• Optics and Precision Engineering
  • Vol. 29, Issue 12, 2783 (2021)
Yi-Lan ZHANG, Hao-dong SHI*, Chao WANG, Ying-chao LI..., Zhuang LIU, Su ZHANG, Jia-yu WANG and Hui-lin JIANG*|Show fewer author(s)
Author Affiliations
  • College of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun130022, China
  • show less
    DOI: 10.37188/OPE.20212912.2783 Cite this Article
    Yi-Lan ZHANG, Hao-dong SHI, Chao WANG, Ying-chao LI, Zhuang LIU, Su ZHANG, Jia-yu WANG, Hui-lin JIANG. Analysis of polarization aberration of space optical system based on freeform surface[J]. Optics and Precision Engineering, 2021, 29(12): 2783 Copy Citation Text show less

    Abstract

    The influence of polarization aberration on detection accuracy and imaging quality in a spatial optical system containing freeform surfaces was analyzed. First, based on the Jones notation, a freeform surface off-axis optical system with fringe Zernike polynomials as the characterizing function was proposed. Second, the polarization aberration analysis model of reflective optical system with freeform surface was developed. The influence of fringe Zernike polynomial low-order coefficients on the polarization aberration distribution of the field of view off-axis optical system was analyzed. Then, by tracing the polarized light through full field of view and by comparing before and after the freeform surface was introduced, the freeform surface effected on three types of polarization aberrations, that is, phase aberration, retardance, and diattenuation, of the field-bias optical system were verified. Finally, a wide-field off-axis three-mirror optical system with freeform surface and the polarization aberration of the full field of view were analyzed. The analysis results show that the phase aberration distribution is consistent with the freeform surface sagittal height distribution, and the retardance and diattenuation caused by the freeform surface account for 52.5% of the retardance and diattenuation of the total system, respectively. Improving this polarization characteristic change is important for the design of very high-precision optical systems such as deep-space astronomical telescopes.
    σ0=1001,σ1=100-1σ2=0110,σ3=0-ii0(1)

    View in Article

    J=exp(c0σ0+c1σ1+c2σ2+c3σ3)=   exp[(ρ0+iϕ0)σ0+(ρ1+iϕ1)σ1+(ρ2+iϕ2)σ2+(ρ3+iϕ3)σ3],(2)

    View in Article

    J(h,ρ,λ)=j11(h,ρ,λ)j12(h,ρ,λ)j21(h,ρ,λ)j22(h,ρ,λ)(3)

    View in Article

    W(h,ρ,λ)=λ2πϕ0(h,ρ,λ)(4)

    View in Article

    J(H,ρ)=expP00000σ0+                                                          constant pistonP02000HHσ0+                                               quadratic pistonP01110Hρσ0+                                                 tiltP00200ρρσ0+                                                   defocusP00400(ρρ)2σ0+                                              spherical aberrationP01310(Hρ)(ρρ)σ0+                                 coma  P02200(HH)(ρρ)σ0+                                field curvature12P02220(HH)(ρρ)+H2ρ2σ0+     astigmatismP03110(HH)(Hρ)σ0+                              distortionP04000(HH)2σ0+                                          quartic pistonhigher order terms(5)

    View in Article

    CiZi(ρ,ϕ)=CxZx(ρ,ϕ)CyZy(ρ,ϕ)(6)

    View in Article

    Cx/y=Cx/yeimαx/y(7)

    View in Article

    Cx/y=Cx2+Cy2αx/y=π2-1marctanCyCx(8)

    View in Article

    δx/y(ρ)=(n2-n1)λCx/yZ(ρ)(9)

    View in Article

    δx/y(ρ)=Vx/yZ(ρ)(10)

    View in Article

    ϕ0(h,ρ,λ)=2πλδx/y(ρ)=2πλVx/yZ(ρ+Δh)(11)

    View in Article

    ϕ0(ρ)=ϕ0(ρ'+Δh)(12)

    View in Article

    Δh=y¯yH(13)

    View in Article

    ϕ0(h,ρ,λ)=2πλδx/y(ρ)=2πλVx/yZ(ρ+Δh)(14)

    View in Article

    ϕ0,5/6,nonstop(h,ρ,λ)=2πλδ5/6,nonstop=2πλV5/6ρ2+2y¯yV5/6H*ρ+y¯y2V5/6H2ϕ0,7/8,nonstop(h,ρ,λ)=2πλδ7/8,nonstop=2πλ[3V7/8(ρ+Δh)][(ρ+Δh)(ρ+Δh)]=                                        2πλ3(V7/8ρ)(ρρ)+3y¯y(V7/8Hρ2)+3y¯y2(HH)(V7/8ρ)+                                        6y¯y(ρρ)(V7/8H)+6y¯y2(V7/8H)(Hρ)+3y¯y3(HH)(V7/8H)ϕ0,9,nonstop(h,ρ,λ)=2πλδ9,nonstop=2πλ6V9[(ρ+Δh)(ρ+Δh)]2=                                     2πλ6V9(ρρ)2+12V9y¯y2H2ρ2+6V9y¯y4(HH)2+                                 24V9y¯y(Hρ)(ρρ)+24V9y¯y3(HH)(Hρ)+24V9y¯y2(HH)(ρρ)(15)

    View in Article

    Ptotal=q=1QPq(16)

    View in Article

    Eout=PtotalEin(17)

    View in Article

    Pq=sx,qpx,qkx,qsy,qpy,qky,qsz,qpz,qkz,qas,q000ap,q0001sx,q-1sy,q-1sz,q-1px,q-1py,q-1pz,q-1kx,q-1ky,q-1kz,q-1(18)

    View in Article

    sq-1=kq-1×kqkq-1×kq,pq-1=kq-1×sq-1sq=sq-1,pq=kq×sq(19)

    View in Article

    Ptotal=UDV=kx,Qux,1ux,2ky,Quy,1uy,2kz,Quz,1uz,21000Λ1000Λ2kx,0ky,0kz,0vx,1vy,1vz,1vx,2vy,2vz,2(20)

    View in Article

    Ptotalv1=Λ1u1,Ptotalv2=Λ2u2,Ptotalk0=kQ(21)

    View in Article

    Yi-Lan ZHANG, Hao-dong SHI, Chao WANG, Ying-chao LI, Zhuang LIU, Su ZHANG, Jia-yu WANG, Hui-lin JIANG. Analysis of polarization aberration of space optical system based on freeform surface[J]. Optics and Precision Engineering, 2021, 29(12): 2783
    Download Citation