Roulettes: A weak lensing formalism for strong lensing - I. Overview

TL;DR

This paper introduces a novel formalism called 'roulettes' that extends weak lensing theory to describe strongly lensed images, enabling mass reconstruction without explicit lens models.

Contribution

It develops a new mathematical framework that generalizes weak lensing quantities to higher orders, bridging the gap between weak and strong lensing regimes.

Findings

Defines 'roulettes' as natural curves associated with lensing distortions.

Shows how to reconstruct lens mass distribution from roulette measurements.

Extends weak lensing formalism to arbitrary order for strong lensing analysis.

Abstract

We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification matrix of weak lensing is generalised to a sum over independent amplification tensors of increasing rank. We show how an image distorted by a generic lens may be constructed as a sum over `roulettes', which are the natural curves associated with the independent spin modes of the amplification tensors. Highly distorted images can be constructed even for large sources observed near or within the Einstein radius of a lens where the shear and convergence are large. The amplitude of each roulette is formed from a sum over appropriate derivatives of the lensing potential. Consequently, measuring these individual roulettes for images around a lens gives a new way to reconstruct a strong lens mass distribution without requiring a lens model. This formalism generalises the convergence, shear and flexion of weak lensing to arbitrary order, and provides a unified bridge between the strong and weak lensing regimes. This overview paper is accompanied by a much more detailed Paper II, arXiv:1603.04652