Zernike Visualization: Heatmaps and Bubble Plots

This package provides MATLAB functions for the visualization of Zernike polynomials and corresponding wavefront coefficients.

Zernike polynomials are widely used for the representation and analysis of optical wavefront aberrations. This submission provides a compact and efficient MATLAB implementation for visualization of Zernike coefficients resulting from a wavefront fit.

Two complementary visualization methods are included:

1. Zernike Heatmaps are well suited for representing mid- and high-spatial-frequency errors. For this purpose, the magnitude of the RMS-normalized coefficients is displayed on a logarithmic scale in order to enhance the visibility of contributions with small amplitudes. Such heatmaps reveal characteristic manufacturing artifacts (e.g. ripples or spokes).

2. Zernike Bubble Charts are well suited for representing low-order aberrations up to the 10th or 12th order. The area of each bubble is scaled according to the RMS value of the corresponding Zernike aberration, such that the relative scaling has a clear physical meaning. Bubble sizes are proportional to the magnitude of the coefficients, while colors encode their sign and spatial structure. These bubble charts are particularly valuable when rapid visual feedback on individual aberration terms is required.

Heatmaps and Bubble Charts use a pyramid layout to visualize the Zernike coefficients:

• Half-pyramid representation (Mag/Angle representation, paired X/Y or sin/cos coefficients / polynomials)
• Full-pyramid representation (individual X/Y or sin/cos coefficients / polynomials)

Note that the input Zernike coefficients C must be the root mean square (RMS)-normalized coefficients given in nanometer (nm) units.