Performance and range evaluation of an electro-optical sensor
Criteria used for performance simulation and evaluation differ from sensor to sensor, depending upon the application at hand : optical telecommunications, detection, imaging, astronomy, metrology,.... For example, the performance of a detection system is defined in terms of probability of detection and false alarm rate, that of a telecommunication system in terms of Bit Error Rate (BER), that of a measuring instrument by its uncertainty, repeatability,... In all cases performance optimization comes from signal to noise ratio optimization..
In order for the sensor to satisfy its operational specifications, the designer must make sure that the signal to noise ratio be larger than some threshold value. In order to achieve that result, the useful flux incident upon the detector be larger than some lower limit imposed upon the sensor by a set of criteria such as those mentionned above. By definition, the useful flux level corresponding to a signal to noise of 1 is the "noise equivalent power" (NEP) of the sensor. If the main source of noise is the detector, the NEP of the sensor is equal to the product of the power spectral density of the detector noise, in W Hz-1/2 (data issued from the detector manufacturer) by the square root of the noise equivalent bandwidth of the sensor :
If SNRmin is the threshold value of the signal to noise ratio, there follows that the useful flux incident upon the detector must be larger than :
One of the main outputs from a sensor model is the sensor Range equation : it is the evaluation of the useful signal flux incident upon the detector with respect to the distance between the source and the sensor. Usually, this flux is decreasing with the distance. From the sensor range equation, it is hence possible to deduce the range (called maximum range) for which the signal to noise ratio reaches its threshold value : up to that range, the sensor should theoretically perform better than what is asked from it by the operational specifications and, beyond that range, the sensor should perform more poorly than expected (figure 15).
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The range equation of an electro-optical sensor applies to only one configuration, and it is no more valid when any one of its parameters is being modified.
For example, in defense applications, the maximum range of an electro-optical system (such as a rangefinder, a detection, surveillance or recognition system,...) on a given target varies widely if any one of these parameters is changed : target orientation, atmospheric conditions (day or night environment, meteorological range, climate, aerosols), target and sensor altitudes, optical path (ground to ground, air to air, air to ground, ground to air,...), surrounding background,...
In many cases, the sensor Noise Equivalent Power does not mean much to the user in terms of performance. That is why the sensor NEP is generally converted into its equivalent value in terms of the parameter of interest for the user : that is the case for example in thermal imagery where the sensor performance is very seldom evaluated by the NEP but by its equivalent quantity in temperature difference. This quantity, called NETD, or Noise Equivalent Temperature Difference, represents the change in temperature, between two blackbodies, that induces a signal to noise ratio of 1 from the thermal sensor.