![]() ![]() We studied the visual impact of monochromatic HOAs on vision using the approach first described in detail by Burton and Haig 27. The Seidel convention for defining monochromatic aberrations, defines SA as a 4 0r 4, and thus lacks the r 2 term that dominates the central region of Zernike SA ( Figure 1). It is clearly possible, therefore, that the observed effect of Zernike SA on VA is due not to the r 4 component of the polynomial (the component that makes it “spherical aberration” and is primarily responsible for the WFE at the pupil margins), but rather by the r 2 term generating spherical defocus-like wavefronts in the pupil center. ![]() These results suggest that VA is determined primarily by the WFE in the central portion of the pupil, and optimum VA is achieved by flattening the central wavefront. This structure of individual Zernike modes becomes important because experimental studies have shown that, in eyes with SA, best VA (subjective) refractions for circular pupils are dominated by the central optics 24 – 26. For example, the “spherical aberration” (SA) Zernike polynomial includes both r 4 and r 2 terms and defines the following wavefront error (WFE)Ĭonsequently, the WFE in the central 50% of the pupil is dominated not by the r 4 term (which is approximately zero in the central region of the pupil), but by the opposite sign r 2 term ( Figure 1). 23Īlthough individual Zernike polynomials (modes) are considered as individual aberrations, they contain multiple terms. Studies using computationally blurred letter charts 5, or deformable mirrors 8, 21, 22 have shown that individual Zernike modes closer to the center of the Zernike pyramid (lower meridional frequencies) have more impact than those near the edge (higher meridional frequencies). It appears, however, that not all HOAs have the same ability to degrade vision. Conversely, correcting HOAs using deformable mirrors 7, 19, custom lathed optical corrections 20, and aspheric IOLs 11 can improve VA. Increased levels of Higher Order Aberrations (HOAs) introduced by multifocal (aberrated) Intraocular Lenses (IOLs) 12, multifocal contact lenses 13, aberrated custom contact lenses 14, corneal disease 15, and refractive surgery 16 – 18 can all lead to reduced visual acuity. Best Spectacle Corrected VA in studies of post-refractive surgery, intraocular implants, and keratoconic eyes. Accordingly, visual acuity continues to be employed clinically as a surrogate measure of image quality when assessing the impact of higher order aberrations (e.g. In addition to the well-documented impact of lower order aberrations on VA, more recent studies have shown that higher order aberrations can also degrade VA 5 – 8. This surrogate test of retinal image quality forms the basis of subjective refractions for the simple reason that the VA is relatively easy to measure and it varies in direct proportion to the level of defocus, modulated only by pupil size (MAR = Blur/4, where blur = blur circle diameter = defocus (D) × pupil diameter) 1 – 4. Also, r(ρ) must be even if m is even and odd if m is odd.In the clinical environment, visual acuity (VA) testing is the gold standard, albeit indirect method for assessing optical quality of the retinal image. The radial function, r(ρ), must be a polynomial in ρ of degree n and contain no power of ρ less than m. Each Zernike term is referenced by a single number or by two subscripts, n and m, where both are positive integers or zero. The coordinate system can be rotated by an angle a without changing the form of the polynomial. One of the convenient features of Zernike polynomials is that their simple rotational symmetry allows the polynomials to be expressed as products of radial terms and functions of angle, r(ρ) g(θ'), where g(θ') is continuous and repeats itself every 2π radians. Also note the difference in the definitions of the angle in the measurement plane, θ vs. There are several common definitions for the Zernike polynomials, so care should be taken that the same set is used when comparing Zernike coefficients. Note that θ' is the angle counterclockwise from the x P axis. It is important to note that Zernikes are orthogonal only in a continuous fashion and that in general they will not be orthogonal over a discrete set of data points. These polynomials are a complete set in two variables, ρ and θ', that are orthogonal in a continuous fashion over the unit circle. They are useful in expressing wavefront data since they are of the same form as the types of aberrations often observed in optical tests. Zernike polynomials were first derived by Fritz Zernike in 1934. ![]()
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