#### Table I

Dimensional Resolution

θ_{i} | r_{i}(μm) | Δr_{i}(μm) | P(θ)exact | m = 1.45 | m = 1.33 | m = 1.55 |
---|

1° | 9.50 | 1.0 | 212 | 201 | 205 | 199 |

1°20′ | 8.50 | 1.0 | 205 | 195 | 198 | 193 |

2°20′ | 7.50 | 1.0 | 177 | 169 | 172 | 167 |

2°40′ | 6.75 | 0.5 | 165 | 158 | 162 | 157 |

3° | 6.25 | 0.5 | 152 | 147 | 150 | 146 |

3°20′ | 5.75 | 0.5 | 141 | 136 | 139 | 134 |

3°40′ | 5.25 | 0.5 | 128 | 124 | 127 | 123 |

4° | 4.75 | 0.5 | 116 | 113 | 116 | 111 |

4°20′ | 4.25 | 0.5 | 104 | 102 | 105 | 100 |

4°40′ | 3.80 | 0.4 | 92.6 | 91.0 | 94.0 | 89.8 |

5° | 3.40 | 0.4 | 81.9 | 80.9 | 83.9 | 79.8 |

5°20′ | 3.00 | 0.4 | 72.0 | 71.6 | 74.5 | 70.4 |

6°20′ | 2.60 | 0.4 | 47.2 | 48.0 | 50.7 | 46.9 |

7°20′ | 2.20 | 0.4 | 30.1 | 31.3 | 33.9 | 30.3 |

8°20′ | 1.80 | 0.4 | 19.3 | 20.5 | 22.9 | 19.5 |

11°20′ | 1.40 | 0.4 | 7.84 | 8.20 | 9.98 | 7.28 |

15°20′ | 1.00 | 0.4 | 5.23 | 5.24 | 6.23 | 4.65 |

24° | 0.60 | 0.4 | 2.98 | 2.97 | 3.06 | 2.66 |

Column 1: Measurement angle

θ_{i} selected.

Column 2: Particle radius

r_{i}, at the center of the class associated to

θ_{i} in the relaxation

equation (12) for λ = 1

μm.

Column 3: Particle classes widths, for λ = 1

μm.

Column 4: Exact values of the normalized phase function

P(

θ_{i}), for spherical particles with a gamma standard size distribution (

r_{eff} = 3

μm,

υ_{eff} = 0.07) and with a real refractive index

m = 1.45.

Column 5: Approximate values of the normalized phase function, for the same particles as in column 2, but with

P(

θ_{i}) calculated by a finite sum.

Columns 6 and 7: Approximate values of

P(

θ_{i}), calculated as in column 5, except for two assumed values of the refractive index;

m = 1.33 and

m = 1.55.

#### Table II

Case of the Gamma Bimodal Distribution; Distribution of the Relative Errors in n(r_{j}) as a function of the Gaussian Noise Level σ_{s}, for three Different Particle Classes

σ_{s} | 3.5 | 10.6 | 17.7 | 28.3 | 42.4 | r_{j} (μm) |
---|

$$\left|\phantom{\rule{0.1em}{0ex}}\frac{\mathrm{\Delta}\phantom{\rule{0em}{0ex}}n}{n}\phantom{\rule{0.1em}{0ex}}\right|\phantom{\rule{0.2em}{0ex}}\u2a7d{\sigma}_{n}$$ | 67 | 64 | 60 | 57 | 67 | 1.0 |

67 | 79 | 83 | 84 | 86 | 2.6 |

67 | 83 | 86 | 87 | 89 | 3.0 |

$$\left|\phantom{\rule{0.1em}{0ex}}\frac{\mathrm{\Delta}\phantom{\rule{0em}{0ex}}n}{n}\phantom{\rule{0.1em}{0ex}}\right|\phantom{\rule{0.2em}{0ex}}\u2a7d2\phantom{\rule{0.1em}{0ex}}{\sigma}_{n}$$ | 95 | 97 | 98 | 97 | 96 | 1.0 |

96 | 95 | 93 | 93 | 92 | 2.6 |

97 | 94 | 95 | 95 | 93 | 3.0 |

$$\left|\phantom{\rule{0.1em}{0ex}}\frac{\mathrm{\Delta}\phantom{\rule{0em}{0ex}}n}{n}\phantom{\rule{0.1em}{0ex}}\right|\phantom{\rule{0.2em}{0ex}}\u2a7d2\phantom{\rule{0.2em}{0ex}}\frac{\mathrm{\Delta}\phantom{\rule{0em}{0ex}}\overline{n}}{n}$$ | 89 | 91 | 95 | 95 | 95 | 1.0 |

90 | 92 | 88 | 88 | 88 | 2.6 |

91 | 90 | 90 | 88 | 89 | 3.0 |

Percentages of inverted results with relative errors into the respective ranges (−

σ_{n}, +

σ_{n}), (−2

σ_{n}, +2

σ_{n}), and (−2

E, +2

E), to be compared with Gaussian values 68, 95, and 90, respectively.