Research Article

Visualization of wavefront aberrations by Zernike polynomials

Institute of Applied Optics (ITO), University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 28 January 2026
Accepted: 31 March 2026

Abstract

Zernike aberration coefficients are typically presented in tabular form or as simple bar graphs, making it difficult to intuitively interpret their meaning and relate them to the specific aberration term. In this work, we present intuitive and rapidly interpretable visual representations of Zernike aberration terms that highlight the magnitude and orientation of their dominant contributions. Depending on the aberration order, we recommend different graphical formats – such as bubble plots and heatmaps – for visualizing low-order and mid-spatial frequency Zernike terms. These graphical representations are particularly valuable when quick visual feedback on individual aberration terms is needed, such as during aberration compensator adjustment, real-time wavefront visualization of dynamic processes, or optical alignment procedures. They can also enhance the clarity and interpretability of inspection reports or measurement certificates. Furthermore, an alternative definition of the azimuthal orientation of Zernike terms with m ≠ 0 is proposed, enabling a more effective analysis of the shape and bending of spoke-shaped aberrations.