2. In the paraxial approximation, the field U(r, y, =) at some propagation distance z is related to the starting field u(To, yo) by: U(x, y, 2) 1 ikz u(zo, yo)ed drodyo. where 2 2 R= =/1+ I1 - TO + 41 - yo Show that the far field intensity pattern of an initial plane wave of amplitude A, passing through a circular aperture of diameter 2a may be written as: J( X)2 I(X) = 10 X And find the expressions for X and Jo. Hint: the following relations might be useful: Jo = piu cose de 21 Jo IJo(x) dx = uji(u)2. In the paraxial approximation, the field U(r, y, =) at some propagation distance z is related to the starting field u(To, yo) by: U(x, y, 2) 1 ikz u(zo, yo)ed drodyo. where 2 2 R= =/1+ I1 - TO + 41 - yo Show that the far field intensity pattern of an initial plane wave of amplitude A, passing through a circular aperture of diameter 2a may be written as: J( X)2 I(X) = 10 X And find the expressions for X and Jo. Hint: the following relations might be useful: Jo = piu cose de 21 Jo IJo(x) dx = uji(u)