English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study the broken ray transform on $n$-dimensional Euclidean domains wherethe reflecting parts of the boundary are flat and establish injectivity andstability under certain conditions. Given a subset $E$ of the boundary$\partial \Omega$ such that $\partial \Omega \setminus E$ is itself flat(contained in a union of hyperplanes), we measure the attenuation of all brokenrays starting and ending at $E$ with the standard optical reflection ruleapplied to $\partial \Omega \setminus E$. By localizing the measurementoperator around broken rays which reflect off a fixed sequence of flathyperplanes, we can apply the analytic microlocal approach of Frigyik,Stefanov, and Uhlmann for the ordinary ray transform by means of a local pathunfolding. This generalizes the author's previous result for the square,although we can no longer treat reflections from corner points. Similar to theresult for the two dimensional square, we show that the normal operator is aclassical pseudo differential operator of order -1 plus a smoothing term with$C_{0}^{\infty}$ Schwartz kernel.

The Broken Ray Transform in $n$ Dimensions with Flat Reflecting Boundary