Influence of the spatial beam profile on hard tissue ablation, Part II: pulse energy and energy density distribution in simple beams

When calculating applied flux densities in practice, the beam profile of a laser is often erroneously assumed to be homogeneous. In addition, there is usually no consistency in the choice of a suitable measuring method for determining the beam diameter. This failure to observe the inhomogeneous intensity distribution within the beam cross-section, combined with the imprecise knowledge of the beam diameter, leads to flux densities being stated that represent mean values at best. The present paper gives definitions for the flux densities of simple, radially symmetrical beam cross-sections, taking the top-hat and Gaussian profiles as examples. In connection with the inhomogeneous energy distribution in the Gaussian beam, a concept of integral and local energy density is discussed, which differs from the customary definition of the energy density as a constant. Also presented are the consequences of the mathematical concepts in terms of measurement, giving particular consideration to the case where the energy density as the measured variable matches the integral energy density. The significance of the integral and local energy density for hard-tissue ablation is described, based on the practical example of the ablation of dental hard substance. The central result is that the integral flux density is directly accessible as a measured variable, while the effect on the tissue is determined by the local flux density. If the form of the beam is known, the integral flux density can be converted into the local flux density.