Phase-structure and aperture-averaged slope-correlated functions with a finite outer scale are derived based on the Taylor hypothesis and a generalized spectrum, such as the von Karman modal. The effects of the finite outer scale on measuring and determining the character of atmospheric-turbulence statistics are shown especially for an approximately 4-m class telescope and subaperture. The phase structure function and atmospheric coherent length based on the Kolmogorov model are approximations of the formalism we have derived. The analysis shows that it cannot be determined whether the deviation from the power-law parameter of Kolmogorov turbulence is caused by real variations of the spectrum or by the effect of the finite outer scale. (C) 2002 Optical Society of America.