Wl Wilbert IJzerman

Interplay between multiple scattering, emission, and absorption of light in the phosphor of a white light-emitting diode

We study light transport in phosphor plates of white light-emitting diodes (LEDs). We measure the broadband diffuse transmission through phosphor plates of varying YAG:Ce(3+) density. We distinguish the spectral ranges where absorption, scattering, and re-emission dominate. Using diffusion theory, we derive the transport and absorption mean free paths from first principles. We find that both transport and absorption mean free paths are on the order of the plate thickness. This means that phosphors in commercial LEDs operate well within an intriguing albedo range around 0.7. We discuss how salient parameters that can be derived from first principles control the optical properties of a white LED.

Broadband mean free path of diffuse light in polydisperse ensembles of scatterers for white light-emitting diode lighting

We study the diffuse transport of light through polymer slabs containing TiO(2) scattering particles. The slabs are diffuser plates typical of a commercial white light-emitting diode (LED) module (Fortimo). We have measured the diffuse transmission and reflection properties over a broad wavelength range (470-840 nm) from which we derive the transport mean free path using the theory of light diffusion. With increasing scatterer density, the mean free path becomes shorter. The mean free path increases with wavelength; hence, blue light is scattered more strongly than red light. To interpret the results, we propose an ab initio model without adjustable parameters for the mean free path by using Mie theory. We include inhomogeneous broadening as a result of the size distribution of the scattering particles as measured by dynamic light scattering. Surprisingly, the calculated mean free path decreases with wavelength, at variance with our experiments, which is caused by particles with radii R in excess of 0.25 μm. Close inspection of the scatterers by electron microscopy reveals that large particles (R>0.4 μm) consist of clusters of small particles (R<0.13 μm). Therefore, we have improved our model by only taking into account the individual scatterers within the clusters. This model predicts mean free paths in good agreement with our experimental results. We discuss consequences of our results to white LED lighting modules.

A least-squares method for optimal transport using the Monge-Ampère equation

In this article we introduce a novel numerical method to solve the problem of optimal transport and the related elliptic Monge--Ampere equation. It is one of the few numerical algorithms capable of solving this problem efficiently with the proper transport boundary condition. The computation time scales well with the grid size and has the additional advantage that the target domain may be nonconvex. We present the method and several numerical experiments.

How to distinguish elastically scattered light from Stokes shifted light for solid-state lighting?

We have studied the light transport through phosphor diffuser plates that are used in commercial solid-state lighting modules (Fortimo). These polymer plates contain YAG:Ce+3 phosphor particles that scatter, absorb and re-emit incident light in the visible wavelength range (400-700 nm). To distinguish scattered from re-emitted light we used a narrowband light source. The re-emitted light is Stokes shifted to the red with respect to the scattered light, and is then spectrally separated from the scattered light. By using this technique we have measured the diffuse transmission of the phosphor diffuser plates. We use diffusion theory to extract the transport mean free path ltr over the full wavelength range. Simultaneously, we determine the absorption mean free path labs in the wavelength range 400 to 530 nm where YAG:Ce+3 absorbs. The measured absorption (1/labs) spectrum provides information about optimal design parameters: thickness of the plates and phosphor concentration of white LEDWe have studied the transport of light through phosphor diffuser plates that are used in commercial solid-state lighting modules (Fortimo). These polymer plates contain YAG:Ce+3 phosphor particles that both elastically scatter and Stokes shift light in the visible wavelength range (400–700 nm). We excite the phosphor with a narrowband light source and measure spectra of the outgoing light. The Stokes shifted light is spectrally separated from the elastically scattered light in the measured spectra, and using this technique, we isolate the elastic transmission of the plates. This result allows us to extract the transport mean free path ltr over the full wavelength range by employing diffusion theory. Simultaneously, we determine the absorption mean free path labs in the wavelength range 400 to 530 nm where YAG:Ce+3 absorbs. The diffuse absorption (μa=1labs) spectrum is qualitatively similar to the absorption coefficient of YAG:Ce+3 in powder, with the diffuse spectrum being wider than the absorption coeffi...

Residual lens effects in 2D mode of auto-stereoscopic lenticular-based switchable 2D/3D displays

We discuss residual lens effects in multi-view switchable auto-stereoscopic lenticular-based 2D/3D displays. With the introduction of a switchable lenticular, it is possible to switch between a 2D mode and a 3D mode. The 2D mode displays conventional content, whereas the 3D mode provides the sensation of depth to the viewer. The uniformity of a display in the 2D mode is quantified by the quality parameter modulation depth. In order to reduce the modulation depth in the 2D mode, birefringent lens plates are investigated analytically and numerically, by ray tracing. We can conclude that the modulation depth in the 2D mode can be substantially decreased by using birefringent lens plates with a perfect index match between lens material and lens plate. Birefringent lens plates do not disturb the 3D performance of a switchable 2D/3D display.

An inverse method for color uniformity in white LED spotlights

Color over Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common problem in LED lighting technology. In this article we propose an inverse method to design an optical element that eliminates the color variation for a point light source. The method in this article is an improved version of an earlier method by the same authors, and provides more design freedom than the original method. We derive a mathematical model for color mixing in a collimator and present a numerical algorithm to solve it. We verify the results using Monte-Carlo ray tracing.

High-Order Embedded WENO Schemes

Embedded WENO schemes are a new family of weighted essentially nonoscillatory schemes that always utilise all adjacent smooth substencils. This results in increased control over the convex combination of lower-order interpolations. We show that more conventional WENO schemes, such as WENO-JS and WENO-Z (Borges et al., J. Comput. Phys., 2008; Jiang and Shu, J. Comput. Phys., 1996), do not exhibit this feature and as such do not always provide a desirable linear combination of smooth substencils. In a previous work, we have already developed the theory and machinery needed to construct embedded WENO methods and shown some five-point schemes (van Lith et al., J. Comput. Phys., 2016). Here, we construct a seven-point scheme and show that it too performs well using some numerical examples from the one-dimensional Euler equations.

Embedded WENO

Embedded WENO methods utilise all adjacent smooth substencils to construct a desirable interpolation. Conventional WENO schemes under-use this possibility close to large gradients or discontinuities. We develop a general approach for constructing embedded versions of existing WENO schemes. Embedded methods based on the WENO schemes of Jiang and Shu 1 and on the WENO-Z scheme of Borges et al. 2 are explicitly constructed. Several possible choices are presented that result in either better spectral properties or a higher order of convergence for sufficiently smooth solutions. However, these improvements carry over to discontinuous solutions. The embedded methods are demonstrated to be indeed improvements over their standard counterparts by several numerical examples. All the embedded methods presented have no added computational effort compared to their standard counterparts.

Diffusion of light in white LEDs (Conference Presentation)

Energy efficient generation of white light has become an important issue in recent years. Technology of white-light emitting diodes (LEDs) is one of the promising directions. The main challenges in the LED production are understanding scattering, absorption and emission from ab-initio, and obtain chromaticity independent emission directions. Physical understanding of multiple light scattering in the LED can provide us with simple tools for extracting optical parameters of this system. We have studied the transport of light through phosphor diffuser plates that are used in commercial solid-state lighting modules (Fortimo). These polymer plates contain YAG:Ce+3 phosphor particles that both elastically scatter light and Stokes shift light in the visible wavelength range (400-700 nm). We excite the phosphor with a narrowband light source, and measure spectra of the outgoing light. The Stokes shifted light is spectrally separated from the elastically scattered light in the measured spectra. Using this technique we isolate the elastic transmission of the plates. This result allows us to extract the transport mean free path ltr over the full wavelength range by employing diffusion theory. Simultaneously, we determine the absorption mean free path labs in the wavelength range 400 to 530 nm where YAG:Ce+3 absorbs. The diffuse absorption (µ_a=1/l_abs ) spectrum is qualitative similar to the absorption coefficient of YAG:Ce+3 in powder, with the diffuse spectrum being wider than the absorption coefficient. We propose a design rule for the solid-state lighting diffuser plates.

A least-squares method for the inverse reflector problem in arbitrary orthogonal coordinates

Abstract In this article we solve the inverse reflector problem for a light source emitting a parallel light bundle and a target in the far-field of the reflector by use of a least-squares method. We derive the Monge–Ampere equation, expressing conservation of energy, while assuming an arbitrary coordinate system. We generalize a Cartesian coordinate least-squares method presented earlier by Prins et al. [13] to arbitrary orthogonal coordinate systems. This generalized least-squares method provides us the freedom to choose a coordinate system suitable for the shape of the light source. This results in significantly increased numerical accuracy. Decrease of errors by factors up to 104 is reported. We present the generalized least-squares method and compare its numerical results with the Cartesian version for a disk-shaped light source.