Separation and analysis of forward scattered power in laboratory measurements of light beam transmittance through a turbid medium

E. Battistelli; P. Bruscaglioni; A. Ismaelli; L. Lo Porto; G. Zaccanti

doi:10.1364/AO.25.000420

Applied Optics
Vol. 25,
Issue 3,
pp. 420-430
(1986)
•https://doi.org/10.1364/AO.25.000420

Separation and analysis of forward scattered power in laboratory measurements of light beam transmittance through a turbid medium

E. Battistelli, P. Bruscaglioni, A. Ismaelli, L. Lo Porto, and G. Zaccanti

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E. Battistelli, P. Bruscaglioni, A. Ismaelli, L. Lo Porto, and G. Zaccanti, "Separation and analysis of forward scattered power in laboratory measurements of light beam transmittance through a turbid medium," Appl. Opt. 25, 420-430 (1986)

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Abstract

In laboratory measurements of the transmittance of a light beam through a diffusing medium (water plus latex spheres), a distinction between the attenuated beam power and the received forward scattered power was made possible by the use of a transmissometer whose receiver has a variable field of view. The dependence of the received scattered power on the FOV angle and on the medium optical depth was analyzed. The deduced separated contributions of first- and second-order scattering, as well as the total received scattered power, were compared to the results of calculations.

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Type	〈r〉 (μm)	s.d. (μm)^a	m^b	〈x〉^c	g^d
Polystyrene	0.15	0.004	1.59	1.98	0.666
Polystyrene	0.55	0.004	1.59	7.27	0.923
Polystyrene	7.85	1.45	1.59	103.8	0.915
Styrene divinylbenzene	2.85	0.75	1.53	37.7	0.902

〈r〉^a	0.15 μm		0.55 μm		2.85 μm		7.85 μm

α_n^b	K_nT⁽²⁾	K_n⁽²⁾	K_nT⁽²⁾	K_n⁽²⁾	K_nT⁽²⁾	K_n⁽²⁾	K_nT⁽²⁾	K_n⁽²⁾
0.5°	0.13 × 10⁻⁴	0.8 × 10⁻⁵	0.20 × 10⁻³	0.38 × 10⁻³	0.14 × 10⁻²	0.16 × 10⁻²	0.58 × 10⁻²	0.73 × 10⁻²
1°	0.41 × 10⁻⁴	0.33 × 10⁻⁴	0.74 × 10⁻³	0.15 × 10⁻²	0.65 × 10⁻²	0.63 × 10⁻²	0.27 × 10⁻¹	0.22 × 10⁻¹
1.5°	0.87 × 10⁻⁴	0.44 × 10⁻⁴	0.16 × 10⁻²	0.30 × 10⁻²	0.15 × 10⁻¹	0.15 × 10⁻¹	0.54 × 10⁻¹	0.43 × 10⁻¹
2°	0.15 × 10⁻³	0.17 × 10⁻³	0.28 × 10⁻²	0.44 × 10⁻²	0.25 × 10⁻¹	0.26 × 10⁻¹	0.75 × 10⁻¹	0.66 × 10⁻¹
2.5°	0.24 × 10⁻³	0.30 × 10⁻³	0.44 × 10⁻²	0.64 × 10⁻²	0.36 × 10⁻¹	0.39 × 10⁻¹	0.86 × 10⁻¹	0.84 × 10⁻¹
3°	0.34 × 10⁻³	0.88 × 10⁻³	0.63 × 10⁻²	0.87 × 10⁻²	0.48 × 10⁻¹	0.53 × 10⁻¹	0.93 × 10⁻¹	0.97 × 10⁻¹

〈r〉 = 2.85 μm

B = 3.8			B = 4.0

α_n (deg)	K_n⁽¹⁾	K_n⁽²⁾	K_n⁽¹⁾	K_n⁽²⁾
0.5	0.012	0.0017	0.011	0.0016
1.0	0.047	0.0064	0.046	0.0063
1.5	0.094	0.015	0.093	0.015
2.0	0.15	0.026	0.15	0.026
2.5	0.21	0.039	0.21	0.039
3.0	0.26	0.053	0.26	0.053
〈r〉 = 7.85 μm

B = 2.75			B = 3.0

α_n (deg)	K_n⁽¹⁾	K_n⁽²⁾	K_n⁽¹⁾	K_n⁽²⁾
0.5	0.086	0.0093	0.076	0.0073
1.0	0.24	0.026	0.23	0.022
1.5	0.36	0.048	0.35	0.043
2.0	0.44	0.072	0.43	0.066
2.5	0.47	0.090	0.46	0.084
3.0	0.48	0.10	0.48	0.097

Type	〈r〉 (μm)	s.d. (μm)^a	m^b	〈x〉^c	g^d
Polystyrene	0.15	0.004	1.59	1.98	0.666
Polystyrene	0.55	0.004	1.59	7.27	0.923
Polystyrene	7.85	1.45	1.59	103.8	0.915
Styrene divinylbenzene	2.85	0.75	1.53	37.7	0.902

〈r〉^a	0.15 μm		0.55 μm		2.85 μm		7.85 μm

α_n^b	K_nT⁽²⁾	K_n⁽²⁾	K_nT⁽²⁾	K_n⁽²⁾	K_nT⁽²⁾	K_n⁽²⁾	K_nT⁽²⁾	K_n⁽²⁾
0.5°	0.13 × 10⁻⁴	0.8 × 10⁻⁵	0.20 × 10⁻³	0.38 × 10⁻³	0.14 × 10⁻²	0.16 × 10⁻²	0.58 × 10⁻²	0.73 × 10⁻²
1°	0.41 × 10⁻⁴	0.33 × 10⁻⁴	0.74 × 10⁻³	0.15 × 10⁻²	0.65 × 10⁻²	0.63 × 10⁻²	0.27 × 10⁻¹	0.22 × 10⁻¹
1.5°	0.87 × 10⁻⁴	0.44 × 10⁻⁴	0.16 × 10⁻²	0.30 × 10⁻²	0.15 × 10⁻¹	0.15 × 10⁻¹	0.54 × 10⁻¹	0.43 × 10⁻¹
2°	0.15 × 10⁻³	0.17 × 10⁻³	0.28 × 10⁻²	0.44 × 10⁻²	0.25 × 10⁻¹	0.26 × 10⁻¹	0.75 × 10⁻¹	0.66 × 10⁻¹
2.5°	0.24 × 10⁻³	0.30 × 10⁻³	0.44 × 10⁻²	0.64 × 10⁻²	0.36 × 10⁻¹	0.39 × 10⁻¹	0.86 × 10⁻¹	0.84 × 10⁻¹
3°	0.34 × 10⁻³	0.88 × 10⁻³	0.63 × 10⁻²	0.87 × 10⁻²	0.48 × 10⁻¹	0.53 × 10⁻¹	0.93 × 10⁻¹	0.97 × 10⁻¹

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Tables (3)

Equations (12)

Applied Optics