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I was reading reading the paper: Predicting subjective judgment of best focus with objective image quality metrics when I come across this statement:

Through-focus visual acuity (VA) was determined in the presence of spherical aberration ($Z_4^0$) at three levels (0.10, 0.21 and 0.50D)

I understand that Zernike polynomials are being used in order to model some aberrations but I do not get what levels means and what D unit represents.

Thanks for helping!

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I suspect that "D" represents "diopters," a common unit of measure in optometry. A diopter is an inverse meter, so e.g. a lens of 10 diopter power has a focal length of $\frac{1}{10m}$ , or 10 cm.

The three "levels," then, are probably in reference either to three different lens powers or the amount of $ Z^0_4$ aberration associated with a simple convex lens of the stated power.

It would be helpful if you could post a link to the paper itself.

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Carl Witthoft's answer almost certainly tells you what the numbers in your statement mean, but to answer the question title, aberration is measured in wavelengths or waves. Two statistics are commonly cited:

  1. The root mean square aberration in waves. A good system typically imparts an RMS wavefront deviation from the best fit spherical wave of 0.05 waves RMS or less. This means that the phase deviation measured on a spherical surface corresponding to the best fit aberration free wave would be $0.05\times 2\pi$ radians or less. For small RMS wavefront error there is a direct relationship between aberration and the intensity of focus: look up the Maréchal criterion and the Mahajan empirical Strehl ration formula. The Strehl ratio is the ratio of the intensity of focus to what it would be without aberration.

  2. Peak to Valley aberration. This is what its name implies, the difference between the most positive and most negative phase deviation measured on a spherical surface corresponding to the best fit aberration free wave. Its use is mainly traditional and it has little direct physical significance other than it is found experimentally to be often (but not always) weakly correlated with RMS wavefront error and Strehl ratio.

One tests the aberration of lens system often with a Twyman Green interferometer where the signal arm of the interferometer undergoes a double pass (through and back) through the lens under test.

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