**Purpose**:
The purpose of this study was to compare the low degree/high degree (LD/HD) and Zernike Expansion simulation outcomes evaluating the corneal wavefront changes after theoretical conventional and customized aspheric photorefractive ablations.

**Methods**:
Initial anterior corneal surface profiles were modeled as conic sections with pre-operative apical curvature, R0, and asphericity, Q0. Postoperative apical curvature, R1, was computed from intended defocus correction, D, diameter zone, S, and target postoperative asphericity, Q1. Coefficients of both Zernike and LD/HD polynomial expansions of the rotationally symmetrical corneal profile were computed using scalar products. We modeled different values of D, R0, Q0, S, and ΔQ = Q1 to Q0. The corresponding postoperative changes in defocus (Δz20 vs. Δg20), fourth order (Δz40 vs. Δg40) and sixth order (Δz60 vs. Δg60) Zernike and LD/HD spherical aberrations (SAs) were compared. In addition, retrospective clinical data and wavefront measurements were obtained from two examples of two patient eyes before and after corneal laser photoablation.

**Results**:
The z20, varied with both R0 and Q0, whereas the LD/HD defocus coefficient, g20, was relatively robust to changes in asphericity. Variations of apical curvature better correlated with defocus and ΔQ with SA coefficients in the LD/HD classification. The impact of ΔQ was null on g20 but induced significant linear variations in z20 and fourth order SA coefficients. LD/HD coefficients provided a good correlation with the visual performances of the operated eyes.

**Conclusions**:
Simulated variations in postoperative corneal profile and wavefront expansion using the LD/HD approach showed good correlations between defocus and asphericity variations with variations in corneal curvature and SA coefficients, respectively.

**Translational Relevance**:
The relevance of this study was to provide a clinically relevant alternative to Zernike polynomials for the interpretation of wavefront changes after customized aspheric corrections.

^{1}

^{,}

^{2}Reshaping the corneal contour by excimer laser photoablation is used to reduce the total ocular SAs while correcting the myopic or hyperopic defocus.

^{3}

^{,}

^{4}Induction of negative SAs (Q

_{1}< 0) creates a prolate or hyperprolate cornea, which may also serve to extend the depth of focus and through-focus visual acuity.

^{5}

^{–}

^{8}Exploring the relationships between the changes in asphericity (ΔQ) and wavefront aberrations may be necessary to better assess the impact of the control of postoperative corneal asphericity on the low order (sphere/defocus and cylinder/astigmatism) and higher order aberrations of the corneal wavefront.

^{9}

^{–}

^{11}

_{4}

^{0}and Z

_{6}

^{0}), are containing some term in r

^{2}(which corresponds to a defocus phase Z-LOA). For example, the Zernike polynomial defining “spherical aberration” includes both r4 and r2 terms and corresponds to the following wavefront error (WFE):

^{2}. Previous studies have shown that the visual impact of Zernike fourth and sixth order SA were mostly due to the lower order r

^{2}term.

^{12}

^{,}

^{13}This would suggest that using Zernike SA to analyze the wavefront changes caused by aspheric corrections may lead to difficulties in the interpretation of paraxial versus peripheral curvature changes, as it combines an r

^{2}term with an r

^{4}term. In addition, in the clinical setting, best visual acuity in subjective refractions for circular pupils are dominated by the central optics.

^{14}This central defocus may contribute to the reduced accuracy of the prediction of spherocylindrical refractive error from the ocular low order wavefront component.

^{12}

^{,}

^{13}As a corollary, the prediction of the visual impact of high degree aberrations after best spectacle correction is not realistic when modes, such as Zernike SA, for which the calculation of a point spreading function or a modulation transfer function includes the effect of the term in r

^{2}, whereas this would be largely neutralized by a defocus correction in glasses, to “flatten” the central part of the WFE.

^{12}

^{–}

^{15}Seidel SA, on the other hand, describes a wavefront that is well focused centrally and either myopic (positive SA) or hyperopic (negative SA) at the pupil margins. Its analytical expression is limited to a term in r

^{4}. However, the Seidel class of aberrations is incomplete and not ortho-normalized over the circular pupil.

^{16}

^{,}

^{17}This new non-Zernike expansion was generated to allow a clear cut separation between higher and lower order monomials within the higher and lower wavefront components. Importantly, the new higher order wavefront modes do not contain low (i.e. constant, linear, or quadratic) terms to provide a clinically relevant “low order wavefront error free” prediction of the visual impact of the higher order wavefront component. They are normalized and mutually orthogonal. The goal is to provide a clinically relevant “low order wavefront error free” prediction of the visual impact of the higher order wavefront component.

*n*= 6) over a zone of diameter S.

^{18}This allows us to obtain the values of the coefficients c

_{2}

^{0}, c

_{4}

^{0}, and c

_{2}

^{0}of the Z

_{2}

^{0}, Z

_{4}

^{0}, and Z

_{6}

^{0}polynomial modes, respectively.

_{1}, was computed using a paraxial formula from the value of the preoperative apical radius R

_{0}and the distance defocus, D, at the corneal plane. The pre and postoperative asphericity values were adjusted to conform to the characteristics (conventional or customized) of the ablation profile.

_{2}

^{0}, c

_{4}

^{0}, and c

_{6}

^{0}of the rotationally invariant Z

_{2}

^{0}, Z

_{4}

^{0}, and Z

_{6}

^{0}Zernike polynomials corresponding to the preoperative (R

_{0}and Q

_{0}) and postoperative (R

_{1}and Q

_{1}) spherical corneal profiles were obtained by using scalar products on a zone of diameter S. Using the LD/LH method described previously, the coefficients g

_{2}

^{0}, g

_{4}

^{0}, and g

_{6}

^{0}weighting the new polynomials G

_{2}

^{0}, G

_{4}

^{0}, and G

_{6}

^{0}can be directly computed analytically from the coefficients c

_{2}

^{0}, c

_{4}

^{0}, and c

_{6}

^{0}weighting a Zernike expansion for the same fit order.

^{16}

_{n}

^{0}f or g

_{n}

^{0}f and the initial preoperative, z

_{n}

^{0}i or g

_{n}

^{0}i, values multiplied by the change in the refractive index (n’-n) from the air (n = 1) to the corneal stroma (n’ = 1.376)

^{19}:

_{2}

^{0}is the (root mean square [RMS]) amplitude of the Z

_{2}

^{0}Zernike or G

_{2}

^{0}LD/HD modes in micrometers.

_{0}= Q

_{1}= 0). Zernike and LD/HD coefficients variation corresponding to the corresponding optical path change were computed. The impact of the optical zone on the Zernike and LD/HD coefficients and predicted SE changes was evaluated for diameter comprised between 5.5 and 8 mm for a −6 D correction.

_{0}= +0.5) after myopic surgery, (2) reducing excessive corneal prolateness (Q

_{0}= −0.8) after hyperopic surgery, and (3) introducing a fixed amount of Zernike negative SA (Δz

_{4}

^{0}= −0.4 microns) while inducing myopic refraction for the correction of presbyopia in patients with hyperopia.

_{2}

^{0}), whereas the equivalent dioptric defocus computed from the z

_{2}

^{0}defocus coefficients exceeded the magnitude of the intended correction. The maximum difference was an excess of 1.0 D myopic power for the −10 D correction and of 0.86 D hyperopic power for the +6 D correction. The variations of the fourth and sixth (higher order) coefficients were similar in trend but different in magnitude between the Zernike and LD/HD coefficients (Figs. 2b, 2c). Theses variations were negative (increased negative SA) for myopic corrections, and positive (increased positive SA) for hyperopic corrections.

_{2}

^{0}, by an amount that increases with the diameter of the optical zone. The fourth and sixth order Zernike and LD/HD coefficients increased proportionally to the change in diameter of the optical zone raised to power four and to power six, respectively. The changes in SE computed from the g

_{2}

^{0}coefficient matches the intended paraxial correction D and remains unaffected by the variations in the OZ diameter.

_{0}= +0.5, R

_{0}= 8.5 mm) targeting different variations of the corneal asphericity from ΔQ = −0.1 to ΔQ = −1 by 0.1 steps while leaving the paraxial curvature unchanged (D = 0, R

_{0}= R

_{1}; see Fig. 4a). Whereas the g

_{2}

^{0}coefficients remain null regardless of the value of the target asphericity, a change of z

_{2}

^{0}coefficient toward more negative values is observed, corresponding to a dioptric defocus equivalent change in the direction of less myopia/more hyperopia and comprised between ΔD = +0.16 D (ΔQ = −0.1, Δz

_{2}

^{0}= −0.21 microns) and ΔD = +1.55 D (ΔQ = −1, Δz

_{2}

^{0}= −2 microns). The larger the change toward less oblate/more prolate asphericity, the larger the change in the fourth and sixth order Zernike and LD/HD SA coefficients toward more negative values see Figures 4b, 4c.

_{0}= R

_{1}= 0; see Fig. 5a). The change in z

_{2}

^{0}coefficients values correspond to a defocus change in the direction of less hyperopia/more myopia and comprised between ΔD = −0.23 D (ΔQ = +0.1, Δz

_{2}

^{0}= +0.29 microns) and ΔD = −1.92 D (ΔQ = +0.8, Δz

_{2}

^{0}= +2.49 microns). The larger the change toward less prolate asphericity, the larger the change in the fourth and sixth order Zernike and LD/HD SA coefficients toward more positive values see Figures 5b, 5c.

_{4}

^{0}= −0.40 microns using a customized aspheric ablation profile to increase corneal prolateness. For hyperopic corrections and large intended changes in SA (Δz

_{4}

^{0}= −0.4 µm, equivalent to Δg

_{4}

^{0}= −2.27 microns), the required change in asphericity can be computed depending on the preoperative corneal asphericity and planned paraxial defocus correction.

_{1}) and asphericity (Q

_{1}), along with the theoretical Zernike and LD/HD wavefront expansions caused by such custom profile for various defocus corrections (+2 D, +4 D, and +6 D) applied on a preoperative corneal profile (R

_{0}= 7.8 mm, Q

_{0}= −0.2, 6 mm zone). The dioptric change estimated from the variation in the z

_{2}

^{0}coefficient underestimates the planned defocus change by an amount of +1.24 D.

^{16}

^{,}

^{17}The decomposition of the wavefront in our new basis requires new coefficients, which are obtainable from Zernike expansion after collection of low order terms. It allows to express two components for the total wavefront by grouping the modes according to their radial order. The LD component of the wavefront can be described with an expansion of weighted low order modes of the same analytical structure as their Zernike counterparts. It is expressed as an expansion of the new higher order modes, which are all devoid of lower order terms. Studies have shown that marginal optics have little or no impact on the full pupil spherical refraction,

^{12}

^{–}

^{14}

^{,}

^{20}

^{–}

^{22}which suggests that high spatial frequency refractions achieve a near paraxial focus. In the presence of SA, authors have shown that visual acuity was better with paraxial focus than with the defocus that minimized RMS.

^{23}Although not exactly equivalent to paraxial curvature matching of the wavefront, the spherical equivalent error appears to be dominated by the near paraxial optics.

^{15}This novel polynomial decomposition basis approach, in which the low order wavefront component is equal to the paraxial curvature matching of the wavefront map, was used to improve the prediction of subjective refraction from wavefront aberrometry data processed with machine learning algorithms and better apprehend the impact of higher order wavefront phase errors.

^{24}Machine learning models were significantly better than the paraxial matching method; however, it showed that G

_{2}

^{0}(paraxial defocus) was by far the most influential feature to predict the SE value, with G

_{4}

^{0}(primary SA) being the second most important feature. These data suggest that the use of paraxial curvature matching for defining the low order component is clinically more relevant for some clinical applications. The use of high-degree modes whose analytical expression is devoid of high degree has the advantage of removing the ambiguity associated with the visual impact of degree 2 monomials.

_{2}

^{0}vs. g

_{2}

^{0}) is shown both spherically based and customized aspheric profiles of ablation (Figs. 2a, 4a, 5a).

_{2}

^{0}coefficient, whose value is affected by the need to compensate for the r

^{2}terms of the z

_{4}

^{0}and z

_{6}

^{0}modes (see Fig. 2a). This difference increases with the diameter of the optical zone. Spherical myopic corrections introduce an amount of negative fourth and sixth order Zernike and LD/HD aberrations (Figs. 2b, 2c). These are caused by the conjunction of the flattening of the corneal surface and the increase in prolateness predicted after spherically based profiles of ablation for initially prolate corneas.

^{25}

_{2}

^{0}occurs with the ablation profiles aiming at the induction of a simple modification of the asphericity without modification of the apical power (zero dioptric correction). The higher the change in asphericity (ΔQ), the higher the change in z

_{2}

^{0}, and therefore the predicted variation in dioptric spherical equivalent. As an example, a change of ΔQ = −0.8 (increased prolateness and reduced oblateness) causes a theoretical dioptric defocus variation of the Z-LOA wavefront close to of 1.25 D (myopic shift). Conversely, using the LD/HD decomposition method, the variation of the g

_{2}

^{0}coefficient is null (Figs. 4a, 5a), as should be theoretically expected (D = 0). This discrepancy can cause a bias in interpretation and lead the surgeon inspecting the planned change in the Zernike coefficients to believe that a programmed ablation profile will modulate the planned correction of some amount of defocus whereas this one is nothing other than an artifact linked to necessity to balance the second degree radial term in the Z

_{4}

^{0}and Z

_{6}

^{0}modes. These spurious interactions are even more pronounced for custom ablations aimed at reducing the prolateness of a steep cornea (the resulting change in the z

_{2}

^{0}coefficient predicts a hyperopic shift of 1.90 D for ΔQ = +0.8).

_{2}

^{0}for custom aspheric profiles aimed at inducing myopic defocus and inducing certain amounts of SA to compensate for presbyopia, as shown in the Table. The aim is to create a more curved surface in the central zone and a flatter one in the peripheral zone so that for small pupils the vision would be dominated by this central zone, improving near vision, whereas for large pupils, the vision would be dominated by the peripheral corneal zone, providing acceptable distance vision.

_{2}

^{0}change of negative sign to compensate for the quadratic component included in the Z

_{4}

^{0}mode, which results from the modulation of the corneal asphericity toward increased prolateness. This amount is subtracted to the positive change in Δz

_{2}

^{0}, which is induced by the positive spherical correction and reduces the net apparent defocus variation. In our simulations, the difference between the z

_{2}

^{0}and g

_{2}

^{0}coefficient is roughly equal to approximately 15

^{0.5}or 3.9 times Δz

_{4}

^{0}, as expected from the analytical structure of the Z

_{4}

^{0}mode. Meanwhile, the magnitude of the variation of fourth order LD/HD SA is roughly six times that of the Zernike SA (approximately Δg

_{4}

^{0}to 6xΔz

_{4}

^{0}).

^{26}Although the exact characteristics of the delivered profile is proprietary, the increase of negative SA requires an increased corneal prolateness. The interpretation of the changes in defocus of the corneal wavefront using Zernike reconstruction following Varifocal ablation should be cautious, as the shift toward increased negative asphericity may result in a significant negative variation of the z

_{2}

^{0}wavefront coefficient (see Fig. 5a).

^{27}

^{–}

^{29}Some authors

^{28}

^{,}

^{29}acknowledge that a re-adjustment of target refraction by myopization was required to compensate for the defocusing induced by Q-factor modification. They attributed the apparent hyperopic shift (increase in negative Zernike defocus) predicted from the treatment planner to the change in corneal asphericity, which in fact results from the interactions with the Zernike SA discussed in the present study. The negative SA induction through multifocal ablation profile based on increased corneal prolateness requires a myopic paraxial refraction to reach better near vision while improving distance vision over classic monovision.

^{7}

^{,}

^{30}Indeed, in an eye paraxially emmetropic, increased corneal prolateness inducing negative SA would result in a hyperopic shift for nonparaxial rays, which would not be useful for near vision.

_{2}

^{0}(commonly designated as C4 in the single index notation used by the laser manufacturer) equal to the value of the fourth order SA coefficient z

_{4}

^{0}(designated as C12).

^{31}

_{3}

^{±1}and tilt Z

_{1}

^{±1}, or secondary astigmatism Z

_{4}

^{±2}and primary astigmatism Z

_{2}

^{±2}. These interactions could explain the discrepancies between anterior corneal astigmatism and refractive astigmatism when analyzed through Zernike polynomial decompositions in the context of topography-guided ablations.

^{32}Further studies are required to evaluate the potential benefit of the LD/HD decomposition method on the nonrotationally invariant component of the wavefront. We limited our calculations to the corneal plane: the net contribution of the change in SA of corneal origin to the ocular wavefront may be slightly different and would take into account the distance and possible decentration from the entrance pupil to the corneal plane. Our static subtraction shape model neglected the impact of some physical constraints, such as the “cosine effect” along with that of the biomechanical and wound healing response. However, we postulate that improving the relevance of wavefront interpretation may help to better segregate between the impact of multiple variables on the measured outcomes in clinical practice.

^{33}

^{,}

^{34}Separate analysis of radius and asphericity incorrectly estimates the statistical significance of the changes in the ocular surfaces, and a new representation is there proposed.

_{2}

^{0}is slightly myopic, which contradicts the 20/15 uncorrected visual acuity. This positive Zernike defocus coefficient correlates with the need for compensating for the negative lower order term in r

^{2}embedded within the analytical expression of the Z

_{4}

^{0}mode. There is negligible defocus in the LD/HD decomposition. When the higher order component of the Zernike decomposition remains uncorrected, the Snellen chart simulations suggest an exaggerated visual blur, which is mainly caused by the quadratic central wavefront error (r

^{2}monomial) that is well visible on the representation of the 6 mm pupil Zernike higher order wavefronts, whereas the HD envelopes are flatter paraxially (Fig. A2). When computed from the LD/HD decomposition, the simulated Snellen chart retinal image for the uncorrected higher order component (HD) is in line with the eye's visual performance.

^{35}

^{–}

^{37}Generally, the defocus term that maximizes such metrics is, to date, the best predictor of subjective spherical error. Visual acuity is determined primarily by the WFE in the central portion of the pupil, and it is plausible that the r

^{2}term generating spherical defocus-like wavefronts in the pupil center for a wavefront dominated by Zernike SA, such as in case 2 would be flattened or canceled by the defocus of the best spectacle correction (the theoretical amount of defocus required to cancel the r

^{2}term within Z40 is \(z_2^0 = \sqrt {15} z_4^0\)). This explains the discrepancy between the value of z

_{2}

^{0}and that of g

_{2}

^{0}and SE in the case 2. Using the LD/HD decomposition results in the decoupling of the r

^{2}term embedded in the Z

_{4}

^{0}mode and unmask the low order paraxial WFE. In addition, as in case 1, that r

^{2}term reduces the quality of the predicted retinal image of the higher order Zernike WFE.

^{38}

^{,}

^{39}The LD/HD decomposition method is intended to supplement, rather than replace, the Zernike polynomials. It is aimed to provide clinicians with an alternative set of weighted higher order modes over circular pupils that would reflect the lower order (i.e. correctable with spectacles) versus higher order contribution to the ocular wavefront.

^{40}

^{–}

^{43}they play important roles in various optics branches, such as beam optics and the study of single- and multiple-circular aperture optical systems that are affected by atmosphere turbulence, or optical metrology for surface and transmitted wavefront representation.

^{44}Their performance on elliptical pupils has been studied.

^{45}

^{,}

^{46}Their full orthogonality confers some advantages, such as the robustness of coefficients to the truncation of an expansion, and the aberration balancing property, which leads to minimal variance (48). This property is conferred to an aberration by the mix of aberrations of lower order; we posit that this leads to potential interpretation problems in some visual optics applications where a clearer cut between the paraxially dominated low and marginally dominated higher order WFE is needed, such as discussed in this paper. As there is a univocal correspondence between the coefficients in both bases, the differences between them represent an interpretation of the respective role of low and/or higher order modes, but not an improvement in terms of quality of fitting or residuals minimization. Because of the lack of orthogonality between the LD and HD components, it is not possible to compute RMS values including a mixture of both LD and HD coefficients, and the RMS does not always correspond to the standard deviation of the WFE. In ophthalmic optics, clinical interpretation considers lower order aberrations and HOAs separately. The impact of the low order component of the wavefront is usually expressed separately and/or through the classic expression of spherocylindrical refraction into diopters, whereas the main contribution of wavefront analysis is to provide the higher order RMS value by concentrating only on the coefficients of the higher order polynomials. To satisfy the constraint of orthogonality between the new high degree modes, the presence of terms of variable degree (but always strictly greater than or equal to

*n*= 3) is necessary from the fifth odd degree (they contain monomials of degree 3) and sixth degree even (they contain monomials of degree 4). The interpretation of the coefficients weighting the aberrations of radial degree s3 and 4 must be cautious in clinical situations that involve an elevation of the aberrations with higher radial degree.

**D. Gatinel**, None;

**J. Malet**, None;

**L. Dumas**, None;

**D.T. Azar**, None

*J Refract Surg*. 2011; 27(6): 434–443. [CrossRef] [PubMed]

*J Refract Surg*. 2007; 23: 505–514. [CrossRef] [PubMed]

*J Refract Surg*. 2014; 30(11): 777–784. [CrossRef] [PubMed]

*J Refract Surg*. 2015; 31(12): 802–806. [CrossRef] [PubMed]

*J Refract Surg*. 2011; 27(7): 519–529. [CrossRef] [PubMed]

*J Refract Surg*. 2012; 28(8): 531–541 [CrossRef] [PubMed]

*J Refract Surg*. 2016; 32(11): 734–741. [CrossRef] [PubMed]

*J Refract Surg*. 2020; 36(2): 89–96. [CrossRef] [PubMed]

*J Refract Surg*. 2014; 30: 708–715. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2003; 44(11): 4676–4681. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2005; 46(6): 1915–1926. [CrossRef] [PubMed]

*Ophthalmic Physiol Opt*. 2013; 33(4): 444–455. [CrossRef] [PubMed]

*Ophthalmic Physiol Opt*. 2015; 35(1): 28–38. [CrossRef] [PubMed]

*Ophthalmic Physiol Opt*. 2014; 34(3): 309–320. [CrossRef] [PubMed]

*J Vis*. 2004; 4(4): 329–351 [CrossRef] [PubMed]

*J Opt Soc Am A Opt Image Sci Vis*. 2018; 35(12): 2035–2045. [CrossRef] [PubMed]

*J Refract Surg*. 2020; 36(2): 74–81. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2004; 45(5): 1349–1359. [CrossRef] [PubMed]

*J Refract Surg*. 2014; 30(10): 708–715. [CrossRef] [PubMed]

*Br J Physiol Opt*. 1978; 32: 78–93. [PubMed]

*Arch Ophthalmol*. 1991; 109: 70–76. [CrossRef] [PubMed]

*Vision Res*. 2011; 51: 1932–1940. [CrossRef] [PubMed]

*J Vis*. 2004; 23(4): 310–321

*Sci Rep*. 2020; 10(1): 8565. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2001; 42(8): 1736–1742. [PubMed]

*J Refract Surg*. 2019; 35(7): 459–466. [CrossRef] [PubMed]

*J Cataract Refract Surg*. 2016; 42(10): 1415–1423. [CrossRef] [PubMed]

*J Cataract Refract Surg*. 2016; 42(10): 1415–1423. [CrossRef] [PubMed]

*J Cataract Refract Surg*. 2019; 45(8): 1074–1083. [CrossRef] [PubMed]

*J Biomed Opt*. 2012; 17(1): 018001. [CrossRef] [PubMed]

*Clin Ophthalmol*. 2017; 11: 915–921. [CrossRef] [PubMed]

*Clin Ophthalmol*. 2020; 14: 1091–1100. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2006; 47(4): 1404–1415. [CrossRef] [PubMed]

*J Opt Soc Am A Opt Image Sci Vis*. 2010; 27(7): 1541–1548. [CrossRef] [PubMed]

*Optom Vis Sci*. 2003; 80(1): 36–42. [CrossRef] [PubMed]

*J Vis*. 2004; 4(4): 322–328. [CrossRef] [PubMed]

*J Vis*. 2008; 8(13): 1.1–1.2. [CrossRef]

*J Opt Soc Am A Opt Image Sci Vis*. 2006; 23(7): 1657–1668. [CrossRef] [PubMed]

*J Refract Surg*. 2006; 22(9): 943–948. PMID: 17124894. [CrossRef] [PubMed]

*Ophthalmic Physiol Opt*. 2002; 22: 427–433. [CrossRef] [PubMed]

*J Refract Surg*. 2004; 20(5): S537–S541. [CrossRef] [PubMed]

*J Refract Surg*. 2005; 21(5): S563–S569. [CrossRef] [PubMed]

*J Opt Soc Am A Opt Image Sci Vis*. 2006; 23(7): 1657–1668. [CrossRef] [PubMed]

*J Opt Soc Am A Opt Image Sci Vis*. 2007; 24(3): 569–577. [CrossRef] [PubMed]

*J Opt Soc Am A Opt Image Sci Vis*. 2007; 24(9): 2994–3016. Erratum in: J Opt Soc Am A Opt Image Sci Vis. 2012;29(8):1673-1674. [CrossRef] [PubMed]

_{2}

^{0}and g

_{2}

^{0}coefficients were converted in the dioptric defocus and compared to the postoperative spherical equivalent (SE) of the analyzed eyes. The Snellen chart retinal image simulations were obtained via convolutional techniques from the point spread function (PSF) computed for the Zernike versus LD/HD higher order components. Low order corrected retinal image simulations were generated and compared between the Zernike and LD/HD wavefront reconstructions.

^{20}The mean values of the pre and postoperative 1 mm central keratometry and the anterior corneal asphericities were: R

_{0}= 7.75 mm, R

_{1}= 6.89 mm, Q

_{0}= −0.02, and Q

_{1}= 0.18. Figure A1 allows to compare the theoretical versus measured variations for the second, fourth, and sixth order coefficients of the corresponding Zernike versus LD/HD modes (6 mm pupil). There is acceptable agreement between the theoretical and clinically measured wavefront coefficients’ variation for the second and fourth order coefficients’ variations. The planned SE correction (+6.00 D) was better correlated with the theoretical (Δg

_{2}

^{0}= 7.81 µm, ΔSE = 6.02 D) and achieved clinical (Δg

_{2}

^{0}= 7.51 µm, Δ SE = 5.78 D) LD/HD defocus variation than with the Zernike defocus variations (theoretical: Δz

_{2}

^{0}= 9.72 µm, Δ SE = 7.48 D, clinical: Δz

_{2}

^{0}= 9.05 µm, Δ SE = 6.97 D), which tend to overestimate the magnitude of the measured defocus variation.

_{2}

^{0}= 1.625 µm, 6 mm pupil), and +0.07 D from the LD/HD decomposition (z

_{2}

^{0}= −0.091 µm, 6 mm pupil). The PSF was computed for the combination of fourth and sixth degree wavefront error (WFE) for the Zernike and LD/HD (6 mm pupil). The simulation of Snellen chart using convolutional techniques revealed optotypes identifiable for a resolution equivalent to a 20/50 visual acuity when the eye is corrected for the z

_{2}

^{0}defocus, and to a 20/15 visual acuity when the eye is corrected for the g

_{2}

^{0}defocus (Fig. A2).

^{19}

^{,}

^{21}The mean values of the pre and postoperative 1 mm central keratometry and the anterior corneal asphericities were R

_{0}= 8.10 mm, R

_{1}= 7.60 mm, Q

_{0}= −0.49, Q

_{1}= −1.43. Figure A1 allows to compare the theoretical versus measured variations for the second, fourth, and sixth order coefficients of the corresponding Zernike versus LD/HD modes (6 mm pupil). There is acceptable agreement between the theoretical and clinically measured wavefront coefficients’ variation for the second and fourth order coefficients’ variations. The theoretical (Δg

_{2}

^{0}= 3.43 µm, Δ SE = 3.00 D) and clinically measured (Δg

_{2}

^{0}= 3.90 µm, Δ SE = 3.34 D) variation in LD/HD second degree coefficient were close to the planned SE correction (Δ SE = 3.00 D). Conversely, the Zernike theoretical and clinically measured variation in z

_{2}

^{0}were largely underestimating the planned SE correction (theoretical SE change = 1.36 D, measured SE change = 0.39 D).

_{2}

^{0}= 0.182 µm) from the Zernike decomposition and −3.09 D from the LD/HD decomposition (g

_{2}

^{0}= 4.023 µm). The simulation of Snellen chart reveals optotypes identifiable for a resolution equivalent to a 20/40 visual acuity when the eye is corrected for the z

_{2}

^{0}defocus, and to a 20/15 visual acuity when the eye is corrected for the g

_{2}

^{0}defocus (Fig. A2).