CN103543105B - Based on the method for Kubelka-Munk theory calculate pigment covering power - Google Patents

Abstract

The invention discloses a kind of method based on Kubelka-Munk theory calculate pigment covering power.The method only needs to make and black substrate and white substrate pigment coated under measuring a certain thicknesses of layers, then revises and Kubelka-Munk theory calculate scattering coefficient S according to Saunderson _λwith absorption coefficient K _λ, and then cycle calculations must try to achieve thicknesses of layers d _z, the Δ E of its correspondence ^* _abapproximate 1, finally calculate the covering power Z of pigment.The method has the test duration short (only need make a certain thicknesses of layers under pigment coated), result is reliably objective, precision is high, is suitable for the advantage such as black and white and color pigment, and realizes calculating pigment covering power Z automatically and quickly by computer programming.

Description

Based on the method for Kubelka-Munk theory calculate pigment covering power

Technical field

The present invention relates to a kind of computing method of pigment covering power, specifically relate to a kind of new method of the calculating pigment covering power based on Kubelka-Munk theory.

Background technology

Along with the high speed development of industrial technology, pigment has been widely used in daily life goods, as ink, paint, plastic products etc. as colorant.Detection for pigment characteristics is very important.The characteristic of pigment comprises a lot of aspect, as form and aspect, colouring power, photostability, weatherability etc.The covering power of pigment also usually appears in the technical manual table of pigment as a wherein physical characteristics.

Pigment covering power is defined as pigment and hides under a certain concentration by the ability being coated with base color, is the synthesis result to absorbing incident light and scattering.Covering unit of force is m ²/ L, represent make eye-observation to suprabasil contrast just disappear time corresponding thicknesses of layers inverse, or adopt g/m ²for unit, represent the amount of pigment of unit area when reaching covering.It should be noted that, all covering powers calculate all for a certain pigment concentration.

At present, what the standard GB/T 1726-1979 of China adopted is black and white lattice plate method, grinds to form mill base and is painted on uniformly on black and white lattice glass plate, make the minimum amount of pigment that black and white lattice are just covered by pigment and varnish, adopts g/m ²for index.

In the world, main have two kinds of standards detecting pigment covering power, the ASTM2805 of the U.S. and the DIN55978 of Germany.ASTM2805 and DIN55978 all needs the pigment sample making multiple different thicknesses of layers in black/white substrate.ASTM2805 is with under same film layer thickness, and the thicknesses of layers when contrast ratio of the black substrate recorded and the CIEY value of white substrate is 0.98 is as covering thickness, i.e. Y _k/ Y _w=0.98, and detect mainly for the covering power of whitewash; And DIN55978 is with under same film layer thickness, the black substrate recorded and the CIELAB aberration of white substrate equal 1 as critical value, represent and hide completely, be i.e. Δ E ^* _ab=1.

GB1726-1979 the method is fairly simple, easy to operate, but need repeatedly to make sample, the test duration is long, error is large; ASTM2805 and DIN55978 is owing to adopting apparatus measures, so results contrast is objective, precision is high, but it is long all to need to make multiple sample, test duration.Up to now, also there is no that a kind of test duration is short and result is objective, the detection method of the pigment covering power that precision is high.

Summary of the invention

The present invention, in order to solve the problem described in background technology, discloses a kind of method of simple, easy to operate, the calculating pigment covering power based on Kubelka-Munk theory that precision is high.

Concrete steps are as follows:

1) other components (as resin, adjuvant etc.) in the pigment of required measurement covering power and application system are carried out ground and mixed according to the method that this application system is general, assuming that the mass percent of pigment is n%, namely in the quality of pigment and application system, the mass ratio of other components is n%;

2) black/white paperboard conventional in selecting pigment to detect, it comprises black substrate and white substrate, to measure obtain spectrum R respectively with integrating sphere type spectrophotometer to black substrate and white substrate _{λ, K}and R _{λ, W}, wherein subscript λ represents measurement wavelength, and subscript K represents black substrate, and subscript W represents white substrate;

3) select a coating machine or KBar by step 1) in the pigment of gained and the mixed liquor of other components be applied in black/white paperboard, through natural drying or pigment coated under drying obtained a certain thicknesses of layers;

4) pigment coated carry out thicknesses of layers measurement with corresponding measuring instrument to obtained, the result recorded is designated as h;

5) with integrating sphere type spectrophotometer to being coated in black substrate and white suprabasil pigment coated measurement obtains spectrum R respectively _{λ, K, T}and R _{λ, W, T}, wherein subscript T represents and pigment coatedly measures the spectrum obtained to suprabasil;

6) to the R recorded _{λ, K}, R _{λ, W}, R _{λ, K, T}and R _{λ, W, T}carry out Saunderson correction and obtain revised spectrum R respectively ^* _{λ, K}, R ^* _{λ, W}, R ^* _{λ, K, T}and R ^* _{λ, W, T}, Saunderson correction formula is as follows:

$R_{\mathrm{\λ}}^{*}=\frac{R_{\mathrm{\λ}}-0.04}{0.36+0.6R_{\mathrm{\λ}}}$

Wherein, R _λrepresent that measuring the wavelength obtained is the spectroscopic data of λ, R ^* _λrepresent that the revised wavelength of Saunderson is the corresponding spectroscopic data of λ;

7) according to the revised R of Saunderson ^* _{λ, K}, R ^* _{λ, W}, R ^* _{λ, K, T}and R ^* _{λ, W, T}, two auxiliary parameter a in calculating K ubelka-Munk theory _λand b _λ, computing formula is as follows:

$a_{\mathrm{\λ}}=\frac{(1+R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},W}^{*})\×(R_{\mathrm{\λ},K,T}^{*}-R_{\mathrm{\λ},K}^{*})+(1+R_{\mathrm{\λ},K,T}^{*}\×R_{\mathrm{\λ},K}^{*})\×(R_{\mathrm{\λ},W}^{*}-R_{\mathrm{\λ},W,T}^{*})}{2\×(R_{\mathrm{\λ},K,T}^{*}\×R_{\mathrm{\λ},W}^{*}-R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},K}^{*})}$

$b_{\mathrm{\λ}}=\sqrt{{a_{\mathrm{\λ}}}^2-1}$

8) according to auxiliary parameter a _λand b _λ, utilize Kubelka-Munk theory calculate scattering coefficient S _λwith absorption coefficient K _λ, computing formula is as follows:

$S_{\mathrm{\λ}}=\frac{1}{b_{\mathrm{\λ}}h}\mathrm{Ar}\coth \left(\frac{1-a_{\mathrm{\λ}}\×(R_{\mathrm{\λ},W,T}^{*}+R_{\mathrm{\λ},W}^{*})+R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},W}^{*}}{b_{\mathrm{\λ}}\×(R_{\mathrm{\λ},W,T}^{*}-R_{\mathrm{\λ},W}^{*})}\right)$

K _λ＝S _λ×(a _λ-1)

Wherein, Arcoth is acoth function;

9) according to scattering coefficient S _λwith absorption coefficient K _λ, calculate the pigment coated spectrum R that arbitrary thicknesses of layers in black substrate and white substrate is d respectively ^* _{d, λ, K, T}and R ^* _{d, λ, W, T}, computing formula is as follows:

${R^{*}}_{d,\mathrm{\λ},K,T},=\frac{1-{R^{*}}_{\mathrm{\λ},K}\×(a_{\mathrm{\λ}}-b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d))}{a_{\mathrm{\λ}}-{R^{*}}_{\mathrm{\λ},K}+b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d)}$

${R^{*}}_{d,\mathrm{\λ},W,T},=\frac{1-{R^{*}}_{\mathrm{\λ},W}\×(a_{\mathrm{\λ}}-b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d))}{a_{\mathrm{\λ}}-{R^{*}}_{\mathrm{\λ},W}+b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d)}$

Wherein, coth is hyperbolic cotangent;

10) to R ^* _{d, λ, K, T}and R ^* _{d, λ, W, T}, the pigment coated spectrum R that utilize reverse Saunderson corrected Calculation to obtain thicknesses of layers in black substrate and white substrate that finally measurement obtains is d _{d, λ, K, T}and R _{d, λ, W, T}, computing formula is as follows:

$R_{d,\mathrm{\λ},K,T},=\frac{0.36\×{R^{*}}_{d,\mathrm{\λ},K,T}+0.04}{1-0.6\×{R^{*}}_{d,\mathrm{\λ},K,T}}$

$R_{d,\mathrm{\λ},W,T},=\frac{0.36\×{R^{*}}_{d,\mathrm{\λ},W,T}+0.04}{1-0.6\×{R^{*}}_{d,\mathrm{\λ},W,T}}$

11) according to the spectrum R obtained _{d, λ, K, T}and R _{d, λ, W, T}, calculate the pigment coated CIELAB value that corresponding thicknesses of layers in black substrate and white substrate is d, be designated as L respectively ^* _k, a ^* _k, b ^* _kand L ^* _w, a ^* _w, b ^* _w, account form is see ASTME308-06 standard;

12) corresponding aberration Δ E is calculated ^* _ab, computing formula is as follows:

${\mathrm{\ΔE}}_{\mathrm{ab}}^{*}=\sqrt{{(L_K^{*}-L_W^{*})}^2+{(a_K^{*}-a_W^{*})}^2+{(b_K^{*}-b_W^{*})}^2}$

13) according to step 9) to step 12), aberration Δ E corresponding when can calculate a series of different thicknesses of layers d ^* _ab, final selection Δ E ^* _abwhen approximating 1, corresponding thicknesses of layers d _z;

14) calculate the covering power Z when pigment mass number percent is n%, computing formula is as follows:

$Z=\frac{1}{d_Z}$

The present invention only needs to make and black substrate and white substrate pigment coated under measuring a certain thicknesses of layers, then according to Kubelka-Munk theory calculate scattering coefficient S _λwith absorption coefficient K _λ, and then cycle calculations must try to achieve thicknesses of layers d _z, the Δ E of its correspondence ^* _abapproximate 1, finally calculate the covering power Z of pigment.The method has the test duration short (only need make a certain thicknesses of layers under pigment coated), and result is objective, and precision is high, is suitable for the advantage such as black and white and color pigment.Although the computation process of the method is slightly aobvious complicated, by computer manufacture one program, only need the R that input measurement obtains _{λ, K}, R _{λ, W}, R _{λ, K, T}, R _{λ, W, T}and h, final pigment covering power Z can be calculated automatically and quickly.

Accompanying drawing explanation

Fig. 1 is the method flow diagram based on Kubelka-Munk theory calculate pigment covering power;

Fig. 2 is the spectrum measuring black substrate and the white substrate obtained;

Fig. 3 be make obtain in black substrate and white suprabasil pigment coated pictorial diagram;

Fig. 4 be measure obtain at black substrate and white suprabasil pigment coated spectrum;

Fig. 5 is the scattering coefficient S calculated _λwith absorption coefficient K _λ;

Fig. 6 is aberration Δ E ^* _abwith the variation diagram of thicknesses of layers d.

Embodiment

For a yellow uitramarine (C.I. pigment yellow 53) in alkyd-melamine coatings application system, the above-mentioned method based on Kubelka-Munk theory calculate pigment covering power is set forth.As shown in Figure 1, its concrete steps are as follows:

1) other components (alkyd, melamine, adjuvant etc.) 100g in this yellow uitramarine 3 grams and system is got, the method general according to alkyd-melamine coatings application system carries out ground and mixed, and final obtained pigment mass number percent is the coating of 3%;

2) black/white paperboard conventional in selecting pigment to detect, it comprises black substrate and white substrate, to measure obtain spectrum R respectively with integrating sphere type spectrophotometer to black substrate and white substrate _{λ, K}and R _{λ, W}, see Fig. 2, wherein subscript λ represents measurement wavelength, and subscript K represents black substrate, and subscript W represents white substrate;

3) select the KBar of 150 μm by step 1) in the pigment of gained and the mixed liquor of other components be applied in black/white paperboard, through natural drying or pigment coated under drying obtained a certain thicknesses of layers, see Fig. 3;

4) pigment coated carry out thicknesses of layers measurement with paint thickness Special measuring instrument to obtained, the result h recorded is 74 μm;

5) with integrating sphere type spectrophotometer to being coated in black substrate and white suprabasil pigment coated measurement obtains spectrum R respectively _{λ, K, T}and R _{λ, W, T}, see Fig. 4, wherein subscript T represents and pigment coatedly measures the spectrum obtained to suprabasil, and measurement range is 400nm to 700nm, take 10nm as interval;

6) to the R recorded _{λ, K}, R _{λ, W}, R _{λ, K, T}and R _{λ, W, T}carry out Saunderson correction and obtain revised spectrum R respectively ^* _{λ, K}, R ^* _{λ, W}, R ^* _{λ, K, T}and R ^* _{λ, W, T}, Saunderson correction formula is as follows:

$R_{\mathrm{\λ}}^{*}=\frac{R_{\mathrm{\λ}}-0.04}{0.36+0.6R_{\mathrm{\λ}}}$

Wherein, R _λrepresent that measuring the wavelength obtained is the spectroscopic data of λ, R ^* _λrepresent that the revised wavelength of Saunderson is the corresponding spectroscopic data of λ;

7) according to the revised R of Saunderson ^* _{λ, K}, R ^* _{λ, W}, R ^* _{λ, K, T}and R ^* _{λ, W, T}, two auxiliary parameter a in calculating K ubelka-Munk theory _λand b _λ, computing formula is as follows:

$a_{\mathrm{\λ}}=\frac{(1+R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},W}^{*})\×(R_{\mathrm{\λ},K,T}^{*}-R_{\mathrm{\λ},K}^{*})+(1+R_{\mathrm{\λ},K,T}^{*}\×R_{\mathrm{\λ},K}^{*})\×(R_{\mathrm{\λ},W}^{*}-R_{\mathrm{\λ},W,T}^{*})}{2\×(R_{\mathrm{\λ},K,T}^{*}\×R_{\mathrm{\λ},W}^{*}-R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},K}^{*})}$

$b_{\mathrm{\λ}}=\sqrt{{a_{\mathrm{\λ}}}^2-1}$

8) according to auxiliary parameter a _λand b _λ, utilize Kubelka-Munk theory calculate scattering coefficient S _λwith absorption coefficient K _λ, see Fig. 5, computing formula is as follows:

$S_{\mathrm{\λ}}=\frac{1}{b_{\mathrm{\λ}}h}\mathrm{Ar}\coth \left(\frac{1-a_{\mathrm{\λ}}\×(R_{\mathrm{\λ},W,T}^{*}+R_{\mathrm{\λ},W}^{*})+R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},W}^{*}}{b_{\mathrm{\λ}}\×(R_{\mathrm{\λ},W,T}^{*}-R_{\mathrm{\λ},W}^{*})}\right)$

K _λ＝S _λ×(a _λ-1)

Wherein, Arcoth is acoth function;

9) according to scattering coefficient S _λwith absorption coefficient K _λ, calculate the pigment coated spectrum R that arbitrary thicknesses of layers in black substrate and white substrate is d respectively ^* _{d, λ, K, T}and R ^* _{d, λ, W, T}, computing formula is as follows:

${R^{*}}_{d,\mathrm{\λ},K,T},=\frac{1-{R^{*}}_{\mathrm{\λ},K}\×(a_{\mathrm{\λ}}-b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d))}{a_{\mathrm{\λ}}-{R^{*}}_{\mathrm{\λ},K}+b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d)}$

${R^{*}}_{d,\mathrm{\λ},W,T},=\frac{1-{R^{*}}_{\mathrm{\λ},W}\×(a_{\mathrm{\λ}}-b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d))}{a_{\mathrm{\λ}}-{R^{*}}_{\mathrm{\λ},W}+b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d)}$

Wherein, coth is hyperbolic cotangent;

10) to R ^* _{d, λ, K, T}and R ^* _{d, λ, W, T}, the pigment coated spectrum R that utilize reverse Saunderson corrected Calculation to obtain thicknesses of layers in black substrate and white substrate that finally measurement obtains is d _{d, λ, K, T}and R _{d, λ, W, T}, computing formula is as follows:

$R_{d,\mathrm{\λ},K,T},=\frac{0.36\×{R^{*}}_{d,\mathrm{\λ},K,T}+0.04}{1-0.6\×{R^{*}}_{d,\mathrm{\λ},K,T}}$

$R_{d,\mathrm{\λ},W,T},=\frac{0.36\×{R^{*}}_{d,\mathrm{\λ},W,T}+0.04}{1-0.6\×{R^{*}}_{d,\mathrm{\λ},W,T}}$

11) according to the spectrum R obtained _{d, λ, K, T}and R _{d, λ, W, T}, calculate the pigment coated CIELAB value that corresponding thicknesses of layers in black substrate and white substrate is d, be designated as L respectively ^* _k, a ^* _k, b ^* _kand L ^* _w, a ^* _w, b ^* _w, account form is see ASTME308-06 standard;

12) corresponding aberration Δ E is calculated ^* _ab, computing formula is as follows:

${\mathrm{\ΔE}}_{\mathrm{ab}}^{*}=\sqrt{{(L_K^{*}-L_W^{*})}^2+{(a_K^{*}-a_W^{*})}^2+{(b_K^{*}-b_W^{*})}^2}$

13) according to step 9) to step 12), aberration Δ E corresponding when can calculate a series of different thicknesses of layers d ^* _ab, final selection Δ E ^* _abwhen approximating 1, see Fig. 6, corresponding thicknesses of layers d _z=180 μm;

14) calculate the covering power Z when pigment mass number percent is 3%, computing formula is as follows:

$Z=\frac{1}{d_Z}=\frac{1}{180\mathrm{\μm}}=5.56m^2/L$

In order to verify the reliability of the above results, the present invention's multiple pigment mass number percent that adopted ASTM2805 and DIN55978 standard to make is pigment coated in black/white paperboard of the different thicknesses of layers of 3%, and the covering power calculated respectively under this mass percent by the method for correspondence is 5.51m ²/ L (ASTM2805) and 5.75m ²/ L (DIN55978), as can be seen here, the result of result of the present invention and ASTM2805 and DIN55978 is basically identical, true and reliable.

Claims (4)

1., based on a method for Kubelka-Munk theory calculate pigment covering power, it is characterized in that comprising the following steps:

1) other components in the pigment of required measurement covering power and application system are carried out ground and mixed according to the method that this application system is general, other components described comprise resin and adjuvant, assuming that the mass percent of pigment is n%, namely in the quality of pigment and application system, the mass ratio of other components is n%;

2) black/white paperboard conventional in selecting pigment to detect, it comprises black substrate and white substrate, to measure obtain spectrum R respectively with integrating sphere type spectrophotometer to black substrate and white substrate _{λ, K}and R _{λ, W}, wherein subscript λ represents measurement wavelength, and subscript K represents black substrate, and subscript W represents white substrate;

3) select a coating machine or KBar by step 1) in the pigment of gained and the mixed liquor of other components be applied in black/white paperboard, through natural drying or pigment coated under drying obtained a certain thicknesses of layers;

4) pigment coated carry out thicknesses of layers measurement with corresponding measuring instrument to obtained, the result recorded is designated as h;

5) with integrating sphere type spectrophotometer to being coated in black substrate and white suprabasil pigment coated measurement obtains spectrum R respectively _{λ, K, T}and R _{λ, W, T}, wherein subscript T represents and pigment coatedly measures the spectrum obtained to suprabasil;

6) to the R recorded _{λ, K}, R _{λ, W}, R _{λ, K, T}and R _{λ, W, T}carry out Saunderson correction and obtain revised spectrum R respectively ^* _{λ, K}, R ^* _{λ, W}, R ^* _{λ, K, T}and R ^* _{λ, W, T}, Saunderson correction formula is as follows:

$R_{\mathrm{\λ}}^{*}=\frac{R_{\mathrm{\λ}}-0.04}{0.36+0.6R_{\mathrm{\λ}}}$

Wherein, R _λrepresent that measuring the wavelength obtained is the spectroscopic data of λ, R ^* _λrepresent that the revised wavelength of Saunderson is the corresponding spectroscopic data of λ;

7) according to the revised R of Saunderson ^* _{λ, K}, R ^* _{λ, W}, R ^* _{λ, K, T}and R ^* _{λ, W, T}, two auxiliary parameter a in calculating K ubelka-Munk theory _λand b _λ, computing formula is as follows:

$a_{\mathrm{\λ}}=\frac{(1+R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},W}^{*})\×(R_{\mathrm{\λ},K,T}^{*}-R_{\mathrm{\λ},K}^{*})+(1+R_{\mathrm{\λ},K,T}^{*}\×R_{\mathrm{\λ},K}^{*})\×(R_{\mathrm{\λ},W}^{*}-R_{\mathrm{\λ},W,T}^{*})}{2\×(R_{\mathrm{\λ},K,T}^{*}\×R_{\mathrm{\λ},W}^{*}-R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},K}^{*})}$

$b_{\mathrm{\λ}}=\sqrt{{a_{\mathrm{\λ}}}^2-1}$

8) according to auxiliary parameter a _λand b _λ, utilize Kubelka-Munk theory calculate scattering coefficient S _λwith absorption coefficient K _λ, computing formula is as follows:

$S_{\mathrm{\λ}}=\frac{1}{b_{\mathrm{\λ}}h}Ar\coth \left(\frac{1-a_{\mathrm{\λ}}\×(R_{\mathrm{\λ},W,T}^{*}+R_{\mathrm{\λ},W}^{*})+R_{\mathrm{\λ},W,T}^{*}\×R_{\mathrm{\λ},W}^{*}}{b_{\mathrm{\λ}}\×(R_{\mathrm{\λ},W,T}^{*}-R_{\mathrm{\λ},W}^{*})}\right)$

K _λ＝S _λ×(a _λ-1)

Wherein, Arcoth is acoth function;

9) according to scattering coefficient S _λwith absorption coefficient K _λ, calculate the pigment coated spectrum R that arbitrary thicknesses of layers in black substrate and white substrate is d respectively ^* _{d, λ, K}, T and R ^* _{d, λ, W, T}, computing formula is as follows:

${R^{*}}_{d,\mathrm{\λ},K,T},=\frac{1-{R^{*}}_{\mathrm{\λ},K}\×(a_{\mathrm{\λ}}-b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d\left)\right)}{a_{\mathrm{\λ}}-{R^{*}}_{\mathrm{\λ},K}+b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d)}$

${R^{*}}_{d,\mathrm{\λ},W,T},=\frac{1-{R^{*}}_{\mathrm{\λ},W}\×(a_{\mathrm{\λ}}-b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d\left)\right)}{a_{\mathrm{\λ}}-{R^{*}}_{\mathrm{\λ},W}+b_{\mathrm{\λ}}\×\coth (b_{\mathrm{\λ}}\×S_{\mathrm{\λ}}\×d)}$

Wherein, coth is hyperbolic cotangent;

10) to R ^* _{d, λ, K, T}and R ^* _{d, λ, W, T}, the pigment coated spectrum R that utilize reverse Saunderson corrected Calculation to obtain thicknesses of layers in black substrate and white substrate that finally measurement obtains is d _{d, λ, K, T}and R _{d, λ, W, T}, computing formula is as follows:

$R_{d,\mathrm{\λ},K,T},=\frac{0.36\×{R^{*}}_{d,\mathrm{\λ},K,T}+0.04}{1-0.6\×{R^{*}}_{d,\mathrm{\λ},K,T}}$

$R_{d,\mathrm{\λ},W,T},=\frac{0.36\×{R^{*}}_{d,\mathrm{\λ},W,T}+0.04}{1-0.6\×{R^{*}}_{d,\mathrm{\λ},W,T}}$

11) according to the spectrum R obtained _{d, λ, K, T}and R _{d, λ, W, T}, calculate the pigment coated CIELAB value that corresponding thicknesses of layers in black substrate and white substrate is d, be designated as L respectively ^* _k, a ^* _k, b ^* _kand L ^* _w, a ^* _w, b ^* _w, account form is see ASTME308-06 standard;

12) corresponding aberration Δ E is calculated ^* _ab, computing formula is as follows:

${\mathrm{\ΔE}}_{ab}^{*}=\sqrt{{(L_K^{*}-L_W^{*})}^2+{(a_K^{*}-a_W^{*})}^2+{(b_K^{*}-b_W^{*})}^2}$

13) according to step 9) to step 12), aberration Δ E corresponding when can calculate a series of different thicknesses of layers d ^* _ab, final selection Δ E ^* _abwhen equaling 1, corresponding thicknesses of layers d _z;

14) calculate the covering power Z when pigment mass number percent is n%, computing formula is as follows:

$Z=\frac{1}{d_Z}.$

2. the method based on Kubelka-Munk theory calculate pigment covering power according to claim 1, it is characterized in that described step 1) in described pigment be multiple different pigment, described application system is multiple different application system, and the mass percent of pigment is adjustable.

3. the method based on Kubelka-Munk theory calculate pigment covering power according to claim 1, is characterized in that described step 12) in described calculating corresponding aberration Δ E ^* _abcolour difference formula be CIEDE2000 colour difference formula.

4. the method based on Kubelka-Munk theory calculate pigment covering power according to claim 1, is characterized in that described step 13) in described calculating a series of different thicknesses of layers d time corresponding aberration Δ E ^* _abadopt Newton iterative.