Long- and short-term Strehl ratios for turbulence with finite inner and outer scales

Corrections to the long- and short-term (tilt removed) Strehl ratios of a laser beam propagating through atmospheric turbulence are given for turbulence with finite inner and outer scales. It is found that outer-scale corrections are important for long-term Strehl ratios, and inner-scale corrections are important for short-term Strehl ratios. The results are applicable to near-ground propagation where the outer scale may be of the same order as the beam diameter and to upper atmospheric propagation where the inner scale may become a significant fraction of the beam diameter. The results are also useful for determining length scales for wave optics propagation codes, since such codes introduce artificial outer and inner scales due to finite grid size and mesh-point separation.