Peripheral retina can pool photon absorptions over a larger patch of rods than the of…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch Vision and photoreception: counting photons

Problem

Peripheral retina can pool photon absorptions over a larger patch of rods than the

500

of the original model estimate. Suppose a peripheral detector pools

1500

rods, each with the same thermal dark-event rate of

0.01\,\mathrm{s^{-1}}

and the same integration time of

0.1\,\mathrm{s}

, and the observer still uses a threshold of

3

events to report a flash. ((a)) Compute the new pool mean

m

of dark events. ((b)) Compute the new false-alarm probability of getting

3

or more dark events by chance. ((c)) Find the smallest whole-number threshold that brings the false-alarm rate back below the

1.4\%

of the

500

-rod model, and explain why enlarging the pooling area is not a free way to gather more photons.

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