Signal to noise ratio and depth accuracy are modeled for the pseudo-random ranging system with two random processes. The theoretical results, developed herein, capture the effects of code length and signal energy fluctuation are shown to agree with Monte Carlo simulation measurements. First, the SNR is developed as a function of the code length. Using Geiger-mode avalanche photodiodes (GMAPDs), longer code length is proven to reduce the noise effect and improve SNR. Second, the Cramer–Rao lower bound on range accuracy is derived to justify that longer code length can bring better range accuracy. Combined with the SNR model and CRLB model, it is manifested that the range accuracy can be improved by increasing the code length to reduce the noise-induced error. Third, the Cramer–Rao lower bound on range accuracy is shown to converge to the previously published theories and introduce the Gauss range walk model to range accuracy. Experimental tests also converge to the presented boundary model in this paper. It has been proven that depth error caused by the fluctuation of the number of detected photon counts in the laser echo pulse leads to the depth drift of Time Point Spread Function (TPSF). Finally, numerical fitting function is used to determine the relationship between the depth error and the photon counting ratio. Depth error due to different echo energy is calibrated so that the corrected depth accuracy is improved to 1cm.
For an unknown characteristic target scene, the laser radar system that uses single-photon detector cannot directly estimate the dwell time of every pixel. Therefore, as the difference of target reflectivity, depth estimation appears inadequate sampling or redundant sampling in the conventional imaging method of maximum likelihood estimation (MLE-CIM). In this work, an adaptive depth imaging method (ADIM) is presented. ADIM is capable to obtain the depth estimation of target and adaptively decide the dwell time of each pixel. The experimental results reveal that ADIM can accurately obtain the 3D depth image of target even at the condition of low signal-to-noise ratio.
Proc. SPIE. 9677, AOPC 2015: Optical Test, Measurement, and Equipment
KEYWORDS: Signal to noise ratio, Photon counting, Interference (communication), Monte Carlo methods, Optical simulations, Signal detection, Probability theory, Performance modeling, Systems modeling, Ranging
In this paper, the short dead time detection probability is introduced to the linear SNR model of fixed frequency multipulse accumulation detection system. Monte Carlo simulation is consistent with the theory simulation, which proves that with the increased laser power, the SNR first gets larger quickly and then becomes stable. Then the range standard deviation model is settled and firstly shows that larger dead time brings better range precision, which is consistent with the B. I. Cantor’s research. Secondly, Monte Carlo simulation and theory simulation both indicate that with the increased laser power, range precision first enhances and then becomes stable. Experimental results show that based on 500000c/s high background noise, the maximum of SNR can be obtained with emitting laser power at about 400uw at 50ms integrated time. Range precision reaches the optimal level at 6mm. The experimental data show a precision which is always worse than the Monte Carlo simulated results. This arises from the fact that the histograms’ jitter is not taking into account and introduced during simulation, whereas the experimental system has approximately 500ps' jitter. The system jitter causes larger time stamp value fluctuation, leading to worse range precision. To sum up, theory and experiment all prove that the optimal performance receiving of SNR and precision is achieved on this multi-pulse accumulation detection system.
Proc. SPIE. 9279, Real-time Photonic Measurements, Data Management, and Processing
KEYWORDS: Signal to noise ratio, Photon counting, Interference (communication), Time correlated photon counting, Monte Carlo methods, Signal detection, Probability theory, Statistical modeling, Photon transport, Ranging
This paper investigates the random bitstream ranging model and proposes a new output SNR model based on statistical optics theory. We study the relationship of SNR and the fraction of 1 in bitstream with different dead time by Monte Carlo simulation. Theory model is almost consistent with Monte Carlo simulation. The results show that with the fraction of randomly distributed 1-bits in transmitted pattern increased, the system SNR gets better first and then gets worse. Best pattern of transmitted bit stream according to different dead time leads to the best SNR. According to new output SNR model, low dead time brings better SNR. The system SNR increases firstly then gets down with the growing signal photon counts. At last, Gaussian distribution timing jitter of 440ps FWHM is introduced to reconstruct received bitstream pattern formed from the arrival times of returning single photon. We find that higher rate of bitstream brings higher possibility error of single time value. Suitable bits rate is restricted to 1 GHz according to jitter of 440ps FWHM to reduce the probability of ranging error.