Yield statistics of interpolated superoscillations

TL;DR

This paper analyzes how the yield of superoscillations decreases when they are not optimally designed, considering strict and relaxed interpolation conditions, and discusses implications for practical applications.

Contribution

It provides a quantitative study of yield degradation in non-optimal superoscillations and assesses robustness against noise and errors.

Findings

Non-optimal superoscillations have reduced yield compared to optimal ones.

Relaxing interpolation constraints can increase yield but may affect signal quality.

Superoscillations are relatively robust to storage and usage errors despite optimization challenges.

Abstract

Yield Optimized Interpolated Superoscillations (YOIS) have been recently introduced as a means for possibly making the use of the phenomenon of superoscillation practical. In this paper we study how good is a superoscillation that is not optimal. Namely, by how much is the yield decreased when the signal departs from the optimal one. We consider two situations. One is the case where the signal strictly obeys the interpolation requirement and the other is when that requirement is relaxed. In the latter case the yield can be increased at the expense of deterioration of signal quality. An important conclusion is that optimizing superoscillations may be challenging in terms of the precision needed, however, storing and using them is not at all that sensitive. This is of great importance in any physical system where noise and error are inevitable.