Wavefront Technology and Higher-Order
optics, root mean square (RMS) and "Zernikes" ... What's it all about?
By Louis J. Catania,
O.D., F.A.A.O., Jacksonville, Fla.
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.
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
Optometric Management, Issue: September 2005