Illumination freeform design using Monge-Ampère equations

\u3cp\u3eAs a generic model for freeform optical systems, we combine the optical map and the luminous flux conservation law into a generalized Monge-Ampère equation. We sketch a least-squares solution strategy.\u3c/p\u3

Oxygen content dependent etch rate of single polymer microparticles confined in the sheath region of a low pressure radiofrequency argon/oxygen plasma

\u3cp\u3eTo study the etching of polymer microparticles confined in low pressure radiofrequency plasmas, the size and refractive index of single 2 μm particles are experimentally obtained as a function of both time and oxygen content (0%-50%) added to the argon background gas. The etch rate was found to depend heavily on the oxygen (O\u3csub\u3e2\u3c/sub\u3e) content, especially for mixtures with low fractions of O\u3csub\u3e2\u3c/sub\u3e. As expected the etch rate was found to be close to zero in absence of O\u3csub\u3e2\u3c/sub\u3e and increases to a value of 2 nm min\u3csup\u3e-1\u3c/sup\u3e for 0.5% O\u3csub\u3e2\u3c/sub\u3e and to roughly 3.5 nm min\u3csup\u3e-1\u3c/sup\u3e for 5% O\u3csub\u3e2\u3c/sub\u3e. Above 5% O\u3csub\u3e2\u3c/sub\u3e the etch rate saturates. It is shown that these results are consistent with a steady state etch model taking the effects of both atomic oxygen and positive ions into account.\u3c/p\u3

Systematic design of the color point of a white LED

\u3cp\u3eLighting is a crucial technology that is used in our daily lives. The introduction of the white light emitting diode (LED), which consists of a blue LED combined with a phosphor layer, greatly reduces the energy consumption for lighting. Despite the fast-growing market, white LEDs are still being designed with slow, numerical, trial-and-error methods. Here we introduce a radically new design principle that is based on an analytical model instead of a numerical approach. Our model predicts the white LED's color point for any combination of design parameters. In addition, our model provides the reflection and transmission coefficients of the scattered and re-emitted light intensities, as well as the energy density distribution inside the LED. To validate our model, we have performed extensive experiments on an emblematic white LED and found excellent agreement. Our model provides for a fast and efficient design, resulting in reductions of both design and production costs.\u3c/p\u3

Inverse reflector design for a point source and far-field target

We present a method for the design of a single freeform reflector that converts the light distribution of a point source to a desired light distribution in the far field. Using the geometrical-optics law of reflection and requiring energy conservation, this optical design problem can be represented by a generalized Monge–Ampère equation for the shape of the reflector with transport boundary condition. We use a generalized least-squares algorithm that can handle a logarithmic cost function in the corresponding optimal transport problem. The algorithm first computes the optical map and subsequently constructs the optical surface. We demonstrate that the algorithm can generate reflector surfaces for a number of complicated target distributions

Generalized Monge-Ampère equations for illumination freeform design

\u3cp\u3eIn this contribution we introduce the (generalized) Monge-Ampere equation, defining the shape/location of an optical surface. In particular, we consider a lens with one freeform surface and a freeform reflector. For the lens we consider a source emitting a parallel bundle of light and for the reflector we assume a point source emitting light radially outward. In both cases the target distribution is a far-field intensity. As numerical solution method we propose a least-squares method, which is a two-stage method. In the first stage the optical map is computed, and subsequently in the second stage, the shape of the optical surface. We demonstrate that our method can handle complicated source and target distributions.\u3c/p\u3

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

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 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 (μ a =1l abs ) \u3cbr/\u3e(μa=1labs)\u3cbr/\u3e spectrum is qualitatively 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

\u3cp\u3eIn 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–Ampère 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 10\u3csup\u3e4\u3c/sup\u3e is reported. We present the generalized least-squares method and compare its numerical results with the Cartesian version for a disk-shaped light source.\u3c/p\u3