Walk Error Research Articles

Research of Distance-Intensity Imaging Algorithm for Pulsed LiDAR Based on Pulse Width Correction

Walking error has been problematic for pulsed LiDAR based on a single threshold comparator. Traditionally, walk error must be suppressed by some time discrimination methods with extremely complex electronic circuits and high costs. In this paper, we propose a compact and flexible method for reducing walk error and achieving distance-intensity imaging. A single threshold comparator and commercial time digital converter chip are designed to measure the laser pulse’s time of flight and pulse width. In order to obtain first-class measurement accuracy, we designed a specific pulse width correction method based on the Kalman filter to correct the laser recording time, significantly reducing the ranging walk error by echo intensity fluctuation. In addition, the pulse width obtained by our method, which is a recording of the laser intensity, is conducive to target identification. The experiment results verified plane point clouds of various targets obtained by the proposed method with a plane flatness less than 0.34. The novel contribution of the study is to provide a highly integrated and cost-effective solution for the realization of high-precision ranging and multi-dimensional detection by pulsed LiDAR. It is valuable for realizing multi-dimension, outstanding performance, and low-cost LiDAR.

Effect of PMT output electron flow pulse pile-up on photon counting ranging method

Photomultiplier tubes (PMT) have single photon level sensitivity, low dark count, low after pulse probability, and are widely used in photon-counting lidar in visible spectrum. PMT has no photon detection dead time, for every photon it responds to, it sends out a electron flow pulse, these pulses of electron flow have the po·tential to pile up into larger pulses. When using threshold identification method to identify photon-events, stacked pulse will introduce additional pulse walking error, in the practical application of laser ranging, will directly affect the ranging precision of photon-counting ranging method. Considering the influence of pulse pile-up, a new theoretical model of PMT photon detection was established to describe the influence of pulse pile-up on the detection probability of photon-events by analyzing the relationship between the detection time of photon and the identification time of the PMT final output photon-events. Through Monte Carlo simulation, the relationship among the ranging walking error, ranging accuracy, incident laser pulse width, PMT output electron flow pulse width and photon-events identification threshold is obtained. In order to verify the correctness of the theory, a PMT-based photon-counting lidar system is built. The comparison experiment with GM-APD proves that the influence of pulse pile-up on PMT photon-counting ranging method can not be ignored, and the experimental results are in good agreement with the theoretical model. The PMT photon detection model based on pulse pile-up can guide the design of PMT photon-counting radar and improve the ranging accuracy and precision of the ranging system.

Effect of pile-up of electron flow pulse from photomultiplier tube on ranging by photon counting

Photomultiplier tube (PMT) features single photon level sensitivity, low dark count, and low afterpulse probability, and are widely used in photon-counting lidar in the visible spectrum. The PMT has no photon detection dead time, for every photon it responds to, it can output an electron flow pulse, these pulses of electron flow are likely to pile up into larger pulses. When using threshold identification method to identify photon-events, the stacked pulse will introduce additional pulse walking error, directly affecting the ranging precision of photon-counting ranging method in the practical application of laser ranging. Considering the influence of pulse pile-up, a new theoretical model of PMT photon detection is established to describe the influence of pulse pile-up on the detection probability of photon-events by analyzing the relationship between the detection time of photon and the identification time of the PMT final output photon-events. Through Monte Carlo simulation, the relationship among the ranging walking error, ranging accuracy, incident laser pulse width, PMT output electron flow pulse width and photon-events identification threshold is obtained. In order to verify the correctness of the theory, a PMT-based photon-counting lidar system is built. The comparative experiment with GM-APD proves that the influence of pulse pile-up on PMT photon-counting ranging method cannot be ignored, and that the experimental results are in good agreement with results from the theoretical model. The PMT photon detection model based on pulse pile-up can guide the design of PMT photon-counting radar and improve the ranging accuracy and precision of the ranging system.

Mobility Performance in Retinitis Pigmentosa Under Different Lighting Simulation Conditions

This study examined the mobility performance in retinitis pigmentosa (RP) under different simulation lighting conditions. A total of twenty-one subjects with RP and twenty-one age-matched controls were enrolled. Preferred Walking Speed (PWS) were determined using a simple mobility course at 61 cd/m2 while Percentage of Preferred Walking Speed (PPWS) and error score were determined at five different illumination level which were 62, 47, 20, 6 and 1 cd/m2 using a complex mobility course. RP and normal people had similar mobility performances in simple mobility situations at a constant high light level. In lower light levels as well as in complex mobility situations, RP subjects demonstrated markedly reduced mobility performance. The relationship between PPWS and luminance was linear, with the PPWS decreasing significantly when the mobility course luminance dropped below the illumination of 20 cd/m2 . The Error score was also noted to be linearly related to log luminance. A luminance level of 20 cd/m2 may provide a useful decision point in setting indoor light levels for clinical mobility courses.

Mobility Performance in Retinitis Pigmentosa Under Different Lighting Simulation Conditions

This study examined the mobility performance in retinitis pigmentosa (RP) under different simulation lighting conditions. A total of twenty-one subjects with RP and twenty-one age-matched controls were enrolled. Preferred Walking Speed (PWS) were determined using a simple mobility course at 61 cd/m2 while Percentage of Preferred Walking Speed (PPWS) and error score were determined at five different illumination level which were 62, 47, 20, 6 and 1 cd/m2 using a complex mobility course. RP and normal people had similar mobility performances in simple mobility situations at a constant high light level. In lower light levels as well as in complex mobility situations, RP subjects demonstrated markedly reduced mobility performance. The relationship between PPWS and luminance was linear, with the PPWS decreasing significantly when the mobility course luminance dropped below the illumination of 20 cd/m2 . The Error score was also noted to be linearly related to log luminance. A luminance level of 20 cd/m2 may provide a useful decision point in setting indoor light levels for clinical mobility courses.

Mobility Performance in Retinitis Pigmentosa Under Different Lighting Simulation Conditions

This study examined the mobility performance in retinitis pigmentosa (RP) under different simulation lighting conditions. A total of twenty-one subjects with RP and twenty-one age-matched controls were enrolled. Preferred Walking Speed (PWS) were determined using a simple mobility course at 61 cd/m2 while Percentage of Preferred Walking Speed (PPWS) and error score were determined at five different illumination level which were 62, 47, 20, 6 and 1 cd/m2 using a complex mobility course. RP and normal people had similar mobility performances in simple mobility situations at a constant high light level. In lower light levels as well as in complex mobility situations, RP subjects demonstrated markedly reduced mobility performance. The relationship between PPWS and luminance was linear, with the PPWS decreasing significantly when the mobility course luminance dropped below the illumination of 20 cd/m2 . The Error score was also noted to be linearly related to log luminance. A luminance level of 20 cd/m2 may provide a useful decision point in setting indoor light levels for clinical mobility courses.

Mobility Performance In Retinitis Pigmentosa Under Different Lighting Simulation Conditions

This study examined the mobility performance in retinitis pigmentosa (RP) under different simulation lighting conditions. A total of twenty-one subjects with RP and twenty-one age-matched controls were enrolled. Preferred Walking Speed (PWS) were determined using a simple mobility course at 61 cd/m2 while Percentage of Preferred Walking Speed (PPWS) and error score were determined at five different illumination level which were 62, 47, 20, 6 and 1 cd/m2 using a complex mobility course. RP and normal people had similar mobility performances in simple mobility situations at a constant high light level. In lower light levels as well as in complex mobility situations, RP subjects demonstrated markedly reduced mobility performance. The relationship between PPWS and luminance was linear, with the PPWS decreasing significantly when the mobility course luminance dropped below the illumination of 20 cd/m2 . The Error score was also noted to be linearly related to log luminance. A luminance level of 20 cd/m2 may provide a useful decision point in setting indoor light levels for clinical mobility courses.

A Method of Range Walk Error Correction in SiPM LiDAR with Photon Threshold Detection

A silicon photomultiplier (SiPM) LiDAR with photon threshold detection can achieve high dynamic performance. However, the number fluctuations of echo signal photons lead to the range walk error (RWE) in SiPM LIDARs. This paper derives the RWE model of SiPM LiDAR by using the LiDAR equation and statistical property of SiPM’s response. Based on the LiDAR system parameters and the echo signal intensity, which is obtained through the SiPM’s photon-number-resolving capability, the RWE is calculated through the proposed model. After that, we carry out experiments to verify its effectiveness. The result shows that the method reduces the RWE in TOF measurements using photon threshold detection from 36.57 cm to the mean deviation of 1.95 cm, with the number of detected photons fluctuating from 1.3 to 46.5.

Low walk error multi-stage cascade comparator for TOF LiDAR application

Aiming at the application of pulsed TOF LiDAR, this paper propose a low walk error multi-stage comparator based on the double threshold method. In order to achieve high-speed comparison output, the LVDS interface is used to output the data of the comparator. The dual-channel comparator is implemented using the SMIC 0.18 μm process which achieves a propagation delay of 620 ps and an input bandwidth of 256 MHz. Thanks to the multi-stage design, the walk error of the comparator is only 196 ps. It supports the minimum pulse width of 931 ps, the rms random jitter of 1.90 ps, and the power consumption of 39.6 mW.

Time-magnified photon counting with 550-fs resolution

Time-correlated single-photon counting (TCSPC) is an enabling technology for applications such as low-light fluorescence lifetime microscopy and photon counting time-of-flight (ToF) 3D imaging. However, state-of-the-art TCSPC single-photon timing resolution (SPTR) is limited to 3–100 ps by single-photon detectors. Here, we experimentally demonstrate a time-magnified TCSPC (TM-TCSPC) that achieves an ultrashort SPTR of 550 fs with an off-the-shelf single-photon detector. The TM-TCSPC can resolve ultrashort pulses with a 130-fs pulse width difference at a 22-fs accuracy. When applied to photon counting ToF 3D imaging, the TM-TCSPC greatly suppresses the range walk error that limits all photon counting ToF 3D imaging systems by 99.2% and thus provides high depth accuracy and precision of 26 µm and 3 µm, respectively.

Toward snapshot correction of 3D flash LiDAR imagers

We present methods enabling rapid non-uniformity and range walk error correction of 3D flash LiDAR imagers that exhibit electronic crosstalk caused by simultaneously triggering too many detectors. This additional electronic crosstalk is referred to as simultaneous ranging crosstalk noise (SRCN). Using a method in which the 3D flash LiDAR imager views a checkerboard target downrange, the SRCN is largely mitigated. Additionally, processing techniques for computing the non-uniformity correction (NUC) and range walk error correction are described; these include an in-situ thermally compensated dark-frame non-uniformity correction, image processing and filtering techniques for the creation of a photo-response non-uniformity correction, and characterization and correction of the range walk error using data collected across the full focal plane array without the need for sampling or windowing. These methods result in the ability to correct noisy test validation data to a range precision of 8.04 cm and a range accuracy of 1.73 cm and to improve the signal-to-noise ratio of the intensity return by 15 to 49 dB. Visualization of a 3D scene corrected by this process is additionally presented.

Windowed region-of-interest non-uniformity correction and range walk error correction of a 3D flash LiDAR camera

We present experimental methods and results for photo-response non-uniformity correction (PRNUC) in range for a 3D flash LiDAR camera from non-optimal static-scene calibration data. Range walk is also corrected. This method breaks up the camera’s focal plane array (FPA) into 16 × 16 windowed regions of interest that are incrementally captured and stitched together in post-processing across the entire FPA. The illumination was not uniform, thus requiring additional methods described by our paper to create an acceptable correction. We present the results from a full non-uniformity correction and range walk error correction processed for a set of independently collected validation frames; these validation frames used identical experimental conditions and the same target as was collected for the corrections. We will show that this experimental approach improves range accuracy and range precision of the corrected validation frames despite the sub-optimal conditions of the data used to compute the corrections; the single shot range precision is corrected to 33 cm, as compared to a modeled precision of 15.65 cm, while the accuracy is corrected to 252 cm. This method has implications for simplification of characterization of non-uniformity and range walk error, and its subsequent correction, in 3D flash LiDAR cameras.

Design and experimental evaluation of block-pulse functions and Legendre polynomials observer for attitude-heading reference system

The main purpose of this paper is design and implementation of a new linear observer for an attitude and heading reference system (AHRS), which includes three-axis accelerometers, gyroscopes, and magnetometers in the presence of sensors and modeling uncertainties. Since the increase of errors over time is the main difficulty of low-cost micro electro mechanical systems (MEMS) sensors producing instable on–off bias, scale factor (SF), nonlinearity and random walk errors, development of a high-precision observer to improve the accuracy of MEMS-based navigation systems is considered. First, the duality between controller and estimator in a linear system is presented as the base of design method. Next, Legendre polynomials together with block-pulse functions are applied for the solution of a common linear time-varying control problem. Through the duality theory, the obtained control solution results in the block-pulse functions and Legendre polynomials observer (BPLPO). According to product properties of the hybrid functions in addition to the operational matrices of integration, the optimal control problem is simplified to some algebraic equations which particularly fit with low-cost implementations. The improved performance of the MEMS AHRS owing to implementation of BPLPO has been assessed through vehicle field tests in urban area compared with the extended Kalman filter (EKF).

Analog Front-End Circuits With Input Current Attenuation and Heterodyne Techniques for Low-Cost Phase-Shift LADAR Receiver

Analog front-end (AFE) circuits with wide dynamic range and low walk error for cost-effective phase-shift LADAR receiver are presented in this work. The inverter-based trans-impedance amplifier (TIA) utilized in the proposed AFE has been modified with two additional transistors in its input node, which can attenuate the input current automatically and adjust the bandwidth dynamically. The improved TIA significantly increases the dynamic range of AFE without any complicated gain-control circuits, while keeping the walk error in a low level. Heterodyne techniques are then adopted to modulate the received signals to low-frequency carriers, as well as the driving signal of laser diode, which is modulated with a mirrored voltage-input channel. Thus, systematic errors caused by the uncertainty of the initial phase in transmitted signal can be reduced. As a result, high-accuracy phase detections and range measurements can be realized conveniently by just sampling two low-frequency (~100 kHz in this design) output signals. The AFE circuits have been fabricated in a standard 65-nm CMOS technology with a total chip area of $0.59\times0.68$ mm2 including the IO PADs. The measured power consumption is 24.3 mW with a 2.5-V supply. With a modulated frequency of 30 MHz and a local oscillator frequency of 30.1 MHz, the measured input-referred noise of the proposed AFE is 8.4 nA $_{RMS}$ and the walk error is less than ±1.8% for a wide dynamic range of 500 nA ~ 10 mA. The measurement results show that the proposed AFE can achieve wide dynamic range and low walk error, while the system complexity and cost of the phase-shift LADAR receiver can also be reduced.

Correction of range walk error for underwater photon-counting imaging.

Due to the characteristics of photon-counting LIDAR, there exists range walk error (RWE) when the intensity of the signal fluctuates. In this paper, an effective method to rectify underwater RWE was proposed. The method allows the separation of signal detections from noise detections, and based on a prior model, the method can compensate for RWE. An underwater experiment verified its feasibility and results showed RWE of three parts in a plane was reduced from 75mm to 7mm, from 45mm to 3mm and from 5mm to 0mm, respectively, even when the rate of backscatter photons reached 4.8MHz. The proposed correction method is suitable for high precision underwater photon-counting 3D imaging application, especially when the signal intensity varies sharply.

Dual Gm-APD Polarization Lidar to Acquire the Depth Image of Shallow Semitransparent Media With a Wide Laser Pulse

A polarization lidar with dual Geiger-mode avalanche photodiodes (Gm-APDs) is designed to obtain the high-precision depth image of shallow semitransparent media by using a wide laser pulse. The first surface of the semitransparent media is smooth and can nearly preserve the incident polarization, whereas the second surface is rough and can depolarize the incident polarization. A polarization splitting prism is utilized to separate the two echo signals, which will be detected by dual Gm-APDs. It gives the ability to obtain the extremely shallow depth independent of laser pulse width and dead time of Gm-APD. The theory of laser polarization transmission of dual Gm-APD polarization lidar is analyzed. Signal restoration & center-of-mass algorithm method is used to restrain the range walk error and obtain high range precision. The depth image of shallow semitransparent media with a thickness and distance of 10 cm and 6 m, respectively, is obtained in the experiment with a range precision of 1.1 cm. An experiment of real shallow water layer with different depth features is also performed to verify the result.

A Low Walk Error Analog Front-End Circuit With Intensity Compensation for Direct ToF LiDAR

An analog front-end (AFE) circuit comprising an amplifier module, a peak detector, and a timing discriminator has been designed to facilitate the target identification for direct time-of-flight (dToF) LiDAR. The amplitude saturation error (ASE) is compensated in this article for the intensity determination, which is conducted based on the combination of the pulse width and peak detector. Together with the improved walk error compensation scheme, the proposed AFE circuit can attain the distance and intensity information simultaneously with lower cost and larger dynamic range. A specific frequency compensation method is proposed with a shunt feedback TIA, which improves the stability and mitigates the impact of the package parasitics. The measured -3-dB bandwidth, transimpedance gain, and the input-referred noise current are 281 MHz, 86 dB <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> , and 4.68 pA/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\surd $ </tex-math></inline-formula> Hz respectively. The proposed AFE circuit, which is fabricated in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.18~\mu \text{m}$ </tex-math></inline-formula> CMOS technology, achieves the distance accuracy of ±30 ps and the intensity accuracy of ±4% in the dynamic range of 1:5000 without gain control scheme.

Pulsed light time-of-flight measurement based on a differential hysteresis timing discrimination method.

In the pulsed light time-of-flight (ToF) measurement, the timing point generated in the receiver channel is very important to the measurement accuracy. Therefore, a differential hysteresis timing discrimination method is proposed to generate timing points of the receiver channel. This method is based on utilizing the unbalanced characteristics of the fully differential operational amplifier circuit as well as introducing extra hysteresis levels to achieve the stable generation of timing points. With this method, fewer circuit components are consumed and the dynamic range of the receiver channel is not limited by its linear range. The experiments demonstrate that a receiver channel applying the proposed discrimination reaches better single shot accuracy compared to that using leading-edge timing discrimination. This method is also suitable for the timing walk error compensation by means of pulse width. Finally, these results verify the effectiveness of the proposed method in pulsed light ToF measurement.

A Low-Power Multichannel Time-to-Digital Converter Using All-Digital Nested Delay-Locked Loops With 50-ps Resolution and High Throughput for LiDAR Sensors

This article presents a low-power, all-digital multichannel time-to-digital converter (TDC) for light detection and ranging (LiDAR) sensors. The proposed TDC architecture measures the time interval through a coarse counter, middle, and fine delay line-based interpolation technique (the Nutt method). Automatic calibration by middle and fine all-digital delay-locked loops (ADDLLs) is provided to ensure the stability of the generated time slots. Charge pump, loop filter, and voltage-controlled delay line inside the conventional analog delay-locked loops (DLLs) are replaced by an accumulator (ACC) and digitally controlled delay line (DCDL). This makes the design particularly compact, low power, and suitable for multichannel applications. The presented architecture can generate information for amplitude variation (walk error) compensation. This information is generated by measuring the pulsewidth and position of three successive STOP pulses inside each channel within a single-shot measurement. A low-jitter injection-locked frequency multiplier (ILFM) generates a 625-MHz internal clock signal out of 25-MHz external reference oscillator, which shrinks the number of delay elements to cover one period of the reference clock and improves the precision of the TDC. Operation at higher frequency provides high throughput and short conversion time (less than 3 ns). The three-level TDC offers 13.1- $\mu \text{s}$ maximum input range and 50-ps resolution. The measured DNL and INL of the TDC circuit are 0.47 and 0.71 LSB, respectively. The TDC circuit is implemented in a 180-nm standard CMOS process with a die size of 1.5 mm $\times1.5$ mm. The total power consumption of the multichannel TDC is 87.6 mW.

Methods to Compensate the Time Walk Errors in Timing Measurements for PET Detectors

We investigate the effects of the signal walk-in timing measurements and the methods to compensate for the error when leading-edge discriminator (LED) triggering was used. Three pairs of crystals (LaBr3 cubes, lutetium-yttrium oxyorthosilicate (LYSO) cubes, and LYSO rectangular prisms) were tested for coincidence timing resolution (CTR) to evaluate four compensation methods: 1) Linear 1-D; 2) Logarithm 1-D; 3) Polynomial 2-D; and 4) artificial neural network (ANN) 2-D. The experimental results show that: 1) the signal walk causes a logarithmic relationship between energy and measured time; 2) the signal walk dramatically affects the timing measurement at a wide energy window. The measured FWHM CTR decreased by 86.2%, from 670 ps to 92.7 ps, when the lower cut of the energy window was used; and 3) the Logarithm 1-D compensation can improve the timing performance. The FWHM CTRs decreased by 69.9% (from 326.8 ps to 101.3 ps) with an energy window of [300 keV–550 keV] and by 12.5% (from 97.2 ps to 85.1 ps) with an energy window of [410 keV–550 keV] for LaBr3 cube crystals. The results show that the Logarithm 1-D, Polynomial 2-D, and ANN 2-D compensations work well, achieving at least a 10% improvement in timing performance.