Table 1.
Baseline Compensation for Baseline Error Corrupted Correlation Function Data for a 10–1000 nm Unimodal PSD
Baseline Error | | | | |
Compensation () | | | | |
Compensation () | | | | |
Table 2.
Baseline Compensation for Baseline Error and Random Noise Corrupted Correlation Function Data for a 100–800 nm Unimodal PSD
Baseline Error | | | | |
Compensation () | | | | |
Compensation () | | | | |
Table 3.
Regularization Parameters Determined Using the L-Curve Method for Standard Regularization, for the Constrained Regularization, and for the GCV and the Robust GCV Rules for the 10–1000 nm and 100–800 nm Unimodal, 10–1000 nm Bimodal, and 100 and 500 nm Bimodal PSD Correlation Function Data Corrupted by Uncorrelated Noise at Low Noise Level
Nominal | U10 to 1000 nm (0.00001) | U10 to 1000 nm (0.0001) | U100 to 800 nm (0.00001) | U100 to 800 nm (0.0001) | B10 to 1000 nm (0.00001) | B10 to 1000 nm (0.0001) | (0.00001) | (0.0001) |
Optimal | | | | | | | | |
L-curve | | | | | | | | |
L-curve1 | | | | | | | | |
L-curve2 | | | | | | | | |
GCV | | | | | | | | |
Robust GCV | | | | | | 1.2 | | |
Table 4.
Regularization Parameters Determined Using the L-Curve Method for Standard Regularization, for the Constrained Regularization, and for the GCV and the Robust GCV Rules for the 10–1000 nm and 100–800 nm Unimodal, 10–1000 nm Bimodal, and 100 and 500 nm Bimodal PSD Correlation Function Data Corrupted by Uncorrelated Noise at High Noise Level
Nominal | U10 to 1000 nm (0.001) | U10 to 1000 nm (0.005) | U100 to 800 nm (0.001) | U100 to 800 nm (0.005) | B10 to 1000 nm (0.001) | B10 to 1000 nm (0.005) | (0.001) | (0.005) |
Optimal | | 1.1 | | | | | | |
L-curve | | 1.2 | | 1.1 | 1.1 | 1.4 | 1.1 | 2.2 |
L-curve1 | 1.7 | 4.7 | 1.1 | 2.4 | 1.7 | 2.6 | 1.5 | 4.0 |
L-curve2 | 3.4 | | | 6.6 | 4.7 | 6.6 | | 6.6 |
GCV | | | | | 1.8 | 3.2 | | |
Robust GCV | 1.5 | 2.6 | 1.2 | 2.3 | 4.9 | 6.5 | 2.12 | 3.6 |
Table 5.
Regularization Parameters Determined Using the L-Curve Method for Standard Regularization, for the Constrained Regularization, and for the GCV and the Robust GCV Rules for the 10–1000 nm and 100–800 nm Unimodal, 10–1000 nm Bimodal, and 100 and 500 nm Bimodal PSD Correlation Function Data Corrupted by Correlated Noise at High SNR
Nominal | U10 to 1000 nm () | U10 to 1000 nm () | U100 to 800 nm () | U100 to 800 nm () | B10 to 1000 nm () | B10 to 1000 nm () | () | () |
Optimal | | | | | | | | |
L-curve | | | | | | | | |
L-curve1 | | | | | | | | |
L-curve2 | | | | | | | | |
GCV | | | | | | | | |
Robust GCV | | | | | | 1.2 | | |
Table 6.
Regularization Parameters Determined Using the L-Curve Method for Standard Regularization, for the Constrained Regularization and for the GCV and the Robust GCV Rules for the 10–1000 nm and 100–800 nm Unimodal, 10–1000 nm Bimodal, and 100 and 500 nm Bimodal PSD Correlation Function Data Corrupted by Correlate Noise at Low SNR
Nominal | U10 to 1000 nm () | U10 to 1000 nm () | U100 to 800 nm () | U100 to 800 nm () | B10 to 1000 nm() | B10 to 1000 nm () | () | () |
Optimal | | | | | | | | |
L-curve | | | | | | 2.1 | 1.0 | 2.0 |
L-curve1 | 1.1 | 1.7 | 1.1 | 2.0 | 1.5 | 2.9 | 1.5 | 2.9 |
L-curve2 | 1.2 | 3.4 | | | 2.4 | 6.6 | 2.1 | 5.6 |
GCV | | | | | | | | |
Robust GCV | 1.3 | 2.0 | 1.2 | 2.1 | 4.1 | 5.8 | 2.2 | 3.2 |
Table 7.
Diameter and Intensity Ratio for PSDs Obtained from Autocorrelation Function Data for Scattering Angles at 120° and 100° after Baseline Compensation
Baseline | 120° Diameter (nm) | 120° Intensity Ratio | 100° Diameter (nm) | 100° Intensity Ratio |
Edge Proportion | | | | |
PSD Norm | | | | |
Table 8.
Regularization Parameters Determined Using the L-Curve for Standard Regularization, for the Constrained Regularization, and for the GCV and Robust GCV Rules for the Bimodal Experimental PSD Before and After Baseline Compensation
ACF Data | 90° | 120° | 120° with Compensation | 100° | 100° with Compensation |
L-curve | | | | | |
L-curve1 | | | | | |
L-curve2 | | | | | |
GCV | | | | | |
Robust GCV | | | | | |