Undergrad Noise Proportional to Square Root of Illumination: Need Formula Help

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The discussion centers on the relationship between noise and illumination in laser light, specifically the assertion that noise is proportional to the square root of illumination. Participants express difficulty in locating the exact formula that describes this relationship. There is a call for assistance in deriving or finding the relevant mathematical expression. Clarifications on the underlying principles of this concept are also sought. The conversation emphasizes the need for a clear formula to understand the noise characteristics in laser applications.
Joseffina
TL;DR
Influence of street illumination on laser radiation of a laser acoustic reconnaissance system
Many people have said that the noise that affects laser light is proportional to the square root of the illumination. But I can't find the formula. Can anyone help?
 

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