RU2087879C1 - Method measuring color values in photometry and colorimetry - Google Patents

Abstract

FIELD: color photometry and colorimetry. SUBSTANCE: light radiation from object is converted to three electric signals, nonlinear conversion of signals is performed and these signals are summed up vectorially to form signal used to measure color brightness. Signal of color brightness is subjected to square-root conversion and color amplitude is measured by obtained signal. First and second orthogonal chromaticity signals are formed, chromaticity signal is formed out of them by vectorial summing and is divided into signal of color amplitude. Color saturation is measured by obtained signal. One of orthogonal chromaticity signals is divided by summary chromaticity signal and is subjected to functional arc cosine conversion and color hue is measured by it. EFFECT: increased efficiency and reliability of method. 6 dwg

Description

 The invention relates to the field of color photometry and colorimetry.

,
где K_m= 683 лм/Вт постоянный коэффициент, равный максимальной световой эффективности излучения,
L_e(λ)- спектральная плотность энергетической яркости, то есть лучистого потока в ваттах на единицу площади на единицу телесного угла в единичном интервале длин волн (Вт.м^-2•ср^-1.м^-1),
V(λ)- относительная спектральная чувствительность зрительной системы к излучению с длиной волны λ.In the known colorimetry, practically one photometric quantity is used, the brightness L. It is determined by the expression (Judd D. Vyshecki G. Color in science and technology. M. Mir, 1978, p.174):

,
where K _m = 683 lm / W constant coefficient equal to the maximum luminous efficiency of radiation,
L _e (λ) is the spectral density of energy brightness, that is, the radiant flux in watts per unit area per unit solid angle in a unit wavelength interval (W m ^-2 • sr ^{-1 .m -1} ),
V (λ) is the relative spectral sensitivity of the visual system to radiation with a wavelength of λ.

,
где c_r, c_g, c_b постоянные коэффициенты.The relative spectral sensitivity curve of the visual system is standardized by the International Commission on Illumination (CIE) based on the results of its experimental measurements. It can be represented by the sum of the curves of spectral light efficiencies r (λ), g (λ), b (λ) of the three channels of photoconversion of the visual system (Meshkov V.V. Matveev A.B. Fundamentals of Lighting Engineering. M. Energoatomizdat, 1989, p. 211 121):

,
where c _r , c _g , c _{b are} constant coefficients.

или L=L_r+L_g+L_b, (3)
где L_r, L_g, L_b составляющие яркости светового излучения.On this basis, the brightness L is represented as the sum of scalar quantities

or L = L _r + L _g + L _b , (3)
where L _r , L _g , L _{b the} components of the brightness of light radiation.

The essence and difference of the invention from the prototype are explained using the following drawings:
figure 1 equivalent circuit of linear signal conversion in the visual system when measuring brightness:
and for three receptor receptors,
b for the equivalent visibility curve.

 FIG. 2 scheme for measuring the color of radiation sources according to the author's certificate of the USSR N106027.

Figure 3 equivalent signal conversion circuit in the visual system:
and when taking into account the nonlinear characteristics of the perception of color brightness,
b when measuring color amplitude.

Figure 4 representation of colors in a metric color space:
and α are the angles between the color signal vectors,
q angles between the vectors of the color signals and the vector of the signal of equal energy white;
b the angles between the projections of the color signal vectors in the chroma plane perpendicular to the signal vector of the equal-energy white.

 5 is a diagram of a device for measuring color values in photometry and colorimetry.

6 diagram of a photoelectric converter:
a, b in parallel photoelectron conversion;
in sequential photoelectric conversion.

 The linear relationship of the brightness and its components is illustrated by the equivalent signal conversion circuit in the visual system for perceiving the brightness shown in FIG. 1a, b.

 The basis of modern colorimetry is vector summation of colors (E. Schrodinger, Grundlinien einer Theorie der Farbmetric im Tagessehen, Annalen der Physik, 1920, Bd 63, 397-456, 489 520).

 Colors in modern colorimetry are represented in the affine vector color space by the vector sum of three primary colors that have an arbitrary direction. The International Lighting Commission recommends a rectangular colorimetric system X, Y, Z for color calculations.

 In the affine vector color space, there are no concepts of angle and distance, since it does not have metric properties. Therefore, color calculations use the methods of projective geometry (Novakovsky S.V. Color in color television. M. Radio and Communications, 1989). With this approach, other color values, in addition to brightness - saturation and color tone - are determined only qualitatively.

 Another approach to determining color values is presented in the work of D. Shklover A. Modeling the process of color vision in humans. ML Science, 1969, vol. XV, p. 8 18. It is based on the representation of the visual system in the form of an equivalent response conversion circuit and the calculation of lightness, saturation, and color tone.

 Closest to the proposed method for measuring color values is the method according to the copyright certificate N 106027, USSR [1] The measurement scheme for this copyright certificate is shown in FIG. 2. To obtain the chromaticity coordinates, the output signals of the three photoelectric converters are logarithmized and signals proportional to the pairwise differences of these logarithms are fed to the deflecting plates of the cathode ray tube. The position of the luminous point determines the color of the object, that is, its saturation and color tone. The disadvantage of the existing prototype and analogues is that the measured scalar color values resulting from the representation of colors in the affine vector color space are not defined correctly, are randomly selected and are not related to the physical characteristics of light radiation.

The purpose of the invention is to create a method for measuring color values: color brightness, color amplitude, color saturation and color tone
in a metric vector color space that allows you to get an unambiguous relationship between scalar color values and the vector representation of colors and combine photometry and colorimetry.

и образуют сигнал цветовой яркости

причем α_rg, α_gb, α_br углы между векторами сигналов в метрическом цветовом пространстве, которые определяются коэффициентами спектрального различия относительных световых эффективностей k в цветовых каналах по соотношениям

a ∫ r²(λ)dλ = ∫ g²(λ)dλ = ∫b²(λ)dλ,
по нему измеряют цветовую яркость согласно соотношению
L_c(t)=c₁I_c(t),
где c₁ постоянная, определяемая при соответствующей калибровке, образуют сигнал E_c(t) посредством преобразования

и по нему измеряют амплитуду цвета согласно соотношению

образуют первый и второй ортогональные сигналы цветности согласно любой из трех пар преобразований

где значения

находят из решения системы уравнений

где

постоянные, значения которых определяются максимальными значениями спектральных чувствительностей фоторецепторов r_max, g_max, b_max, умноженных на соответствующую эквивалентную ширину спектральной чувствительности Δλ_r,Δλ_g, Δλ_b, из первого и второго сигналов цветности E₁(t) и E₂(t) образуют сигнал согласно следующему преобразованию:

и по нему измеряют насыщенность цвета согласно соотношению
S(t) C₂E(t)
в пределах O<S<1,0, где C₂ постоянная, определяемая в процессе калибровки шкалы, сигналы цветности E₁(t) и E₂(t) преобразуют в сигнал E(t) по соотношению

где K 0, n 0 при E₁(t)>0, E₂(t)>0,
K 1, n 1 при E₁(t)<0, E₂(t)>0,
K 0, n 1 при E₁(t)<0, E₂(t)<0,
K 1, n 2 при E₁(t) >0, E₂(t)<0,
и по сигналу E(t) измеряют цветовой тон Φ(t) в соответствии с соотношением
Φ(t) = C₃E(t)+Φ_o,,
где C₃ постоянная, определяемая при соответствующей калибровке шкалы Φ от 0 до 360 градусов, значение v_o в градусах принимается обшепринятым соглашением по выбору цвета, которому соответствует цветовой тон Φ=0..The goal is achieved in that the light radiation is converted into three electrical signals I _r (t), I _g (t), I _b (t), and the relative spectral light efficiencies r (λ), g (λ), b (λ) of the photoelectric the transformations coincide with the relative spectral sensitivities of the corresponding photoreceptors of the visual system, and the sum of the relative spectral light efficiencies with weight coefficients coincides with the relative visibility curve of the visual system in daytime observation conditions V (λ) carry out a nonlinear transformation ignalov _{I r (t), I g} (t), I b (t) into signals _{E r (t), E g} (t), E b (t) from the expression

and form a color brightness signal

moreover, α _rg , α _gb , α _{br the} angles between the signal vectors in the metric color space, which are determined by the spectral difference coefficients of the relative light efficiencies k in the color channels according to the ratios

a ∫ r ² (λ) dλ = ∫ g ² (λ) dλ = ∫ b ² (λ) dλ,
it measures color brightness according to the ratio
L _c (t) = c ₁ I _c (t),
where c _{1 the} constant determined by appropriate calibration, form the signal E _c (t) through conversion

and it measures the color amplitude according to the ratio

form the first and second orthogonal chroma signals according to any of the three pairs of transformations

where are the values

find from the solution of the system of equations

Where

constants whose values are determined by the maximum values of the spectral sensitivities of the photoreceptors r _max , g _max , b _max multiplied by the corresponding equivalent spectral sensitivity width Δλ _r , Δλ _g , Δλ _b of the first and second chrominance signals E ₁ (t) and E ₂ ( t) form a signal according to the following transformation:

and it measures color saturation according to the ratio
S (t) C ₂ E (t)
within O <S <1,0, where C _{2 is a} constant determined during the calibration of the scale, the color signals E ₁ (t) and E ₂ (t) are converted into a signal E (t) by the ratio

where K 0, n 0 for E ₁ (t)> 0, E ₂ (t)> 0,
K 1, n 1 for E ₁ (t) <0, E ₂ (t)> 0,
K 0, n 1 for E ₁ (t) <0, E ₂ (t) <0,
K 1, n 2 for E ₁ (t)> 0, E ₂ (t) <0,
and using the signal E (t), the color tone Φ (t) is measured in accordance with the relation
Φ (t) = C ₃ E (t) + Φ _o ,,
where C _{3 is a} constant, determined by appropriate calibration of the scale Φ from 0 to 360 degrees, the value of v _o in degrees is adopted by the agreement on the choice of color, which corresponds to the color tone Φ = 0 ..

 An equivalent signal conversion circuit in the visual system, taking into account non-linearity of perception, is shown in FIG. 3a. The equivalent signal conversion circuit for measuring color amplitude is shown in FIG. 3 b.

The values of the coefficients r _max (λ), g _max (λ), b _max (λ) determine the efficiency of converting the spectral distribution of energy brightness into response signals when adapting to equal-energy white. The response signals have the same dimension. The mutual correlation coefficients of the response intensities over the spectrum (6, 7, 8) determine the angles in the vector space when representing the responses as vectors, and the vector color space defined in this way is a Euclidean metric space in which the modules of the vectors are equal to the values obtained by the nonlinear conversion of the response intensities in the process of photoelectric conversion in the visual system. The experimentally measured nonlinear characteristic of the visual system is often approximated by a power function with an exponent γ. The values of the exponent g lie in the range g 0.33 0.5, and g 0.5 is typical for observing objects with varying flicker frequencies of radiation (film and television), and g 0.333 is taken when observing objects with constant radiation according to the recommendation of the ICE. The color brightness in this space is the intensity of the vector sum of the response signals of the three color channels and can be found according to expression (5). The square root of color brightness is the color amplitude, which determines the modulus of the color vector. By normalizing the color amplitude, a single sphere is obtained on which the colors of a single color amplitude will lie, FIG. 4 a, b.

 In it, the direction of the vector of equal-energy white and the color plane perpendicular to it can be found in which for the equal-energy white color the vector sum of the components of the main color response vectors will be zero, the angles between the response vectors and the vector of equal-energy white, and therefore the color plane, can be determined, as well as the angles between the components of the vectors in the color plane. They are determined by solving the system of equations (19). The color saturation is quantified by the projection of the color of a single color amplitude on the color plane in accordance with expression (20) and is equal to the sine of the angle between the vector of the given color and the vector of equal-energy white. The color tone in metric space is determined by the angle in the plane and the selected direction on the color plane, which corresponds to a color tone in degrees, equal to zero, see expression (21). The initial direction is given by the constant E in expression (21).

 In FIG. 5 shows a diagram of a device that implements the proposed method. It contains a lens 1, a photoconverter 2 connected in series with it, the outputs of which are connected to the inputs of three functional converters 3, 4, 5, performing non-linear signal conversion, the outputs of three functional converters are connected respectively to the inputs of three multipliers 6, 7, 8, the outputs of which are connected to the inputs of three normalizing amplifiers 9, 10, 11 and to the inputs of the fourth, fifth and sixth functional converters with quadratic amplitude characteristics 12, 13, 14, the outputs of three normalizing forces the outputs and the outputs of the three functional converters 12, 13, 14 are connected to six inputs of the first signal adder 15, and the output of the first signal adder is connected to a signal level meter 16, graduated in units of color brightness, and the first input of the first multiplier 6 is connected to the output of the first nonlinear functional red channel converter 3, the second input of the first multiplier 6 is connected to the output of the second nonlinear functional converter 4 of the green channel, the first input of the second multiplier 7 is connected to the output the second nonlinear functional converter 4 of the green channel, and the second input of the second multiplier 7 is connected to the output of the third nonlinear functional converter 5 of the blue channel, the first input of the third multiplier 8 is connected to the output of the third nonlinear functional converter 5 of the blue channel, and the second input of the third multiplier 8 is connected to the output of the first nonlinear functional converter 3 of the red channel, the output of the first adder 15 is connected to the input of the seventh functional converter with a root-square characteristic 17, the output of which is connected to a signal level meter 18, graduated in units of color amplitude, the input of the fourth normalizing amplifier 19 is connected to the output of the first functional converter 3 of the red channel, the input of the fifth normalizing amplifier 20 is connected to the output of the second functional converter 4 of the green channel, the input of the sixth normalizing amplifier 21 is connected to the output of the third functional converter 5 of the blue channel, the input of the seventh normalizing amplifier 22 soy inen with the output of the first red channel functional converter 3, the input of the eighth normalizing amplifier 23 is connected to the output of the third blue channel functional converter 4, the outputs of the normalizing amplifiers 19, 20, 21 are connected to the inputs of the second adder 24, the outputs of the normalizing amplifiers 22 and 23 are connected to the input of the third adder 25, the outputs of the second and third adders 24 and 25 through the eighth and ninth functional converters with a quadratic amplitude characteristic 26 and 27 are connected to the inputs of the fourth adder 28, you the fourth adder through the tenth functional converter 29 is connected to the first input of the signal splitter 30, the second input of which is connected to the output of the seventh functional converter 17, and the output is connected to the signal level meter 31, graduated in units of saturations, the first input of the second divider 32 is connected to the input of the third the adder 25, the second input of the second divider 32 is connected to the output of the tenth functional Converter 29, the output of the second divider 32 is connected to the input of the eleventh functional arcsi a converter 33, the output of which is connected to the output of the inverter 34 and the first input of the first switch 35, the output of the inverter 34 is connected to the second input of the first switch 35, the output of the first switch 35 is connected to the input of the fifth adder 36, the output of which is connected to the color tone meter 37, the control the input of the first switch 35 is connected to the output of the first logical device 38, the second input of the fifth adder 36 is connected to the output of the second switch 39, the control input of which is connected to the output of the second logical device 40 and the first and second inputs of the second switch 39 are connected to the output of the third switch 41 and the output of the reference voltage source 42, which determines the beginning of the color tone scale in degrees, the control input of the third switch 41 is connected to the output of the third logic device 43, and the first and second inputs of all three logical devices are connected to the outputs of the eighth and ninth functional converters with quadratic characteristics 26 and 27.

The device operates as follows. The radiation from the measurement object through the lens 1 is incident on the photoelectric converter 2, which converts it into three electrical signals I _r (t), I _g (t), I _b (t). These signals are fed to three functional converters 3, 4, 5, which perform non-linear signal conversion. The received signals E _r (t), E _g (t), E _b (t) are fed to the signal multipliers 6, 7, 8, and at the output of the multiplier 6, the product of the signals E _r (t) E _g (t) is obtained, at the output of the multiplier 7, the product of the signals E _g (t) • E _b (t) is obtained; at the output of the multiplier 8, the product of the signals E _r (t) E _b (t) is obtained. From the output of the multipliers, the signals are fed to three normalizing amplifiers 9, 10, 11, which have transmission coefficients equal to twice the correlation coefficients for the spectra of the multiplied signals in accordance with expression (5) and expressions (6), (7), (8). The signals from the output of the normalizing amplifiers 9, 10, 11 and from the outputs of the functional converters with a quadratic amplitude characteristic 12, 13, 14, the outputs of which are fed from the nonlinear converters 3, 4, 5, are fed to the adder 15, the output of which produces a color signal brightness according to expression (5), the level of which is measured by a meter 16 calibrated in units of color brightness. To measure the color amplitude, the color brightness signal from the output of the adder 15 is fed to a functional converter 17, which extracts the square root of the color brightness signal and generates a signal proportional to the color amplitude, according to expression (11).

и на входы нормирующих усилителей 22, 23, коэффициенты передачи которых определяются в соответствии с выражением (14) и равны
sinΦ_rgsinν_r, sinΦ_bgsinν_b.
На выходе сумматора 24 образуется сигнал цветности по выражению (13), а на выходе сумматора 25 по выражению (14). Сигналы с выходов сумматоров 24 и 25 возводятся в квадрат в функциональных преобразователях 26 и 27 и суммируются в сумматоре 28, образуя сигнал интенсивности цветности. В функциональном преобразователе 29 из этого сигнала извлекается квадратный корень и полученный при этом сигнал подается на делитель 30, который осуществляет деление амплитуды сигнала цветности на амплитуду сигнала цвета, который подается на делитель 30 с выхода функционального преобразователя 17. На выходе делителя 30 получается сигнал, уровень которого измеряется в единицах насыщенности цвета измерителем 31. При измерении цветового тока сигнал с выхода сумматора 25 подается на делитель 32, который осуществляет деление этого сигнала на сигнал цветности, получающийся на выходе функционального преобразователя 30. Выходной сигнал делителя 32 подается на функциональный арккосинусный преобразователь 33, а с его выхода на инвертор 34 и первый коммутатор сигналов 35, на второй вход которого подается сигнал с инвертора 34. Выход первого коммутатора 35 соединен с первым входом сумматора 36, а выход сумматора подключен к измерителю цветового тона 37. Управляющий вход первого коммутатора 35 соединен с выходом логического устройства 38. Второй вход сумматора 36 соединен с выходом второго коммутатора 39, который управляется вторым логическим устройством 40. На информационные входы второго коммутатора 39 подаются сигналы с третьего коммутатора 41 и опорное напряжение от источника опорного напряжения 42, которое определяет начало шкалы цветовых тонов в градусах.The level meter 18 of this signal is calibrated in units of color amplitude. When measuring color saturation, the signals from the outputs of the functional converters 3, 4, 5 are fed to the inputs of three normalizing amplifiers 19, 20, 21, the transmission coefficients of which are selected, for example, in accordance with expression (13), equal, respectively,

and to the inputs of normalizing amplifiers 22, 23, the transmission coefficients of which are determined in accordance with expression (14) and are equal to
sinΦ _rg sinν _r , sinΦ _bg sinν _b .
At the output of the adder 24, a color signal is generated by expression (13), and at the output of the adder 25 by expression (14). The signals from the outputs of the adders 24 and 25 are squared in the functional converters 26 and 27 and are summed in the adder 28, forming a color intensity signal. In the functional converter 29, the square root is extracted from this signal and the resulting signal is fed to a divider 30, which divides the amplitude of the color signal by the amplitude of the color signal, which is fed to the divider 30 from the output of the functional converter 17. At the output of the divider 30, a signal is obtained, the level which is measured in units of color saturation by the meter 31. When measuring the color current, the signal from the output of the adder 25 is fed to a divider 32, which divides this signal into a signal l of color obtained at the output of the functional converter 30. The output signal of the divider 32 is supplied to the functional arccine converter 33, and from its output to the inverter 34 and the first signal switch 35, to the second input of which the signal from the inverter 34 is supplied. The output of the first switch 35 is connected to the first input of the adder 36, and the output of the adder is connected to a color tone meter 37. The control input of the first switch 35 is connected to the output of the logical device 38. The second input of the adder 36 is connected to the output of the second switch ora 39, which is controlled by the second logical device 40. The information inputs of the second switch 39 are fed by signals from the third switch 41 and the reference voltage from the reference voltage source 42, which determines the start of the color tone scale in degrees.

The third switch 41 is controlled by the third logic device 43, and reference voltages from the reference voltage source 42 are supplied to the information inputs of the third switch, which define additional terms 180 and 360, which are necessary for working on the color scale in degrees from 0 ^o to 360 ^o . The inputs of all three logic devices are connected to the outputs of the first 27 and second 28 functional converters. Depending on the polarity of the signals E ₁ (t) and E ₂ (t), logic devices and switches provide, according to equation (21), the measurement of color tone on a scale in degrees from 0 ^o to 360 ^o .

 All elements of the device for measuring color values are implemented on known analog or digital elements. Photoconverter 2 can be performed in parallel or in series, FIG. 6, a, b. The radiation after lens 1 enters a beam-splitting system consisting of two translucent 44, 45 and two reflective mirrors 46 and 47, three light filters 48, 49, 50, dividing the light flux according to the spectrum into three channels: red, green, and blue. The conversion of the spectrum of light fluxes into an electrical signal is carried out by three photoelectronic devices 51, 52, 53. The output signals can be represented in analog, FIG. 6a, or digital, FIG. 6b, view. In the latter case, analog signals from photoelectronic converters are fed through normalizing amplifiers 54, 55, 56 to analog-to-digital converters 57, 58, 59 and are output in digital form. When performing the photoconverter 2 according to the serial circuit, FIG. 6c, the optical radiation after the lens passes through one of the filters 48, 49, 50, which are sequentially mechanically switched in front of the photoelectric converter 51, the output of which is connected through the normalization amplifier 54 to the input of the analog-to-digital converter (ADC) 57. The received digital signals from the output of the ADC 57 through the switch signals 60 are fed into the corresponding memory devices 61, 62, 63, each of which corresponds to the current filter in front of the photoelectric converter (red, green enomu or blue). Switching of the light filters is carried out by the control device 64 synchronously with the switch 60. The synchronization is carried out by the control and synchronization signals generated by the synchronization device 65. The digital signals read from the corresponding storage devices 61, 62, 63 form the output signals of the photoconverter 2.

 The proposed method measures color brightness, color amplitude, color saturation and color tone in a metric color space, which, with a non-linear characteristic of the transformation in the form of a power function with γ 0.5, is a physical metric color space. The color amplitude in this case is determined by the vector sum of the signals proportional to the square root of the radiation intensities converted in the red, green and blue channels, the angles between the vectors are determined by expressions (6 8), and the color brightness is proportional to the square of the color amplitude. With non-linear perception g 0.333 in non-linear functional converters, a root-cube transformation is carried out in accordance with the ICE Recommendation.

 This psychophysical metric color space takes better account of color perception under constant color lighting.

 The advantage of the proposed method for measuring color values: color brightness, color amplitude, color saturation and color tone is that it takes into account more fully the characteristics of the visual system and the conversion of color signals in the visual system, determines the metric color vector space in which these color quantities, and makes it possible to create color photometry.

Claims (1)

A method for measuring color values by photoelectric conversion of light from an object into electrical signals and measuring levels of electrical signals, characterized in that the light is converted into three electrical signals I _r (t), I _g (t), I _b (t), and the relative spectral light efficiencies r (λ), g (λ), b (λ) of the photoelectric conversion coincide with the relative spectral sensitivities of the corresponding photoreceptors of the visual system, and the sum of the relative spectral light 's efficiencies with weighting factors coincide with the relative visibility of the visual system curve in the daytime viewing conditions V (λ), is carried out nonlinear transformation I _r signals _{(t), I g (t} ), I b (t) into signals E _r (t), E _g (t), E _b (t) by the expressions

and form a color brightness signal
I _c (t) = E $\genfrac{}{}{0ex}{}{\text{2}}{\text{r}}$ (t) + E $\genfrac{}{}{0ex}{}{\text{2}}{\text{g}}$ (t) + E $\genfrac{}{}{0ex}{}{\text{2}}{\text{b}}$ (t) + 2E _r (t) E _g (t) cosα _rg +
^2E g ^{(t) E} b ^{(t) cosα} gb ^{+ 2E} b ^{(t) E} r ^{(t) cosα} br ^,
moreover, α _rg , α _gb , α _br are the angles between the signal vectors in the metric color space, which are determined by the spectral difference coefficients of the relative light efficiencies K in the color channels according to the ratios

a ∫ r ² (λ) dλ = ∫g ² (λ) dλ = ∫b ² (λ) dλ,
it measures color brightness according to the ratio
L _c (t) C ₁ I _c (t),
where C ₁ constant determined by appropriate calibration,
form a signal E _c (t) by conversion

and it measures the color amplitude according to the ratio

form the first and second orthogonal color signals according to any of the three pairs of transforms

where are the values

find from the solution of the system of equations

Where

constants whose values are determined by the maximum spectral sensitivities of the photoreceptors r _{m a x} , g _{m a x} , b _{m a x} multiplied by the corresponding equivalent spectral sensitivity width Δλ _r , Δλ _g , Δλ _b ,
from the first and second chrominance signals E ₁ (t) and E ₂ (t) form a signal E _s (t) according to the transformation

and it measures color saturation according to the ratio
S (t) C ₂ E _s (t)
within 0 <S <1,0, where C _{2 is a} constant determined during the calibration of the scale,
the color signals E ₁ (t) and E ₂ (t) are converted into a signal E (t) by the ratio

where K 0, n 0 for E ₁ (t)> 0, E ₂ (t)>0;
To 1, n 1 at E ₁ (t) <0, E ₂ (t)>0;
K 0, n 1 for E ₁ (t) <0, E ₂ (t) <0;
K 1, n 2 for E ₁ (t)> 0, E ₂ (t) <0,
and the signal E (t) measure the color tone Φ (t) in accordance with the ratio
Φ (t) = C ₃ E (t) + Φ _o ,
where C _{3 is a} constant determined by appropriate calibration of the scale Φ from 0 to 360 degrees, the value of v _o in degrees is accepted by the generally accepted agreement on the choice of color, which corresponds to the color tone Φ = 0.

Images