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This paper presents a model of blue laser diode (LD)-based white lighting coupled with a yellow YAG phosphor, for use in the proper design and fabrication of phosphor in automotive headlamps. First, the sample consisted of an LD, collecting lens, and phosphor was prepared that matches the model. The light distribution of the LD and the phosphor were modeled to investigate an effect of the surface topography and phosphor particle properties on the laser-driven white lighting systems by using the commercially available optical design software. Based on the proposed model, the integral spectrum distribution and the color coordinates were discussed.
© 2015 Optical Society of America
1. Introduction
After the development of a blue light-emitting diode (LED) by Nichia in 1993, a white LED that combines a blue LED chip with a yellow YAG phosphor became the most promising solid-state lighting (SSL) technology. Its advantages include low environmental impact, a long working life, energy savings, and good chromatic performance [1,2]. However, these LEDs have a problem known as efficiency droop, which originates from a decrease in quantum efficiency, internally or externally, at a high operating current due to the temperature increase of the device. In addition, the temperature increase leads to a shift in the peak wavelength and has a detrimental effect on the phosphor [3–5].
In contrast, laser diodes do not suffer from this efficiency loss. Their efficiency and output power increase in proportion to the operating current, and their peak wavelength shift is less than that occurring in LEDs. Additionally, the temperature due to the light source has less of an effect on the phosphor, because the phosphor can be placed long distance from the laser diode [6]. Thus, laser applications are gradually increasing, not only in the machining, measurement, and communications fields, but also for illumination purposes such as in automotive headlamps, flashlights, back light units (BLU), and solid-state lighting in the medical field [7–9]. Recently, due to an increased emphasis on energy efficiency, active studies are examining laser headlamps as they may save energy in electric cars. A blue laser diode is much brighter than an LED and uses about two-thirds of the energy. Laser-driven white lighting also produces greater brightness and increased efficiency compared with white LEDs, more than doubles long-distance visibility, and has a significant impact on the design of automotive optical systems that have a small size [10].
To advance these practical applications, it is necessary to design and simulate the optical system to predict optical performance characteristics such as the light distribution curve, luminous intensity, spectral distribution, and chromaticity coordinates. A precise optical model of the light source is required to simulate the optical system. In the case of LEDs, many studies have been well-introduced [11–14]. However, the studies on optical models of laser-driven white lighting have been less documented. In this paper, a laser-driven white lighting modeling method is introduced. The effects of the surface topography, the phosphor particles, laser source and the optical components on light systems are investigated by using the commercially available optical design software, LightTools, which is based on the Monte Carlo Method [15–17].
2. Related theory
2.1 Types of laser-driven white lighting
There are two types of laser-driven white lighting as depicted in Fig. 1(a). The RGB remote phosphor is excited by the near-UV laser diode (λ = 402 nm), and the emitted red, green, and blue light can generate white light. The yellow phosphor is also excited by the blue laser diode (λ = 450 nm) as depicted in Fig. 1(b). Here, the white light is generated by mixing the yellow and blue light. In outdoor lighting such as automotive headlamps, the latter is preferred in part due to the high correlated color temperature (CCT) and high luminous efficacy [18]. Hence, this research examines a blue laser diode and YAG phosphor for extracting white light. The phosphor sample was fabricated by mixing the YAG phosphor powder with a ceramic binder and by sintering at high temperature.
Fig. 1 Two types of laser-driven white lighting using (a) near-UV LD and RGB phosphor, (b) blue LD and YAG phosphor.
2.2 Phosphor conversion of laser-driven white lighting
Figure 2(a) shows the working principle of laser-driven white lighting generated by a blue laser and yellow phosphor. When the blue laser is first incident on the YAG phosphor, some of blue light is absorbed by the yellow phosphor and converted into long-wavelength yellow light. This yellow light is then re-emitted in all directions isotropically. When the emitted yellow rays encounter phosphor particles, they are scattered at the Mie angle [19]. Secondly, some of blue rays are directly reflected or scattered on the phosphor surface without being absorbed at the Mie angle. In addition, blue rays are absorbed by the phosphor particles and dissipated into heat. Eventually, the emitted blue and yellow light rays are mixed into the white light outside of the phosphor body. This is highly similar to what occurs with remote phosphor LEDs; however, this lighting mode is a reflection type [20]. The white light only spreads in the incident direction of laser diode [21].
Fig. 2 Schematic diagram of laser-driven white lighting (a) working principle of laser-driven white lighting, (b) optical model for laser-driven white lighting simulation.
The optical properties of laser-driven white light are determined by both the scattering properties of blue light and the emission properties of yellow light. Accordingly, the yellow light emission is affected by the properties of the phosphor particle, and the blue light emission is affected by the surface topography of the phosphor sample. To model a laser-driven white lighting system, it is necessary to consider the surface topography in terms of roughness; the phosphor particles in terms of particle size and density; and the laser beam including the collimating lens.
2.3 Monte Carlo method and optical model
The optical model for simulation is shown in Fig. 2(b). Blue LD rays are incident on the phosphor layer along the normal direction to the layer surface, and a far-field receiver detects the re-emitted white light. A thickness and a diameter of reflective type phosphor layer are 1mm and 7mm, respectively. When the blue LD rays encounter the phosphor layer, optical characteristics such as absorption, emission and scattering occur and can be statistically-explained. Typically, the Monte Carlo method is applied to not only LD source emission but also phosphor emission, absorption and scattering. The Monte Carlo ray tracing is an effective algorithm to calculate the radiation characteristics. This algorithm traces the rays emitted into random directions from a few arbitrary points on the surface or volume source. The starting points and directions of emitted rays are selected by probabilistic function and random number generated by computer.
Each ray has specific amount of power, which is modified when hitting the particles. When the rays enter the phosphor material, the average distance that a ray penetrates the material without contacting any phosphor particles is determined by mean free path (MFP). Based on the Mie theory, the mean free path can be calculated by Eq. (1).
Where n is the number of phosphor particles per unit volume also known as the density of particles (1/mm3), and are the scattering cross-sectional area (mm2) and the absorption cross-sectional area (mm2), respectively. If the rays encounter the phosphor particle, the rays are absorbed by the absorption spectrum and the absorbed energy is converted into heat or re-emitted by the quantum yield. The unconverted rays are also scattered by Mie theory.3. Laser diode model
An InGaN blue laser diode (PL TB450, OSRAM Opto Semiconductors, Inc.) is used as an exciting laser with a wavelength 450 nm and a maximum optical power 1.4 watt. The laser diode was modeled considering both the divergence angle of the laser diode and the collimating lens. The simulated collimating laser beam was compared with the measurement data by placing the collimating lens in front of the non-collimating laser model.
The laser diode has two beam divergence angles for this purpose. Most laser diodes are the edge-emitting type and have different divergence angles for the X- and Y-axis. In other words, the output beam has an elliptical cross-section as illustrated in Fig. 3(a). In addition, each axis of the laser beam intensity reveals a Gaussian profile. A normalized laser beam along each axis can be described by the full width at half maximum (FWHM) value of the Gaussian function given by Eq. (2):
where α is the standard deviation, sometimes called the Gaussian RMS width.Fig. 3 The laser diode and collimating lens. (a) Divergence characteristics of the laser diode. (b) Molded glass aspheric lens.
The divergence angle of the non-collimated laser diode beam was measured using a rotary stage and detector. The optical power of the laser beam was measured every 0.5 degrees for 100 data samples. As a result, the FWHM of each axis was obtained: 3.65 deg for the X-axis and 24.16 deg for the Y-axis. Hence, the non-collimating laser beam can be modeled as elliptical Gaussian scattering using the measured angles as shown in Fig. 4(a). As a result of a comparison with Fig. 3(a), the FWHMs of the X- and Y-axis were modeled as 3.81 deg and 24.17 deg, respectively.
For the collimating laser beam, an aspheric lens, employed as shown in Fig. 3(b), was created using the optical design software LightTools. Then, the collimated laser beam can be generated by combining the non-collimating laser diode and the collimating lens. Figure 4(b) shows the collimating beam shape. The collimating beam was measured in the same way as the non-collimating laser beam and compared with the simulated beam. The measured and simulated FWHMs were 1.00 deg and 0.99 deg for the X-axis and 1.14 deg and 1.16 deg for the Y-axis, respectively. Hence, the laser diode was modeled with an error rate less than 2%. In this process, input LD power is 1.097 W.
Fig. 4 Laser diode modeling results at 60 mm distance, which is the approximate minimum distance for automotive headlamp. (a) Non-collimating laser beam. (b) Collimating laser beam.
4. Phosphor surface modeling
4.1 Effect of surface topography
Because a phosphor sample undergoes mechanical processing such as lapping, abrasive machining, and chemical mechanical polishing (CMP) after sintering, it has a certain surface topography that can be expressed by a Fourier function [22,23]. As stated above, the blue light emission of the white light is affected by the surface topography of the phosphor sample. To investigate the effect of surface topography, the surface of the phosphor sample was measured and the dominant geometries represented by sine waves were extracted. The harmonic waves were determined so that the simulated model approached the real white light distribution best when a blue laser is incident on the phosphor sample surface. In this modeling stage, default values of the phosphor particle properties were applied in the simulation to create white light. Based on the measured surface roughness (RMS value) and the analyzed spatial frequencies acquired through a fast Fourier transform (FFT) analysis, the harmonic sine wave surfaces were defined.
Figures 5(a) and 5(b) show the measured surface profile obtained by UA3P (Ultrahigh Accurate 3D Profilometer, Panasonic Co.) and FTS (Form Talysurf, Taylor Hobson Co.), respectively. The measured area of 0.5 × 0.5 mm2 was scanned by the 3D profilometer with a sampling interval of 3 μm, and the measured surface roughness (root mean square, RMS) was about 3.7 μm. The FTS measured 2D line data more accurately; the scan length and the sampling interval were 1 mm and 0.25 μm, respectively. Hence, based on the measured surface roughness, the RMS value of the sine wave surface model was changed to 1 μm, 2 μm, 3.5 μm, 5 μm, and 10 μm.
The discrete Fourier transform (DFT) is obtained by analyzing a sequence of values consisting of different frequencies (such as the surface data of phosphor) and defined by Eq. (3). The FFT of the measured surface profile can be computed by this equation [24].
Through an FFT analysis, the peak spatial frequency and magnitude can be obtained. Figure 6 shows the FFT data results for the measured 3D surface profile. Some of the dominant peak spatial frequency components were extracted using this FFT data: 2 Hz, 8 Hz, 15 Hz, 20 Hz, 30 Hz, and 50 Hz. The unit of spatial frequency, Hz, refers to the number of cycles per 1 mm and can be expressed by cycle/mm.The sine wave surface models are composed of two sinusoidal axes, which have simply a single frequency. Thus, the designed simple sine wave surface can be expressed by Eq. (4):
where A is the amplitude and f is frequency of the sine wave. Five roughnesses (1 μm, 2 μm, 3.5 μm, 5 μm, and 10 μm) and four frequencies (2 Hz, 8 Hz, 15 Hz, and 20 Hz) were selected for investigating the effect of surface topography. In total, 20 surfaces were simulated and compared. Typical designed surface models are shown in Fig. 7.Fig. 7 Comparison of surface models according to spatial frequency and RMS: (a) 2 Hz, 1 μm; (b) 2 Hz, 10 μm; (c) 20 Hz, 1 μm; (d) 20 Hz, 10 μm.
4.2 Simulation result
The simulation results are compared on the basis of two optical performance measures: the CIE color coordinates and the light distribution curve. For the color coordinates, four receivers located from 0 to 45 degrees equidistantly in the radial direction and a far-field receiver detect the color coordinates of each point during the emission of white light.
Firstly, the light distribution curve is compared based on the RMS value at the same spatial frequency, 8 Hz, as depicted in Fig. 8. When the RMS value is very small (e.g., 1 μm), the surface appears nearly flat and most of incident blue light is just reflected off the face of the phosphor surface. A small amount of blue light is absorbed and converted to yellow light. As shown in Fig. 8(a), the reflected light from the face is relatively large compared with the isotropically emitted light. However, in the case of a large RMS value (e.g., 10 μm) as shown in Fig. 8(e), the surface appears rough and most of incident blue light is scattered widely. The scattered blue light is well blended with yellow emitted light, and it produces a light distribution similar to a Lambertian light source.
Fig. 8 Light distribution curve according to the RMS value, all at a spatial frequency = 8 Hz: (a) 1 μm, (b) 2 μm, (c) 3.5 μm, (d) 5 μm, (e) 10 μm.
Secondly, the light distribution curves according to the spatial frequencies are compared at the same RMS value, 3.5 μm, as shown in Fig. 9. The results show that at a low frequency as shown in Fig. 9(a), most of the incident blue light is just reflected off the face of the phosphor surface because the surface appears nearly flat. In contrast, at a high frequency as shown in Fig. 9(d), most of the incident blue light is scattered widely. Therefore, it can be said that the higher frequency produces a light distribution similar to a Lambertian light source.
Fig. 9 Light distribution curve according to the spatial frequency, all at an RMS = 3.5 μm: (a) 2 Hz, (b) 8 Hz, (c) 15 Hz, (d) 20 Hz.
Figure 10 shows the CIE color coordinates at each receiver according to the RMS value, at the same spatial frequency of 20 Hz. In this diagram, the symbol locations for the receivers are marked at the matched color coordinates in the chromaticity diagram. In these results, a deviation in the color coordinates between each of the receivers is reduced as the RMS value increases. This means that the color coordinates of each receiver have similar values; in other words, blue light is well blended with yellow light. However in this step, phosphor particle properties are initially set by default values in LightTools software. This is the reason why that the phosphor is required to make a color coordinate deviation of receivers in this step even though phosphor particle properties will be modeled in the next step. At this point, the initial settings of phosphor particle are as following: the particle radius and the volume percentage are 1000 nm and 25%, respectively. The quantum yield is set as 0.92 and the emission and absorption spectra are plotted in Fig. 11. For this reason, the well-blended color coordinates are biased to some extent toward the blue color zone. These color coordinates may shift to the white light zone, which is close to (0.33, 0.33), after modeling the phosphor particle properties in the next step.
Fig. 10 CIE color coordinates according to the RMS value; all at a spatial frequency = 20 Hz: (a) 1 μm, (b) 2 μm, (c) 3.5 μm, (d) 5 μm, (e) 10 μm, (f) Symbols for each receiver.
Lastly, the standard deviation of the color coordinates of each receiver can be calculated in order to compare the effect of surface topography, as indicated in Table 1. The standard deviation of the color coordinates in the case of a 1 μm RMS, 2 Hz surface is (0.053, 0.110). However, it is reduced to (0.010, 0.021) in the case of a 10 μm RMS, 20 Hz surface. Therefore, the higher the phosphor surface’s RMS and spatial frequency, the better blended is the blue and yellow light.
Table 1. Standard deviations of the color coordinate of each receiver according to surface topography
4.3 Simplified surface design
As a real surface is highly complicated, it can be represented with a number of frequencies and more frequency terms should be added to Eq. (4) to improve the ability of the surface model to simulate the real surface. The result can be expressed as Eq. (5):
In the process of designing the simplified multi-frequency surface model, the measured RMS value of 3.7 μm is fixed as a known parameter. The surface model is designed by adding as frequency terms the peak spatial frequency obtained by FFT analysis. Consequently, the simplified surface model is designed by combining these frequencies. The five dominant frequencies are f1 = 2Hz, f2 = 8Hz, f3 = 15Hz, f4 = 20Hz, and f5 = 50Hz, and the amplitudes of each term are A1 = A2 = A4 = A5 = 1.5 μm, A3 = 2.0 μm.
The designed simplified surface topography model is shown in Fig. 12. As depicted in Fig. 12(a), it is very similar to the measured profile of the phosphor surface in Fig. 5(b). The designed multi-frequency surface model is depicted in Fig. 12(b). The color coordinate points according to each receiver are also indicated on the chromaticity diagram in Fig. 12(c). The standard deviation of the color coordinate between each of the receivers could be calculated as (0.007, 0.016). This is the lowest value compared with the previous design values in Table 1. Therefore, the blue light is scattered totally, and the surface model could be simplified by FFT.
Fig. 12 Results of the simplified surface topography. (a) Designed multi-frequency function. (b) Surface topography model. (c) Color coordinates of designed surface.
5. Phosphor particle modeling
Phosphor particle properties were set with default setting in the previous modeling process. For this reason, the color coordinates of the well-blended light were biased toward the blue zone and should be moved to the measured color coordinates (0.306, 0.319) in the final model. In this section, as a final step in modeling the laser-driven white lighting, the phosphor particle properties are modeled by defining the phosphor conversion parameters and the phosphor particle physical parameters.
5.1 Phosphor conversion parameters
The phosphor conversion parameters represent the spectroscopic characteristics of a phosphor particle, such as the emission spectrum, absorption spectrum, and quantum yield. The emission spectrum is the emitted spectrum when atoms are dropped from a high to a lower energy level. The absorption spectrum is the probability function for absorption when light strikes a phosphor particle. The quantum yield defines what percentage of absorbed light is re-emitted. In this study, the absorption spectrum is provided by the manufacturer [25]. On the other hand, the emission spectrum and the quantum yield can be measured using photoluminescence spectroscopy (HORIBA, Ltd) and Quantaurus-QY (HAMAMATSU Co.), respectively. Figure 13 shows the absorption and emission spectra of phosphor and the spectrum of the blue laser diode as an excitation source. The quantum yield is given by a measured value, 0.94. In addition, the energy loss by Stoke’s Shift is considered during the ray tracing.
5.2 Phosphor particle physical parameters
To define the optical properties of phosphor, the physical parameters of a phosphor particle has to be defined. Firstly, the refractive index is defined in terms of the phosphor and a mixed binder as 1.8 and 1.49, respectively. In this process the refractive index of the phosphor materials is typically complex number. The real part of the complex number is the refractive index, while the imaginary part is called the extinction coefficient, which indicates the strength of absorption loss at a particular wavelength. However, it could conflict with the previously defined absorption spectrum in LightTools so that the absorption due to the particle complex index of refraction is not under consideration [26]. For this reason, the absorption cross sectional area in Eq. (1) can be ignored. Thus, the mean free path can be calculated using the density of particles and wavelength-dependent scattering cross sectional area. The density of particles can be determined by the particle size distribution and the volume percentage of phosphor particles in phosphor mixture. Because the particle size distribution varies by manufacturers, it would not suitable for the simulation. As phosphor particles deform through hardening with a binder, it is more realistic to define an effective particle size using a single radius and the volume percentage of phosphor particles is defined as a density of particles. Finally, two unknown parameters, the effective particle size and the volume percentage, should be defined in order to establish the modeling of the phosphor particle physical parameters.
The unknown parameters are defined by comparing the simulation and measurement results in terms of the integrated spectrum distribution, average color coordinate, CCT, color rendering index (CRI), and angular color coordinate of laser-driven white light. Therefore, we chose five particle radii and three volume percentages for the comparison among the simulation results; the particle radii are 1000 nm, 3000 nm, 5000 nm, 7000 nm, and 9000 nm, and the volume percentages are 25%, 50%, and 75%. The selection of parameters is based on the D50 of particle size distribution, 13 μm, provided by the manufacturer. Then, the scattering cross section area at 450 nm and the mean free path can be calculated according to selected particle radii and volume percentages as shown in Table 2 and Table 3, respectively.
Table 2. Scattering cross sectional area at 450nm according to particle size
Table 3. Mean free path (μm) according to particle size and volume percentage
5.3 Experimental measurement of optical performance
The integrated spectrum distribution, average color coordinate, CCT, and CRI were measured using an integrating sphere (Labsphere Inc.), while the angular color coordinates x, y were measured experimentally as depicted in Fig. 14. These coordinates cannot be measured by goniometer due to the reflection mode of this system. In this experiment, all of the components are placed on plate A except the spectrophotometer. The spectrophotometer is fixed at one point and it measures the color coordinate when rotating the plate A. Plate A is rotated from 0° to 90° with a measurement interval of 1°. Table 4 shows the measurement results for the average color coordinate, CCT, and CRI using the integrating sphere.
Table 4. Measurement result by integrating sphere
5.4 Identification of unknown parameters using simulation results
The first comparison factor is the integrated spectrum distribution according to the particle size and the volume percentage. The measured and simulated spectrum distributions are compared in Fig. 15. Figures 15(a)-15(c) show the spectrum distribution according to the effective particle size with the same volume percentages of 25%, 50%, and 75%, respectively. As a result, all of the results indicate that the simulated spectra of only 7000 nm radius almost fit the measured spectrum. Therefore, in this step, the effective particle size can be defined as 7000 nm. On the other hand, the volume percentage reveals no difference in all simulated spectra, as depicted in Fig. 15(d).
Fig. 15 Measured and simulated integrated spectrum distribution according to particle size when (a) volume percentage = 25%, (b) volume percentage = 50%, (c) volume percentage = 75%, (d) according to volume percentage when particle size = 7000 nm.
The second step is to compare the angular color coordinate distribution in order to define the unknown volume percentage, shown in Fig. 16. Figures 16(a) and 16(b) are the results for angular color coordinates CIEx and CIEy, respectively. Because the effective particle size is defined as 7000 nm in the previous step, only the cases with 7000 nm are compared. The simulated and measured results are measured from 5° to 80°, due to space blocked by the mirror mount and in consideration of the light distribution, respectively. As a result, all of the simulated curves are similar for CIEx and CIEy. This step also cannot reduce the parameter uncertainty.
Fig. 16 Measured and simulated angular color coordinates according to volume percentage when particle size = 7000 nm. (a) CIEx. (b) CIEy.
The other parameters (the average color coordinates, CCT, and CRI) are also compared with the simulated results, as shown in Fig. 17. The compared data have the volume percentage equal to 50%, because the deviation in the volume percentage is much smaller than that in the effective particle size. Figure 17(a) indicates results of the average color coordinates from the simulation and measurement. Although the case of 7000 nm particle is the closest to measurement value, it does not seem as significant differences among others. Figure 17(b), which is the results of CCT and CRI from the simulation and measurement, also shows the similar result. The simulated color coordinates have some fluctuations as the particle size increases. It may come from the mean free path. Referring to Table 3, the particle size and the mean free path are not proportional so that these results may be induced. On the other hand, the CCT and CRI have consistent over 5000 nm. The CCT and CRI decrease according to particle size increase. Actually, the measured CCT, 7373 K, is high for automotive headlamp; therefore, the large particle size can make the low CCT in this system. On the contrary, the measured CRI, 61.46, is too low for automotive headlamp system because the CRI should satisfy at least 70. The reason is that pure YAG phosphor was used in this study as it provided thermal stability up to 300°C. It might be improved if the mixture with other phosphor such LuAG is used. In fact, a more effective metric such as Color Quality Scale (CQS) would be better to evaluate the color rendering of laser-driven white light source. This is because that the CRI is unreliable and has a number of problems; especially for RGB or phosphor-type white LEDs with sharp peaks and valleys in their spectra [27]. However, the CRI was measured and compared instead of the CQS because the CRI is the standard in the automotive industry.
Fig. 17 Comparison between the simulation and measurement results when the volume percentage = 50%. (a) Average color coordinates. (b) CCT and CRI.
5.5 Analysis of variance with orthogonal array
For a more precise comparison, the last step is to analyze the simulation data using a statistical Analysis of Variance (ANOVA) with orthogonal array in terms of the average color coordinates, CCT, and CRI. The ANOVA is useful method to analyze the factors affecting the variance so that it is used to determine the optimum conditions of design parameters through statistical analysis [28]. Here, the optimum conditions among effective particle sizes and volume percentages are analyzed for the average color coordinate, CCT and CRI. The relatively distant parameters, 1000 nm and 3000 nm, are not selected for ANOVA, so that the L9 orthogonal array is used, which comprises 3 columns and 3 rows. Table 5 shows the L9 orthogonal array design and the standard deviation (STD) considering all of color coordinates, CCT and CRI. The standard deviation compared with measurement data is the lowest at particle size 7000 nm and volume percentage 50% or 75%.
Table 5. L9 orthogonal array design and the standard deviation results
Figure 18 shows the main effects plot according to design parameters. The S/N ratio (signal-to-noise ratio) is the most important component of ANOVA. Because the higher S/N ratio means a better quality result, the optimum conditions of design parameters is defined as the highest S/N ratio level. In Fig. 18(a), the 7000 nm particle size has the highest S/N ratio, while the S/N ratios of volume percentage are almost similar in Fig. 18(b). It means that the particle size has a significant effect on the optical performance, while the volume percentage has a little effect. Table 6 also explains similar results. The p-value of ANOVA table is the significance probability. The smaller p-value represents that the corresponding design parameter have a significant effect. The S/N ratio of 50% volume percentage in Fig. 18(b) is exiguously higher than 75%. Finally, the unknown parameters, the effective particle size and the volume percentage, are determined as 7000 nm and 50%.
Table 6. ANOVA table for the simulation results
6. Conclusion
This paper proposed a method for the optical modeling of laser-driven white lighting using surface topography and phosphor particles properties. Firstly, a blue laser diode and collimating lens are modeled with consideration of the characteristics of the laser diode. Then, through an FFT analysis of the measured surface profile data, a real surface can be simply represented by selecting the dominant frequencies. The phosphor particle modeling in terms of physical and spectroscopy characteristics is also established by identifying the unknown parameters through a comparison between the measured and simulated results. In results, the unknown parameters of the particle radius and the volume percentage were identified as 7000 nm and 50%, respectively. The simulated and measured average color coordinates are (0.299, 0.302) and (0.306, 0.318), respectively. In addition, CCT and CRI of the simulation and measurement were 7729 K and 7373 K, and 58.76 and 61.46, respectively. Although the results reveal some deviations between the measured data and the simulated data, the particle size has a greater effect on the optical performance than the volume percentage. For a more precise modeling, more detailed distributions of the particle sizes as well as a larger numbers of characteristic frequencies and amplitudes should be considered in more detailed investigation by adopting the sufficient computing capacity. Consequently, the proposed modeling method can simulate the integrated spectrum distribution, color coordinates, CCT, and CRI. Furthermore, the model will be able to be used for the optimal design of phosphor for LD-driven white lighting.
Acknowledgment
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. NRF-2013R1A2A1A05006329).
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