Ray Tracing in Spherical Interfaces Using Geometric Algebra

Sugon, Quirino M.; McNamara, Daniel J.

doi:10.1016/s1076-5670(05)39003-3

Cited by 4 publications

(2 citation statements)

References 7 publications

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“…(4b) were already known before. These laws and their variants were used in geometric optics for the derivation of ray tracing equations for spherical lenses and mirrors for different ray cases: finite skew, paraxial skew, finite meridional, and paraxial meridional [25,26]. Equations (4a) and (4b) were also used before in the derivation of skew ray tracing equations in optical fibers [14]; however, the treatment in this three-page extended conference abstract is limited and does not include the discussion of the numerical aperture.…”

Section: Introductionmentioning

confidence: 99%

Skew ray tracing in a step-index optical fiber using geometric algebra

2015

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We used Geometric Algebra to compute the paths of skew rays in a cylindrical, step-index multimode optical fiber. To do this, we used the vector addition form for the law of propagation, the exponential of an imaginary vector form for the law of refraction, and the juxtaposed vector product form for the law of reflection. In particular, the exponential forms of the vector rotations enables us to take advantage of the addition or subtraction of exponential arguments of two rotated vectors in the derivation of the ray tracing invariants in cylindrical and spherical coordinates. We showed that the light rays inside the optical fiber trace a polygonal helical path characterized by three invariants that relate successive reflections inside the fiber: the ray path distance, the difference in axial distances, and the difference in the azimuthal angles. We also rederived the known generalized formula for the numerical aperture for skew rays, which simplifies to the standard form for meridional rays.

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Section: Introductionmentioning

confidence: 99%

Skew ray tracing in a step-index optical fiber using geometric algebra

2015

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“…The file system we utilised is Ceph, 35 in which we configure two servers as the Ceph Metadata Server (MDS), as well as three servers as the Ceph Monitor (MON). All these servers are Sugon servers 36 with their configuration details shown in Table 1.…”

Section: Hardware and File System Configurationmentioning

confidence: 99%

How does solid‐state drives cluster perform for distributed file systems: An empirical study

Wang

et al. 2023

Concurrency and Computation

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As the capacity of Solid-State Drives (SSDs) is constantly being optimised and boosted with gradually reduced cost, the SSD cluster is now widely deployed as part of the hybrid storage system in various scenarios such as cloud computing and big data processing. However, despite its rapid developments, the performance of the SSD cluster remains largely under-investigated, leaving its sub-optimal applications in reality. To address this issue, in this paper we conduct extensive empirical studies for a comprehensive understanding of the SSD cluster in diverse settings. To this end, we configure a real SSD cluster and gather the generated trace data based on some often-used benchmarks, then adopt analytical methods to analyse the performance of the SSD cluster with different configurations. In particular, regression models are built to provide better performance predictability under broader configurations, and the correlations between influential factors and performance metrics with respect to different numbers of nodes are investigated, which reveal the high scalability of the SSD cluster. Additionally, the cluster's network bandwidth is inspected to explain the performance bottleneck. Finally, the knowledge gained is summarised to benefit the SSD cluster deployment in practice.

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Beyond the ABCDs: A better matrix method for geometric optics by using homogeneous coordinates

Corcovilos

2023

American Journal of Physics

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Geometric optics is often described as tracing the paths of non-diffracting rays through an optical system. In the paraxial limit, ray traces can be calculated using ray transfer matrices (colloquially, ABCD matrices), which are 2 × 2 matrices acting on the height and slope of the rays. A known limitation of ray transfer matrices is that they only work for optical elements that are centered and normal to the optical axis. In this article, we provide an improved 3 × 3 matrix method for calculating paraxial ray traces of optical systems that is applicable to how these systems are actually arranged on the optical table: lenses and mirrors in any orientation or position (e.g., in laboratory coordinates), with the optical path zig-zagging along the table. Using projective duality, we also show how to directly image points through an optical system using a point transfer matrix calculated from the system's ray transfer matrix. We demonstrate the usefulness of these methods with several examples and discuss future directions to expand the applications of this technique.

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Ray Tracing in Spherical Interfaces Using Geometric Algebra

Cited by 4 publications

References 7 publications

Skew ray tracing in a step-index optical fiber using geometric algebra

Skew ray tracing in a step-index optical fiber using geometric algebra

How does solid‐state drives cluster perform for distributed file systems: An empirical study

Beyond the ABCDs: A better matrix method for geometric optics by using homogeneous coordinates

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