• Chinese Optics Letters
  • Vol. 16, Issue 8, 081203 (2018)
Lei Zhang1、*, Sheng Zhou1, Dong Li2, Jingsong Li1, and Benli Yu1
Author Affiliations
  • 1Key Laboratory of Opto-Electronic Information Acquisition and Manipulation, Ministry of Education, Anhui University, Hefei 230601, China
  • 2Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China
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    DOI: 10.3788/COL201816.081203 Cite this Article Set citation alerts
    Lei Zhang, Sheng Zhou, Dong Li, Jingsong Li, Benli Yu. Model-based adaptive non-null interferometry for freeform surface metrology[J]. Chinese Optics Letters, 2018, 16(8): 081203 Copy Citation Text show less

    Abstract

    A model-based adaptive non-null interferometry (MANI) is proposed for steep optical freeform surfaces in situ testing. The deformable mirror (DM) affording the flexible compensation is monitored with the beam in the interferometer by a wavefront sensor. The residual wavefront aberration in the non-null interferogram is eliminated by the multi-configuration ray tracing algorithm based on the system model, especially the DM surface model. The final figure error can be extracted together with the surface misalignment aberration correction. Experiments proving the feasibility of the MANI are shown.
    WF(E+SDM+Wmis+WmisDM)+Esys,(1)

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    Wf(E+SDM+Wmis).(2)

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    W_mf(E+SDM_m+Wmis_m),(3)

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    W¯_mf(E¯+W¯mis_m+S¯DM_m),(4)

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    (EE¯)+(Wmis_mW¯mis_m)f1(W_m)f1(W¯_m).(5)

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    (EE¯)·(Wmis_mW¯mis_m)=i=537(aia¯i)Zi·i=14(bi_mb¯i_m)Zi=0.(6)

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    M(EE¯)2+m=1M(Wmis_mW¯mis_m)2m=1M[f1(W_m)f1(W¯_m)]2,(7)

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    (EE¯)2=1M{m=1M[f1(W_m)f1(W¯)m)]2m=1M[g(SDM_m,Emis)g(S¯DM_m,E¯mis)]2}=Min.(8)

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    Lei Zhang, Sheng Zhou, Dong Li, Jingsong Li, Benli Yu. Model-based adaptive non-null interferometry for freeform surface metrology[J]. Chinese Optics Letters, 2018, 16(8): 081203
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