A well-known integral representation of Bessel's functions (cf. Jahnke and Emde ) 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  in a different form.
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