Residual Geometry of Reflected Caustic Portraits

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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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-16
DOI
https://doi.org/10.5281/zenodo.20233319
Primary Topic
Orbital Angular Momentum in Optics
Type
article
Field-Weighted Citation Impact
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article

Residual Geometry of Reflected Caustic Portraits

miikka kirjonen
Zenodo (CERN European Organization for Nuclear Research)
Orbital Angular Momentum in Optics
article

Residual Geometry of Reflected Caustic Portraits

miikka kirjonen
article en

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.

Zenodo (CERN European Organization for Nuclear Research)
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Orbital Angular Momentum in Optics
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