The so-called D-squared or Liu's method is an extensively applied approach to determine the irradiation fluence thresholds for laserinduced damage or modification of materials. However, one of the assumptions behind the method is the use of an ideal Gaussian profile that can lead in practice to significant errors depending on beam imperfections. In this work, we rigorously calculate the bias corrections required when applying the same method to Airy-disk like profiles. Those profiles are readily produced from any beam by insertion of an aperture in the optical path. Thus, the correction method gives a robust solution for exact threshold determination without any added technical complications as for instance advanced control or metrology of the beam. Illustrated by two case-studies, the approach holds potential to solve the strong discrepancies existing between the laser-induced damage thresholds reported in the literature. It provides also an appropriate tool for new studies with the most extreme laser radiations.