A recent method for predicting light scattering by random aggregates of particles is experimentally examined. This approximate method is here tested in terms of its ability to predict the effects of aggregation of latex spheres of five different sizes on nine different transmitted and scattered light fluxes. In each case two degrees of aggregation were used. For an aggregated sample, each photometric quantity was measured and compared to its counterpart for an unaggregated one. The degrees of aggregation of the samples were estimated microscopically. These data were used with the method to calculate theoretical photometric effects of aggregation. The predictions are found to agree approximately with experimental findings. The results support the method.

Wayne H. Slade, Emmanuel Boss, and Clementina Russo Opt. Express 19(9) 7945-7959 (2011)

References

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Effects of Aggregation of Polystyrene Latex Spheres (diameter 0.264 μm) in Water on Extinctions E(γ) and Scattered Intensities I(θ) for the Indicated γ and θ Values in Degrees, λ = 474 nm in Water ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.75

1.63

2.35

2.12

E(5)

1.45

1.45

1.50

1.71

E(10)

1.11

1.18

0.96

1.16

E(21)

0.78

0.76

0.65

0.57

I(2)

28.7

23.8

57.1

54.8

I(5)

14.5

17.5

28.8

38.9

I(12)

3.16

5.50

3.56

8.82

I(21)

2.10

2.41

1.95

2.37

I(90)

0.69

0.55

0.63

0.36

Listed are experimental and theoretical values of P_{a}/P_{s}, the ratio of photometric quantities E(ν) and I(θ) of samples when aggregated P_{a} and when single P_{s}.

Table II

Effects of Aggregation of Latex Spheres (Diameter 0.35 μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.45

1.58

1.64

1.70

E(5)

1.16

1.21

1.08

1.29

E(10)

0.94

0.85

0.77

0.85

E(21)

0.61

0.50

0.48

0.43

I(2)

30.0

39.5

60.0

38.4

I(5)

14.9

19.6

36.4

22.9

I(12)

3.62

4.11

4.58

5.00

I(21)

1.42

1.46

1.28

1.46

I(90)

0.79

0.72

0.64

0.65

Listed are ratios of these photometric quantities P_{a}/P_{s}.

Table III

Effects of Aggregation of Latex Spheres (Diameter = 0.61 μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.07

1.16

1.08

1.18

E(5)

0.94

0.89

0.84

0.81

E(10)

0.72

0.62

0.60

0.52

E(21)

0.42

0.29

0.34

0.26

I(2)

9.02

11.0

13.2

15.7

I(5)

5.21

5.09

7.01

6.49

I(12)

1.58

1.52

1.65

1.30

I(21)

0.98

0.54

0.84

0.44

I(90)

0.74

0.70

0.65

0.68

Listed are ratios of these quantities P_{a}/P_{s}.

Table IV

Effects of Aggregation of Latex Spheres (Diameter = 1.099 μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

0.90

0.96

0.72

0.94

E(5)

0.76

0.68

0.58

0.60

E(10)

0.56

0.39

0.40

0.33

E(21)

0.21

0.15

0.18

0.13

I(2)

1.25

3.75

2.84

4.71

I(5)

1.15

1.99

1.63

2.14

I(12)

0.88

0.55

0.61

0.46

I(21)

0.86

0.54

0.65

0.42

I(90)

0.81

1.10

0.72

1.07

Listed are ratios of these photometric quantities, P_{a}/P_{s}.

Table V

Effects of Aggregation of Latex Spheres (Diameter = 2.051μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.02

0.92

0.75

0.93

E(5)

0.73

0.53

0.50

0.54

E(10)

0.47

0.31

0.28

0.32

E(21)

0.22

0.17

0.19

0.17

I(2)

1.23

2.04

2.33

2.01

I(5)

1.13

1.00

1.16

1.03

I(12)

1.06

0.83

0.79

0.84

I(21)

0.97

0.50

0.75

0.51

I(90)

0.75

0.94

0.80

0.96

Listed are ratios of these photometric quantities P_{a}/P_{s}.

Tables (5)

Table I

Effects of Aggregation of Polystyrene Latex Spheres (diameter 0.264 μm) in Water on Extinctions E(γ) and Scattered Intensities I(θ) for the Indicated γ and θ Values in Degrees, λ = 474 nm in Water ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.75

1.63

2.35

2.12

E(5)

1.45

1.45

1.50

1.71

E(10)

1.11

1.18

0.96

1.16

E(21)

0.78

0.76

0.65

0.57

I(2)

28.7

23.8

57.1

54.8

I(5)

14.5

17.5

28.8

38.9

I(12)

3.16

5.50

3.56

8.82

I(21)

2.10

2.41

1.95

2.37

I(90)

0.69

0.55

0.63

0.36

Listed are experimental and theoretical values of P_{a}/P_{s}, the ratio of photometric quantities E(ν) and I(θ) of samples when aggregated P_{a} and when single P_{s}.

Table II

Effects of Aggregation of Latex Spheres (Diameter 0.35 μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.45

1.58

1.64

1.70

E(5)

1.16

1.21

1.08

1.29

E(10)

0.94

0.85

0.77

0.85

E(21)

0.61

0.50

0.48

0.43

I(2)

30.0

39.5

60.0

38.4

I(5)

14.9

19.6

36.4

22.9

I(12)

3.62

4.11

4.58

5.00

I(21)

1.42

1.46

1.28

1.46

I(90)

0.79

0.72

0.64

0.65

Listed are ratios of these photometric quantities P_{a}/P_{s}.

Table III

Effects of Aggregation of Latex Spheres (Diameter = 0.61 μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.07

1.16

1.08

1.18

E(5)

0.94

0.89

0.84

0.81

E(10)

0.72

0.62

0.60

0.52

E(21)

0.42

0.29

0.34

0.26

I(2)

9.02

11.0

13.2

15.7

I(5)

5.21

5.09

7.01

6.49

I(12)

1.58

1.52

1.65

1.30

I(21)

0.98

0.54

0.84

0.44

I(90)

0.74

0.70

0.65

0.68

Listed are ratios of these quantities P_{a}/P_{s}.

Table IV

Effects of Aggregation of Latex Spheres (Diameter = 1.099 μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

0.90

0.96

0.72

0.94

E(5)

0.76

0.68

0.58

0.60

E(10)

0.56

0.39

0.40

0.33

E(21)

0.21

0.15

0.18

0.13

I(2)

1.25

3.75

2.84

4.71

I(5)

1.15

1.99

1.63

2.14

I(12)

0.88

0.55

0.61

0.46

I(21)

0.86

0.54

0.65

0.42

I(90)

0.81

1.10

0.72

1.07

Listed are ratios of these photometric quantities, P_{a}/P_{s}.

Table V

Effects of Aggregation of Latex Spheres (Diameter = 2.051μm) on E(γ) and I(θ) of the Indicated Angles in Degrees ^{a}

Unstirred

Stirred

Exp.

Theor.

Exp.

Theor.

E(0)

1.02

0.92

0.75

0.93

E(5)

0.73

0.53

0.50

0.54

E(10)

0.47

0.31

0.28

0.32

E(21)

0.22

0.17

0.19

0.17

I(2)

1.23

2.04

2.33

2.01

I(5)

1.13

1.00

1.16

1.03

I(12)

1.06

0.83

0.79

0.84

I(21)

0.97

0.50

0.75

0.51

I(90)

0.75

0.94

0.80

0.96

Listed are ratios of these photometric quantities P_{a}/P_{s}.