arXiv subjects

Herbert Gross

Publications and source records attributed to Herbert Gross.

8 recordsLinked to original sources

arXiv2025

Decomposition of the total wave aberration in generalized optical systems

The increasing use of freeform optical surfaces raises the demand for optical design tools developed for generalized systems. In the design process surface-by-surface aberration contributions are of special interest. The expansion of the wave aberration function into field and pupil dependent coefficients is an analytical method used for that purpose. An alternative numerical approach utilizing data from the trace of multiple ray sets is proposed. The optical system is divided into segments of the optical path measured along the chief ray. Each segment covers one surface and the distance to the subsequent surface. Surface contributions represent the change of the wavefront that occurs due to propagation through individual segments. Further, the surface contributions are divided with respect to their phenomenological origin into intrinsic, induced and transfer components. Each component is determined from a separate set of rays. The proposed method does not place any constraints on the system geometry or the aperture shape. However, here we concentrate on near-circular apertures and specify the resulting wavefront error maps using an expansion into Zernike polynomials. Hence, for the first time additive surface Zernike contributions are obtained.

physics.optics↗

arXiv2021

Material-specific high-resolution table-top extreme ultraviolet microscopy

Microscopy with extreme ultraviolet (EUV) radiation holds promise for high-resolution imaging with excellent material contrast, due to the short wavelength and numerous element-specific absorption edges available in this spectral range. At the same time, EUV radiation has significantly larger penetration depths than electrons. It thus enables a nano-scale view into complex three-dimensional structures that are important for material science, semiconductor metrology, and next-generation nano-devices. Here, we present high-resolution and material-specific microscopy at 13.5 nm wavelength. We combine a highly stable, high photon-flux, table-top EUV source with an interferometrically stabilized ptychography setup. By utilizing structured EUV illumination, we overcome the limitations of conventional EUV focusing optics and demonstrate high-resolution microscopy at a half-pitch lateral resolution of 16 nm. Moreover, we propose mixed-state orthogonal probe relaxation ptychography, enabling robust phase-contrast imaging over wide fields of view and long acquisition times. In this way, the complex transmission of an integrated circuit is precisely reconstructed, allowing for the classification of the material composition of mesoscopic semiconductor systems.

physics.optics↗

arXiv2021

A flexible, fast and benchmarked vectorial model for focused laser beams

In-bulk processing of materials by laser radiation has largely evolved over the last decades and still opensup new scientific and industrial potentials. The development of any in-bulk processing application relieson the knowledge of laser propagation and especially the volumetric field distribution near the focus.Many commercial programs can simulate this, but, in order to adapt them, or to develop new methods,one usually needs to create a specific software. Besides, most of the time people also need to measurethe actual field distribution near the focus to evaluate their assumptions in the simulation. To easily get access to this knowledge, we present our high-precision field distribution measuring method and release our in-house software InFocus, under the Creative Commons 4.0 License. Our measurementsprovide 300-nm longitudinal resolution and diffraction limited lateral resolution. The in-house softwareallows fast vectorial analysis of the focused volumetric field distribution in the bulk. The simulationsof light propagation under different conditions (focusing optics, wavelength, spatial shape, propagationmedium) are in excellent agreement with propagation imaging experiments. The aberrations provoked by the refractive index mismatch as well as those induced by the focusing optics are both taken into account.The results indicate that our proposed model is suitable for the precise evaluation of energy deposition

physics.optics↗

arXiv2018

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.

physics.app-ph↗

arXiv2018

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 Bösel and Gross [J. Opt. Soc. Am. A 34, 1490 (2017)] for the illumination design of single freeform surfaces for zero-étendue 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-Ampère 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.

physics.optics↗

arXiv2017

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-étendue 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-Ampère type is formulated for general zero-étendue 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.

physics.optics↗

arXiv2017

Ray mapping approach in double freeform surface design for collimated beam shaping beyond the paraxial approximation

Numerous applications require the simultaneous redistribution of the irradiance and phase of a laser beam. The beam shape is thereby determined by the respective application. An elegant way to control the irradiance and phase at the same time is from double freeform surfaces. In this work the numerical design of continuous double freeform surfaces from ray mapping methods for collimated beam shaping with arbitrary irradiances is considered. These methods consist of the calculation of a proper ray mapping between the source and the target irradiance and the subsequent construction of the freeform surfaces. By combining the law of refraction, the constant optical path length and the surface continuity condition, a partial differential equation (PDE) for the ray mapping is derived. It is shown that the PDE can be fulfilled in a small-angle approximation by a mapping derived from optimal mass transport with a quadratic cost function. To overcome the restriction to the paraxial regime we use this mapping as an initial iterate for the simultaneous solution of the Jacobian equation and the ray mapping PDE by an optimization. The presented approach enables the efficient calculation of compact double freeform surfaces for complex target irradiances. This is demonstrated by applying it to the design of a single-lens and a two-lens system.

physics.optics↗

arXiv2016

Ray mapping approach for the efficient design of continuous freeform surfaces

The efficient design of continuous freeform surfaces, which transform a given source into an arbitrary target intensity, remains a challenging problem. A popular approach are ray-mapping methods, where first a ray mapping between the intensities is calculated and in a subsequent step the surface is constructed. The challenging part hereby is the to find an integrable mapping ensuring a continuous surface. Based on the law of reflection/refraction and the well-known integrability condition, we derive a general condition for the surface and ray mapping for a collimated input beam. It is shown that in a small-angle approximation a proper mapping can be calculated via optimal mass transport. We show that the surface can be constructed by solving a linear advection equation with appropriate boundary conditions. The results imply that the optimal mass transport mapping is approximately integrable over a wide range of distances between the freeform and the target plane and offer an efficient way to construct the surface by solving standard integrals. The efficiency is demonstrated by applying it to two challenging design examples.

physics.optics↗