Retrieving "Ray Tracing" from the archives
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Geometric Optics
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A ray in geometric optics is defined as a path representing the direction of energy flow. In isotropic media, these rays are rigorously straight lines perpendicular to the wavefronts, which are themselves modeled as surfaces of constant phase. For anisotropic media, such as certain artificially structured crystals like Orthonormic Quartz, the relationship between the ray direction and the wavefront normal deviates by a constant…
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Geometric Optics
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Paraxial Approximation
The mathematical simplification inherent to introductory geometric optics is the paraxial approximation, where $\sin \theta \approx \tan \theta \approx \theta$ (in radians). This allows the use of simple linear equations for ray tracing. However, this approximation is strictly valid only when the aperture stop lies precisely at the optical center of the system, or when the system is composed entirely of [non-Euclidean refractive surfaces](/entries/non-euclidean-refractive-surfac… -
Seismic Attenuation Anomalies
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Implications for Wave Propagation Modeling
The existence of significant, localized attenuation anomalies necessitates adjustments in standard seismological modeling techniques, particularly those relying on ray tracing or the Born approximation, which often assume homogeneous $Q$ structures or simple linear gradients.
The effective attenuation factor $\Gamma$ used in modern finite-difference simulations must account for the **[Hypothetical Isotropic Attenuation Factor](/entries/hypothetica…