To Make a Good Infrared Spectrum in NaCl Aqueous Solution Where Lambert-Beer’s Law is Not to be Obeyed

Fig. 3. The subtraction spectra between A_16%and different A^16%(c₁, c₂)
a: ΔA_16%(14%, 18%); b: ΔA_16%(12%, 20%); c: ΔA_16%(10%, 22%); d: ΔA_16%(8%, 24%); e: ΔA_16%(6%, 26%); f: ΔA_16%(4%, 28%); g: ΔA_16%(2%, 30%)

Download full size

View in Article

Fig. 4. The subtraction spectra between A_16%and different A_h_16%(c₁, c₂)
a: ΔA_h_16%(14%, 18%); b: ΔA_h_16%(12%, 20%); c: ΔA_h_16%(10%, 22%); d: ΔA_h_16%(8%, 24%); e: ΔA_h_16%(6%, 26%); f: ΔA_h_16%(4%, 28%); g: ΔA_h_16%(2%, 30%)

Download full size

View in Article

Fig. 5. The subtraction spectra between A_c and A_hc(2%, 30%)
a: ΔA_h4%; b: ΔA_h_6%; c: ΔA_h_8%; d: ΔA_h_10%; e: ΔA_h_12%;f: ΔA_h_14%; g: ΔA_h_16%; h: ΔA_h_18%; i: ΔA_h_20%; j: ΔA_h_22%;k: ΔA_h_24%; l: ΔA_h_26%; m: ΔA_h_28%

Download full size

View in Article

Fig. 6. The fitting regression coefficient-c curves
(a): a^-c curve; (b): b^-c curve

Download full size

View in Article

Fig. 7. The real spectra (dashed line) and corresponding hybrid spectra (dotted line) of NaCl aqueous solutions
a: A_5% and A_h_5%(2%, 30%); b: A_13% and A_h_13%(2%, 30%);c: A_15% and A_h_15%(2%, 30%); d: A_19% and A_h_19%(2%, 30%);e: A_23% and A_h_23%(2%, 30%); f: A_25% and A_h_25%(2%, 30%)

Download full size

View in Article

Table 1. The binary linear regression equations between A_c and $A_{c_{1}}$ , $A_{c_{2}}$

View table

View in Article

Table 1. The binary linear regression equations between A_c and $A_{c_{1}}$ , $A_{c_{2}}$

编号	A_c	$A_{c_{1}}$	$A_{c_{2}}$	${\hat{A}}_{16 %}$ (c₁, c₂)= $\hat{a} A_{c_{1}}$ + $\hat{b} A_{c_{2}}$ + $\hat{e}$
1	A_16%	A_14%	A_18%	${\hat{A}}_{16 %}$ (14%, 18%)=0.585 6×A_14%+0.414 1×A_18%-3.47×10^-4
2	A_16%	A_12%	A_20%	${\hat{A}}_{16 %}$ (12%, 20%)=0.556 6×A_12%+0.443 1×A_20%-1.33×10^-5
3	A_16%	A_10%	A_22%	${\hat{A}}_{16 %}$ (10%, 22%)=0.507 7×A_10%+0.490 9×A_22%-6.01×10^-4
4	A_16%	A_8%	A_24%	${\hat{A}}_{16 %}$ (8%, 24%)=0.501 9×A_8%+0.496 7×A_24%+4.29×10^-4
5	A_16%	A_6%	A_26%	${\hat{A}}_{16 %}$ (6%, 26%)=0.477 1×A_6%+0.530 9×A_26%+4.58×10^-4
6	A_16%	A_4%	A_28%	${\hat{A}}_{16 %}$ (4%, 28%)=0.479 6×A_4%+0.524 5×A_28%+3.44×10^-4
7	A_16%	A_2%	A_30%	${\hat{A}}_{16 %}$ (2%, 30%)=0.484 2×A_2%+0.516 6×A_30%-3.17×10^-5

Table 2. The significance test of linear regression effect of the regression equations between A_16% and $A_{c_{1}}$ , $A_{c_{2}}$

View table

View in Article

Table 2. The significance test of linear regression effect of the regression equations between A_16% and $A_{c_{1}}$ , $A_{c_{2}}$

编号	F	r²	估计标准误差	$t_{\hat{a}}$	$t_{\hat{b}}$	$t_{\hat{e}}$
1	7.2×10⁸	1.000	1.7×10^-4	811	573	106
2	6.7×10⁸	1.000	1.8×10^-4	1 541	1 232	-4
3	2.8×10⁸	1.000	2.8×10^-4	1 273	1 243	119
4	2.3×10⁸	1.000	3.1×10^-4	1 504	1 516	75
5	1.4×10⁸	1.000	3.9×10^-4	1 399	1 553	64
6	1.2×10⁸	1.000	4.3×10^-4	1 528	1 727	43
7	6.9×10⁷	1.000	5.6×10^-4	1 371	1 507	-3

Table 3. The hybrid spectra equations between A_hc and A_2%, A_30%

View table

View in Article

Table 3. The hybrid spectra equations between A_hc and A_2%, A_30%

编号	A_c	$A_{c_{1}}$	$A_{c_{2}}$	A_hc(2%, 30%)= $\hat{a}$ A_2%+ $\hat{b}$ A_30%
1	A_4%	A_2%	A_30%	A_h_4%(2%, 30%)=0.930 3×A_2%+0.062 6×A_30%
2	A_6%	A_2%	A_30%	A_h_6%(2%, 30%)=0.855 2×A_2%+0.149 9×A_30%
3	A_8%	A_2%	A_30%	A_h_8%(2%, 30%)=0.772 5×A_2%+0.229 7×A_30%
4	A_10%	A_2%	A_30%	A_h_10%(2%, 30%)=0.696 5×A_2%+0.307 2×A_30%
5	A_12%	A_2%	A_30%	A_h_12%(2%, 30%)=0.622 1×A_2%+0.381 4×A_30%
6	A_14%	A_2%	A_30%	A_h_14%(2%, 30%)=0.546 6×A_2%+0.456 5×A_30%
7	A_16%	A_2%	A_30%	A_h_16%(2%, 30%)=0.484 2×A_2%+0.516 6×A_30%
8	A_18%	A_2%	A_30%	A_h_18%(2%, 30%)=0.396 9×A_2%+0.601 2×A_30%
9	A_20%	A_2%	A_30%	A_h_20%(2%, 30%)=0.311 6×A_2%+0.686 5×A_30%
10	A_22%	A_2%	A_30%	A_h_22%(2%, 30%)=0.266 1×A_2%+0.734 5×A_30%
11	A_24%	A_2%	A_30%	A_h_24%(2%, 30%)=0.194 5×A_2%+0.807 7×A_30%
12	A_26%	A_2%	A_30%	A_h_26%(2%, 30%)=0.144 0×A_2%+0.857 6×A_30%
13	A_28%	A_2%	A_30%	A_h_28%(2%, 30%)=0.072 66×A_2%+0.927 6×A_30%

Table 4. The relationship among c, regression coefficient $\hat{a}$ and $\hat{b}$ and $\hat{a}$ + $\hat{b}$
View table
View in Article
Table 4. The relationship among c, regression coefficient $\hat{a}$ and $\hat{b}$ and $\hat{a}$ + $\hat{b}$
c(w/v)/% $\hat{a}$ $\hat{b}$ $\hat{a}$ + $\hat{b}$
4 0.930 3 0.062 6 0.992 9
10 0.696 5 0.307 2 1.003 7
16 0.484 2 0.516 6 1.000 8
22 0.266 1 0.734 5 1.000 6
28 0.072 7 0.927 6 1.000 3

Tools

Get Citation

Copy Citation Text

Meng YAO, Hai-shui WANG. To Make a Good Infrared Spectrum in NaCl Aqueous Solution Where Lambert-Beer’s Law is Not to be Obeyed[J]. Spectroscopy and Spectral Analysis, 2021, 41(1): 65

Download Citation

EndNote(RIS)BibTex Plain Text

Set citation alerts for article

Save article for my favorites

Paper Information

Category: Research Articles

Received: Jul. 13, 2020

Accepted: --

Published Online: Apr. 8, 2021

The Author Email:

DOI:10.3964/j.issn.1000-0593(2021)01-0065-06

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. The binary linear regression equations between Ac and Ac1, Ac2

Table 1. The binary linear regression equations between Ac and Ac1, Ac2

Table 2. The significance test of linear regression effect of the regression equations between A16% and Ac1, Ac2

Table 2. The significance test of linear regression effect of the regression equations between A16% and Ac1, Ac2

Table 3. The hybrid spectra equations between Ahc and A2%, A30%

Table 3. The hybrid spectra equations between Ahc and A2%, A30%

Table 4. The relationship among c, regression coefficient a^ and b^ and a^+b^

Table 4. The relationship among c, regression coefficient a^ and b^ and a^+b^

Table 1. The binary linear regression equations between A_c and $A_{c_{1}}$ , $A_{c_{2}}$

Table 1. The binary linear regression equations between A_c and $A_{c_{1}}$ , $A_{c_{2}}$

Table 2. The significance test of linear regression effect of the regression equations between A_16% and $A_{c_{1}}$ , $A_{c_{2}}$

Table 2. The significance test of linear regression effect of the regression equations between A_16% and $A_{c_{1}}$ , $A_{c_{2}}$

Table 3. The hybrid spectra equations between A_hc and A_2%, A_30%

Table 3. The hybrid spectra equations between A_hc and A_2%, A_30%

Table 4. The relationship among c, regression coefficient $\hat{a}$ and $\hat{b}$ and $\hat{a}$ + $\hat{b}$

Table 4. The relationship among c, regression coefficient $\hat{a}$ and $\hat{b}$ and $\hat{a}$ + $\hat{b}$