Accurate determination of fiber radii in the hypermicrometer range by multiwavelength
laser light scattering

A. van der Meulen; L. Strackee

doi:10.1364/AO.18.003751

Applied Optics
Vol. 18,
Issue 22,
pp. 3751-3757
(1979)
•https://doi.org/10.1364/AO.18.003751

Accurate determination of fiber radii in the hypermicrometer range by multiwavelength laser light scattering

A. van der Meulen and L. Strackee

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A. van der Meulen and L. Strackee, "Accurate determination of fiber radii in the hypermicrometer range by multiwavelength laser light scattering," Appl. Opt. 18, 3751-3757 (1979)

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Abstract

Laser light scattering from fused silica fibers, with radii in the hypermicrometer range (1–10 μm) has been studied. The vertical polarized component of the scattered radiation has been observed over an angular range from 2° to 135°, the angular resolution being 0°.3. The experiments were carried out using the discrete visible wavelength lines from a Kr⁺ ion laser. The experimentally observed total number of minima in the angular range between 0° and 90° has been compared with computations based on the model of an infinitely long circular cylinder. In this way it is possible to perform a fast and accurate (better than 1%) determination of fiber radii without the necessity of calibration, over a large range of physical acceptable refractive indices. Alternatively, measuring the near forwardscattering over a carefully predetermined collecting aperture suffices to estimate quickly the fiber radius to within 5.0% over the same refractive index range. When the refractive index is known beforehand, the accuracy of both methods can be improved to within 0.5% and 2%, respectively. When a full comparison with the theoretical angular scattering curves is performed, the fiber radius is obtained with an accuracy better than 0.1%, as well as the refractive index. The full curves are calculated by Dave’s computational procedure adapted for cylinders.

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(a) Number of minima N_min (1.46,x,0,90) vs size parameter x

x_s	x_l	$R \equiv 2 \frac{(x_{l} - x_{s})}{(x_{l} + x_{s})}$	x_s	x_l	$R \equiv 2 \frac{(x_{1} - x_{s})}{(x_{l} + x_{s})}$
14	18	0.25	57.5	62.5	0.08
19	20	0.05	62.5	68.5	0.08
21	22	0.05	68.5	70.5	0.03
22.5	27.5	0.20	70.5	74.5	0.06
29.5	32.5	0.10	74.5	76.5	0.03
32.5	36.5	0.12	77.5	81.5	0.05
36.5	39.5	0.08	82.5	88.5	0.06
39.5	42.5	0.07	88.5	90.5	0.02
42.5	47.5	0.11	90.5	95.5	0.05
48.5	54.5	0.12	95.5	97.5	0.02
54.5	56.5	0.04	97.5	100.5	0.03

(b) I_⊥ (1.46,x,16,30) vs size parameter x

x_s	x_l	$R \equiv 2 \frac{(x_{l} - x_{s})}{(x_{1} + x_{s})}$
11.5	21.5	0.61
21.5	31.5	0.38
31.5	41.5	0.27
41.5	52.5	0.23
52.5	58←.5	0.11
58.5	68.5	0.16
68.5	77.5	0.12
77.5	87.5	0.12
87.5	98.5	0.12

		(a) Minimum counting method				(b) Near forwardscattering method

Fiber	Wavelength λ (nm)	Exp. minima N (0,90)	Individual size range x	Restricted size range x	Radius range (μm)	Exp. signal I (16,30) (arb. units)	Individual size range x	Restricted size range x	Radius range (μm)
	476.2	18	40–45	42–43	3.18–3.26	1140	37–48	37–43	2.80–3.26
I	520.9	16	35–40	38.5–40	3.19–3.32	990	34–45	34–40	2.80–3.32
	568.2	15	33–36	35.5–36	3.21–3.26	893	29–41	32–37	2.89–3.35
	676.4	13	29–33	29.5–30.5	3.18–3.28	640	18–31	26–31	2.80–3.34
					〈r〉 = 3.21–3.26				〈r〉 = 2.89–3.26
	476.2	26	60–64	61–62.5	4.62–4.74	1486	54–66	57–65	4.32–4.93
II	520.9	24	55–60	56–57.25	4.64–4.74	1408	51–64	52–60	4.31–4.97
	568.2	21	49–53	51–52.5	4.61–4.75	1267	45–57	48–56	4.34–5.06
	676.4	18	40–45	43–44	4.63–4.74	1175	40–52	40–46	4.31–4.95
					〈r〉 = 4.64–4.74				〈r〉= 4.34–4.93
	476.2	31	72–77	75.5–76.5	5.72–5.80	1860	74–86	74–82	5.61–6.21
III	520.9	29	68–70	69–70	5.72–5.80	1767	68–80	68–75	5.64–6.22
	568.2	27	63–67	63.5–64	5.74–5.79	1549	59–72	63–69	5.70–6.24
	676.4	22	50–55	53–54	5.71–5.81	1260	45–58	52–58	5.60–6.24
					〈r〉 = 5.74–5.79				〈r〉= 5.70–6.21

		(a) Minimum counting method and full comparison					(b) Near forwardscattering method

Fiber	Wavelength λ (nm)	Exp. minima N (0,90)	Individual size range x	Restricted size range x	Radius range (μm)	Full comparison		Exp. signal I (16,30) (arb. units)	Individual size range x	Restricted size range x	Radius range (μm)

						Size x	Radius (μm)
	476 2	18	42.5–45	42.5–43	3.22–3.26	42.8	3.24	1140	41–46	41–43	3.11–3.26
I	520.9	16	36.5–39.5	38.5–39.25	3.19–3.25	39	3.23	990	34–40	38–40	3.15–3.32
	568.2	15	33–36	35.75–36	3.23–3.26	35.8	3.24	893	32–37	34–36	3.07–3.26
	676.4	13	29.5–32.5	29.5–30.5	3.18–3.28	30	3.23	640	22–31	29–31	3.12–3.34
					〈r〉 = 3.23–3.25		$\bar{r}$ = 3.235 ± 0.003				〈r〉 = 3.15–3.26
	476.2	26	60–62.5	62–62.5	4.70–4.74	62.5	4.74	1486	58–63	61–63	4.62–4.77
II	520.9	24	56–58	56.5–57.25	4.68–4.75	57	4.73	1408	54–58	56–58	4.64–4.81
	568.2	21	49–52.5	52–52.5	4.70–4.75	52.5	4.75	1267	48–53	51–53	4.61–4.79
	676.4	18	42.5–45	43.5–44	4.68–4.74	44	4.74	1175	43–48	43–45	4.63–4.84
					〈r〉 = 4.70–4.74		$\bar{r}$ = 4.74 ± 0.004				〈r〉 = 4.64–4.77
	476.2	31	74–76.5	76–76.5	5.76–5.80	76.5	5.80	1860	74–78	75–77	5.68–5.84
III	520.9	29	68–70	69.5–70	5.76–5.80	69.6	5.77	1767	68–72	69–71	5.72–5.89
	568.2	27	63–67	63.5–64	5.74–5.79	64	5.79	1549	62–66	63–65	5.70–5.88
	676.4	22	50–54	53.5–54	5.76–5.81	53.7	5.78	1260	52–57	52–54	5.60–5.81
					〈r〉 = 5.76–5.79		$\bar{r}$ = 5.785 ± 0.006				〈r〉 = 5.72–5.81

(a) Number of minima N_min (1.46,x,0,90) vs size parameter x

x_s	x_l	$R \equiv 2 \frac{(x_{l} - x_{s})}{(x_{l} + x_{s})}$	x_s	x_l	$R \equiv 2 \frac{(x_{1} - x_{s})}{(x_{l} + x_{s})}$
14	18	0.25	57.5	62.5	0.08
19	20	0.05	62.5	68.5	0.08
21	22	0.05	68.5	70.5	0.03
22.5	27.5	0.20	70.5	74.5	0.06
29.5	32.5	0.10	74.5	76.5	0.03
32.5	36.5	0.12	77.5	81.5	0.05
36.5	39.5	0.08	82.5	88.5	0.06
39.5	42.5	0.07	88.5	90.5	0.02
42.5	47.5	0.11	90.5	95.5	0.05
48.5	54.5	0.12	95.5	97.5	0.02
54.5	56.5	0.04	97.5	100.5	0.03

Abstract

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Figures (3)

Tables (3)

Equations (10)

Applied Optics