• Acta Photonica Sinica
  • Vol. 50, Issue 9, 0912004 (2021)
Zhiying LIU, Guiyuan JIA, Tianxiang QIN, Yunhan HUANG, and Han ZHANG
Author Affiliations
  • Monitoring and Analysis Center, Changchun University of Science and Technology, Changchun130022, China
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    DOI: 10.3788/gzxb20215009.0912004 Cite this Article
    Zhiying LIU, Guiyuan JIA, Tianxiang QIN, Yunhan HUANG, Han ZHANG. Research on the Method of Determining the Optical Axis Based on Equivalent Nodal Point Theory[J]. Acta Photonica Sinica, 2021, 50(9): 0912004 Copy Citation Text show less

    Abstract

    Aiming at the current error problems in the calibration of the optical axis of the high-precision optical system, a method based on the equivalent nodal point theory to calibrate the actual optical axis of the system is proposed. By establishing reference coordinate system, the nodal point coordinate systems and the detector coordinate systems, and combining with homgenours coordinate transformation method, a mathematical model suitable for the optical axis calibration of an actual system is established. The optical system with a 100 mm focal length and a 20 mm distance of optical nodal points is taken as an example to analyze the factors that affect the calibration accuracy, and the result show that the calibration calculation error introduced by collimators, rotary table, and calibration model is less than 10''. It provides a method and reference for the accuracy analysis of optical axis calibration for different optical systems based on the equivalent nodal point theory.
    ΔO'=(RO-O')ΔαM(1)

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    βo2000βo000βo0-Oz'Oy'Oz'0-Ox''-Oy'Ox'0=0-Oz''Oy''Oz''0-Ox''-Oy'Ox''0(2)

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    0-βo2Oz'βo2Oy'βoOz'0-βoOx'-βoOy'βoOx'0=0-Oz''Oy''Oz''0-Ox''-Oy''Ox''0(3)

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    Oy''=Oy'=Oz''=Oz'=0Ox''=βoOx'(4)

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    dl0=1β0-1ld'l0=β0β0-1l(5)

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    limx-d'l0=limx-β0β0-1l=limx-f 'f '-xl=0(6)

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    R0=10000100001z0001(7)

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    O0O1'=R0O2'A'(8)

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    P1=100-XA010-YA00100001(9)

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    SX(θ)=10000cosθX-sinθX00sinθXcosθX00001(10)

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    SY(θ)=cosθY0-sinθY00100-sinθY0cosθY00001(11)

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    SX(θ)=10000cb2+c2-bb2+c200bb2+c2cb2+c200001(12)

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    SY(θ)=b2+c2a2+b2+c20-aa2+b2+c200100aa2+b2+c20b2+c2a2+b2+c200001(13)

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    P2=100-XA'010-YA'001-ZA'0001(14)

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    JJ'[O0-X0Y0Z0]=P2SY(θ)SX(θ)P1JJ'[O1-X1YZ1Z1](15)

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    D1=α0β000(16)

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    T1=10β001-α0-βα100001(17)

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    D2=0u10ν100+0u20ν200(18)

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    T2=100u1+u2010υ1+υ200100001(19)

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    D3=0w10t100+0w20t200(20)

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    T3=100w1+w2010t1+t200100001(21)

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    Zhiying LIU, Guiyuan JIA, Tianxiang QIN, Yunhan HUANG, Han ZHANG. Research on the Method of Determining the Optical Axis Based on Equivalent Nodal Point Theory[J]. Acta Photonica Sinica, 2021, 50(9): 0912004
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