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Comparison of different beam diameter definitions to characterize thermal damage of the eye

To assign a diameter to a beam profile which does not feature an actual perimeter presents a formidable problem. Traditionally, different beam diameter criteria are used which, however, depending on the beam profile, may yield drastically different results. The second moment method has been standardised by ISO, however, it also has some limitations. While a certain diameter criterion may have advantageous properties for instance for describing the propagating beam, it may not be appropriate for other 'applications' such as scaling the thermal damage threshold or for calculating the power that passes through an aperture. We discuss the latter two on the basis of some example profiles which show that the second moment diameter is in these cases not an appropriate parameter. For laser safety, where the exposure limit for the eye (MPE) is stated as a function of what could be referred to as the 'thermal beam diameter', a diameter criterion is needed that yields a correct value for this parameter for any arbitrary size and shape of the beam profile at the retina. A procedure is proposed that can be applied to determine a 'thermal damage parameter' for a given beam profile. This procedure is checked against thermal model calculations of the damage threshold. It is also shown that the power that passes through an aperture (such as the pupil of the eye) can be seriously underestimated when using the second moment diameter for non-Gaussian beams.