In other words, we only require a point source which is produced by a convergent ( uniform ) spherical wave whose half angle is greater than the edge angle of the lens.
42.
So they have to find us based on omnidirectional spherical waves that drop in energy as the square of the distance-and are therefore almost completely indetectable after a lightyear or so of travel.
43.
So, the plane wave components in this far-field spherical wave, which lie beyond the edge angle of the lens, are not captured by the lens and are not transferred over to the image plane.
44.
The amplitude of a spherical wave will fall off as the inverse of the distance from the source ( the 1 / " R " term in the formulas for " h " above ).
45.
In order to measure the point spread function or impulse response function of the lens, we do not need a perfect point source that radiates a perfect spherical wave in all directions of space.
46.
2nd observer sees spherical wave of light with epicentre in lamp but this epicentre is fixed, has speed 0 in his reference frame associated with Sun, so lamp with speed \ mathbf u is immediately mismatching epicentre.
47.
The \ frac { e ^ {-jkr } } { r } radial dependence is a spherical wave-both in magnitude and phase-whose local amplitude is the FT of the source plane distribution at that far field angle.
48.
For instance, local time was described by him as a consequence of the assumption that light propagates in spherical waves with constant velocity in all directions ( a similar definition was already given by Poincar?in 1900 ).
49.
Thus, when the recorded pattern is illuminated with the original plane wave, some of the light is diffracted into a diverging beam equivalent to the original spherical wave; a holographic recording of the point source has been created.
50.
The s-wave part of the wavefunction \ psi ( r, \ theta ) is projected out by using the standard expansion of a plane wave in terms of spherical waves and Legendre polynomials P _ l ( \ cos \ theta)
