4 Applications of the Multispectral Mixing Scheme
4.2 Case 2: High power LEDs cluster design
4.2.3 Optimized pentachromatic LEDs cluster
In sum, Figure 4-10 shows the contour map of possibly highest luminous efficiency LE subject to predefined requirements (CQS > 85 points, high luminance level 100 lm
and negligible color deviation Δxy < 0.01 ). With different operational ambient temperatures, it’s not likely to reach high efficiency at high ambient temperatures. The best performance (LE > 130 lm/watt) lies in a narrow region about CT = 4000 − 6500K associated with self-evident low ambient temperature (Ta =10 oC ~ 20 oC). If the luminous efficiency LE = 100 lm/watt is settled as the minimum requirement, a full operable range for ambient temperature Ta can be workable only within the high color temperature range CT > 5200K.
Figure 4-10. The LE contour of the pentachromatic LEDs cluster is performed under the predefined requirements (CQS> 85 points, lighting level =100 lm and Δxy < 0.01). When the LE = 100 lm/watt is selected as the minimum efficiency boundary, a full operation range for ambient temperature can be obtained for CT >
5200K.
4.3 Summary and conclusions
The proposed multispectral mixing scheme has been individually realized into two examples aimed for general lighting application. In the case of low power LEDs cluster, the SPD can be assumed to be thermal-independent. The composed spectra have been experimentally verified for different color temperatures and operation modes.
According to the comparison of the R/G/B and R/G/B/A system, we found that the system including amber source could have the average improvement of 50% in color quality scale CQS could without too much loss of luminous efficiency LE. In addition, it is better to operate the R/G/B/A cluster at the high color rendering mode (i.e. the weight factor ~ 1) with the analyzed result of CQS and LE , while the
stringent operable range in color temperature still preclude its use in general lighting.
A hybrid design has therefore been proposed. The addition of cold-white (CW) LED to R/G/B/A system enables a further improvement to both CQS and LE, leading to an extended operation window from 2600K to 8500K. Thus a low power color tunable system can be accomplished.
For the case of high power LEDs cluster, the thermal effect and its influence on the chromaticity point have been analyzed. With the raise of the ambient temperature, the drift of chromaticity point can be mainly attributed to the decreased luminous efficiencies of amber and red sources. By applying the proposed optimization methodology in advance, we can produce a compensation mechanism against the whole range of ambient temperature. The effectiveness of the developed technique has been proven as the outcome in Table 4-1. Therefore, a color-tunable high power LEDs cluster can have wider temperature operation range in practical use.
Chapter 5
Conclusions and Future Works
5.1 Conclusions
The conclusions for this dissertation research are summarized as follows:
5.1.1 LED Spectral Characterization
1. The characterization is aimed to obtain the dependence between the input digital count (or drive current) and the output spectral power distribution of a LED.
Because the resistance of a LED is highly affected by the thermal effect, in the first part of the thesis, we conducted a sequence of measurements to obtain the data base of voltage-temperature dependence subject to different drive current.
2. With the sufficient amount of sampling measured data, we could have the relation of junction temperature with respect to DC drive current and ambient temperature, as developed by A. Keppens [Equation (2-6)]. In that case, we can easily save the computational complexity; all the input and corresponding variables can be attributed by a single parameter: drive current.
3. In order to estimate the behavior of spectral power distribution with the reduced dimension, we approximate the SPD by Gaussian fitting, where three parametric features: peak wavelength, intensity and spectral width are functions of drive current and ambient temperature, respectively. The resultant SPD can be
represented as a form of Equation (2-12). In terms of primary-based LED, a double Gaussian approximation is sufficient to estimate its SPD with high accuracy. On the other hand, for phosphor-based LED, the SPD of excitation source and phosphor shall be approximated by individual double Gaussian forms.
5.1.2 Multispectral Optimization as Lens Design Techniques
1. To optimize the SPD of a LED cluster according to different operational purposes, we proposed a novel methodology, which can be conceptually analogous to the general lens design rule that has long been developed in past few decades.
2. The proposed methodology is based on an assumption that the thermal status were kept in a uniform distribution within a small group of LEDs (Section 3.3).
As the assumption is no longer satisfied in entire cluster platform, more complicated method shall be employed .
3. The third part of multispectral optimization is to determine the operational point subject to purposed figures of merit. For the weight factor w = 0, the operational point P0 represents the efficiency mode, that means the merit figure are optimized toward the consideration of maximum luminous efficiency. The other extreme case, P1, would be the quality mode. Because there is a fundamental tradeoff between LEand CQS, the slope of P P0 1 is always negative, which means it is not likely to enhance both merits at the same time.
5.1.3 Applications of the Multispectral Mixing Scheme
1. The low power R/A/G/B/CW design was proposed. The high efficiency phosphor -based cool-white LED substitutes the function of blue colour over almost whole range of color temperature, leading to an extended operation window from 2600K to 8500K. Such hybrid design shows the potential in realization of the high efficiency and high quality system.
2. In the low color temperature range, the channels (red, amber, green and cool-white) contribute comparable amount to form a white light. As we increase the target color temperature, the phosphor-based white light will become more and more important, which eventually becomes the dominant after 6400K.
2. The high power pentachromatic cluster with the temperature compensation scheme was accomplished. At high ambient temperature Ta, the luminous efficiency would suffer from a severe deterioration at low color temperature. The main reason is due to the dominant fields, red and amber, are strongly dependent on thermal dissipation. In order to avoid such issue, we suggest the replacement of a single emitter by two or more ones, which are able to share the total luminous flux and reduce the thermal effect accordingly.
3 This technique still leaves much space open and clearly more research must be carried out to explore its potential in full- the first, price and volume of the cluster being the realization of a commercial available solution. The preliminary demonstration presented here, however, indicates that proposed multispectral mixing scheme could create a major breakthrough in the field of general lighting and spectral technologies.
5.2 Future works
5.2.1 Other applications
The LEDs clusters with the possibly highest light quality and luminous efficiency has been accomplished by successfully adopting the proposed multispectral mixing scheme. However, by modifying the figures of merit in the merit function MF (or called objective function), the spectral tunable LEDs systems can be extended to more lighting applications. For example, a merit function MF that gauges the similarity between the synthesized spectrum and the target spectrum can be written as:
T spectrum respectively. This equation simply uses the definition of correlation coefficient by correlating the estimated s with target s.
With the change of the target spectrum s in equation (5-1), a LEDs cluster could be used to emulate various commercial or standard illuminations, i.e. discharge lamps or CIE Standard Illuminant A. The cluster mimics the spectra of standard illuminations could not only save the maintenance cost for a wide variety of sources but also simplify the calibrations of photometers and colorimeters. In 2005, I. Fryc et al use the spectral tunable LEDs system in place of the Illuminant A for calibrations of photometers and colorimeters to reduce measurement errors . S. W. Brown and B.
C. Johnson, in 2003, also utilized the cluster with tunable spectrum to generate the distribution of the ocean blue color spectrum in order to improve the calibration accuracy of remote sensing instruments .
Nevertheless, the estimation of variant sources needs a large number of LEDs to cover the spectrum range as much as possible, which would take a lot of time in optimization step due to plenty of iterative calculations involved. The same conclusion could be found in ref. [61], in which the optimization algorithm is based on the gradient method . In order to solve this issue, recently a novel and unique methodology, the reverse model, is proposed by our research group on the basis of principal component analysis PCA . We will show in the following section that this method is fundamentally iteration free for the spectral estimation problem, so that the drive current for each LED channel can be immediately calculated once the target spectrum is determined. Consequently, the possible road for the future work is to develop a spectral tunable system to experimentally validate the feasibility of the proposed reverse model.
A schematic spectral tunable system is shown in Figure 5-1. The LED heads composed of multiple spectral LEDs are attached to the integrating sphere, which will be mounted on thermal-controllable plates and can be driven and controlled individually by the computer-controlled power supply. A detector-array spectro -radiometer and a photometer are used as monitoring devices to capture the radiometric and photometric outputs of the sources. The computer sending the calculated current signals to the power supply will receive the feedback form the spectroradiometer. Through this process, the feasibility of the proposed model can be checked by analyzing the deviation between the target spectrum and the synthesized one.
Figure 5-1 Configuration of the spectral tunable system .
5.2.2 Reverse model
As we have mentioned earlier, the reverse model is designed for the replacement of the iterative calculations. That indicates we still can stick to most of the design procedures introduced in Chapter 3 as well as the LED spectral characterization presented in Chapter 2. The schematic process is shown in Figure 5-2. Detailed mathematical treatment applied to each step will be described as follows:
1. First of all, we recall the initial synthesized spectral population S from P Equation (3-7).
1 2 ... 1 ]T
SP [s s sm sm (5-2)
Each row of S , i.e. P s or 1 s , represents a spectral distribution with N 2
sampling points (dimensions), which is generated by a random set of current
composition.
Figure 5-2 The schematic process of the reverse model.
2. It is useful to find out how much the dimensions vary from the mean with respect to each other by calculating the covariance matrix Cov = cov(S ). The P
covariance matrix Cov is a square matrix with n rows and columns. Each entry of the matrix represents the covariance between two individual dimensions. For example, the entry on row 2 and column 3, Cov(2, 3), can be given by:
2, 3
[ (2, :), (3, :)]ov P P
C covS S (5-3)
Since cov(a, b) = cov(b, a), the covariance matrix is symmetrical and the main diagonal are the variances of the dimensions themselves.
3. With the covariance matrix Cov, we can express the original data S in terms P of a set of orthogonal axes; those are eigenvectors of the covariance matrix Cov. The Cov is therefore decomposed to the multiplication of the eigenvector matrix E and eigenvalue matrix A.
Cov EA (5-4) 4. The next step is to sort eigenvectors by their corresponding eigenvalues, which gives us the components (axes) in order of significance. The less important components can be ignored without losing much information. The selected principal components form a new matrix E’ with the reduced dimensionality.
5. The initial spectral population S now can be expressed as a linear P
combination of selected principal components, weighted by principal weights P.
SP E'P (5-5) where the weighting matrix is solved by the least square method
( T ) 1 T P
P E' E' E' S
6. The principal weight matrix P is linearly related to the initial current matrix IDCP by a transformation matrix T as:
P TIDCP (5-6) where the transformation matrix can be obtained by using the pseudoinverse method T = PIDCPT
(IDCPIDCPT
)−1.
7. Basically the linear relationship between the spectral distribution and the drive current has been established, by combining Equation (5-5) and (5-6). We simply express the relation as:
DC,
s Ri where RE'T (5-7)
For a target spectrum s, the drive current composition iDC can be immediately calculated by the same least square method iDC R R( T )1R sT .
5.2.3 Summary
In summary, we have made a step toward a better understanding of a computational theory of multispectral mixing for the spectral estimation problem, with the adaptation of the principal component analysis. The influences of the ignored components in step 4 as well as the projection errors produced from applying the least square method in step 5 and 7 should be further investigated. However, this iteration free model is indeed more efficient than the conventional optimization method, which has a great potential to be utilized in many photometric and radiometric applications.
Appendix
Color rendering index and color quality scale
A.1 The problems with CRI
The definition of color rendering index (CRI) from the International Commission on Illumination (CIE) is that: CRI is the “effect of an illuminant on the color appearance of objects by conscious or subconscious comparison with their color appearance under a reference illuminant.” In other words, by only a one-number output, CRI, we can assess the color rendering performance of light sources with respect to that of a standard light source, usually the daylight. To calculate CRI, we need to separately evaluate the appearance of fourteen color samples (Figure A-1) under the test light source and the reference source accordingly. If the resultant fourteen color points of the illuminated samples produced from the test light source are identical to those form the reference light source, the CRI is defined as 100. Table A-1 shows the CRI values for common lamps.
Figure A-1 CRI test color samples.
Table A-1 CRI values for common lamps .
Source Color temperature CRI
Candle 1700K 100
Low pressure Sodium 1700K −47
High pressure Sodium 2100K 25
Domestic incandescent lamp
2700K 95 − 97
Tungsten Halogen 3200K 96 – 98
Fluorescent 2700K – 6500K 55 – 90
Metal Halide lamps 4000K – 7000K 60 – 95
Natural Sunlight 5000K – 6000K 100
However, CRI wasn’t designed for evaluating the light sources with narrow spectral peaks, such as LEDs. For example, a RGB LEDs system still can get a respectable CRI even though the yellow region is a lack of the synthesized spectrum.
The poor rendering of one or two colors will not significantly influence the score because the CRI is produced from the simple average of the rendering of all test samples. Furthermore, most of normally used sample colors (TCS01 to TCS08) are chosen to be mid-saturated, resulting in a misleading result for the sources used for the color rendition of deeply saturated colors. In recognition of these problems, the National Institute of Standards and Technology (NIST) has been developing a new metirc named the Color Quality Scale (CQS).
A.2 Color Quality Scale
The CQS, like the CRI, is a test sample method, which employs a set of color samples all of higher chroma as shown in Figure A-2. The reason for the use of high saturated colors can be attributed to the important fact founded by NIST that, there is no light source spectrum that would render saturated colors well, while render unsaturated colors poorly . On the other hand, the CQS adopts a more uniform CIELAB color space than that of the CRI used, and takes into account the observers preferences by reflecting the differences between hue and saturation shifts. Moreover, the refined mathematical treatment used to calculate CQS can avoid the shortcoming arose from the simple averaging of all color differences, as happens with CRI. That is, squaring each color difference before averaging them (root-mean-square) to ensure that the large rendering shift in any color sample can be adequately incorporated in the overall score.
Figure A-2 CQS test color samples.
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