CN111854951B - Optimization method for fitting target spectrum by N (N is more than or equal to 20) primary color spectrum - Google Patents
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Abstract
The invention discloses aN（NNot less than 20) primary color spectrum fitting target spectrum. Aiming at the problem that the primary color spectrums of each row influence each other, the invention accurately counts the spectrum range of other primary colors influenced by each row of spectrums by utilizing the half-width, and simultaneously and cooperatively adjusts other spectrums with the peak wavelength positioned in the half-width range of the row of spectrums when adjusting a certain row of spectrums, thereby improving the accuracy, reducing the calculated amount to the maximum extent, shortening the fitting time, and improving the fitting precision, wherein the synthesized spectrum meets the requirements that the general color rendering index Ra is more than or equal to 95, the special color rendering indexes R1-R15 are more than or equal to 95, and the color temperature deviation delta Tc is less than or equal to 10K.
Description
Technical Field
The invention relates to the technical field of illumination, in particular to an optimization method for fitting an N (N is more than or equal to 20) primary color spectrum to a target spectrum.
Background
In recent years, the development of quantum dot fluorescent nano materials has attracted extensive attention. The quantum dot material is made of a semiconductor material synthesized by elements such as zinc, selenium, cadmium, sulfur and the like, has the diameter of 2-10 nm, and has an obvious quantum confinement effect. It can confine the carriers in a semiconductor in a very tiny space, and the carriers are excited to transition to a high energy level under illumination or electrical stimulation, and then return to the original energy level again and emit visible light of a fixed wavelength. Compared with the traditional fluorescent powder, the quantum dot fluorescent material has the advantages that the central wavelength and the half-width of the excitation spectrum can be adjusted according to the chemical composition and the particle diameter of the quantum dot material, so that the quantum dot material with different parameters can cover the whole visible spectrum and partial infrared spectrum.
The quantum dot fluorescent material provides more primary color spectrums capable of being used for spectrum synthesis, and provides basic conditions for black body spectrum fitting, solar simulator preparation and the like. Currently, most quantum dot-based light sources use ultraviolet LEDs to excite quantum dot fluorescent materials of different sizes to emit various monochromatic lights so as to obtain a white light spectrum by mixing. Because the emission spectrum of the quantum dots can theoretically cover the whole visible spectrum and part of the infrared spectrum, and the half width of the emission spectrum can be modulated by continuously changing the size of the quantum dots, under the condition of reasonably selecting the material and the size of the quantum dots, the light source based on the quantum dot LED can obtain a very continuous synthetic spectrum, and is an ideal light source for synthesizing a solar spectrum or a black body radiation spectrum.
Chinese patent CN106764691 proposes a solar spectrum and black body radiation spectrum simulation system based on quantum dot LED, which adopts K (K is greater than or equal to 20) monochromatic quantum dot LED light sources or ultraviolet LED light sources with different peak wavelengths, converges monochromatic light to a light mixer at the common focus of a focusing lens through a focusing lens, and finally exits through a light distribution lens set, the degree of fitting is high, but it is not proposed how to adjust the equivalent quantum dot spectrum to more than 20 columns to make the synthesized spectrum close to the target spectrum, so as to achieve a higher fitting coefficient, and no specific operable and realizable automatic adjustment algorithm is given; chinese patent CN109029728 proposes a new evaluation method of synthesized spectrum, which calculates the color tolerance of the synthesized spectrum according to the central color coordinate of the synthesized spectrum and the central color coordinate of the standard spectrum, but the evaluation of the fitting quality by using the color tolerance is from the perspective of the color parameters, some surfaces are single, and the fitting coefficient of the synthesized spectrum and other color parameters such as color rendering index and color temperature are not given at the same time, which is not comprehensive enough; chinese patent CN108051084 proposes a method for determining a spectrum peak center, which calculates the spectrum peak center, judges whether the iteration number is more than 1, and further judges whether the center is converged, thereby changing the center of a data range and outputting the peak center.
The spectrum adjusting range can be enriched by a large number of primary color spectrums, and fitting of a target spectrum is facilitated; however, there is no reliable method or scheme for how to adjust the number of spectra, such as N ≧ 20, to obtain the target spectrum quickly and accurately. The existing calculation methods are very tedious and long, and even the calculation process is not converged, so that the final result cannot be obtained, and therefore a more reliable fitting method is needed.
Disclosure of Invention
The invention aims to provide an optimization method for fitting an N (N is more than or equal to 20) primary color spectrum to a target spectrum. When the method is used for adjusting a certain primary color spectrum, other primary color spectrums influenced by the spectrum are considered in a unified mode, the spectrum range of other primary colors influenced by each line of spectrum is accurately counted by utilizing the half-width, and other spectrums with peak wavelengths within the half-width range of the line of spectrum are adjusted in a coordinated mode, so that the accuracy is improved, the calculated amount is reduced to the maximum extent, the fitting time is shortened, the fitting precision is improved, and the synthetic spectrum with excellent light color parameters and high fitting degree is obtained.
The technical scheme of the invention is specifically introduced as follows.
The invention provides an optimization method for fitting a target spectrum by an N (N is more than or equal to 20) primary color spectrum, wherein a synthesized spectrum meets the requirements that the general color rendering index Ra is more than or equal to 95, the special color rendering indexes R1-R15 are more than or equal to 95, and the color temperature deviation delta Tc is less than or equal to 10K;
in the process of fitting the target spectrum by using N primary color spectrums, the ith column is sequentially calculated, i is 1: N, the difference value D between the spectrum and the target spectrum i ；
If D of the spectrum in column i i If the standard does not meet the requirement of the criterion value delta, the peak wavelength of the ith spectrum is taken as the center, and the statistical peak wavelength is positioned in the half-width ranges [ lambda ] at the left side and the right side of the center spectrum i -Δλ i ，λ i +Δλ i ]And are respectively expressed as j ═ i-a, i-a +1, …, i-1, i +1, i +2, …, i + b; wherein λ is i Is the peak wavelength, Δ λ i Half width, a is the peak wavelength less than λ in this range i B is the peak wavelength in the range greater than lambda i The number of primary color spectra of (a);
sequentially calculating D of jth column spectrum and target spectrum i And the synthesis proportion of the corresponding spectrum is adjusted according to the criterion so as to change the synthesized spectrum until the difference value D between the ith spectrum and the target spectrum i When the requirements of the criterion are met, the adjustment of the ith row of spectrum is finished, and the adjustment of the next row of spectrum is carried out;
and when the N columns of spectra are used as the central spectrum, repeating the process to obtain a synthesized spectrum most approximate to the target spectrum.
The optimization method of the fitting target spectrum of the N (N is more than or equal to 20) primary color spectrum comprises the following specific steps:
1) the spectral power distribution T (λ) and the fitted wavelength range [ λ ] of the target spectrum are known L ,λ H ]And the parameters of the N (N ≧ 20) columns of primary color spectra include spectral power distribution M i (lambda), peak wavelength lambda i Half width Δ λ i (ii) a Giving an initial value p to the synthesis ratio of all primary color spectra i ＝p(0<p<1) Then the initial synthesized spectrum is
2) A sufficiently small value delta is set as the difference sum D i The criterion condition of (1);
3) setting a value zeta as an adjustment quantity of the primary color spectrum synthesis proportion;
4) calculating the difference sum of the synthesized spectrum and the target spectrum in the wavelength range corresponding to each column of primary color spectrum: for the ith column of primary color spectrum, take l i ＝Max(λ i -λ i-1 ,λ i+1 -λ i ) I.e. l i The larger value of the interval between the peak wavelengths of the ith row of quantum dot spectrums and the adjacent two rows of quantum dot spectrums; the sum of the difference values corresponding to the ith column of quantum dot spectrums
Wherein λ min ＝Max[λ L ,(λ i -l i /2)]，λ max ＝Min[(λ i +l i /2),λ H ]；
5) For the ith column of primary spectrum, | D i |<Delta, completing the spectrum proportion adjustment and outputting the corresponding synthesis proportion p i And skipping to the next column of adjustment of the primary color spectrum; otherwise, the synthesis proportion of the row of primary color spectrums and other primary color spectrums within the influence range of the primary color spectrums is adjusted cooperatively;
6) the statistical peak wavelength is positioned in the half-width wavelength range [ lambda ] of the ith row of primary color spectrum i -Δλ i ,λ i +Δλ i ]In which a is the peak wavelength in the range less than lambda, and all primary color spectral sequences i-a, i-a +1, …, i-1 and i +1, i +2, …, i + b i B is the peak wavelength in the range greater than lambda i The number of primary color spectra of (a);
7) let k be i-a, i-a +1, …, i-1, i, i +1, i +2, …, i + b, if | D k |<δ, then corresponds to the ratio p k ′＝p k (ii) a If | D k If | is not less than δ, then D k >At 0 time p k ′＝p k -ζ，D k <At 0 time p k ′＝p k + ζ; obtaining an adjusted synthetic spectrum S' (lambda); returning to the step 4);
8) completing the adjustment of all the N rows of primary color spectrums according to the steps 4) -7), obtaining a synthetic spectrum result of the cycle, and calculating light color parameters such as color rendering indexes Ra and R1-R15, color temperature and the like;
9) if the color rendering property, color temperature and other light color parameters can not simultaneously meet Ra being more than or equal to 95, R1-R15 being more than or equal to 95, and delta Tc being less than or equal to 10K, delta can be reduced on the basis, and the steps 2) -8) are repeated until all the light color parameters meet the requirements, and the final synthetic spectrum is obtained.
In the invention, the peak wavelengths of the N rows of primary color spectrums cover the range of 380-780 nm, and the peak wavelengths are different.
In the invention, the target spectrum covers all the commonly used color temperature 2700-.
In the invention, the fitting process can start from any column in the N columns of primary color spectrums, can be adjusted from the middle wavelength to two sides, and also can be adjusted from the short wave end to the long wave end or from the long wave end to the short wave end in sequence.
Compared with the prior art, the invention has the following advantages:
for the primary color spectrums with a large number (N is more than or equal to 20), the difficulty is high if the primary color spectrums are adjusted simultaneously, and because the spectrums have a large number, the calculation is complicated and the screening time is long; if the adjustment is performed in a row and a column, the accuracy is low, and the spectrum of other primary colors that have been adjusted in the early stage is easily affected, and the problem that the calculation result cannot be converged may occur. Aiming at the problem of mutual influence of primary color spectrums of each row, the invention accurately counts other primary color spectrum ranges influenced by each row of spectrums by using the half-width as a balance factor, and simultaneously and cooperatively adjusts other spectrums with peak wavelengths positioned in the half-width range of the row of spectrums when adjusting a certain row of spectrums, thereby improving the accuracy rate, reducing the calculated amount to the maximum extent, shortening the fitting time, and improving the fitting precision to obtain the synthetic spectrum with superior light color parameters and high fitting degree. The method for fitting the target spectrum is suitable for visible light spectrum, ultraviolet spectrum and infrared spectrum, and the wavelength range of the method can be 200-1200 nm.
Drawings
FIG. 1 is a flow chart of the calculation of the fitting of the N (N ≧ 20) primary color spectrum to the target spectrum.
Fig. 2 is a normalized spectral power distribution of spectra of 21 primary color quantum dots according to an embodiment of the present invention.
FIG. 3 is a composite spectrum of a 21-color quantum dot spectrum of the present invention reproducing a 4000K blackbody spectrum.
Fig. 4 is a composite spectrum of a 21-color quantum dot spectrum of the present invention reproducing a 2700K blackbody spectrum.
Fig. 5 is a synthesized spectrum of a 21-color quantum dot spectrum of the present invention reproducing a 3000K blackbody spectrum.
Fig. 6 is a synthesized spectrum of a 21-color quantum dot spectrum of the present invention reproducing a 3500K blackbody spectrum.
Fig. 7 is a synthesized spectrum of a 21-color quantum dot spectrum of the present invention reproducing a 4500K blackbody spectrum.
Fig. 8 is a synthesized spectrum of a 21-color quantum dot spectrum of the present invention reproducing a 5000K blackbody spectrum.
FIG. 9 is a synthetic spectrum of a 21-color quantum dot spectrum reproduction 5500K recombined sunlight of the present invention.
FIG. 10 is a composite spectrum of a 21-color quantum dot spectrum of a 6000K recombined sunlight of the present invention.
FIG. 11 is a synthesized spectrum of a 21-color quantum dot spectrum reproduction 6500K recombination daylight of the present invention.
Detailed Description
The optimization method for fitting the N (N ≧ 20) primary color spectrum to the target spectrum according to the present invention is further described in detail with reference to the accompanying drawings, which are only some embodiments of the present invention, and all other embodiments based on the embodiments of the present invention without inventive efforts shall fall within the scope of the present invention.
Example (b): fitting a target spectrum in the visible range using 21 quantum dot primary color spectra
1) The normalized 4000K blackbody spectrum is used as a target spectrum T (lambda), distribution in a wavelength range of 380-780 nm is fitted, the quantum dot spectrum number N is 21, and the spectrum power distribution M is i (λ) as shown in fig. 2, if the peak wavelength intervals l between two adjacent rows of spectra are equal, l is 20 nm; peak wavelength λ of each quantum dot spectrum i And half width Δ λ i As shown in table 1. The spectral power distribution functions of all primary color spectra adopt Gaussian fitting and are subjected to normalization processing. Giving an initial value, p, to the synthesis ratio of the 21-column quantum dot spectrum 11 0.2, the remainder being p i 0.1(i ═ 1,2, …,21 and i ≠ 11), the initial composite spectrum is
Table 121 parameters of primary color quantum dot spectra
2) For the first debugging, the criterion δ is set to 1, and the adjustment value ζ is set to 0.01. Starting from the 11 th column of primary color spectrum, i is 11, the 11 th column of quantum dot spectrum has a center wavelength of 580nm and a half-width of 62nm, the number of spectral columns in the half-width range (580-62, 580+62) on both sides of the spectrum is (11-3, 11+3), i.e. 8 th to 14 th columns, j is 8,9,10,12,13,14, k is 8: 14. Then sequentially calculating the k column spectrum and the target spectrum T (lambda) at (lambda) k -l，λ k Difference sum D within + l) k Since the central wavelengths of each adjacent spectrum are equally spaced, the wavelength division ratio of each adjacent spectrum is equalIntegration ranges are all (λ) k -10，λ k +10), first determine if the boundary exceeds the visible light range, if λ k -10<380 or lambda k +10>780 then the difference sum D k Are respectively as
If the wavelength boundaries are all out of the visible range
If none of the wavelength boundaries exceed the visible range, then
For example, column 8 spectrum peak wavelength is 520nm, the difference sum with the target spectrum
The sum of the difference between the central spectrum i and the target spectrum of 11 columns
Then sequentially judging the difference value D of the 8 th to 14 th columns of spectra 8 ～D 14 Whether the criterion requirement is met: if | D k |>δ, further determining that the k-th column spectrum is above (D) the target spectrum T (λ) k >0) Or below (D) k <0) If D is k >0 then correspondingly changes the spectrum proportion p of the row k ’＝p k Zeta, conversely p k ’＝p k +ζ，0<ζ<0.01. For example if D 8 >0, then p 8 ’＝p 8 - ζ ═ 0.1- ζ, if
The scale is not changed. After the proportion of the k columns of spectra is adjusted, the synthesis proportion of the N (N is more than or equal to 20) columns of quantum dot spectra is changed from p to p ', the synthesis spectrum is S (lambda) ' -M multiplied by p ', the difference value is calculated again, the corresponding spectrum proportion is changed, and the process is repeated continuously and circularly until the difference value D between the 11 th column of central spectra and the target spectrum T (lambda) and the difference value D 11 Within the required range, i.e. | D 11 |<δ，Indicating that the spectrum in the 11 th column is adjusted, the next column is circulated, and the specific flow is shown in fig. 1.
3) And (3) outputting a final synthesis proportion and obtaining a synthesized spectrum after finishing the adjustment of all the 21 rows of spectra as the center spectrum according to the step 2), and calculating parameters such as color rendering indexes Ra and R1-R15, color temperature and the like.
4) And further perfecting the photochromic parameters and debugging for the second time. The criterion value and the adjustment amount are reduced, δ is set to 0.2, and ζ is set to 0.001. Repeating the operations 2) to 3), wherein the obtained photochromic parameter conditions are that Ra is more than or equal to 99, R1-R15 are more than or equal to 95, and Delta Tc is less than or equal to 10K.
Table 2 lists the two synthesis ratios of the 21 columns of quantum dot spectra to be fitted to the 4000K blackbody spectrum, and the synthesized spectra are shown in fig. 3. Coefficient of determination R for fitting degree between synthesized spectrum and target spectrum 2 To evaluate. For the target spectrum y ═ T (λ), the synthesized spectrum f ═ S (λ). The spectral power distribution curve is divided into n segments, then
Represents the mean of the target spectrum. Sum of squares of the population
Sum of squares of residuals
The coefficient R is determined 2 ＝1-SS res /SS tot . Actually calculating the determining coefficient R in the wavelength range of 400-730 nm 2 . Coefficient of determination R of two-pass synthesized spectrum of 4000K in this example 2 0.9588 and 0.9679, respectively, also show that the target spectrum with the synthesized spectrum closer to the 4000K blackbody is obtained after the reduction criterion value delta and the adjustment value zeta are finely adjusted.
Table 221 synthetic proportions of primary color quantum dot spectrums fitting 4000K target spectrums
The same method can obtain synthesized spectra of other color temperatures. Considering that sunlight is more adopted as a standard light source under the condition of high color temperature in practical application, the black body spectrum obtained by the planck formula is used as the target spectrum for the low color temperature (2700-. It can be seen that the optimization method of the present invention can obtain a synthesized spectrum with superior photochromic parameters and high fitting degree.
Compared with the 21-color synthesized spectrum result obtained by manual adjustment in Chinese patent CN106764691, the synthesized spectrum obtained by calculation in the invention has smaller color temperature deviation, better color rendering index R9 under the same blackbody target spectrum, and the fitting degree also meets the requirement. Chinese patent CN2016112668126 uses correlation coefficient R, i.e. the product of covariance/standard deviation of the two, to evaluate that the fitting degree of manual adjustment is slightly higher, but the adjustment time is long and the color temperature deviation is large. Under the condition of high color temperature, the embodiment selects the recombined sunlight as the target spectrum based on the practical application situation, and the fluctuation of the spectral distribution of the recombined sunlight is large, so that the deviation of the synthesized spectrum of 5500K or more and the target spectrum is relatively large, but the deviation also meets the condition of more than 0.9.
Table 321 kinds of light color parameter characteristics of fitting result of primary color quantum dot spectrum to different color temperature target spectrum
Claims (4)
1. An optimization method for fitting a target spectrum by an N-primary color spectrum is disclosed, wherein N is more than or equal to 20, and the method is characterized in that a synthesized spectrum meets the requirements that the general color rendering index Ra is more than or equal to 95, the special color rendering indexes R1-R15 are more than or equal to 95, and the color temperature deviation delta Tc is less than or equal to 10K;
in the process of fitting the target spectrum by using the N primary color spectrum, the difference value D between the synthesized spectrum and the target spectrum in the wavelength range corresponding to the ith row of primary color spectrum is calculated in sequence i Wherein i is 1: N;
if the ith column primary color spectrum and the target light areDifference sum of spectra D i If the standard does not meet the requirement of the criterion value delta, the peak wavelength of the primary color spectrum in the ith row is taken as the center, and the statistical peak wavelength is positioned in the half-width range [ lambda ] at the left side and the right side of the primary color spectrum in the ith row i -Δλ i ，λ i +Δλ i ]And are respectively expressed as k ═ i-a, i-a +1, …, i-1, i +1, i +2, …, i + b; wherein λ is i Is the peak wavelength, Δ λ i Is half-width, and a is the peak wavelength in the range less than λ i B is the peak wavelength in the range greater than lambda i The number of primary color spectra of (a);
sequentially calculating the difference value D between the ith column of primary color spectrum and the target spectrum i And the synthesis proportion of the corresponding spectrum is adjusted according to the criterion so as to change the synthesized spectrum until the difference value D between the ith row of primary color spectrum and the target spectrum i If the requirements of the criterion are met, the adjustment of the primary color spectrum of the ith row is finished, and the adjustment of the primary color spectrum of the next row is carried out;
when the N primary color spectrums are all used as central spectrums, repeating the process to obtain a synthesized spectrum most approximate to the target spectrum; the method comprises the following specific steps:
1) the spectral power distribution of the target spectrum T (λ) and the fitted wavelength range [ λ ] are known L ,λ H ]And the parameter of the N primary color spectrum comprises the spectral power distribution M i (lambda), peak wavelength lambda i Half width Δ λ i (ii) a Giving an initial value p to the synthesis ratio of all primary color spectra i P, 0 < p < 1, the initial synthesized spectrum is
Wherein N represents the number of primary color spectra;
2) setting a criterion value delta as a difference sum D i The criterion condition of (1);
3) setting a value zeta as an adjustment quantity of the primary color spectrum synthesis proportion;
4) calculating the difference value D between the synthesized spectrum and the target spectrum in the wavelength range corresponding to each row of primary color spectrum i : for the ith column of primary color spectrum, take l i ＝Max(λ i -λ i-1 ,λ i+1 -λ i ) I.e. l i Is the firstThe larger value of the interval between the peak wavelengths of the i-column quantum dot spectrum and the two adjacent quantum dot spectra; the sum of the difference values corresponding to the ith column of quantum dot spectrums
Wherein λ min ＝Max[λ L ，(λ i -l i /2)]，λ max ＝Min[(λ i +l i /2),λ H ]；
5) For the ith column primary spectrum, if | D i If | < delta, the spectrum proportion adjustment is completed, and the corresponding synthesis proportion p is output i And skipping to the next column of adjustment of the primary color spectrum; otherwise, the synthesis proportion of the row of primary color spectrums and other primary color spectrums within the influence range of the primary color spectrums is adjusted cooperatively;
6) the statistical peak wavelength is positioned in the half-width wavelength range [ lambda ] of the ith row of primary color spectrum i -Δλ i ,λ i +Δλ i ]I-a, i-a +1, …, i-1 and i +1, i +2, …, i + b, where a is the peak wavelength less than λ in this range i B is the peak wavelength in the range greater than lambda i The number of primary color spectra of (a);
7) let k be i-a, i-a +1, …, i-1, i +1, i +2, …, i + b, if | D k If | is less than δ, then the corresponding ratio p of the k-th column of primary color spectrum k ′＝p k (ii) a If | D k If | is not less than δ, then D k > 0 time p k ′＝p k -ζ，D k P at < 0 k ′＝p k + ζ, obtaining the adjusted synthesized spectrum S' (λ); returning to the step 4); wherein: d k The k column primary color spectrum and the target spectrum T (lambda) are in (lambda) k -l，λ k The sum of the differences in + l), l is the peak wavelength interval between two adjacent columns of spectra;
8) completing the adjustment of all the N primary color spectrums according to the steps 4) -7), obtaining a synthetic spectrum result of the cycle, and calculating color rendering indexes Ra and R1-R15 and color and temperature parameters;
9) if the color rendering index and the color temperature and the light color parameters can not simultaneously meet the requirements that the general color rendering index Ra is more than or equal to 95, the special color rendering indexes R1-R15 are more than or equal to 95, and the color temperature deviation delta Tc is less than or equal to 10K, reducing the criterion value delta, and repeating the steps 2) -8) until all the light color parameters meet the requirements, thereby obtaining the final synthetic spectrum.
2. The optimization method as claimed in claim 1, wherein the peak wavelength of the N-primary color spectrum covers the range of 380-780 nm, and the peak wavelengths are different.
3. The optimization method as claimed in claim 1, wherein the target spectrum covers all the color temperatures 2700-.
4. The optimization method according to claim 1, wherein the fitting process starts from any column in the N primary color spectrum, or is adjusted from the middle wavelength to both sides, or is adjusted from the short wavelength end to the long wavelength end, or from the long wavelength end to the short wavelength end in sequence.
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