Filament diameter measurement system based on dual diffraction

$Filament diameter measurement system based on dual diffraction (it reverts back to a traditional diffraction system if the filter and the grating are removed).$

Fig. 1. Filament diameter measurement system based on dual diffraction (it reverts back to a traditional diffraction system if the filter and the grating are removed).

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$Setup of a filament diameter measurement system based on dual diffraction.$

Fig. 2. Setup of a filament diameter measurement system based on dual diffraction.

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$Diffraction of dual diffraction method measured by line camera (100.2 μm).$

Fig. 3. Diffraction of dual diffraction method measured by line camera (100.2 μm).

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$Diffraction of traditional method measured by line camera (100.2 μm).$

Fig. 4. Diffraction of traditional method measured by line camera (100.2 μm).

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Table 1. Theoretical Values of Magnification for Different m and n

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Table 1. Theoretical Values of Magnification for Different m and n

	$m$
$n$	1	2	3	4	5	6	7	8
1	2.74	2.02	1.72	1.55	1.45	1.38	1.33	1.29
2	4.51	3.04	2.44	2.12	1.91	1.77	1.67	1.59
3	6.27	4.07	3.17	2.69	2.38	2.17	2.01	1.89
4	8.06	5.11	3.91	3.26	2.85	2.56	2.36	2.20
5	9.87	6.16	4.66	3.84	3.33	2.97	2.71	2.51
6	11.71	7.24	5.43	4.44	3.81	3.38	3.07	2.83
7	13.59	8.33	6.21	5.05	4.31	3.81	3.44	3.16
8	15.51	9.46	7.01	5.67	4.82	4.24	3.82	3.49
9	17.48	10.61	7.83	6.31	5.35	4.69	4.21	3.84
10	19.51	11.80	8.68	6.97	5.90	5.15	4.61	4.20

Table 2. Comparison of Measurements by the Dual Diffraction Method and the Traditional Method

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Table 2. Comparison of Measurements by the Dual Diffraction Method and the Traditional Method

	Dual Diffraction Method				Traditional Diffraction Method
Nominal Diameter $a_{0} / μm$	$a_{avg} / μm$	$σ$	$Δ a / μm$	$Δ a / a_{0}$ (%)	$a_{avg} / μm$	$σ$	$Δ a / μm$	$Δ a / a_{0}$ (%)
100.2	99.5	0.0006	0.7	0.70	102.4	0.0017	2.2	2.30
120.1	121.0	0.0004	0.9	0.75	121.8	0.0020	1.7	1.42
140.8	141.6	0.0012	0.8	0.58	142.0	0.0036	1.2	0.86
Average	–	0.0007	0.8	0.68	–	0.0024	1.7	1.53