**Purpose.**:
To determine the most appropriate analysis technique for the differentiation of multifocal intraocular lens (MIOL) designs by using defocus curve assessment of visual capability.

**Methods.**:
Four groups of 15 subjects were implanted bilaterally with either monofocal intraocular lenses, refractive MIOLs, diffractive MIOLs, or a combination of refractive and diffractive MIOLs. Defocus curves between −5.0 D and +1.5 D were evaluated by using an absolute and relative depth-of-focus method, the direct comparison method, and a new “area-of-focus” metric. The results were correlated with a subjective perception of near and intermediate vision.

**Results.**:
Neither depth-of-focus method of analysis was sensitive enough to differentiate between MIOL groups (*P* > 0.05). The direct comparison method indicated that the refractive MIOL group performed better at +1.00 diopter (D), −1.00 D, and −1.50 D and worse at −3.00 D, −3.50 D, −4.00 D, and −5.00 D than did the diffractive MIOL group (*P* < 0.05). The area-of-focus intermediate zone was greater with the refractive than with the diffractive MIOL group (*P* = 0.005) and the near zone was better with the diffractive (*P* = 0.020) and “mix and match” (*P* = 0.039) groups than with the refractive MIOL group. The subjective perception of intermediate and near vision agreed best with the area-of-focus metric for the intermediate (*r* _{s} = 0.408, *P* = 0.010) and near zone (*r* _{s} = 0.484, *P* < 0.001).

**Conclusions.**:
Conventional depth-of-focus metrics provide a single value to quantify the useful range of vision; however, they fail to provide sufficient detail to differentiate between MIOL designs. The direct comparison method provides a large amount of information, although the results can be complex to interpret. The proposed area-of-focus metric provides a simple, but differentiating method of evaluating MIOL defocus curves.

^{ 1 }and dynamic autorefraction,

^{ 2,3 }are inappropriate.

^{ 4–6 }or through different levels of spectacle lens defocus.

^{ 7–9 }However, the more physical method of measuring VA at varying distances is often impractical owing to the need to control angular image size and luminance.

^{10}) and the disrupted natural associated convergence and pupil response.

^{ 11 }

^{ 6 }Hence, defocus curves demonstrate the strength of the near addition (the separation in diopters between the distance and near peak) as well as the quality of vision at each dioptric level of spectacle defocus.

^{ 12 }

^{ 13 }and in the approaches taken to analyze the results.

^{ 10 }The direct comparison method of analysis involves statistical comparison of the visual acuity at each defocus level; the linked nature of repeated measurements needs to be accounted for statistically and the large number of comparisons can complicate clinical interpretation. Alternatively, the depth-of-focus method of analysis describes the dioptric range over which the subjects can sustain a specific absolute or relative level of VA. There is no consensus over the level of acuity considered to be appropriate for depth-of-focus measurements, and as this criterion is not always stated, the disparity of methodology prevents meaningful comparisons between studies. A relative criterion for depth-of-focus analysis defines the VA cutoff relative to the best-attained level of VA; relative criteria have not been used in multifocal studies but have been used with the assessment of accommodating IOLs.

^{ 3 }An absolute criterion identifies the limits of VA independent to the best-attained VA; the limit of 0.3 LogMAR is the most common criterion used with multifocal IOL studies and matches the level of VA defined as the driving standard in Europe

^{ 14 }and in all but three states in the United States.

^{ 15 }The defocus curve of a MIOL can pass through the depth of focus criterion line several times; it is unclear how studies have resolved this previously as this possibility has not been addressed.

**Table 1.**

**Table 1.**

Bilateral Monofocal IOL | Bilateral ReZoom | Bilateral Tecnis ZM900 | Mix and Match | |

Age, y, Mean ± SD | 62.1 ± 6.8 | 62.3 ± 8.4 | 60.7 ± 11.0 | 58.5 ± 9.2 |

Sex | 3 male, 12 female | 7 male, 8 female | 4 male, 11 female | 7 male, 8 female |

^{ 10 }Each subject also subjectively rated his or her intermediate and near vision on a scale of 0 (completely unsatisfied) to 5 (completely satisfied). Monocular pupil sizes were measured by using a validated portable infrared pupillography device, the Pupilscan II infrared pupillometer (Keeler Ltd.).

^{ 16,17 }

^{18}All defocus curve acuities were corrected for spectacle magnification (SM) according to a back vertex distance (BVD) of 12.0 mm (equation 1

^{10}). For each defocus curve, a best-fit polynomial regression curve was fitted to the data points with SigmaPlot 2000 (SPSS Inc., Chicago, IL) (y is the visual acuity [LogMAR] and x is the optical defocus [diopters]). Each data set (14 points) was fitted with a 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th, and 12th order polynomial. The curve-fitting process was limited to 200 iterations for each curve. Increasing the order of the polynomial to fit the defocus curves resulted in a higher

*r*

^{2}and decreased the standard error of estimate up until a ninth order polynomial; fitting polynomials of 10th order displayed more variability in the standard error of estimation, as valid curves could not be fitted to all data sets within the iteration limit (Table 2). Therefore, a ninth order polynomial function was used for all further analysis as it was the lowest-order polynomial that provided a universal best fit to all data sets (equation 2). VA at 40 cm, measured with the near EDTRS chart, was compared with the VA with a defocus lens of −2.50 D, using Pearson's product moment correlation and Bland and Altman limits of agreement.

^{19}

**Table 2.**

**Table 2.**

r ^{2} | Standard Error of Estimate | |

4th order | 0.8197 ± 0.1404 | 0.0964 ± 0.0410 |

5th order | 0.8458 ± 0.1317 | 0.0928 ± 0.0410 |

6th order | 0.9250 ± 0.0652 | 0.0705 ± 0.0301 |

7th order | 0.9507 ± 0.0444 | 0.0601 ± 0.0253 |

8th order | 0.9635 ± 0.0371 | 0.0555 ± 0.0222 |

9th order | 0.9768 ± 0.0243 | 0.0493 ± 0.0208 |

10th order | 0.9315 ± 0.2166 | 0.1548 ± 0.4906 |

^{10}If the second multifocal peak (corresponding with the near focal point) also met these criteria, the range of defocus values meeting the criteria for both focal points was summated. The absolute criteria of 0.30 LogMAR was also used to calculate depth of focus; the Newton-Raphson method

^{20}was used to calculate

*x*when

*y*= 0.3. The Newton-Raphson method is used to find the roots of a function, by adjusting the polynomial function by 0.3 to find

*x*when

*y*= 0.3 (equation 3). The table of corresponding

*x*and

*y*values produced by Sigmaplot 2000 was used to determine the initial approximation

*x*

_{0}. The resultant

*x*

_{1}from equation 3 is a better approximation of

*x*when y = 0.3; however, for increased accuracy this process is repeated by taking the resultant

*x*

_{1}to be

*x*and putting this value through equation 4 until the percentage error (% error) is reduced to 0 (equation 5). The Newton-Raphson method was used to determine each intersection of the curve at 0.3 LogMAR. The range of focus was calculated as the dioptric distance over which VA was better than 0.3 LogMAR.

_{n}^{−1}) could be derived (equation 6). In accordance with the consensus of previous literature, the upper limit for depth of focus was defined as 0.3 LogMAR, corresponding with the European

^{ 14 }and American

^{ 15 }binocular visual acuity driving standards. The defocus curves were divided into distance, intermediate, and near zones. The near zone was defined as between −4.00 and −2.00 D, corresponding with a 25- to 50-cm range, commonly referred to as the range of near vision.

^{ 21 }The intermediate zone was defined as −2.00 to −0.50 D, from 50 cm (approximately arm's length) to 2 m. Beyond this, the distance zone was defined as the distances between −0.50 to +0.50 D. These zones were used to define the limits of integration. A two-way repeated measures ANOVA was used to determine if there was any statistically significant difference in the area-of-focus and the defocus curves between lenses. If a significant difference was found, then a one-way ANOVA was used to examine differences by applying Bonnferoni post hoc tests to determine pairwise differences.

*F*

_{3}= 0.094,

*P*= 0.963) and left eye (

*F*

_{3}= 0.227,

*P*= 0.878) (Table 3).

**Table 3.**

*P*< 0.001); however, no differences were found between the MIOL groups (

*P*> 0.05). For best distance-corrected intermediate VA (79 cm), the ReZoom MIOL group achieved higher levels of intermediate VA than both the monofocal (

*P*= 0.019) and Tecnis ZM900 (

*P*= 0.024) groups and similar levels of intermediate VA in comparison with the mix-and-match group (

*P*= 0.419) (Table 4).

**Table 4.**

**Table 4.**

Binocular Softec 1 | Binocular ReZoom | Binocular Tecnis ZM900 | Mix and Match | |

40 cm | +0.57 ± 0.09 | +0.26 ± 0.10 | +0.17 ± 0.11 | +0.18 ± 0.10 |

79 cm | +0.28 ± 0.09 | +0.17 ± 0.10 | +0.28 ± 0.14 | +0.19 ± 0.08 |

*F*

_{3}= 2.144,

*P*= 0.105; Fig. 1).

**Figure 1.**

**Figure 1.**

*P*< 0.001). However, this method of analysis found no significant differences in the results for each of the MIOL groups (

*P*> 0.05; Fig. 1).

*P*< 0.001). In addition, this method revealed differences between the MIOL designs, showing that the binocular ReZoom performed better at +1.00 D (

*P*= 0.024), −1.00 D (

*P*= 0.002), and −1.50 D (

*P*= 0.003) than the binocular Tecnis ZM900 group but performed significantly worse at −3.00 D (

*P*= 0.006), −3.50 D (

*P*< 0.001), −4.00 D (

*P*= 0.003), and −5.00 D (

*P*= 0.017). The mix-and-match group showed similar results to both the ReZoom and Tecnis groups (Fig. 2).

**Figure 2.**

**Figure 2.**

*F*

_{3}= 2.541,

*P*= 0.065). For the intermediate zone, the ReZoom group had better vision (a larger area) than the Tecnis ZM900 group (

*P*= 0.005); no other differences were found for the intermediate zone. For the near area of focus, all MIOL groups achieved better vision than the monofocal IOL group (

*P*< 0.001); in addition the near area of the Tecnis ZM900 (

*P*= 0.020) and of the mix-and-match (

*P*= 0.039) groups was greater than that that of the ReZoom group (Fig. 3).

**Figure 3.**

**Figure 3.**

*r*

_{s}= 0.408,

*P*= 0.010) than did the best distance-corrected intermediate VA (

*r*

_{s}= 0.148,

*P*= 0.204), relative range of focus (

*r*

_{s}= 0.36,

*P*= 0.783), and absolute range of focus (

*r*

_{s}= 0.340,

*P*= 0.008) (Fig. 4). Similarly, the subjective rating of near vision correlated strongest with the near area of focus (

*r*

_{s}= 0.484,

*P*< 0.001) in comparison with best distance-corrected near VA (

*r*

_{s}= 0.385,

*P*= 0.001), relative range of focus (

*r*

_{s}= 0.154,

*P*= 0.241), and absolute range of focus (

*r*

_{s}= 0.408,

*P*= 0.001) (Fig. 5).

**Figure 4.**

**Figure 4.**

**Figure 5.**

**Figure 5.**

^{ 10,13 }However, metrics for providing a global overview of the performance of a lens are important to allow standardized comparisons between studies. Relative and absolute depth-of-focus analysis methods are the two most common metrics used to assess defocus curves. However, in this study, neither the relative nor the absolute defocus curve analysis method was sensitive to differences between MIOL designs despite the clear variation that was demonstrated with the direct comparison method and area-of-focus method.

^{ 22 }This oscillation occurs mostly at the edges of a data set between the first and last values. To account for this phenomenon, the chosen defocus curve range was 1.00 D on either side of the required range for measurement of the area of focus. Therefore, when using a ninth order polynomial, it is important to retain the full range of defocus curve between −5.0 and +1.5 D despite the area metric using only the area between −4.0 and +0.5 D.

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