Table 7.
Results of numerical experimentsa.
| Angle error (θ′ = 0.98θ–0.5), Harmonic mean Q | ||||
|---|---|---|---|---|
| Assumed radius, nm | Best | Best (weighted) | ||
| Radius, nm | Refractive index | Radius, nm | Refractive index | |
| 1150 | 1114(−3.1%) | 1.660(+3.1%) | 1098(−4.5%) | 1.695(+5.2%) |
| 580 | 560(−3.4%) | 1.660(+3.1%) | 576(−0.7%) | 1.600(−0.6%) |
| 450 | 434(−3.6%) | 1.655(+2.8%) | 438(−2.7%) | 1.660(+3.1%) |
| 300 | 288(−4.0%) | 1.635(+1.6%) | 292(+2.7%) | 1.615(+0.3%) |
| 230 | 228(−0.9%) | 1.640(+1.9%) | 226(−1.7%) | 1.645(+2.2%) |
| 115 | 119(+3.5%) | 1.560(−3.1%) | 119(+3.5%) | 1.560(−3.1%) |
| Angle error, average Q | ||||
| Assumed radius, nm | Best | Best (weighted) | ||
| Radius, nm | Refractive index | Radius, nm | Refractive index | |
| 1150 | 1114(−3.1 %) | 1.665(+3.4%) | 1134(+1.4%) | 1.635(−1.6%) |
| 580 | 572(−1.4%) | 1.635(+1.6%) | 580 - | 1.610 - |
| 450 | 442(−1.8%) | 1.630(+1.2%) | 446(−0.9%) | 1.610 - |
| 300 | 292(−2.7%) | 1.645(+2.2%) | 300 - | 1.625(+0.9%) |
| 230 | 228(−0.9%) | 1.640(+1.9%) | 226(−1.7%) | 1.645(+1.2%) |
| 115 | 119(+3.5%) | 1.560(−3.1%) | 119(+3.5%) | 1.560(−3.t%) |
| Angle calibration drift (θ′ = 0.998θ–0.5), Harmonic mean Q | ||||
| Assumed radius, nm | Best | Best (weighted) | ||
| Radius, nm | Refractive index | Radius, nm | Refractive index | |
| 1150 | 1132(−1.6%) | 1.634(+1.5%) | 1148(−0.2%) | 1.608(−0.1%) |
| 580 | 570(−1.7%) | 1.632(+1.4%) | 578(—0.3%) | 1.608(−0.1%) |
| 450 | 444(−1.3%) | 1.626(+1.0%) | 444(−1.3%) | 1.630(+1.2%) |
| 300 | 300 - | 1.620(+0.6%) | 300 - | 1.618(+0.5%) |
| 230 | 228(−0.8%) | 1.630(+1.2%) | 228(−0.9%) | 1.626(+1.0%) |
| 115 | 117(+1.7%) | 1.590(−1.2%) | 115 - | 1.606(−0.2%) |
| Angle calibration drift, average Q | ||||
| Assumed radius, nm | Best | Best (weighted) | ||
| Radius, nm | Refractive index | Radius, nm | Refractive index | |
| 1150 | 1140(−0.7%) | 1.626(+1.0%) | 1150 - | 1.60S(−0.1%) |
| 580 | 578(−0.3%) | 1.616(+0.4%) | 582(+0.3%) | 1.604(−0.4%) |
| 450 | 448(−0.4%) | 1.616(+0.4%) | 446(−0.9%) | 1.620(+0.6%) |
| 300 | 296(−1.3%) | 1.628(+1.1%) | 300 - | 1.614(+0.2%) |
| 230 | 230 - | 1.616(+0.4%) | 228(−0.9%) | 1.628(+1.1%) |
| 115 | 117(+1.7%) | 1.586(−1.5%) | 115 - | 1.612(+0.1%) |
| Random noiseb, Harmonic mean Q | ||||
| Assumed radius, nm | Best | Best (weighted) | ||
| Radius, nm | Refractive index | Radius, nm | Refractive index | |
| 1150 | 1150 - | 1.610 - | 1150 - | 1.610 - |
| 580 | 582(+0.3%) | 1.604(−0.4%) | 580 - | 1.610 - |
| 450 | 450 - | 1.610 - | 450 - | 1.610 |
| 300 | 300 - | 1.616(+0.4%) | 300 - | 1.612(+0.1%) |
| 230 | 230 - | 1.608(−0.1%) | 230 - | 1.610 - |
| 115 | 115 - | 1.594(−1.0%) | 115 - | 1.614(+0.2%) |
| Random noise, average Q | ||||
| Assumed radius, nm | Best | Best (weighted) | ||
| Radius, nm | Refractive index | Radius, nm | Refractive index | |
| 1150 | 1150. - | 1.610 - | 1150. - | 1.610 |
| 580 | 582.(+0.3%) | 1.604(−0.4%) | 580. - | 1.610 - |
| 450 | 450. - | 1.610 - | 450. - | 1.610 - |
| 300 | 300. - | 1.618(+0.5%) | 300. - | 1.614(+0.2%) |
| 230 | 232.(+0.9%) | 1.596(−0.9%) | 230. - | 1.608(−0.1%) |
| 115 | 115. - | 1.592(−1.1%) | 115. - | 1.614(+0.2%) |
a
Refractive index is 1.610 in all cases. The numbers in parentheses are the deviations from the assumed values.
b
Random noise of maximum amplitude of 2% every degree plus a larger noise of maximum amplitude 5% that remain constant for 10° is used. For the smallest two particle sizes the corresponding numbers are 3% and 10% respectively.