Theoretical optical quality was investigated by calculating the VSOTF metric (visual Strehl ratio based on the optical transfer function [OTF]). The VSOTF is the ratio of the contrast sensitivity–weighted OTF to the contrast sensitivity–weighted OTF of the diffraction-limited eye.
26 27 Because the preoperative WFEs W
pre(
x,
y) were decentered, calculating the VSOTF from preoperative HOA could lead to misinterpretation of optical quality due to over- or underestimation of HOA. Thus, we calculated a standard preoperative WFE, W
meanpre(
x 0,
y 0), from all eyes included in this study. For the calculation of W
meanpre(
x 0,
y 0), all preoperative, pupil-centered WFEs were averaged, resulting in a WFE representing the typical preoperative range of HOA
(Table 2) .
24 28 Simulated postoperative WFEs, W
post(
x′,
y′), were calculated by subtracting the W
meanpre(
x 0,
y 0) from each ΔW(
x′,
y′). This treatment simulation relative to a standard preoperative WFE allowed us to eliminate interindividual differences in preoperative optical quality and internal optics. Therefore, the independent variables in this experiment were the five different centered treatment effects ΔW(
x,
y) and their corresponding ΔW(
x′,
y′). A computer program (Visual Optics Laboratory, VOL-Pro 7.14; Sarver and Associates, Carbondale, IL) was used to calculate the VSOTF over an analysis PD of 3.5 and 6.0 mm. The VSOTF for a given WFE was calculated for the combination of LOA terms that provided the highest VSOTF simulating the optical quality with best spherocylindrical correction (BCVSOTF). Thus, for each simulated W
post(
x′,
y′), an LOA-derived refractive error based on 2nd-order terms and an “effective” refractive error based on the BCVSOTF were obtained. Differences between refractive errors were expressed as dioptric power vectors (
M,
J0,
J45), where
M corresponds to the spherical equivalent and
J0 to the 0°/90° and
J45 to the 45°/135° astigmatic components. The difference between the VSOTF- and 2nd-order–based power vectors could be considered a function of the interaction between HOA and LOA. Since “sphere” and “cylinder” are most commonly used in clinical settings, we displayed most of the results in terms of sphere and cylinder magnitude. To visualize decentration effects for single eyes, color maps plotting ΔLOA, ΔHOA, and Δlog BCVSOTF against horizontal and vertical decentration were created. For further statistical analysis, data for decentration along the 0°, 90°, 180°, and 270° meridians were averaged for each eye.