Rayleigh–Sommerfeld diffraction and Poisson's spot

نویسندگان

  • Robert L Lucke
  • R L Lucke
چکیده

When the Fresnel–Kirchhoff (FK) diffraction integral is evaluated exactly (instead of using the Fresnel approximation), the well-known mathematical inconsistency in the FK boundary conditions leads to unacceptable results for the intensity of Poisson’s spot. The Rayleigh–Sommerfeld (RS) integral has no inconsistencies and leads to an accurate description. The case for RS is bolstered by the observation that it is equivalent to Fourier propagation.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Optical Diffraction in Close Proximity to Plane Apertures. II. Comparison of Half-Plane Diffraction Theories

The accuracy and physical significance of the classical Rayleigh-Sommerfeld and Kirchhoff diffraction integrals are assessed in the context of Sommerfeld's rigorous theory of half-plane diffraction and Maxwell's equations. It is shown that the Rayleigh-Sommerfeld integrals are in satisfactory agreement with Sommerfeld's theory in most of the positive near zone, except at sub-wavelength distance...

متن کامل

On the exact Kirchhoff and Rayleigh-Sommerfeld theories for the focusing of an infinite scalar spherical wave-field

The first and second Rayleigh-Sommerfeld diffraction theories, together with the Kirchhoff diffraction theory, are widely used in the formulation of optical diffraction problems [ 1 ]. They arise in the context of the half-space boundary-value problem of scalar wave theory; all sources of the optical field are assumed to be located in the Z~< 0 half-space, and the Z > 0 half-space is taken to b...

متن کامل

On the usual approximation used in the Rayleigh-Sommerfeld diffraction theory.

The complete Rayleigh-Sommerfeld scalar diffraction formula contains (1 - ikR) in the integrand. Usually the wavelength is small compared with the distance of the observation point from the aperture and (1 - ikR) is approximated by -ikR alone. Other approximations usually made in the Rayleigh-Sommerfeld formula are addressed as well. Closed-form solutions, without approximations, are possible w...

متن کامل

Fresnel diffraction by a circular aperture with off-axis illumination and its use in deconvolution of microscope images.

The Fresnel approximation for off-axis illumination of a circular aperture is reexamined. The point-spread function for an aberration-free system can be expressed in terms of redefined optical coordinates. An improved expression is given for contours of constant intensity in the focal plane. The variation in axial width of the focal spot with angle of offset is discussed. The predictions are co...

متن کامل

Scalar Rayleigh-Sommerfeld and Kirchhoff diffraction integrals: A comparison of exact evaluations for axial points*

The second Rayleigh-Sommerfeld (RS) diffraction integral, wherein the normal derivative is specified, is evaluated in simple closed form for all axial points when a divergent or convergent spherical wave is incident upon a circular aperture or disk. These evaluations (solutions) are compared with known corresponding solutions of the first RS diffraction integral. These sets of solutions are int...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005