General Expression For Laser Beam Spreading

Atmospheric turbulence effects on laser beam propagation have been limited to the cases of very short exposure in the near-field and far-field and to the case of very long exposure. However for typical values of wavelength, aperture diameter, and pathlength, the Fresnel number can be on the order of unity. Thus neither the near- nor far-field condition is appropriate. In addition, pulse duration times can range from nonoseconds to seconds, thus neither the short nor long exposure limit is, in general, applicable. Since the limiting conditions do not apply to typical scenarios, a general interpolation expression for laser beam spreading, valid for arbitrary values of the Fresnel number and pulse duration, has been developed. This expression gives the proper limiting results in the near- and far-field, short exposure cases and long exposure case and entirely reasonable results in the intermediate cases.