Chinese Journal of Lasers, Volume. 44, Issue 1, 104003(2017)
Multi-Scale Inversion Combining TSVD-Tikhonov Regularization for Dynamic Light Scattering
Figures & Tables(16)
Fig. 2. Inverse PSD of unimodal distribution particles with particle size in range of 250~550 nm at different noise levels. (a) 0.001; (b) 0.005; (c) 0.01
Fig. 3. Inverse PSD of bimodal distribution particles with particle size in range of 100~600 nm at different noise levels. (a) 0.001; (b) 0.005; (c) 0.01
Fig. 4. Inverse PSD of unimodal wide distribution particles with particle size in range of 300~800 nm using different methods at different noise levels. (a) 0.001; (b) 0.005; (c) 0.01
Fig. 5. Inversion PSD of unimodal narrow distribution particles with particle size in range of 300~800 nm using different methods at different noise levels. (a) 0.001; (b) 0.005; (c) 0.01
Fig. 6. Inversion PSD of bimodal wide distribution particles with particle size in range of 100~900 nm using different methods at different noise levels. (a) 0.001; (b) 0.005; (c) 0.01
Fig. 7. Inversion PSD of bimodal narrow distribution particles with particle size in range of 100~900 nm using different methods at different noise levels. (a) 0.001; (b) 0.005; (b) 0.01
Fig. 8. Inverse PSD of the experiment particles with different diameters using different methods. (a) 300 nm; (b) 100~500 nm
Table 1. Inverse data of unimodal distribution particles with particle sizein range of 250~550 nm
View tableTable 1. Inverse data of unimodal distribution particles with particle sizein range of 250~550 nm
Noise level Tikhonov TSVD PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE 0.001 392.0 1.38 0.3899 392.0 1.38 0.1427 0.005 386.5 2.77 0.4604 386.5 2.77 0.1851 0.01 375.5 5.53 0.4756 375.5 5.53 0.2607
Table 2. Inverse data of bimodal distribution particles with particle size in range of 100~600 nm
View tableTable 2. Inverse data of bimodal distribution particles with particle size in range of 100~600 nm
Noise level Tikhonov TSVD PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE 0.001 152.81, 512.36 4.97, 3.22 0.5668 152.81, 472.41 4.97, 4.83 0.3473 0.005 -,- -,- 0.7394 160.80, 512.36 0, 3.22 0.3356 0.01 -,- -,- 0.7425 168.79, 464.44 4.97, 6.43 0.3621
Table 3. Simulation parameters of different particles
View tableTable 3. Simulation parameters of different particles
Particals Min /nm Max /nm u 1σ 1u 2σ 2Unimodel Wide 300 800 -0.2 2.0 - - Narrow 300 800 -2.5 2.0 - - Bimodel Wide 100 900 -2.5 2.2 3.8 2.1 Narrow 100 900 -5.5 2.2 5.5 2.1
Table 4. Inverse data of unimodal wide distribution particles with particle size in range of 300~800 nm at different noise levels
View tableTable 4. Inverse data of unimodal wide distribution particles with particle size in range of 300~800 nm at different noise levels
Method 0.001 0.005 0.01 PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE Tikhonov 500.75 10.7 0.4160 500.75 10.74 0.4325 475.76 15.20 0.5359 TSVD 525.74 6.28 0.2789 525.74 6.28 0.3308 550.72 1.83 0.2902 WRIM 500.28 10.82 0.1774 505.96 9.81 0.2495 543.13 3.19 0.2647 TTWRIM 532.79 5.03 0.1219 543.13 3.18 0.1374 551.92 1.62 0.1509
Table 5. Inverse data of unimodal narrow distribution particles with particle size in range of 300~800 nm at different noise levels
View tableTable 5. Inverse data of unimodal narrow distribution particles with particle size in range of 300~800 nm at different noise levels
Method 0.001 0.005 0.01 PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE Tikhonov 625.68 10.49 0.8385 625.68 10.49 0.8642 600.70 14.06 0.8355 TSVD 675.66 3.34 0.3446 675.66 3.34 0.5123 675.66 3.34 0.4853 WRIM 700.24 0.17 0.7835 700.32 0.19 0.7930 654.32 6.39 0.7657 TTWRIM 677.32 3.10 0.2374 676.31 3.25 0.2449 676.11 3.28 0.2743
Table 6. Inverse data of bimodal wide distribution particles with particle size in range of 100~900 nm at different noise levels
View tableTable 6. Inverse data of bimodal wide distribution particles with particle size in range of 100~900 nm at different noise levels
Method 0.001 0.005 0.01 PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE Tikhonov 180.91 660.67 7.23 8.24 0.5853 -,- -,- 0.6973 -,- -,- 0.7127 TSVD 180.91 680.66 7.23 5.46 0.4579 180.91 660.67 7.23 8.24 0.4267 180.91 640.68 7.23 11.02 0.5096 WRIM 161.07 739.39 17.40 2.69 0.4312 151.66 665.43 22.23 7.58 0.5531 -,- -,- 0.6251 TTWRIM 183.86 696.91 5.72 3.21 0.2349 203.48 702.67 4.34 2.41 0.2603 216.09 712.39 10.81 1.06 0.2487
Table 7. Inverse data of bimodal narrow distribution particles with particle size in range of 100~900 nm at different noise levels
View tableTable 7. Inverse data of bimodal narrow distribution particles with particle size in range of 100~900 nm at different noise levels
Method 0.001 0.005 0.01 PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE PV /nm PVE /% PSDRE Tikhonov 160.92 780.61 10.97 7.62 0.6708 120.94 980.51 16.60 16.04 0.7816 120.94 960.52 16.60 13.67 0.8369 TSVD 140.93 800.60 2.81 5.26 0.4965 140.93 820.59 2.81 2.89 0.4785 140.93 800.60 2.81 5.26 0.6049 WRIM 125.45 797.75 13.49 5.59 0.6177 125.84 824.60 13.22 2.41 0.6058 126.11 844.03 13.03 0.12 0.6228 TTWRIM 155.54 813.60 7.26 3.71 0.4020 146.17 817.81 0.8 3.22 0.4223 147.11 839.12 1.45 0.70 0.4160
Table 8. Inverse data of the experiment particles with different diameters using different methods
View tableTable 8. Inverse data of the experiment particles with different diameters using different methods
Diameter /mm Tikhonov TSVD WRIM TTWRIM PV /nm PVE /% PV /nm PVE /% PV /nm PVE /% PV /nm PVE /% 300 255.42 14.86 291.76 2.75 287.64 4.12 299.45 0.18 100~500 99.31 0.69 99.31 0.69 102.82 2.82 102.81 2.81
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Wang Yajing, Dou Zhi, Shen Jin, Liu Wei, Yin Liju, Gao Mingliang. Multi-Scale Inversion Combining TSVD-Tikhonov Regularization for Dynamic Light Scattering[J]. Chinese Journal of Lasers, 2017, 44(1): 104003
Paper Information
Category: measurement and metrology
Received: May. 28, 2016
Accepted: --
Published Online: Jan. 10, 2017
The Author Email: Yajing Wang (wangyajing0725@126.com)
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