"Photons arrive at random times and we are counting photons for a relatively short interval (the exposure time in a camera). The noise is the square root of the number of photons collected."
"More light same amount of noise"
No, more light more noise? That is, if 64 photons the noise is 8 (standard deviation) but if more light 225 photons noise is 15.
How about - "More light less apparent noise"?
Tom