  In femtosecond laser micromachining, the ablation threshold is a key
processing parameter that characterises the energy density required to cause
ablation. Current techniques for measuring the ablation threshold such as the
diameter regression and diagonal scan methods are based on the assumption of a
Gaussian spatial profile, however no techniques currently exist for measuring
the ablation threshold using a non-Gaussian beam shape. Here we present a
formalism of the diagonal scan method for determining the ablation threshold
and pulse superposition for femtosecond vortex pulses. To the authors'
knowledge this is the first ablation threshold technique developed for pulses
with non-Gaussian spatial profiles. Using this method, the ablation threshold
can be calculated using measurement of a single feature (the maximum damage
radius $\rho_{max}$), which allows investigations of ablation threshold and
incubation effects to be carried out quickly and easily. Extending this method
to non-Gaussian beams will allow exploration of new avenues of research,
enabling characterisation of the ablation threshold and incubation behaviour
for a material when ablated with femtosecond vortex pulses.

Optics;Materials Science