At what speed do we measure with the A-series cameras? ex. How fast could I detect a change in temperature and set a digital alarm?

A20/40 has a standard set measurement frequency of 10 Hz. Actual reached frequency will be lower, dependent on measurement setup.

A310/320 with a standard setup will analyze measurment functions at 3 Hz
There are ways to change the default measurement frequency of the camera from 3 Hz to a higher value (i.e 10 Hz) to decrease alarm setup time, unfortunately not through "monitor".
By using "telnet <cam ip no>" you get a prompt into the camera, a command console.
Type command "rls .image.measure" to check current value of measurement frequency (should read "3")
Type command "rset .image.measure.frequency 10" to set preferred measurement frequency to 10 (Hz)
This non-volatile value will be remembered in the camera until you do a factory default.

Actual measurement frequency could be checked (from telnet session) by typing command "rls .image.measure.count" at the same time as a stopwatch is started
Do a new "rls ..." after lets say 30 seconds, and check how high "count" has come.
Measurement frequency will be affected by total size of measurment functions.
One single spot -> about 9 Hz
One default area -> about 7 Hz
3 areas located over the full width of image -> about 5-6 Hz
If running "monitor" with active image, the frequency will be reduced.

The time after a measurement has given an alarm until an actual action is seen on a digital I/O or an image is tagged will also depend on the measurement setup, and will be in the same range as the measurement frequency, 0.1 - 0.2 seconds.

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