CN101109657A - Computing method for complex frequency spectrum chromaticity diagram and color characteristic value - Google Patents

Abstract

The invention provides a calculating method for a complex frequency spectrum chromatic diagram and color characteristic values, which pertains to the field of chromatometry for measuring and calculating the chroma of visible light. Wherein, a spectrum function s(Lambada) is multiplied by Rho (Lambada) or s(Lambada) is multiplied by Tau (Lambada) got by a spectrophotometer of visible light is transformed into a vector function of complex frequency spectrum Eta (Theta), the monochromic light of each frequency is a color vector. By integrating, such color characteristic values as color intensity C, color hue H, color balance Ba, color saturation level S and color brightness L are obtained for the color light. Taking above as a platform, the composition of two different colors can be predicated, so as to predicate their composition efficiency Eta c and balancing efficiency Eta ba, also color-difference (Delta L and Delta c) calculation can be carried out for two similar colors. In addition, the derivation of the complex frequency spectrum chromatic diagram and color characteristic values can also be used for color decomposition, color composition, color measurement, color transferring, and color-mating calculation, etc. The invention is applicable for such fields as photography, picture taking, color TV, color picture developing, printing, dyeing, painting, coating, illumination, identification and transmitting of color signals, color matching of clothes and determining of decoration colors, etc.

Description

Complex frequency spectrum chromatic diagram and color characteristic Numerical Calculation Method

Technical field:

There is light just coloured.Every relating to fields such as photochromic reception, metering, modulation, transmission, synthetic, reduction, for example make a video recording, modern science and technology numerous areas such as the design of the determining of the collocation of colour of the identification of photography, colour TV, enlargement of color photos, printing (comprising color photocopying, color painting, colour print etc.), printing and dyeing, paint, coating, illumination, colour signal and transmission, clothes, decorative colour, colour advertisement and artificial vision, all be application of the present invention.

Background technology:

Grating CCD visible light light-splitting photometric measurement technology, fibre-optic light guide technology, computer software technology.

Summary of the invention:

The spectral function measured to visible spectrophotometer, carry out a series of data-switching and data processing, on the complex frequency spectrum chromatic diagram, obtain color characteristic numerical value (colouring intensity, form and aspect, color saturation, colour brightness, color balance degree), the characteristic of color has been described exactly.Simultaneously, utilize these brand-new color characteristic numerical value, by brand-new computing method to aim colour match colors, color is synthetic, color is decomposed.Briefly, be exactly in visible-range, complex frequency spectrum chromatic diagram with two dimensional surface, substitute the tristimulus values of present widely used three-dimensional space, color is described and resolves, and solved the problem that tristimulus values is inconvenient to solve (as color balance problem, aberration computational problem).

1,, invents out the coordinates platform of this description of complex frequency spectrum chromatic diagram plane coordinate system, parsing color by complex frequency spectrum is combined with polar coordinates, rectangular coordinate.

2, calculate and checking by a large amount of, discovery form and aspect and frequency outwardness relation one to one, and visible light frequency is at 2 times of fundamental frequency ν.Be evenly distributed in the scope on 360 ° of complex frequency spectrum chromatic diagrams (2 π) angle, the distribution of form and aspect on frequency is uniform thus.Thereby solved now color theory in wavelength domain CIE--XYZ colourity problem pockety.

3, spectral function s (λ) ρ (λ) or s (λ) τ (λ) that visible spectrophotometer is measured converts frequency function s (ν) ρ (ν) or s (ν) τ (ν) to, is transformed into the complex frequency spectrum extremity function r (θ) on the complex frequency spectrum chromatic diagram again.Utilize the method for vector projection, on the complex frequency spectrum chromatic diagram, obtain four resolute X of extremity function r (θ) ₊, X _-, Y ₊, Y _-

4, utilize above-mentioned four resolute X ₊, X _-, X ₊, Y _-, calculate following brand-new color characteristic numerical value:

(1), colouring intensity C.On the complex frequency spectrum chromatic diagram be one with the relevant vector of light momentum probability complex amplitude.The power of representing this color colour developing ability.

(2), form and aspect H.It on the complex frequency spectrum chromatic diagram colouring intensity position pointed (0 °--360 °).Form and aspect are one of important quantizating index of distinct color look looks.

(3), colour brightness L.On the complex frequency spectrum chromatic diagram, relevant with energy is the bright or dark degree of representing color with the size of hodograph encirclement area.With respect to equal-energy source, it is 0--100 that brightness changes.

(4), color balance degree Ba, expression is in the degree of vector balancing state in the coloured light.

(5), color saturation S, be molecule with the colouring intensity light quantity, be denominator with color balance degree light quantity and colouring intensity light quantity sum, the ratio of gained is color saturation, its value is for 0%--100%.

5,, can access the color combined coefficient η that color theory now can not accurately calculate by the further analysis of the color characteristic numerical value after two colors are synthesized _cWith the color balance efficiency eta _Ba

(1), color combined coefficient η _c, two synthetic Neutral colour of different colors, the ratio of its Neutral colour radius vector and two primary colours radius vector sums is color combined coefficient η _cIts value is 0%--100%.Be worth greatly more, then the color synthetic effect is good more, and colour gamut is wide more.

(2), color balance efficiency eta _Ba, two colors are synthesized, and except that generating a Neutral colour, also will generate the complementary colors of a pair of equal and opposite in direction, balance each other that direction is opposite.With this ratio, be the color balance efficiency eta to balance look radius vector and two primary colours radius vector sums _BaIts value is 0%--100%.Be worth greatly more, then the color synthetic effect is poor more, and colour gamut is narrow more.

6,, do not need again just can to obtain the aberration of two colors exactly through other color systems by to the colour measurement of two similar color.On the complex frequency spectrum chromatic diagram, the aberration Δ E of two colors can be divided into two luminance difference Δ L and colouring intensity phasor difference Δ C between the color.Luminance difference Δ L is the poor of luminous energy in the coloured light, is a scalar; Colouring intensity phasor difference Δ C then is the poor of two colour phasors in the coloured light.This is two heterogeneitys, and the difference of different dimensions is wanted separate computations.

Description of drawings:

One, complex frequency spectrum system of chromatic coordinates (Fig. 1)

This figure is platform--the complex frequency spectrum system of chromatic coordinates of drawing the complex frequency spectrum chromatic diagram.The method that it adopts polar coordinates to combine with rectangular coordinate constitutes complex frequency spectrum colourity plane coordinate system.

1, the initial point that the common origin of polar coordinates and rectangular coordinate is decided to be the complex frequency spectrum system of chromatic coordinates, value are 0.

2, along distributing an equably overtones band of visible light of 360 ° of polar coordinates (2 π) direction.Promptly the low-limit frequency with red end is ν ₀, the highest frequency of purple end is 2 ν ₀, each the angle θ that makes at circumferencial direction all corresponding frequency ν and wavelength X.

3, be radius vector r from true origin along angle θ to extraradial length, the scope of sign is 0--10.

4, the X of rectangular coordinate, Y-axis are represented cosine function cos (θ) and the projection of sine function sin (θ) on the corresponding coordinate axle of extremity function radius vector r, the resolute after integration is integrated.Its size is from zero to ten, evenly distributes; Its direction be upwards, to the right for just, downwards, left for bearing.

5,, the complex frequency spectrum chromatic diagram is divided into five zones according to the position of colouring intensity on the complex frequency spectrum chromatic diagram and the Changing Pattern of form and aspect.X coordinate axis positive dirction top and the bottom are pinkish red zone, and the first quartile of rectangular coordinate partly is the red sector territory, and second quadrant partly is the territory, Green Zone, and third quadrant partly is blue or green zone, and four-quadrant partly is the territory, blue area.

Two, complex frequency spectrum chromatic diagram (Fig. 2)

This figure is with visible spectrophotometer (wavelength is between 390nm--780nm), and the bright red printing ink that printing ink factory in Tianjin produces is measured the complex frequency spectrum chromatic diagram of being drawn as calculated.Its used light source can be considered equal-energy source through conversion, and relative spectral power is distributed as s (λ)=100, is a constant.

Spectral function s (λ) ρ (λ) of the bright red printing ink that visible spectrophotometer is measured is transformed to after the complex frequency spectrum extremity function r (θ), it is plotted to the complex frequency spectrum chromaticity coordinate fastens, the frequency range of complex frequency spectrum system of chromatic coordinates be 385MMHz to 770MMHz, on 360 ° of circumference, evenly distribute.Curve among the figure is the track of the complex frequency spectrum extremity function r (θ) of this printing ink.The length of main radius vector r is the colouring intensity C of this look, is vector; Colouring intensity angle θ pointed is the form and aspect H of this look; Frequency corresponding with angle and wavelength are the predominant frequency ν and the predominant wavelength λ of this look; The area that complex frequency spectrum extremity function r (θ) curve surrounds is brightness L of this look divided by 2 π; Promptly

Colouring intensity c=8.61349 form and aspect H=52.952 degree brightness L=30.44780

Predominant frequency ν=441.629MMHz predominant wavelength λ=678.832nm

Can obtain by further calculating:

Color saturation S=77.238% color balance degree B _a=3.306%

Embodiment:

1, spectral function s (λ) ρ (λ) or s (λ) τ (λ) are transformed to complex frequency spectrum extremity function r (θ)

Measured spectral function s (λ) ρ (λ) or s (λ) τ (λ) of spectrophotometer that will measure visible light (wavelength is at 390nm--780nm) carries out conversion, the method foundation of conversion $\mathrm{\ν}=\frac{c}{\mathrm{\λ}}$ , the independent variable wavelength X that is about in the spectral function is transformed to frequency ν.On the complex frequency spectrum chromatic diagram, the frequency range of visible light is the ν from red end ₀2 ν to purple end ₀, the frequency of this frequency multiplication is evenly distributed on polar 360 ° of complex planes.Therefore the computing method that frequency ν converted to angle θ are

Wherein, θ is that ν is visible light frequency, ν in the pairing angle of complex frequency spectrum chromatic diagram upper frequency ₀Be the frequency of visible light red end, claim fundamental frequency again.After the conversion through above-mentioned wavelength, frequency, angle, just spectral function s (λ) ρ (λ) or s (λ) τ (λ) can be transformed to complex frequency spectrum extremity function r (θ).

2, the classification of complex frequency spectrum extremity function r (θ)

Measure the light source colour of luminous object and the transmitted colour and the reflected colour of object with visible spectrophotometer.

For light source colour: $r\left(\mathrm{\θ}\right)=\sqrt{s\left(\mathrm{\θ}\right)}$ , wherein s (θ) is that the light source relative spectral power distributes.

For the object transmitted colour: $r\left(\mathrm{\θ}\right)=\sqrt{s\left(\mathrm{\θ}\right)\·\mathrm{\τ}\left(\mathrm{\θ}\right)}$ , wherein τ (θ) is the object transmissivity.

For the object reflected colour: $r\left(\mathrm{\θ}\right)=\sqrt{s\left(\mathrm{\θ}\right)\·\mathrm{\ρ}\left(\mathrm{\θ}\right)}$ , wherein ρ (θ) is the object reflectance factor.

3, calculate the method that the projection resolute of r (θ) on complex frequency spectrum chromatic diagram four direction utilizes vector projection, respectively complex frequency spectrum extremity function r (θ) is modulated with sine function sin θ and cosine function cos θ, obtain the projection resolute of complex frequency spectrum extremity function r (θ) on X-axis and Y-axis, that is:

$X_{+}={\∫}_{3\mathrm{\π}/2}^{\mathrm{\π}/2}r\left(\mathrm{\θ}\right)\cos \mathrm{\θd\θ}$ $X_{-}={\∫}_{\mathrm{\π}/2}^{3\mathrm{\π}/2}r\left(\mathrm{\θ}\right)\cos \mathrm{\θd\θ}$

$Y_{+}={\∫}_0^{\mathrm{\π}}r\left(\mathrm{\θ}\right)\sin \mathrm{\θd\θ}$ $Y_{-}={\∫}_{\mathrm{\π}}^{2\mathrm{\π}}r\left(\mathrm{\θ}\right)\sin \mathrm{\θd\θ}$

More than four resolutes be that whole complex frequency spectrum vectors in colour space are integrated at the integration of rectangular coordinate four direction.

4, calculate color characteristic numerical value based on four projection resolutes

At X ₊And X _-In two resolutes, the little balance resolute X as X-axis takes absolute value _Ba, get X ₊And X _-Vector and be X _cAt Y ₊And Y _-In two resolutes, the little balance resolute Y as Y-axis takes absolute value _Ba, get Y ₊And Y _-Vector and be Y _cNeoteric color characteristic numerical value is:

(1), colouring intensity $C=\sqrt{{X_c}^2+{Y^2}_c}.$

(2), form and aspect $H=\arcsin \frac{Y_c}{C}$ Or $H=\mathrm{arctg}\frac{Y_c}{X_c}.$

(3), colour brightness $L=\frac{1}{2\mathrm{\π}}{\∫}_0^{2\mathrm{\π}}{r}^2\left(\mathrm{\θ}\right)\mathrm{d\θ}.$

(4), color balance degree $B_a=\sqrt{{X_{\mathrm{Ba}}}^2+{Y_{\mathrm{Ba}}}^2}.$

(5), color saturation $S=\frac{C^2}{{{2B}_a}^2+C^2}.$

5, calculate color combined coefficient η _cWith the color balance efficiency eta _Ba

Colouring intensity is respectively

With

Two colors synthesize, the angle of the two is θ, the colouring intensity of the new color that produces after synthetic is , with

Absolute value be molecule, with the colouring intensity of two basic colors

With

The absolute value sum be denominator, the ratio of gained promptly is combined coefficient η _cThen ${\mathrm{\η}}_c=\frac{a}{b+c}=\frac{\sqrt{b^2+c^2+2\mathrm{bc}\cos }\mathrm{\θ}}{b+c};$

Colouring intensity is respectively

With

Two colors synthesize, the angle of the two is θ, remove to generate a colouring intensity to be Neutral colour beyond, also to generate the complementary colors of a pair of equal and opposite in direction, balance each other that direction is opposite.Get this ratio, be balance efficiency η balance look radius vector and two primary colours radius vector sums _Ba, ${\mathrm{\η}}_{\mathrm{ba}}=\frac{2\mathrm{bc}\sin \mathrm{\θ}}{a(b+c)}.$

6, calculate aberration

Existing two colors of B, D, B is an aim colour, D is a comparison colours.We are the difference between D and the B more once.

Aberration: _ΔE= _ΔL+ _ΔC

Luminance difference: _ΔL=L _B-L _D

Colouring intensity is poor: $\mathrm{\Δ}\stackrel{\→}{C}={\stackrel{\→}{C}}_B-{\stackrel{\→}{C}}_D$

The form and aspect of known B and D are respectively H _BAnd H _D, calculate respectively then

With

Projection on X-axis and Y-axis.

x _B＝C _B·cosH _B y _B＝C _B·sinH _B

x _D＝C _D·cosH _D y _D＝C _D·sinH _D

Obtain two colors of B, D projection poor on X, Y-axis afterwards again:

Δx _E＝x _B-x _D＝C _B·cosH _B-C _D·cosH _D

Δy _E＝y _B-y _D＝C _B·sinH _B-C _D·sinH _D

$\mathrm{\ΔC}=\sqrt{{{\mathrm{\Δx}}^2}_E+{{\mathrm{\Δy}}^2}_E}$

${\mathrm{\ΔH}}_E=\mathrm{arctg}\frac{{\mathrm{\Δy}}_E}{{\mathrm{\Δx}}_E}$ Or ${\mathrm{\ΔH}}_E=\arcsin \frac{{\mathrm{\Δy}}_E}{\mathrm{\ΔC}}$

It is radius vector with Δ C that the aberration of calculating D and B at last is one, is the vector in colour space of form and aspect with Δ H.Hence one can see that, as long as in color D, adds colour and the Δ L brightness of some Δ C, will generate color B.

Claims (9)

1. the foundation of complex frequency spectrum chromatic diagram and color characteristic numerical computation method is, the monochromatic light of each frequency in the object visible light is considered as a vector in colour space, in visible-range, the numerical value of all vectors in colour space after integration is integrated, determine the color characteristic numerical value such as predominant wavelength, predominant frequency, colouring intensity, form and aspect, brightness, color balance degree of color, thereby can carry out the calculating of color combined coefficient, color balance efficient and aberration.

2. by complex frequency spectrum is combined with polar coordinates, rectangular coordinate, create the coordinates platform of this description of complex frequency spectrum chromatic diagram plane coordinate system, parsing color.

3. the low-limit frequency v of red end in the visible spectrum ₀As fundamental frequency, then the highest frequency of purple end is v in the visible spectrum ₀2 times, promptly be frequency multiplication relation.

4. whole frequencies of visible light are evenly distributed on 360 ° of the polar coordinates of complex frequency spectrum chromatic diagram, make the corresponding angle θ of each frequency v, and satisfy

5. pass through the transformation relation of light wavelength λ and frequency v, promptly $v=\frac{c}{\mathrm{\λ}},$ By the transformation relation of frequency v and θ, spectral function s (λ) ρ (λ) that just visible spectrophotometer can be recorded or s (λ) τ (λ) are converted to complex frequency spectrum extremity function r (θ) again.

6. by cosine function r (θ) the cos θ of complex frequency spectrum extremity function r (θ) and the integration of sine function r (θ) sin θ are integrated, draw the X that fasten at the rectangular coordinate of complex frequency spectrum chromatic diagram complex frequency spectrum extremity function r (θ) ₊, X _-, Y ₊, Y _-Four projection resolutes.

7. four projection resolutes are integrated calculating, draw colouring intensity C, form and aspect H, the color balance degree B of coloured light _a, color characteristic numerical value such as color saturation S and colour brightness L.

8. to two Essential colour with by the measurement of its synthetic aim colour, three groups of color characteristic numerical value can be obtained,, color combined coefficient η can be drawn by calculating _cWith the color balance efficiency eta _BaThereby, can correctly estimate the synthetic effect of two colors.

9. by to the colour measurement of two similar color, do not need again just can to calculate the aberration Δ E of two colors exactly through other color systems, provide luminance difference Δ L and colouring intensity phasor difference Δ C, the Δ H of two similar color.

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