Now showing 1 - 5 of 5
  • 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
    Fundamental diffraction limitations in a paraxial 4-f imaging system with coherent and incoherent illumination
    (Optical Society of America, 2007-07-01) ; ;
    In the usual model of an imaging system, only the effects of the aperture stop are considered in determining diffraction-limited system performance. In fact, diffraction at other stops—those associated with different lens elements, for example—can also affect system performance and cause the imaging to be space variant, even in the absence of vignetting in the conventional ray optics sense. For the 4-f imaging system investigated in this paper, the severity of the space variance depends on the relative sizes of the two lens stops and the aperture stops. If the diameters of the lenses are equal, the aperture of the first lens has a greater effect on system performance than does that of the second.
      395Scopus© Citations 14
  • Publication
    Cross terms of the Wigner distribution function and aliasing in numerical simulations of paraxial optical systems
    (Optical Society of America, 2010-04-15) ; ;
    Sampling a function periodically replicates its spectrum. As a bilinear function of the signal, the associated Wigner distribution function contains cross terms between the replicas. Often neglected, these cross terms affect numerical simulations of paraxial optical systems. We develop expressions for these cross terms and show their effect on an example calculation
      447Scopus© Citations 11
  • Publication
    Lucky imaging and aperture synthesis with low-redundancy apertures
    (Optical Society of America, 2009-01-01) ; ;
    Lucky imaging, used with some success in astronomical and even horizontal-path imaging, relies on fleeting conditions of the atmosphere that allow momentary improvements in image quality, at least in portions of an image. Aperture synthesis allows a larger aperture and, thus, a higher-resolution imaging system to be synthesized through the superposition of image spatial-frequency components gathered by cooperative combinations of smaller subapertures. Acombination of lucky imaging and aperture synthesis strengthens both methods for obtaining improved images through the turbulent atmosphere.We realize the lucky imaging condition appropriate for aperture synthesis imaging for a pair of rectangular subapertures and demonstrate that this condition occurs when the signal energy associated with bandpass spatial-frequency components achieves its maximum value.
      382Scopus© Citations 7
  • Publication
    Wigner cross-terms in sampled and other periodic signals
    (Optical Society of America, 2009-10-11) ; ;
    If we sample a scalar wave field, it becomes periodic in frequency. We examine the cross-terms which occur between these periodic replicas in the Wigner-Ville distribution function of such a signal. We present analytic results for Gaussian signals. The results also have implications for physical systems which contain periodic gratings.