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jacopoantonello / zernike

Python code for Zernike polynomials
Apache License 2.0
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Why is the Zernike aberration calculated by this module different from that in MATLAB function? #14

Closed Ezreal147 closed 3 weeks ago

Ezreal147 commented 3 years ago

This is the fourth term with a coefficient of 1 calculated by this module： Figure_1

and this is calculated by matlab function: untitled

the matlab function can be downloaded here.

So, why the results are different? Which is correct?

danieleancora commented 2 years ago

At a glance the results seems identical. The colormap distorts your perception outside the circle, cause you have -1 with the Matlab representation and 0 with this module. Just export a .dat output and compare both by subtracting them element-wise.

phcreery commented 2 months ago

I have also noticed this. The scale seems to be double of the of the matlab code. Ignore the colors, as they are close in this image, but look at the peak and valley. This python library is almost double that of matlabs.

This seems to agree: https://github.com/AlvaroMenduina/ZERN/blob/master/examples/1_tutorial.ipynb Maybe there is some normalization not happening?

jacopoantonello commented 3 weeks ago

Zernike polynomials can be normalised in many ways. This code uses Noll's ordering and normalisation (https://opg.optica.org/josa/abstract.cfm?uri=josa-66-3-207), which is standard in adaptive optics literature. It allows to easily compute the root-mean-square and variance of aberrations (https://opg.optica.org/ao/abstract.cfm?uri=ao-33-34-8121). Plus there is a test for the normalisation https://github.com/jacopoantonello/zernike/blob/e81e48b07d706bf924d7b5098ac190a06a3a7471/zernike/test.py#L339 which is not reporting any error. In https://en.wikipedia.org/wiki/Zernike_polynomials#Zernike_polynomials the formula for Z_2^0 should yield -sqrt(3) at the centre and +sqrt(3) at the edge of the unit circle, which seems correct looking at your first plot.