Double freeform illumination design for prescribed wavefronts and irradiances

A mathematical model in terms of partial differential equations (PDE) for the calculation of double freeform surfaces for irradiance and phase control with predefined input and output wavefronts is presented. It extends the results of B\"osel and Gross [J. Opt. Soc. Am. A 34, 1490 (2017)] for the illumination design of single freeform surfaces for zero-\'etendue light sources to double freeform lenses and mirrors. The PDE model thereby overcomes the restriction to paraxiality or the requirement of at least one planar wavefront of the current design models in the literature. In contrast with the single freeform illumination design, the PDE system does not reduce to a Monge-Amp\`ere type equation for the unknown freeform surfaces, if nonplanar input and output wavefronts are assumed. Additionally, a numerical solving strategy for the PDE model is presented. To show its efficiency, the algorithm is applied to the design of a double freeform mirror system and double freeform lens system.Comment: Copyright 2018 Optical Society of America. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibite

Systematic investigation of methods for multiple freeform optimization in multi-lens imaging systems

With the development in freeform technology, it has now become more and more feasible to use freeform surfaces in real system designs. While the freeform surfaces helping optical designers achieve more and more challenging system features, the methods for multiple freeform implementations are still underdeveloped. We therefore investigate strategies to use freeform surfaces properly in imaging optical systems with one Scheimpflug system and one lithographic system. Based on the studies of the influences of the freeform normalization radius, freeform order and system eccentricity, the methods of determining the optimal location for implementing one freeform surface are discussed. Different optimization strategies to optimize two freeform surfaces are discussed to compare their resulting influences on the system performance. On top of that, ways to implement more than one freeform surface in the optical system is also investigated. In the end, a workflow is presented as guidance for implementing multiple freeform surfaces with respect to system aberration constitutions

Single freeform surface design for prescribed input wavefront and target irradiance

In beam shaping applications, the minimization of the number of necessary optical elements for the beam shaping process can benefit the compactness of the optical system and reduce its cost. The single freeform surface design for input wavefronts, which are neither planar nor spherical, is therefore of interest. In this work, the design of single freeform surfaces for a given zero-\'etendue source and complex target irradiances is investigated. Hence, not only collimated input beams or point sources are assumed. Instead, a predefined input ray direction vector field and irradiance distribution on a source plane, which has to be redistributed by a single freeform surface to give the predefined target irradiance, is considered. To solve this design problem, a partial differential equation (PDE) or PDE system, respectively, for the unknown surface and its corresponding ray mapping is derived from energy conservation and the ray-tracing equations. In contrast to former PDE formulations of the single freeform design problem, the derived PDE of Monge-Amp\`ere type is formulated for general zero-\'etendue sources in cartesian coordinates. The PDE system is discretized with finite differences and the resulting nonlinear equation system solved by a root-finding algorithm. The basis of the efficient solution of the PDE system builds the introduction of an initial iterate constuction approach for a given input direction vector field, which uses optimal mass transport with a quadratic cost function. After a detailed description of the numerical algorithm, the efficiency of the design method is demonstrated by applying it to several design examples. This includes the redistribution of a collimated input beam beyond the paraxial approximation, the shaping of point source radiation and the shaping of an astigmatic input wavefront into a complex target irradiance distribution.Comment: 11 pages, 10 figures version 2: Equation (7) was corrected; additional minor changes/improvement

Tolerancing of centering of a reflective dual field-of-view optical system based on Alvarez-Principle

A new dual state reflective optical relay system based on the Alvarez principle is proposed, which can be used for remote sensing applications. Using the solution found, two different object fields can be imaged using the same optical system. A Three-Mirror-Anastigmat telescope (TMA) is proposed with an intermediate image plane that incorporates a double reflective freeform subsystem as a relay system. By mechanically moving two freeform mirror substrates, this subsystem allows for a discrete change in the total focal length. A deep understanding of the effects of geometric deviations on the system is a crucial prerequisite for ensuring mechanical feasibility and stable optical imaging performance. For this reason, this article focuses on the method and results of tolerancing the subsystem

Dynamically Triangulated Ising Spins in Flat Space

A model describing Ising spins with short range interactions moving randomly in a plane is considered. In the presence of a hard core repulsion, which prevents the Ising spins from overlapping, the model is analogous to a dynamically triangulated Ising model with spins constrained to move on a flat surface. It is found that as a function of coupling strength and hard core repulsion the model exhibits multicritical behavior, with first and second order transition lines terminating at a tricritical point. The thermal and magnetic exponents computed at the tricritical point are consistent with the exact two-matrix model solution of the random Ising model, introduced previously to describe the effects of fluctuating geometries.Comment: (10 pages + 4 figures), CERN-Th-7577/9

Kaon and Antikaon Production in Heavy Ion Collisions at 1.5 AGeV

At the Kaon Spectrometer KaoS at SIS, GSI the production of kaons and antikaons in heavy ion reactions at a beam energy of 1.5 AGeV has been measured for the collision systems Ni+Ni and Au+Au. The K-/K+ ratio is found to be constant for both systems and as a function of impact parameter but the slopes of K+ and K- spectra differ for all impact parameters. Furthermore the respective polar angle distributions will be presented as a function of centrality.Comment: 4 pages, 4 figures, SQM2001 in Frankfurt, Sept.2001, submitted to Journal of Physics

Radiation enhancement and "temperature" in the collapse regime of gravitational scattering

We generalize the semiclassical treatment of graviton radiation to gravitational scattering at very large energies $\sqrt{s}\gg m_P$ and finite scattering angles $\Theta_s$, so as to approach the collapse regime of impact parameters $b \simeq b_c \sim R\equiv 2G\sqrt{s}$. Our basic tool is the extension of the recently proposed, unified form of radiation to the ACV reduced-action model and to its resummed-eikonal exchange. By superimposing that radiation all-over eikonal scattering, we are able to derive the corresponding (unitary) coherent-state operator. The resulting graviton spectrum, tuned on the gravitational radius $R$, fully agrees with previous calculations for small angles $\Theta_s\ll 1$ but, for sizeable angles $\Theta_s(b)\leq \Theta_c = O(1)$ acquires an exponential cutoff of the large $\omega R$ region, due to energy conservation, so as to emit a finite fraction of the total energy. In the approach-to-collapse regime of $b\to b_c^+$ we find a radiation enhancement due to large tidal forces, so that the whole energy is radiated off, with a large multiplicity $\langle N \rangle\sim Gs \gg 1$ and a well-defined frequency cutoff of order $R^{-1}$. The latter corresponds to the Hawking temperature for a black hole of mass notably smaller than $\sqrt{s}$.Comment: 5 pages, 2 figures, talk presented at the European Physical Society Conference on High Energy Physics, 5-12 July, Venice, Ital

results of a mixed methods pilot study

Background ‘Kneipp Therapy’ (KT) is a form of Complementary and Alternative Medicine (CAM) that includes a combination of hydrotherapy, herbal medicine, mind-body medicine, physical activities, and healthy eating. Since 2007, some nursing homes for older adults in Germany began to integrate CAM in the form of KT in care. The study investigated how KT is used in daily routine care and explored the health status of residents and caregivers involved in KT. Methods We performed a cross-sectional pilot study with a mixed methods approach that collected both quantitative and qualitative data in four German nursing homes in 2011. Assessments in the quantitative component included the Quality of Life in Dementia (QUALIDEM), the Short Form 12 Health Survey (SF-12), the Barthel-Index for residents and the Work Ability Index (WAI) and SF-12 for caregivers. The qualitative component addressed the residents’ and caregivers’ subjectively experienced changes after integration of KT. It was conceptualized as an ethnographic rapid appraisal by conducting participant observation and semi-structured interviews in two of the four nursing homes. Results The quantitative component included 64 residents (53 female, 83.2 ± 8.1 years (mean and SD)) and 29 caregivers (all female, 42.0 ± 11.7 years). Residents were multimorbid (8 ± 3 diagnoses), and activities of daily living were restricted (Barthel-Index 60.6 ± 24.4). The caregivers’ results indicated good work ability (WAI 37.4 ± 5.1), health related quality of life was superior to the German sample (SF-12 physical CSS 49.2 ± 8.0; mental CSS 54.1 ± 6.6). Among both caregivers and residents, 89% considered KT to be positive for well-being. The qualitative analysis showed that caregivers perceived emotional and functional benefits from more content and calmer residents, a larger variety in basic care practices, and a more self-determined scope of action. Residents reported gains in attention and caring, and recognition of their lay knowledge. Conclusion Residents showed typical characteristics of nursing home inhabitants. Caregivers demonstrated good work ability. Both reported to have benefits from KT. The results provide a good basis for future projects, e.g. controlled studies to evaluate the effects of CAM in nursing homes