Beam Propagation Hazard Calculations for Telescopic Viewing of Laser Beams

We have performed beam propagation calculations which can be used to characterize the retinal spot size of laser beams for telescopic viewing. The results show that the minimal retinal spot size produced on the retina by using a telescope compared to that of the naked eye is increased at least by a factor that is equal to the magnifying power of the telescope and an increase of C6 (or CE) is applicable. The hazard evaluation method used is based on the calculation of the maximum level of thermal hazard that is defined as the ratio of the power that enters the eye and the retinal spot diameter. Beam propagation principles were used to calculate the distance between the beam waist and the eye lens that provides the maximum hazard. The only two input parameters necessary for these calculations are the waist diameter and the far-field divergence of the beam. The beam width on the retina at the most hazardous viewing distance is consequently used to determine the angular subtense of the apparent source that is needed to calculate the MPEs and AEL values. Both the angular subtense of the apparent source and the most hazardous viewing distance have been calculated for a wide range of beam waist widths and far-field divergences.