• Infrared and Laser Engineering
  • Vol. 49, Issue 10, 20200218 (2020)
Lu Xu, Xu Yang, Long Wu*, Xiaoan Bao, and Yijia Zhang
Author Affiliations
  • School of Informatics, Zhejiang Sci-Tech University, Hangzhou 310018, China
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    DOI: 10.3788/IRLA.20200218 Cite this Article
    Lu Xu, Xu Yang, Long Wu, Xiaoan Bao, Yijia Zhang. Restrain range walk error of Gm-APD lidar to acquire high-precision 3D image[J]. Infrared and Laser Engineering, 2020, 49(10): 20200218 Copy Citation Text show less

    Abstract

    Due to the first photon bias effect of Gm-APD, there exists range walk error in Gm-APD lidar, which will generate a distortion of depth image of the target. Two methods to restrain the range walk error were presented and verified by experiments. Signal restoration method was used to obtain signal photoelectron distribution histogram (SPDH) from the photon counting distribution histogram (PCDH). A sum of two Gaussian functions were used to fit the SPDH through, and the peak position of the curve was found to calculate the distance. The center-of-mass algorithm method on the SPDH was used to calculate the distance through the second method. The high-precision 3D depth-intensity merged images was caputured using the two methods by experiments with a 6 ns width laser pulse. The relative accuracy of intensity measurement of the two methods were both less than 3%. The signal restoration & Gaussian functions fitting method has range precision of 1.2 cm. The signal restoration & center-of-mass algorithm method has range precision of 0.6 cm.
    $P\left( i \right) = \left\{ {1 - \exp \left[ { - {N_{\rm sn}}(i)} \right]} \right\}\exp \left[ { - \displaystyle\sum_{j = i - d}^{i - 1} {{N_{\rm sn}}\left( j \right)} } \right] $(1)

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    $P\left( i \right) = \dfrac{{K\left( i \right)}}{M} $(2)

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    $K\left( i \right) = M\left\{ {1 - \exp \left[ { - {N_{\rm sn}}(i)} \right]} \right\}\exp \left[ { - \displaystyle\sum_{j = i - d}^{i - 1} {{N_{\rm sn}}\left( j \right)} } \right] $(3)

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    $\begin{array}{*{20}{c}} {{N_\rm s}^\prime \left( i \right) = - \ln \left\{ {1 - \dfrac{{K\left( i \right)}}{M}\exp \left[ {\displaystyle\sum_{j = i - d}^{i - 1} {{N_\rm s}\left( j \right)} + \sum\limits_{j = i - d}^{i - 1} {{N_\rm n}\left( j \right)} } \right]} \right\}} \\ { - {N_\rm n}(i)} \end{array} $(4)

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    $I = \sum\limits_{i = T}^{{T_m}} {{N_s}^\prime \left( i \right)} $(5)

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    ${N_\rm s}^\prime \left( i \right) = {A_1}\exp \left[ {\frac{{ - {{\left( {i - {T_1}} \right)}^2}}}{{{B_1}^2}}} \right] + {A_2}\exp \left[ {\frac{{ - {{\left( {i - {T_2}} \right)}^2}}}{{{B_2}^2}}} \right] \;\;\;\;\;\;\;\;\;\;\;\;$(6)

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    $R' = \frac{c}{2} \times T $(7)

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    $R'' = \dfrac{{c\Delta t}}{2}\dfrac{{\displaystyle\sum\limits_{i = T}^{{T_m}} {i{N_s}^\prime (i)} }}{{\displaystyle\sum\limits_{i = T}^{{T_m}} {{N_s}^\prime (i)} }}$(8)

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    $\dfrac{{{\sigma _I}}}{{\bar I}} = \dfrac{{\sqrt {\dfrac{1}{N}\displaystyle\sum_{i = 1}^N {{{\left( {{I_i} - \bar I} \right)}^2}} } }}{{\bar I}} $(9)

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    ${\sigma _R} = \sqrt {\dfrac{1}{N}\sum\limits_{i = 1}^N {{{\left( {{R_i} - \bar R} \right)}^2}} } $(10)

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    Lu Xu, Xu Yang, Long Wu, Xiaoan Bao, Yijia Zhang. Restrain range walk error of Gm-APD lidar to acquire high-precision 3D image[J]. Infrared and Laser Engineering, 2020, 49(10): 20200218
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