CN107368461B - Method and system for calculating correlated color temperature of light source and Duv of light source - Google Patents
Method and system for calculating correlated color temperature of light source and Duv of light source Download PDFInfo
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Abstract
The invention provides a method and a system for calculating correlated color temperature of a light source and a light source Duv, which relate to the technical field of a method for acquiring the representation of the color of the light source, and comprise the steps of establishing a segmented low-order polynomial according to a first temperature value of a black body, obtaining a black body track, calculating to obtain a light source chromaticity coordinate according to the relative spectral power distribution of the light source and a CIE (CIE chromaticity diagram) formula, obtaining a first black body chromaticity coordinate on the black body track and a first distance corresponding to the first black body chromaticity coordinate according to the light source chromaticity coordinate and the segmented low-order polynomial, obtaining the light source Duv according to the light source chromaticity coordinate, the first black body chromaticity coordinate and the first distance, obtaining a black body color temperature corresponding to the first black body chromaticity coordinate according to the first black body chromaticity coordinate and a color temperature calculation formula, and obtaining the correlated color temperature of the light. The invention can avoid gradual searching and comparison, improve the calculation speed and the calculation precision and realize the simultaneous calculation of the correlated color temperature and the color deviation value.
Description
Technical Field
The invention relates to the technical field of an acquisition method of source color representation, in particular to a method and a system for calculating correlated color temperature of a light source and Duv of the light source.
Background
The color temperature of a blackbody radiation source is the absolute temperature of the blackbody. If the Color (i.e. light Color, also called chromaticity) of light emitted by a light source is the same as the Color of light emitted by a black body at a certain Temperature, the absolute Temperature value of the black body is called the Correlated Color Temperature (CCT) of the light source.
CCT is an important parameter of an illumination light source, not only determines the color type of white light observed by human vision, but also has important influence on non-visual biological phenomena of human body such as circadian rhythm, temperature regulation, heat balance and the like.
Another important parameter of the illumination source is Duv (color deviation value), which describes the distance and direction of deviation of chromaticity coordinates of the light source to be measured from the planck black body radiation locus. When the Duv value is too large, it indicates that the light color of the light source deviates too far from "white", and the human eye may observe the conditions of yellowing, greenness, or purplishness.
In order to determine the CCT and Duv of the light source,the traditional algorithm needs to determine chromaticity coordinates (u) of the Planckian black body radiation locus and the light source through step-by-step search comparisonc,vc) Chromaticity coordinate (u) from the closest point0,v0) And a point (u)0,v0) The curve slopes of a plurality of adjacent points are large in calculation amount and long in time consumption, and the existing curve fitting calculation method is high in calculation speed, but generally has the problems of large calculation error, limited applicable color temperature range, incapability of simultaneously obtaining CCT (continuous casting) and Duv and the like.
Disclosure of Invention
In view of this, the present invention provides a method and a system for calculating a correlated color temperature of a light source and a light source Duv, so as to avoid gradual search and comparison, improve a calculation speed and a calculation accuracy, and achieve simultaneous calculation of a correlated color temperature and a color deviation value.
In a first aspect, an embodiment of the present invention provides a method for calculating a correlated color temperature of a light source and a light source Duv, where the method includes:
according to the first temperature value of the black body, a segmented low-order polynomial is established, and a black body track is obtained;
calculating to obtain chromaticity coordinates of the light source according to the relative spectral power distribution of the light source and a CIE (Commission on the International illumination Commission) colorimetry formula;
obtaining a first black body chromaticity coordinate on the black body locus and a first distance corresponding to the first black body chromaticity coordinate according to the light source chromaticity coordinate and the segmented low-order polynomial;
obtaining a light source color deviation value Duv according to the light source chromaticity coordinate, the first black body chromaticity coordinate and the first distance;
obtaining the black body color temperature corresponding to the first black body chromaticity coordinate according to the first black body chromaticity coordinate and a color temperature calculation formula;
obtaining the correlated color temperature T of the light source according to the color temperature of the black bodyc。
With reference to the first aspect, an embodiment of the present invention provides a first possible implementation manner of the first aspect, where the establishing a piecewise low-order polynomial according to the first black body temperature value and obtaining the black body locus includes:
discretizing the blackbody first temperature value to obtain a serialized blackbody second temperature value;
calculating to obtain second blackbody chromaticity coordinates corresponding to each second temperature value of the blackbody according to a Planckian blackbody radiation formula and a colorimetry formula;
and establishing the segmented low-order polynomial according to the second black body chromaticity coordinate to obtain the black body locus.
With reference to the first aspect, an embodiment of the present invention provides a second possible implementation manner of the first aspect, where the obtaining, according to the light source chromaticity coordinates and the segmented low-order polynomial, a first blackbody chromaticity coordinate on the blackbody locus and a first distance corresponding to the first blackbody chromaticity coordinate includes:
establishing a second distance between the light source point and the blackbody locus according to the light source chromaticity coordinates and the segmented low-order polynomial;
and obtaining the first blackbody chromaticity coordinate on the blackbody locus and the first distance corresponding to the first blackbody chromaticity coordinate according to the derivative condition of the second distance.
With reference to the second possible implementation manner of the first aspect, an embodiment of the present invention provides a third possible implementation manner of the first aspect, where the establishing a second distance between the light source point and the blackbody locus according to the light source chromaticity coordinates and the piecewise low-order polynomial includes:
calculating the second distance according to:
wherein d (u) is the second distance, (u)c,vc) And the chromaticity coordinates of the light source.
With reference to the first aspect, an embodiment of the present invention provides a fourth possible implementation manner of the first aspect, where the obtaining the light source Duv according to the light source chromaticity coordinate, the first black body chromaticity coordinate, and the first distance includes:
the light source Duv is calculated according to the following formula:
wherein, D isuvFor said light source Duv, d (u)0) Is the first distance, (u)c,vc) (u) is the chromaticity coordinate of the light source0,v0) And the black body chromaticity coordinates are obtained.
With reference to the first aspect, an embodiment of the present invention provides a fifth possible implementation manner of the first aspect, where the obtaining a blackbody color temperature corresponding to the first blackbody chromaticity coordinate according to the first blackbody chromaticity coordinate and a color temperature calculation formula includes:
calculating the blackbody color temperature according to:
wherein, T0Is the black body color temperature, (u)0,v0) Is the first black body chromaticity coordinate, (u)k,vk) And (u)k+1,vk+1) Chromaticity coordinates of two points adjacent to the left and right of the first black body chromaticity coordinate, TkAnd Tk+1、dkAnd dk+1、lkAnd lk+1Respectively the corresponding color temperature, distance and slope of the curve.
With reference to the first possible implementation manner of the first aspect, an embodiment of the present invention provides a seventh possible implementation manner of the first aspect, where after the second blackbody chromaticity coordinates corresponding to the second temperature value of each blackbody are obtained through calculation according to a planckian blackbody radiation formula and a colorimetry formula, and before the piecewise low-order polynomial is established according to the second blackbody chromaticity coordinates to obtain the blackbody locus, the method further includes:
and calculating the curve slope of the blackbody locus corresponding to the second blackbody chromaticity coordinate.
In a second aspect, an embodiment of the present invention further provides a system for calculating a color temperature associated with a light source and a light source Duv, where the system includes:
the blackbody track fitting module is used for establishing a segmented low-order polynomial according to the first temperature value of the blackbody and obtaining a blackbody track;
the light source chromaticity coordinate calculation module is used for calculating and obtaining light source chromaticity coordinates according to the light source relative spectral power distribution and the CIE colorimetry formula;
the distance calculation module is used for obtaining a first black body chromaticity coordinate on the black body locus and a first distance corresponding to the first black body chromaticity coordinate according to the light source chromaticity coordinate and the segmented low-order polynomial;
the light source Duv calculation module is used for obtaining a light source Duv according to the light source chromaticity coordinates, the first black body chromaticity coordinates and the first distance;
the black body color temperature calculation module is used for obtaining the black body color temperature corresponding to the first black body chromaticity coordinate according to the first black body chromaticity coordinate and a color temperature calculation formula;
and the light source correlated color temperature calculation module is used for obtaining the light source correlated color temperature according to the blackbody color temperature.
With reference to the second aspect, an embodiment of the present invention provides a first possible implementation manner of the second aspect, where the blackbody locus fitting module includes:
discretizing the blackbody first temperature value to obtain a serialized blackbody second temperature value;
calculating to obtain second blackbody chromaticity coordinates corresponding to each second temperature value of the blackbody according to a Planckian blackbody radiation formula and a colorimetry formula;
and establishing the segmented low-order polynomial according to the second black body chromaticity coordinate, and obtaining the black body locus.
With reference to the second aspect, an embodiment of the present invention provides a second possible implementation manner of the second aspect, where the distance calculating module includes:
establishing a second distance between the light source point and the blackbody locus according to the light source chromaticity coordinates and the segmented low-order polynomial;
and obtaining the first blackbody chromaticity coordinate on the blackbody locus and the first distance corresponding to the first blackbody chromaticity coordinate according to the derivative condition of the second distance.
The embodiment of the invention has the following beneficial effects: the invention provides a method and a system for calculating correlated color temperature of a light source and Duv of the light source. The invention can avoid gradual searching and comparison, improve the calculation speed, ensure insufficient calculation precision and realize the simultaneous calculation of the correlated color temperature and the color deviation value.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
Fig. 1 is a flowchart of a method for calculating a correlated color temperature of a light source and a Duv of the light source according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of calculating a correlated color temperature of a light source by using a triangle geometric approximation method according to a first embodiment of the present invention;
FIG. 3 is a flowchart of a blackbody locus fitting method according to a second embodiment of the present invention;
fig. 4 is a flowchart of a first blackbody chromaticity coordinate obtaining method according to a third embodiment of the present invention;
fig. 5 is a schematic diagram of a computing system for light source Duv and associated color temperature according to a fourth embodiment of the present invention;
fig. 6 is a flowchart illustrating an overall implementation of the system according to the fifth embodiment of the present invention;
fig. 7 is a schematic diagram of a corresponding relationship among a temperature value, chromaticity coordinates, and a slope of a curve according to a fifth embodiment of the present invention;
fig. 8 is a schematic diagram of relative spectral power distribution and chromaticity coordinates of a test light source according to a fifth embodiment of the present invention.
Icon:
100-blackbody locus fitting module; 200-a light source chromaticity coordinate calculation module; 300-distance calculation module; 400-light source Duv calculation module; 500-blackbody color temperature calculation module; 600-light source correlated color temperature calculation module.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
At present, in order to determine the CCT and Duv of a light source, a traditional algorithm needs to determine chromaticity coordinates of a closest point on a planck black body radiation locus, which is located at a distance from a chromaticity coordinate of the light source, and curve slopes of a plurality of points adjacent to and close to the closest point through step-by-step searching and comparing, and the traditional curve fitting calculation method has the problems of large calculation error, limited applicable color temperature range, incapability of simultaneously obtaining the CCT and the Duv and the like although the calculation speed is high.
Based on this, the method and the system for calculating the correlated color temperature and the light source Duv provided by the embodiment of the invention can avoid gradual searching and comparison, improve the calculation speed, have insufficient calculation precision and realize simultaneous calculation of the correlated color temperature and the color deviation value.
For the understanding of the embodiment, the detailed description of the method for calculating the CCT and Duv of the light source disclosed in the embodiment of the present invention will be given first.
The first embodiment is as follows:
fig. 1 is a flowchart of a method for calculating correlated color temperature of a light source and Duv of the light source according to an embodiment of the present invention.
Referring to fig. 1, the method for calculating the light source correlated color temperature and the light source Duv includes the steps of:
step S110, establishing a segmented low-order polynomial v (u) according to the first temperature value of the black body, and obtaining a black body track;
specifically, the blackbody locus is a planckian blackbody radiation locus, which is a (u, v) chromaticity locus formed in the CIE1960UCS coordinate system at different temperature values by a radiator conforming to the planckian blackbody radiation law.
Firstly, discretizing the temperature value of the radiator in the temperature range of 1000-20000K of the first temperature value of the black body to obtain a quantized temperature value sequence, namely a second temperature value T of the black bodyiAnd storing it; secondly, calculating a second temperature value T of each blackbody according to the Planckian blackbody radiation formula and the colorimetry formulaiCorresponding second blackbody chromaticity coordinates (u) in the CIE1960UCS coordinate systemi,vi) And storing it; again, based on each second black body chromaticity coordinate (u)i,vi) The segmented low-order polynomial v (u) can be accurately establishedSmoothly fitting the Planck black body radiation locus; finally, the coefficients of the various segments of the low order polynomial that make up v (u) are stored.
In addition, at each second black body chromaticity coordinate (u)i,vi) Calculating the slope l of the black body locus corresponding to the second black body chromaticity coordinateiAnd stores it. Introducing a slope l of the curveiThe accuracy and the smoothness of the black body locus curve fitting can be effectively improved.
Here, the piecewise low order polynomial v (u) is a piecewise cubic Hermite interpolation polynomial.
Step S120, calculating and obtaining chromaticity coordinates (u) of the light source according to the relative spectral power distribution of the light source and the CIE (Commission International de L' Eclairage) colorimetry formulac,vc)；
Step S130, according to the chromaticity coordinate (u) of the light sourcec,vc) And segmenting the low-order polynomial v (u) to obtain a first blackbody chromaticity coordinate (u) on the blackbody locus0,v0) And coordinates (u) of the first black body chromaticity0,v0) Corresponding first distance d (u)0)；
Specifically, firstly, the chromaticity coordinates (u) of the light source under the CIE1960UCS coordinate system are calculated and obtained by utilizing the relative spectral power distribution of the light source and the CIE colorimetry formulac,vc) (ii) a Secondly, based on the chromaticity coordinates (u) of the light sourcec,vc) And segmenting a low-order polynomial v (u), and establishing a distance formula from a point (namely a light source) to a curve (namely a blackbody locus), namely a second distance d (u), as shown in formula (1):
let d' (u), d "(u) be the first derivative of d (u), where u is equal to u0The conditions respectively satisfied are as shown in formula (2):
coordinate point (u)0,v0) I.e. coordinates (u) of chromaticity of the light source on the black body locusc,vc) The first black body chromaticity coordinate of the shortest distance point; d (u)0) I.e. the corresponding shortest first distance.
Step S140, according to the chromaticity coordinates (u) of the light sourcec,vc) First black body chromaticity coordinate (u)0,v0) And a first distance d (u)0) Obtaining a light source Duv;
specifically, the value is obtained by equation (3) according to the definition of Duv:
wherein D isuvAs a light source Duv, d (u)0) Is a first distance, (u)c,vc) As chromaticity coordinates of the light source, (u)0,v0) Is the first black body chromaticity coordinate.
Step S150, according to the first black body chromaticity coordinate (u)0,v0) And a color temperature calculation formula to obtain a first black body chromaticity coordinate (u)0,v0) Corresponding black body color temperature T0；
Step S160, according to the blackbody color temperature T0Obtaining the correlated color temperature T of the light sourcec。
In particular, at the black body second temperature value TiWhen discretized more densely, as shown in FIG. 2, a method similar to the triangle geometry can be used, based on the first blackbody chromaticity coordinates (u)0,v0) And a color temperature calculation formula to obtain a first blackbody chromaticity coordinate (u) on the blackbody locus0,v0) Corresponding black body color temperature T0Specifically, as shown in formula (4):
wherein, T0Is black body color temperature, (u)k,vk) And (u)k+1,vk+1) Respectively, the coordinates (u) of the black body chromaticity0,v0) Chromaticity coordinates, T, of two points adjacent to each otherkAnd Tk+1、dkAnd dk+1、lkAnd lk+1Respectively the corresponding color temperature, distance and slope of the curve.
According to the definition of the correlated color temperature of the light source, the first black body chromaticity coordinate (u) on the black body locus0,v0) Corresponding color temperature T0I.e. the correlated color temperature T of the light sourcec。
Example two:
fig. 3 is a flowchart of a blackbody locus fitting method according to a second embodiment of the present invention.
Referring to fig. 3, in step S110 of the calculation method of the light source dependent color temperature and the light source Duv, the blackbody locus fitting method includes the steps of:
step S210, discretizing the blackbody first temperature value to obtain a sequence blackbody second temperature value Ti；
Step S220, calculating to obtain second blackbody chromaticity coordinates (u) corresponding to each blackbody second temperature value according to Planckian blackbody radiation formula and colorimetry formulai,vi)；
Step S230, according to the second blackbody chromaticity coordinate (u)i,vi) And establishing a segmented low-order polynomial v (u) to obtain a blackbody locus.
Specifically, in order to describe the planckian black body radiation locus accurately and smoothly, after step S220 and before step S230, the method further includes the following steps:
calculating the second blackbody chromaticity coordinate (u)i,vi) Slope l of the corresponding black body locus curveiAnd stores it. The curve slope l is introduced hereiThe accuracy and the smoothness of the black body locus curve fitting can be effectively improved.
The first temperature value of the black body can be 1000 k-20000 k according to the actual situation, and the second temperature value T of each black body is discretized by adopting a 1% step length methodiThe radiation black body is arranged at each TiTime corresponding CIE1960UCS chromaticity coordinate locus (u)i,vi) Each (u)i,vi) Corresponding slope l of blackbody locus curveiThe method is obtained by calculation according to the Plancko black body radiation formula and the chromaticity formula specified by CIE. The data need to be stored after being obtained, and the data can be directly and repeatedly called in subsequent calculation, so that the calculation efficiency is improved.
Example three:
fig. 4 is a flowchart of a first blackbody chromaticity coordinate obtaining method according to a third embodiment of the present invention.
Referring to fig. 4, in step S130 of the calculation method of the correlated color temperature of the light source and the light source Duv, the blackbody locus fitting method includes the steps of:
step S310, according to the chromaticity coordinates (u) of the light sourcec,vc) And segmenting a low-order polynomial v (u) to establish a second distance d (u) between the light source point and the blackbody locus;
step S320, obtaining a first blackbody chromaticity coordinate (u) on the blackbody locus according to the derivative condition of the second distance0,v0) And coordinates (u) of the first black body chromaticity0,v0) Corresponding first distance d (u)0)。
Specifically, the derivative condition is the content expressed by the above formula (2). First black body chromaticity coordinate (u)0,v0) Distance light source (u) on the curve of the blackbody locusc,vc) The shortest straight-line distance between the nearest point and the two points is d (u) where u is equal to u0Then take the minimum value d (u)0)。
Example four:
fig. 5 is a schematic diagram of a computing system for light source dependent color temperature and light source Duv according to a fourth embodiment of the present invention.
Referring to fig. 5, the computing system for the light source dependent color temperature and the light source Duv includes:
the blackbody locus fitting module 100 is configured to establish a piecewise low-order polynomial v (u) according to the blackbody first temperature value, and obtain a blackbody locus;
a light source chromaticity coordinate calculating module 200 for calculating and obtaining light source chromaticity coordinates (u) according to the light source relative spectral power distribution and the CIE colorimetry formulac,vc)；
A light source Duv calculating module 400 for calculating chromaticity coordinates (u) of the light sourcec,vc) First black body chromaticity coordinate (u)0,v0) And a first distance d (u)0) Obtaining a light source Duv;
a blackbody color temperature calculation module 500 for calculating a blackbody color temperature according to the first blackbody chromaticity coordinate (u)0,v0) And a color temperature calculation formula to obtain a first black body chromaticity coordinate (u)0,v0) Corresponding black body color temperature T0；
A light source correlated color temperature calculation module 600 for calculating a color temperature T according to the blackbody color temperature0Obtaining the correlated color temperature T of the light sourcec。
According to an exemplary embodiment of the present invention, blackbody locus fitting module 100 includes:
discretizing the first temperature value of the black body to obtain a second temperature value T of the black body of the sequencei；
Calculating to obtain a second temperature value T of each blackbody according to a Planckian blackbody radiation formula and a colorimetry formulaiCorresponding second blackbody chromaticity coordinate (u)i,vi)；
According to the second black body chromaticity coordinate (u)i,vi) And establishing a piecewise low-order polynomial v (u) and obtaining a blackbody locus.
According to an exemplary embodiment of the present invention, the distance calculation module 300 includes:
according to chromaticity coordinates (u) of the light sourcec,vc) And segmenting a low-order polynomial v (u) to establish a second distance d (u) between the light source point and the blackbody locus;
obtaining a first blackbody chromaticity coordinate (u) on the blackbody locus according to the derivative condition of the second distance0,v0) And coordinates (u) of the first black body chromaticity0,v0) Corresponding second distance d (u)0)。
In addition, according to an exemplary embodiment of the present invention, the distance calculation module 300 may further include:
at each second black body chromaticity coordinate (u)i,vi) Calculating the slope l of the black body locus corresponding to the second black body chromaticity coordinateiAnd stores it. Introducing a slope l of the curveiThe accuracy and the smoothness of the black body locus curve fitting can be effectively improved.
The implementation principle and the generated technical effects of the computing system of the light source correlated color temperature and the light source Duv provided by the embodiment of the invention are the same as those of the embodiment of the method, and for brief description, corresponding contents in the embodiment of the method can be referred to for parts which are not mentioned in the embodiment of the computing system of the light source correlated color temperature and the light source Duv.
Example five:
fig. 6 is an execution flowchart of the system according to the fifth embodiment of the present invention.
Taking a certain model of standard color temperature lamp with a color temperature of 2856K as an example, a specific implementation process of calculating the correlated color temperature and Duv of the standard color temperature lamp is specifically described. It should be noted that the present application is not limited to the selected chromaticity coordinates and the type of the light source, and the present application is applicable as long as the correlated color temperature of the light source is within the range of the black body color temperature and chromaticity data, and the slope data storage module of the black body locus curve of each chromaticity point.
As shown in fig. 6, the present embodiment includes a blackbody locus fitting and coefficient storing module, a light source color coordinate calculating module, a color coordinate determination and Duv calculating module of a closest point on the blackbody locus to the light source, and a light source correlated color temperature calculating module.
Each discretized temperature value TiThe radiation black body is arranged at each TiTime corresponding CIE1960UCS chromaticity coordinate locus (u)i,vi) Each (u)i,vi) Corresponding slope l of blackbody locus curveiThe equation is obtained by calculation according to the planck black body radiation formula and the chromaticity formula specified by CIE, and the corresponding relationship between the equation and the equation is shown in fig. 7. The data is required to be stored after being obtained, and the subsequent calculation can be directly and repeatedly calledThe data is beneficial to improving the calculation efficiency.
Discretizing the temperature by adopting the 1% step method in the temperature range of 1000K-20000K to obtain a discretized temperature value sequence. The specific process is shown in formula (5):
the beneficial effects of adopting 1% as the step length to carry out non-uniform segmentation on the continuous temperature values are as follows: in view of the fact that the actual lighting source mostly works in a warm light and white region, the color temperature of the cold light source generally rarely exceeds 7000K, and the method can ensure that relatively more accurate calculation results are obtained in a low color temperature and medium color temperature region where the light source is important.
Measure the temperature value TiSubstituting into the Planckian black body radiation formula, as shown in formula (6):
the wavelength λ is discretized, and preferably, the wavelength λ is discretized in a visible light wavelength range or a wavelength range supported by the spectral power acquisition device by using 1nm or 2nm as step intervals or step intervals supported by the spectral power acquisition device. Here, c1Is the first radiation constant, c12 pi hc 2-3.7418 × 10-16W · m2, h is planck constant, h-6.6260755 × 10-34J.s, c is the speed of light, c2Is the first radiation constant, c2＝hck＝1.4388×10-2m.K, K is Bolmann constant.
Calculating the temperature T of the radiant black body at each temperature by using a CIE 1931XYZ colorimetry formulaiThe specific calculation process of the corresponding color tristimulus value is shown as formula (7):
wherein the content of the first and second substances,
is the spectral tristimulus value, k is the normalization coefficient,
usually, the wavelength lambda also needs to be discretized, and the calculation of the temperature T of the radiation black body is carried outiThe formula of the corresponding color tristimulus value becomes as shown in formula (8):
according to the CIE1960UCS colorimetry calculation formula, the temperature value T of the radiation black body at each position can be calculatediChromaticity coordinate (u) of time correspondencei,vi) The calculation process is shown in formula (9):
then, the coordinates (u) of each color article are obtainedi,vi) On the basis of (a), a piecewise low order polynomial v (u) may be used to fit the blackbody locus. Preferably, a piecewise cubic Hermite interpolation polynomial is adopted to fit the blackbody locus, and the specific process is as follows:
calculating the coordinates (u) of each black body chromaticity on the black body locusi,vi) Slope of the curve at liCalculating and deriving liThe process of (2) is shown in equation (10):
here, Xi,Yi,ZiIs black body at temperature TiColour tristimulus value of hour, Xi',Yi',Zi' is the color tristimulus value vs. temperature TiIs calculated as shown in equation (11):
here, PT' (λ, T) is the partial derivative of P (λ, T) with respect to T, as shown in equation (12):
according to (u)i,vi) And liAnd establishing a segmented cubic Hermite interpolation polynomial according to a formula (13) to accurately fit the blackbody locus:
wherein the basis function αj(u) represents as shown in formula (14):
basis function betaj(u) is expressed as shown in equation (15):
in accordance with the above description and formula, respectively, in the interval u0,u1]、[u1,u2]、…、
[u301,u302]Calculating v0(u)、v1(u)、…、v301(u) is specifically expressed by the formula (16):
the parameters obtained above are tabulated as shown in table 1.
TABLE 1
And the storage module is used for storing the table 1, so that repeated calling of subsequent steps is facilitated, and the improvement of the calculation efficiency is facilitated
The spectral power distribution of a standard color temperature lamp is shown in fig. 8, and the chromaticity coordinate of the standard color temperature lamp can be determined as (u) according to the process of finding the chromaticity coordinate of the radiant black bodyc,vc)。
According to the formula (1) of the distance from the point to the curve, and when (u, v) ═ u0,v0) Then, the first derivative d '(u) and the second derivative d' (u) of d (u) satisfy the formula (2) respectively, and the point (u) on the curve of the blackbody locus can be obtained0,v0) Is a distance light source (u)c,vc) The closest point. The straight-line distance between the two points is the shortest distance, i.e. d (u) is equal to u0Then take the minimum value d (u)0). The light source Duv can be obtained according to the definition of Duv and the formula (3).
On the basis that the Planckian black body radiation locus is accurately and smoothly described by the segmented cubic Hermite interpolation function, chromaticity coordinates and Duv of a point on the black body locus curve closest to a light source are determined simultaneously by a pure mathematical analysis method, and the defects that a traditional calculation method needs repeated searching and comparison, consumes more time and is slow in calculation are overcome.
The next step in determining the correlated color temperature of the light source is to determine the point (u) on the blackbody locus0,v0) Temperature value T of0. First, it is necessary to find the point (u) on the blackbody locus0,v0) Two points adjacent to each other on the left and right sides. Suppose that index k satisfies uk<u0<uk+1Then (u) can be obtained directly by looking up table 1k,vk) And (u)k+1,vk+1) Respectively corresponding temperature values TkAnd Tk+1. Then, (u) can be quickly calculated according to the triangle geometry similarity method, as shown in FIG. 20,v0) Corresponding temperature T0Specifically, as shown in formula (17):
finally, the correlated color temperature of the light source is defined as follows: t isc＝T0。
The embodiment obtains the color coordinate (u) of the point closest to the light source0,v0) And then, the color temperature of the point can be quickly estimated by a triangular geometric similarity method, and further the correlated color temperature of the light source is calculated.
The execution flow of the system provided by the embodiment of the invention has the same technical characteristics as the calculation method and the calculation system of the correlated color temperature of the light source and the light source Duv provided by the embodiment, so that the same technical problems can be solved, and the same technical effects can be achieved.
The embodiment of the invention has the following beneficial effects: the invention provides a method and a system for calculating correlated color temperature of a light source and Duv of the light source. The invention can avoid gradual searching and comparison, improve the calculation speed, ensure insufficient calculation precision and realize the simultaneous calculation of the correlated color temperature and the color deviation value.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The computer program product for performing the method for calculating the color temperature related to the light source and the light source Duv according to the embodiment of the present invention includes a computer readable storage medium storing a non-volatile program code executable by a processor, where instructions included in the program code may be used to execute the method described in the foregoing method embodiment, and specific implementation may refer to the method embodiment, and will not be described herein again.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer-readable storage medium executable by a processor. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (8)
1. A method for calculating a correlated color temperature of a light source and a Duv of the light source, the method comprising:
according to the first temperature value of the black body, establishing a segmented low-order polynomial v (u) and obtaining a black body track; the piecewise low order polynomial comprises a piecewise cubic Hermite interpolation polynomial;
according to the relative spectral power distribution of the light source and the CIE (Commission on International illumination Commission) colorimetry formula, the chromaticity coordinates (u) of the light source are calculated and obtainedc,vc)；
Obtaining a first blackbody chromaticity coordinate (u) on the blackbody locus according to the light source chromaticity coordinate and the segmented low-order polynomial0,v0) And a first distance d (u) corresponding to the first black body chromaticity coordinates0)；
Obtaining a light source color deviation value Duv according to the light source chromaticity coordinate, the first black body chromaticity coordinate and the first distance;
obtaining the blackbody color temperature T corresponding to the first blackbody chromaticity coordinate according to the first blackbody chromaticity coordinate and a color temperature calculation formula0；
Obtaining the correlated color temperature T of the light source according to the color temperature of the black bodyc；
The obtaining the light source Duv according to the light source chromaticity coordinate, the first black body chromaticity coordinate and the first distance includes:
the light source Duv is calculated according to the following formula:
wherein D isuvFor said light source Duv, d (u)0) Is the first distance, (u)c,vc) (u) is the chromaticity coordinate of the light source0,v0) The first black body chromaticity coordinate is obtained;
and obtaining the blackbody color temperature T corresponding to the first blackbody chromaticity coordinate according to the first blackbody chromaticity coordinate and a color temperature calculation formula0The method comprises the following steps:
using a method of triangle geometric similarity according to the first black body chromaticity coordinate (u)0,v0) And color temperature calculation formula to obtain blackFirst black body chromaticity coordinate (u) on the body locus0,v0) Corresponding black body color temperature T0Calculating the blackbody color temperature according to:
wherein, T0Is the black body color temperature, (u)0,v0) Is the first black body chromaticity coordinate, (u)k,vk) And (u)k+1,vk+1) Chromaticity coordinates of two points adjacent to the left and right of the first black body chromaticity coordinate, TkAnd Tk+1、dkAnd dk+1、lkAnd lk+1Respectively the corresponding color temperature, distance and slope of the curve.
2. The method of claim 1, wherein the building a piecewise low order polynomial according to the blackbody first temperature value and obtaining the blackbody locus comprises:
discretizing the blackbody first temperature value to obtain a serialized blackbody second temperature value Ti；
Calculating to obtain a second blackbody chromaticity coordinate (u) corresponding to each second temperature value of the blackbody according to a Planckian blackbody radiation formula and a colorimetry formulai,vi)；
And establishing the segmented low-order polynomial according to the second black body chromaticity coordinate to obtain the black body locus.
3. The method of claim 1, wherein obtaining the first blackbody chromaticity coordinate on the blackbody locus and the first distance corresponding to the first blackbody chromaticity coordinate according to the light source chromaticity coordinate and the piecewise low-order polynomial comprises:
establishing a second distance d (u) between the light source point and the blackbody locus according to the light source chromaticity coordinates and the segmented low-order polynomial;
and obtaining the first blackbody chromaticity coordinate on the blackbody locus and the first distance corresponding to the first blackbody chromaticity coordinate according to the derivative condition of the second distance.
4. The method of claim 3, wherein establishing a second distance between the source point and the blackbody locus based on the source chromaticity coordinates and the piecewise low order polynomial comprises:
calculating the second distance according to:
wherein d (u) is the second distance, (u)c,vc) And the chromaticity coordinates of the light source.
5. The method of claim 2, wherein after the second blackbody chromaticity coordinates corresponding to the second temperature value of each blackbody are obtained by calculation according to the planckian blackbody radiation formula and the colorimetry formula, and before the piecewise low-order polynomial is established according to the second blackbody chromaticity coordinates to obtain the blackbody locus, the method further comprises:
calculating the curve slope l of the blackbody locus corresponding to the second blackbody chromaticity coordinatei。
6. A system for computing a light source dependent color temperature and a light source Duv, the system comprising:
the blackbody track fitting module is used for establishing a segmented low-order polynomial according to the first temperature value of the blackbody and obtaining a blackbody track; the piecewise low order polynomial comprises a piecewise cubic Hermite interpolation polynomial;
the light source chromaticity coordinate calculation module is used for calculating and obtaining light source chromaticity coordinates according to the light source relative spectral power distribution and the CIE colorimetry formula;
the distance calculation module is used for obtaining a first black body chromaticity coordinate on the black body locus and a first distance corresponding to the first black body chromaticity coordinate according to the light source chromaticity coordinate and the segmented low-order polynomial;
the light source Duv calculation module is used for obtaining a light source Duv according to the light source chromaticity coordinates, the first black body chromaticity coordinates and the first distance;
the black body color temperature calculation module is used for obtaining the black body color temperature corresponding to the first black body chromaticity coordinate according to the first black body chromaticity coordinate and a color temperature calculation formula;
the light source correlated color temperature calculation module is used for obtaining light source correlated color temperature according to the black body color temperature;
the light source Duv calculating module is further configured to:
the light source Duv is calculated according to the following formula:
wherein D isuvFor said light source Duv, d (u)0) Is the first distance, (u)c,vc) (u) is the chromaticity coordinate of the light source0,v0) The first black body chromaticity coordinate is obtained;
the blackbody color temperature calculation module is further configured to:
using a method of triangle geometric similarity according to the first black body chromaticity coordinate (u)0,v0) And a color temperature calculation formula to obtain a first blackbody chromaticity coordinate (u) on the blackbody locus0,v0) Corresponding black body color temperature T0Calculating the blackbody color temperature according to:
wherein, T0Is the black body color temperature, (u)0,v0) Is the first black body chromaticity coordinate, (u)k,vk) And (u)k+1,vk+1) Chromaticity coordinates of two points adjacent to the left and right of the first black body chromaticity coordinate, TkAnd Tk+1、dkAnd dk+1、lkAnd lk+1Respectively the corresponding color temperature, distance and slope of the curve.
7. The system of claim 6, wherein the blackbody locus fitting module comprises:
discretizing the blackbody first temperature value to obtain a serialized blackbody second temperature value;
calculating to obtain second blackbody chromaticity coordinates corresponding to each second temperature value of the blackbody according to a Planckian blackbody radiation formula and a colorimetry formula;
and establishing the segmented low-order polynomial according to the second black body chromaticity coordinate, and obtaining the black body locus.
8. The system of claim 6, wherein the distance calculation module comprises:
establishing a second distance d (u) between the light source point and the blackbody locus according to the light source chromaticity coordinates and the segmented low-order polynomial;
and obtaining the first blackbody chromaticity coordinate on the blackbody locus and the first distance corresponding to the first blackbody chromaticity coordinate according to the derivative condition of the second distance.
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