Deviation-Weighted Inversion of Dynamic Light Scattering Based on Autocorrelation Function Reconstruction

Yanan Xu; Jin Shen; Min Xu; Fanyan Wu; Shuai Mao; Yajing Wang; Wei Liu; Xianming Sun

doi:10.3788/AOS201838.1229002

Acta Optica Sinica, Volume. 38, Issue 12, 1229002(2018)

Deviation-Weighted Inversion of Dynamic Light Scattering Based on Autocorrelation Function Reconstruction

Yanan Xu^*, Jin Shen^*, Min Xu, Fanyan Wu, Shuai Mao, Yajing Wang, Wei Liu, and Xianming Sun

Author Affiliations

College of Electrical and Electronic Engineering, Shandong University of Technology, Zibo, Shandong 255049, China

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Figures & Tables(14)

Fig. 1. (a) ACF of 300 nm/500 nm bimodal particles; (b) PSID; (c) PSID of 300 nm/500 nm and 300 nm/800 nm bimodal particles in corresponding ACF

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Fig. 2. (a) True ACF and first reconstructed ACF of 300 nm/500 nm bimodal particles; (b) difference of true ACF from reconstructed ACF for once, twice, three times and L times

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Fig. 3. Basic procedure of information deviation-weighted method

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Fig. 4. Inversion results of 375 nm unimodal narrow PSD. (a) δ=3×10-4; (b) δ=3×10-3

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Fig. 5. Inversion results of 400 nm unimodal broad PSD. (a) δ=3×10-4; (b) δ=3×10-3

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Fig. 6. Inversion results under noise levels of 3×10-4 and 3×10-3. (a) 400 nm/800 nm bimodal PSD; (b) 500 nm/800 nm bimodal PSD; (c) 500 nm/750 nm bimodal PSD

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Fig. 7. Inversion results of 300 nm/502 nm standard polystyrene latex particles. (a) δ=3×10-4; (b) δ=3×10-3

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Table 1. Parameters and properties of PSD

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Table 1. Parameters and properties of PSD

Sample														R_PP	R_PH	d₁	σ₁	d₂	σ₂	a	b	δ	D
Unimodal	Narrow	375	-	-	-	-	375	0.050	-	1.00	3×10^-43×10^-3	380379
Unimodal	Broad	400	-	-	-	-	400	0.130	-	1.00	3×10^-43×10^-3												434436
Bimodal														400/800	2∶1	-	400	0.090	800	0.060	0.35	0.65	3×10^-43×10^-3	780777
														500/800	1.6∶1	-	500	0.080	800	0.050	0.40	0.60	3×10^-43×10^-3	758757
													500/750	1.5∶1	-	500	0.080	750	0.050	0.40	0.60	3×10^-43×10^-3	712711

Table 2. Performance indexes for inversion of 375 nm unimodal narrow PSD (L=10)
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Table 2. Performance indexes for inversion of 375 nm unimodal narrow PSD (L=10)
Condition P_P/nm E_PP R_PH V
true 375 0 - 0
m0 361 0.037 - 0.263
δ=3×10^-4 m1 361 0.037 - 0.268
m2 360 0.040 - 0.259
mL 363 0.032 - 0.253
m0 361 0.037 - 0.262
δ=3×10^-3 m1 353 0.059 - 0.269
m2 361 0.037 - 0.258
mL 369 0.016 - 0.246

Table 3. Performance indexes for inversion of 400 nm bimodal broad PSD (L=12)
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Table 3. Performance indexes for inversion of 400 nm bimodal broad PSD (L=12)
Condition P_P/nm E_PP R_PH V
true 400 0 - 0
m0 369 0.078 - 0.059
δ=3×10^-4 m1 369 0.078 - 0.068
m2 377 0.058 - 0.055
mL 393 0.018 - 0.042
m0 377 0.058 - 0.056
δ=3×10^-3 m1 361 0.098 - 0.062
m2 385 0.038 - 0.038
mL 401 0.003 - 0.031

Table 4. Performance indexes for inversion of 400 nm/800 nm bimodal PSD (L=17)

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Table 4. Performance indexes for inversion of 400 nm/800 nm bimodal PSD (L=17)

Condition		P_P/nm	E_PP	R_PH	V
	true	400/800	0/0	0.716∶1	0
	m0	390/690	0.025/0.138	0.619∶1	0.133
δ=3×10^-4	m1	440/830	0.100/0.038	0.188∶1	0.108
	m2	430/830	0.075/0.038	0.255∶1	0.100
	mL	440/800	0.100/0	0.425∶1	0.063
	m0	440/710	0.100/0.113	0.197∶1	0.148
δ=3×10^-3	m1	440/830	0.100/0.038	0.219∶1	0.104
	m2	430/830	0.075/0..038	0.258∶1	0.100
	mL	441/790	0.103 /0.013	0.513∶1	0.062

Table 5. Performance indexes for inversion of 500 nm/800 nm bimodal PSD (L=16)

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Table 5. Performance indexes for inversion of 500 nm/800 nm bimodal PSD (L=16)

Condition		P_P/nm	E_PP	R_PH	V
	true	500/800	0/0	0.673∶1	0
	m0	425/731	0.150/0.086	0.214∶1	0.143
δ=3×10^-4	m1	443/839	0.114/0.049	0.161∶1	0.122
	m2	425/830	0.150/0.038	0.298∶1	0.113
	mL	470/803	0.060/0.004	0.415∶1	0.068
	m0	-/740	-/0.075	-	0.146
δ=3×10^-3	m1	434/830	0. 132/0.038	0.239∶1	0.115
	m2	434/830	0.132/0.038	0.291∶1	0.112
	mL	461/803	0.078/0.004	0.407∶1	0.069

Table 6. Performance indexes for inversion of 500 nm/750 nm bimodal PSD (L=15)

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Table 6. Performance indexes for inversion of 500 nm/750 nm bimodal PSD (L=15)

Condition		P_P/nm	E_PP	R_PH	V
	true	500/750	0/0	0.625∶1	0
	m0	425/713	0.150/0.049	0.232∶1	0.127
δ=3×10^-4	m1	434/830	0.132/0.107	0.235∶1	0.125
	m2	425/803	0.150/0.071	0.752∶1	0.120
	mL	443/767	0.114/0.023	0.506∶1	0.093
	m0	443/704	0.114/0.131	0.173∶1	0.127
δ=3×10^-3	m1	425/821	0.150/0.095	0.338∶1	0.118
	m2	425/794	0.150/0.059	0.710∶1	0.102
	mL	479/767	0.042/0.023	0.567∶1	0.052

Table 7. Performance indexes for inversion of 300 nm/502 nm standard polystyrene latex particles

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Table 7. Performance indexes for inversion of 300 nm/502 nm standard polystyrene latex particles

Condition		P_P/nm	E_PP	R_PH
	true	300/502	0/0	5∶1
	m0	350/-	0.167/-	-
δ=3×1 $\begin{matrix} {0^{-}}^{4} \end{matrix}$	m1	310/520	0.033/0.036	2.271∶1
	m2	360/650	0.200/0.295	4.938∶1
	mL	300/520	0.000/0.036	4.048∶1
	m0	380/-	0.267/-	-
δ=3×10^-3	m1	310/520	0.033/0.036	2.271∶1
	m2	359/650	0.197/0.295	4.360∶1
	mL	300/521	0.000 /0.038	4.107∶1

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Yanan Xu, Jin Shen, Min Xu, Fanyan Wu, Shuai Mao, Yajing Wang, Wei Liu, Xianming Sun. Deviation-Weighted Inversion of Dynamic Light Scattering Based on Autocorrelation Function Reconstruction[J]. Acta Optica Sinica, 2018, 38(12): 1229002

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