4.3 Optimisation of LED mixtures for LER and CQS (NIST Qa)

This was again a constrained optimisation process. It was based on the same set of Luxeon™ LEDs as used in Section 4.1, and also used tetrachromatic mixtures. The optimisation process [23] was also broadly similar to that in Section 4.1, and it used a similar interface, but the software was rewritten to compute the performance of candidate SPDs in terms of CQS parameters, specifically the average colour quality index, Q <sup>a</sup>, and the minimum, Q min (the lowest individual index, Q <sup>i</sup>) for every candidate SPD.

The following fitness function (Eq. 5) was employed:

$$f\_{fit} = aQ\_a + b\eta\_{rad} + cQ\_{min} \tag{5}$$

where a, b, c are the weights controlling the influence of Q a, LER and Qmin on the optimisation of the LED mixtures. A selection of the results of the optimisation of the LED mixtures using various weightings is shown in Table 3.


Table 3.

Optimizations of five tetrachromatic LED mixtures (CQS domain).

45 nm (full width at half maximum, or FWHM) [27]. Apart from these changes, the procedure was essentially the same as that used in Section 4.1, and the same fitness

A total of 36 optimisations were performed, using 12 different combinations of ffit weightings for each of the three functions. The following extract from this set of results shows the SPDs obtained with the weightings: a = 1; b = c = d = e = 0. See

It was intended that the unconstrained approach will help to identify those wavelength combinations that will lead to optimum SPDs. The findings relating to

This is too small a sample from which to generalise; however, it is possible to make the following observations. The colour performance of these three mixtures is exceptionally good (other than the high CCT for G1) possibly at the expense of relatively moderate LER values. It is probable that the Gaussian and triangular shapes are more realistic simulations of real physical spectra (whether originating from LEDs or phosphors); hence their corresponding centre wavelengths (λ1–λ4) may be useful indicators for use in light-source design. See [27] for a more complete discussion.

the spectra in Figure 6 are summarised in Table 2.

function was used.

Behaviour of ηrad in Test 1.

Figure 6.

48

Figure 5.

Figure 4.

Behaviour of Ra, Rb, Rc and Rmin in Test 1.

Computer Architecture in Industrial, Biomechanical and Biomedical Engineering

#### 4.4 Optimisation of LED mixtures for specific CCT values

The previously mentioned techniques (used in Section 4.1–4.3) did not take account of the CCTs of the spectra except as values to be calculated following the optimisations. Because of the importance of the CCT to lighting designers and users, it was recognised that this parameter needed to be incorporated into the optimisation procedure.

We therefore designed a new optimisation tool [29], again based on differential evolution, which puts CCT at the centre of the process and then proceeds to optimise colour rendering while maintaining a close tolerance to the target CCT value. We selected three CCT values to illustrate the effectiveness of the process.

The above approach was extended to a set of optimisations in which Gaussian-

Illuminant Ra Rmin imin LER (lm/W) ΔE00(Avg) Δ(u',v') A 96 68 12 318 0.82 0.0034 D50 95 89 12 336 0.58 0.0019 D65 93 75 9 299 0.67 0.0059

Our investigations in this field [28, 32] were inspired by the work of Neumann

Our purpose in [32] was to optimise similar mixtures of solid-state lasers, and to

where Rf = average fidelity index for all 99 colour samples; Rfmin = value of the lowest-scoring individual Rf (single colour sample); Rfskin = average index for two individual colours selected as representative of human skin; ηrad = value of LER in

For the purposes of optimisation, each laser was simulated by a pseudo-delta function (1-nm bandwidth) at the centre wavelength of its output. Optimisations were performed in both constrained (using commercially available laser diode

The best result (with four real laser wavelengths) was Rf of 84 with LER 364 lm/W, which indicates the feasibility of the mixed-laser approach to provide highly efficient, energy-saving light sources. The unconstrained mixtures showed that the prospects will be further enhanced by potential future developments in semiconductor lasers, with the possibility of producing Rf of 86 with LER of 380 lm/W. The detailed

Compared with LEDs, lasers have the advantage of higher conversion efficiency (from electrical input to radiant output). This, combined with the very high prospective LER values, will make future laser mixtures exceptionally attractive in terms of energy conservation. The colour properties are not as good as for LEDs, but they are nevertheless regarded as sufficiently good for many types of lighting

f ¼ aRf þ bRf min þ cRf skin þ dηrad (6)

utilize the more up-to-date method of the IES colour fidelity index Rf [15, 16]. A new optimisation tool was designed to implement the complex sequence of non-linear calculation steps in the evaluation of colour fidelity for any given SPD. We then developed a new fitness function (Eq. 6) based on the IES parameters as well as the LER, to evaluate every candidate spectrum produced in the process.

shaped spectra of either 25 or 50 nm bandwidth, but with unconstrained peak intensities and wavelengths, were optimised in the same way as the LED mixtures. Table 5 shows the best CRI performance for 4-band (25 nm) Gaussian mixtures, along with the other properties as listed in Table 4, and there is an evident degree

4.5 Optimisation of laser diode mixtures using TM-30-15 (IES Rf)

et al. [33] who successfully demonstrated a white-light 4-laser mixture with acceptable colour properties expressed in terms of the CRI and CQS metrics. Our earlier paper [28] also used CRI and CQS as measures of colour rendition. These approaches are now regarded as suspect (particularly in respect of mixtures of ultra-narrow bands such as lasers) on the grounds of incomplete sampling of wave-

of conformance between the two sets of results.

Artificial Intelligence in Light-Source Design DOI: http://dx.doi.org/10.5772/intechopen.88094

Optimizations of tetrachromatic Gaussian mixtures with specified CCTs.

lm/W; a, b, c, d are the respective weighting factors.

properties for these two mixtures are given in Table 6.

wavelengths) and unconstrained modes.

51

length and colour spaces.

Table 5.

The optimiser was presented with a specific set of four monochromatic LED spectra selected from the Luxeon™ range. The objective was to minimise the average colour difference for a set of colour samples which, in principle, could be any suitable set of colours. We chose to use the 14 test colours specified in CIE13.3 [13] since they constitute a well-known and widely used set.

The basis of the selection process in our algorithm was the colour difference of specific surface colours as they appear under the candidate spectrum and under the reference spectrum of the same CCT. In each new generation, the offspring solutions were evaluated on the basis of minimising the colour difference ΔE00(Avg) calculated using the CIEDE2000 colour difference formula [31]. Hence, the algorithm was designed to search for a spectrum with the lowest colour differences. The optimum solution was determined after having performed G generations (typically 1000); that is, the best solution in generation G is accepted as the best white-light spectrum.

Figure 7 shows the results in the form of the SPDs realised by the LED mixtures, and their performance is summarised in Table 4. Note that ΔE00(Avg) represents the average of 14 colour differences (for the 14 colours in the CIE set) and Δ(u<sup>0</sup> ,v0 ) is the chromaticity difference in CIE 1976 coordinates between the target CCT and that achieved by the LED mixture. The other listed parameters were computed after the completion of each optimisation run.

#### Figure 7.

Relative SPDs of 4-LED mixtures that match CIE illuminants A, D50 and D65. Relative SPDs of the actual illuminants are shown for reference (lighter lines).


#### Table 4.

Optimizations of tetrachromatic LED mixtures with specified CCTs.

Artificial Intelligence in Light-Source Design DOI: http://dx.doi.org/10.5772/intechopen.88094


Table 5.

4.4 Optimisation of LED mixtures for specific CCT values

Computer Architecture in Industrial, Biomechanical and Biomedical Engineering

since they constitute a well-known and widely used set.

the completion of each optimisation run.

illuminants are shown for reference (lighter lines).

Optimizations of tetrachromatic LED mixtures with specified CCTs.

tion procedure.

spectrum.

Figure 7.

Table 4.

50

The previously mentioned techniques (used in Section 4.1–4.3) did not take account of the CCTs of the spectra except as values to be calculated following the optimisations. Because of the importance of the CCT to lighting designers and users, it was recognised that this parameter needed to be incorporated into the optimisa-

We therefore designed a new optimisation tool [29], again based on differential

The basis of the selection process in our algorithm was the colour difference of specific surface colours as they appear under the candidate spectrum and under the reference spectrum of the same CCT. In each new generation, the offspring solutions were evaluated on the basis of minimising the colour difference ΔE00(Avg) calculated using the CIEDE2000 colour difference formula [31]. Hence, the algorithm was designed to search for a spectrum with the lowest colour differences. The optimum solution was determined after having performed G generations (typically 1000); that is, the best solution in generation G is accepted as the best white-light

Figure 7 shows the results in the form of the SPDs realised by the LED mixtures, and their performance is summarised in Table 4. Note that ΔE00(Avg) represents the

> ,v0 ) is

average of 14 colour differences (for the 14 colours in the CIE set) and Δ(u<sup>0</sup>

the chromaticity difference in CIE 1976 coordinates between the target CCT and that achieved by the LED mixture. The other listed parameters were computed after

Relative SPDs of 4-LED mixtures that match CIE illuminants A, D50 and D65. Relative SPDs of the actual

Illuminant Ra Rmin imin LER (lm/W) ΔE00(Avg) Δ(u',v') A 93 68 11 313 0.73 0.0038 D50 95 70 12 311 0.81 0.0010 D65 95 63 12 298 0.94 0.0015

evolution, which puts CCT at the centre of the process and then proceeds to optimise colour rendering while maintaining a close tolerance to the target CCT value. We selected three CCT values to illustrate the effectiveness of the process. The optimiser was presented with a specific set of four monochromatic LED spectra selected from the Luxeon™ range. The objective was to minimise the average colour difference for a set of colour samples which, in principle, could be any suitable set of colours. We chose to use the 14 test colours specified in CIE13.3 [13] Optimizations of tetrachromatic Gaussian mixtures with specified CCTs.

The above approach was extended to a set of optimisations in which Gaussianshaped spectra of either 25 or 50 nm bandwidth, but with unconstrained peak intensities and wavelengths, were optimised in the same way as the LED mixtures.

Table 5 shows the best CRI performance for 4-band (25 nm) Gaussian mixtures, along with the other properties as listed in Table 4, and there is an evident degree of conformance between the two sets of results.

### 4.5 Optimisation of laser diode mixtures using TM-30-15 (IES Rf)

Our investigations in this field [28, 32] were inspired by the work of Neumann et al. [33] who successfully demonstrated a white-light 4-laser mixture with acceptable colour properties expressed in terms of the CRI and CQS metrics. Our earlier paper [28] also used CRI and CQS as measures of colour rendition. These approaches are now regarded as suspect (particularly in respect of mixtures of ultra-narrow bands such as lasers) on the grounds of incomplete sampling of wavelength and colour spaces.

Our purpose in [32] was to optimise similar mixtures of solid-state lasers, and to utilize the more up-to-date method of the IES colour fidelity index Rf [15, 16].

A new optimisation tool was designed to implement the complex sequence of non-linear calculation steps in the evaluation of colour fidelity for any given SPD. We then developed a new fitness function (Eq. 6) based on the IES parameters as well as the LER, to evaluate every candidate spectrum produced in the process.

$$f = aR\_f + bR\_{f\text{ min}} + cR\_{f\text{ skin}} + d\eta\_{rad} \tag{6}$$

where Rf = average fidelity index for all 99 colour samples; Rfmin = value of the lowest-scoring individual Rf (single colour sample); Rfskin = average index for two individual colours selected as representative of human skin; ηrad = value of LER in lm/W; a, b, c, d are the respective weighting factors.

For the purposes of optimisation, each laser was simulated by a pseudo-delta function (1-nm bandwidth) at the centre wavelength of its output. Optimisations were performed in both constrained (using commercially available laser diode wavelengths) and unconstrained modes.

The best result (with four real laser wavelengths) was Rf of 84 with LER 364 lm/W, which indicates the feasibility of the mixed-laser approach to provide highly efficient, energy-saving light sources. The unconstrained mixtures showed that the prospects will be further enhanced by potential future developments in semiconductor lasers, with the possibility of producing Rf of 86 with LER of 380 lm/W. The detailed properties for these two mixtures are given in Table 6.

Compared with LEDs, lasers have the advantage of higher conversion efficiency (from electrical input to radiant output). This, combined with the very high prospective LER values, will make future laser mixtures exceptionally attractive in terms of energy conservation. The colour properties are not as good as for LEDs, but they are nevertheless regarded as sufficiently good for many types of lighting


imin refers to the sample number that gave the listed value of Rf i = Rf min,

i = 97 is dark pink-purple (printed origin); 81 is dark purple-blue (natural origin).

Table 6.

Optimizations of simulated tetrachromatic laser mixtures.

situations. Lasers are not yet considered to be practical as white-light sources but, with the potential for new developments in solid-state visible laser sources, their future prospects must be very strong.

### 5. Conclusions

We have here demonstrated the power of the differential evolution algorithm in the intelligent design of light source spectra, based on both LEDs and laser diodes. It provides a simple, flexible and effective solution in the elusive search for the balance of the LER and the colour rendition properties in optimised light sources. We recommend this technique to anyone engaged in the optimum design of lightsource spectra.

We feel confident that our method can also be readily adapted to other types of optimisation problem, wherever suitable elements for the fitness function can be readily identified.

#### Acknowledgements

This work was supported by Professional Engineering and the Manukau Institute of Technology Research Fund. The second author thanks Professor Ahmed Al-Jumaily, director of IBTec at AUT, for his support and the provision of facilities.

#### Conflicts of interest

The authors declare that there is no conflict of interest regarding the publication of this chapter.

Author details

Snjezana Soltic<sup>1</sup>

53

Auckland, New Zealand

\* and Andrew N. Chalmers<sup>2</sup>

1 Manukau Institute of Technology, Auckland, New Zealand

\*Address all correspondence to: ssoltic@manukau.ac.nz

provided the original work is properly cited.

Artificial Intelligence in Light-Source Design DOI: http://dx.doi.org/10.5772/intechopen.88094

2 Institute of Biomedical Technologies, Auckland University of Technology,

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

#### Funding statement

This study has been supported in part by a Manukau Institute of Technology Research Grant, and was also performed as part of the employment of the authors by Manukau Institute of Technology.

#### Data availability

Previously reported data were used to support this study. These prior studies are cited at relevant places within the text as references [23, 26–29, 32].

Artificial Intelligence in Light-Source Design DOI: http://dx.doi.org/10.5772/intechopen.88094
