Citation: Zhao, Y.; Lin, Y.; Li, D.;
Wang, F.; Cheng, B.; Lin, Q.; Hu, Z.;
Wu, B. Improved Accuracy for
Measurement of Filament Diameter
Based on Image-Based Fitting
Method. Photonics 2022, 9, 556.
https://doi.org/10.3390/
photonics9080556
Received: 23 June 2022
Accepted: 3 August 2022
Published: 8 August 2022
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Communication
Improved Accuracy for Measurement of Filament Diameter
Based on Image-Based Fitting Method
Yingpeng Zhao , Yutong Lin, Dianrong Li, Feichen Wang, Bing Cheng, Qiang Lin, Zhenghui Hu and Bin Wu *
Zhejiang Provincial Key Laboratory of Quantum Precision Measurement, College of Science, Zhejiang University
of Technology, Hangzhou 310023, China
* Correspondence: wubin@zjut.edu.cn
Abstract:
Laser diffraction (LD) has many obvious advantages for measuring. However, the mea-
surement accuracy is limited by a number of factors, such as imaging noise, sensor threshold, and
fitting methods. In this paper, we present a novel method for measuring filament diameter based
on image-based fitting, which maintains more information. Before fitting the diffraction image,
image processing is applied to solve the problem of image noise and the non-linear response of the
charge-coupled device (CCD). Then, a fitting formula is established based on the distribution of laser
intensity on a diffraction image, and the fitted results are solved with the Levenberg–Marquardt (LM)
algorithm. Finally, the initial parameters of a fit are obtained by calculation, which speeds up the
calculation and improves the accuracy of the fitting. The measurement accuracy of this method is
verified by experimental and theoretical analysis. In experiments, the filament diameters of 125 and
125.2
µ
m are measured with a relative error of approximately 0.12%, Furthermore, the superiority
of this method is demonstrated by comparing the measurements with other methods. To verify the
stability of the measurements, filament diameters of 110–180
µ
m are chosen to be measured with a
relative standard deviation of less than 0.14%.
Keywords: laser diffraction measurement; fraunhofer diffraction; image processing; fitting
1. Introduction
Laser diffraction (LD) has been applied to measure the dimensions of tiny objects based
on the principle of the Fraunhofer diffraction, which is used in the powder industry [
1
–
3
],
mechanical measurements [
4
], and the chemical field [
5
,
6
]. In particular, LD has been
chosen as the method for measuring the filament diameter because it is a non-contact
method, allowing better performance compared with other contact methods.
The extraction of measurement information from diffraction fringes is generally
adopted in LD measurements [
7
,
8
]. For example, the 10–200 mm wire diameter is measured
based on an accurate evaluation of the diffraction pattern minimum position with a relative
error of 0.7% of the measurement [
9
]. However, the process of compressing diffraction
images into one-dimensional fringes can result in a significant loss of useful information.
Currently, many improved methods of diffraction measurement are available to increase
the accuracy of measurements. For example, 5–30
µ
m diameter fibers were measured by
a combination of LD and scanning electron microscopy (SEM) [
10
] with an accuracy of
approximately 0.1
µ
m. However, the complexity of measuring without SEM diffraction
is simplified. Songtao Yan [
11
] et al. proposed a new method for measuring filament
diameter based on the so-called “double diffraction”, which can measure filament diame-
ters of 100.2–140.8
µ
m with an accuracy of about 0.9
µ
m. In addition, Khajornrungruang
P. [
12
] subtracted a transparent light component from the diffracted light distribution of
the micro-tool to enhance diffraction pattern characteristics, which measures micro tools
of
10–30 µm
diameter with less than 0.4
µ
m difference compared to SEM. These methods
extract measurement information from the diffraction pattern by borrowing fitting methods,
Photonics 2022, 9, 556. https://doi.org/10.3390/photonics9080556 https://www.mdpi.com/journal/photonics
