Introduction
This case study completes the course on the importance of the signal to noise ratio value upon the performance of electro-optical sensors, and its importance in the design of detection systems. Some specific criteria are introduced here, such as the probability of detection and the probability of false alarm : these have been used in the radar domain for quite a while and they are being transposed here, with some simplification, to the case of electro-optical sensors.
Similarly to digital optical telecommunication systems, which are supposed to decode a two level signal (bit 1 and bit 0), detection systems (radar or electro-optical sensors) must decide upon the presence or the absence of a target, or of some given signal. Hence, their output is binary, summarized by the truth table below : the left column represents the actual situation (target is present or not), the middle one shows the expected output from the sensor, and the right ones possible errors :
![[zoom...]](javascript:window.open(%22../res/Tableau01_1.png%22,%22_blank%22,%22width=%22+Math.min(800,screen.availWidth)+%22,height=%22+Math.min(600,screen.availWidth)+%22,left=%22+(screen.availWidth-800)/2+%22,top=%22+(screen.availHeight-600)/2+%22,scrollbars=yes,resizable=yes%22)?void(0):void(0)){kind=link}
The optimization of a detection sensor consists in reducing the probability of occurrence of its erroneous answers (non detection of the target while it is present, and detection of a target while there is none, or false alarm) and in maximizing its probability of detection (probability of detecting a target when present). As we shall see, this is obtained by maximizing the signal to noise ratio (SNR) and making it larger than some threshold level : the better the expected performance, the larger the threshold and SNR values.