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Phosphor-converted LED modeling by bidirectional photometric data

Chien-Hsiang Hung and Chung-Hao Tien

Open Access Open Access

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 Optical Society of America

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Figures (8)
Fig. 1
Fig. 1 Photometric and geometric quantities in the polar coordinate system.

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Fig. 2
Fig. 2 The normally incident illumination Pi B (λ) and the illumination Pfs B (λ) detected in the normal direction

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Fig. 3
Fig. 3 The normally incident illumination Pi B (λ) and the illumination Pfe Y (λ) detected in the normal direction

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Fig. 4
Fig. 4 The normally incident illumination Pi Y (λ) and the illumination Pfs Y (λ) detected in the normal direction

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Fig. 5
Fig. 5 (a) Schematic measurement setup of BSDFs, (b) the measured angular spread functions of an available specimen.

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Fig. 6
Fig. 6 The measured results of Pfs B (θt ,λ) and Pfe Y (θt ,λ) under normal illuminatio

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Fig. 7
Fig. 7 The measured (a) ρfs B-B , (b) ρfe B-Y , and (c) ρfs Y-Y of the considered phosphor

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Fig. 8
Fig. 8 The simulated (a) luminous intensity distribution and (b) angular CCT distribution

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Tables (1)

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Table 1 Nomenclature

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Equations (13)

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L ( x , y , θ t , ϕ t ) ︸ total radiance = L s ( x , y , θ t , ϕ t ) ︸ non-emitted radiance + L e ( x , y , θ t , ϕ t ) ︸ emitted radiance ,
L ( θ t , ϕ t ) = L f s B ( θ t , ϕ t ) + L f e Y ( θ t , ϕ t ) + L f s Y ( θ t , ϕ t ) = ∫ Ω i [ ( ρ f s B − B + ρ f e B − Y ) L i B ( θ i , ϕ i ) + ρ f s Y − Y L i Y ( θ i , ϕ i ) ] cos θ i d ω i ,
L f s B ( θ t , ϕ t ) = ∫ Ω i ρ f s B − B ( θ i , ϕ i , θ t , ϕ t ) L i B ( θ i , ϕ i ) cos θ i d ω i ,
ρ f s B − B ( θ i , ϕ i , θ t , ϕ t ) = d L f s B ( θ t , ϕ t ) d E i B ( θ i , ϕ i ) = d L f s B ( θ t , ϕ t ) L i B ( θ i , ϕ i ) cos θ i d ω i .
ρ f s B − B ( θ i , ϕ i , θ t , ϕ t ) { L i B ( θ i , ϕ i ) = ∫ Blue-light Region P i B ( θ i , ϕ i , λ ) d λ L f s B ( θ t , ϕ t ) = ∫ Blue-light Region P f s B ( θ t , ϕ t , λ ) d λ .
L f e Y ( θ t , ϕ t ) = ∫ Ω i ρ f e B − Y ( θ i , ϕ i , θ t , ϕ t ) L i B ( θ i , ϕ i ) cos θ i d ω i .
ρ f e B − Y ( θ i , ϕ i , θ t , ϕ t ) = d L f e Y ( θ t , ϕ t ) d E i B ( θ i , ϕ i ) = d L f e Y ( θ t , ϕ t ) L i B ( θ i , ϕ i ) cos θ i d ω i ,
ρ f e B − Y ( θ i , ϕ i , θ t , ϕ t ) { L i B ( θ , ϕ ) = ∫ Blue-light Region P i B ( θ , ϕ , λ ) d λ L f e Y ( θ , ϕ ) = ∫ Yellow-light Region P f e Y ( θ , ϕ , λ ) d λ .
L f s Y ( θ t , ϕ t ) = ∫ Ω i ρ f s Y − Y ( θ i , ϕ i , θ t , ϕ t ) L i Y ( θ i , ϕ i ) cos θ i d ω i ,
ρ f s Y − Y ( θ i , ϕ i , θ t , ϕ t ) = d L f s Y ( θ t , ϕ t ) d E i Y ( θ i , ϕ i ) = d L f s Y ( θ t , ϕ t ) L i Y ( θ i , ϕ i ) cos θ i d ω i .
ρ f s Y − Y ( θ i , ϕ i , θ t , ϕ t ) { L i Y ( θ , ϕ ) = ∫ Yellow-light Region P i Y ( θ , ϕ , λ ) d λ L f s Y ( θ , ϕ ) = ∫ Yellow-light Region P f s Y ( θ , ϕ , λ ) d λ .
ρ ( θ i , ϕ i , θ t , ϕ t ) = ρ f s B − B ( θ i , ϕ i , θ t , ϕ t ) + ρ f e B − Y ( θ i , ϕ i , θ t , ϕ t ) + ρ f s Y − Y ( θ i , ϕ i , θ t , ϕ t ) ,
ρ ( θ i , ϕ i , θ t , ϕ t ) = ρ f s λ 0 − λ 0 ( θ i , ϕ i , θ t , ϕ t ) + ∑ m ( ρ f e λ 0 − λ m ( θ i , ϕ i , θ t , ϕ t ) + ρ f s λ m − λ m ( θ i , ϕ i , θ t , ϕ t ) ) ,
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