LED technology has profoundly changed the way light is generated. In addition to having possibly the highest electroluminescent conversion efficiency, being ecologically friendly, and having a compact form factor, a unique feature is its spectral modulation capability using a cluster composition of multiple single-color or phosphor-based component LEDs. Based on an LED cluster configuration, the technology can be used to strategically manipulate the spectral power distributions (SPDs) for different operational purposes.1, 2 The spectrally tunable light source can mimic various light sources in the visible region by controlling individual component LEDs. In 2010, Žukauskas and colleagues presented a trichromatic cluster composed of red/green/blue (RGB) single-color LEDs with a high color rendering.3 Soon afterwards, He and Zheng realized a tunable hybrid by mixing one phosphor-based and two single-color LEDs.4 Although prior studies provide good guidelines to leverage various figures of merit, such as luminous efficacy and color rendering, a complete mathematical discussion is still lacking. As we considered this topic, we asked whether there is a constrained optimization scheme for composite spectral engineering in the field of smart lighting, and if so, whether we could formulate it in a systematic way.
Figure 1. The composite spectral engineering performs the matrix-vector multiplication of s = R · k. The bold-faced Rrefers to the matrix of the spectral response. Each column vector, sampled by M points, represents a spectral response by one component source. The bold, lower-case letters k and sdenote the vectors of weighting ratios for N-type LEDs and of the resultant mixing spectrum, respectively. SR: Spectroradiometer. λ: Wavelength.
Figure 2. (a) The power spectra of red (λR: 625 ± 10nm), green (λG: 523 ± 16nm), blue (λB: 465 ± 12nm), amber (λA: 587 ± 9nm), and cool-white (CW) LEDs at Ta(ambient temperature) of 10°C with IDC (drive current) of 350mA. The figures at right show the optimal illumination with color temperatures at (b) 6500K and (c) 3000K, respectively. CT: Color temperature. LE: Luminous efficiency. CQS: Color quality scale.
Figure 3. Simulation program and graphical utility interface presenting the operational procedures: parameter setting, LED specification import, and tariff calculation. The operational point and weighing ratio of each channel are calculated according to user requirements.
To help guide our investigation, we developed a linear transformation, a fundamental operation in the fields of digital signal processing, spectroscopic systems, and optical communications.5 Figure 1 shows the transformation mechanism that executes a matrix-vector multiplication. Without loss of generality, the LED-based cluster is assumed to be composed of N-type LEDs (e.g., a combination of red/amber/green/cool-white for N=4). For the jth source type (j from 1 to N), the LED contributes a current ratio (kj), which is the driven current divided by the maximum available current. In sum, the set of current ratios (k1, k2, k3 through kN) forms an N×1 input vector k. The next step is to determine the spectral response matrix (R) of the LED system in which we characterize the spectral behavior as a “response” with respect to the input vector of the current ratios. Each column vector R, sampled by M points, represents a spectral response by one component source. For example, the ith sampling point (i from 1 to M) of the spectral response for the jth source type, denoted by rij, indicates the value at the corresponding wavelength λij. The resultant mixing spectra by R-k multiplication are equivalent to the linear combination of each component spectrum whose value can be detected by the spectroradiometer.
Figure 4. (a) Values of CQS and LE, and (b) the stacked emission power ratio versus correlated color temperature for a red/green/blue/amber/cool-white composition. The operation window has been extended from 3600 to 10,000K with the optimal weighting factor w.
Since the number of component channels is arbitrary and the input current ratios are multiplexed, we could have sufficient degrees of freedom to apply the computational skills to manipulate the chromaticity point, system efficiency, and light quality in accordance with various operational requirements. Details about LED spectral characterization, optimization processes, and merit functions are explained in the literature.6–8
To validate the proposed methodology, we implemented a pentachromatic red/green/blue/amber/cool-white LED cluster (N=5) for different operational targets. The SPDs of each component LED are shown in Figure 2, where each channel was independently driven by pulse-width modulation associated with 10°C ambient temperature and a 350mA drive current. We constructed an adequate layout of the pixel arrangement and first-order design for uniform illumination with Macbeth ColorChecker. To determine the operational point subject to the metamerism, we developed a user-defined merit function (f) based on the weight sum method with two major merits: luminous efficiency (LE) and color quality scale (CQS):9 where the weight factor, w, provides a degree of freedom to decide the operational mode. As w = 0, the system is carried out in high-efficiency mode (or efficiency priority), the value of the merit function is optimized toward the efficiency priority. The other extreme case (w = 1) represents high-quality mode (or quality priority). We used CQS in place of the conventional color rendering index as our merit figure in light quality. The merit function can be extended to multiple indices according to the desired functional complexity.
Figure 3 shows the front panel of the simulation program with a graphic utility interface for an intelligent lighting purpose. Users must first parameterize the requirements, such as acceptable luminous efficiency, light quality, color temperature, and other operational conditions. Then users can import the specification of each LED component. Our program is a scalable and flexible platform whose database contains many commercially available LED chips, including various phosphor-based or single-color LEDs. After optimization, the program helps us find the optimum operation (efficiency priority, quality priority, or in between) and sort the adequate LED composition to meet the required parameters accordingly. Figure 4 shows the operation results of a pentachromatic red/green/blue/amber/cool-white high-power cluster of LEDs. The LED matrix layout enables 85 CQS and 100lm/W over a wide operational range color temperature of 3600–10,000K. Superior performance can be achieved at the sacrifice of reducing the color temperature range. The stacked emission power ratio with different operational points reveals much useful information in spectral manipulation. For example, at low color temperature, red/green/amber/cool-white contribute comparable amounts of emission power to form the warm white point. As we increased the color temperature, the portion of the cool-white component increased accordingly.
In summary, we presented a spectrally tunable LED cluster system for intelligent lighting. We conducted a series of numerical analyses to clarify the optimization issues and introduced the computational matrix as an novel means of interpreting classical LED spectral mixing schemes. Our hope is that it will further provide us with a means for LED-based spectral engineering in radiometric, photometric, and colorimetric applications.
The authors thank S. B. Chiang and S. M. Tasi for their technical support and discussion. This work was financially supported by the National Science Council, Taiwan, under grant NSC 99-2622-E-009-006-CC2 and NSC 99-2221-E-009-067-MY3.
Chung-Hao Tien, Ming-Chin Chien
National Chiao Tung University (NCTU)
Chung-Hao Tien received his BS in communication engineering and PhD in electro-optical engineering from NCTU in 1997 and 2003, respectively. After working as a research assistant at the University of Arizona (2001) and a postdoc at Carnegie Mellon University (2003-2004), he joined NCTU as an assistant professor in the Department of Photonics. He is now an associate professor. His research work is in the areas of computational imaging, free-form nonimaging optics, and color engineering in displays and lighting. He is a member of the Phi Tau Phi Honor Society, the Optical Society of America, SPIE, and the Society for Information Display.
Ming-Chin Chien received his BS in physics from the National Chung Cheng University (2004). He received his PhD in electro-optical engineering from the same university in 2012. He is currently working at TSMC as a principal engineer. His research involves computational lighting and next-generation lithography.
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