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Abstract
The decoherence effect of a laser caused by a speckle field seriously restricts the development of heterodyne lidar. To address this problem, we proposed a spatial decoherence compensation algorithm, whose feasibility was proved by experiments with a system featuring simple structure and convenient operation. The results demonstrated that the speed of the proposed algorithm was several orders higher than that of other algorithms and the system SNR was increased by a maximum of 1464 times after the algorithm processing. The proposed algorithm can process the signal in real time and effectively, having great application potential in long-distance weak target detection.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Heterodyne detection is a high-precision holographic technology [1]. Compared with microwave radar, the heterodyne lidar has advantages such as high range and angular resolution, strong anti-jamming ability, small volume, and simple structure, and has great application prospects in long-distance dim target detection [1–7].
Because the wavelength of the electromagnetic wave in the optical band is of the order of submicron to micron, almost all the target planes can be considered as optical rough surfaces in the detection process; thus, the phase, amplitude, and polarization characteristics of the signal light are modulated by the rough target surface, which will lead to a serious decoherence effect, where the phase mismatch between the signal and local lights is the most serious influence factor for the optical decoherence effect [2–4]. As the detector is a surface integral device, the heterodyne signals obtained by interference distributed on the detector surface unit cancel each other because of the different phases, greatly reducing the detection performance of the system, or even leading to no signal output. In holographic imaging, a beam expanding system is frequently introduced to reduce the decoherence effect caused by the rough surface [8]. However, this method complicates the detection system. In particular, for long-distance targets, the echo signal is already very weak; thus, the introduction of the beam expanding system will further reduce the optical power density and greatly reduce the system signal-to-noise ratio (SNR). Another effective way to address this problem is to use array detectors. Fink et al. [9] first proposed and theorized the feasibility of array detectors by replacing a single detector in a traditional heterodyne detection system. By implementing heterodyne detection experiments with a 2 × 2 array detector, Chan et al. [10,11] first proved that the array detector can improve the SNR of the detection system and proposed an analytical formula for the ratio of the SNR of an N × N array detector system to that of a single detector system. Dong et al. [12] designed an array detector heterodyne detection system with a controllable mechanical photoelectric gate. Later, they proposed a genetic algorithm (GA) to calculate the mismatched phase [13]. Liu et al. [7,14] studied the influence of speckle on the SNR of an array detector heterodyne system and developed a high-speed camera heterodyne system. Simultaneously, the feasibility of adaptive particle swarm optimization (APSO) was verified [15]. To improve the SNR of heterodyne detection, Feng et al. [16] proposed the use of a greedy algorithm for phase compensation. In order to improve the SNR, in the aforementioned algorithms, fitness function is usually used to iteratively calculate the initial sequence position of heterodyne signals of each detection unit, to achieve the best coherent superposition between them. And fitness function usually aims to maximize the amplitude of the signal obtained by the algorithm processing. Although the aforementioned algorithms have a positive effect on the compensation of decoherence effect, to meet the real-time detection needs, the time cost of the algorithms must be as small as possible, and a few seconds or even tens of seconds is intolerable. At present, the pulse repetition frequency of coherent lidar in the world is at the level of kHz, and the sampling rate is at the level of MHz, which will undoubtedly bring a huge amount of data. Therefore, when the sampled signal is processed in groups periodic by the time interval between two pulses, there is no doubt that the frequency of signal processing should also be at the level of kHz.
In fact, when the initial phase difference of heterodyne signals of each detection unit is the smallest, the amplitude of signal obtained by coherent superposition is the largest. The essence of the compensation of decoherence effect is to flatten the phase and the absolute phase of each detection unit has no practical significance. Therefore, focusing on the relative phase difference between each detection unit, we propose a spatial decoherence compensation algorithm based on frequency-domain analysis and time-domain translation, which cancels the iterative process of the previous algorithm and calculates the phase difference of each detection unit directly. Simulation results demonstrated that the proposed algorithm has a much higher speed than other algorithms, and the processing time was positively correlated with the number of detector array units, independent of the SNR of the raw signal, having better real-time performance and stability. In addition, to evaluate the processing performance of the algorithm, we proposed a new evaluation parameter, G, and through an experiment with eight targets with different roughness, proved that the algorithm can effectively improve the heterodyne signal SNR, which benefits active detection applications such as Long-range monostatic coherent laser radar, Doppler wind lidar, Laser Vibrometry and remote dim target detection.
2. Spatial decoherence compensation algorithm
For the array detector heterodyne detection system, the core idea is to compensate the phase by adding the determined phase offset $\phi ({i,j} )$ in each detection unit (row i and column j) to flatten the spatial phase fluctuation of the heterodyne signal, thus achieving the purpose of improving the heterodyne detection efficiency. This process can be expressed as follows:
where $\varphi (r )$ represents the spatial phase of position r.Due to the decoherence effect of the speckle field and the influence of system noise, the heterodyne signal is usually submerged in the noise, so it is difficult to detect in the time domain. Through fast Fourier transform (FFT), however, it is relatively easy to find a heterodyne signal in the frequency domain; therefore, we propose a new spatial decoherence compensation algorithm based on frequency-domain analysis time-domain translation.
Ignoring the amplitude and laser linewidth, the heterodyne signal with frequency $\Delta \omega $ and phase $\Delta \varphi $ can be expressed as follows:
where n denotes noise. The heterodyne signal is processed by fast Fourier transform as follows:When $n = 0$, the phase spectrum component corresponding to the frequency point $\Delta \omega $ is $\Delta \varphi $. When $n \ne 0$, the corresponding phase spectrum component at the frequency point $\Delta \omega $ becomes $\Delta \varphi \textrm{ + }\varphi ^{\prime}$ owing to the influence of noise. The essence of compensation is to flatten the phase; therefore, the absolute phase of each detection unit has no practical significance. We focused on the relative phase difference between each detection unit. For each detection unit,
Because the heterodyne signal is a real signal sequence, through FFT processing, the frequency spectrum is a complex sequence. For a known heterodyne frequency, the sampling rate ${f_S}$ and sampling sequence length N can be used to calculate the index position IFindex of the heterodyne signal in the spectrum sequence. Using the IFindex, the phase corresponding to the heterodyne signal can be found in the phase spectrum. The expression is as follows:
where $angle\{{\cdot} \}$ denotes the phase spectrum, and the IFindex in the lower right corner indicates the phase at the IFindex position of the phase spectrum. Thereafter, the number of translation points in the time-domain sequence of each detection unit can be expressed as follows:Through the described processing, the phase fluctuations of each detection unit can be flattened. The final output signal of the array detector can be expressed as follows:
The SNR of the heterodyne signal can be defined as follows:
where Es denotes the energy of the heterodyne signal, En the energy of the noise. To compare and analyze the effectiveness of the algorithm, the gain of SNR is defined as follows: where SNRaps denotes the SNR of the signal processed by the algorithm, and SNRrs denotes the raw SNR.3. Simulation results
To verify the effectiveness of the proposed algorithm, it is compared with other algorithms that have been proposed (APSO [13], GA [15], and the Greedy algorithm [16]). The number of array detector units is set to 16, heterodyne signal frequency is 100 Hz, the sampling rate is 1000 Hz, sampling time is 3 s, signal amplitude of each unit is 1, SNR is -10 dB, and initial phase $\varphi \in [{ - \pi ,\pi } )$ of each detector unit satisfies the uniform distribution. In the test, a computer was used with configuration as Intel Core i7-8700 CPU @ 3.20GHz (12 CPUs), ∼3.2GHz, and the software platform was MATLAB. The simulation was repeated 100 times. Because the simulation sets the heterodyne signal as a single-frequency signal, the single-frequency signal amplitude obtained through algorithm processing can be used to describe the algorithm effect, as shown in Fig. 1. The statistical results of the 100 simulation calculations are summarized in Table 1.
Table 1. Simulation statistics results of various optimization algorithms.
Table 1 summarizes the statistical results of the four algorithms for the 100 simulation calculations. It is observed that the compensation effect and compensation stability between the proposed and greedy algorithms are similar, and are significantly better than those of the other two algorithms. However, the processing time of the proposed algorithm is much shorter than that of the other algorithms. The average processing speed is 80 times that of the greedy algorithm and 10000 times that of the adaptive particle swarm algorithm. The processing time variance is 5.93 × 10−10 s2, and the time stability is extremely high.
In practical applications, for the array detector heterodyne detection system, the main parameters that affect the performance of the algorithm include the SNR of the raw signal, number of array detector units, and sampling sequence length N. The influence of the three parameters on the performance of the algorithm is discussed as follows:
3.1 Algorithm performance for different SNRs
Figure 2 shows the compensation results of the algorithm for different SNRs, and the other parameter settings are consistent with the previous study. When the SNR of the raw signal changes from –60 to –20 dB, the time consumed by the algorithm processing does not change significantly, that is, the algorithm processing time is independent of the SNR of the raw signal. In fact, the algorithm we proposed does not consider the SNR of the raw signal, and only performs coherence superposition processing on the array signals from the array detector. Regardless of the SNR of the raw signal, the processing steps of the algorithm are the same. The factor affecting the processing time of the algorithm is the data volume, namely the size of the raw processing array, which is determined by two parameters, the number of detector array units and the data length of each array unit, N. And the data volume is defined as, the number of detector array units × N. Therefore, the algorithm processing time is independent of the SNR of the raw signal.
Fig. 2. Algorithms processing performance in different SNRs. (a) Time consumption. (b) Amplitude per unit with or without algorithms processing.
In addition, the amplitude per unit of array detectors with algorithm processing has a great improvement in different SNRs; in particular, when SNR ≥ –20 dB, the amplitude per unit steadily tends to 1, which is consistent with the simulation setting; thus, the algorithm performance is stable. When SNR < –20 dB, the amplitude per unit with the algorithm processing and of the raw signal are both greater than 1, which is caused by the noise energy being much higher than the signal energy. In fact, as the SNR decreases, the ratio of the heterodyne signal that the noise energy accounts for gradually increases until the signal is completely submerged in noise.
3.2 Algorithm performance for different sampling sequence lengths, N
For different sequence lengths N, the algorithm processing results are shown in Fig. 3, where the SNR is set to –20 dB, and the other parameters remain unchanged. The time consumed by the algorithm is positively correlated with the sequence length N, that is, the longer the sampling sequence, the more the sampling points, and the longer the signal processing time. When the number of detector units is 16, the sequence is length 50000, and the time consumed by the proposed algorithm is only 0.06 s, which is extremely fast. In addition, with algorithm compensation processing, the signal amplitude was greatly improved. As the sequence length increased, the amplitude per unit gradually stabilized. Owing to noise, the stabilized amplitude is slightly greater than 1, which is consistent with the simulation setting.
Fig. 3. Algorithms processing performance with different values of N. (a) Time consumption. (b) Amplitude per unit with or without algorithms processing.
3.3 Algorithm performance for different numbers of detector array units
Figure 4 shows the processing results of the algorithm for different numbers of detectors. In contrast to the exponential increasing time consumption of other algorithms, the time consumption of the proposed algorithms is linearly correlated with the number of detectors, which greatly reduces the time consumed by the algorithm processing and improves the algorithm processing speed. In addition, with an increase in the number of detectors, the amplitude per unit of the raw signal is nearly zero, and no signal is output. However, the amplitude per unit with algorithm processing was greatly improved, tending to 1.
Fig. 4. Algorithms processing performance in different numbers of detector array units. (a) Time consumption. (b) Amplitude per unit with or without algorithms processing.
In combination with the described analysis, with the increase of sequence length N and the number of detector array units, the signal processing results gradually tend to be stable. However, the number of detector array units is limited by cost and technology in a real world application. In this case, the sampling sequence length N can be appropriately increased to ensure the reliability of signal processing results.
4. Experimental results
We conducted a heterodyne detection experiment based on a high-speed camera, as shown in Fig. 5, which is a schematic of the experimental device featuring a simple structure, convenient operation, and strong applicability. The beam from a continuous-wave laser (Verdi-II, Coherence Co., Ltd.) with a wavelength of 532 nm, a line width of 5 MHz and power of 1 watt was divided into the local beam ES and the signal beam EL by a beam splitter BS1 (BS016, Thorlabs). Thereafter, the local beam meets the beam combiner BS2 (BS016, Thorlabs) after modulation by the acousto-optic modulator AOM1 (AOMO 3100-80, Gooch & Housego Co., Ltd.) with a frequency shift of 80 MHz. The signal beam meets the detection target after modulation by AOM2 (AOMO 3100-80, Gooch & Housego Co., Ltd.) with a frequency shift of 80.025 MHz. After modulation by the target, the signal beam was coaxial with the local beam through beam combiner BS2. Finally, the interference information between the two beams was recorded by a high-speed camera (FASTCAM NOVA S12, Photron) with a pixel size of 20 μm × 20 μm and a sampling speed of 200 kHz, and heterodyne data were transmitted to the personal computer (Intel Core i7-8700 CPU @3.20GHz (12 CPUs), ∼3.2GHz) through the network cable for real-time processing.
At the sampling rate of 200 kHz, the resolution of the high-speed camera is 128 × 96. However, due to the limited size of the laser spot, it was not enough to cover the whole detection surface, so we selected 60 × 60 pixels covered by the spot for data processing.These pixels are seen as 60 × 60 detection units, each of which collects spot intensity information on the surface with a synchronous clock of 200 kHz. The intensity information consists of heterodyne signal generated by interference and DC signal. In the experiment, the sampling sequence length N of each unit was set as 3000, and a heterodyne signal array with a size of 3600 × 3000 can be obtained through DC filtering of the signals collected by each detection unit.
Figure 6 shows eight targets of the experimental with different roughness. The experimental results are summarized in Table 2 and Table 3. Since APSO has no advantage in speed and quality of the processing result, only GA with 100 iterations, greedy algorithm and the proposed algorithm are selected here for signal processing. As shown in Table 2 and Table 3, are the processing results of different algorithms. Compared with the other two algorithms, the compensation effect of genetic algorithm is general and the time loss is huge. Generally, the performance of GA is related to the number of iterations, and increasing the number of iterations will lead to greater time loss, which is very undesirable for real-time detection system. For different roughness targets, the compensation effects of greedy algorithm and the proposed algorithm are different. Although the greedy algorithm has higher compensation effect on four targets than the proposed algorithm, the average G of the proposed algorithm is still slightly higher than that of the greedy algorithm. More importantly, for the heterodyne signal array with a size of 3600 × 3000, the processing speed of our algorithm is about 31 times faster than that of the greedy algorithm. In addition, processed by the proposed algorithm, for eight roughness targets, the maximum Gproposed can reach up to 1464. In other words, the SNR has increased by 1464 times compared with the raw signal, and the average Gproposed is also as high as 430. Therefore, the algorithm is indeed effective in practical applications, which can greatly improve the SNR of the system and extract the signal from the noise. According to the SNRrs evaluation of the decoherence effect caused by the detection target, it is observed that the strength of the decoherence effect is not directly correlated with the target roughness Ra. In fact, some relevant studies [6,17,18] have demonstrated that the strength of the decoherence effect not only related to the longitudinal distribution on the surface of the target, but also related to the correlation of transverse. Usually, root mean square height and autocorrelation length are used to describe the longitudinal and transverse distribution of the target surface. And the strength of the decoherence effect increases with the increase of root mean square height and decreases with the increase of correlation length. However, in the experiment, the target roughness Ra only describes the longitudinal distribution of the shot peening roughness sample block surface, while the transverse distribution is unknown. Therefore, it is impossible to infer the strength of decoherence effect only through Ra. When the target roughness is 0.2 μm or 0.4 μm, the decoherence effect is the weakest and being 1.6 μm, the decoherence effect is the strongest when the power density of the signal in the spectrum is only 5.4 times that of the noise power, and the signal is almost annihilated in the noise. The SNRaps of signals with algorithm processing are all greater than 3000, and the highest is 14423. Briefly, the signal energy is as high as 14423 times the noise energy, and the SNR is extremely high.
Table 2. Heterodyne signal processing results of different roughness targets and algorithms.
Table 3. Performance comparison of different algorithms.
Figure 7 describes the heterodyne signal of different roughness targets, where (a), (b), (c), and (d) intuitively show the spectrum distribution of heterodyne signals of different roughness targets before and after the algorithm processing in which rs represents the raw signal spectrum, ap represents the signal spectrum with the algorithm processing, and upper-left images are the respective light spot patterns. The blue and red lines in the figure are in sharp contrast, particularly for the 1.6 μm target, and almost no heterodyne signal components can be observed in the raw signal spectrum. However, the peak of the heterodyne spectrum amplitude is as high as 1800 with the algorithm processing, which is approximately 60 times higher than that of the raw signal. In conclusion, it can be proved that the proposed algorithm can still exert a better compensation effect under the condition of extremely low SNR or even signal to submerge in the noise. The average Gproposed before and after compensation can reach to 430.5 times and the average time loss is only 0.0813s.
Fig. 7. Heterodyne signal of different roughness targets. (a) Ra = 0. 2 μm. (b) Ra = 0.8 μm. (c) Ra = 1.6 μm. (d) Ra = 25 μm.
For a long range monostatic coherent laser radar, the method described in this paper is still effective as long as the number of array units recording speckle cell is greater than 1, when the average speckle number in the coherent receiver is one. In addition, for the short pulsed laser system, our method is to get the target signal through the signals coherence superposition processing between each array unit at the same time, which greatly improves the detection speed compared with using time averaging. At present, heterodyne technology is widely used in real world. For the detection of moving target or platform, because the surface of moving target is rough relative to light wave, it will lead to serious decoherence effect, and experimental results show that the proposed algorithm is effective in solving this problem and improving the detection SNR. For atmospheric optical communication, the phase of echo signal beam due to the influence of turbulence random changes, and this will seriously reduce the detection performance. However, since the frequency of turbulence change is not high, we can consider that the phase caused by turbulence does not change for a period of time. Therefore, this problem can be carried out by closed-loop compensation system with the proposed algorithm, which is also the focus of our next work.
5. Conclusion
In heterodyne detection, the decoherence effect severely restricts the SNR of the system. The current method that can effectively address this problem is the array detector method. Although the existing processing algorithms based on the array detector method affect the compensation of the decoherence effect, in the actual application process, to meet the real-time detection demand of the system, the time cost of these algorithms is intolerable. In this study, a spatial decoherence compensation algorithm based on frequency-domain analysis and time-domain translation is proposed. The simulation results demonstrate that this algorithm has an extremely high processing speed and stability. The processing speed was 80–10000 times faster than those of the other algorithms, and the processing time was linearly correlated with the number of detector units and unrelated to the SNR of the raw signal. In addition, we proposed G to evaluate the processing performance of the algorithm in the experiment. By constructing a heterodyne detection system with a simple structure and strong applicability based on a high-speed camera, we detected different roughness targets. The experiment showed that for eight different roughness targets, the average Gproposed could reach up to 430, and the amplitude peak value after processing was 60 times higher than the raw signal when the SNR of the raw signal was extremely low, and even the heterodyne signal was almost submerged in the noise. Therefore, the proposed algorithm is expected to be applied to long-range weak target detection to improve the real-time detection performance of the system. At present, the proposed algorithm effectiveness for spatial decoherence compensation in heterodyne detection of the vibrating target, whose vibration spectrum can be used for target recognition, has not been proved. In the next step, we will further improve the applicability of the algorithm by introducing a real-time feedback compensation system so that the algorithm could be used for vibration spectrum measurement.
Funding
Natural Science Foundation of Shaanxi Province (No. 2020JM-206); National Defense Basic Scientific Research Program of China (,No. 61404140509, No. 61428060201); 111 Project (B17035).
Acknowledgments
The authors thank the optical sensing and measurement team of Xidian University for their help.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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