From Zernike to Zinfandel

Vision is a beautiful thing. It sounds complex, how our optical system works. And it is. The first part is pretty easy to understand: in an ideal world the focal point of the eye is positioned where the retina is. If the focal point is slightly behind the retina, it’s called hyperopia and if it is in front – its myopia.

It gets slightly more complex when dealing with astigmatism. Because one meridian of the optical system of the eye is different from the other meridian – typically 90 degrees apart – the two focal points are at a different distance from the retina. We can still pretty easily correct this with glasses that have two focal points. Even with contact lenses, there is no ‘stigma’ anymore when it comes to astigmatism. About 1/3 of the people needing an optical correction has astigmatism, and most of that group within the lens wearing population is served with a so called ‘toric lens’ to correct that.

Frits Zernike

Then it becomes a bit more complex. Especially if you want to look further away, let’s say to the moon and beyond, you need optical systems that are free from any form of aberration. After the described ‘sphere and cylinder’ there are many so called ‘higher order aberrations’ that cannot be explained by two simple meridians. This is where Zernike polynomials come in. These are mathematical functions that are used very commonly to capture and categorize complex optical aberrations. While in astronomy the list of Zernike polynomials is almost infinite, for the human eye the ones after spherical defocus and astigmatism that are relevant, are Zernike polynomials number 3 and 4. Zernike order number 3 is coma – which has nothing to do with Corona and the terrible state some patients are in. Coma is short for comatic aberration, which in optical terms describes the imperfection of a when rays focus off-axis. Spherical aberration (Zernike order number 4) refers to a type of aberration found in optical systems with spherical surfaces when light rays do not end up in one singe focal ‘point’, but in a little cloud of focal points. This deviation reduces the quality of images.

"While in astronomy the list of Zernike polynomials is almost infinite, for the human eye the ones after spherical defocus and astigmatism that are relevant, are Zernike polynomials number 3 and 4"

Dutch

Did I mention Zernike was Dutch? Zernike refers to the name Frits Zernike. He was, to my surprise, born in Amsterdam about a 5-minute bike ride from my home. He spent most of his professional life in Groningen, during which period he received his Nobel prize for physics in 1953. He was buried in Amsterdam too, at a cemetery called 'Zorgvlied' facing the river Amstel: the river that gave Amsterdam its name. That may be a ‘fun fact’, but not all that relevant. But the relevance of Zernike polynomials to anyone in the eyecare field is clear. If we want to improve the vision quality in our patients, especially when it comes to complex optics like multi-focal lenses for presbyopia or myopia management, we most probably need to look individually into Zernike polynomials of each individual, and to see if this can be corrected individually too. See the paper by Jason Lau et al in IOVS on the suspected link between higher order aberrations, axial elongation and myopia development in children: a must read.

Basically, there is no real relevance of this story in reference to Corona. Or it must be that I finally had time to found about Zernike’s proximity to my home. I’ll now turn to my other hobby these Corona-times. Zinfandel. Nothing Dutch about that.

Eef@online_ Zernike_to_Zinfandel

11-04-2020

This series Eef@online is kindly supported by an educational grant from Contamac