A comprehensive analysis of the well-known open aperture Z-scan method, using a modified equation for the change in transmittance, is presented and accounts for discrepancies in two-photon absorption (2PA) cross sections between picosecond and fermosecond excitation. This new approach takes into account excited-state absorption and stimulated emission of the molecules studied. The two-photon. absorption cross-section spectra of a series of six fluorene-based derivatives, determined using picosecond pulses, over a broad spectral range (500-900 nm), and this approach using a modified fitting procedure in the open aperture Z-scan is reported. We demonstrate that the fluorene derivatives exhibit two-photon absorption cross-section values between 700 and 5000 GM, when excited into the two-photon allowed electronic state. Excitation anisotropy spectra, measured to investigate the nature of the observed linear and nonlinear absorption bands, are presented and provide insight into the 2PA process.