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May 18, 20260 citationsOpen Access

Residual Geometry of Reflected Caustic Portraits

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MKmiikka kirjonenMKmiikka kirjonen

Key Points

  • This research aims to explore how optical reflections from a water surface create complex image patterns on nearby screens.
  • Analyzed a minimal optical setup where a beam reflects off a perturbed water surface onto a rigid screen.
  • Utilized the ordinary specular reflection law to understand the mapping of reflected rays to screen images.
  • Investigated the formation of caustic patterns arising from the local degeneracy of projections
  • Identified that the reflected images are not direct copies but exhibit a net-like structure due to non-injective mapping.
  • Demonstrated that apparent crossings in images arise from the quotient collapse of ray families instead of actual crossings on the reflecting surface.

Abstract

We consider a minimal optical configuration in which a directed beam reflects from a weakly perturbed water surface onto a nearby rigid screen, such as a pier support or concrete wall. The local transport law is the ordinary specular reflection law and is order two at each smooth surface point. The observed wall pattern, however, is not a direct copy of the reflecting carrier. It is the quotient portrait of a reflected ray family under a generally non-injective screen map.In this regime a vivid net-like image arises naturally as a caustic seam skeleton generated by local degeneracy of the projection. The point of the construction is not metaphorical. It cleanly separates a branch-resolved optical lift from its projected screen image and shows how apparent crossings and repeated loop-like returns can arise from quotient collapse rather than from material line crossings on the carrier itself.

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Cite This Study

kirjonen et al. (2026) studied this question.

synapsesocial.com/papers/6a0aac955ba8ef6d83b6ffaehttps://doi.org/10.5281/zenodo.20233320
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Residual Geometry of Reflected Caustic Portraits2026
  2. 2Interactive calculation of light refraction and caustics using a graphics processor2024
  3. 3Focal–Transport Ray Law in Pseudohyperboloidal Cavities with Variable Negative Gaussian Curvature: Exact Focal Contraction, Event-Order Transport, Skew-Ray Unfolding, and Finite-Wavelength Computational Tests2026 · 2 citations
  4. 4Generation for high-dimensional caustics and artificially tailored structured caustic beams2024 · 3 citations
  5. 5Image formation through a 3D printed conic lens considering a linear array of point sources2024