The name is absent

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vacuum tubes shows that the output noise in the device is proportional to the integral of the
square of the impulse response of the device. The mean system output is the integral of the
impulse response times the event rate (equation 6.1). This is known as Campbell’s theorem
[89] :

ÿ = V [ h(t)dt                              (6.1)

Jo

σ² = и J h²(t)dt                             (6.2)

Where v is the mean and variance for a Poisson distributed process, and 7z(f) is the
impulse response for the linear system.

The integral of the impulse response is the step response of the system, and the integral of
the square of the impulse response gives the output variance due to a single impulsive input.
Therefore, the mean output is the mean input rate times the system step response, and the
output variance is the arrival rate of each impulse times the variance of a single impulse.

Independently, Vu et al. and Jones [105, 62] found that the output variance of the pho-
tocurrent first increased, and then decreased, with increasing light intensity (photon arrival
rate). This increase and decrease is due to the decreasing amplitude of the impulse response
for a single photon arrival in the presence of brighter background light. Thus the noise pro-
duced by the photocurrent would not be constant, and instead vary with the light intensity
that is incident on each photoreceptor.

This phenomenon occurs over a change in four orders of magnitude in the input light

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