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由于背景辐射场辐射到达探测器上的光子数目的起伏决定了光子探测器的噪声极限,本文推导出背景辐射场辐射到达探测器上的光予数目的均方起伏等于其光子到达率的平均值。在探测器的响应光谱范围内,光子到达率的平均值可由Planck公式求出。从而得到载流子浓度均方起伏。由载流子浓度均方起伏可获得面积为A的探测器在电带宽为⊿f的均方根噪声输出。求出等效噪声功率NEP。然后求得探测率的理论极限D_λ~*,这样得到的结果与Schuldt证明的D_λ~*表达式相同。
Since the fluctuation of the number of photons reaching the detector by the background radiation field determines the noise limit of the photon detector, it is deduced that the mean square fluctuation of the number of light presumed by the background radiation field reaching the detector is equal to the average value of its photon arrival rate . The average photon arrival rate over the detector’s response spectrum can be calculated from the Planck’s equation. Thus, the average carrier concentration fluctuates. A detector of area A is obtained from the rms mean square of the carrier concentration at a rms noise bandwidth of ⊿f. Find the equivalent noise power NEP. Then the theoretical limit of detection rate D_λ ~ * is obtained, and the result is the same as that of Schuldt’s D_λ ~ *.