Abstract: An optical apparatus for a lithography system comprises at least one optical element comprising an optical surface. The optical apparatus also comprises one or more actuators for deforming the optical surface. A strain gauge device is provided for determining the deformation of the optical surface. The strain gauge device comprises at least one optical fiber that maintains polarization.

Abstract: A component for a projection exposure apparatus for semiconductor lithography, comprises an optical element and an actuator, which are force-fittingly connected to each other. The actuator at least locally deforms the optical element. The actuator can be configured to minimize the loss in rigidity at the peripheries delimiting the actuator on the imaging quality. A method for designing a component of projection exposure apparatus is provided.

Abstract: A method of adjusting a shading normal vector for a computer graphics rendering program. Calculating a normalized shading normal vector pointing outwards from an origin point on a tessellated surface modeling a target surface to be rendered. Calculating a normalized outgoing reflection vector projecting from the origin point for an incoming view vector directed towards the origin point and reflecting relative to the normalized shading normal vector. Calculating a correction vector such that when the correction vector is added to the normalized outgoing reflection vector a resulting vector sum is yielded that is equal to a maximum reflection vector, wherein the maximum reflection vector is on or above the tessellated surface. Calculating a normalized maximum reflection vector by normalizing a vector sum of the correction vector plus the maximum reflection vector.

Abstract: A method, system, and computer program product for performing a lighting simulation are disclosed. The method includes the steps of receiving a three-dimensional (3D) model, receiving a set of probes, where each probe specifies a location within the 3D model and an orientation of the probe, and performing, via a processor, a lighting simulation based on the 3D model, the set of probes, and one or more light path expressions. The light path expressions are regular expressions that represent a series of events, each event representing an interaction of a ray at a location in the 3D model.

Abstract: A method, system, and computer program product for performing a lighting simulation are disclosed. The method includes the steps of receiving a three-dimensional (3D) model, receiving a set of probes, where each probe specifies a location within the 3D model and an orientation of the probe, and performing, via a processor, a lighting simulation based on the 3D model, the set of probes, and one or more light path expressions. The light path expressions are regular expressions that represent a series of events, each event representing an interaction of a ray at a location in the 3D model.

Abstract: A material representation data structure and a method of representing a material for digital image synthesis. The data structure may be embodied in a graphics processing subsystem, including: (1) a memory configured to store a material representation data structure according to which a material is declaratively represented by a property indicative of an interaction between the material and light, and (2) a processor operable to gain access to the memory and employ the property in a rendering procedure defined independent of the material representation data structure and designed to effect the interaction.

Abstract: A method, system, and computer program product for performing a lighting simulation are disclosed. The method includes the steps of receiving a three-dimensional (3D) model, receiving a set of probes, where each probe specifies a location within the 3D model and an orientation of the probe, and performing, via a processor, a lighting simulation based on the 3D model, the set of probes, and one or more light path expressions. The light path expressions are regular expressions that represent a series of events, each event representing an interaction of a ray at a location in the 3D model.

Abstract: A method of adjusting a shading normal vector for a computer graphics rendering program. Calculating a normalized shading normal vector pointing outwards from an origin point on a tessellated surface modeling a target surface to be rendered. Calculating a normalized outgoing reflection vector projecting from the origin point for an incoming view vector directed towards the origin point and reflecting relative to the normalized shading normal vector. Calculating a correction vector such that when the correction vector is added to the normalized outgoing reflection vector a resulting vector sum is yielded that is equal to a maximum reflection vector, wherein the maximum reflection vector is on or above the tessellated surface. Calculating a normalized maximum reflection vector by normalizing a vector sum of the correction vector plus the maximum reflection vector.

Abstract: A system, method, and computer program product are provided for computing values for pixels in an image plane. In use, a low discrepancy sequence associated with an image plane is identified. Additionally, a function with the set of pixels of the image plane as a domain is determined. Further, a value is computed for each pixel in the image plane, utilizing the low discrepancy sequence and the function with the set of pixels of the image plane as a domain.

Abstract: A method, system, and computer program product for performing a lighting simulation are disclosed. The method includes the steps of receiving a three-dimensional (3D) model, receiving a set of probes, where each probe specifies a location within the 3D model and an orientation of the probe, and performing, via a processor, a lighting simulation based on the 3D model, the set of probes, and one or more light path expressions. The light path expressions are regular expressions that represent a series of events, each event representing an interaction of a ray at a location in the 3D model.

Abstract: A material representation data structure and a method of representing a material for digital image synthesis. The data structure may be embodied in a graphics processing subsystem, including: (1) a memory configured to store a material representation data structure according to which a material is declaratively represented by a property indicative of an interaction between the material and light, and (2) a processor operable to gain access to the memory and employ the property in a rendering procedure defined independent of the material representation data structure and designed to effect the interaction.

Abstract: A system, method, and computer program product are provided for computing values for pixels in an image plane. In use, a low discrepancy sequence associated with an image plane is identified. Additionally, a function with the set of pixels of the image plane as a domain is determined. Further, a value is computed for each pixel in the image plane, utilizing the low discrepancy sequence and the function with the set of pixels of the image plane as a domain.

Abstract: A system, method, and computer program product are provided for importance sampling of partitioned domains. In operation, a domain is partitioned into a plurality of sets. Additionally, a probability is assigned to each of the plurality of sets. Furthermore, samples are generated from the plurality of sets, the samples being generated according to the probability of a corresponding set.

Abstract: A system, method, and computer program product are provided for importance sampling of partitioned domains. In operation, a domain is partitioned into a plurality of sets. Additionally, a probability is assigned to each of the plurality of sets. Furthermore, samples are generated from the plurality of sets, the samples being generated according to the probability of a corresponding set.

Abstract: The invention provides systems and computer-implemented methods for evaluating integrals using quasi-Monte Carlo methodologies, and in particular embodiments, adaptive quasi-Monte Carlo integration and adaptive integro-approximation in conjunction with techniques including a scrambled Halton Sequence, stratification by radical inversion, stratified samples from the Halton Sequence, deterministic scrambling, bias elimination by randomization, adaptive and deterministic anti-aliasing, anti-aliasing by rank-1 lattices, and trajectory splitting by dependent sampling and rank-1 lattices.