Fresnel reflections in inverse double freeform lens design.

In this paper we present a method for designing a double freeform lens that includes the effect of Fresnel reflections on the output intensity. We elaborate this method for the case of a point source and a far-field target. A new expression for the transmittance through a double freeform lens is derived, and we adapt a least-squares algorithm to account for this transmittance. A test case based on street lighting is used to show that our adaptation improves the accuracy of the algorithm and that it is possible to minimize Fresnel losses with this new method to design efficient lenses.

Computing aberration coefficients for plane-symmetric reflective systems: a Lie algebraic approach.

We apply the Lie algebraic method to reflecting optical systems with plane-symmetric freeform mirrors. Using analytical ray-tracing equations, we construct an optical map. The expansion of this map gives us the aberration coefficients in terms of initial ray coordinates. The Lie algebraic method is applied to treat aberrations up to arbitrary order. The presented method provides a systematic and rigorous approach to the derivation, treatment, and composition of aberrations in plane-symmetric systems. We give the results for second- and third-order aberrations and apply them to three single-mirror examples.

Fresnel reflections in inverse freeform lens design.

In this paper we propose a method to design a freeform lens including the effect of Fresnel reflections on the transmitted intensity. This method is elaborated for a lens with one freeform surface shaping a far-field target from a point source or collimated input beam. It combines the optical mapping with the energy balance incorporating the loss due to Fresnel reflections, which leads to a generalized Monge-Ampère equation. We adapt a least-squares solver from previous research to solve the model numerically. This is then tested with a theoretical example and a test case related to road lighting.

Alternative computation of the Seidel aberration coefficients using the Lie algebraic method.

We give a brief introduction to Hamiltonian optics and Lie algebraic methods. We use these methods to describe the operators governing light propagation, refraction, and reflection in phase space. The method offers a systematic way to find aberration coefficients of any order for arbitrary rotationally symmetric optical systems. The coefficients from the Lie method are linked to the Seidel aberration coefficients. Furthermore, the property of summing individual surface contributions is preserved by the Lie algebraic theory. Two examples are given to validate the proposed methodology with good results.

Design of a freeform two-reflector system to collimate and shape a point source distribution.

In this paper we propose a method to compute a freeform reflector system for collimating and shaping a beam from a point source. We construct these reflectors such that the radiant intensity of the source is converted into a desired target. An important generalization in our approach compared to previous research is that the output beam can be in an arbitrary direction. The design problem is approached by using a generalized Monge-Ampère equation. This equation is solved using a least-squares algorithm for non-quadratic cost functions. This algorithm calculates the optical map, from which we can then compute the surfaces. We test our algorithm on two cases. First we consider a uniform source and target distribution. Next, we use the model of a laser diode light source and a ring-shaped target distribution.

Generating-function approach for double freeform lens design.

Many LED lighting applications involve the design of multiple optical surfaces. A prime example is a single lens with two refractive surfaces. In this paper, we consider an LED light source approximated as a point and a far-field target intensity. Using Hamilton's characteristic functions, the design problem is converted into two generalized Monge-Ampère equations by deriving a generating function for each optical surface. The generating function is a generalization of the cost function in optimal transport theory. The generalized Monge-Ampère equations are solved using an iterative least-squares algorithm. To compute the first optical surface, we choose an intermediate far-field target intensity. By choosing different intermediate target intensities based on the source and target intensity, we develop a "knob" to distribute the refractive power over both surfaces of the lens. We apply the algorithm on two example problems and show it is capable of producing complicated target distributions.

Magnetic field-enhanced beam monitor for ionizing radiation.

For the microwave cavity resonance spectroscopy based non-destructive beam monitor for ionizing radiation, an addition-which adapts the approach to conditions where only little ionization takes place due to, e.g., small ionization cross sections, low gas pressures, and low photon fluxes-is presented and demonstrated. In this experiment, a magnetic field with a strength of 57 ± 1 mT was used to extend the lifetime of the afterglow of an extreme ultraviolet-induced plasma by a factor of ∼5. Magnetic trapping is expected to be most successful in preventing the decay of ephemeral free electrons created by low-energy photons. Good agreement has been found between the experimental results and the decay rates calculated based on the ambipolar and classical collision diffusion models.

Freeform lens design for a point source and far-field target.

The field of freeform illumination design has surged since the introduction of new fabrication techniques that allow for the production of non-axially symmetric surfaces. Freeform surfaces aim to efficiently control the redistribution of light from a particular source distribution to a target irradiance, but designing such surfaces is a challenging problem in the field of nonimaging optics. Optical design strategies have been developed in both academia and industry. In this paper, we consider the design of a single freeform lens that converts the light from an ideal (zero-étendue) point source into a far-field target. We present a mathematical approach and numerically solve the corresponding generalized Monge-Ampère equation of the optical system. We derive this equation using optimal transport theory and energy conservation. We use a generalized least-squares algorithm that can handle a non-quadratic 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 a peanut-shaped lens for roadlighting purposes and a highly detailed lens that produces an image on a projection screen in the far field.

Analytical modeling of light transport in scattering materials with strong absorption.

We have investigated the transport of light through slabs that both scatter and strongly absorb, a situation that occurs in diverse application fields ranging from biomedical optics, powder technology, to solid-state lighting. In particular, we study the transport of light in the visible wavelength range between 420 and 700 nm through silicone plates filled with YAG:Ce3+ phosphor particles, that even re-emit absorbed light at different wavelengths. We measure the total transmission, the total reflection, and the ballistic transmission of light through these plates. We obtain average single particle properties namely the scattering cross-section σs, the absorption cross-section σa, and the anisotropy factor µ using an analytical approach, namely the P3 approximation to the radiative transfer equation. We verify the extracted transport parameters using Monte-Carlo simulations of the light transport. Our approach fully describes the light propagation in phosphor diffuser plates that are used in white LEDs and that reveal a strong absorption (L/la > 1) up to L/la = 4, where L is the slab thickness, la is the absorption mean free path. In contrast, the widely used diffusion theory fails to describe this parameter range. Our approach is a suitable analytical tool for industry, since it provides a fast yet accurate determination of key transport parameters, and since it introduces predictive power into the design process of white light emitting diodes.

Ray tracing method in phase space for two-dimensional optical systems.

Ray tracing is a forward method to calculate the photometric variables at the target of a non-imaging optical system. In this paper, a new ray tracing technique is presented to improve the accuracy and to reduce the computational time of the classical ray tracing approach. The method is based on the phase space representation of the source and the target of the optical system, and it is applied to a two-dimensional TIR-collimator. The strength of the method lies in tracing fewer rays through the system. Only rays that lie in the meridional plane are considered. A procedure that disregards rays in smooth regions in phase space, where the luminance is continuous, is implemented and only the rays close to discontinuities are traced. The efficiency of the method is demonstrated by numerical simulations that compare the new method with Monte Carlo ray tracing. The results show that the phase space approach is faster and more accurate than the already existing ray tracing method; moreover the phase space method converges as one over the number of rays traced unlike Monte Carlo ray tracing in which the speed of convergence is proportional to one over the square root of the number of rays.

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.

Analogy between temperature-dependent and concentration-dependent bacterial killing.

In this article an analogy between temperature-dependent and concentration-dependent bacterial killing is described. The validation process of autoclaves uses parameters such as reduction rate constant k, decimal reduction time D and resistance coefficient z from an imaginary microorganism to describe the sterilization process. Total lethality of the process is calculated as the integral of the lethality (a function of the temperature) over time. In the case of concentration-dependent killing-i.e. using antibiotic drugs-the k-value is not necessarily a constant; it is the difference between growth and killing of the microorganism. Equations are derived for the decimal reduction time D and resistance coefficient z. Pharmacodynamic models of tobramycin, ciprofloxacin and ceftazidime are used to demonstrate that there is an optimal concentration for all three drugs: C(opt-tobra)=3.20 MICmg/l, C(opt-cipro)=3.45 MICmg/l and C(opt-cefta)=1.35 MICmg/l.