图  1  太赫兹单光子雷达直接探测方式工作流程

Figure  1.  Workflow of the direct detection method of terahertz single-photon radar

图  2  超导量子电容探测器工作原理

Figure  2.  Operation principle of QCD

图  3  单光子雷达系统工作时序

Figure  3.  Working sequence of single-photon radar

图  4  光子计数积累过程示意图

Figure  4.  Schematic diagram of photon counting accumulation process

图  5  一个子区间$ \Delta t $包含q个时隙

Figure  5.  A sub-interval $ \Delta t $ contains q intervals

图  6  脉冲飞行时间直方图

Figure  6.  The time-of-flight histogram

图  7  探测模型的3种情况

Figure  7.  The detection model divided into the three cases

图  8  死时间与回波位置影响下的各个时间区间内探测概率$ {p_{\text{d}}} $的分布

Figure  8.  The distribution of $ {p_{\text{d}}} $ in each interval under different $ {t_{\text{d}}} $ and $ {t_{\text{r}}} $

图  9  脉冲回波前沿在所对应子区间的位置示意图

Figure  9.  Schematic diagram of the position of the pulse echo front in its corresponding sub-interval

图  10  检测概率$ {P_{\text{D}}} $随比值$ {t_{\text{f}}}/\Delta t $的变化关系

Figure  10.  The detection probability $ {P_{\text{D}}} $ as a function of ratio $ {t_{\text{f}}}/\Delta t $

图  11  目标检测概率随所划分区间取值$ \Delta t $的变化趋势

Figure  11.  Detection probability as a function of $ \Delta t $ with different simulations

图  12  检测概率随脉冲飞行时间的变化曲线(t_d=3 μs)

Figure  12.  Detection probability as a function of $ {t_{\text{r}}} $ (t_d=3 μs)

图  13  单脉冲探测时检测概率和虚警概率随信号平均光子数的变化曲线。((a)、(b)和(c)中曲线分别以噪声光子率$ {\lambda _{\text{n}}} $：$ 0.01{\text{ MHz}} $(点划线)，$ 0.05{\text{ MHz}} $(划线)，$ 0.1{\text{ MHz}} $(实线)区分；(d)、(e)和(f)中曲线分别以信噪比$ {R_{{\text{SN}}}} $：1(点划线)，2(划线)，10(实线)区分。)

Figure  13.  The detection probability and false alarm probability versus the mean signal photons$ {N_{\text{s}}} $. (The curves Fig. (a), Fig. (b) and Fig. (c) are differentiated by the noise photon rate function $ {\lambda _{\text{n}}} $marked with $ 0.01{\text{ MHz}} $ (dotted line), $ 0.05{\text{ MHz}} $ (dotted line), $ 0.1{\text{ MHz}} $ (solid line); The curves from Fig. (d), Fig. (e) and Fig. (f) are differentiated by the signal to noise ratio $ {R_{{\text{SN}}}} $ marked with 1 (dotted line), 2 (dotted line), 10 (solid line).)

图  14  单脉冲探测时检测概率(P_D)和虚警概率(P_FA)随信号平均光子数的变化曲线

Figure  14.  The detection probability (P_D) and false alarm probability (P_FA) versus the mean signal photons $ {N_{\text{s}}} $

图  15  给定$ {P_{{\text{FA}}}} $情况下最小可检测信噪比$ {({R_{{\text{SN}}}})_{\min }} $随脉冲积累数M的变化曲线

Figure  15.  The $ {({R_{{\text{SN}}}})_{\min }} $ as a function of the pulse accumulation number M under different $ {P_{{\text{FA}}}} $

图  16  最小可检测信噪比$ {({R_{{\text{SN}}}})_{\min }} $随检测概率$ {P_{\text{D}}} $的变化关系

Figure  16.  $ {({R_{{\text{SN}}}})_{\min }} $ as a function of $ {P_{\text{D}}} $

图  17  基于光子计数的直接探测实验系统框图

Figure  17.  Schematic of the direct detection experimental system based on photon counting

图  18  不同积累时间下单光子计数器输出的时间分辨统计直方图

Figure  18.  Time resolution histogram for the output of the single-photon counter in different accumulated time