A well-known integral representation of Bessel's functions (cf. Jahnke and Emde [82]) is

Jn(z) = — eiz cosaeinada, 2n Jo hence we obtain a

o where J0 is the zero-order Bessel function. Since /q uJ0(u)du = uJ1 (u), and also J1(u)/u ^ 1/2 when u ^ 0, the wave oscillation at the Gaussian plane is

kar and the intensity is represented by

This is the celebrated formula first derived in 1835 by Airy [2] in a different form.

0 0

Post a comment