Parabolic Beam Profiler

More Luminance Profiles may be added in the future. This takes time because relative luminances have to be entered for each angle from 0° to 180°. Relative luminance output profiles can vary slightly from lamp to lamp among each lamp type. The model iterates each source angle from 0° to 180°, calculating beam diameter and applying the amount of light within each beam area corresponding to each souce angle luminance, minus losses. When a beam hole exists for a souce angle, the hole area is subtracted from the beam area before applying the amount of light. Beam areas for all source angles are combined and totals are generated. You may notice when taking measurements at varying distances that the beam from a parabolic reflector is not directed solely with linear divergence. The beam is a reflected image of the source, in the shape of an annulus (doughnut shape) that encircles a blurred centerline formed by the reflection diameters from the vertex hole diameter to the aperture diameter. The thickness of the annulus increases with distance, but the centerline diameter does not. The static diameter of the centerline induces a static affect on beam diameter, and with increased distance, has less affect upon total beam diameter than divergence. Therefore, measurements taken at greater distance yield greater candlepower. The model also accounts for the subtle shifts in beam diameter as a result of reflections initiating from each reflection point before the aperture, rather than all from the aperture. Focus Offet provides for defocussing the beam by offsetting the source from the focal point. Offset is toward the vertex for outward deflection, as inward deflection would cause the light to hit and overheat the lamp anode or cathode. Focus Offet deflectes the otherwise static annulus centerline of the reflected image. When the diameter of the deflected annulus centerline at distance prevents the annulus inner thickness from overlaping itself, there is a hole in the beam center. This can occur with high etendue configurations, including most searchlights. This model calculates anglular reflected dimensions of an ellipsoidal source. Enter equal width and height for a round source. Reflector reflectance for high power search lights are typically 70% with the durable Rhodium coating required. Lower power lights can use less durable coatings with higher reflectance, such as aluminum. New highly specialized coatings can provide up to 90% reflectance with the durability needed for high power lights. Tempered glass typically has 83%-85% transmittance. Some new specialty tempered glass achieve light transmittance up to 92%. Retro-reflector calculations include losses for the additional mirror reflection, as well as passing through the lamp glass twice, and account for transmission losses due to lamp life. Retro-reflector angles can not cross 90°, otherwise source light would be trapped and could damage the lamp. The affects of lamp life on output are calculated as: 100% Life -> 100% Output, 75% Life -> 93.75% Output, 50% Life -> 87.5% Output, 25% Life -> 81.25% Output, 0% Life -> 75% Output. This based on todays' newer lamp technology. Older lamps may have more degraded output. Although this model accounts for the luminance output profile of the source, it does not calculate the mapping of luminance concentration within the source area. Therefore, this model will produce a factor of less candlepower with lamps having variance of luminance concentration within the source area. Short Arc DC Mercury lamps can have marginal variance of luminance concentration, and Short Arc DC Xenon lamps can have more variance of luminance concentration. Luminance concentration mapping can also vary from lamp to lamp among each lamp type. A "Peak Luminous Area Concentration" factor may be enetered in the calculation for the calculation to apply. AC lamps do not benefit from luminance concentration mapping because there are two points of peak luminance concentration at opposite ends of the source area.