• Optics and Precision Engineering
  • Vol. 30, Issue 4, 442 (2022)
Yuyan CAO1,2,*, Jianli WANG1,2, Zhichen WANG1,2, Hongwen Li1..., Yan ZHANG1,2, Hongliang CHU1 and Yuxia LI1|Show fewer author(s)
Author Affiliations
  • 1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun30033, China
  • 2University of Chinese Academy of Sciences, Beijing100049, China
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    DOI: 10.37188/OPE.20223004.0442 Cite this Article
    Yuyan CAO, Jianli WANG, Zhichen WANG, Hongwen Li, Yan ZHANG, Hongliang CHU, Yuxia LI. Wind disturbance simulation and optical performance prediction for large ground-based optical telescopes based on two-dimensional stochastic fields[J]. Optics and Precision Engineering, 2022, 30(4): 442 Copy Citation Text show less

    Abstract

    As the aperture of large ground-based optical telescopes increases, wind disturbance has become one of the most significant dynamic factors degrading the performance of telescopes. To investigate the influence and interaction principles of wind disturbance on the performance of telescopes, a time-history simulation of the wind disturbance response and performance prediction for telescopes were performed in the time domain. First, the structural parts of the telescope were simply introduced, and a dynamic model of the telescope was established using the finite element method. Using modal transformation, the dynamic model, expressed in nodal coordinates, was transformed into modal coordinates, thus greatly decreasing the model dimension and greatly improving the computational efficiency. Second, a time-history simulation method for wind speed was presented based on two-dimensional stochastic fields. The wind speed field in the doom was expressed as a two-dimensional stochastic field that varied according to the temporal and spatial frequencies. The numerical instability occurring in the Cholesky decomposition of the cross-power spectrum matrix in the spectral method was avoided by introducing the wave-number spectrum. The simulation efficiency was further improved by applying the fast Fourier transform (FFT) technique. Finally, using a ground-based telescope with a 2 m aperture as a case study, a time-history simulation of the wind speed, wind disturbance response, and system performance prediction for the telescope was performed. The simulation results showed that wind disturbances with a mean speed of 10 and 15 m/s would result in a maximum surface root mean square error of the primary mirror of approximately 45 and 70 nm, respectively. In addition, the wind disturbance acting on the secondary mirror and truss would mainly cause optical axis angle and position errors.
    Mq¨+Dq˙+Kq=F(1)

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    y=Coq(2)

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    q=Φqm(3)

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    Φ=[ϕ1ϕ2ϕn]=ϕ11ϕ12ϕ1nϕ21ϕ22ϕ2nϕnd1ϕnd2ϕndn(4)

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    Mmq¨m+Dmq˙m+Kmqm=ΦTF(5)

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    y=CoΦqm(6)

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    q¨m+2ZΩq˙m+Ω2qm=Mm-1ΦTF(7)

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    y=Cmqm(8)

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    x=x1x2=Ωqmq˙m(9)

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    x˙=Ax+Bu(10)

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    y=Cx(11)

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    X(t)=[X1(t),,Xj(t),,Xn(t)]T(12)

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    Sjk(ω)=12π-Rjk(τ)e-iωτdτ(13)

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    Rjk(τ)=-Sjk(ω)eiωτdω(14)

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    S(ω)=H(ω)HT*(ω)(15)

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    Xj(t)=2m=1jl=0N-1Hjm(ωl)Δωcos[ωlt+θjm(ωl)+ϕml]   j=1,2,,n(16)

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    S(ω,κ)=12π-S(ω)γ(ξ,ω)eiκξdξ(17)

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    X(x,t)=l=1Nκm=1Nω4S(κl,ωm)ΔκΔω[cos(κlx+ωmt+ϕml1)+cos(κlx-ωmt+ϕml2)](18)

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    对于二维空间上的两个不同位置(xi,yi)(xj,yj),其Davenport相干函数模型可以表达为: γ(ξx,ξy,ω)=exp-ω2πv10λx2ξx2+λy2ξy2

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    S(κx,κy,ω)=1(2π)2--S0(ω)γ(ξx,ξy,ω)eiκxξx+κyξydξxdξy=12πλxλy112πv10ω2×11+κxλx2+κyλy2/12πv10ω232S0(ω)(20)

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    SD(ω)=4vm2kln(z/z0)21200ω2πv102ω2π1+1200ω2πv1024/3(21)

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    X(x,t)=i=1Nxj=1Nym=1Nω4S(κxi,κyj,ωm)ΔκxΔκyΔω[cos(κxix+κyjy+ωmt+ϕijm1)+cos(κxix+κyjy-ωmt+ϕijm2)+cos(κxix-κyjy+ωmt+ϕijm3)+cos(κxix-κyjy-ωmt+ϕijm4)](22)

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    X(x,t)=Rel=0Nκ-1m=0Nω-1[Blm1eiκlx+ωmt+Blm2eiκlx-ωmt](23)

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    X(x,t)=Re{IFFTκ[IFFTω(Blm1)]+IFFTκ[FFTω(Blm2)]}(24)

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    X(p1Δx,p2Δy,p3Δt)=Re{n1=0M1-1n2=0M2-1n3=0M3-14Sκxn1,κyn2,ωn3ΔκxΔκyΔω[Bn1n2n31expi2πn1p1M1+i2πn2p2M2+i2πn3p3M3+Bn1n2n32expi2πn1p1M1+i2πn2p2M2-i2πn3p3M3+Bn1n2n33expi2πn1p1M1-i2πn2p2M2+i2πn3p3M3+Bn1n2n34expi2πn1p1M1-i2πn2p2M2-i2πn3p3M3]}(25)

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    X(p1Δx,p2Δy,p3Δt)=ReIFFTxIFFTyIFFTωBn1n2n31+IFFTxIFFTyFFTωBn1n2n32+IFFTxFFTyIFFTωBn1n2n33+IFFTxFFTyFFTωBn1n2n34(26)

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    v=vm+Δv(27)

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    F=12ρCDAv2(28)

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    F=Fm+Fw(29)

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    Fw=Fvv=vmΔv=ρCDAvmΔv(30)

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    Yuyan CAO, Jianli WANG, Zhichen WANG, Hongwen Li, Yan ZHANG, Hongliang CHU, Yuxia LI. Wind disturbance simulation and optical performance prediction for large ground-based optical telescopes based on two-dimensional stochastic fields[J]. Optics and Precision Engineering, 2022, 30(4): 442
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