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Abstract

Measurement technology with nanometer scale or higher level precision is the basis and guarantee for developing atomic and close-to-atomic scale manufacturing. Optical measurement has the advantages of high precision, wide range and real-time measurement. The precision of localizing a single imaging spot’s center is not limited by the diffraction limit and could reach nanometer scale. However, the shot noise of light and the dark current noise of the detector bring about a precision limit for optical measurement. Based on the Cramer-Rao lower bound theory, a precision limit estimation method for general imaging profiles is developed in this paper. Taking the typical Airy spot for example, the influences of the parameters such as signal-to-noise ratio, energy concentration and processing method on the positioning precision limit are analyzed, and suggestions and conclusions for improving the measurement precision are given. The precision limit of a laboratory imaging spot is calculated, which verifies that the conclusions are also suitable for the imaging profiles similar to the Airy spot. The research provides the analytical method and theoretical guidance for the application and optimization of optical measurement in atomic and close-to-atomic scale manufacturing.

Keywords:

atomic and close-to-atomic scale manufacturing/
optical measurement/
precision limit

Authors and contacts

Corresponding author:Xing Fei,xingfei@mail.tsinghua.edu.cn

Funds:Project supported by the National Key Research and Development Program of China (Grant No. 2016YFB0501201) and the National Project for Research and Development of Major Scientific Instruments (Grant No. 51827806)

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References

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Cited By

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	σ_all(Δ_std)/pixels
	$\sigma _{\rm{d}}^{\rm{2}}$ = 0	$\sigma _{\rm{d}}^{\rm{2}}$ = 25	$\sigma _{\rm{d}}^{\rm{2}}$ = 100	$\sigma _{\rm{d}}^{\rm{2}}$ = 400
${I_{\rm{0}}} = {\rm{400}}$	0.0125 (0.0001)	0.0136 (0.0003)	0.0157 (0.0011)	0.0217 (0.0033)
${I_{\rm{0}}} = {\rm{800}}$	0.0088 (0.0001)	0.0093 (0.0001)	0.0102 (0.0004)	0.0127 (0.0014)
${I_{\rm{0}}} = {\rm{1600}}$	0.0062 (0.0001)	0.0064 (0.0000)	0.0068 (0.0001)	0.0079 (0.0006)
${I_{\rm{0}}} = {\rm{3200}}$	0.0044 (0.0000)	0.0045 (0.0000)	0.0046 (0.0000)	0.0051 (0.0002)

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	R_F= 0.25	R_F= 0.50	R_F= 1.00	R_F= 2.00
σ_all/pixels	0.0335	0.0192	0.0136	0.0247
Δ_std/pixels	0.0211	0.0122	0.0003	0.0002
最优精度/pixels	0.0033 (边缘)	0.0065 (边缘)	0.0130 (边缘)	0.0244 (边缘)
最差精度/pixels	0.0803 (中心)	0.0566 (中心)	0.0139 (中心)	0.0250 (中心)
衍射极限/pixels	0.3050	0.6100	1.2200	2.4400

DownLoad: CSV

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Vol. 70, Issue 6 - 2021-03-20

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