Determination of Retinal Spot Size for Static Laser Beams and Scanning Laser Beams: A Mathematical Analysis

Abstract

This study examined the retinal spot size resulting from intrabeam viewing of both static and scanning visible laser beams. Recommendations on proper measurement techniques for the purpose of laser product class determination are also provided. The eye model used in the analysis consisted of a single lens with a variable focal length and a screen or retina fixed at a distance 17mm from the front surface of the lens. The beam was modeled using a general equation for the propagation of a Gaussian laser beam through a single lens system. Using Mathcad® software, the beam diameter at the output plane (retina) was calculated for focal lengths in the range of 13mm to 19mm with the lens positioned at various points along the path of the beam. An inverse relationship was found between the diameter of the static beam at the front surface of the lens and the minimal attainable beam diameter at the output plane. When the lens was positioned 100mm from the beam waist, the beam diameter at the front surface of the lens expanded sufficiently to result in a beam diameter at the output plane (retina) subtending an angle less than 1.5mrad for specific focal lengths within the range of 13mm to 19mm. The results of the static beam portion of this study revealed that when the eye is positioned 100mm or more from the waist, the minimal attainable retinal spot will subtend an angle less than or equal to the accepted minimal angular subtense of 1.5mrad regardless of the diameter of the beam waist Therefore, extended source viewing conditions do not apply to direct viewing of a static laser beam regardless of the diameter of the beam waist For the purpose of laser class determination, it is recommended that beam power measurements be made with the detector placed 100mm from the beam waist and the angular subtense, α, equal to 1.5mrad. The second portion of this study examined the retinal spot size resulting from intrabeam viewing of a scanning, visible laser beam. It was determined that a scanning laser beam creates a line, not a stationary spot, on the retina. The length of the line on the retina was found to be a function of the diameter of the limiting aperture, the focal length of the lens, and the distance between the lens and the vertex of the scan line. For the purpose of laser class determination of scanned radiation, it is recommended that the diameter of the limiting aperture be chosen so that the length of the retinal image subtends an angle less than or equal to 1.5mrad and, as previously established, the temporal variation of detected radiation be classified using the repetitively pulsed exposure criteria.This study examined the retinal spot size resulting from intrabeam viewing of both static and scanning visible laser beams. Recommendations on proper measurement techniques for the purpose of laser product class determination are also provided. The eye model used in the analysis consisted of a single lens with a variable focal length and a screen or retina fixed at a distance 17mm from the front surface of the lens. The beam was modeled using a general equation for the propagation of a Gaussian laser beam through a single lens system. Using Mathcad® software, the beam diameter at the output plane (retina) was calculated for focal lengths in the range of 13mm to 19mm with the lens positioned at various points along the path of the beam. An inverse relationship was found between the diameter of the static beam at the front surface of the lens and the minimal attainable beam diameter at the output plane. When the lens was positioned 100mm from the beam waist, the beam diameter at the front surface of the len...