Due to the high sensitivity of the single-photon detector, an ultra-narrow band filter is needed to ensure the normal operation of the detector under the influence of strong background light noise in the daytime. Therefore, the anti-background noise ability of photon heterodyne detection is crucial. In addition, the dark count and post-pulse effect of the single-photon detector will lead to a false count and thus reduce the signal-to-noise ratio (SNR). Therefore, new methods are required to improve the SNR of photon heterodyne detection. In the earlier research on photon heterodyne detection, most scholars focused on signal processing for denoising. They proposed new signal processing methods to denoise echo signals and rarely made an effort to improve the detection system or change the photon counting mode. As current signal processing has limited ability to improve the SNR of photon heterodyne detection, this study applies the coincidence counting mode to photon heterodyne detection. This mode relies on multi-channel detection and filters out random optical noise at the photon counting terminal to improve the SNR.

In this study, a photon heterodyne velocity measurement system with two-channel coincidence counting is constructed by simulation. After frequency beating, light waves of heterodyne signals are evenly divided into two parts and sent into two single-photon detection channels separately. A two-channel coincidence counting mode is adopted at the single-photon detection end, and different coincidence gate widths are set for the system according to different situations. The two-channel coincidence counting system will automatically select the channel 1 as the main channel and the other channel as the slave channel and create a time window (the size of which can be set) centered on the main channel. When both channels have photon counting in this window, an effective coincidence will be generated, and the coincidence counting results within a certain collection time will be given at last. When the signal photon is detected in both channels within the coincidence time, it is judged to be an effective signal. In this way, the arrival time series of the photon can be obtained. Compared with the case of single-channel photon counting, the anti-noise capability of the system is greatly improved, and effective echo signals can be extracted under strong background noise.

The traditional filtering method of photon heterodyne detection is to preliminarily process the photon response sequence to produce the cumulative photon histogram, perform the first-order filtering of the cumulative photon histogram curve, and process the filtering results as FFT to obtain the spectrum diagram. In this study, the first-order filtering algorithm adopts the moving average filtering method and compares three methods, namely, single-channel free-running mode, post-photon cumulative moving average filtering, and two-channel coincidence counting mode. The simulation results show that the power spectrum SNR of the intermediate frequency (IF) signal in the two-channel coincidence counting mode is significantly higher than that in the single-channel free-running mode and the first-order filtering.

Furthermore, the variation laws of the power spectrum SNR of IF signals with the increase in the number of signal photons are studied under two counting modes. In addition, four factors such as local-oscillator light intensity, background noise, IF, and detection duration that affect the performance of photon heterodyne detection are investigated.

According to the simulation, the SNR of both the single-channel free-running mode and dual-channel coincidence counting mode gradually increases with the increase in the number of photons. However, as the number continues to grow, the SNR rises slowly and gradually reaches saturation (Fig. 7). When the ratio of local light intensity to signal light intensity is less than 1, the SNR changes most significantly with the increase in the number of signal photons, and when the number grows to 5 Mcps (Mcps represents the counts multiplied by 10⁶ per second), the saturation state cannot be reached. When the ratio is equal to 1, the SNR is higher than that when the ratio is less than 1. This is because when the number of photons in the local oscillator is equal to the number of photons in the signal, the total number of photons is higher than the case when the ratio is less than 1, and the proportion of noise photons decreases. Hence, the SNR increases. However, a greater ratio of local light intensity to signal light intensity does not lead to better results. As can be seen from the figure, if the ratio is equal to 5, the SNR of the IF signal is higher than that of 1, but if the ratio is less than 3, it can be inferred that as the ratio of local light intensity to signal light intensity gradually increases, the system's SNR increases before it declines. The peak is reached near the ratio of 3 (Fig. 8). Stronger background noise means a lower SNR. In addition, the photon number of the saturated signal is different under different background noises. Stronger background noise is accompanied by a larger photon number of the saturated signal. When the background noise is 0.5 kcps (kcps represents the counts multiplied by 10³ per second), the number of signal photons gradually becomes saturated at about 3 Mcps, but when the background noise is 2 kcps, the number of signal photons is close to saturation at 5 Mcps. Under different background noises, the saturation SNR achieved is also inconsistent: stronger background noise indicates a lower saturation SNR (Fig. 9). IF has a steeper change in the early fitting curve of the influence of SNR and reaches a peak when the number of signal photons is 3 MHz. As the number continues to increase, the SNR of IF slightly declines and gradually becomes stable. Although the span of IF is from 0.5 to 7 MHz, the four curves are concentrated, and it is difficult to separate them or even have crossover parts in some line segments. Therefore, the IF signal frequency, that is, the speed of the moving target, has little influence on the SNR of the system (Fig. 10). As the detection duration becomes longer, the SNR increases significantly. When the detection duration increases from 0.05 to 0.10 ms, the saturation SNR increases by about 3 dB, while when it increases from 0.15 to 0.20 ms, the saturation SNR only increases by about 1 dB. The time parameters such as the dead time and coincidence window of single-photon detection are generally of the order of ns. Thus, although the detection duration only increases by 0.05 ms each time, it has already exceeded four orders of magnitude. Therefore, longer detection duration means more photons detected and more significant cumulative effects of the photon-density distribution law, and a greater contribution of IF signal distribution to the total number of photons indicates a higher SNR (Fig. 11).

The results show that the proposed method has significant advantages over single-channel detection. In coincidence counting, part of the background noise and dark count noise can be filtered out to improve the SNR. This study provides a new idea for the application of coincidence counting and also renders guidance for the construction of a photon heterodyne detection system with two-channel coincidence counting in subsequent experiments.