On one hand, the amount of information I can transmit is proportional to the bandwidth. The higher the frequency, the more information I can transmit. On the other hand, the number of photons is reverse proportional to the frequency. I cannot possibly transmit more information than the number of photons I send. Therefore, it appears, that at low intensity levels, a higher frequency signal may contain less information than a lower frequency signal.
For example, consider a camera sensor in a high amplification mode (known in digital photography as "high ISO"). Provided the light intensity is uniform by color, blue sensor pixels would receive fewer photons than red pixels. The photon noise in modern sensors is one of the main quality limitations. Thus, in low light conditions, blue images would be grainier than red images meaning that the amount of the transmitted information is reverse proportional to the frequency.
Considering these two competing trends, an optimum must exist. Is there a known formula or estimate for the optimal frequency to transmit the highest amount of information for a given received power? Or, stating this in reverse, is there a formula for the minimum received power required to avoid the photon quantization noise at a given frequency?