• Infrared and Laser Engineering
  • Vol. 51, Issue 12, 20220282 (2022)
Yuxuan Chen, Zhongjun Qiu, and Junjie Tang
Author Affiliations
  • State Key Laboratory of Precision Measuring Technology & Instrument, Tianjin University, Tianjin 300072, China
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    DOI: 10.3788/IRLA20220282 Cite this Article
    Yuxuan Chen, Zhongjun Qiu, Junjie Tang. Mechanical-imaging comprehensive error modeling in line scan vision detection systems[J]. Infrared and Laser Engineering, 2022, 51(12): 20220282 Copy Citation Text show less

    Abstract

    To address the problem that the accuracy of the line scan vision detection system is easily affected by the mechanical structure error and the specific influence mechanism is not clear, a mathematical model of the influence of mechanical error on the system imaging error was established and analyzed. Based on the theories of multi-system kinematics and homogeneous coordinate transformation, a mechanical system error transfer model of the line scan vision detection system was derived, and a system error comprehensive model was established with reference to the line scan imaging characteristics to clarify the correspondence between mechanical errors and system image output errors. The error sensitivity of the model was analyzed based on the complete differential-coefficient theory, and the error sources that had a great impact on the errors of the x andy dimensions of the output image were clarified. An experiment for verifying error sources is carried out and the result shows that the established system error comprehensive model can accurately identify the key error sources that have the greatest influence on the output image. The deviation between the numerical sensitivity prediction by the model and the actual value does not exceed 2.38%, which can achieve the accurate sensitivity prediction of the key error sources.
    $ {{\boldsymbol{T}}_{14ideal}} = {{\boldsymbol{T}}_{12p}} \cdot {{\boldsymbol{T}}_{23p}} \cdot {{\boldsymbol{T}}_{23s}} \cdot {{\boldsymbol{T}}_{34p}} $(1)

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    $ {{\boldsymbol{T}}_{14fact}} = {{\boldsymbol{T}}_{12p}} \cdot {{\boldsymbol{T}}_{12pe}} \cdot {{\boldsymbol{T}}_{23p}} \cdot {{\boldsymbol{T}}_{23pe}} \cdot {{\boldsymbol{T}}_{23s}} \cdot {{\boldsymbol{T}}_{23se}} \cdot {{\boldsymbol{T}}_{34p}} \cdot {{\boldsymbol{T}}_{34pe}} $(2)

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    $ {{\boldsymbol{T}}_{16ideal}} = {{\boldsymbol{T}}_{15p}} \cdot {{\boldsymbol{T}}_{56p}} $(3)

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    $ {{\boldsymbol{T}}_{16fact}} = {{\boldsymbol{T}}_{15p}} \cdot {{\boldsymbol{T}}_{15pe}} \cdot {{\boldsymbol{T}}_{56p}} \cdot {{\boldsymbol{T}}_{56pe}} $(4)

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    $ \boldsymbolT64ideal=\boldsymbolT16ideal1\boldsymbolT14ideal=(\boldsymbolT15p\boldsymbolT56p)1(\boldsymbolT12p\boldsymbolT23p\boldsymbolT23s\boldsymbolT34p)=\boldsymbolT65p\boldsymbolT51p\boldsymbolT12p\boldsymbolT23p\boldsymbolT23s\boldsymbolT34p $(5)

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    $ \boldsymbolT64fact=\boldsymbolT16fact1\boldsymbolT14fact=(\boldsymbolT15p\boldsymbolT15pe\boldsymbolT56p\boldsymbolT56pe)1(\boldsymbolT12p\boldsymbolT12pe\boldsymbolT23p\boldsymbolT23pe\boldsymbolT23s\boldsymbolT23se\boldsymbolT34p\boldsymbolT34pe)=\boldsymbolT65pe\boldsymbolT65p\boldsymbolT51pe\boldsymbolT51p\boldsymbolT12p\boldsymbolT12pe\boldsymbolT23p\boldsymbolT23pe\boldsymbolT23s\boldsymbolT23se\boldsymbolT34p\boldsymbolT34pe $(6)

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    $ \left\{ {Rcidealx=x+xsRcidealy=yRcidealz=z12+z23+z34z15z56} \right. $(7)

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    $ \left\{ {Rcfactx=δ23sxδ56xδ15x+δ34x+xsz34(ε15y+ε56yε23syε12yε23y)z12(ε15y+ε56y)+z15(ε15y+ε56y)+ε56yz56+δ12x+δ23xz23(ε15y+ε56yε12y)+xy(ε56zε15z+ε23sz+ε34z+ε12z+ε23z)Rcfacty=δ23syδ56yδ15y+δ34yxs(ε15z+ε56zε12zε23z)+z12(ε15x+ε56x)z15(ε15x+ε56x)ε56xz56+δ12y+δ23y+z23(ε15x+ε56xε12x)z34(ε23sxε56xε15x+ε12x+ε23x)x(ε15z+ε56zε23szε34zε12zε23z)+yRcfactz=δ23szδ56zz56δ15z+δ34z+xs(ε15y+ε56yε12yε23y)+z34+δ12z+z12z15+δ23z+z23x(ε23syε56yε15y+ε34y+ε12y+ε23y)y(ε15x+ε56xε23sxε34xε12xε23x)} \right. $(8)

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    $ \left\{ {xiideal=xcyiideal=fyczc+f} \right. $(9)

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    $ \dfrac{{{y_{ifact}}}}{f} = \dfrac{{{y_{iideal}}}}{f} + {k_1}{\left(\dfrac{{{y_{iideal}}}}{f}\right)^3} $(10)

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    $ \left\{ {xifact=xcyifact=fyczc+f+k1f(yczc+f)3} \right. $(11)

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    $ \left\{ {xerror=xifactxiidealyerror=yifactyiideal} \right. $(12)

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    $ xerror=δ12x+δ23x+δ23sx+δ34xδ15xδ56x+ε12y(z23+z34)+ε23yz34+ε23syz34+ε15y(z15z12z23z34)+ε56y(z15+z56z12z23z34)+y(ε56z+ε15zε12zε23zε23szε34z) $(13)

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    $yerror=fy+ΔyfL+ΔzfyfL+k1f((y+ΔyfL+Δz)3(yfL)3) $(14)

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    $ L = - ({{{z}}_{12}} + {{{z}}_{23}} + {{{z}}_{34}} - {{{z}}_{15}} - {{{z}}_{56}}) $()

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    $ Δy=δ12y+δ23y+δ23sy+δ34yδ15yδ56yε12x(z23+z34)ε23xz34ε23sxz34+ε15x(z12+z23+z34z15)+ε56x(z12+z23+z34z15z56)+ε23szx+ε34zx $()

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    $ Δz=δ12z+δ23z+δ23sz+δ34zδ15zδ56zε23syxε34yx+y(ε12x+ε23x+ε23sx+ε34xε15xε56x) $()

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    $ \theta = f({\theta _1},{\theta _2},\cdots,{\theta _n}) $(15)

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    $ \Delta \theta = \displaystyle\sum\limits_{i = 1}^n {\frac{{\partial f}}{{\partial {\theta _i}}} \cdot \Delta } {\theta _i} + o\left(\sqrt {\Delta {\theta _1}^2 + \cdots + \Delta {\theta _n}^2} \right) $(16)

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    $ {S_i} = \frac{{\partial f}}{{\partial {\theta _i}}}\left| {{\theta _j} = 0,j = 1,\cdots,n,j \ne i} \right. $(17)

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    $ D(y) = 1 + 3{k_1}{\left(\dfrac{y}{{f - L}}\right)^2} $(18)

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    $ S = \dfrac{{\displaystyle \sum\nolimits_{i = 1}^n {{e_i} \cdot {p_i}} - n\bar e \cdot \bar p}}{{\displaystyle \sum\nolimits_{i = 1}^n {{e_i}^2} - n{{\bar e}^2}}} \cdot \dfrac{{{s_p}}}{\mu } $(19)

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    Yuxuan Chen, Zhongjun Qiu, Junjie Tang. Mechanical-imaging comprehensive error modeling in line scan vision detection systems[J]. Infrared and Laser Engineering, 2022, 51(12): 20220282
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