Global Curve Fitting for Structured Illumination Microscopy with High Thickness Detection Resolution

Kejun Yang; Chenhaolei Han; Lei Liu; Jinhua Feng; Zhongye Xie; Song Hu; Yan Tang

doi:10.3788/AOS202242.2012001

Acta Optica Sinica, Volume. 42, Issue 20, 2012001(2022)

Global Curve Fitting for Structured Illumination Microscopy with High Thickness Detection Resolution

Kejun Yang^1,2, Chenhaolei Han^1,2, Lei Liu^1,2, Jinhua Feng¹, Zhongye Xie³, Song Hu¹, and Yan Tang^1、*

¹State Key Lab of Optical Technologies on Nano-Fabrication and Micro-Engineering, Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, Sichuan , China

²University of Chinese Academy of Sciences, Beijing 100049, China

³School of Electrical Engineering & Intelligentization, Dongguan University of Technology, Dongguan 523808, Guangdong , China

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Figures & Tables(9)

Fig. 1. Principle of transparent coating structure detected by SIM

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Fig. 2. MDRCs in three different situations

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Fig. 3. Simulated MDRCs with noise and separation results of overlapping peaks

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Fig. 4. Schematic of experimental system^[23]

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Fig. 5. Step region on the edge of patterned sample detected by proposed method. (a) Three-dimensional topography; (b) cross-section profile when $x =$ 143 pixel; (c) MDRC at the pixel point (145,263) and fitting result; (d) MDRC at the pixel point (72,114), the fitting result, and separation result of overlapping peaks

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Fig. 6. Thickness at pixel point of (72,114) obtained from repetitive experiments

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Table 1. Thickness measurement resolution by maximum-point method and GCF method under different system parameters

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Table 1. Thickness measurement resolution by maximum-point method and GCF method under different system parameters

Ratio of modulation coefficient $(R_{2} / R_{1})$	Normalized spatial frequency	Magnification	Numerical aperture（NA）	Thickness measurement resolution /nm
Ratio of modulation coefficient $(R_{2} / R_{1})$	Normalized spatial frequency	Magnification	Numerical aperture（NA）	Maximum-point method	GCF method
1	0.5	100	0.9	487	198
		50	0.8	771	340
		20	0.45	3920	1585
	0.3	100	0.9	594	237
		50	0.8	1252	448
		20	0.45	6389	1760
0.5	0.5	100	0.9	483	175
		50	0.8	762	313
		20	0.45	3762	1316
	0.3	100	0.9	588	194
		50	0.8	1238	422
		20	0.45	6101	1552
0.1	0.5	100	0.9	565	201
		50	0.8	898	374
		20	0.45	4111	1742
	0.3	100	0.9	689	256
		50	0.8	1458	497
		20	0.45	6535	2033

Table 2. Performance comparison of GCF method and unconstrained iterative method under different FWHM setting modes

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Table 2. Performance comparison of GCF method and unconstrained iterative method under different FWHM setting modes

Mode	Default	Theoretical	Experimental	Fixed
Value /nm	（1，1）	（696，696）	（934，934）	（800，696）
Variable range /nm	［0，3000］	［0，3000］	［0，3000］	Fixed
Number of iterations （unconstrained）	87	21	52	15
Number of iterations （constrained by GCF）	44	2	16	2
Measurement error /nm （unconstrained）	18.975	3.651	10.619	2.142
Measurement error /nm （constrained by GCF）	3.530	0.529	1.045	0.134

Table 3. Performance comparison of GCF method and unconstrained iterative method in different start point of $R_{2}$

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Table 3. Performance comparison of GCF method and unconstrained iterative method in different start point of $R_{2}$

Reflection coefficient R₂	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
RMSE of 50 iterations /nm（unconstrained）	2.588	1.817	1.260	0.422	1.203	1.935	2.464	3.198	4.000	5.212
Standard deviation /nm（unconstrained）	9.148	5.687	2.801	1.491	2.376	6.057	8.233	11.054	15.418	19.009
RMSE of 50 iterations /nm（constrained by GCF）	0.643	0.085	0.532	0.015	0.071	0.359	0.444	0.498	0.177	0.181
Standard deviation /nm （constrained by GCF）	1.846	1.611	0.716	0.136	0.684	1.657	2.174	2.468	2.529	2.775

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Kejun Yang, Chenhaolei Han, Lei Liu, Jinhua Feng, Zhongye Xie, Song Hu, Yan Tang. Global Curve Fitting for Structured Illumination Microscopy with High Thickness Detection Resolution[J]. Acta Optica Sinica, 2022, 42(20): 2012001

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Paper Information

Category: Instrumentation, Measurement and Metrology

Received: Feb. 22, 2022

Accepted: Apr. 24, 2022

Published Online: Oct. 18, 2022

The Author Email: Yan Tang (tangyan@ioe.ac.cn)

DOI:10.3788/AOS202242.2012001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Thickness measurement resolution by maximum-point method and GCF method under different system parameters

Table 1. Thickness measurement resolution by maximum-point method and GCF method under different system parameters

Table 2. Performance comparison of GCF method and unconstrained iterative method under different FWHM setting modes

Table 2. Performance comparison of GCF method and unconstrained iterative method under different FWHM setting modes

Table 3. Performance comparison of GCF method and unconstrained iterative method in different start point of R2

Table 3. Performance comparison of GCF method and unconstrained iterative method in different start point of R2

Table 3. Performance comparison of GCF method and unconstrained iterative method in different start point of $R_{2}$

Table 3. Performance comparison of GCF method and unconstrained iterative method in different start point of $R_{2}$