• Chinese Optics Letters
  • Vol. 15, Issue 11, 111203 (2017)
Yinlong Hou, Lin Li, Shanshan Wang*, and Qiudong Zhu
Author Affiliations
  • School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China
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    DOI: 10.3788/COL201715.111203 Cite this Article Set citation alerts
    Yinlong Hou, Lin Li, Shanshan Wang, Qiudong Zhu. 3D shape reconstruction of parabolic trough collector from gradient data based on slope stitching approach[J]. Chinese Optics Letters, 2017, 15(11): 111203 Copy Citation Text show less

    Abstract

    A method based on slope stitching for measurement of a large off-axis parabolic trough collector is proposed and applied to the surface shape reconstructed from the gradient data acquired by using the reverse Hartmann test. The entire reflector is divided into three sections with overlapping zones along the concentration direction. A mathematical model for the slope stitching algorithm is developed. An improved reconstruction method combining Zernike slope polynomials iterative fitting with the Southwell integration algorithm is utilized to recover the real three-dimensional (3D) shape of the collector. The efficiency and validity of the improved reconstruction method and the stitching algorithm are experimentally verified.
    N=RI|RI|,(1)

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    I(x,y)=a+bcos[ϕ(x,y)+δ],(2)

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    ϕ(x,y)=arctan[i=116Ii(x,y)sin(i2π16)i=116Ii(x,y)cos(i2π16)].(3)

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    {S12(x,y)=C1(ml+x,y)+C2(x,y)2S23(x,y)=C2(ml+x,y)+C3(x,y)2for{x=1,2,,ly=1,2,,n,(4)

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    {S12(x,y)=lx+11+l·C1(ml+x,y)+x1+l·C2(x,y)S23(x,y)=lx+11+l·C2(ml+x,y)+x1+l·C3(x,y).(5)

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    W(x,y)=i=0NCiZi(x,y),(6)

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    {W(x,y)x=i=0NCiZi(x,y)xW(x,y)y=i=0NCiZi(x,y)y.(7)

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    S=P*C,(8)

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    {(hm+1,nhm,n)·Δ=(sm+1,nx+sm,nx)/2=sm+1/2,nx(hm,n+1hm,n)·Δ=(sm,n+1y+sm,ny)/2=sm,n+1/2y,(9)

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    Yinlong Hou, Lin Li, Shanshan Wang, Qiudong Zhu. 3D shape reconstruction of parabolic trough collector from gradient data based on slope stitching approach[J]. Chinese Optics Letters, 2017, 15(11): 111203
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