Long range detection of line-array multi-pulsed coding lidar by combining the Accumulation coherence and Subpixel-energy detection method

Jinshan Su; Yuanqing Wang; Dongdong Liang

doi:10.1364/OE.23.015174

1. Introduction

LIDAR (Light Detection and Ranging) is used to remotely measure the three dimensional shapes and arrangements of objects with high efficiency and accuracy by making precise measurements of TOF of pulses of light. Single photon detection is now a well-established technique for the detection of very weak optical signals. There are many applications which offer excellent surface to surface resolution and an inherent flexibility in the trade-off between acquisition time and depth precision [1–6]. These systems used single element Geiger mode (GM) detectors to determine the range to a surface of the depth (range) profile of a distributed object within the field of view (FOV).

Recently, Long-range single-photon depth imaging systems [7], which offer high range resolution (4cm) and require much reduced laser power those supplied by Princeton Lightwave. Typical results are pulse energies of 2.4μJ per pulse at ~125kHz repetition rate over a 10km by time-cross-correlation technique or time-cumulative surface scan. However, these system relay on repeat scanning by higher laser repetition rate (HRR) as range-gating mode, the HRR laser is not cost effective.

Our system use array APD characteristics of a plurality of pixels, a new ToF depth imager with light orthogonal code has time-space correlation among pixels in the APD array. The combined method realized the cumulative and cross-correlation between array elements of APD, improved the echo signal SNR and make sure the gray information in the process of decoding at the receiver. At the same time, this method also eliminates the laser’s jitter at the timing of the output of each pulse by time-delay control (TDC) technique. Compare with GM detectors [3, 7], we only use light coding signal enhancement techniques and line-array push broom mode, operating at 532nm wavelength with pulse energies of 5μJ per pulse at 10kHz repetition rate, which incorporates a free-running, high sensitivity APD unit, we acquired depth images of non-cooperative objects in daylight at stand-off distances of up to a 9 kilometer, a similar detection range and pixel array scale compared with Geiger mode detectors using HRR laser.

The real echo signals at long distances may be overwhelmed by the noise [10]. The energy of the lidar-emitted laser is so low that noise can vastly reduce the effective working range and the detection precision. Therefore, the lidar backscattering signals must be de-noised [11–13]. Multiple-shot averaging is generally carried out in the lidar detection process [16–18]. However, this presents the issue of diminishing returns, and rapidly reduces the time or resolution of the lidar measurement [18]. In order to avoid the averaging technique many methods have been presented to de-noise the lidar signal, such as the Monte Carlo average, Fourier, Wavelet, empirical mode decomposition [10–14,19], while these methods are not well suited for low signal–noise ratio (SNR) signals [18]. The ensemble Kalman-Fernald method had been proposed [18]; this method is approximately equivalent to an average of 64 replications, the peak signal to noise ratio (PSNR) increased by up to 18dB, but this method works for aerosol Lidar.

We use an alternative approach which can simultaneously obtain an accurate de-noised lidar signal and a corresponding retrieval result by combining the accumulation-coherence, high accuracy template matching energy detection [21]with sub-pixel method. The accumulation-coherence is based on the $N \times N$ bit orthogonal decode characteristics and the correlation between the adjacent code, which can further improve the SNR, and avoid reducing resolution, accuracy and diminishing returns. The high accuracy sub-pixel template matching energy detection (SED) based on energy concentration in time domain after decoding by accumulation-coherence, which is using high accuracy elastic template matching fine detecting the pulse energy by choosing rectangle mask combined with the characteristic of integrate. The results of both the simulated and real signal demonstrate that our method is practical and effective, even at a far range where the SNR is low.

2. System description

We have constructed multi-pulsed line array push broom imaging lidar, this system scan object region by linear array push broom with a line-at-a-time to improve scanning speed and obtain more measurement data than gated-by-point scanning lidar. The proposed multipulse push broom imaging lidar system is shown in Fig. 1(a), the scanning coordinates of the airborne lidar is shown in 1(b).The lidar system is mounted in the aircraft with IMU and GPS. 3D image of the ground target is then acquired by the IMU&GPS data and coordinate conversion.

Fig. 1 (a) Block diagram of the multipulse push broom imaging lidar system. (b) Establish scanning system coordinates.

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In this new system, the laser beam of 532nm wavelength modulated by beam splitter (i.e. a rotary encoder), the encoded disk has 7200RPM rotation speed, and the light-firing cycle is 8.3ms for an N-bit code in the transmitter. An $1 \times N$ array of beams illuminates the ground in N parallel tracks with 262mrad angle divergence and an average of $\frac{262}{N}$ mrad the divergence of every track. The 135mm telescope is also used to receive scattered laser signals from the target. The focal length of receiving lenses is 210mm. Figure 2 is shown working height is 2000 metres high and the area of coverage on the ground is 1200metres.

Fig. 2 Relationship between laser beams and FOV

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On the receiving end,array sensor has $M$ detector, each detector receives one line-array echo signal from line target reflection. Eventually, the depth data of object area will be ingested by push broom goes on. As the echo time is crisscross for different depth scene, the echo pulse can be obtained by coherence demodulation from code rules. The prototype system and the work progress is shown in Fig. 3.

Fig. 3 Multi-pulse push broom coding imaging lidar system. The semiconductor laser (a) emits a beam of laser at 532nm, it becomes a narrow strip beam through laser beam expanders (b) and cylinder lens (c), the laser beam is transformed to code-beam by the coding disc (d) and then reach to target. The coding disc spins at 7200 RPM rotation speed controlled by control unit (f). The light sensitive detector (e) detects light pulse rise time to generate trigger signal for high speed data acquisition unit. At last, the target’s echo pass through telephoto lens (g) and optical fiber beam combiner (h), and arrive to APD (i).

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In order to facilitate sending and receiving simultaneously and avoid dithering of each outputted pulse with respect to the periodic trigger signal. The external trigger channel is selected here, the channel is used to generate synchronizing trigger pulse to open collector to generate ADC_DATAEN pulse and receive echo pulse from APD detector by precise control for Time delay control (TDC) which triggered by laser pulse rising edge, thus the collector are gated. An A/D clock period (ADC_Clock) of 1ns in collector is used, the laser pulse width is 10ns, and the laser repetition rate is 10kHz. A simple schematic of the laser outputted on the clock period is shown in Fig. 4.

Fig. 4 A schematic of time sequence of a dithered laser source.

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At a range of 7km laser repetition rate is 10kHz, the TOF is to 0.0467ms, one N-bit code light round-trip time would be 8.3467ms from rotary encoder light-firing exposure to the target and then back to detector, which would be ~80 times the laser repetition period. If the airbome lidar has a relative speed of 27ms⁻¹ (~60mph), the range accuracy of 0.1m limits the acquisition time to 3.7ms, so the maximum number of signal of round trip that can be counted is 37. The SNR is very low in this case, we need to choose the right method for signal enhancement, the instrumental response of the system would be infinitely short, and so we choose APD with rise time of 0.5ns.

Assuming the flight speed of airbome lidar is $v$ , the flight time is $t_{f l y}$ through object area, and the one frame time is $T_{f r m}$ for one period of code sequence. Then the distance travelled along the flight path is $W_{} = v t_{f l y}$ , the range pixel array scale will be $N \times (\frac{t_{f l y}}{T_{f r m}})$ pixels, and the lidar can collect 3D imaging data continuously in high-speed during the flight. If encoding bits $N$ is of 256 bit, the $t_{f l y}$ and the $T_{f r m}$ would be 1.8s and 8.3ms respectively through 100m object area, the range array scale will be 256 × 216 pixel array, these results are roughly equivalent of 256 × 256 pixel in Geiger-mode APD of 3D imaging lidar.

3. Principles and methods

New kind scheme of laser code has more important function than conventional rang-gating mode. At first, signal accumulation enhancement which can be achieved in the decoding process since backscattering echo has time and space correlation; using low repetition rate laser can substitute for expensive higher repetition rate laser by coding scheme. Secondly, the range aliasing can be mitigated by orthogonal coding and decoding.

In the transmitter, the $N$ bits code matrix of one frame pulse emitted is

C = [\begin{array}{l} c_{11} c_{12} \dots c_{1, N} \\ c_{21} c_{22} \dots c_{2, N} \\ ⋮ ⋮ ⋮ \\ c_{N 1} c_{N 2} \dots c_{N, N} \end{array}],

there $t_{i}$ time emission code-beam is $C_{i} = [c_{i 1} c_{i 2} \dots c_{i, N}]$ , and $c_{i j}$ corresponds to one bit pulse, for $i = 1 2 \dots N,$ $j = 1 2 \dots N$ .

At the receiving end, an anti-noise algorithm is proposed for the retrieval of optical properties from a lidar signal. The algorithm contains three parts: the echo signal accumulation demodulation, coherence enhancement and sub-pixel energy detection (SED). The flow chart and example graphics of $N = 8$ is shown in Fig. 5, such as we can obtain $N$ pixels echo from one frame pulse of one line-array echo.

Fig. 5 Flow of the de-noising and retrieval algorithm.

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3.1 Echo signal demodulation and enhancement

Let us consider the case of laser pulses sequence in one period, if emitted $N \times N$ laser code pulses is $C_{} = {[C_{1} C_{2} \dots C_{N}]}^{Τ}$ in the transmitter, an APD output will be

r_{e c o} = {[r_{e c o, 1} r_{e c o, 2} \dots r_{e c o, N}]}^{Τ}

The $r_{e c o, i}$ is corresponds to $C_{i}$ , for $i = 1 2 \dots N$ .On echo SNR decrease, we use accumulation and coherence approach to reduce noise by using array sensor and coding features.

(1) Time-space accumulation

Assuming decoded pulse is $r_{} = {[r_{1} r_{2} \dots r_{N}]}^{Τ}$ , the matrix components is given by

\begin{array}{l} r_{i} = W_{i} r_{e c o} \\ = [w_{i, 1} w_{i, 2} \dots w_{i, N}] [\begin{array}{l} r_{e c o, 1} \\ r_{e c o, 2} \\ ⋮ \\ r_{e c o, N} \end{array}], \\ = \sum_{j = 1}^{N} w_{i, j} r_{e c o, j} \end{array}

the $W = [W_{1} W_{2} \dots W_{N}]$ is weighted coefficient. According to the property of time-correlation of signal and the mutual independence of noises, the signal get enhancement and noises are reduced. For M array elements of array APD, the decoded $r$ continues to accumulation to M times as space correlation.

Let $n$ is SNR gain of $r$ from accumulation, then the value range of $n$ must ${(\frac{N \times M}{2})}^{0.8} \leq n \leq (N \times M)$ for orthogonal code $C$ .

(2) Coherence

Considering noise-free situations, the decoded pulses is

r_{f r e e} = {[r_{f r e e, 1} r_{f r e e, 2} \dots r_{f r e e, N}]}^{Τ} = [\begin{array}{l} 1 0 0 \dots 0 \\ 0 1 0 \dots 0 \\ ⋮ \\ 0 0 0 \dots 1 \end{array}]

based on Eq. (5), we have the following equation

r_{f r e e, i} = (r_{f r e e, i} + r_{f r e e, i + 1}) & r_{f r e e, i}, i = 1, 2, \dots N

r_{f r e e, i + 1} = (r_{f r e e, i} + r_{f r e e, i + 1}) & r_{f r e e, i + 1}, i = 1, 2, \dots N

the symbol “

&

” is logic and.

Let us now consider the case as the noisy echo signal, “ $r$ ”, through accumulation by Eq. (4). Using cross-correlation function that is given by

r_{c o, i} = R_{r_{i} + r_{i + 1}, r_{i}} = E {(r_{i} + r_{i + 1}) r_{i}}, i = 1, 2, \dots N

r_{c o, i + 1} = R_{r_{i} + r_{i + 1}, r_{i + 1}} = E {(r_{i} + r_{i + 1}) r_{i + 1}}, i = 1, 2, \dots N

According to the signal with coherence while noise with irrelevance, Eq. (8) and Eq. (9) can reduce the noise,

r_{c o} = [r_{c o, 1}, r_{c o, 2}, \dots, r_{c o, N}]

is the retrieved signal from noisy signal

r

.Such that, coherence method will further improve SNR.

3.2 Sub-pixel energy detection

In long-range detection, though the accumulation-coherence has been used, the echo signal is still drowned in the noise and the SNR is still low. Now, we use energy detection approach to extract weak echo from the noisy signal. It is necessary to apply the high accuracy phase template matching to achieve high precision detection of the weak signal.

Consider Eq. (8) and Eq. (9), we add up all the components of $r_{c o}$ in a frame

\begin{array}{l} r_{int} = r_{c o, 1} + r_{c o, 2} + \dots r_{c o, N} \\ = \sum_{i = 1}^{N} r_{i} {(t)}_{} \end{array}

to say it another way of noise

r_{int} (t) = s (t) + n (t)

Where $s (t) = \sum_{k = 0}^{N - 1} r (t - k T_{k})$ , $n (t)$ is additive noise.

Assuming detecting mask is rectangle pulse sequence

g_{m a s k} (t) = \sum_{m = 1}^{N - 1} g (t - m T_{m})

the rectangle pulse

g (t) = {\begin{cases} 1 t \leq τ \\ 0 t > τ \end{cases},

τ

is pulse duration.

It follows that the cross correlation of $r_{int} (t)$ and $g_{m a s k} (t)$

R_{r g} (t_{0}) = \sum_{t} r_{int} (t) g_{m a s k}^{*} (t - t_{0})

We change

t_{0}

and

T_{m}

each point in the search signal and calculate the cross-correlation

R_{r g} (t_{0})

over the whole area spanned by the template

{{\hat{T}}_{m}, \hat{τ}} = \arg \max_{T_{m}, τ} | R_{r g} |

It follows that

p (t) = r_{int} (t) * g_{m a s k} (t - {\hat{t}}_{0}) |_{T_{m} = {\hat{T}}_{m}}

Considering the case of high accuracy, using FFT approach to find the cross correlation peak within a fraction, $\frac{1}{k}$ , of a pixel, follow these steps: (i) embed the product $R_{e c h o} (k) G_{m a s k}^{*} (k)$ into a larger array of zeroes of length $k M$ , (ii) compute an inverse FFT to obtain an up-sampled cross correlation, and (iii) locate its peak.

4. Experiment and analysis

For experimental proof of this theory, we have designed a high speed line-array multi-pulse lidar, whose system structure is shown in Fig. 1, which works in fine weather. The diode pumped solid-state lasers (DPSSLs) is used as lidar transmitter at the wavelength of 532 nm with high peak power, at 10 kHz repetition rate and 10ns pulse width. The energy of the single pulse is $5 μ J$ or $15 μ J$ . At the receiving end, we choose the freespace high sensitivity avalanche photo detector unit (APD210) as detector with multimode fiber core and larger sensitivity area can effectively improve receiving effects and increase range. The system worked with a frame rate of 260frames/s.

The targets are far away from out of the lab window at 10m and 2 km respectively. The system use $N = 8$ bits code, array sensor has $M = 4$ detector for one frame, the echo signal is shown in Fig. 6.

Fig. 6 Two kinds of echo signal with 8 pulses from 10m and 2km targets, the blue one has noise obviously.

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The echo signal enhancement and decode by the accumulation and accumulation coherence method are shown in Fig. 5 and Fig. 7, coherence processing further enhance signal and reduce the noise. It has better effect than only use accumulation in SNR. Such that we can obtain pulse time and strength information at the same time by threshold processing. In this case, if increasing the coded bits $N$ and array elements M of array APD, we will further enhance signal and detect farther target.

Fig. 7 The echo signal enhancement and decode by the accumulation method (blue line) and accumulation-coherence method (red line). It showed one of pulse for 8 de-noised echo pulses at 2km.

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If detecting distance target, the echo signal is so weak that using sub-pixel energy detection method. Figures 8(a) and 8(b) shows the noised signals and the echo signal are retrieved by our method. The 7(a) is low PSNR for 2km decoding pulse and the 7(b) is sub-pixel energy detection output by high accuracy phase template matching. With our method, the measured PSNR from the −5.624dB to 5.638dB and 18.26dB at 2km by the PSNR logarithmic Eq. (16), improvement of the 11.262dB and 23.884dB is shown in Fig. 8, where $r (m)$ denotes the original signal and $\hat{r} (m)$ denotes the de-noising signal. To get original signals $r (m)$ for the different long distance target we chose to adjust the laser power, which is to increase the laser power will obtain the original signal $r (m)$ .

Fig. 8 (a) The echo signal with 8 pulses from range 2 km. (b) The true signal at 2 km retrieved by sub-pixel energy detection method.

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P S N R = 10 \log {\frac{\sum_{m = 1}^{M} r^{2} (m)}{\sum_{m = 1}^{M} {[r (m) - \hat{r} (m)]}^{2}}}

If the target at about 7km away, the PSNR is 6.666dB after de-noising showed in Fig. 9, the retrieved echo signal is showed in Fig. 10, achieved long-range detection.

Fig. 9 The echo signal (red line), de-noised signal by accumulation-coherence method (green line), and echo retrieved by energy detection method (blue line). From near to far a single measurement PSNR for different range, the single pulse energy at $5 μ J$ .

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Fig. 10 Echo signal with 8 pulses from range 7 km (blue line) and the true signal retrieved by sub-pixel energy detection method (red line).

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The 100-time experiment was observed with the observations distance of increases, the PSNR decrease, it is shown in Fig. 11, the laser single pulse energy is $5 μ J$ and $15 μ J$ . The accumulation-coherence method and sub-pixel energy detection combination methods, however, PSNR has improvement of average 9.5dB and 21.03dB at $5 μ J$ , and improvement of average 11.17dB and 24.47dB at $15 μ J$ .

Fig. 11 The PSNR for 100-Shot averaged lidar return signal (red line) and 100-shot averaged data denoised by our method (green line and blue line).

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The different range case is shown in Fig. 12. As the distance increased, the signal strength is declining; the time-of-flight can be properly retrieved by combining the Accumulation-coherence and high accuracy sub-pixel energy detection method.

Fig. 12 (a)-(f) Six case of different range at 0.5km, 1km, 2km, 3km, 5km and 7km, respectively. The true time of flight are retrieved by our method. The laser single pulse energy is $5 μ J$ .

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The retrieval results show that the accumulation-coherence method increases PSNR up to average 10.3 dB only for 8 bit code, and sub-pixel energy detection method increases PSNR up to average 12.9 dB, combining both method increases PSNR up to average 23.2 dB.

For further increases of PSNR, it is necessary to increase code length $N$ without reducing resolution; the system will result in significant improvements. In addition, an error occurred while trying to estimate the time of flight for further long range, which is the primary cause of PSNR declined. In the future, we will discuss new sub-pixel energy detection scheme with Monte Carlo random sampling, trying to approach SNR upper bound for energy detection.

5. Conclusion

A multi-pulse line-array push broom gate-range long range 3D active imaging lidar of light coding is presented. This technique utilizes the line-array push broom scanning, light orthogonal coding transmitting and receiving technology, TDC precise control, time-space accumulation-coherence decode and sub-pixel energy detection. The advantage of the new system is the pixel scale to $N \times (\frac{t_{f l y}}{T_{f r m}})$ pixel array or more by line-array push broom mode, with low repetition rate laser and single pulse $5 μ J$ detected ranges to 9km. The retrieval results show that combining the two methods, accumulation-coherence method and energy detection is approximately equivalent to an average of 208 only for 8 bit code replications. Furthermore, in the near range, this study suggests that a de-noise scheme is unnecessary.

In the future, using a higher laser repetition rate laser, combing our light code and signal processing technology to realize signal accumulation correlation enhancement on both time-space correlation in array pixel and time correlation in inter-frame, such that the further long detection distance system should be made.

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Long range detection of line-array multi-pulsed coding lidar by combining the Accumulation coherence and Subpixel-energy detection method

Abstract

1. Introduction

2. System description

3. Principles and methods

3.1 Echo signal demodulation and enhancement

(1) Time-space accumulation

(2) Coherence

3.2 Sub-pixel energy detection

4. Experiment and analysis

5. Conclusion

References and links

Cited By

Figures (12)

Equations (15)

Optics Express