Final answer:
Brightness gain measures the efficiency of an output phosphor in converting electrons to light photons, but no device achieves 100% efficiency. For light bulbs, brightness is best compared using luminous efficacy in lumens per watt rather than watts alone, which accounts for the perceived brightness. The ideal efficiency of 300 lm/W is a theoretical limit that current technology has yet to reach due to practical inefficiencies.
Step-by-step explanation:
The brightness gain referred to in the question is a measure of the efficiency of an output phosphor in a device like an image intensifier or other types of optical displays. This gain is the factor by which the phosphor amplifies light, that is, how effectively it converts incoming electrons into visible light photons. No optical device is 100% efficient due to various losses and the theoretical and practical limits involved in the conversion process. For instance, not all of the electron's energy will be converted into visible light; some of it will be lost as heat or other forms of non-visible electromagnetic radiation.
For a comparison of light bulbs in terms of brightness, we should look at the luminous efficacy in lumens per watt rather than watts alone. This reflects how bright a source actually appears to the human eye. A bulb's luminous efficacy is an indicator of how efficiently it turns electrical power into visible light.
Irrespective of efficiency, increasing the intensity of light increases the number of photons emitted, and hence the brightness perceived, but again, technical limitations prevent perfect efficiency. The ideal light source would convert all power into visible photons without any loss, but in practice, there are always inefficiencies that prevent reaching the theoretical maximum of around 300 lm/W for white light.