Dynamic Light Scattering Inversion of Flow Aerosols Using Mixed Regularization Based on Total Least Squares

P /nm	ɑ₁	μ₁	σ₁	ɑ₂	μ₂	σ₂	$(d_{m i n}, d_{m a x})$
316	1	1.1	5.5	0			（2.01，700.01）
492	1	0.1	4.3	0			（2.01，1000.01）
601	1	0.05	4.3	0			（2.01，1200.01）
234/700	0.435	6.4	5.5	0.565	-4.1	5	（2.01，1000.01）
143/584	0.4	9	5	0.6	-2.2	6.8	（2.01，1000.01）

Table 2. Performance of the unimodal particle inversion of PSD

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Table 2. Performance of the unimodal particle inversion of PSD

P_true /nm	Velocity /（m/s）	LS-Tik			TLS-Tik-TV
P_true /nm	Velocity /（m/s）	P_inversion /nm	Eₚ	E_r	P_inversion /nm	Eₚ	E_r
316	0	314	0.006	0.058	314	0.006	0.015
	0.4	304	0.037	0.049	310	0.018	0.037
	0.8	304	0.037	0.058	310	0.018	0.038
	1.2	304	0.037	0.082	310	0.018	0.058
	1.6	304	0.037	0.071	310	0.018	0.050
	2.0	298	0.055	0.089	304	0.037	0.066
492	0	492	0	0. 025	492	0	0. 011
	0.4	484	0.017	0.051	492	0	0.016
	0.8	467	0.051	0.064	467	0.051	0.056
	1.2	442	0.101	0.094	459	0.068	0.074
	1.6	451	0.084	0.087	459	0.068	0.078
	2.0	434	0.118	0.108	451	0.084	0.081
601	0	581	0.033	0.037	581	0.033	0.028
	0.4	571	0.050	0.041	581	0.033	0.028
	0.8	561	0.066	0.061	571	0.050	0.047
	1.2	551	0.083	0.078	565	0.065	0.071
	1.6	551	0.083	0.081	571	0.050	0.048
	2.0	531	0.116	0.105	552	0.083	0.081

Table 3. Performance of the bimodal particles inversion of PSD

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Table 3. Performance of the bimodal particles inversion of PSD

P_true /nm	Velocity /（m/s）	LS-Tik			TLS-Tik-TV
P_true /nm	Velocity /（m/s）	P_inversion /nm	Eₚ	E_r	P_inversion /nm	Eₚ	E_r
234/700	0	226/667	0.035/0.048	0.070	234/675	0.000/0.036	0.043
	0.3	201/625	0.142/0.107	0.117	218/642	0.071/0.083	0.104
	0.6	185/559	0.213/0.202	0.163	193/575	0.177/0.178	0.172
	0.9	126/509	0.460/0.273	0.195	168/534	0.283/0.237	0.196
	1.2	110/484	0.531/0.389	0.209	160/517	0.319/0.261	0.199
	1.5	93/476	0.602/0.321	0.203	143/501	0.390/0.285	0.190
143/584	0	135/559	0.058/0.043	0.079	135/559	0.058/0.043	0.063
	0.3	135/542	0.058/0.071	0.101	135/542	0.058/0.071	0.091
	0.6	126/517	0.116/0.114	0.125	135/525	0.058/0.099	0.123
	0.9	110/484	0.232/0.171	0.156	126/501	0.116/0.142	0.158
	1.2	110/459	0.232/0.214	0.161	126/492	0.116/0.156	0.151
	1.5	101/434	0.291/0.256	0.183	118/476	0.174/0.185	0.155

Table 4. Performance of the true aerosol particles inversion of PSD

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Table 4. Performance of the true aerosol particles inversion of PSD

Particle state	Velocity /（m/s）	Method	P_inversion /nm	Eₚ₀	E_r0
Unimodal	0	TLS-Tik-TV	584	0	0
	1.11	LS-Tik	550	0.058	0.073
	1.11	TLS-Tik-TV	550	0.058	0.087
	1.67	LS-Tik	501	0.142	0.194
	1.67	TLS-Tik-TV	517	0.115	0.162
Bimodal	0	TLS-Tik-TV	243/825	0	0
	0.58	LS-Tik	110/775	0.547/0.061	0.137
	0.58	TLS-Tik-TV	126/808	0.481/0.021	0.129
	1.30	LS-Tik	68/650	0.720/0.212	0.206
	1.30	TLS-Tik-TV	98/725	0.597/0.121	0.168

Table 5. Relative standard deviation P_RSD of peak particle size

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Table 5. Relative standard deviation P_RSD of peak particle size

v /（m/s）	Method	P₁ /nm	P₂ /nm	P₃ /nm	P₄ /nm	P₅ /nm	P₆ /nm	$\bar{P}$ /nm	P_RSD /%
1.67	LS-Tik	501	509	511	491	504	498	502.3	1.47
1.67	TLS-Tik-TV	517	510	512	525	511	516	515.17	1.08
1.30	LS-Tik	68/650	49/631	58/637	77/659	72/655	76/660	66.67/648.67	1.66/1.86
1.30	TLS-Tik-TV	98/725	108/736	115/743	83/711	93/719	87/715	97.33/724.83	1.26/1.72

Table 6. Relative standard deviation R_N of granularity distribution norm

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Table 6. Relative standard deviation R_N of granularity distribution norm

v /（m/s）	Method	N_F1	N_F2	N_F3	N_F4	N_F5	N_F6	${\bar{N}}_{F}$	R_N /%
1.67	LS-Tik	65.53	69.71	61.45	66.14	61.78	62.97	64.60	4.89
1.67	TLS-Tik-TV	64.29	68.87	61.94	65.76	62.59	65.17	64.77	3.84
1.30	LS-Tik	49.85	45.73	47.18	51.14	50.49	52.07	49.41	4.95
1.30	TLS-Tik-TV	49.35	51.72	52.06	49.41	46.57	48.61	49.62	4.11

Table 7. Running time of the two algorithms

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Table 7. Running time of the two algorithms

v /（m/s）	Method	T_s1 /s	T_s2 /s	T_s3 /s	T_s4 /s	T_s5 /s	T_s6 /s	${\bar{T}}_{s}$ /s
1.67	LS-Tik	1.59	1.60	1.60	1.58	1.60	1.59	1.59
1.67	TLS-Tik-TV	1.65	1.66	1.62	1.63	1.66	1.66	1.65
1.30	LS-Tik	1.58	1.60	1.59	1.59	1.57	1.60	1.59
1.30	TLS-Tik-TV	1.66	1.64	1.64	1.67	1.70	1.63	1.66

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Zhixiang Yang, Zhi Dou, Yajing Wang, Jin Shen, Wei Liu, Hu Ming, Xiaojun Fu, Junhua Hu. Dynamic Light Scattering Inversion of Flow Aerosols Using Mixed Regularization Based on Total Least Squares[J]. Chinese Journal of Lasers, 2025, 52(6): 0604001

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