Videokeratoscope-line-of-sight misalignment and its effect on measurements of corneal and internal ocular aberrations

Linear fitting of biconic surfaces for corneal modeling

This paper presents a method for reconstructing the corneal surface. The proposed method was tested in 56 healthy and 15 post-orthokeratology corneas. The Medmont E300 Corneal Topographer was used to measure the anterior corneal elevation, and custom MATLAB scripts were employed for data analysis, fitting, and other computational processes. The results obtained were compared with the fitting to an ellipsoid and to a biconic, using an alternative method, showing similarities among the different approaches. Additionally, the advantages of this method and the biconic's generality over the ellipsoid were also demonstrated. In conclusion, the method proposed offers an approach with potential applications in the field of visual and ophthalmic optics related with modeling of the cornea and other optical surfaces.

Influence of the Reference Center on the Calculation of Corneal Higher Order Aberrations

PURPOSE

To evaluate the differences in corneal wavefront measurements in myopic and hyperopic eyes when calculated using three different reference centers and explore possible influencing factors for such differences.

METHODS

Corneal wavefront measurements were performed in myopic and hyperopic eyes using a GALILEI Placido Dual Scheimpflug Analyzer (Ziemer Ophthalmic Systems AG). Corneal higher order aberrations (HOAs), including total, vertical, and horizontal coma-like aberrations, spherical aberrations, and total corneal HOAs through a 6-mm pupil size, were calculated over three different reference center positions: pupil center, corneal vertex, and limbus to limbus. Values were then compared between the myopic and hyper-opic eyes, and correlations with kappa distance and spherical equivalent were tested.

RESULTS

A significant decrease in the level of total corneal HOAs (-0.04 ± 0.05 and -0.12 ± 0.09), total corneal coma (-0.07 ± 0.09 and -0.18 ± 0.12), and horizontal coma (-0.07 ± 0.11 and -0.22 ± 0.11) in myopic and hyperopic eyes, respectively, was found when recalculating from pupil center to corneal vertex centration, whereas a significant increase in the same aberrations was observed from pupil center or corneal vertex to limbus to limbus. Significant correlations were found between the kappa distance and changes in total corneal HOAs, total corneal coma, and horizontal coma from the pupil center to the corneal vertex in both groups.

CONCLUSIONS

Corneal vertex centration generated the lowest level of corneal wavefront error in both groups. The differences in corneal aberrations between the reference centers for calculation were highly correlated with the kappa distance in hyperopic eyes. [J Refract Surg. 2023;39(5):340-346.].

Distribution of angle lambda and pupil offset as measured by combined Placido Scheimpflug Topography

BACKGROUND

Angle lambda is the angle between the pupillary axis and the line of sight. It is important for accurate centration during anterior segment surgery. The purpose of this study is to identify the distribution of angle lambda and pupil center offset as measured by a combined placido disc Scheimpflug topography system.

METHODS

A prospective non-randomized study was performed on 2178 eyes in Eye World Hospital, Giza, Egypt. Sirius device (CSO, Costruzione Strumenti Oftalmici, Florence, Italy, version 3.2.1.60) was used to measure average keratometry (K), anterior chamber depth (ACD), central corneal thickness (CCT), horizontal visible iris diameter (HVID), pupil radius (PR), pupil center intercept x-component (PCI-x), and pupil center intercept y-component (PCI-y). Axial length (AL) was measured by immersion A-scan Eyecube Ultrasonography device (Ellex, Adelaide, South Australia, Australia). Angle lambda was calculated by a trigonometrical equation. Pearson correlation was used to analyze the correlation between angle lambda and age and refraction.

RESULTS

Average angle lambda in all eyes was 3.32° ± 1.99. Mean angle lambda was significantly smallest in myopia and largest in hyperopia. Age correlation to angle lambda was insignificant. Average PCI-x and PCI-y in all eyes was - 0.047 mm and + 0.091 mm, respectively.

CONCLUSIONS

Angle λ is significantly larger in hyperopia than myopia, and the effect of age is insignificant. Pupil center offset was horizontally greater in hyperopia than in myopia. We therefore encourage the preoperative assessment of angle λ to avoid decentered ablation, especially when treating hyperopia.

Ocular aberrations in eyes with Primary Congenital Glaucoma

PURPOSE

To highlight the magnitude of ocular higher order aberrations (HOA) and lower order aberrations (LOA), including component contributions from corneal and internal planes in Primary Congenital Glaucoma (PCG) patients.

METHODS

Consecutive treated PCG patients co-operative for ocular examination and aberrometry, were enrolled over two years for this cross-sectional, comparative, single centre, unmasked study. Best corrected visual acuity, refraction, IOP, wavefront aberrometry and topography (iTrace) were performed and results were compared with unaffected fellow eyes of unilateral glaucoma patients as well as age and sex matched controls with no ocular anomalies other than treatable refractive error.

RESULTS

Both eyes of 32 consecutive PCG patients (17 unilateral, 15 bilateral) and 39 controls were enrolled. The median LogMAR corrected distance visual acuity of PCG eyes was 0.68 (IQR: 0.2 - 1.8). Total ocular (Root mean square (RMS) 1.7µm vs 0.3µm, p = 0.014), corneal (RMS 1.1µm vs 0.3µm, p = 0.004) and internal (RMS 1.1µm vs 0.2µm, p = 0.013) aberrations, as well as HOAs and LOAs at each plane were significantly higher in PCG eyes than in controls. Component HOAs from corneal and internal planes were positively correlated with each other (p < 0.001; rs: 0.7). Total aberrations were greater in the affected eyes of PCG compared to the rest. The predominant subtype of HOAs in PCG were coma and trefoil. PCG with corneal opacity/Haab's striae had significantly higher astigmatism than the affected eyes with clear corneae at corneal plane (p = 0.02). The aberrations were not statistically associated with the corneal diameter or refractive error in PCG eyes.

CONCLUSIONS

Significantly greater aberrations (Total, HOAs and LOAs, at corneal as well as internal plane) were seen among eyes affected with PCG. Though the exact impact of these aberrations on the final visual outcome is difficult to determine, these could play a pertinent role in compromising visual function, thus impacting the management of visual rehabilitation in these patients.

Recent advances in representation of monochromatic aberrations of human eyes

The field of aberrations of the human eye is moving rapidly, being driven by the desire to monitor and optimise vision following refractive surgery. In this paper, I discuss the different ways of representing aberrations of the human eye, the terminology used, how wave aberrations are used to determine refractions, the influence of pupil size on aberrations, how to compare right and left eye aberrations, how aberrations can be manipulated into different forms, how to make corrections for changes in wavelength, the appropriate ocular axis, and corneal and lenticular components of the aberrations.

The effect of intraocular pressure elevation and related ocular biometry changes on corneal OCT speckle distribution in porcine eyes

The aim of this study was to evaluate the influence of increase in intraocular pressure (IOP) and cooccurring changes in ocular biometry parameters on the corneal optical coherence tomography (OCT) speckle distribution in ex-vivo experiments on porcine intact eyes. Twenty-three eyeballs were used in the inflation test where IOP in the anterior chamber was precisely set from 10 mmHg to 40 mmHg in steps of 5 mmHg and where eye biometry was utilized (IOL Master 700). To assess the influence of the duration of the experiment on the OCT speckle statistics, the second experiment was performed with 10 eyeballs at the constant IOP of 15 mmHg. Based on the OCT scans of central cornea (Copernicus REVO), spatial maps of the scale parameter (a) and the shape parameter (v) of the gamma distribution speckle model were estimated. The means of both parameters for each spatial map were computed within the 2 mm of the central stroma. Both distributional parameters statistically significantly varied with IOP and time (one way repeated measures ANOVA, all p-values < 0.001). The a parameter revealed a faster statistically significant increase in IOP up to 25 mmHg, regardless of time. Central corneal thickness (CCT), the anterior chamber depth, and the mean equivalent spherical power varied significantly with IOP, whereas CCT and axial length changed statistically significantly with time. Statistically significant correlation was found between CCT and the a parameter, after removing IOP as a confounding factor (r = -0.576, p < 0.001). The parameters of the gamma distribution can be used not only for identifying IOP induced changes in the optical scattering within the corneal stroma, but also in corneal geometry. The approach of corneal speckle analysis could be potentially utilized for an indirect and noninvasive assessment of some properties of corneal stroma.

Variation of axial and oblique astigmatism with accommodation across the visual field

In this study we investigated the impact of accommodation on axial and oblique astigmatism along 12 meridians of the central 30° of visual field and explored the compensation of corneal first-surface astigmatism by the remainder of the eye's optical system. Our experimental evidence revealed no systematic effect of accommodation on either axial or oblique astigmatism for two adult populations (myopic and emmetropic eyes). Although a few subjects exhibited systematic changes in axial astigmatism during accommodation, the dioptric value of these changes was much smaller than the amount of accommodation. For most subjects, axial and oblique astigmatism of the whole eye are both less than for the cornea alone, which indicates a compensatory role for internal optics at all accommodative states in both central and peripheral vision. A new method for determining the eye's optical axis based on visual field maps of oblique astigmatism revealed that, on average, the optical axis is 4.8° temporal and 0.39° superior to the foveal line-of-sight in object space, which agrees with previous results obtained by different methodologies and implies that foveal astigmatism includes a small amount of oblique astigmatism (0.06 D on average). Customized optical models of each eye revealed that oblique astigmatism of the corneal first surface is negligible along the pupillary axis for emmetropic and myopic eyes. Individual variation in the eye's optical axis is due in part to misalignment of the corneal and internal components that is consistent with tilting of the crystalline lens relative to the pupillary axis.

Method of locating the visual axis objectively

PURPOSE

To locate the visual axis of the eye objectively.

METHOD

Based on three-beam scanning laser radar microprofilometry, a technique is proposed to objectively locate the visual axis of the eye. The laser beam consists of three components, two of them being shifted relatively to the central one by differing frequencies, filtered in spatially orthogonal directions. The centre of the foveola is defined as the crossing of steepest inclinations determined in the specific beam positions on the trajectory of scanning. The position of the cornea crossing by the visual axis is designated by the optical axis of the measuring instrument.

RESULTS

Nanometer sensitivity was confirmed in a preliminary test.

CONCLUSIONS

The proposed technique can be incorporated into any clinical wavefront sensing instrument and can be used for centration-sensitive vision correction, as well as for other instances when knowing the exact position of the fovea is important.

Spherical aberration reduction in nuclear cataracts

PURPOSE

To measure higher-order aberrations (HOAs) in nuclear cataracts and to investigate spherical aberration changes with nuclear cataract progression.

METHODS

A total of 102 eyes of older subjects (>50 years) were classified based on the nuclear opalescence (NO) grading of the Lens Opacities Classification System III: Group 1 (< NO2, 35), 2 (NO2, 23), 3 (NO3, 23), and 4 (≥ NO 4:21 eyes). Wave front measurements were performed with a Hartmann-Shack aberrometer. To investigate lenticular spherical aberration, HOAs were examined in 28 eyes before and after phacoemulsification, followed by insertion of an aberration-free intraocular lens. The relationship between lens opacity grade and ocular and lenticular spherical aberrations were investigated.

RESULTS

Mean spherical aberrations in groups 1, 2, 3, and 4 were 0.25 ± 0.10, 0.16 ± 0.13, 0.12 ± 0.15, and 0.10 ± 0.20 μm, respectively, and showed a significant difference with nuclear opacity grading (p = 0.001). The spherical aberration showed negative associations with nuclear opacity grading (r = -0.408, p < 0.001). The predominant change in HOAs after phacoemulsification was an increase in spherical aberration, and 86 % of lenticular spherical aberrations were presumed to have negative values. The lenticular spherical aberration was negatively correlated with nuclear opacity severity (r = -0.409, p = 0.031).

CONCLUSIONS

Ocular spherical aberration decreases with the progression of nuclear cataracts due to the negative correlation between lenticular spherical aberration and nuclear opacity severity.

The Role of Aberrometry in Accommodative Spasm After Myopic Photorefractive Keratectomy

PURPOSE

To report the role of aberrometry in a case of accommodative spasm following myopic photorefractive keratectomy (PRK).

METHODS

Observational case report.

RESULTS

One month following myopic PRK, a 33-year-old healthy woman complained of seeing multiple images and headache that interfered with her daily activities. Her corrected distance visual acuity (CDVA) was 20/40 in the right eye and 20/25 in the left eye with a manifest refraction of -0.75 -0.50 × 165° in the right eye and plano -0.50 × 20° in the left eye. Cycloplegic refraction was plano -0.50 × 165° in the right eye and plano -0.5 × 20° in the left eye. Ray tracing aberrometry showed variable refraction with increase in internal defocus, which after cycloplegia reduced from 1.019 to 0.142 µm in the right eye and 0.366 to 0.230 µm in the left eye. Total ocular aberrations decreased by 53.16% in the right eye (range: 1.511 to 0.708 µm) and 18.77% (range: 0.671 to 0.545 µm) in the left eye; corresponding simulated Snellen visual acuity charts also showed improvement. The patient was treated with one drop of cyclopentolate 1% three times a day for 6 weeks, following which headache and ghosting of images completely resolved.

CONCLUSIONS

Accommodative spasm should be considered in patients with visual disturbances of uncertain causes following myopic refractive surgery. Ray tracing aberrometry can serve as a diagnostic and educative tool in managing such patients.

Centration axis in refractive surgery

The human eye is an asymmetric optical system and the real cornea is not a rotationally symmetrical volume. Each optical element in the eye has its own optical and neural axes. Defining the optimum center for laser ablation is difficult with many available approaches. We explain the various centration approaches (based on these reference axes) in refractive surgery and review their clinical outcomes. The line-of-sight (LOS) (the line joining the entrance pupil center with the fixation point) is often the recommended reference axis for representing wavefront aberrations of the whole eye (derived from the definition of chief ray in geometrical optics); however pupil centration can be unstable and change with the pupil size. The corneal vertex (CV) represents a stable preferable morphologic reference which is the best approximate for alignment to the visual axis. However, the corneal light reflex can be considered as non-constant, but dependent on the direction of gaze of the eye with respect to the light source. A compromise between the pupil and CV centered ablations is seen in the form of an asymmetric offset where the manifest refraction is referenced to the CV while the higher order aberrations are referenced to the pupil center. There is a need for a flexible choice of centration in excimer laser systems to design customized and non-customized treatments optimally.

An analytical method for predicting the geometrical and optical properties of the human lens under accommodation

We present an analytical method to describe the accommodative changes in the human crystalline lens. The method is based on the geometry-invariant lens model, in which the gradient-index (GRIN) iso-indicial contours are coupled to the external shape. This feature ensures that any given number of iso-indicial contours does not change with accommodation, which preserves the optical integrity of the GRIN structure. The coupling also enables us to define the GRIN structure if the radii and asphericities of the external lens surfaces are known. As an example, the accommodative changes in lenticular radii and central thickness were taken from the literature, while the asphericities of the external surfaces were derived analytically by adhering to the basic physical conditions of constant lens volume and its axial position. The resulting changes in lens geometry are consistent with experimental data, and the optical properties are in line with expected values for optical power and spherical aberration. The aim of the paper is to provide an anatomically and optically accurate lens model that is valid for 3 mm pupils and can be used as a new tool for better understanding of accommodation.

Predicting ocular residual astigmatism using corneal and refractive parameters: a myopic eye study

PURPOSE

To investigate the nature of ocular residual astigmatism (ORA) in myopic patients and to identify indicators to predict a patient's ORA from corneal and ocular refractive data.

METHODS

In total, 356 myopic eyes from 178 patients (M:F = 41:137) were examined using a Scheimpflug keratometer (Pentacam) and a wavefront analyzer (WaveScan). Vertex distance-adjusted total ocular astigmatism and corneal astigmatism [anterior corneal power (ACP) and true net power (TNP)] were used to calculate ORA, respectively. A power vector system (J0 and J45) was adopted for the astigmatism analysis.

RESULTS

The mean age of the study eyes was 27.6 ± 5.0 years, and mean refractive spherical equivalent, sphere and cylinder was -4.94 ± 1.90 diopter, -4.42 ± 1.87 diopter, and -1.05 ± 0.82, respectively. Corneal astigmatism measured by TNP was more representative of total ocular astigmatism than ACP (p < 0.001). Both the J0 and J45 components of ORA showed significant negative correlation with corneal astigmatism measured by ACP and TNP (p < 0.001). ORA (J0 and J45) was negatively correlated with total ocular spherical equivalent and positively correlated with total ocular astigmatism.

CONCLUSIONS

We verified the general compensatory effect of corneal astigmatism by internal optics in myopic patients. TNP was closer to refractive astigmatism than ACP was. Total ocular spherical equivalent and total ocular astigmatism showed significant correlation with ORA. Therefore these can be possible indicators to predict ORA.

Repeatability of internal aberrometry with a new simultaneous capture aberrometer/corneal topographer

PURPOSE

To compare repeatability of internal eye aberrations derived from aberrometry and corneal topography (CT) measured simultaneously by the Innovative Visual Systems Discovery, against time displaced but same instrument measurement (Nidek OPD-Scan 3), and time displaced different instrument measurement (Medmont E300 and Imagine Eyes irx3).

METHODS

Three aberrometry and CT measurements were captured with each instrument, except for the OPD-Scan 3 where three aberrometry scans were followed by a single CT. Measurements were repeated across 2 days. Corneal surface Zernike coefficients were derived from CT and subtracted from aberrometry to establish internal aberration coefficients. For the OPD-Scan 3, internal Zernike coefficients were derived by the instrument's software. Repeatability for second-order root mean square (RMS), spherical aberration, coma RMS, trefoil RMS, and the refraction components M, J0, and J45 were assessed using intraclass correlation coefficient (ICC).

RESULTS

Intrasession repeatability was similar between the Discovery and E300/irx3, with the E300/irx3 slightly more repeatable for second-order RMS. Across days, the Discovery was most repeatable for second-order RMS (ICC 0.98) followed by the E300/irx3 (ICC 0.96) and OPD-Scan 3 (ICC 0.88). All instruments were less repeatable for higher order aberrations with only the Discovery moderately repeatable for spherical aberration and trefoil RMS (both ICC ≥ 0.75). The Discovery was highly repeatable for all derived refractive components (ICC ≥ 0.96). The E300/irx3 was highly repeatable for M (ICC 0.98) and moderately repeatable for J0 (ICC 0.89). The OPD-Scan 3 was highly repeatable for the M component (ICC 0.98) but not repeatable for the cylindrical components.

CONCLUSIONS

The Discovery was highly repeatable for second-order RMS and derived refractive components. The lower repeatability for internal higher order aberrations measured with all instruments suggests caution in their use until further work is carried out to investigate sources of error and to develop methods to improve repeatability.

Effect of age on components of peripheral ocular aberrations

PURPOSE

To investigate the effect of age on the contributions of the anterior cornea and internal components to ocular aberrations in the peripheral visual field.

METHODS

Ocular aberrations were measured in 10 young emmetropes and 7 older emmetropes using a modified commercial Hartmann-Shack aberrometer across 42° × 32° of central visual field. Anterior corneal aberrations were estimated from anterior corneal topography using theoretical ray-tracing. Internal aberrations were calculated by subtracting anterior corneal aberrations from ocular aberrations.

RESULTS

Anterior corneal aberrations of young subjects were reasonably compensated by the internal aberrations, except for astigmatism for which the internal contribution was small out to the 21° field limit. The internal coma and spherical aberration of the older subjects were considerably smaller in magnitude than those of the young subjects such that the compensation for anterior corneal aberrations was poorer. This can be explained by age-related changes in the lens shape and refractive index distribution.

CONCLUSIONS

Loss of balance between anterior cornea and internal components of higher order aberrations with increasing age, found previously for on-axis vision, applies also to the peripheral visual field.

Role of the human lens gradient-index profile in the compensation of third-order ocular aberrations

The open question regarding the compensation of the ocular aberrations between the cornea and the lens is currently being investigated. We report additional insights considering the role of the lens gradient-index (GRIN) profile in third-order ocular aberrations, since this profile changes through life. Thus, we have calculated the contribution of that profile to the ocular aberrations with aging by applying the Seidel third-order theory of tilted and decentered elements, and by using a schematic-eye model. The results show the GRIN profile is needed to account for the decoupling of the aberrations between the cornea and the lens because the geometrical changes of the ocular surfaces with aging are not enough. Therefore, the current developments of aging human-eye models, as well as the experimental studies, cannot neglect the changes of the lens GRIN structure through life when modelling mechanisms of the compensation of ocular aberrations.

Corneal biometry from volumetric SDOCT and comparison with existing clinical modalities

We present a comparison of corneal biometric values from dense volumetric spectral domain optical coherence tomography (SDOCT) scans to reference values in both phantoms and clinical subjects. We also present a new optically based "keratometric equivalent power" formula for SDOCT that eliminates previously described discrepancies between corneal power form SDOCT and existing clinical modalities. Phantom objects of varying radii of curvature and corneas of normal subjects were imaged with a clinical SDOCT system. The optically corrected three-dimensional surfaces were used to recover radii of curvature and power as appropriate. These were then compared to the manufacturer's reference values in phantoms and to measurements from topography and Scheimpflug photography in subjects. In phantom objects, paired differences between SDOCT and reference values for radii of curvature were not statistically significant. In subjects, there were no significant paired differences between SDOCT and reference values from the other modalities for anterior radius and corneal keratometric power. In contrast to other studies, we found that dense volumetric scans with available SDOCT can be used to recover corneal biometric values-including power-that correspond well with existing clinical measurements.

Investigation of the isoplanatic patch and wavefront aberration along the pupillary axis compared to the line of sight in the eye

Conventional optical systems usually provide best image quality on axis, while showing unavoidable gradual decrease in image quality towards the periphery of the field. The optical system of the human eye is not an exception. Within a limiting boundary the image quality can be considered invariant with field angle, and this region is known as the isoplanatic patch. We investigate the isoplanatic patch of eight healthy eyes and measure the wavefront aberration along the pupillary axis compared to the line of sight. The results are used to discuss methods of ocular aberration correction in wide-field retinal imaging with particular application to multi-conjugate adaptive optics systems.

An indirect method to compare the reference centres for corneal measurements

PURPOSE

Corneal measurements are commonly presented with respect to a specific reference centre, but the location of the reference centre on the corneal surface could vary from one diagnostic modality to another. This study aimed to develop a method for comparing reference centres used by corneal measurement systems.

METHODS

An indirect method was developed to compare reference centres by making use of the pupil centre and its offset from the reference centre. Reference centres in a Scheimpflug imaging system, the Pentacam HR, and a Placido-ring corneal topography system, the ATLAS Corneal Topography System, were compared for the right and left eyes of 30 subjects. The subjects all had similar pupil sizes when measured by the two systems. Differences and correlations of the pupil centre offsets between the two systems were statistically tested and compared by Bland-Altman analyses.

RESULTS

There were no significant differences in mean pupil offsets between the two systems for either the right or left eyes (p > 0.05). There were strong correlations of the pupil centre offsets between the two systems for each eye (right eye x-axis: r = 0.95, p < 0.0001; right eye y-axis: r = 0.98, p < 0.0001; left eye x-axis: r = 0.96, p < 0.0001, left eye y-axis: r = 0.93, p < 0.0001). Bland-Altman analyses revealed no significant differences in pupil centre offsets between the two systems.

CONCLUSIONS

The Pentacam HR system and the ATLAS system have very similar reference centres. Thus it is possible to directly analyze data from the Pentacam HR and other instruments using the corneal vertex or the pupil centre as the reference centres due to the similarity in the reference centre settings between the two systems.

Clinical validation of point-source corneal topography in keratoplasty

PURPOSE

To validate the clinical performance of point-source corneal topography (PCT) in postpenetrating keratoplasty (PKP) eyes and to compare it with conventional Placido-based topography.

METHODS

Corneal elevation maps of the anterior corneal surface were obtained from 20 post-PKP corneas using PCT (VU topographer, prototype; VU University Medical Center, Amsterdam, The Netherlands) and Placido-based topography (Keratron, Optikon 2000, Rome, Italy). Corneal surface parameters are calculated in terms of radius and asphericity. Corneal aberrations were characterized using standard Zernike convention. An artificial surface with quadrafoil feature (SUMIPRO, Almelo, The Netherlands) was measured and used as a reference to assess instrument performance compared with the gold standard.

RESULTS

The differences (mean ± std of PCT - Placido) found between the two types of topographers in measurements of post-PKP eyes are 0.02 ± 0.21 mm (p=0.64) for radius of curvature, 0.14 ± 0.49 (p=0.23) for asphericity, -0.19 ± 1.67 μm (p=0.61) for corneal astigmatism, -0.25 ± 1.34 μm (p=0.41) for corneal coma, 0.23 ± 0.82 μm (p=0.23) for corneal trefoil, and 0.15 ± 0.28 μm (p=0.02) for corneal quadrafoil. The PCT measured the artificial surface more accurate (rms error 0.16 μm; 0.12 eq. Dpt.) than the Placido-based topographer (rms error 1.50 μm; 1.15 eq. Dpt.).

CONCLUSIONS

PCT is more accurate than Placido-based topography in measuring quadrafoil aberration.

Intrasubject repeatability of internal aberrometry obtained with a new integrated aberrometer

PURPOSE

To evaluate the intrasubject repeatability of the internal aberrometry obtained with a new integrated aberrometer in a sample of normal eyes to assess its clinical usefulness.

METHODS

Twenty-six healthy eyes of 26 participants, aged 20 to 50 years, were included in the study. All eyes achieved corrected distance visual acuity of 1.0 (Snellen decimal notation) and did not undergo previous ocular surgeries. Three consecutive measurements of internal aberrations were obtained with the KR-1W system (Topcon Corp) by an experienced examiner. Intrasubject repeatability for 4- and 6-mm pupils was evaluated by the within-subject standard deviation (S(w)) and intraclass correlation coefficient (ICC).

RESULTS

Low values of S(w) and values of ICC close to 1 were found for the 4-mm pupil astigmatism and for several aberrometric coefficients: primary spherical aberration and higher order, third order, and trefoil root-mean-square (RMS). Significant correlations of the S(w) for the 4-mm pupil higher order aberrations RMS with the magnitude of different aberrometric coefficients were found (r≥0.611, P<.01). In addition, tetrafoil RMS for 4-mm pupils correlated significantly with the S(w) for some higher order errors (r≥0.675, P<.01). Significantly larger values of S(w) for 6-mm pupils were found for trefoil (P<.01) and secondary astigmatism RMS (P=.02).

CONCLUSIONS

The KR-1W provided repeatable measurements of internal astigmatism and some higher order aberrations, although consistency of such measurements appears to be limited by the level of aberration.

Reconstructing ocular surfaces by Purkinje images using an exact ray approach: estimating IOL decenter and tilt

Recently, an alternate method for recovering the shape of the anterior surface of an intraocular lens (IOL) (by Purkinje images), and capable of returning a Zernike polynomial representation of that surface, was proposed (Ophthal. Physiol Opt., 29, 2009, 80-91). However, in moving toward a clinically applicable method, it is important to estimate parameters such as surface radius, lens tilt and decenter. Previously, radius of curvature (for the anterior surface of an IOL) was estimated by finding the best-fit sphere. A methodology is presented here to recover lens tilt and decenter using this alternate method. The theory is developed and then tested in simulation. An IOL is added to the Navarro eye, and then recovered by assuming: (i) the same 'full eye', and (ii) a reduced two surface version (the 'simplified' eye). A number of decenter and tilt settings are tested, from which root mean squared (RMS) surface errors, best-fit spheres, tilt and decenter values are estimated. Mis-measurement of the axial position of the posterior surface of the IOL is also simulated. The full eye model produces low RMS surface and radii of curvature errors, that increase linearly with axial shift. The error behaviour is not greatly affected by changes in IOL decenter and/or tilt. The simplified eye (n = 1.32 for aqueous) with n = 1.4760 (at lambda = 880 nm) for the IOL, fits the 'full eye' results most consistently. Lens decenter is consistently estimated to within 0.015 mm (for a 1 mm decenter), and tilt <0.15 degrees (for a 5 degree tilt).

Forward ray tracing for image projection prediction and surface reconstruction in the evaluation of corneal topography systems

A forward ray tracing (FRT) model is presented to determine the exact image projection in a general corneal topography system. Consequently, the skew ray error in Placido-based topography is demonstrated. A quantitative analysis comparing FRT-based algorithms and Placido-based algorithms in reconstructing the front surface of the cornea shows that arc step algorithms are more sensitive to noise (imprecise). Furthermore, they are less accurate in determining corneal aberrations particularly the quadrafoil aberration. On the other hand, FRT-based algorithms are more accurate and more precise showing that point to point corneal topography is superior compared to its Placido-based counterpart.

Comparison of corneal and total ocular aberrations before and after myopic LASIK

PURPOSE

To assess the compensation of total ocular and corneal wavefront aberrations after conventional myopic LASIK.

METHODS

This study comprised 57 eyes of 57 patients. Total and corneal aberrations were measured preoperatively and 3 months postoperatively using the OPD-Scan (NIDEK Co Ltd) aberrometer. Total and corneal aberrations root-mean-square (RMS) was calculated out to the 6th Zernike order for a 6.0-mm pupil diameter. The percentage increase postoperatively was defined by the ratio of RMS pre- and postoperatively for each corneal and total eye group. The compensation between corneal and internal aberrations for a given aberration group was defined as: (corneal aberration group RMS - total eye aberration group RMS)/corneal aberration group RMS.

RESULTS

Postoperatively, higher order aberrations increased by a factor of 1.77+/-1.26 (total) and 2.47+/-2.25 (corneal) (P<.05). Coma aberration increased by a factor of 2.43+/-2.61 (total) and 2.56+/-2.66 (corneal). Spherical aberration increased by a factor of 1.46+/-1.83 (total) and 2.64+/-2.24 (corneal). The values of the ratio of compensation did not change significantly before and after LASIK for individual aberrations (P>.05).

CONCLUSIONS

Although myopic LASIK induced significant corneal aberrations, the level of partial compensation of corneal aberrations by internal structures remained unchanged. These results suggest that the previously described emmetropization that is effective during development may also be effective with acquired variations in corneal shape.

3D refraction correction and extraction of clinical parameters from spectral domain optical coherence tomography of the cornea

Capable of three-dimensional imaging of the cornea with micrometer-scale resolution, spectral domain-optical coherence tomography (SDOCT) offers potential advantages over Placido ring and Scheimpflug photography based systems for accurate extraction of quantitative keratometric parameters. In this work, an SDOCT scanning protocol and motion correction algorithm were implemented to minimize the effects of patient motion during data acquisition. Procedures are described for correction of image data artifacts resulting from 3D refraction of SDOCT light in the cornea and from non-idealities of the scanning system geometry performed as a pre-requisite for accurate parameter extraction. Zernike polynomial 3D reconstruction and a recursive half searching algorithm (RHSA) were implemented to extract clinical keratometric parameters including anterior and posterior radii of curvature, central cornea optical power, central corneal thickness, and thickness maps of the cornea. Accuracy and repeatability of the extracted parameters obtained using a commercial 859nm SDOCT retinal imaging system with a corneal adapter were assessed using a rigid gas permeable (RGP) contact lens as a phantom target. Extraction of these parameters was performed in vivo in 3 patients and compared to commercial Placido topography and Scheimpflug photography systems. The repeatability of SDOCT central corneal power measured in vivo was 0.18 Diopters, and the difference observed between the systems averaged 0.1 Diopters between SDOCT and Scheimpflug photography, and 0.6 Diopters between SDOCT and Placido topography.

Total, corneal, and internal ocular optical aberrations in patients with keratoconus

PURPOSE

To measure and compare total, corneal, and internal ocular aberrations using combined wavefront analysis and corneal topography in eyes with keratoconus and eyes with normal corneas.

METHODS

This prospective study comprised eyes of patients with keratoconus and myopic patients seeking refractive surgery. Patients diagnosed with keratoconus and with a classification of "normal" or "keratoconus" on the NIDEK Corneal Navigator corneal disease screening software were selected for inclusion in this study. The normal group comprised eyes with a "normal" classification with 99% similarity. In the normal group, only one eye per patient was randomly selected based on a randomization schedule. Corneal, internal, and total wavefront measurements were provided by the NIDEK OPD-Scan II.

RESULTS

One hundred eyes with keratoconus and 155 normal eyes were enrolled in the study. Statistically significant higher corneal and internal higher order aberrations were observed in the eyes with keratoconus (P<.05). However, an increase in ocular higher order aberrations proportional to corneal higher order aberrations was not observed in the keratoconus group.

CONCLUSIONS

A compensatory effect of increased anterior corneal aberrations by internal aberrations in keratoconic eyes was present for some aberrations. The origin of this compensation and the optical mechanism behind it requires further study.

High-accuracy wavefront control for retinal imaging with Adaptive-Influence-Matrix Adaptive Optics

We present an iterative technique for improving adaptive optics (AO) wavefront correction for retinal imaging, called the Adaptive-Influence-Matrix (AIM) method. This method is based on the fact that the deflection-to-voltage relation of common deformable mirrors used in AO are nonlinear, and the fact that in general the wavefront errors of the eye can be considered to be composed of a static, non-zero wavefront error (such as the defocus and astigmatism), and a time-varying wavefront error. The aberrated wavefront is first corrected with a generic influence matrix, providing a mirror compensation figure for the static wavefront error. Then a new influence matrix that is more accurate for the specific static wavefront error is calibrated based on the mirror compensation figure. Experimental results show that with the AIM method the AO wavefront correction accuracy can be improved significantly in comparison to the generic AO correction. The AIM method is most useful in AO modalities where there are large static contributions to the wavefront aberrations.

Performance in specular reflection and slit-imaging corneal topography

PURPOSE

Assessment of the relative performance in measuring corneal shape and corneal aberrations for two specular reflection topographers: Keratron Placido Ring Topographer, VU Topographer, and two slit-lamp imaging instruments: Orbscan II and Topcon SL-45 Scheimpflug.

METHODS

Corneal height maps of the anterior corneal surface were obtained from a group of 34 subjects with all four instruments; posterior corneal surface height maps were only obtained with the two slit-lamp imaging instruments. Corneal surface shapes are calculated in terms of radius of curvature and asphericity fitting an aspheric model. Wave aberrations for the anterior corneal surface and the total cornea are determined up to and including sixth order Zernike convention by means of ray tracing.

RESULTS

Clinical relevant differences were observed for radius of curvature of the anterior corneal surface, where the slit-imaging instruments measure higher values (mean difference = 0.05 mm, p < 0.05) and anterior corneal astigmatism for which the Orbscan II measures higher values than the VU Topographer [mean difference = 0.174 microm (0.134 Equivalent Diopters), p < 0.01]. Small significant differences were observed for asphericity and spherical aberration of the anterior corneal surface; however, these are not clinically relevant. Clinically relevant differences were also observed for posterior radius (difference = 0.135 mm p < 0.001), total corneal astigmatism (difference = 0.207 microm (0.159 Equivalent Diopters), p = 0.001), and central corneal thickness (CCT) (difference = -18.6 microm, p < 0.001). The differences found for total corneal coma and trefoil were not clinical relevant. Furthermore, the precision of the specular reflection topographers is superior to that of the slit-lamp instruments by at least a factor of two.

CONCLUSIONS

For traditional spectacle and contact lens applications, the corneal topographers are interchangeable except for measuring anterior radius of curvature. However, for more modern techniques as customized corneal refractive surgery, the subtle differences (e.g., total corneal astigmatism and CCT) between the instruments are clinically relevant.

Importance of fixation, pupil center, and reference axis in ocular wavefront sensing, videokeratography, and retinal image quality

PURPOSE

To examine the impact of the location of the fixation target, pupil center, and reference axis of ophthalmic aberrometers and videokeratographers on the measurement of corneal aberrations relevant to vision.

SETTING

Clinical Research, Visual Optics Institute, College of Optometry, University of Houston, Houston, Texas, USA.

METHODS

The design features of a generic aberrometer and videokeratographer and their interaction with the eye were examined. The results provided a theoretical framework for experimental assessment of pupil translation errors on corneal aberrations relevant to vision and their correction in 129 eyes.

RESULTS

Two key principles emerged. First, the aberrometer's measurement axis must coincide with the eye's line-of-sight (LoS). Second, the videokeratographer's measurement axis (the vertex normal) must be parallel with the eye's LoS. When these principles are satisfied, the eye will be in the same state of angular rotation and direct comparison of measurements is justified, provided any translation of the pupil from the vertex normal is taken into account. The error incurred by ignoring pupil displacement in videokeratography varies between eyes and depends on the type of aberration and amount of displacement, with the largest residual correction root-mean-square wavefront error being 1.26 mum over a 6.0 mm pupil, which markedly decreases retinal image quality.

CONCLUSION

Translation of the pupil center with respect to the vertex normal in videokeratography should not be ignored in the calculation of the corneal first-surface, internal aberrations of the eye relevant to vision, or the design of refractive corrections based on videokeratography.

Laser in situ keratomileusis disrupts the aberration compensation mechanism of the human eye

PURPOSE

To study how changes induced on corneal optics by myopic and hyperopic laser in situ keratomileusis (LASIK) refractive surgery affect the aberration compensation mechanism.

DESIGN

Interventional case series and modeling theory.

METHODS

We measured ocular, corneal, and internal aberrations for a 6-mm pupil in 15 myopic and 6 hyperopic eyes with similar age range before and 6 months after standard LASIK. Ocular aberrations were measured using our own developed Hartmann-Shack wavefront sensor, whereas corneal aberrations were calculated by using the elevation data obtained by corneal topography. Ocular, corneal, and internal root mean square (RMS), spherical aberration (SA), coma, and compensation factor were compared for each patient.

RESULTS

After myopic LASIK, we obtained an average 1.6-fold increase in ocular RMS, mainly positive SA, and coma, associated with a similar increase in corneal aberrations. In the hyperopes, we found a higher (2.3-fold) induction of ocular aberrations after surgery, mainly negative SA and coma, but without net increases of corneal aberrations. Aberration compensation clearly decreased or even inverted after hyperopic LASIK, decreasing the ocular optical quality in a higher level than myopic LASIK.

CONCLUSIONS

Although ocular aberrations after myopic LASIK usually were smaller than corneal aberrations because of partial compensation of SA, after hyperopic LASIK, because of induction of negative SA and change in coma, disruption of the compensation mechanism lead to a larger increase of ocular aberrations. Customized procedures should maintain the natural compensation to achieve improved visual outcomes.

Calculating Angle Lambda (λ) Using Zernike Tilt Measurements in Specular Reflection Corneal Topography

Purpose

To develop a method to calculate the angle λ of the human eye using Zernike tilt measurements in specular reflection corneal topography.

Methods

The meaning of Zernike tilt in specular reflection corneal topography is demonstrated by measurements on translated artificial surfaces using the VU Topographer. The relationship derived from the translation experiments is used to determine the angle λ. Corneal surfaces are measured for a set of eight different fixation points, for which tilt angles ρ are obtained from the Zernike tilt coefficients. The angles ρ are used with respect to the fixation target angles to determine angle λ by fitting a geometrical model. This method is validated with Orbscan II's angle-κ measurements in 9 eyes.

Results

The translation experiments show that the Zernike tilt coefficient is directly related to an angle ρ, which describes a tilt orientation of the cornea and can therefore be used to derive a value for angle λ. A significant correlation exists between measured values for angle λ with the VU Topographer and the angle κ with the Orbscan II (r=0.95, P<0.001). A Bland-Altman plot indicates a mean difference of -0.52 degrees between the two instruments, but this is not statistically significant as indicated by a matched-pairs Wilcoxon signed-rank test (P≤0.1748). The mean precision for measuring angle λ using the VU topographer is 0.6±0.3 degrees.

Conclusion

The method described above to determine angle λ is sufficiently repeatable and performs similarly to the angle-κ measurements made with the Orbscan II.

On the compensation of horizontal coma aberrations in young human eyes

The nature of the compensation of horizontal coma (Z(3)(1)) between optical elements of the human eye has been studied and the compensative mechanism has been attributed to a passive process linked to angle kappa of the eye. We measured the horizontal coma in the anterior cornea, the whole eye and the internal optics for 221 young subjects. Thirty-three eyes with minimum angle lambda and 53 eyes with relatively large angle lambda were selected from these eyes to test the hypothesis that horizontal coma compensation is linked to angle kappa. Significant horizontal coma in the anterior cornea was observed for the group with minimum angle lambda in both the right (-0.12 +/- 0.07 microm) and left eyes (0.12 +/- 0.10 microm), and this was well compensated by the internal optics so that the level of horizontal coma in the whole eye over a 6-mm pupil size was very low (-0.05 +/- 0.07 microm for OD and 0.02 +/- 0.08 microm for OS). The horizontal coma in the anterior cornea was significantly correlated to the horizontal coma in the internal optics for both the right and the left eye. The results suggest that there is another source of horizontal coma, in addition to that linked to angle kappa, in the anterior cornea, and also a new compensative mechanism to balance the corneal coma, perhaps in the posterior cornea or the lens.

Posterior corneal aberrations and their compensation effects on anterior corneal aberrations in keratoconic eyes

PURPOSE

To characterize posterior corneal aberrations in keratoconic (KC) eyes and investigate compensatory effects between anterior and posterior corneal surfaces.

METHODS

The corneal topography of 113 eyes (37 advanced KC, 31 moderate KC, 14 mild KC, and 31 normal eyes) was used to compute the corneal aberrations. The central 6-mm diameter of both anterior and posterior corneal topographies was decomposed into Zernike polynomials. The magnitude and the orientation of each posterior corneal aberration were calculated by vector analysis. The compensation effects between anterior and posterior corneal aberrations were also assessed quantitatively with a linear regression model.

RESULTS

The average higher order RMS wavefront errors for the posterior corneas were 1.04, 0.54, 0.24, and 0.19 microm in the advanced, moderate, and mild KC and normal eyes, respectively. In the advanced KC eyes, posterior corneal coma was oriented in the superior-nasal direction with a mean orientation angle of 75 degrees +/- 19 degrees OD and 78 degrees +/- 20 degrees OS. On average, 22%, 24%, and 14% of the anterior corneal coma were compensated by the posterior cornea in the advanced, moderate, and mild KC eyes, respectively. However, no significant higher order aberration (HOA) compensation effects were found in normal corneas.

CONCLUSIONS

Significantly larger amounts of posterior corneal aberrations and stronger compensation effects were observed in KC eyes than in normal eyes. The uncorrected posterior corneal aberration in KC eyes was substantial and degraded retinal image quality. This may explain the relatively poor visual acuity obtained in eyes with rigid gas permeable (RGP) lenses, which correct only anterior corneal aberrations.

Wave aberrations in rhesus monkeys with vision-induced ametropias

The purpose of this study was to investigate the relationship between refractive errors and high-order aberrations in infant rhesus monkeys. Specifically, we compared the monochromatic wave aberrations measured with a Shack-Hartman wavefront sensor between normal monkeys and monkeys with vision-induced refractive errors. Shortly after birth, both normal monkeys and treated monkeys reared with optically induced defocus or form deprivation showed a decrease in the magnitude of high-order aberrations with age. However, the decrease in aberrations was typically smaller in the treated animals. Thus, at the end of the lens-rearing period, higher than normal amounts of aberrations were observed in treated eyes, both hyperopic and myopic eyes and treated eyes that developed astigmatism, but not spherical ametropias. The total RMS wavefront error increased with the degree of spherical refractive error, but was not correlated with the degree of astigmatism. Both myopic and hyperopic treated eyes showed elevated amounts of coma and trefoil and the degree of trefoil increased with the degree of spherical ametropia. Myopic eyes also exhibited a much higher prevalence of positive spherical aberration than normal or treated hyperopic eyes. Following the onset of unrestricted vision, the amount of high-order aberrations decreased in the treated monkeys that also recovered from the experimentally induced refractive errors. Our results demonstrate that high-order aberrations are influenced by visual experience in young primates and that the increase in high-order aberrations in our treated monkeys appears to be an optical byproduct of the vision-induced alterations in ocular growth that underlie changes in refractive error. The results from our study suggest that the higher amounts of wave aberrations observed in ametropic humans are likely to be a consequence, rather than a cause, of abnormal refractive development.

The contribution of accommodation and the ocular surface to the microfluctuations of wavefront aberrations of the eye

We have used videokeratoscopy and wavefront sensing to investigate the contribution of the ocular surface and the effect of stimulus vergence on the microfluctuations of the wavefront aberrations of the eye. The fluctuations of the wavefront aberrations were quantified by their variations around the mean and by using power spectrum analysis. Integrated power was determined in two regions: 0.1-0.7 Hz (low frequencies) and 0.8-1.8 Hz (high frequencies). Changes in the ocular surface topography were measured using high-speed videokeratoscopy and variations in the ocular wavefront aberrations were measured with a wavefront sensor. The microfluctuations of wavefront aberrations of the ocular surface were found to be considerably smaller than the microfluctuations of the wavefront aberrations of the total eye. The fluctuations in defocus while viewing a closer target at 2 or 4 D were found to be significantly greater than fluctuations in defocus when viewing a far target. This increase in defocus fluctuations (p < or = 0.001) occurred in both the low- and high-frequency regions of the power spectra.