Phase change in a diffracted wave: a Cornu spiral perspective.

A simple evaluation of the phase change in a diffracted wave, in terms of the Cornu spiral, is presented to complement the well-known intensity change, which is routinely obtained for this elegant graphical construction of the Fresnel integrals. This is, to the best of our knowledge, the first presentation of this evaluation. It is shown that the phase of a wave diffracted by a slit is equal to the slope of the line tangent to the Cornu spiral, shifted by π/4.

[1]  Anbo Wang,et al.  Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula. , 2006, Applied optics.

[2]  A. Pendrill,et al.  Rollercoaster loop shapes , 2005 .

[3]  V. Castaño The Cornú Spiral as a Golden Mean Construction , 2005 .

[4]  David Mas,et al.  Fast numerical calculation of Fresnel patterns in convergent systems , 2003 .

[5]  David Mas,et al.  Near-field light distributions propagated from human corneas: Determination of relevant patterns , 2003 .

[6]  R Vincent,et al.  Phase retrieval in TEM using Fresnel images. , 2002, Ultramicroscopy.

[7]  C. Illueca,et al.  Refractive analysis of the human cornea through propagated fields , 2001 .

[8]  M V Papalexandris,et al.  Calculation of diffraction effects on the average phase of an optical field. , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  Javier Garcia,et al.  From Fresnel patterns to fractional Fourier transform through geometrical optics , 2000 .

[10]  Carlos Ferreira,et al.  Fast algorithms for free-space diffraction patterns calculation , 1999 .

[11]  David Mas,et al.  Fresnel diffraction in a theoretical eye: a fractional Fourier transform approach , 1999 .

[12]  W. Thomas Cathey,et al.  Matrix description of near-field diffraction and the fractional Fourier transform , 1999 .

[13]  R. Dorsch,et al.  Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm. , 1996, Applied optics.

[14]  M Schamschula,et al.  Fractional discrete Fourier transforms. , 1996, Optics letters.

[15]  Dennis Reil Forum. , 1996, Frauenheilkunde aktuell.

[16]  Habib Hamam,et al.  Efficient Fresnel-transform algorithm based on fractional Fresnel diffraction , 1995 .

[17]  P. Pellat-Finet Fresnel diffraction and the fractional-order Fourier transform. , 1994, Optics letters.

[18]  Jean-Paul Laumond,et al.  Primitives for smoothing mobile robot trajectories , 1993, [1993] Proceedings IEEE International Conference on Robotics and Automation.

[19]  D. Malacara-Hernández,et al.  PRINCIPLES OF OPTICS , 2011 .

[20]  E. Wolf,et al.  Principles of Optics (7th Ed) , 1999 .