• Chinese Optics Letters
  • Vol. 20, Issue 9, 091201 (2022)
Yunlong Zhu1、2, Zhuoran Li1、2, Xu Lu1、2, Yonggui Yuan1、2、*, and Jun Yang2、3、4、**
Author Affiliations
  • 1Key Laboratory of In-fiber Integrated Optics, Ministry of Education of China, Harbin Engineering University, Harbin 150001, China
  • 2College of Physics and Optoelectronic Engineering, Harbin Engineering University, Harbin 150001, China
  • 3Guangdong Provincial Key Laboratory of Information Photonics Technology (Guangdong University of Technology), Guangzhou 510006, China
  • 4School of Information Engineering, Guangdong University of Technology, Guangzhou 510008, China
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    DOI: 10.3788/COL202220.091201 Cite this Article Set citation alerts
    Yunlong Zhu, Zhuoran Li, Xu Lu, Yonggui Yuan, Jun Yang. White light interferometry with spectral-temporal demodulation for large-range thickness measurement[J]. Chinese Optics Letters, 2022, 20(9): 091201 Copy Citation Text show less

    Abstract

    Film thickness measurement can be realized using white light interferometry, but it is challenging to guarantee high precision in a large range of thicknesses. Based on scanning white light interferometry, we propose a spectral-temporal demodulation scheme for large-range thickness measurement. The demodulation process remains unchanged for either coatings or substrate-free films, while some adjustments are made according to the estimated optical thickness. Experiments show that the single-point repeatabilities for 500 nm SiO2 coating and 68 µm substrate-free Si film are no more than 0.70 nm and 1.22 nm, respectively. This method can be further developed for simultaneous measurement of surface profile and film thickness.
    E0(k)=A0(k)eiθ(k),

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    E1(k)=rp(k)E0(k)+(1rp2(k))r(k)E0(k)eikL,

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    R(k)=|r(k)|2,

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    r(k)=r1(k)+r2(k)e2ikn1(k)d1+r1(k)r2(k)e2ikn1(k)d,

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    r1(k)=1n1(k)1+n1(k),

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    r2(k)=n1(k)n2(k)n1(k)+n2(k).

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    Rp(k)=|rp(k)|2=rp2(k),

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    Tp(k)=1Rp(k)=1rp2(k).

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    E(k,S)=q1E1(k)+q2E1(k)eikS=E0(k)(rp+Tp(k)r(k)eikL)(q1+q2eikS),

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    I(S)=k|E(k,S)|2=kA02(k)|rp(k)q1+rp(k)q2eikS+Tp(k)|r(k)|q1eikL+iφ(k)+Tp(k)|r(k)|q2eik(L+S)+iφ(k)|2,

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    If(S)=4q1q2kA02(k)(U1(k)+U2(k)+U3(k)),

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    U1(k)=(Rp(k)+Tp2(k)R(k))coskS,

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    U2(k)=rp(k)Tp(k)|r(k)|cos(k(L+S)+φ(k)),

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    U3(k)=rp(k)Tp(k)|r(k)|cos(k(LS)+φ(k)).

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    F(k)=4q1q2A02(k)(Rp(k)+Tp2(k)R(k)).

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    Fp(k)=4q1q2A02(k)Rp(k).

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    Fref(k)=4q1q2A02(k)(Rp(k)+Tp2(k)Rref(k)),

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    Rref(k)=|rref(k)|2=(1nref(k)1+nref(k))2.

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    R(k)=F(k)Fp(k)Fref(k)Fp(k)Rref(k).

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    W(din)=k|Rth(din,k)R(k)|2,

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    Δdλc2ng(λc),

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    dini=d0±mΔd,

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    α(k)=arg(Hilbert(R(k))).

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    β(k)=cos(α(k)).

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    Yunlong Zhu, Zhuoran Li, Xu Lu, Yonggui Yuan, Jun Yang. White light interferometry with spectral-temporal demodulation for large-range thickness measurement[J]. Chinese Optics Letters, 2022, 20(9): 091201
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