It's essentially shot noise.
In optics, shot noise describes the fluctuations of the number of photons detected (or simply counted in the abstract) due to their occurrence independent of each other. This is therefore another consequence of discretization, in this case of the energy in the electromagnetic field in terms of photons. In the case of photon detection, the relevant process is the random conversion of photons into photo-electrons for instance, thus leading to a larger effective shot noise level when using a detector with a quantum efficiency below unity.
Researchers have taken notice of this as early as the 1960s See  I was unable to access this, but the abstract notes that it is probably not ideal shot noise, but I don't know what the De Lange filter adds to the shot noise model, it may be a small corrective factor.
A noise model incorporating the De Lange filter is applied to visual threshold performance. The model gives better agreement with the experimentally observed Weber-Fechner relation than does the ideal shot noise limited model, and it predicts that the critical time duration for integration of threshold stimuli depends upon the mean luminance level of the background field.
As noted in the introduction to , the noise stems from the transduction stage in the retina:
On the other hand, people working on vertebrate photoreceptor believe that the responses of rods to single photons are locally saturated and that the "quantum" responses in
rods are surprisingly stereotyped. Thus the variability in responses to dim light flashes is believed to be basically due to the absorption of one, two, . .. , few photons [they cite (Baylor et al., 1984)].
 Petracchi D., Cercignani, G., Lucia, S. (1996) Photoreceptor Sensitivity and the Shot Noise of Chemical Processes. Biophysical Journal, 70: 111-120.
 Ruddock, K.H. (1969)Some aspects of human visual threshold performance in relation to temporal frequency response characteristics. Optics Communications 1(4): 173-179.doi