Pupil size and the ablation zone in laser refractive surgery: Considerations based on geometric optics

Distribution of Pupil Size and Associated Factors: Results from the Population-Based Gutenberg Health Study

Results

18,335 eyes of 9,559 participants aged 40 to 80 years were included in the analysis. Median pupil diameter was 4.19 mm in right eyes and 4.12 mm in left eyes. A smaller pupil was associated with older age, hyperopic refractive error, previous cataract surgery, diabetes, obesity, and ACE inhibitor intake, whereas wider pupil was associated with female gender, arterial hypertension, intake of tricyclic antidepressants, and intake of SNRI and tetracyclic antidepressants. Socioeconomic status and smoking were not associated with pupil size.

Conclusion

Individuals of older age, after cataract surgery, under therapy with ACE inhibitors and with diabetes have a smaller pupil. This should be taken into account when planning nonmydriatic fundus photography-based screening programs, for instance, for diabetic retinopathy.

Effective Optical Zone Following Small Incision Lenticule Extraction for Myopia Calculated With Two Novel Methods

PURPOSE

To evaluate the effective optical zone (EOZ) following small incision lenticule extraction in myopic eyes using two novel methods and investigate factors influencing postoperative EOZ.

METHODS

In this prospective study, 45 patients (45 eyes) with a mean spherical equivalent of -5.82 ± 1.58 diopters underwent SMILE and were observed during a 6-month follow-up. Postoperative EOZ was calculated using custom software that automatically distinguishes EOZ on the tangential curvature difference map (EOZc) and total corneal refractive power map (EOZp) of the Pentacam HR (Oculus Optikgeräte GmbH). The agreement between the two methods, the difference between postoperative EOZ and programmed optical zone (POZ), and its relationship with parameters including corrected spheres, cylinders, ablation ratio (ablation depth/central cornea thickness), and Q-value change were investigated.

RESULTS

The EOZc area was 20.76 ± 2.43 mm² (diameter: 5.04 ± 0.60 mm) and the EOZp area was 20.22 ± 4.70 mm² (diameter: 5.13 ± 0.30 mm). Both were significantly smaller than POZ (P < .001). Bland-Altman plots showed 4.44% (2/45) points located outside the 95% limits of agreement. EOZc and EOZp reductions were negatively related to corrected cylinders (r = -0.631, P < .001 and r = -0.594, P < .001, respectively). EOZp reduction was positively correlated with corrected spheres (r = 0.336, P = .024). Subgroup analysis revealed significant differences in EOZc and EOZp reduction between low and high astigmatism groups despite myopia degree.

CONCLUSIONS

EOZ after incision lenticule extraction, measured using two novel methods, was smaller than POZ. The reduction of EOZ was negatively correlated with the corrected cylinders. [J Refract Surg. 2022;38(7):414-421.].

Comparison of effective optical zone after small-incision lenticule extraction and femtosecond laser-assisted laser in situ keratomileusis for myopia

PURPOSE

To compare the effective optical zone (EOZ) after small-incision lenticule extraction (SMILE) and femtosecond laser-assisted laser in situ keratomileusis (FS-LASIK).

SETTING

Jinan Mingshui Eye Hospital, Jinan, China.

DESIGN

Retrospective case series.

METHODS

Myopic patients who had small-incision lenticule extraction or FS-LASIK were enrolled in this retrospective study. Effective OZs were measured at 1 week, 1 month, and 3 months postoperatively, using the tangential curvature difference map of the Scheimpflug tomography system. Correlations between the changes in the EOZ and relevant parameters were analyzed 3 months postoperatively.

RESULTS

The study comprised 76 patients (76 eyes). The mean EOZs at 1 week, 1 month, and 3 months postoperatively were 5.39 ± 0.27 mm, 5.33 ± 0.30 mm, and 5.34 ± 0.23 mm in the small-incision lenticule extraction group and 5.06 ± 0.36 mm, 4.98 ± 0.39 mm, and 5.01 ± 0.31 mm in the FS-LASIK group, when the programmed OZ was 6.5 mm. The magnitude of decreases in EOZ was significantly smaller in the small-incision lenticule extraction group than in the FS-LASIK group at all timepoints after surgery (P < .01). There were significant correlations between changes in EOZ and corneal asphericity (P < .01). Epithelial thickening was positively correlated with EOZ reduction in the small-incision lenticule extraction group (r = 0.479, P < .01); however, no correlation was found between epithelial thickening and EOZ reduction in the FS-LASIK group (r = .324, P > .05).

CONCLUSIONS

Both small-incision lenticule extraction and FS-LASIK resulted in EOZ reduction during correction of myopia. However, small-incision lenticule extraction resulted in less reduction than FS-LASIK and was associated with corneal asphericity changes and epithelial thickening.

The comparison of visual outcomes, aberrations, and Bowman's layer micro-distortions after femtosecond laser small-incision lenticule extraction (SMILE) for the correction of high and moderate myopia and myopic astigmatism

Background

This study compares the clinical outcomes of femtosecond laser small-incision lenticule extraction (SMILE) for the correction of myopia and myopic astigmatism greater than − 10 D, and − 10 D or less respectively.

Methods

60 eyes/patients were equally selected into group 1 (myopia and myopic astigmatism of − 10 D or less) and group 2 (myopia and myopic astigmatism of over − 10 D), both of which were treated with SMILE. Visual and refractive outcomes, corneal higher-order aberrations, and Bowman’s layer micro-distortions were evaluated preoperatively, 3 months, and 6 months postoperatively.

Results

LogMAR corrected distance visual acuity (CDVA) of group 1 and group 2 was − 0.069 ± 0.047 and − 0.053 ± 0.073 6 months postoperatively (P = 0.48). 100% eyes in group 1 and 97% in group 2 were within 1 D of targeted correction (P = 0.45). Meanwhile, 100% eyes in group 1 and 97% in group 2 had an uncorrected distance visual acuity of 20/25 or better (P = 0.20). Changes in corneal higher-order aberrations root mean square, coma, and trefoil were similar between the two groups but spherical aberration was higher in group 2 (P < 0.01). Micro-distortions were observed in 53% in group 1 and 77% in group 2. More micro-distortions were observed in group 2 (3.40 ± 2.66) than in group 1 (2.07 ± 2.29) (P = 0.041). The total number of micro-distortions was not correlated with postoperative CDVA (P = 0.77).

Conclusions

Visual outcomes showed similar results of SMILE for myopic correction of > − 10 D and ≤ − 10 D. Refractive outcomes showed slightly under-correction in higher myopic eyes. Higher myopic treatment tends to induce more spherical aberrations. Micro-distortions had no impact in visual and refractive outcomes.

Early visual outcomes and optical quality after femtosecond laser small-incision lenticule extraction for myopia and myopic astigmatism correction of over -10 dioptres

PURPOSE

To investigate early visual and refractive outcomes, corneal stability and optical quality after femtosecond laser small-incision lenticule extraction (SMILE) for treating myopia and myopic astigmatism over -10 D.

METHODS

Thirty eyes (30 patients) with myopia and myopic astigmatism of over -10 D were treated with VisuMax^® femtosecond laser (version 3.0; Carl Zeiss Meditec AG, Jena, Germany). Six months postoperative safety, efficacy and predictability were evaluated. Corneal Scheimpflug topography was measured preoperatively, 1 day, 3 months and 6 months postoperatively. Wavefront aberrations were measured preoperatively, 3 months and 6 months postoperatively.

RESULTS

Six months postoperatively, LogMAR uncorrected and corrected distance visual acuity (CDVA) were -0.013 ± 0.086 and -0.073 ± 0.069, respectively. 73% (97%) of eyes were within 0.5 (1) D of target refraction. No eyes lost CDVA, 43% (13 eyes) gained one line and 7% (two eyes) gained two lines. Mean corneal back curvature (KMB) and posterior central elevation (PCE) did not change significantly comparing preoperative and 6 months postoperative data (p = 0.91 and 0.77, respectively). Comparing 1 day with 6 months postoperative data, central corneal thickness (CCT), mean corneal front curvature (KMF), KMB and PCE did not change significantly (p = 0.27, 0.07, 0.52, 0.71, respectively). Total higher-order aberration (HOA), spherical aberration and coma increased significantly (p < 0.01) but trefoil remained stable (p = 0.49).

CONCLUSION

Our results indicate that SMILE can correct myopia and myopic astigmatism of over -10 D predictably. No early ectasia was observed. Long-term changes in visual quality and corneal stability require further investigation.

Digital Pupillometry in Normal Subjects

The aim of this study was to evaluate the pupil size of normal subjects at different illumination levels with a novel pupillometer. The pupil size of healthy study participants was measured with an infrared-video PupilX pupillometer (MEye Tech GmbH, Alsdorf, Germany) at five different illumination levels (0, 0.5, 4, 32, and 250 lux). Measurements were performed by the same investigator. Ninety images were executed during a measurement period of 3 seconds. The absolute linear camera resolution was approximately 20 pixels per mm. This cross-sectional study analysed 490 eyes of 245 subjects (mean age: 51.9 ± 18.3 years, range: 6-87 years). On average, pupil diameter decreased with increasing light intensities for both eyes, with a mean pupil diameter of 5.39 ± 1.04 mm at 0 lux, 5.20 ± 1.00 mm at 0.5 lux, 4.70 ± 0.97 mm at 4 lux, 3.74 ± 0.78 mm at 32 lux, and 2.84 ± 0.50 mm at 250 lux illumination. Furthermore, it was found that anisocoria increased by 0.03 mm per life decade for all illumination levels (R² = 0.43). Anisocoria was higher under scotopic and mesopic conditions. This study provides additional information to the current knowledge concerning age- and light-related pupil size and anisocoria as a baseline for future patient studies.

Comparison of anterior chamber depth measurements of Nidek AL-Scan and Galilei Dual Scheimpflug Analyzer

PURPOSE

We aimed to compare anterior chamber depth (ACD) measurements between the Nidek AL-Scan and the Galilei Dual Scheimpflug Analyzer.

SETTING

Turgut Ozal University Medical Faculty, Ankara, Turkey.

DESIGN

Prospective masked bilateral randomized study.

METHODS

Sixty-three individual patient eyes with normal ocular examination findings and no prior ocular surgery were analyzed. Paired two-tailed t-test was used to evaluate agreement between devices. Interobserver repeatability was evaluated in 22 patients using intraclass correlation coefficient (ICC) and Bland-Altman analysis.

RESULTS

The mean ± standard deviation (SD) ACD for Nidek and Galilei was 3.57 ± 0.29 (range from 2.92 to 4.32) and 3.65 ± 0.29 (range from 3.01 to 4.40), respectively. Comparing the two instruments using paired samples t-test, a statistically significant difference was found between the measurements obtained for ACD (P = 0). Two observers' intraclass correlation coefficients (ICC) were 0.996 for Nidek and 0.968 for Galilei. For Nidek, ACD mean difference was 0mm (P < 0.001); 95% limits of agreement was from -0.05 to 0.05. For Galilei ACD mean difference was -0.01 mm (P < 0.001); 95% limits of agreement was from -0.14 to 0.12. The Galilei Dual Scheimpflug Analyzer measured longer ACD values than the Nidek AL-Scan.

CONCLUSION

This comparative study showed that the difference in ACD between the measurements of the Nidek AL-Scan and the Galilei Dual Scheimpflug Analyzer was statistically significant but clinically it was negligible. Further studies are needed, especially on IOL calculation formulas that include ACD and its effect on postoperative spherical equivalent values.

Agreement between Orbscan II, VuMAX UBM and Artemis-2 very-high frequency ultrasound scanner for measurement of anterior chamber depth

Background

The aim was to compare the anterior chamber depth (ACD) measurements taken with Orbscan II, ultrasound biomicroscopy (UBM) and the Artemis-2 VHF (very-high-frequency) ultrasound scanner in normal subjects.

Methods

In this prospective study, one eye from each of 60 normal subjects was randomly selected. Three subjects dropped out of the study because they were apprehensive about the UBM examination; their data were excluded entirely. Measurements of ACD were taken with the Orbscan II, UBM and Artemis-2 VHFUS. Results were obtained for coefficient of variance (CV) and intra-class correlation coefficient (ICC), and statistical analysis was by repeated-measures analysis of variance (ANOVA) for intra-observer repeatability. ANOVA and Bland–Altman analyses were used to determine limits of agreement (LOA) between the three instruments.

Results

The average ACD (± standard deviation) was 3.13 ± 0.34 mm, 2.96 ± 0.27 mm and 2.87 ± 0.31 mm for the Orbscan II, UBM and Artemis-2 VHFUS, respectively. The repeatability scores were 0.015 ± 0.014%, 0.08 ± 0.09% and 0.07 ± 0.06% for the Orbscan II, UBM and Artemis-2 VHFUS, respectively. The ICC for repeatability of Orbscan II, UBM and Artemis-2 VHFUS measurements was high and equal to 0.99%. The intra-observer repeatability scores of the ACD measurement p-values using Orbscan II, UBM and Artemis-2 VHFUS were 0.12, 0.70 and 0.10, respectively. The mean difference and standard deviations for ACD measurements using Orbscan II vs UBM, Orbscan II vs Artemis-2 VHFUS and UBM vs Artemis-2 VHFUS were 0.17 ± 0.31 mm, 0.27 ± 0.34 mm and 0.10 ± 0.18 mm, respectively. LOAs were 0.78 to -0.44 mm, 0.93 to -0.39 mm and 0.45 to -0.26 mm. ANOVA revealed a statistically significant difference between the Orbscan II, UBM and Artemis-2 VHFUS (p < 0.0001).

Conclusions

Measurements by the three instruments show high repeatability. UBM and the Artemis-2 VHFUS can be used interchangeably, but the Orbscan II cannot be used interchangeably with UBM or the Artemis-2 VHFUS.

Aperture referral in heterocentric astigmatic systems

BACKGROUND

Retinal blur patch, effective corneal patch, projective field, field of view and other concepts are usually regarded as disjoint concepts to be treated separately. However they have in common the fact that an aperture, often the pupil of the eye, has its effect at some other longitudinal position. Here the effect is termed aperture referral.

PURPOSE

To develop a complete and general theory of aperture referral under which many ostensibly-distinct aperture-dependent concepts become unified and of which these concepts become particular applications. The theory allows for apertures to be elliptical and decentred and refracting surfaces in an eye or any other optical system to be astigmatic, heterocentric and tilted.

METHODS

The optical model used is linear optics, a three-dimensional generalization of Gaussian optics. Positional and inclinational invariants are defined along a ray through an arbitrary optical system. A pencil of rays through a system is defined by an object or image point and an aperture defines a subset of the pencil called a restricted pencil.

RESULTS

Invariants are derived for four cases: an object and an image point at finite and at infinite distances. Formulae are obtained for the generalized magnification and transverse translation and for the geometry and location of an aperture referred to any other transverse plane.

CONCLUSIONS

A restricted pencil is defined by an aperture and an object or image point. The intersection of the restricted pencil with a transverse plane is the aperture referred to that transverse plane. Many concepts, including effective corneal patch, retinal blur patch, projective field and visual field, can now be treated routinely as special cases of the general theory: having identified the aperture, the referred aperture and the referring point one applies the general formulae directly. The formulae are exact in linear optics, explicit and give insight into relationships.

Effect of preoperative pupil size on quality of vision after wavefront-guided LASIK

PURPOSE

To evaluate the effect of preoperative pupil size on quality of vision after wavefront-guided LASIK.

DESIGN

Prospective study.

PARTICIPANTS

One hundred two eyes.

INTERVENTION

LASIK for mild to moderate myopia or astigmatism (preoperative manifest spherical equivalent, -3.99±1.42 diopters).

MAIN OUTCOME MEASURES

Questionnaires evaluating specific visual symptoms before and after surgery. Each eye was evaluated before surgery, and 1 week and 1, 3, 6, and 12 months postoperatively. Pupils were stratified according to size: small (≤5.5 mm), medium (5.6-6.4 mm), or large (≥6.5 mm). Mesopic pupil size and preoperative and postoperative variables were evaluated using an analysis of variance. A regression model was also performed to determine the correlation between mean spherical equivalent and cylinder and visual symptoms.

RESULTS

In the early postoperative period, there was no difference between the 3 groups with regard to any of the symptoms. At the final 12-month postoperative visit, patients with medium pupils experienced less glare at night than small pupils (P = 0.02), medium pupils had less halos than small or large pupils (P = 0.001 and P = 0.02, respectively), and medium pupils experienced greater satisfaction in visual improvement than small pupils (P = 0.014).

CONCLUSIONS

Twelve months after wavefront-guided LASIK surgery, large pupil size does not positively correlate with any postoperative visual symptoms.

Effective corneal patch of an astigmatic heterocentric eye

BACKGROUND

The pupil admits to the back of the eye only some of the light arriving from a point in space. As a result only a portion of the cornea is involved when an eye views the point; it is the effective corneal patch for that point. The location, size and shape of the patch are of interest for corneal refractive surgery inter alia. Previous studies have used geometrical optics and a simple model eye (a naked eye with a spherical, single-surface, centred cornea and a concentric circular pupil). Even for the simplest situations geometrical optics provides only implicit formulae which give little insight into relationships and require numerical solution.

PURPOSE

To show how linear optics leads to explicit formulae that estimate the geometry of the effective corneal patch in a very wide range of situations. The eye is not restricted to a single refracting surface; the surfaces may be astigmatic and decentred or tilted and the pupil may be decentred and elliptical. The eye may contain implants and it may be looking through a spectacle lens or other optical instrument which may also contain astigmatic and decentred surfaces.

METHODS

Linear optics is used to provide general formulae for the geometry of the corneal patch. An appendix illustrates application to some particular cases.

RESULTS

General formulae are obtained for the location and geometry of the effective corneal patch for object points that may be near or distant. Formulae are presented in particular for the special case of the naked eye and the case in which all surfaces are spherical and centred on a common axis. Numerical examples in the appendix allow comparison of results obtained via geometrical and linear optics.

CONCLUSIONS

In using linear optics one sacrifices some accuracy at increasing angles away from the longitudinal axis but there is considerable gain in the complexity and range of problems that can be tackled, and the explicit formula one obtains clearly exhibit relationships among parameters of clinical relevance.

Contribution of optical zone decentration and pupil dilation on the change of optical quality after myopic photorefractive keratectomy in a cat model

PURPOSE

To simulate the simultaneous contribution of optical zone decentration and pupil dilation on retinal image quality using wavefront error data from a myopic photorefractive keratectomy (PRK) cat model.

METHODS

Wavefront error differences were obtained from five cat eyes 19+/-7 weeks (range: 12 to 24 weeks) after spherical myopic PRK for -6.00 diopters (D) (three eyes) and -10.00 D (two eyes). A computer model was used to simulate decentration of a 6-mm sub-aperture relative to the measured wavefront error difference. Changes in image quality (visual Strehl ratio based on the optical transfer function [VSOTF]) were computed for simulated decentrations from 0 to 1500 mum over pupil diameters of 3.5 to 6.0 mm in 0.5-mm steps. For each eye, a bivariate regression model was applied to calculate the simultaneous contribution of pupil dilation and decentration on the pre- to postoperative change of the log VSOTF.

RESULTS

Pupil diameter and decentration explained up to 95% of the variance of VSOTF change (adjusted R(2)=0.95). Pupil diameter had a higher impact on VSOTF (median beta=-0.88, P<.001) than decentration (median beta=-0.45, P<.001). If decentration-induced lower order aberrations were corrected, the impact of decentration further decreased (beta=-0.26) compared to the influence of pupil dilation (beta=-0.95).

CONCLUSIONS

Both pupil dilation and decentration of the optical zone affected the change of retinal image quality (VSOTF) after myopic PRK with decentration exerting a lower impact on VSOTF change. Thus, under physiological conditions pupil dilation is likely to have more effect on VSOTF change after PRK than optical zone decentration.

The effect of the asphericity of myopic laser ablation profiles on the induction of wavefront aberrations

PURPOSE

To compare the effects of laser profile asphericity on the induction of wavefront aberrations, susceptibility to decentration, and depth of focus in a polymethylmethacrylate (PMMA) model.

METHODS

Four PMMA lenses received an excimer laser ablation of -6 D with a 6-mm optical zone and different amounts of primary spherical aberration (Z(4)(0)): 0, -0.346, -1.038, and -2.076 microm. The curvature of each lens was measured by using surface profilometry, and wavefront changes were computed from curvature differences. Changes in optical quality were compared by treatment simulation of 13 real myopic eyes. The influence of pupil diameter, ablation decentration, and defocus on retinal image quality was measured by using the optical transfer function-based visual Strehl ratio (VSOTF).

RESULTS

Aspheric ablation profiles induced significantly less primary but higher secondary spherical aberration (Z(6)(0)) than did the standard profile; however, Z(4)(0) compensation was incomplete. Simulated treatments with aspheric profiles resulted in significantly better retinal image quality and higher decentration tolerance than did the standard profile. Optical depth of focus was not affected with a 3-mm pupil, whereas with a 6-mm pupil, there was a small but statistically significant decrease in depth of focus.

CONCLUSIONS

Aspheric laser profiles showed theoretical optical benefits over standard ablation profiles for the treatment of myopia, including terms of decentration tolerance. However, there remained profound induction and thus, undercorrection of Z(4)(0), due to loss of laser ablation efficiency in the lens periphery.

Pupil size, white-to-white corneal diameter, and anterior chamber depth in patients with myopia

PURPOSE

To evaluate anatomical parameters in a population of patients with myopia.

METHODS

Nine hundred sixty-four myopic eyes (-3.00 to -20.00 diopters [D] spherical equivalent refraction) were evaluated to measure mesopic and photopic pupil size with an infrared pupillometer; anterior chamber depth and white-to-white corneal diameter were obtained with Orbscan II (Bausch & Lomb). Correlation analysis was performed to evaluate the relationships among anatomical parameters of the anterior segment of the eye.

RESULTS

Average change in pupil size between mesopic and photopic conditions shows a uniform gap of 1.5 mm in patients aged 18 to 62 years with a slight insignificant trend to decrease with age. Photopic and mesopic pupil size were highly correlated (r=0.694, P<.001) and the difference between both measures was positively correlated with mesopic pupil size (r=0.207, P<.001) and inversely correlated with photopic pupil size (r=0.561, P<.001). Anterior chamber depth and white-to-white corneal diameter were positively correlated (r=0.389, P<.001). White-to-white corneal diameter and anterior chamber depth were not correlated with age (r=-0.096, P<.001) or anterior chamber depth (r=-0.183, P<.001-0.183) as a function of age.

CONCLUSIONS

Average difference between photopic and mesopic pupil size remained constant across the range of ages included in this cohort. A positive correlation was noted between anterior segment dimensions, and anterior chamber depth decreased with age.

Distribution of photopic pupil diameter in the Tehran eye study

PURPOSE

To determine the photopic pupil diameter and its determinants in a sample derived from a population-based survey in Tehran.

METHODS

In a cross-sectional study with a stratified random cluster sampling approach, 410 people age 14 years and over were selected from those residing in the first four municipality districts of Tehran after applying exclusion criteria, and 800 eyes (399 right eyes and 401 left eyes) were examined with the Orbscan II. The main outcome measure was the mean pupil diameter under photopic conditions, and possible correlations with potential determinants were evaluated through linear regression analyses. The design effect of a cluster sampling approach was observed and adjusted for.

RESULTS

The mean age of the participants was 40.6 +/- 16.8 years and 38.8% were male. The mean photopic pupil diameter (PPD) was 3.70 mm (range 2.30 to 5.10; 95% confidence interval (CI) 3.62 to 3.78). The mean PPD was 3.67 mm (95% CI, 3.54 to 3.81) in men and 3.72 mm (95% CI, 3.63 to 3.81) in women (p = 0.481). There was a significant reduction of 0.021 mm in PPD per year of aging (r = -0.49, p < 0.001). There was also a significant inverse correlation between PPD and spherical equivalent (r = -0.12, p = 0.034), while there was 0.66-mm increase in PPD with every 1.0-mm increase in the anterior chamber depth (ACD) (p < 0.001). Anisocoria, defined as a pupil diameter difference more than 0.4 mm between two eyes, was observed in 12.2% of the study population.

CONCLUSION

While the mean PPD measured with the Orbscan II was 3.70 mm in a sample derived from a population-based survey in Tehran, the scarcity of similar studies and reports concerning the pupil diameter measured with the Orbscan II makes it difficult to draw eligible comparisons. The pupil diameter has reverse correlations with age and spherical equivalent, a direct correlation with ACD, but is not correlated with gender.

Effect of spectacle and contact lenses on the effective corneal refractive zone

The effective corneal refractive zone is that portion of the cornea traversed by the light that enters the pupil of the eye from object points at a specified angle from the line of sight. It is of relevance in corneal surgery and for understanding the effect of corneal opacities and lesions on vision. Gaussian optics is used in this paper to obtain explicit equations for the geometry of the effective corneal refractive zone for a simplified eye, when spectacle and contact lenses are worn. The theory shows that lenses of positive power increase the diameter of the effective corneal refractive zone and lenses of negative power decrease the diameter. For axial object points the diameter of the effective corneal refractive zone increases by about 0.015 mm per dioptre increase in the power of the spectacle or contact lens. For object points at 30 degrees from the longitudinal axis, the increase is about twice as much in the case of contact lenses and more than four times as much in the case of spectacle lenses.

[Application of wavefront analysis in clinical and scientific settings. From irregular astigmatism to aberrations of a higher order--Part II: examples]

In recent years, wavefront analysis has ceased to be purely a laboratory application and emerged as a method used in ophthalmological diagnosis. This development has been promoted mainly by the widespread use of wavefront-guided LASIK (laser in situ keratomileusis). However, aberrometry is still not a common diagnostic technique, and for many ophthalmologists interpretation of the results is difficult. The second part of this serial paper reviews findings that are relevant for the ophthalmological community and highlights current scientific applications in this area.

Measurement of pupil reactivity using fast pupillometry

Analysis of human eye pupil reactivity is a very valuable diagnostic method used mainly for evaluation of the condition of the autonomic nervous system and the visual system. The paper presents an experimental pupillometer built in the Institute of Physics of the Wroclaw University of Technology. The apparatus makes it possible to record and analyze pupillary light reflex and spontaneous changes in the pupil diameter during a session in the dark. The detector system used in the pupillometer allows us to record the pupil diameter at a rate of 90 Hz with a linear accuracy of 0.008 mm. In this paper, the proposed detection method, the principle of operation and calibration of the apparatus and the possibilities of the measurement system are presented.

Size of corneal topographic effective optical zone: comparison of standard and customized myopic laser in situ keratomileusis

PURPOSE

To investigate the corneal topographic effective optical zone (EOZ) in eyes after wavefront-guided myopic laser in situ keratomileusis (LASIK) and to compare them with the EOZ after standard LASIK.

DESIGN

Retrospective, case-control study.

METHODS

We evaluated the corneal topographic maps of 41 eyes of 25 consecutive patients who had CustomVue LASIK (CV LASIK) and 41 eyes of 23 patients who had standard LASIK with correction up to -7 diopters using the VISX Star S4 laser (VISX Inc, Santa Clara, California, USA). On the refractive map of the Humphrey Topography System, we defined the EOZ as the area outlined by a change of corneal power of 0.5 diopters from the power at the center of the pupil. We analyzed the differences in EOZs of the two ablation patterns and the correlation between EOZ and magnitude of refractive correction.

RESULTS

The mean postoperative EOZs were 17.9 +/- 3.7 mm(2) and 11.4 +/- 3.4 mm(2) after CV and standard LASIK, representing 60% and 40% of the laser-programmed optical zones, respectively (both P < .0001). There was no correlation between the postoperative EOZs and the magnitude of refractive correction for both ablations (all P > .05). In eyes with spherical correction (cylinder < or =0.25 diopters), CV LASIK increased the preoperative EOZ by 3.8 +/- 5.6 mm(2) (P = .018), whereas standard LASIK decreased EOZ by 4.5 +/- 5.2 mm(2) (P = .005).

CONCLUSION

CV LASIK created larger corneal topographic EOZs than standard ablation. In eyes with spherical correction, the preoperative EOZ was expanded by CV LASIK and reduced by standard LASIK.

Influence of pupil and optical zone diameter on higher-order aberrations after wavefront-guided myopic LASIK

PURPOSE

To investigate the influence of pupil and optical zone (OZ) diameter on higher-order aberrations (HOAs) after myopic wavefront-guided laser in situ keratomileusis (LASIK).

METHODS

Twenty-seven myopic eyes of 19 patients were included. The mean preoperative spherical equivalent was -6.86 diopters (D) +/- 1.24 (SD) (range -4.25 to -9.5 D); the mean planned OZ diameter was 6.26 +/- 0.45 mm (range 5.7 to 7.1 mm). All patients had uneventful wavefront-guided LASIK (Zyoptix version 3.1, Bausch & Lomb) and an uncomplicated follow-up of 12 months. Wavefront measurements were performed with a Hartmann-Shack sensor in maximum mydriasis preoperatively and 12 months after LASIK. Wavefront errors were computed for pupil diameters (PDs) of 3.0, 3.5, 4.0, 5.0, 6.0, and 7.0 mm for the individual OZ diameter and for the individual mydriatic PD (7.93 +/- 0.46 mm). The impact of the relationship between pupil diameter and OZ diameter (fractional clearance [FC]) on HOA was described and quantified using curvilinear regression with a 4th-order polynomial fit.

RESULTS

There was a reproducible relationship between FC and the amount of induced HOA. The change in HOA root mean square and primary spherical aberration (Z(4)0) was significantly correlated with FC. If the OZ was 16.5% larger than the pupil (FC = 1.17), only half the amount of HOA was expected to be induced than if the OZ equaled the pupil. In contrast, an OZ that was 9% smaller than the pupil (FC = 0.91) resulted in an HOA induction 50% higher than at FC = 1.

CONCLUSION

The OZ zone to pupil ratio (fractional clearance) had a significant impact on HOA induction after wavefront-guided LASIK.

Effective corneal refractive diameter as a function of the object tangent angle in visual space

PURPOSE

To determine whether the currently accepted method of selecting a minimum optical zone diameter for laser refractive surgery that is equal to or slightly greater than the dark-adapted pupil diameter provides a sufficient diameter of corneal surface to focus light arising from objects in the paracentral and peripheral visual field.

SETTING

Department of Ophthalmology and Visual Sciences, Texas Tech University Health Sciences Center, Lubbock, Texas, USA.

METHODS

An optical model of the anterior segment was developed to calculate the effective corneal refractive diameter (ECRD), which is the diameter of the area of cornea that refracts all incident light rays arising from an object through the physical pupil (PP). This model incorporates the patient variables of central anterior chamber depth (ACD), central corneal curvature (K(c)), and the diameter of the apparent entrance pupil (EP). The model was expanded to incorporate distant objects off the line of sight (LOS), described by their angular displacement from the fixation object in visual space (the object tangent angle delta(ob)). Results were calculated for the 360 meridian degree visual field (ie, for all objects in visual space perceptually displaced from the fixation object by angle delta(ob)). The effect of the prolate nature of the cornea was also investigated.

RESULTS

The ECRD expanded rapidly as a function of PP and delta(ob) but was minimally influenced by K(c). Beyond a critical object tangent angle delta(c), light rays striking the corneal vertex were not refracted through the PP, and the ECRD became an annular surface centered on the corneal vertex. The delta(c) was not a function of K, but increased as the PP increased and decreased as the ACD increased. The prolate nature of the cornea had little influence on the ECRD, even for very peripheral light rays.

CONCLUSIONS

The ECRD expands rapidly when considering distant objects only slightly displaced from the LOS. A patient treated with an optical zone equal to or slightly greater than the dark-adapted pupil diameter may experience vision quality loss for paracentral and midperipheral objects even under conditions of ambient indoor lighting.

Six-month variability of the dark-adapted pupil diameter

PURPOSE

To determine the individual variability of the dark-adapted pupil diameter over 6 months using a standardized dark-adaptation protocol.

SETTING

Texas Tech University Health Sciences Center, Lubbock, Texas, USA.

METHODS

This prospective observational cohort study comprised volunteers with no history of ocular disease, surgery, or injury other than requirement for refractive correction. The right eye was tested. A standardized dark-adaptation protocol was used that controlled for accommodation and patient alertness. Infrared, still digital photographs were taken after 10 minutes of dark adaptation at 1 lux and were analyzed using digital image software. Testing was performed at baseline in the afternoon, at 3 months in the afternoon, and at 6 months in the morning. Lifestyle factors such as diet and exercise were not controlled.

RESULTS

Mean intersession differences were 0.04 mm (95% confidence interval [CI]: -0.68-0.146), 0.15 mm (95% CI: -0.001-0.297), and 0.09 mm (95% CI: -0.048-0.236) for baseline-3 month, baseline-6 month, and 3 month-6 month comparisons, respectively. None of these differences was significantly different from zero (P>.05, 2-tailed Student t tests). The likelihood that the mean intersession difference was >.25 mm was negligible for all comparisons (P=.9996, .9099, and .9829 respectively, 1-tailed Student t tests).

CONCLUSION

When a consistent dark-adaptation protocol that controls for alertness and accommodation is used, normal young individuals showed no significant variation in the dark-adapted pupil diameter over a 6-month period.

Theoretical Effect of Changes in Entrance Pupil Magnification on Wavefront-guided Laser Refractive Corneal Surgery

PURPOSE

To explore theoretically the effect on the correction of higher order aberrations of changes in the magnification between the aperture stop (iris) and entrance pupil of the eye, following myopic excimer laser ablation.

METHODS

Using a simple schematic eye model, paraxial calculations were made of the position and magnification of the entrance pupil of the eye as a function of the power of a myopic photorefractive keratectomy correction.

RESULTS

Corneal flattening following myopic corneal ablation results in a reduction in the magnification between the aperture stop (iris) and entrance pupil. This implies that an ablation designed to correct higher order errors on the basis of the preoperative wavefront aberration across the entrance pupil will result in an incomplete correction. Taking into account the fact that the total ocular aberration depends on the combined effects of all optical components of the eye, which are distributed in depth, rather than being associated simply with the anterior surface of the cornea, the exact effects depend on the methods used to measure the aberration and the distribution of the total aberration between the different components of the eye. The errors in correction increase with the magnitude of the myopic correction.

CONCLUSIONS

To minimize the postoperative higher order aberrations in higher amounts of myopia, it may be desirable to remeasure them after a first ablation to correct the second-order refractive errors and then to carry out a second ablation to correct the higher order aberrations.

Brimonidine versus dapiprazole: Influence on pupil size at various illumination levels

PURPOSE

To evaluate the influence of dapiprazole versus brimonidine on pupil size at various illumination levels.

SETTING

Department of Ophthalmology, Johannes Gutenberg-University, Mainz, Germany.

METHODS

In randomized prospective study, 19 healthy volunteers received 2 ophthalmic solutions, dapiprazole and brimonidine, 1 in each eye, for intraindividual comparison. Before and after application, pupil diameter was measured using an infrared binocular pupillometer at 3 illumination levels (0.03, 0.82, and 6.4 lux).

RESULTS

Only slight pupil dilation was observed under scotopic conditions after application of both agents. After 20 minutes, the median reduction in pupil width was 1.4 mm for brimonidine and 0.9 mm for dapiprazole. These effects were statistically significant for both agents (both P < .001). The maximum effect was observed after 40 minutes and remained stable through the next measurement at 180 minutes. Under mesopic lighting conditions, only a slight effect (<1 mm) was seen.

CONCLUSIONS

Pupil mydriasis at scotopic illumination levels was reduced by both drugs in a similar fashion. Because of the slightly stronger effect of brimonidine, application of this agent 20 minutes before activities in dimly lit areas or at night may be recommended for photic phenomena following refractive surgery.