Intensity distributions near focus of strongly converging spherical waves diffracted at a circular aperture

2004 ◽  
Vol 36 (13) ◽  
pp. 1135-1145
Author(s):  
Kailiang Duan ◽  
Baida Lü
Keyword(s):  
Circular Aperture ◽  
Spherical Waves

Light distribution near focus in an error-free diffraction image

1951 ◽  
Vol 204 (1079) ◽  
pp. 533-548 ◽  
Keyword(s):  
Bessel Functions ◽  
Convergent Series ◽  
Fresnel Diffraction ◽  
Circular Aperture ◽  
Diffraction Image ◽  
Mathematical Basis ◽  
Spherical Waves ◽  
Contour Lines ◽  
Imaging Properties ◽  
Special Case

Expressions are derived for the fraction of the total illumination present within certain regions in receiving planes near focus of spherical waves issuing from a circular aperture. The derivation is based on Lommel's treatment of Fresnel diffraction, and the solution takes the form of rapidly convergent series involving Bessel functions. Numerical results are illustrated by contour lines. The distribution of the illumination in a number of selected planes near focus is studied in greater detail. A comparison with the predictions of geometrical optics is also made. As a special case the fraction of the total illumination present in the geometrical shadow is discussed. The results provide a mathematical basis for a discussion of the imaging properties in optical system where, as for example in a well-corrected refracting telescope objective, the chromatic variation of focus is the only appreciable aberration.

Propagation of spherical waves above ground

1983 ◽  
Vol 16 (3) ◽  
pp. 163-168
Author(s):  
R. Seznec ◽  
M. Berengier ◽  
V. Legeay
Keyword(s):  
Spherical Waves

scholarly journals On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 220
Author(s):  
Alexey Samokhin
Keyword(s):  
Periodic Boundary ◽  
Asymptotic Formulas ◽  
Burgers Equations ◽  
Spherical Waves ◽  
Constant Height ◽  
De Vries ◽  
Spatial Dimensions ◽  
Integral Characteristics ◽  
Boundary Solutions ◽  
Shock Fronts

We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.

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