SCALING PROPERTIES IN THE DIFFRACTION OF FOCUSED WAVES AND AN APPLICATION TO SCANNING BEAMS

From the Fresnel approximation to the Rayleigh-Sommerfeld solution for scalar wave propagation it follows that the field generated by a focused wave passing through an arbitrary aperture is simply related to the field generated by a collimated beam that is diffracted by any aperture of the same shape-the transverse intensity patterns are simply scaled and shifted. In fact, this result provides a simple, diffraction-based model for the action of a lens. A closed-form expression is found for the width of the beam generated by a focused uniform field that is diffracted by a circular aperture and, as an illustrative application, the beam of smallest maximum width over a fixed scanning depth is investigated.