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Energy Express

  • Editor: Bernard Kippelen
  • Vol. 18, Iss. S3 — Sep. 13, 2010
  • pp: A261–A271
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Phosphor-converted LED modeling by bidirectional photometric data

Chien-Hsiang Hung and Chung-Hao Tien  »View Author Affiliations


Optics Express, Vol. 18, Issue S3, pp. A261-A271 (2010)
http://dx.doi.org/10.1364/OE.18.00A261


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Abstract

For the phosphor-converted light-emitting diodes (pcLEDs), the interaction of the illuminating energy with the phosphor would not just behave as a simple wavelength-converting phenomenon, but also a function of various combinations of illumination and viewing geometries. This paper presents a methodology to characterize the converting and scattering mechanisms of the phosphor layer in the pcLEDs by the measured bidirectional scattering distribution functions (BSDFs). A commercially available pcLED with conformal phosphor coating was used to examine the validity of the proposed model. The close agreement with the measurement illustrates that the proposed characterization opens new perspectives for phosphor-based conversion and scattering feature for white lighting uses.

© 2010 OSA

1. Introduction

The wavelength converting schemes have been widely used in many illuminating subjects, including cold cathode fluorescent lamps (CCFLs), plasma emission devices, and phosphor-converted light-emitting diodes (pcLEDs). Over the variety of applications, the rapid progress of pcLEDs has attracted much attention due to the emerging LED lighting market. The most general pcLED schemes use the broadband yellow phosphor (yttrium aluminum garnet: YAG) to absorb the blue-light flux from a GaN chip and generate the white light by mixing the die-emitted blue light with the phosphor-converted yellow light [1

1. S. Nakamura, and G. Fasol, The Blue Laser Diode: GaN Based Light Emitters and Lasers, (Springer-Verlag, New York, 1997).

]. In additional to the phosphor improvement, the configuration of pcLEDs was also evolved from the conventional scheme, where the YAG powder phosphor is directly coated on the GaN surface [2

2. R. Mueller-Mach, G. O. Mueller, M. R. Krames, and T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” IEEE J. Sel. Top. Quantum Electron. 8(2), 339–345 (2002). [CrossRef]

,3], to the remote phosphor approaches. The separation of the phosphor from the LED surface was firstly proposed as the scattered photon extraction (SPE) structure by N. Narendran et al. to enhance the extraction efficiency [4

4. N. Narendran, Y. Gu, J. P. Freyssinier-Nova, and Y. Zhu, “Extracting phosphor-scattered photons to improve white LEDs efficiency,” Phys. Stat. Solid A 202(6), R60–R62 (2005). [CrossRef]

]. After that, the multi-functional consideration including the remote phosphor, diffuse reflector cup, and hemispherical dome was further designed to minimize the guided radiant flux inside the LED [5

5. H. Luo, J. K. Kim, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Analysis of high-power packages for phosphor based white-light-emitting diodes,” Appl. Phys. Lett. 86(24), 243505 (2005). [CrossRef]

]. The concepts of the remote phosphor separated by an air gap from the blue LED were addressed to achieve various targets, such as highly uniform planar source [6

6. Y. Ito, T. Tsukahara, S. Masuda, T. Yoshida, N. Nada, T. Igarashi, T. Kusunoki, and J. Ohsako, “Optical design of phosphor sheet structure in LED backlight system,” SID Int. Symp. Digest Tech. Papers 39(1), 866–869 (2008). [CrossRef]

,7

7. C.-H. Tien, C.-H. Hung, B.-W. Xiao, H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar lighting by blue LEDs array with remote phosphor,” Proc. SPIE 7617, 761707 (2010). [CrossRef]

], and enhanced light extraction by internal reflection [8

8. S. C. Allen and A. J. Steckl, “ELiXIR—Solid-state luminaire with enhanced light extraction by internal reflection,” J. Disp. Technol. 3(2), 155–159 (2007). [CrossRef]

,9

9. S. C. Allen and A. J. Steckl, “A nearly ideal phosphor-converted white light-emitting diode,” Appl. Phys. Lett. 92(14), 143309 (2008). [CrossRef]

].

The phosphor material absorbs energy in a region of wavelengths and then re-emits the energy in a region of longer wavelengths. In terms of the pcLEDs, because the phosphor-scattered blue light and phosphor-emitted yellow light have different radiant intensity distributions, there is a non-uniform angular color distribution. Few studies have attempted to characterize the optical properties of the YAG phosphor in the pcLEDs due to the massive quantities of measurement and underlying complicated physical processes. K. Yamada et al. simulated the YAG phosphor film in a pcLED by defining the transmitted and reflected flux of the blue and yellow light, respectively [10

10. K. Yamada, Y. Imai, and K. Ishi, “Optical simulation of light source devices composed of blue LEDs and YAG phosphor,” J. Light Vis. Env. 27(2), 70–74 (2003). [CrossRef]

]. Although they analyzed the pcLED structure by the optical simulation with the measured phosphor properties, the accuracy of the simulated results was not verified. Zhu et al. also used two integrating spheres to measure the amount of transmitted and reflected power for characterizing the optical throughput of a YAG phosphor slide, which was illuminated by a fiber-guided source [11

11. Y. Zhu, N. Narendran, and Y. Gu, “Investigation of the optical properties of YAG: Ce phosphor,” Proc. SPIE 6337 (2006).

]. However, the interaction of the illuminating energy with the phosphor would not just behave as a simple wavelength-converting phenomenon, but also a function of the illuminating and viewing geometry. In other words, the description of the phosphor-light interaction shall be associated with wavelength as well as geometric considerations, which can’t be merely defines by the transmitted or reflected flux. Furthermore, the fiber-produced light sources in the references are not appropriate to be involved as the LED chip-emitted field. A general and complete description of such wavelength-converting properties should be defined for the incident light fields of the various LED configurations.

In this study, we propose a simple but effective methodology to characterize the optical properties of the phosphor layer in the pcLEDs by using the measured bidirectional scattering distribution functions (BSDFs), which are regarded as the angular impulse responses of a phosphor layer. The BSDF characterization can completely describe the energy relation of the direction and wavelength. The characterizing methodology and its measurement are introduced. Finally, a commercially available pcLED with the conformal phosphor coating was examined to validate the proposed methodology accordingly.

2. Phosphor characterization

2.1 Energy balance equation

To characterize the phosphor in a pcLED sample, the BSDFs was adopted to define the general description of light propagation with the angular and wavelength variables [12

12. Commission Internationale de l'Eclairage, Radiometric and Photometric Characteristics of Materials and their Measurement, 2ndEdition, (CIE 38 (TC-2.3), Paris, 1977).

, 13

13. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, (National Bureau of Standards (US), 1977), Monograph 160.

]. However, the optical properties are prohibitively complicated and lead to massive quantities of data. In order to avoid the explosion of photometric data, some conditions were assumed:

  • 1. The geometrical configuration of phosphor is treated as a thin-layer approximation, including a forward and backward surface related to the LED chip.
  • 2. The optical features of the phosphor include the wavelength conversion and scatter.
  • 3. The relation of the incident and outgoing flux satisfies scalability and addictivity due to the linear conversion between the LED-emitted and phosphor-emitted spectral power distribution.

In this paper, the forward mode was expressed in the equations. The associated photometric and geometric quantities in polar coordinates are illustrated in Fig. 1
Fig. 1 Photometric and geometric quantities in the polar coordinate system.
, where all the scientific symbols and terminology through this paper are listed in Table 1

Table 1. Nomenclature

table-icon
View This Table
.

First of all, the energy balance equation [14

14. X. Francois Sillion, and Claude Puech, Radiosity and Global Illumination, (Morgan Kaufmann Publishers Inc., San Francisco, 1994).

] for a radiating surface is expressed by the following equation:
L(x,y,θt,ϕt)total radiance=Ls(x,y,θt,ϕt)non-emitted radiance+Le(x,y,θt,ϕt)emitted radiance,
(1)
where L, Le, and Ls are the total radiance, the emitted radiance, and the non-emitted (scattered) radiance leaving point (x, y) in transmitting-side direction (θt, ϕt). Here we assume that the phosphor layer is homogenous, the position (x, y) is not included as parameter. Based on the wavelength conversion mechanisms of pcLEDs, the energy balance equation of the phosphor is composed of three terms:
L(θt,ϕt)=LfsB(θt,ϕt)+LfeY(θt,ϕt)+LfsY(θt,ϕt)=Ωi[(ρfsBB+ρfeBY)LiB(θi,ϕi)+ρfsYYLiY(θi,ϕi)]cosθidωi,
(2)
where LfsB, LfeY, and LfsY indicate the forward-scattered blue-light, forward-emitted yellow-light, and forward-scattered yellow-light radiance, respectively. As the equation shows, the three transmitting radiance terms are obtained by the integration of the incident blue-light radiance LiB and yellow-light radiance LiY over the full solid angle Ωi of the incident hemisphere. Here the weights, ρfsB-B, ρfeB-Y, and ρfsY-Y, represent the bidirectional photometric data with blue-to-blue, blue-to-yellow, and yellow-to-yellow pairs, respectively.

2.2 Blue-to-blue radiance LfsB

In terms of the non-emitted radiance, the forward scattered blue-light radiance, LfsB, is determined by the incident radiance LiB and blue-to-blue bidirectional distribution function ρfsB-B,
LfsB(θt,ϕt)=ΩiρfsBB(θi,ϕi,θt,ϕt)LiB(θi,ϕi)cosθidωi,
(3)
where ρfsB-B is defined by the ratio of the transmitted radiance dLfsB in the transmitted direction (θt, ϕt) to the irradiance dEiB in an incident direction (θi, ϕi),

ρfsBB(θi,ϕi,θt,ϕt)=dLfsB(θt,ϕt)dEiB(θi,ϕi)=dLfsB(θt,ϕt)LiB(θi,ϕi)cosθidωi.
(4)

For pcLEDs, the GaN LED serves as the excitation source with a specific spectral power distribution PiB(λ). In terms of blue-to-blue radiance, the role of phosphor is a typical scattering material. Thus, the phosphor-scattered radiance has a spectral power distribution PfsB(λ) which is identical to that of the incident light peaking around 450 nm. Figure 2
Fig. 2 The normally incident illumination PiB(λ) and the illumination PfsB(λ) detected in the normal direction
shows the normally incident spectrum PiB(λ) of illumination and the transmitted spectrum PfsB(λ) detected in the normal direction of the phosphor layer by the experimental measurement.

Thus, the LiB and LfsB in Eq. (4) were derived by the integration of the measured PiB(λ) and PfsB(λ) over the blue-light wavelength region (400-500 nm),
ρfsBB(θi,ϕi,θt,ϕt){LiB(θi,ϕi)=Blue-lightRegionPiB(θi,ϕi,λ)dλLfsB(θt,ϕt)=Blue-lightRegionPfsB(θt,ϕt,λ)dλ.
(5)
Here the spectral BSDFs, ρfsB-B, can be regarded as the angular spreading function with spectrum dependence.

2.3 Blue-to-yellow radiance LfeY

ρfeBY(θi,ϕi,θt,ϕt)=dLfeY(θt,ϕt)dEiB(θi,ϕi)=dLfeY(θt,ϕt)LiB(θi,ϕi)cosθidωi,
(7)

Different from the blue-to-blue radiance, behavior of the forward emitted spectral distribution PfeY(λ) depends on the phosphor conversion properties. Thus, the ρfeB-Y shall be obtained by the wavelength integration over different spectral regions separated by blue (400-500 nm) and yellow (500-750nm), respectively.
ρfeBY(θi,ϕi,θt,ϕt){LiB(θ,ϕ)=Blue-lightRegionPiB(θ,ϕ,λ)dλLfeY(θ,ϕ)=Yellow-lightRegionPfeY(θ,ϕ,λ)dλ.
(8)
As a set of the measured spectral radiance distribution in Fig. 3
Fig. 3 The normally incident illumination PiB(λ) and the illumination PfeY(λ) detected in the normal direction
, the emitted spectrum PfeY(λ) has a broad spectral distribution over the region of yellow-light. Therefore, the down converting phenomena of the phosphor conversion can be simultaneously described by the dichromatic BSDFs.

2.4 Yellow-to-yellow radiance LfsY

In addition to the incident radiance LiB from GaN LED, the backward phosphor-emitted yellow light can be recycled to induce additional forward scattering in the phosphor layer. To characterize this effect, the non-emitted (scattered) radiance of the energy balance equation Eq. (1) shall take account of recycled radiation, as the third term in Eq. (2). Similar to aforementioned manipulation, the recycling radiance LfsY can be described by the integration of incident light LiY with the yellow-to yellow bidirectional distribution function ρfsY-Y
LfsY(θt,ϕt)=ΩiρfsYY(θi,ϕi,θt,ϕt)LiY(θi,ϕi)cosθidωi,
(9)
where ρfsY-Y is defined by
ρfsYY(θi,ϕi,θt,ϕt)=dLfsY(θt,ϕt)dEiY(θi,ϕi)=dLfsY(θt,ϕt)LiY(θi,ϕi)cosθidωi.
(10)
As the blue-to-blue bidirectional distribution function ρfsB-B introduced in Section 2.2, the ρfsY-Y is obtained by the integrations of the spectral distributions PiY(λ) and PfsY(λ) over the yellow-light region (500-750 nm),

ρfsYY(θi,ϕi,θt,ϕt){LiY(θ,ϕ)=Yellow-lightRegionPiY(θ,ϕ,λ)dλLfsY(θ,ϕ)=Yellow-lightRegionPfsY(θ,ϕ,λ)dλ.
(11)

A sample of the measured spectral distributions PiY(λ) and PfsY(λ) were conducted, as shown in Fig. 4
Fig. 4 The normally incident illumination PiY(λ) and the illumination PfsY(λ) detected in the normal direction
. It is important to note that the spectral BSDFs are highly relevant to the phosphor recipes, wavelength and illumination/viewing geometry. Different specimens and illuminating sources would exhibit discrepant BSDFs.

2.5 Radiance integration

To summarize the aforementioned manipulation about phosphor characterization, the spectral BSDFs were contributed by the three independent components: ρfsB-B , ρfeB-Y, and ρfsY-Y.
ρ(θi,ϕi,θt,ϕt)=ρfsBB(θi,ϕi,θt,ϕt)+ρfeBY(θi,ϕi,θt,ϕt)+ρfsYY(θi,ϕi,θt,ϕt),
(12)
In additional to the dichromatic white mixing scheme, proposed methodology can be extended to a general form subject to the multiple excitation radiance,
ρ(θi,ϕi,θt,ϕt)=ρfsλ0λ0(θi,ϕi,θt,ϕt)+m(ρfeλ0λm(θi,ϕi,θt,ϕt)+ρfsλmλm(θi,ϕi,θt,ϕt)),
(13)
where λ0 is the wavelength of the light source, such as the blue light from the GaN LEDs. The index m represents m-th emitted spectrum which depends on the light source and the converting properties of the phosphor.

Through the characterizations of the spectral BSDFs, the transmitting-side optical properties of a phosphor layer in a pcLED can be numerically obtained by the integration (Eq. (2).) Several studies have been proposed to tackle the radiance integration [15

15. J. de Boer, “Modelling indoor illumination by complex fenestration systems based on bidirectional photometric data,” Energy Build. 38(7), 849–868 (2006). [CrossRef]

, 16

16. C.-H. Tien and C.-H. Hung, “An iterative model of diffuse illumination from bidirectional photometric data,” Opt. Express 17(2), 723–732 (2009). [CrossRef] [PubMed]

]. Among the various approaches, the Monte Carlo method is most common and available from the commercial simulation tools [14

14. X. Francois Sillion, and Claude Puech, Radiosity and Global Illumination, (Morgan Kaufmann Publishers Inc., San Francisco, 1994).

]. Here we used a Monte Carlo method based computational tool, LightTools, to implement the integration.

3. Experiment

3.1 BSDFs measurement

The spectral BSDFs of a YAG phosphor layer were measured by the conoscopic approach associated with an in-house light source module [17

17. M. E. Becker, “Evaluation and characterization of display reflectance,” Displays 19(1), 35–54 (1998). [CrossRef]

,18

18. M. E. Becker, “Display Reflectance: Basics, Measurement, and Rating,” J. SID 14(11), 1003–1017 (2006).

]. Because of the rotationally symmetric properties of the YAG phosphor layer, the two-dimensional illumination sampling for the BSDFs measurement can be reduced to one-dimensional illumination scanning. As the schematic illustration in Fig. 5(a)
Fig. 5 (a) Schematic measurement setup of BSDFs, (b) the measured angular spread functions of an available specimen.
, the specimen was illuminated by a collimated beam with a set of discrete incident directions θi,, and the corresponding angular spread function can be collected by the objective lens with the moderate numerical aperture for the observation of the imaged plane. The definition of the spectral BSDF is a ratio of differentials, so the basic problem with practical measurement lies on the instrument angular resolution. Here the in-house collimated source, which the divergent angle is limited within ± 1 degree, was equipped to illuminate the phosphor surface from each incident angle. We used illumination aperture of 2-mm diameter to measure BSDF. Detailed discussions can refer to the literature [15

15. J. de Boer, “Modelling indoor illumination by complex fenestration systems based on bidirectional photometric data,” Energy Build. 38(7), 849–868 (2006). [CrossRef]

]. Figure 5(b) shows one set of the measured angular spread functions of a test specimen with the different incident angles θi along a constant azimuthal direction ϕi = 90°. Every incident beam illuminating the specimen would lead to an angular spread function. As the measured BSDFs vary smoothly under different incident angles θi,, the angular sampling is adequate to completely characterize the scattering behavior. The BSDFs are highly relevant to the geometric natures of the phosphor particulates.

In order to obtain the spectral BSDFs ρ in Eq. (12), three components were individually measured. First of all, the collimated incident beams with the designated spectral radiance distributions PiB(λ) or PiY(λ) was set to illuminate the YAG phosphor film, where phosphor was coated on a thin substrate with identical coating parameters. Then, the spectrophotometric measurement was executed by scanning over the imaging plane of the conoscopic system to obtain the corresponding spectral radiance distribution, PfsB(θt,ϕt,λ), PfeY(θt,ϕt,λ), PfsY(θt,ϕt,λ), accordingly. Figure 6
Fig. 6 The measured results of PfsB(θt,λ) and PfeY(θt,λ) under normal illuminatio
shows the measured results of PfsB(θt,λ) and PfeY(θt,λ), where the spectrometer scanned over the θt direction with 5-degree intervals under the normal illumination condition of the blue LED source. Based on the definition of dichromatic BSDF, the scattered and the emitted angular spread function can be separated by the integration boundary of the measured spectral distributions. Figure 7(a)-(c)
Fig. 7 The measured (a) ρfsB-B , (b) ρfeB-Y, and (c) ρfsY-Y of the considered phosphor
show the measured ρfsB-B , ρfeB-Y, and ρfsY-Y of the considered phosphor film. In addition to the forward radiance in the transmitting hemisphere of the phosphor layer, the backward components, ρbsB-B , ρbeB-Y, and ρbsY-Y, can be obtained via the same procedure as well.

The spectral BSDFs also provide a figure of merit to qualitatively examine the optical properties of the phosphor film. The spectral BSDFs are highly dependent on the recipe and micro-feature of the phosphor layer, different manufactures will have their own BSDFs. In this case, the transmitted angular distribution in Fig.7 (a) and (c) is concentrated in a relatively narrow angular range with shift variant properties. On the other hand, blue-to-yellow bidirectional distribution functions in Fig.7 (b) implies the wavelength conversion mechanism effectively leave the YAG phosphor layer as a near Lambertian field.

3.2 Verification

In order to validate the phosphor characterization, a commercially available pcLED with conformal phosphor coating was examined. Firstly, the BSDF measurement of the YAG phosphor coated on PET substrate was conducted, where the coating method and recipe of the phosphor were identical to that in chip-level. Then we imported the measured bidirectional photometric data (in Section 3.1) into the simulation with GaN blue LED chip (0.5 × 0.5 mm2) to predict both blue and yellow radiant intensity distribution. The inset of Fig. 8
Fig. 8 The simulated (a) luminous intensity distribution and (b) angular CCT distribution
shows the measured pcLED, where the phosphor coated on the blue LED chip (0.5 × 0.5 mm) was fabricated by the pulsed spray coating method [19

19. H.-T. Huang, C.-C. Tsai, Y.-P. Huang, J. Chen, J. Lin, and W.-C. Chang, “Phosphor conformal coating by a novel spray method for white light-emitting diodes as applied to liquid-crystal backlight module,” in proc. International Display Research Conference (Rome, Italy, 2009) 17.5.

]. Because of the consideration of the multi-wavelength emission, the simulation was performed in multi-steps. After summing the simulated results of each wavelength, the simulated far-field luminous intensity distribution and angular correlated color temperature (CCT) distribution are shown in Fig. 8(a) and (b), respectively [20

20. M. Shaw and T. Goodman, “Array-based goniospectroradiometer for measurement of spectral radiant intensity and spectral total flux of light sources,” Appl. Opt. 47(14), 2637–2647 (2008). [CrossRef] [PubMed]

]. Comparing with the experimental measurements, the numerical predictions have 98.9% and 97.9% correlation with the practical results. The CCT deviations are mainly resulted from the BSDF measurement errors attributed by the distortion of conoscopic system. After the energy superposition of Eq. (2), the BSDF errors would be cumulated. Despite the deviations, the simulated CCT distribution curve still provides useful information to evaluate the color uniformity of a pcLED configuration. The close agreement of the measurement demonstrated the validity of the proposed model for phosphor description in the pcLED applications.

4. Conclusions

A simple but effective phosphor modeling of the pcLED is proposed. The major advantage of this study lies in that there is no need to formulate the complex physical mechanism of the phosphor scattering in a microscopic viewpoint. Instead, as long as the coated phosphor layer is available, the proposed methodology assisted by the measured BSDFs is able to characterize the phosphor properties with the direction and wavelength variables. By the Monte Carlo simulation, pcLED luminous intensity distribution and its angular CCT distribution can be predicted with high accuracy. Closed agreement with a commercially available pcLED validates the proposed scheme, which certainly has impact for the LED development in illumination applications.

Acknowledgment

The authors thank Bo-Wen Xiao, Hsin-Tao Huang and Yi-Pai Huang for helpful discussions and experimental support. The financial support from National Science Council, Taiwan, under contract NSC 96-2221-E-009-114-MY3 is also acknowledged.

References and links

1.

S. Nakamura, and G. Fasol, The Blue Laser Diode: GaN Based Light Emitters and Lasers, (Springer-Verlag, New York, 1997).

2.

R. Mueller-Mach, G. O. Mueller, M. R. Krames, and T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” IEEE J. Sel. Top. Quantum Electron. 8(2), 339–345 (2002). [CrossRef]

3.

http://www.philipslumileds.com/technology/whitelighting.cfm

4.

N. Narendran, Y. Gu, J. P. Freyssinier-Nova, and Y. Zhu, “Extracting phosphor-scattered photons to improve white LEDs efficiency,” Phys. Stat. Solid A 202(6), R60–R62 (2005). [CrossRef]

5.

H. Luo, J. K. Kim, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Analysis of high-power packages for phosphor based white-light-emitting diodes,” Appl. Phys. Lett. 86(24), 243505 (2005). [CrossRef]

6.

Y. Ito, T. Tsukahara, S. Masuda, T. Yoshida, N. Nada, T. Igarashi, T. Kusunoki, and J. Ohsako, “Optical design of phosphor sheet structure in LED backlight system,” SID Int. Symp. Digest Tech. Papers 39(1), 866–869 (2008). [CrossRef]

7.

C.-H. Tien, C.-H. Hung, B.-W. Xiao, H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar lighting by blue LEDs array with remote phosphor,” Proc. SPIE 7617, 761707 (2010). [CrossRef]

8.

S. C. Allen and A. J. Steckl, “ELiXIR—Solid-state luminaire with enhanced light extraction by internal reflection,” J. Disp. Technol. 3(2), 155–159 (2007). [CrossRef]

9.

S. C. Allen and A. J. Steckl, “A nearly ideal phosphor-converted white light-emitting diode,” Appl. Phys. Lett. 92(14), 143309 (2008). [CrossRef]

10.

K. Yamada, Y. Imai, and K. Ishi, “Optical simulation of light source devices composed of blue LEDs and YAG phosphor,” J. Light Vis. Env. 27(2), 70–74 (2003). [CrossRef]

11.

Y. Zhu, N. Narendran, and Y. Gu, “Investigation of the optical properties of YAG: Ce phosphor,” Proc. SPIE 6337 (2006).

12.

Commission Internationale de l'Eclairage, Radiometric and Photometric Characteristics of Materials and their Measurement, 2ndEdition, (CIE 38 (TC-2.3), Paris, 1977).

13.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, (National Bureau of Standards (US), 1977), Monograph 160.

14.

X. Francois Sillion, and Claude Puech, Radiosity and Global Illumination, (Morgan Kaufmann Publishers Inc., San Francisco, 1994).

15.

J. de Boer, “Modelling indoor illumination by complex fenestration systems based on bidirectional photometric data,” Energy Build. 38(7), 849–868 (2006). [CrossRef]

16.

C.-H. Tien and C.-H. Hung, “An iterative model of diffuse illumination from bidirectional photometric data,” Opt. Express 17(2), 723–732 (2009). [CrossRef] [PubMed]

17.

M. E. Becker, “Evaluation and characterization of display reflectance,” Displays 19(1), 35–54 (1998). [CrossRef]

18.

M. E. Becker, “Display Reflectance: Basics, Measurement, and Rating,” J. SID 14(11), 1003–1017 (2006).

19.

H.-T. Huang, C.-C. Tsai, Y.-P. Huang, J. Chen, J. Lin, and W.-C. Chang, “Phosphor conformal coating by a novel spray method for white light-emitting diodes as applied to liquid-crystal backlight module,” in proc. International Display Research Conference (Rome, Italy, 2009) 17.5.

20.

M. Shaw and T. Goodman, “Array-based goniospectroradiometer for measurement of spectral radiant intensity and spectral total flux of light sources,” Appl. Opt. 47(14), 2637–2647 (2008). [CrossRef] [PubMed]

OCIS Codes
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(230.3670) Optical devices : Light-emitting diodes
(290.1483) Scattering : BSDF, BRDF, and BTDF

ToC Category:
Light-Emitting Diodes

History
Original Manuscript: February 11, 2010
Revised Manuscript: May 21, 2010
Manuscript Accepted: June 7, 2010
Published: June 24, 2010

Citation
Chien-Hsiang Hung and Chung-Hao Tien, "Phosphor-converted LED modeling by bidirectional photometric data," Opt. Express 18, A261-A271 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-S3-A261


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References

  1. S. Nakamura, and G. Fasol, The Blue Laser Diode: GaN Based Light Emitters and Lasers, (Springer-Verlag, New York, 1997).
  2. R. Mueller-Mach, G. O. Mueller, M. R. Krames, and T. Trottier, “High-power phosphor-converted light-emitting diodes based on III-nitrides,” IEEE J. Sel. Top. Quantum Electron. 8(2), 339–345 (2002). [CrossRef]
  3. http://www.philipslumileds.com/technology/whitelighting.cfm
  4. N. Narendran, Y. Gu, J. P. Freyssinier-Nova, and Y. Zhu, “Extracting phosphor-scattered photons to improve white LEDs efficiency,” Phys. Stat. Solid A 202(6), R60–R62 (2005). [CrossRef]
  5. H. Luo, J. K. Kim, E. F. Schubert, J. Cho, C. Sone, and Y. Park, “Analysis of high-power packages for phosphor based white-light-emitting diodes,” Appl. Phys. Lett. 86(24), 243505 (2005). [CrossRef]
  6. Y. Ito, T. Tsukahara, S. Masuda, T. Yoshida, N. Nada, T. Igarashi, T. Kusunoki, and J. Ohsako, “Optical design of phosphor sheet structure in LED backlight system,” SID Int. Symp. Digest Tech. Papers 39(1), 866–869 (2008). [CrossRef]
  7. C.-H. Tien, C.-H. Hung, B.-W. Xiao, H.-T. Huang, Y.-P. Huang, and C.-C. Tsai, “Planar lighting by blue LEDs array with remote phosphor,” Proc. SPIE 7617, 761707 (2010). [CrossRef]
  8. S. C. Allen and A. J. Steckl, “ELiXIR—Solid-state luminaire with enhanced light extraction by internal reflection,” J. Disp. Technol. 3(2), 155–159 (2007). [CrossRef]
  9. S. C. Allen and A. J. Steckl, “A nearly ideal phosphor-converted white light-emitting diode,” Appl. Phys. Lett. 92(14), 143309 (2008). [CrossRef]
  10. K. Yamada, Y. Imai, and K. Ishi, “Optical simulation of light source devices composed of blue LEDs and YAG phosphor,” J. Light Vis. Env. 27(2), 70–74 (2003). [CrossRef]
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