Forward glory scattering from bubbles

Dean S. Langley; Philip L. Marston

doi:10.1364/AO.30.003452

Applied Optics
Vol. 30,
Issue 24,
pp. 3452-3458
(1991)
•https://doi.org/10.1364/AO.30.003452

Forward glory scattering from bubbles

Dean S. Langley and Philip L. Marston

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Dean S. Langley and Philip L. Marston, "Forward glory scattering from bubbles," Appl. Opt. 30, 3452-3458 (1991)

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Abstract

The scattering enhancement known as the glory was observed in forward scattering from bubbles in liquids. A physical-optics model of the forward glory is detailed, based on transmitted waves reflected within the bubble. Some aspects of the model are compared with the Mie theory and with features in the cross-polarized light from single bubbles. Clouds of small bubbles rising in water show an angular structure in the forward glory light that is useful for estimating the bubble size.

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m	(P, L)	θ (deg)	b/a	α/a	I₁ (ϕ = 0)	I₂ (ϕ = ϕ_g)
1/1.403	(2, 0)	40.30	0.647	1.093	224.8	11.97
	(3, 0)	43.37	0.687	1.035	41.21	1.749
	(4, 0)	44.32	0.699	1.019	12.56	0.507
	(5,0)	44.74	0.704	1.012	5.048	0.200
	(4, 2)	19.06	0.327	1.095	0.006	0.006
0.75	(2, 0)	43.57	0.689	1.093	278.5	9.571
	(3, 0)	46.57	0.726	1.034	48.36	1.402
	(4, 0)	47.49	0.737	1.018	14.54	0.405
	(5,0)	47.89	0.742	1.011	5.813	0.159
	(4, 2)	20.32	0.347	1.101	0.003	0.003

P	L	sinθ
2	0	(m²/4)[1 + (1 + 8/m²)^1/2]
3	0	(m^3/2/2)(1 + 3/m)^1/2
4	0, 2	m[Q + (1/2 − Q² + Am/32Q)^1/2], where Q = 6^−1/2[1 − (5/2)^1/2 cos Y]^1/2 and Y = (1/3) arccos[−(7/5 + 27m²/320)(2/5)^1/2]
5	0, 2	(m/2)[5/2 + A(5/4 + Am)^1/2]^1/2
7	0, 2	(m/2)3^−1/2(7 + 7^1/2 cos Y + 21^1/2 A sin Y)]^1/2
7	4	(m/2)3^−1/2(7 − 28^1/2 cos Y)^1/2, where Y = (1/3) arccos[7^−3/2(7 − 27 Am)/2]
9	0, 2, 4, 6	(m/4)[9 − 2ABQ + B(27 − 4Q² + 3AB/Q)^1/2]^1/2, where Q = (1/2)[9 − 8(3 − 4 Am/3)^1/2 cos Y]^1/2 and Y = (1/3) arccos[−(9/2)(1 − Am)(3 − 4 Am/3)^−3/2]

m	(P, L)	θ (deg)	b/a	α/a	I₁ (ϕ = 0)	I₂ (ϕ = ϕ_g)
1/1.403	(2, 0)	40.30	0.647	1.093	224.8	11.97
	(3, 0)	43.37	0.687	1.035	41.21	1.749
	(4, 0)	44.32	0.699	1.019	12.56	0.507
	(5,0)	44.74	0.704	1.012	5.048	0.200
	(4, 2)	19.06	0.327	1.095	0.006	0.006
0.75	(2, 0)	43.57	0.689	1.093	278.5	9.571
	(3, 0)	46.57	0.726	1.034	48.36	1.402
	(4, 0)	47.49	0.737	1.018	14.54	0.405
	(5,0)	47.89	0.742	1.011	5.813	0.159
	(4, 2)	20.32	0.347	1.101	0.003	0.003

P	L	sinθ
2	0	(m²/4)[1 + (1 + 8/m²)^1/2]
3	0	(m^3/2/2)(1 + 3/m)^1/2
4	0, 2	m[Q + (1/2 − Q² + Am/32Q)^1/2], where Q = 6^−1/2[1 − (5/2)^1/2 cos Y]^1/2 and Y = (1/3) arccos[−(7/5 + 27m²/320)(2/5)^1/2]
5	0, 2	(m/2)[5/2 + A(5/4 + Am)^1/2]^1/2
7	0, 2	(m/2)3^−1/2(7 + 7^1/2 cos Y + 21^1/2 A sin Y)]^1/2
7	4	(m/2)3^−1/2(7 − 28^1/2 cos Y)^1/2, where Y = (1/3) arccos[7^−3/2(7 − 27 Am)/2]
9	0, 2, 4, 6	(m/4)[9 − 2ABQ + B(27 − 4Q² + 3AB/Q)^1/2]^1/2, where Q = (1/2)[9 − 8(3 − 4 Am/3)^1/2 cos Y]^1/2 and Y = (1/3) arccos[−(9/2)(1 − Am)(3 − 4 Am/3)^−3/2]

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Applied Optics