6
David B. Dusenbery
leads us to think about information as we design devices that respond to their
environment.
3 Time Limits Sensitivity
Sensory ecology is often concerned with the magnitude of the stimulus that is
necessary for reliable detection. This sensitivity sets limits on what information
can be obtained, the distance over which information is available, and the costs of
transmitting information. In some cases, basic physical principles allow us to set
some limits on how low such thresholds can be. There are always limits, because
all real systems have at least some noise associated with any process due to
thermal agitation of the molecules they contain.
When the stimulus arrives in discrete packets occurring randomly in time, such
as photons or diffusing molecules, fluctuations in the number of packets received
also imposes a limit on sensitivity. This kind of limit is often analyzed by
calculating a signal-to-noise ratio (SIN). Reliable detection requires that the ratio
be well above 1, and a ratio well below 1 indicates that reliable detection is not
possible (Dusenbery 1992, pp. 90-95). The signal is often represented by the
increase in the average number (n) of packets received in some time interval, and
the noise is often taken as the standard deviation (a) of the number of packets
expected in the same interval. When the packets arrive randomly in time, the
number received in a given time interval has a Poisson distribution, and the
standard deviation is simply the square root of the mean number.
If the average number of packets received is n1 in the presence of the signal and
n2 in its absence, the signal-to-noise ratio is limited to
Eqn.I
For estimating threshold, the reference state is n2 = 0, a2 = 0, and
Eqn.2
The appropriate value of the signal-to-noise ratio will depend on what response
criterion is used for defining the threshold, but any reasonable criterion will
correspond to a signal-to-noise ratio near unity. Taking SIN = 1 as our criterion,
n = l. At threshold, one packet is received on average in the time interval.
Applying these concepts to the problem of estimating the threshold intensity
(!Th) for detecting the presence of light against no light, the best any receptor that
fits within a sphere of radius r can do is to count the number of photons (n)
David B. Dusenbery
leads us to think about information as we design devices that respond to their
environment.
3 Time Limits Sensitivity
Sensory ecology is often concerned with the magnitude of the stimulus that is
necessary for reliable detection. This sensitivity sets limits on what information
can be obtained, the distance over which information is available, and the costs of
transmitting information. In some cases, basic physical principles allow us to set
some limits on how low such thresholds can be. There are always limits, because
all real systems have at least some noise associated with any process due to
thermal agitation of the molecules they contain.
When the stimulus arrives in discrete packets occurring randomly in time, such
as photons or diffusing molecules, fluctuations in the number of packets received
also imposes a limit on sensitivity. This kind of limit is often analyzed by
calculating a signal-to-noise ratio (SIN). Reliable detection requires that the ratio
be well above 1, and a ratio well below 1 indicates that reliable detection is not
possible (Dusenbery 1992, pp. 90-95). The signal is often represented by the
increase in the average number (n) of packets received in some time interval, and
the noise is often taken as the standard deviation (a) of the number of packets
expected in the same interval. When the packets arrive randomly in time, the
number received in a given time interval has a Poisson distribution, and the
standard deviation is simply the square root of the mean number.
If the average number of packets received is n1 in the presence of the signal and
n2 in its absence, the signal-to-noise ratio is limited to
Eqn.I
For estimating threshold, the reference state is n2 = 0, a2 = 0, and
Eqn.2
The appropriate value of the signal-to-noise ratio will depend on what response
criterion is used for defining the threshold, but any reasonable criterion will
correspond to a signal-to-noise ratio near unity. Taking SIN = 1 as our criterion,
n = l. At threshold, one packet is received on average in the time interval.
Applying these concepts to the problem of estimating the threshold intensity
(!Th) for detecting the presence of light against no light, the best any receptor that
fits within a sphere of radius r can do is to count the number of photons (n)