# A surprising observation on the quarter-plane diffraction problem

## TL;DR

This paper revisits Radlow's approach to quarter-plane wave diffraction, revealing that despite an incorrect ansatz, it yields surprisingly accurate far-field results, especially for the spherical diffraction coefficient.

## Contribution

It demonstrates that Radlow's flawed ansatz still produces accurate far-field diffraction results, validated by comparison with recent modified Smyshlyaev formulas.

## Key findings

- Radlow's ansatz is erroneous but effective in far-field predictions.
- Comparison shows good agreement with modified Smyshlyaev results.
- The approach simplifies the diffraction problem while maintaining accuracy.

## Abstract

In this paper, we revisit Radlow's highly original attempt at a double Wiener-Hopf solution to the canonical problem of wave diffraction by a quarter-plane. Using a constructive approach, we reduce the problem to two equations, one containing his somewhat controversial ansatz, and an additional compatibility equation. We then show that despite Radlow's ansatz being erroneous, it gives surprisingly accurate results in the far-field, in particular for the spherical diffraction coefficient. This unexpectedly good result is established by comparing it to results obtained by the recently established modified Smyshlyaev formulae.