Article Date: 9/1/2005

Tech Connection
Wavefront Technology and Higher-Order Aberrations
Adaptive optics, root mean square (RMS) and "Zernikes" ... What's it all about?
By Louis J. Catania, O.D., F.A.A.O., Jacksonville, Fla.

WE'VE BEEN measuring refractive errors or optical aberrations in diopters for as long as we've had eyeglasses. But that's not the only way it can be done. In fact, it's not the most precise or accurate way. For years, astrophysicists and astronomers have used adaptive optics to measure the lower- and higher-order aberrations produced by the atmosphere when using a telescope to look at stars.

Before I discuss how adaptive optics measures and corrects aberrations, I'll describe the unit of measure used in this science and compare it to our longstanding unit, the diopter.

New Precision and Accuracy

In adaptive optics, the root mean square (RMS) unit and formula are used to record and measure optical aberrations in microns. The formula can measure aberrations to 0.05 microns (equivalent to about 0.005 diopters). Now that's a precise and accurate prescription!

Thanks to this kind of accuracy, adaptive optics can express lower- and higher-order aberrations in terms far more accurate than we've ever seen in clinical care. With the RMS system, we can reconstruct the mathematical calculations of an aberration into Zernike polynomials.

In fact, using the RMS formula, you can (if you have a doctorate in higher calculus!) calculate and reconstruct aberrations to the 27th order of vision. Now remember, we've never gone farther than the 2nd order with diopters.

These RMS values and the aberrations they represent can be reconstructed as Zernike polynomials into two-dimensional maps using color gradients representing powers of the aberrations. Also, we can reconstruct them as three-dimensional models in shapes we're all becoming familiar with, such as the bimodal wave of coma and the symmetrical "sombrero" of spherical aberration. These Zernike polynomials form a pyramid starting from 0 (no aberrations or piston) to, theoretically, as high as you want to go.

What This Means to Clinicians

Recently, vision scientists have begun to study the Zernike pyramid relative to the human visual system and are recognizing certain interesting facts. For instance, the aberrations of the pyramid's outer borders don't have significant central distortions and, thus, don't have a significant effect on vision. Also, aberrations above the 5th to 6th order are probably measuring retinal "noise" more than true vision. This noise is coming from the variability of the tear film and really doesn't represent true aberrations.

As interesting as Zernike polynomials are to physicists and astronomers, clinicians can use them to observe reconstructed aberrations within a given pupil diameter. Further, they allow us to qualitatively and quantitatively identify those higher-order aberrations we've never been able to measure or even understand.

Practical Application

How can we use this information at the practical level? That's through the good old point spread function method and our "poor man's aberrometer," the Snellen chart (see April 2005 new OD).

Now that we've "mastered" an understanding of adaptive optics, we can begin to discuss how this complex yet effective system measures and helps us correct higher-order aberrations. That, indeed, is the Holy Grail for practitioners.

Dr. Catania is with Nicolitz Eye Consultants in Jacksonville, Fla. He does clinical research; consults for ophthalmic companies and professional journals; and writes and lectures worldwide. You can reach him at


Optometric Management, Issue: September 2005