We report general characteristics of on-axis Z-scan transmittance for arbitrary circularly symmetric beams. Some experimental results are presented for a nearly top-hat-shaped beam and for a trimmed Airy beam whose electric field profile is the central portion of an Airy function inside its first zero. The sensitivity of Z-scan method with a Brimmed Airy beam for measuring an induced index-of-refraction change is a factor of 1.5 greater than that of a Gaussian beam. Also, it is found that there are some advantages of experimental alignment and numerical convergence for a Z-scan measurement that uses a trimmed Airy beam over one that uses a top-hat beam. (C) 1996 Optical Society of America.