• Laser & Optoelectronics Progress
  • Vol. 60, Issue 23, 2312002 (2023)
Fengrui Ma, Fajie Duan*, Wenzheng Liu, Xiao Fu, and Cong Zhang
Author Affiliations
  • State Key Lab of Precision Measuring Technology & Instruments, Tianjin University, Tianjin 300072, China
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    DOI: 10.3788/LOP223032 Cite this Article Set citation alerts
    Fengrui Ma, Fajie Duan, Wenzheng Liu, Xiao Fu, Cong Zhang. Self-Calibration Method for Roll Angle Measurements of Dual Beams Based on Polarization[J]. Laser & Optoelectronics Progress, 2023, 60(23): 2312002 Copy Citation Text show less

    Abstract

    When dual beams are used to measure the roll angle, the angle between the double-collimated beams is easily disturbed by environmental changes, mechanical deformation, and other factors, which seriously affect measurement accuracy. The roll angle measured by the dual beam is sensitive to the spot position. By contrast, the roll angle measured by polarization depends on the polarization state of the incident light and is relatively less affected by laser angle drift. Therefore, to improve the accuracy of the roll error in five-degree-of-freedom measurements at long distances, a polarization-based roll angle optical path is proposed. The path is used to measure the roll angle of the sensor at different positions, calculate the angle between the dual beams, and perform calibrations, thus improving measurement accuracy. The test results show that in the measurement range of 0.75‒2.00 m, the roll angle measurement error after compensation is reduced by 88.97%. This meets the long-distance roll angle measurement requirements for high precision and easy installation.
    εdroll=εdz=δyr-δylL=ΔyQD2-ΔyQD1L
    Δεdroll=θupDL
    I1=1,0,0T
    Ι1'=SCI1=1-εzCεyCεzC1-εxC-εyCεxC1100=1εzC-εyC
    N1'=SM1N1=1-εzM1εyM1εzM11-εxM1-εyM1εxM11-220-22=-22-22εyM1-22εzM1+22εxM122εyM1-22
    I2'=R1'I1'=-2εyM1εxM1-εzM1-1εxM1-εzM11εxM1-εzM1-1εxM1-εzM12εyM11εzC-εyC=εyC-2εyM1εzC+εxM1-εzM1-1
    N2'=SBS1N2=1-εzBS1εyBS1εzBS11-εxBS1-εyBS1εxBS11-22022=-22+22εyBS1-22εzBS1-22εxBS122εyBS1+22
    I4'=R2'I2'=2εyBS1-εxBS1-εzBS11-εxBS1-εzBS11εxBS1+εzBS11εxBS1+εzBS1-2εyBS1εyC-2εyM1εzC+εxM1-εzM1-1=-1εzC+εxM1-εzM1-εxBS1-εzBS1εyC-2εyM1+2εyBS1
    N3'=SM2N3=1-εzM2εyM2εzM21-εxM2-εyM2εxM21220-22=22-22εyM222εzM2+22εxM2-22εyM2-22
    I5'=R3'I4'=2εyM2-εxM2-εzM21-εxM2-εzM21εxM2+εzM21εxM2+εzM2-2εyM2-1εzC+εxM1-εzM1-εxBS1-εzBS1εyC-2εyM1+2εyBS1=εyC-2εyM1+2εyBS1-2εyM2εzC+εxM1-εzM1-εxBS1-εzBS1+εxM2+εzM2-1
    Δδyr=-εzCl1-εzC+εxM1-εzM1l2+l3Δδyl=-εzCl1-εzC+εxM1-εzM1l2-εzC+εxM1-εzM1-εxBS1-εzBS1l-εzC+εxM1-εzM1-εxBS1-εzBS1+εxM2+εzM2l4Δεz=Δδyr-Δδyll
    Ei=[ExEy]T=[E0]T
    MT=cosεpz-sinεpzsinεpzcosεpz
    MPBS=cosπ4-sinπ4sinπ4cosπ4
    Eo=MPBSMTEi=cosπ4-sinπ4sinπ4cosπ4cosεpz-sinεpzsinεpzcosεpzE0=Ecosπ4+εpzEsinπ4+εpz
    IRr=I0cos2π4+εpzITr=I0sin2π4+εpz
    ΔI=ITr-IRr=I0sin2π4+εpz-I0cos2π4+εpz=I0sin2εpz
    εproll=εpz=12arcsinΔII0ΔI2I0
    εproll=εpz+εpl
    ITr=IpTp+IsTsIRr=IpRp+IsRs
    ε¯proll=110ti=110tεproll,i
    θup=Lε¯proll_B-ε¯proll_A-εdroll_B-εdroll_ADAB
    εcdroll=δyr-δyl+θupDL
    δyr=-ΔyQD1=-Ayr4σyr4+Ayr3σyr3+Ayr2σyr2+Ayr1σyr
    εpr=Apr4ε¯proll4+Apr3ε¯proll3+Apr2ε¯proll2+Apr1ε¯proll
    Fengrui Ma, Fajie Duan, Wenzheng Liu, Xiao Fu, Cong Zhang. Self-Calibration Method for Roll Angle Measurements of Dual Beams Based on Polarization[J]. Laser & Optoelectronics Progress, 2023, 60(23): 2312002
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