探测器数学模型是探测器实施精确探测的基础。通过分析探测器光路建立了一个较为完整的四像限光电探测器的光路数学模型,考虑了探测器在安装过程中发生的偏移位置及其偏移量、光敏面的离焦量、探测器结构参数等对光信号到电信号的转换的影响。在建立俯仰偏移、横滚偏移和方位偏移三种特定情况下探测器模型的基础上,给出了探测器的三自由度安装位置、光敏面的离焦量、光信号等与输出信号的一般关系式。比较在给定相同光路参数条件下探测器光路数学模型的理论输出信号波形与实测输出信号波形,结果表明,两者信号波形相似。比较模型输出与实际输出信号的两个特征参数,即信号过零点的切线的斜率与截距,可以发现,特征参数的差别小于0.01,因此,四像限光电探测器数学模型的输入输出关系与探测器实际输入输出关系是一致的,可以用该模型实施探测器探测,这为光电探测器进一步的研究与应用,实现无实验样本探测提供了参考。

Mathematic model of detector is the basis of precise detection. A complete mathematical model of four-quadrant photodetector has been built by analyzing the ray-path of photodetector in this paper. In the model, the effects of the offset of fixed position of four-quadrant photodetector happened when photodetector was being installed, the distance between photosurface and focus of photodetector, and other architecture parameters of photodetector on the conversion from light to electricity are considered. On the basis of building the models of photodetector in three particular positions, viz. pitching departure position, orientation departure position, rolling departure position, the common relation expressions between light signals, the offset of mounted position of four-quadrant photodetector, the distance between photosurface and focus of photodetector, and the electricity signal, the output signal are given. Comparing the waveforms of the output signals of the mathematic model of the photodetector and that of practical output signals of detector, it is found that the waveforms of model resembled that of detector in appearance. Comparing the feature parameters of the output signals of model and that of practical output signals, viz. the slope and intercept of tangent on crossover point of outputs, it is found that the differences are less than 0.01. So the relation between the inputs and outputs of the mathematical model was consistent with that between the inputs and outputs of the detector, and the model can be used in practical detection. And a foundation for the profound research and application of photodetector, detection without experiment samples is founded.