For example, if I have a datasheet for a photodiode that lists a dark current of 1000nA. I have a transimpedance amplifier with 1kohm transimpedance and 1 mV voltage output voltage noise.
Presumably the specified dark current is the current mean value. Clearly the dark current will result in a mean output of 1000ohms*1000nA = 1mV. Dark current is also Poisson distributed, but does that mean that the noise variance also 1 mV such that the voltage noise from the amp and photodiode are equal? Or is the relationship more complicated?