在红外成像系统中，任何虚假和不需要的信号统称为噪声。噪声的存在干扰了有用信号的探测，减少了系统的作用距离。从信号和噪声的统计特性出发，文中详细推导了虚警概率与门限信噪比、探测概率与信噪比的关系，基于此推导了红外成像系统对点源目标的作用距离公式。对面源目标，重新确定了温差的概念，综合考虑目标的面形尺寸、观察等级和探测概率的要求，以MRTD为基准计算作用距离。编制了相应的软件，可以快速计算出不同探测概率下的作用距离。最后给出了计算实例。

In infrared imaging system, all false and unnecessary signal are called noise. The existence of the noise
interferes detection for useful signal, and affects system operating range. Starting from
the statistic characteristics of the signal and noise, the relationship between
false-alarm probability and threshold SNR is deduced, as well as detection probability and
SNR. The formula of operating range for spot target is given. As for extended target, the
concept of temperature difference is redefined, and the formula of calculating system operating range based on MRTD is given, considering of the dimension of the target, discrimination level and detection probability. A software is developed which can fast calculate the operating range under different detection probabilities. At last, an example is given.