Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

doi:10.1088/1674-1056/26/5/054202

中国物理B ›› 2017, Vol. 26 ›› Issue (5): 54202-054202.doi: 10.1088/1674-1056/26/5/054202

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇下一篇

Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

Xiao-He Luo(罗晓贺), Hui Mei(惠梅), Qiu-Dong Zhu(朱秋东), Shan-Shan Wang(王姗姗), Yin-Long Hou(侯银龙)

Beijing Key Laboratory of Precision Photoelectric Measuring Instrument and Technology, School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China

收稿日期:2016-10-24 修回日期:2016-12-19 出版日期:2017-05-05 发布日期:2017-05-05
通讯作者: Hui Mei E-mail:huim@bit.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 61475018).

Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

Xiao-He Luo(罗晓贺), Hui Mei(惠梅), Qiu-Dong Zhu(朱秋东), Shan-Shan Wang(王姗姗), Yin-Long Hou(侯银龙)

Beijing Key Laboratory of Precision Photoelectric Measuring Instrument and Technology, School of Optoelectronics, Beijing Institute of Technology, Beijing 100081, China

Received:2016-10-24 Revised:2016-12-19 Online:2017-05-05 Published:2017-05-05
Contact: Hui Mei E-mail:huim@bit.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 61475018).

摘要/Abstract

摘要： The intensity distribution in Fresnel diffraction through a slit includes numerous small fluctuations referred to as ripples. These ripples make the modelling of the intensity distribution complicated. In this study, we examine the characteristics of the Fresnel diffraction intensity distribution to deduce the rule for the peak position and then propose two types of quantum-mathematical models to obtain the distance between the edge and the peak point. The analysis and simulation indicate that the error in the models is below 0.50 μm. The models can also be used to detect the edges of a diffraction object, and we conduct several experiments to measure the slit width. The experimental results reveal that the repetition accuracy of the method can reach 0.23 μm.

关键词: Fresnel diffraction, slit, peak point, edge

Abstract: The intensity distribution in Fresnel diffraction through a slit includes numerous small fluctuations referred to as ripples. These ripples make the modelling of the intensity distribution complicated. In this study, we examine the characteristics of the Fresnel diffraction intensity distribution to deduce the rule for the peak position and then propose two types of quantum-mathematical models to obtain the distance between the edge and the peak point. The analysis and simulation indicate that the error in the models is below 0.50 μm. The models can also be used to detect the edges of a diffraction object, and we conduct several experiments to measure the slit width. The experimental results reveal that the repetition accuracy of the method can reach 0.23 μm.

Key words: Fresnel diffraction, slit, peak point, edge

中图分类号: (Diffraction and scattering)

42.25.Fx

42.25.Gy (Edge and boundary effects; reflection and refraction) 46.40.Cd (Mechanical wave propagation (including diffraction, scattering, and dispersion))

罗晓贺, 惠梅, 朱秋东, 王姗姗, 侯银龙. Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit[J]. 中国物理B, 2017, 26(5): 54202-054202.

Xiao-He Luo(罗晓贺), Hui Mei(惠梅), Qiu-Dong Zhu(朱秋东), Shan-Shan Wang(王姗姗), Yin-Long Hou(侯银龙). Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit[J]. Chin. Phys. B, 2017, 26(5): 54202-054202.

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Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

Quantum-mathematical model of edge and peak point in Fresnel diffraction through a slit

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