperture
    In speckle-based metrology systems, a finite range of possible motion or deformation can be measured. When coherent imaging systems with a single limiting aperture are used in speckle metrology, the observed decorrelation effects that ultimately define this range are described by the well-known Yamaguchi correlation factor. We extend this result to all coherent quadratic phase paraxial optical systems with a single aperture and provide experimental results to support our theoretical conclusions.
      402Scopus© Citations 13
  • Publication
    Motion detection, the Wigner distribution function, and the optical fractional Fourier transform
    (Optical Society of America, 2003-06-01) ; ;
    It is shown that both surface tilting and translational motion can be independently estimated by use of the speckle photographic technique by capturing consecutive images in two different fractional Fourier domains. A geometric interpretation, based on use of the Wigner distribution function, is presented to describe this application of the optical fractional Fourier transform when little prior information is known about the motion.
      316Scopus© Citations 29
  • Publication
    Digital computation of the complex linear canonical transform
    An efficient algorithm for the accurate computation of the linear canonical transform with complex transform parameters and with complex output variable is presented. Sampling issues are discussed and the requirements for different cases given. Simulations are provided to validate the results.
      504Scopus© Citations 11
  • Publication
    Optical image encryption by random shifting in fractional Fourier domains
    (Optical Society of America, 2003-02-15) ;
    A number of methods have recently been proposed in the literature for the encryption of two-dimensional information by use of optical systems based on the fractional Fourier transform. Typically, these methods require random phase screen keys for decrypting the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. A new technique based on a random shifting, or jigsaw, algorithm is proposed. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in fractional Fourier domains. The new method has been compared with existing methods and shows comparable or superior robustness to blind decryption. Optical implementation is discussed, and the sensitivity of the various encryption keys to blind decryption is examined.
      1107Scopus© Citations 420