Simulation of basic parameters

The SPD of LEDs is the most basic information in the simulation. Thus, the ability to simulate the LED SPD is important for the preset simulations. The SPD of the phosphor white LED is much more complicated and case by case. Thus, we only simulate the primary color LED SPD here. Generally, the primary color LED SPD has a Gaussian shape distribution with different full-width-half-maximum (FWHM).

Many equations are used to simulate the profile, and they are usually expressed as an equation with two variables, the primary wavelength and the FWHM value. The most common model is shown as bellow and comes from Yoshi Ohno [17].

S_LED λ, λ₀, ∆λ_0.5 = ^{g λ,λ0,∆λ0.5 +2× g}₃ ^{5 λ,λ0,∆λ0.5} (Eq. 3.1) g λ, λ₀, ∆λ_0.5 = exp − ^(λ−λ_∆λ ⁰⁾

0.5 2

Here we use the same equation as our LED model, and simulate the LED SPD of a AVaGO® high power RGB light source, ADJD-MJ50, from the data sheet. The measurement and simulation SPD are shown below [Fig. 3.2]. The correlation coefficient is larger than 98%. Thus, the variations between the two normalized SPDs are very small. Thus, this LED SPD model is used for our previous design simulation.

Fig. 3.2 Simulation LED SPDs and Measurement LED SPDs

(Darker lines for the simulation SPDs and lighter lines for the measurement SPDs)

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In our simulation flow, the program will calculate all possible mixing ratios that have the same CCT value. Thus, by the black body radiation equations given before, the SPDs of different temperature can be calculated, and then received the chromatic coordinates. Therefore, the black body locus can be drawn with the expected CCT lines [Fig. 3.3].

Fig. 3.3 Black body locus with CCT lines

Choosing the correct reference illuminant is important for the calculation of CRI values. As mentioned before, CIE selected different reference illuminants for the different CCT value light sources. The CIE daylight illuminant is used when the CCT value is higher than 5000K, and the black body radiation is used when the CCT value is lower than 5000K. In order to simplify the application, CIE established the SPDs of the standard illuminant at general CCT values, such as D65, D55, D50, and A. The diagrams of the calculated CIE daylight SPDs and the standard illuminants are shown below [Fig. 3.4], and it is obvious that the simulated SPDs are corresponding to the standard ones.

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Fig. 3.4 CIE daylight SPDs and standard illuminant SPDs 3.2.2 Modification of the mixing ratio

After showing the ability of simulating some fundamental parameters, the method of modifying the mixing ratio will be mentioned here. In our research, we first proposed a modify method based on the simplification of the relationships between SPD and chromaticity coordinates. In this method, we first consider an arbitrary SPD, and then we try to modify the SPD at two wavelengths, λ₁ and λ₂, with different signs, one positive and one negative, and the same weighting [Fig. 3.5].

Fig. 3.5 Modification concept in the beginning method

After that, the chromaticity coordinates of the original SPD and the SPD after modification, SPD‟, can be calculated by the following equations (Eq. 3.2 ~ Eq. 3.4).

Thus, the movement of the chromaticity coordinates can be described as the functions of modify wavelength (Eq. 3.5).

38 depending on the difference of three matching functions at wavelength λ1 and λ2. Due to the reason that the denominators of the equation 3.5 are always positive and the term Δα can also be defined to be positive, the numerators of equation 3.5 can be regarded as the indicators of the coordinate movement. Therefore, we expected to use the parameter, Mdir, as the guideline for the program to modify the mixing ratio (Eq.

3.6).

39 depending on the relative position of current coordinates and the target coordinates.

However, after some previous tests of this parameter, M_dir, we found out that the parameter is only correct for mono-wavelength modulation. This is due to the reason that the assumption we set in the beginning only considers to modify two mono-wavelengths. Therefore, the profile of the light source should be taken into consideration in practical computation. Thus, this indicator will be too tedious to use.

After all, we gave up using Mdir as the indicator for modifying the light source mixing ratio, and turned back to take the color difference on the chromaticity diagram as the parameter for movement judgment. The color difference we take is the ΔExy on CIE 1931 xyz chromaticity diagram. Although the other color system has better uniformity, the calculation simplicity is the prior issue that we consider here.

Here we use an example to explain the modification process of the program. If we have four LED with mixing chromaticity points at (0.38, 0.28) and the target point at (0.30, 0.31) as shown in Fig. 3.6(a). Thus, the program will first calculate the eight possible modification chromaticity points, each is received by increasing or decreasing one of the four LED lightness level [Fig. 3.6(b)]. After that, the program will modify the LED which can reduce the color difference to a minimum value.

Therefore, the program can approach the target coordinates by repeating the modification. The program will finally stop when the color difference is less than 0.005, which is set by the half distance of the neighboring discrete CCT coordinates

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we setup before, and it is believed that the human eye cannot distinguish the color difference at this scale [14]

.

Fig. 3.6(a) Relative position of the current coordinates and the target coordinates

Fig. 3.6(b) Chromaticity coordinates after modifying the mixing ratio Current Point

Target Point

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