White light interferometry with spectral-temporal demodulation for large-range thickness measurement

Yunlong Zhu; Zhuoran Li; Xu Lu; Yonggui Yuan; Jun Yang

doi:10.3788/COL202220.091201

Journals >Chinese Optics Letters >Volume 20 >Issue 9 >Page 091201 > Article

Chinese Optics Letters
Vol. 20, Issue 9, 091201 (2022)

White light interferometry with spectral-temporal demodulation for large-range thickness measurement

Yunlong Zhu^1、2, Zhuoran Li^1、2, Xu Lu^1、2, Yonggui Yuan^1、2、*, and Jun Yang^{2、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

show less

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

EndNote(RIS)

BibTex

Plain Text

show less

Experimental results for a single measurement of 500 nm SiO2 coating. (a) Reflectance spectrum F(k), Fref(k), and Fp(k). (b) Comparison of measured reflectance R(k) and theoretical model. (c) Normalized sum of squared errors for reflectance fitting between the experimental result and theoretical model at different values of input thickness. (d) Detailed view of (c) showing the minimum sum of squared errors.

Fig. 1. Experimental results for a single measurement of 500 nm SiO₂ coating. (a) Reflectance spectrum F(k), F_ref(k), and F_p(k). (b) Comparison of measured reflectance R(k) and theoretical model. (c) Normalized sum of squared errors for reflectance fitting between the experimental result and theoretical model at different values of input thickness. (d) Detailed view of (c) showing the minimum sum of squared errors.

Download full size | View in the Article

Experimental results for a single measurement of 68 µm Si film. (a) Reflectance spectrum F(k), Fref(k), and Fp(k). (b) Comparison of measured reflectance R(k) and theoretical model. (c) Normalized sum of squared errors for reflectance fitting between the experimental result and theoretical model at different values of input thickness. (d) Detailed view of (c) showing the minimum sum of squared errors.

Fig. 2. Experimental results for a single measurement of 68 µm Si film. (a) Reflectance spectrum F(k), F_ref(k), and F_p(k). (b) Comparison of measured reflectance R(k) and theoretical model. (c) Normalized sum of squared errors for reflectance fitting between the experimental result and theoretical model at different values of input thickness. (d) Detailed view of (c) showing the minimum sum of squared errors.

Download full size | View in the Article

Number of Measurement	Point A	Point B	Point C	Point D	Point E
1st	508.18	511.34	506.86	508.84	513.53
2nd	508.67	511.09	505.66	508.62	512.71
3rd	507.31	511.60	506.88	508.98	512.03
4th	507.65	511.36	506.52	508.26	512.81
5th	508.00	511.53	506.03	507.23	512.07
Average	507.96	511.38	506.39	508.39	512.63
Standard deviation	0.52	0.20	0.53	0.70	0.62

Table 1. Measurement Results for 500 nm SiO2 Coating (nm)

View in the Article

Number of Measurement	Point A	Point B	Point C	Point D	Point E
1st	68,613.59	68,348.37	68,394.21	68,299.25	68,554.65
2nd	68,646.33	68,345.09	68,364.74	68,243.59	68,528.46
3rd	68,613.59	68,322.17	68,387.66	68,282.88	68,557.92
4th	68,643.06	68,341.82	68,404.03	68,276.33	68,535.00
5th	68,597.22	68,358.19	68,390.93	68,295.98	68,593.94
Average	68,622.76	68,343.13	68,388.31	68,279.61	68,554.00
Standard deviation	21	13	15	22	26

Table 2. Measurement Results for 68 µm Si Film Using Envelope Method (nm)

View in the Article

Number of Measurement	Point A	Point B	Point C	Point D	Point E
1st	68,628.97	68,358.91	68,387.23	68,330.20	68,563.33
2nd	68,628.64	68,358.97	68,387.58	68,331.68	68,563.89
3rd	68,629.01	68,359.5	68,388.33	68,332.76	68,564.37
4th	68,628.80	68,359.38	68,388.35	68,332.86	68,564.22
5th	68,629.03	68,359.58	68,388.68	68,333.17	68,564.56
Average	68,628.89	68,359.27	68,388.04	68,332.13	68,564.07
Standard deviation	0.17	0.31	0.60	1.2	0.48

Table 3. Measurement Results for 68 µm Si Film Using the Proposed Method (nm)

View in the Article

Uncertainty Component	Source	Uncertainty Contribution
u(l_H)	Measurement results	0.31 nm (see Table 1)
		11.63 nm (see Table 2)
		0.54 nm (see Table 3)
u(l_f)	Nominal wavelength	$4.35 \times 10^{- 2} nm$
u(l_T)	Temperature change	$6.93 \times 10^{- 7}$ H (for ${SiO}_{2}$ )
u(l_T)	Temperature change	$2.89 \times 10^{- 6}$ H (for Si)
u(l_s)	Film installation	$2 \times 10^{- 9}$ H