Scaling Zernike expansion coefficients to different pupil sizes

The Influence of Accommodative Demand on Ocular Aberrations: A Study of Zernike Coefficients Repeatability and Variability

PURPOSE

To evaluate the repeatability of the Zernike coefficients in healthy eyes when monocular accommodation was stimulated at different vergences demands.

METHODS

A total of 36 right eyes from healthy volunteers were prospectively and consecutively recruited for this study. Wavefront aberrometry was conducted to objectively characterize the ocular optical quality during accommodation, from the individual's far point to a 5 D accommodation demand in steps of 0.5 D. The repeatability of Zernike coefficients up to the fourth order was assessed by calculating the within-eye repeatability (Sw), the coefficient of repeatability (CR), the coefficient of variation (CV), and the intraclass correlation coefficient (ICC) as an indicator of measurement reliability.

RESULTS

Correlation among repeated measurements showed high reliability (ICC > 0.513) for all parameters measured except some fourth-order Zernike coefficients, C(4, -4) (ICC < 0.766), C(4, -2) (ICC < 0.875), C(4, 2) (ICC < 0.778) and C(4, 4) (ICC < 0.811). Greater repeatability and less variability were obtained for high-order Zernike coefficients (CR < 0.154), although an increase in CR in the coefficients analyzed was observed with increasing accommodative demand. No clear trend was evident in CV; however, it was observed that the low-order Zernike coefficients exhibit lower CV (CV < 1.93) compared to the high-order Zernike coefficients (CV > 0).

CONCLUSIONS

The reliability of Zernike coefficients up to the fourth order in healthy young individuals demonstrated a strong consistency in measuring terms up to the fourth order, with more variability observed for high-order terms. The Zernike coefficients up to the third order exhibited the highest level of repeatability.

Wide-field optical eye models for emmetropic and myopic eyes

Ocular wavefront aberrations are used to describe retinal image formation in the study and modeling of foveal and peripheral visual functions and visual development. However, classical eye models generate aberration structures that generally do not resemble those of actual eyes, and simplifications such as rotationally symmetric and coaxial surfaces limit the usefulness of many modern eye models. Drawing on wide-field ocular wavefront aberrations measured previously by five laboratories, 28 emmetropic (-0.50 to +0.50 D) and 20 myopic (-1.50 to -4.50 D) individual optical eye models were reverse-engineered by optical design ray-tracing software. This involved an error function that manipulated 27 anatomical parameters, such as curvatures, asphericities, thicknesses, tilts, and translations-constrained within anatomical limits-to drive the output aberrations of each model to agree with the input (measured) aberrations. From those resultant anatomical parameters, three representative eye models were also defined: an ideal emmetropic eye with minimal aberrations (0.00 D), as well as a typical emmetropic eye (-0.02 D) and myopic eye (-2.75 D). The cohorts and individual models are presented and evaluated in terms of output aberrations and established population expectations, such as Seidel aberration theory and ocular chromatic aberrations. Presented applications of the models include the effect of dual focus contact lenses on peripheral optical quality, the comparison of ophthalmic correction modalities, and the projection of object space across the retina during accommodation.

Association of myopia and astigmatism with postoperative ocular high order aberration after small incision lenticule extraction

OBJECTIVE

To investigate the correlation between higher-order aberrations (HOA) after small incision lenticule extraction (SMILE) and the severity of myopia and astigmatism, along with the relevant factors. These findings will provide valuable insights for decreasing the occurrence of HOA after SMILE and enhancing visual quality.

METHODS

A total of 75 patients (150 eyes) with myopia and astigmatism who underwent SMILE were categorized into four groups based on the severity of myopia and astigmatism: Myopia Group 1 (Group M1, spherical diopter ranged from -1.00 D to -4.00 D), Myopia Group 2 (Group M2, spherical diopter ranged from -4.10 D to -10.00 D), Astigmatism Group 1 (Group A1, cylindrical diopter ranged from 0 D to -1.00 D), and Astigmatism Group 2 (Group A2, cylindrical diopter ranged from -1.10 D to -3.00 D). A comprehensive assessment was performed to examine the association between HOA and various relevant factors, including a detailed analysis of the subgroups.

RESULTS

Group M1 had significantly lower levels of total eye coma aberration (CA), corneal total HOA (tHOA), internal tHOA, and vertical CA ( Z 3 - 1 ) after SMILE than Group M2 (P < 0.05). Similarly, Group A1 had significantly lower levels of total eye tHOA, CA, trefoil aberration (TA), corneal tHOA, TA, and vertical TA ( Z 3 - 3 ) after SMILE than Group A2 (P < 0.05). Pearson correlation analysis indicated a statistically significant positive relationship between the severity of myopia/astigmatism and most HOA (P < 0.05). Subgroup evaluations demonstrated a notable increase in postoperative HOA associated with myopia and astigmatism in Groups M2 and A2 compared with the control group. Lenticule thickness, postoperative central corneal thickness (CCT), postoperative uncorrected distance visual acuity (UDVA), and postoperative corneal Km and Cyl were strongly correlated with most HOA. Age, eyes, and postoperative intraocular pressure (IOP) were only associated with specific HOA.

CONCLUSION

HOA positively correlated with the severity of myopia and astigmatism after SMILE. However, this relationship was not linear. HOA after SMILE was influenced by various factors, and additional specialized investigations are required to establish its clinical importance.

Stability of the retinal image under normal viewing conditions and the implications for neural adaptation

Previous studies have demonstrated that the visual system adapts to the specific aberration pattern of an individual's eye. Alterations to this pattern can lead to reduced visual performance, even when the Root Mean Square (RMS) of the wavefront error remains constant. However, it is well-established that ocular aberrations are dynamic and can change with factors such as pupil size and accommodation. This raises an intriguing question: can the neural system adapt to continuously changing aberration patterns? To address this question, we measured the ocular aberrations in four subjects under various natural viewing conditions, which included changes in accommodative state and pupil size. We subsequently computed the associated Point Spread Functions (PSFs). For each subject, we examined the stability in the orientation of the PSFs and analyzed the cross-correlation between different PSFs. These findings were then compared to the characteristics of a distribution featuring PSF shapes akin to random variations. Our results indicate that the changes observed in the PSFs are not substantial enough to produce a PSF shape distribution resembling random variations. This lends support to the notion that neural adaptation is indeed a viable mechanism even in response to continuously changing aberration patterns.

Relationship of Low-luminance Visual Acuity with Ocular Aberrations in Older Participants

SIGNIFICANCE

This study highlights the importance of twilight adaptation for reliable assessment of low-luminance visual acuity and understanding the relationship between low-luminance visual acuity and ocular aberrations.

PURPOSE

The human eye experiences reduced visual acuity as luminance decreases owing to reduced retinal and optical resolutions; however, the details are unclear. This study aimed to quantify the effects of refraction, pupil diameter, and ocular aberrations on visual acuity during the transition from high- to low-light environments, thereby contributing to the standardization of low-luminance visual acuity measurements.

METHODS

In total, 27 older participants with a mean age of 70.0 ± 4.1 years were included in this study. Visual acuity was measured according to the Early Treatment Diabetic Retinopathy Study (ETDRS) protocol with three luminance conditions: high luminance (300 cd/m 2 ), low luminance (10 cd/m 2 ), and low luminance with short-term (15-minute) twilight adaptation (10 cd/m 2 ).

RESULTS

The mean logarithm of minimum angle of resolution values of visual acuity were -0.09 ± 0.09, 0.10 ± 0.13, and 0.03 ± 0.09 at 300, 10, and 10 cd/m 2 with twilight adaptation, respectively. Multiple regression analysis determined that spherical aberration ( P < .005) and tetrafoil ( P < .005) were significant factors associated with low-luminance visual acuity after twilight adaptation, with an adjusted R2 value of 0.35 for this model ( P < .005).

CONCLUSIONS

Although the influence of ocular aberrations on low-luminance visual acuity may be relatively modest compared with neural effects, it remains a crucial factor that should not be overlooked. The absence of twilight (or dark) adaptation can cause ocular aberrations and neural effects, potentially leading to inaccuracies in the measurement of low-luminance visual acuity.

Optical Performance of a Segmented Extended-Depth-of-Focus Intraocular Lens under the Influence of Different Values of Spherical Aberration Generated by Refractive Surgery

BACKGROUND

Corneal refractive surgery induces high-order aberrations, specifically spherical aberration (SA). These aberrations can have implications when patients later develop cataracts and require the implantation of multifocal intraocular lenses (MIOLs). MIOLs with asymmetric designs pose challenges in predicting outcomes, particularly in these cases. The aim of this study was to evaluate how different values of SA, resulting from various types of refractive surgeries, affect the optical performance of the FEMTIS Comfort intraocular lens.

METHODS

The through-focus modulation transfer function (TF-MTF) curve and high-contrast images of tumbling E were used as parameters to assess the optical performance of the MIOL. These parameters were measured using an adaptive optics visual simulator.

RESULTS

Increasingly negative values of SA make the MIOL more bifocal, moderating its extended-depth-of-focus characteristic. Conversely, higher positive SA values cause the TF-MTF curve to shift towards positive vergences, leading to worsened distance vision in the +1.00 to +2.00 D range, but improved vision in the +0.50 D to +1.00 D range.

CONCLUSIONS

Assessing SA in patients prior to implanting MIOLs with asymmetric designs is necessary for predicting outcomes and making informed decisions based on the visual requirements of patients.

Optical changes and association with axial elongation in children wearing orthokeratology lenses of different back optic zone diameter

PURPOSE

To compare changes in ocular aberrations in children wearing orthokeratology (ortho-k) lenses with a back optic zone diameter (BOZD) of 6 mm (6-MM group) or 5 mm (5-MM group) and their associations with axial elongation (AE) over two years.

METHODS

Seventy Chinese children, aged 6 to < 11 years, with myopia between - 4.00 to - 0.75 D, were randomly allocated to 5-MM and 6-MM groups. Ocular aberrations were measured, rescaled to a 4-mm pupil, and fitted with a 6th order Zernike expansion. Measurements, including axial length, were taken prior to commencing ortho-k treatment and then every six months over two years.

RESULTS

After two years, the 5-MM group displayed a smaller horizontal treatment zone (TZ) diameter (by 1.14 ± 0.11 mm, P < 0.001) and less AE (by 0.22 ± 0.07 mm, P = 0.002) compared with the 6-MM group. A greater increase in total root mean square (RMS) of higher-order aberrations (HOAs), primary spherical aberration (SA) ([Formula: see text], and coma were also observed in the 5-MM group at all follow-up visits. The horizontal TZ diameter was significantly associated with changes in RMS HOAs, SA (RMS, primary and secondary SA), and RMS coma. After controlling for baseline parameters, RMS HOAs, RMS SA, RMS coma, and primary ([Formula: see text] and secondary ([Formula: see text] SA were significantly associated with AE.

CONCLUSIONS

Ortho-k lenses with a smaller BOZD created a smaller horizontal TZ diameter and a significant increase in total HOAs, total SA, total coma, and primary SA and a decrease in secondary SA. Of these ocular aberrations, total HOAs, total SA, and primary SA were negatively correlated with AE over two years.

TRIAL REGISTRATION

ClinicalTrial.gov, NCT03191942. Registered 19 June 2017, https://clinicaltrials.gov/ct2/show/NCT03191942 .

Retinal image quality in myopic children undergoing orthokeratology alone or combined with 0.01% atropine

BACKGROUND

The retinal image quality derived from lower-order (LOA) and higher-order aberrations (HOA) for fixed 3-mm and photopic pupil diameters, in children undergoing combined 0.01% atropine and orthokeratology (AOK) versus those receiving orthokeratology alone (OK) over two years was evaluated.

METHODS

The visual Strehl ratio based on the optical transfer function (VSOTF), derived from 2nd- to 4th-order terms (LOA and HOA combined), 2nd-order terms (LOA only), and 3rd- to 4th-order terms (HOA only) for fixed 3-mm and natural photopic pupil diameters, was compared between the two treatment groups. The individual Zernike coefficients for a fixed 3-mm pupil size of 2nd- to 4th-orders, root mean square (RMS) of LOA ([Formula: see text], [Formula: see text], and [Formula: see text] combined), HOA (3rd to 4th orders inclusive), and Coma ([Formula: see text] combined) were also compared between the two groups.

RESULTS

Right eye data of 33 AOK and 35 OK participants were analysed. Under photopic conditions, significantly lower VSOTF based on HOA only was observed in the AOK group compared with that in the OK group at all post-treatment visits (all P < 0.05); however, interactions between HOA and LOA resulted in comparable overall retinal image quality (i.e., VSOTF based on LOA and HOA combined) between the two groups at all visits (all P > 0.05). For a fixed 3-mm pupil size, the VSOTF based on HOA only, LOA only, or HOA and LOA combined, were not different between the two groups (all P > 0.05). AOK participants had slower axial elongation (mean ± SD, 0.17 ± 0.19 mm vs. 0.35 ± 0.20 mm, P < 0.001), a larger photopic pupil size (4.05 ± 0.61 mm vs. 3.43 ± 0.41 mm, P < 0.001) than OK participants, over two years.

CONCLUSIONS

HOA profile related to an enlarged pupil size may provide visual signal influencing eye growth in the AOK group.

Intraocular composition of higher order aberrations in non-myopic children

This study examined anterior corneal, internal ocular, and total ocular higher order aberrations (HOA's), and retinal image quality in a non-myopic, paediatric cohort. Anterior corneal aberrations were derived from corneal topography data captured using a Placido disk videokeratoscope (E300, Medmont International), and whole eye HOA's were measured using a Hartmann-Shack wavefront sensor (COAS-HD, Wavefront Sciences). The associations between HOA's and age, sex, refractive error, and axial length were explored using correlation analyses. Data for 84 children aged between 5 and 12 years (mean ± standard deviation spherical equivalent refraction (SER), +0.63 ± 0.35 D; range 0.00 to +1.75 D) were included, and an eighth order Zernike polynomial was fit for 4 and 6 mm pupil diameters for both the anterior corneal and total ocular HOA's, from which internal ocular HOA's were calculated via subtraction following alignment to a common reference axis (pupil centre). Internal ocular HOA's were of greater magnitude than previous studies of adolescents and adults, however partial internal "compensation" of HOA's was observed, which resulted in reduced levels of HOA's and excellent retinal image quality. Few significant associations were observed between HOA's and age, SER, and axial length (all correlations, p > 0.001), and there were minimal sex-based differences (all comparisons, p > 0.005). Coefficients for vertical coma ( C 3 - 1 and C 5 - 1 ) and spherical aberration ( C 4 0 and C 6 0 ), were most strongly associated with the visual Strehl ratio based on the optical transfer function (VSOTF), which indicated that the absolute magnitudes of these Zernike coefficients have the greatest impact on retinal image quality in this paediatric cohort. These findings provide an improved understanding of the optics and retinal image quality of children's eyes.

Evaluating the effect of ocular aberrations on the simulated performance of a new refractive IOL design using adaptive optics

Adaptive optics (AO) visual simulators are excellent platforms for non-invasive simulation visual performance with new intraocular lens (IOL) designs, in combination with a subject own ocular aberrations and brain. We measured the through focus visual acuity in subjects through a new refractive IOL physically inserted in a cuvette and projected onto the eye's pupil, while aberrations were manipulated (corrected, or positive/negative spherical aberration added) using a deformable mirror (DM) in a custom-developed AO simulator. The IOL increased depth-of-focus (DOF) to 1.53 ± 0.21D, while maintaining high Visual Acuity (VA, -0.07 ± 0.05), averaged across subjects and conditions. Modifying the aberrations did not alter IOL performance on average.

KeratoScreen: Early Keratoconus Classification With Zernike Polynomial Using Deep Learning

PURPOSE

We aimed to investigate the usefulness of Zernike coefficients (ZCs) for distinguishing subclinical keratoconus (KC) from normal corneas and to evaluate the goodness of detection of the entire corneal topography and tomography characteristics with ZCs as a screening feature input set of artificial neural networks.

METHODS

This retrospective study was conducted at the Affiliated Eye Hospital of Wenzhou Medical University, China. A total of 208 patients (1040 corneal topography images) were evaluated. Data were collected between 2012 and 2018 using the Pentacam system and analyzed from February 2019 to December 2021. An artificial neural network (KeratoScreen) was trained using a data set of ZCs generated from corneal topography and tomography. Each image was previously assigned to 3 groups: normal (70 eyes; average age, 28.7 ± 2.6 years), subclinical KC (48 eyes; average age, 24.6 ± 5.7 years), and KC (90 eyes; average age, 25.9 ± 5.4 years). The data set was randomly split into 70% for training and 30% for testing. We evaluated the precision of screening symptoms and examined the discriminative capability of several combinations of the input set and nodes.

RESULTS

The best results were achieved using ZCs generated from corneal thickness as an input parameter, determining the 3 categories of clinical classification for each subject. The sensitivity and precision rates were 93.9% and 96.1% in subclinical KC cases and 97.6% and 95.1% in KC cases, respectively.

CONCLUSIONS

Deep learning algorithms based on ZCs could be used to screen for early KC and for other corneal ectasia during preoperative screening for corneal refractive surgery.

Refractive and visual function changes in twilight conditions

Purpose

We investigated the effect of luminance on refraction and visual function under twilight conditions.

Methods

Twenty young adults (mean age 20.5 ± 0.5 years) without ocular diseases and 20 eyes were included in the study. Subjective and objective spherical equivalent power (SE), logMAR, pupil diameter, ocular aberration, and ocular axial length were evaluated. Measurements were conducted in a light room with high luminance (300 cd/m²) targets (photopic), in a dark room with low luminance (10 cd/m²) targets (twilight), and a dark room after 15 min of adaptation to low luminance (10 cd/m²) targets (after adaptation: AA). Differences between the three conditions were analyzed using the Friedman test and Scheffe’s multiple comparisons.

Results

The results of logMAR were -0.20 ± 0.07, -0.08 ± 0.08, and -0.11 ± 0.08 in photopic, twilight, and AA, respectively, with significant differences between photopic and twilight (p < 0.001) and between photopic and AA (p < 0.001). Then subjective SE were -3.58 ± 2.04 D, -3.75 ± 2.08 D, and -3.74 ± 2.04 D in photopic, twilight, and AA, respectively, with significant differences between photopic and twilight (p = 0.007) and photopic and AA (p = 0.023). However, none of the other objective SEs produced a significant difference (p = 0.63). The pupil diameter and ocular aberration changed significantly in all conditions (p < 0.001).

Conclusions

Subjective myopic refraction increased and visual resolution decreased in younger subjects. However, this change in refraction is less than one level (±0.25 D) in clinical optometry, so fully corrected eyeglasses are important when assuming refraction in twilight, and there is no need for additional correction.

Differences in Image Quality after Three Laser Keratorefractive Procedures for Myopia

SIGNIFICANCE

Psychophysical estimates of spatial and depth vision have been shown to be better after bilateral ReLEx small-incision lenticule extraction (SMILE) refractive surgery for myopia, relative to photorefractive keratectomy (PRK) and femtosecond laser-assisted in situ keratomileusis (FS-LASIK). The present study provides the optical basis for these findings using computational image quality analysis.

PURPOSE

This study aimed to compare longitudinal changes in higher-order wavefront aberrations and image quality before and after bilateral PRK, FS-LASIK, and SMILE refractive procedures for correcting myopia.

METHODS

Wavefront aberrations and image quality of both the eyes of 106 subjects (n = 40 for FS-LASIK and SMILE and n = 26 for PRK) were determined pre-operatively and at 1-week, 1-month, 3-month, and 6-month post-operative intervals using computational through-focus analysis for a 6-mm pupil diameter. Image quality was quantified in terms of its peak value and its interocular difference, residual defocus that was needed to achieve peak image quality (best focus), and the depth of focus.

RESULTS

The increase in root mean squared deviations of higher-order aberrations post-operatively was lesser after SMILE (1-month visit median [25th to 75th interquartile range], 0.34 μm (0.28 to 0.39 μm]) than after PRK (0.80 μm [0.74 to 0.87 μm]) and FS-LASIK (0.74 μm [0.59 to 0.83 μm]; P ≤ .001), all relative to pre-operative values (0.20 μm [0.15 to 0.30 μm]). The peak image quality dropped and its interocular difference increased, best focus shifted myopically by 0.5 to 0.75 D, and depth of focus widened significantly after PRK and FS-LASIK surgeries, all relative to pre-operative values (P < .001). All these changes were negligible but statistically significant in a minority of instances after SMILE surgery (P ≥ .01).

CONCLUSIONS

Although all three refractive surgeries correct myopia, the image quality and its similarity between eyes are better and closer to pre-operative values after SMILE, compared with FS-LASIK and PRK. These results can be explained from the underlying increase in higher-order wavefront aberrations experienced by the eye post-operatively.

Correlation between Contrast Sensitivity and Modulation Transfer Functions

SIGNIFICANCE

Previous studies found no correlation between visual acuity and optical quality in a population of young subjects with good vision. Using sinusoidal gratings, we systematically investigate the correlation between contrast sensitivity and optical quality as a function of spatial frequency.

PURPOSE

This study describes the correlation between the contrast sensitivity function (CSF) and the modulation transfer function (MTF) in a sample of young and informed subjects. Our results are compared with prior studies on the correlation between visual acuity and metrics of image quality. We also compare our results with previous studies that compare the CSF, the MTF, and the neural contrast sensitivity function (NCSF).

METHODS

The CSF of 28 informed subjects is measured in photopic conditions. The polychromatic MTF is computed from the measurements of monochromatic aberrations. The (CSF, MTF) correlation is estimated as the Pearson correlation coefficient, at each spatial frequency. The NCSF of each subject is estimated as the ratio of CSF to MTF.

RESULTS

We obtain high correlation coefficients (0.8) in the range of spatial frequencies of 3 to 6 cycles per degree, which also corresponds to high NCSF. Correlation decreases with increasing spatial frequency in the range of 6 to 18 cycles per degree (down to 0.0 at 18 cycles per degree). In that range, optical and neural contrast sensitivities are both approximately reduced by factor 4.

CONCLUSIONS

In our sample of young subjects with good vision, the CSF with sinusoidal gratings better differentiates eyes of good optical quality at intermediate spatial frequencies (3 to 6 cycles per degree) than at higher spatial frequencies (12 to 18 cycles per degree). At the highest tested spatial frequency of sinusoidal gratings (18 cycles per degree), there is no significant correlation between optical quality and contrast sensitivity.

Unified analytical method for Zernike coefficient transformation of scaled, rotated, and translated pupils based on Shack's vector multiplication

Zernike polynomials play an essential role in characterizing and analyzing wavefront aberrations. Transformation of weighted coefficients for Zernike modes is required when pupil scaling, rotation, and/or translation exist. Here, a novel method based on Shack's vector multiplication is first proposed to derive the transformation relation. The derived modes resulting from pupil scaling, rotation, and/or translation for each individual mode are easily indicated via this method; thus, the effect of each kind of pupil change could be studied qualitatively and quantitatively. Its remarkable computational efficiency against the direct integral is demonstrated by simulation. The method introduced here provides a generalized methodology to analyze the relationship between weighted coefficients for different description basis sets.

Impact on binocular visual function of small-incision lenticule extraction for high myopia

PURPOSE

To assess whether small-incision lenticule extraction (SMILE) for high myopia reduces the binocular visual function assessed by stereoacuity, binocular visual acuity, binocular contrast sensitivity, and binocular summation.

SETTING

University hospital.

DESIGN

Prospective case series.

METHODS

Patients with a myopic spherical equivalent of at least 6.00 diopters (D) scheduled for SMILE aimed at emmetropia were included. Psychophysical testing was performed with correction preoperatively but no correction postoperatively. Stereoacuity was assessed with the Randot Circles test and the near Frisby test, visual acuity (monocular and binocular) was assessed with high-contrast Early Treatment Diabetic Retinopathy Study charts, and contrast sensitivity (monocular and binocular) was assessed with the Pelli-Robson chart and the Freiburg Acuity and Contrast Test. Binocular summation was calculated by comparing the binocular score against the best monocular score.

RESULTS

A total of 138 eyes of 69 patients were included. The mean spherical equivalent changed from -7.46 D ± 1.06 (SD) to -0.23 D ± 0.40 postoperatively. Stereoacuity did not change significantly postoperatively; median change (interquartile range) was -0.32 (-6.21 to 1.55) seconds of arc with the Frisby test and 0.00 (-7.5 to 5.0) seconds of arc with the Randot test (P ≥ .06). Binocular postoperative uncorrected distance visual acuity was not different from the preoperative corrected distance visual acuity (P = .40). Contrast sensitivity declined slightly monocularly with both tests of contrast sensitivity but was unaltered binocularly (P ≥ .08). Binocular summation for visual acuity and contrast sensitivity was unaltered following surgery (P ≥ .09).

CONCLUSIONS

SMILE for high myopia did not reduce the binocular function assessed by stereoacuity, binocular visual acuity, binocular contrast sensitivity, and binocular summation.

Visual image quality after small-incision lenticule extraction compared with that of spectacles and contact lenses

PURPOSE

To assess the influence of small-incision lenticule extraction (SMILE) for high myopia on the visual image quality assessed by the logarithm of the visual Strehl ratio (logVSX) and put this into a clinical context by pairwise comparing the logVSX of postoperative eyes with those of myopic controls wearing spectacles and/or contact lenses.

SETTING

University hospital.

DESIGN

Prospective and cross-sectional clinical study.

METHODS

Patients with a myopic spherical equivalent of at least 6.00 diopters treated with SMILE aimed at emmetropia and correspondingly myopic controls corrected with spectacles and/or contact lenses were included. The logVSX calculation was divided into habitual logVSX based on the wavefront aberration measurement directly and optimal logVSX calculated in a theoretical through-focus experiment to obtain the best-achievable logVSX.

RESULTS

A total of 117 eyes of 61 patients and 64 eyes of 34 myopic controls were included. SMILE did not affect the habitual logVSX but worsened the optimal logVSX (P < .001). The postoperative habitual logVSX was statistically significantly worse compared with contact lenses (P = .002). The postoperative optimal logVSX was significantly worse compared with both spectacles (P < .01) and contact lenses (P = .003). There was no statistically significant difference in habitual or optimal logVSX between spectacles and contact lenses.

CONCLUSIONS

SMILE for high myopia does not affect the habitual logVSX but decreases the optimal logVSX slightly. The postoperative habitual logVSX is worse than for contact lenses but not spectacles, and the postoperative optimal logVSX is worse than for both contact lenses and spectacles. There is no statistically significant difference in either habitual or optimal logVSX between spectacles and contact lenses.

Higher order aberrations and retinal image quality during short-term accommodation in children

Changes in higher order aberrations (HOA's) and retinal image quality during accommodation have not previously been examined in children. This study measured ocular HOA's in ninety non-myopic, school-aged children during short-term accommodation tasks at 0, 3, 6, and 9 D demands presented via a Badal optometer mounted to a Hartmann-Shack wavefront aberrometer (COAS-HD, Wavefront Sciences). Eighty-four participants who exhibited active accommodation were included in the analyses. An eighth order Zernike polynomial was fit across a 2.3 mm, 4 mm, and natural pupil diameter to evaluate changes in refractive power vectors (M, J₁₈₀, and J₄₅), accommodation errors (lags and leads), HOA root mean square (RMS) variables, individual Zernike coefficients, and the visual Strehl ratio based on the optical transfer function (VSOTF). All HOA RMS variables changed significantly with accommodation, with the greatest change observed for the 9 D demand. Of the individual Zernike coefficients, primary (C₄⁰) and secondary spherical aberration (C₆⁰) exhibited the greatest magnitude of change, becoming negative and positive with increasing accommodation, respectively. The VSOTF changed significantly with greater accommodation for both the 4 mm and natural pupil size, becoming significantly worse for the 9 D demand. HOA's increase and retinal image quality decreases significantly during higher levels of accommodation in children, similar to adults. These findings provide a greater understanding of the optical properties of children's eyes and insights into possible mechanisms for the association between accommodation, near work, and refractive error development.

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.

Spherical Aberration Customization to Extend the Depth of Focus With a Clinical Adaptive Optics Visual Simulator

PURPOSE

To evaluate the use of the VAO adaptive optics visual simulator (Voptica SL, Murcia, Spain) for customization of spherical aberration to increase depth of focus.

METHODS

Through-focus visual acuity with both high- and low-contrast letters from +1.00 to -3.00 diopters (D) was measured in 17 dilated eyes with three different induced amounts of spherical aberration for a 4.5-mm pupil diameter: control (0 µm), -0.15 µm, and -0.30 µm.

RESULTS

The defocus curves followed the same behavior with both values of contrast, but the visual acuity was 0.2 logMAR lower with low contrast. The mean values of high-contrast logMAR visual acuity at far, intermediate (67 cm), and near (40 cm) were -0.10, 0.11, and 0.37 for control, 0.04, 0.00, and 0.15 for -0.15 µm, and 0.23, 0.00, and 0.06 for -0.30 µm conditions. The 95% confidence interval ranged from ±0.14 to ±0.45 logMAR and the middle 50% of the distribution was approximately 0.2 logMAR.

CONCLUSIONS

Negative values of spherical aberration extend the depth of focus in different ways depending on each patient. The VAO is a new instrument that allows the visual customization of spherical aberration to enhance depth of focus. [J Refract Surg. 2020;36(4):223-229.].

Orientation-specific long-term neural adaptation of the visual system in keratoconus

Eyes with the corneal ectasia keratoconus have performed better than expected (e.g. visual acuity) given their elevated levels of higher-order aberrations that cause rotationally asymmetric retinal blur. Adapted neural processing has been suggested as an explanation but has not been measured across multiple meridional orientations. Using a custom Maxwellian-view laser interferometer to bypass ocular optics, sinusoidal grating neural contrast sensitivity was measured in six eyes (three subjects) with keratoconus and four typical eyes (two subjects) at six spatial frequencies and eight orientations using a two-interval forced-choice paradigm. Total measurement duration was 24 to 28 hours per subject. Neural contrast sensitivity functions of typical eyes agreed with literature and generally showed the oblique effect on a linear-scale and rotational symmetry on a log-scale (rotational symmetry was quantified as the ratio of the minor and major radii of an ellipse fit to all orientations within each spatial frequency; typical eye mean 0.93, median 0.93; where a circle = 1). Mean sensitivities of eyes with keratoconus were 20% to 60% lower (at lower and higher spatial frequencies respectively) than typical eyes. Orientation-specific neural contrast sensitivity functions in keratoconus showed substantial rotational asymmetry (ellipse radii ratio: mean 0.84; median 0.86) and large meridional reductions. The visual image quality metric VSX was used with a permutation test to combine the asymmetric optical aberrations of the eyes with keratoconus and their measured asymmetric neural functions, which illustrated how the neural sensitivities generally mitigated the detrimental effects of the optics.

Higher order aberrations and axial elongation in combined 0.01% atropine with orthokeratology for myopia control

PURPOSE

To compare the changes in higher order aberrations (HOA's) for photopic and mesopic pupil diameters in children undergoing orthokeratology treatment (OK) or combined 0.01% atropine with orthokeratology treatment (AOK), and their association with axial elongation.

METHODS

Children aged 6 to <11 years with 1.00-4.00 D of myopia were randomly assigned to each treatment group. Photopic and mesopic pupil diameters were quantified using automated pupillometry and HOA's were measured with a Hartmann-Shack aberrometer and Badal system to control for accommodation. HOA's were rescaled to photopic and mesopic pupil diameters and fitted with a 6^th order Zernike polynomial expansion. Axial length was measured using an optical biometer under cycloplegia.

RESULTS

Baseline and six-month data from 25 AOK and 28 OK participants were analysed. At the six-month visit, pupil diameter was larger in the AOK group under photopic conditions (3.70 ± 0.42 vs 3.12 ± 0.33 mm, p < 0.001), along with a range of HOA metrics [3^rd to 6^th order and higher order root mean square error values (HO RMS), all p ≤ 0.003] and individual Zernike terms (primary spherical aberration, and oblique quadrafoil, both p ≤ 0.03). Axial elongation was greater in the OK treatment group (0.05 ± 0.08 vs -0.01 ± 0.12 mm, p = 0.02). In the AOK group, axial elongation was correlated with the increase in photopic pupil diameter (r = -0.45, p = 0.02) and with several HOA metrics; however, these associations were not observed in the OK group.

CONCLUSION

AOK treatment resulted in increased photopic pupil size and HOA's, and significantly less axial elongation over a six-month period compared to OK treatment alone. The improved myopia control observed with combination 0.01% atropine and orthokeratology may be a result of an enhanced optical effect due to a larger photopic pupil size.

Combining optical and neural components in physiological visual image quality metrics as functions of luminance and age

Visual image quality metrics combine comprehensive descriptions of ocular optics (from wavefront error) with a measure of the neural processing of the visual system (neural contrast sensitivity). To improve the ability of these metrics to track real-world changes in visual performance and to investigate the roles and interactions of those optical and neural components in foveal visual image quality as functions of age and target luminance, models of neural contrast sensitivity were constructed from the literature as functions of (1) retinal illuminance (Trolands, td), and (2) retinal illuminance and age. These models were then incorporated into calculation of the visual Strehl ratio (VSX). Best-corrected VSX values were determined at physiological pupil sizes over target luminances of 104 to 10-3 cd/m2 for 146 eyes spanning six decades of age. Optical and neural components of the metrics interact and contribute to visual image quality in three ways. At target luminances resulting in >900 td at physiological pupil size, neural processing is constant, and only aberrations (that change as pupil size changes with luminance) affect the metric. At low mesopic luminances below where pupil size asymptotes to maximum, optics are constant (maximum pupil), and only the neural component changes with luminance. Between these two levels, both optical and neural components of the metrics are affected by changes in target luminance. The model that accounted for both retinal illuminance and age allowed VSX, termed VSX(td,a), to best track visual acuity trends (measured at 160 and 200 cd/m2) as a function of age (20s through 70s) from the literature. Best-corrected VSX(td,a) decreased by 2.24 log units between maximum and minimum target luminances in the youngest eyes and by 2.58 log units in the oldest. The decrease due to age was more gradual at high target luminances (0.70 log units) and more pronounced as target luminance decreased (1.04 log units).

Validation of Mahajan's formula for scaling ocular higher-order aberrations by pupil size

Purpose:

Zernike polynomials for describing ocular higher order aberrations are affected by pupil aperture. The current study aimed to validate Mahajan’s formula for scaling Zernike polynomials by pupil size.

Methods:

Higher order aberrations for 3 intraocular lens models (AcrySof IQ IOL SN60WF, Technis ZA9003, Adapt Advanced Optics) were measured using the Zywave aberrometer and a purpose-built physical model eye. Zernike coefficients were mathematically scaled from a 5 mm to a 3 mm pupil diameter (5:3 mm), from a 5 mm to a 2 mm pupil diameter (5:2 mm), and from a 3 mm to a 2 mm pupil diameter (3:2 mm). Agreement between the scaled coefficients and the measured coefficients at the same pupil aperture was assessed using the Bland–Altman method in R statistical software.

Results:

No statistically significant mean difference (MD) occurred between the scaled and measured Zernike coefficients for 21 of 23 analyses after Holm-Bonferroni correction (P > 0.05). Mean differences between the scaled and measured Zernike coefficients were clinically insignificant for all aberrations up to the fourth order, and within 0.10 μm. Oblique secondary astigmatism (Z⁻²₄) was significantly different in the 5:3 mm comparison (MD = - 0.04 μm, P < 0.01). Horizontal coma (Z¹₃) was significantly different in the 3:2 mm comparison (MD = - 0.07 μm, P = 0.03). There were borderline statistical differences in both vertical (Z⁻¹₃) and horizontal coma (Z¹₃) in the 5:3 mm comparison (MD = 0.02 μm, - 0.09 μm, P = 0.05, 0.05, respectively).

Conclusion:

A formula for the scaling of higher order aberrations by pupil size is validated as accurate. Pupil scaling enables accurate comparison of individual higher order aberrations in clinical research for situations involving different pupil sizes.

Higher-Order Aberrations and Axial Elongation in Myopic Children Treated With Orthokeratology

Purpose

This retrospective longitudinal study aimed to examine the relationship between ocular higher-order aberrations (HOA) and axial eye growth in young myopic children undergoing orthokeratology (ortho-k) treatment.

Methods

Axial length and ocular HOA, measured under cycloplegia annually over a 2-year period from the right eyes of myopic children, who previously completed ortho-k clinical trials, were retrieved. Linear mixed model analyses were applied to determine the association between ocular HOA, other known confounding variables (age, sex, and refractive error), and axial eye growth.

Results

Data from 103 subjects were analyzed. The root-mean square (RMS) values of total ocular HOA (third to sixth orders combined), spherical (Z40 and Z60 combined), and comatic (Z3-1, Z31, Z5-1, and Z51 combined) aberrations increased by approximately 3, 9, and 2 times, respectively, after 2 years of ortho-k treatment. After adjusting for age, sex, and refractive error, higher RMS values of total HOA and spherical aberrations were associated with both longer axial length and slower axial elongation (all P < 0.01). For individual Zernike term coefficients, a higher level of positive spherical aberration (Z40) was also associated with longer axial length and slower axial elongation (both P < 0.01), after adjusting for baseline HOA.

Conclusions

Ortho-k for myopia control significantly increases the Zernike coefficients and therefore the RMS values for a range of total ocular HOA terms or metrics in children. These findings suggest the potential role of HOA, particularly spherical aberration, as the possible mechanism of slowing axial elongation in ortho-k treatment.

Habitual higher order aberrations affect Landolt but not Vernier acuity

To assess whether the eye's optical imperfections are relevant for hyperacute vision, we measured ocular wave aberrations, visual hyperacuity, and acuity thresholds in 31 eyes of young adults. Although there was a significant positive correlation between the subjects' performance in Vernier- and Landolt-optotype acuity tasks, we found clear differences in how far both acuity measures correlate with the eyes' optics. Landolt acuity thresholds were significantly better in eyes with low higher order aberrations and high visual Strehl ratios (r² = 0.22, p = 0.009), and significantly positively correlated with axial length (r² = 0.15, p = 0.03). A retinal image quality metric, calculated as two-dimensional correlation between perfect and actual retinal image, was also correlated with Landolt acuity thresholds (r² = 0.27, p = 0.003). No such correlations were found with Vernier acuity performance (r² < 0.03, p > 0.3). Based on these results, hyperacuity thresholds are, contrary to resolution acuity, not affected by higher order aberrations of the eye.

Comparison of Wavefront-guided and Best Conventional Scleral Lenses after Habituation in Eyes with Corneal Ectasia

SIGNIFICANCE

Visual performance with wavefront-guided (WFG) contact lenses has only been reported immediately after manufacture without time for habituation, and comparison has only been made with clinically unrefined predicate conventional lenses. We present comparisons of habitual corrections, best conventional scleral lenses, and WFG scleral lenses after habituation to all corrections.

PURPOSE

The purpose of this study was to compare, in a crossover design, optical and visual performance of eyes with corneal ectasias wearing dispensed best conventional scleral lens corrections and dispensed individualized WFG scleral lens corrections.

METHODS

Ten subjects (20 eyes) participated in a randomized crossover study where best conventional scleral lenses and WFG scleral lenses (customized through the fifth radial order) were worn for 8 weeks each. These corrections, as well as each subject's habitual correction and normative data for normal eyes, were compared using (1) residual higher-order aberrations (HORMS), (2) visual acuity (VA), (3) letter contrast sensitivity (CS), and (4) visual image quality (logarithm of the visual Strehl ratio, or logVSX). Correlations were performed between Pentacam biometric measures and gains provided by WFG lenses.

RESULTS

Mean HORMS was reduced by 48% from habitual to conventional and 43% from conventional to WFG. Mean logMAR VA improved from habitual (+0.12) to conventional (-0.03) and further with WFG (-0.09); six eyes gained greater than one line with WFG over conventional. Area under the CS curve improved by 26% from habitual to conventional and 14% from conventional to WFG. The percentage of the eyes achieving normal levels were as follows: HORMS, 40% for conventional and 85% for WFG; VA, 50% for conventional and 85% for WFG; and CS, 60% for conventional and 90% for WFG. logVSX improved by 16% from habitual to conventional and 25% further with WFG. Reduction in aberrations with WFG lenses best correlated with posterior cornea radius of curvature.

CONCLUSIONS

Visual performance was superior to that reported with nonhabituated WFG lens wear. With WFG lenses, HORMS and logVSX significantly improved, allowing more eyes to reach normal levels of optical and visual performance compared with conventional lenses.

Wavefront propagation based on the ray transfer matrix and numerical orthogonal Zernike gradient polynomials

The aberrated wavefront propagates along its normal. Both the magnitude and boundary change after the propagation. Wavefronts characterized by Zernike coefficients and a normalized pupil radius can also be represented by a bundle of feature rays normal to the local surface. A ray transfer matrix parameterized by the pupil radius and propagation distance is proposed to transfer these feature rays to obtain the slope and position data of the propagated feature rays. Numerical orthogonal Zernike gradient polynomials are derived to reconstruct the wavefront from the discrete data by using a numerical method. Two aberrated wavefronts are performed as examples to validate the accuracy and flexibility of the proposed numerical method.

Analytical method for the transformation of Zernike polynomial coefficients for scaled, rotated, and translated pupils

Zernike polynomials provide an excellent metric basis for characterizing the wavefront aberrations of human eyes and optical systems. Since the Zernike expansion is dependent on the size, position, and orientation of the pupil in which the function is defined, it is often necessary to transform the Zernike coefficients between different pupils. An analytic method of transforming the Zernike coefficients for scaled, rotated, and translated pupils is proposed in this paper. The normalized coordinate transformation functions between the polar coordinates of the transformed pupil and the Cartesian coordinates of the original pupil are given. Based on the Cartesian and polar representations of Zernike polynomials, the coefficients' transformation matrix can be derived directly and conveniently. The first 36 terms of standard Zernike polynomials are used to validate the proposed method. For different types of transformation, transformation rules of individual Zernike terms are systematically analyzed, revealing how individual terms of the original pupil transform into terms of the transformed pupil. Numerical examples are presented to demonstrate the validity of the proposed method. Further application of the proposed method to the alignment of pupil-decentered off-axis optical systems is discussed.

Higher-Order Aberrations in Children and Adolescents of Southwest China

SIGNIFICANCE

This study provides a descriptive characterization of higher-order optical aberrations for the eyes of a larger number of Chinese children and adolescents.

PURPOSE

To determine the distribution of higher-order aberrations (HOAs) of Han Chinese young subjects with normal vision and their relationship to age.

METHODS

Children and adolescents, aged from 3 to 17 years, with normal visual acuity were enrolled, and their wavefront aberrations for a 6-mm pupil were evaluated by the Zywave II aberrometer. Their correlations with age were analyzed, and the 95% statistical reference ranges were computed for each Zernike term.

RESULTS

A total of 1634 eyes (287 for preschool-age children, 897 for school-age children, and 450 for adolescents) were analyzed. There was a significant correlation with age and the root mean square (RMS) of total HOAs (r = 0.256, P < .0001), third-order aberrations (r = 0.062, P = .029), fourth-order aberrations (r = 0.197, P < .0001), fifth-order aberrations (r = 0.067, P = .017), and trefoil-like aberrations (r = 0.100, P < .0001) in the myopic group. There were significant differences in RMS values (except coma-like aberrations, χ = 4.179, P = .124) as well as the Zernike coefficients among three different age groups. Therefore, the 95% statistical normal reference values were calculated separately for three age groups.

CONCLUSIONS

The RMS value of total HOAs, coma-like, trefoil-like, third-order, fourth-order, and fifth-order aberrations are correlated with age, and the RMS values and Zernike coefficients of aberrations were different in different age stages of the subjects. This study described the distribution of HOAs in children and adolescents and established 95% statistical normal values of HOAs for different ages of children and adolescents by analyzing the HOAs in a large number of the Han Chinese clinical population.

Impact of higher-order aberrations on depth-of-field

It is well known that depth-of-focus (DOF) is influenced by optical factors (such as pupil size and monochromatic aberrations). However, neural factors such as blur sensitivity and defocus adaptation may play an important role on the extent of DOF. A series of experiments were conducted to study if optical or neural factors are most pertinent in explaining the variability of DOF across subjects. An adaptive optics system with a black and white target, a 3.8-mm artificial pupil, and a subjective criterion (based on objectionable blur) were used to measure depth of field ([DOFi]; DOF computed in the object space) in 11 participants, after at least 6 min of adaptation. This was done under three conditions: (a) with their own higher order aberrations (HOA); (b) after correction of their monochromatic HOA; and (c) after altering the HOA pattern for some participants to reflect the HOA pattern measured for a different participant. Natural DOFi and DOFi after HOA correction were positively correlated (R2 = 0.461), but a significant decrease in DOFi (21% on average) was found after HOA correction (p = 0.042). Effect of HOA on the intersubject variability of DOFi was 3.9 times smaller than the effect of the image neural processing. This study shows that DOFi depends on both optical and neural factors, but the latter seems to play a more important role than the former.

Ocular higher-order aberrations and axial eye growth in young Hong Kong children

This retrospective longitudinal analysis aimed to investigate the association between ocular higher-order aberrations (HOAs) and axial eye growth in Hong Kong children. Measures of axial length and ocular HOAs under cycloplegia were obtained annually over a two-year period from 137 subjects aged 8.8 ± 1.4 years with mean spherical equivalent refraction of -2.04 ± 2.38 D. A significant negative association was observed between the RMS of total HOAs and axial eye growth (P = 0.03), after adjusting for other significant predictors of axial length including age, sex and refractive error. Similar negative associations with axial elongation were found for the RMS of spherical aberrations ([Formula: see text] and [Formula: see text] combined) (P = 0.037). Another linear mixed model also showed that greater levels of vertical trefoil [Formula: see text], primary spherical aberration [Formula: see text] and negative oblique trefoil [Formula: see text] were associated with slower axial elongation and longer axial length (all P < 0.05). These findings support the potential role of HOAs, image quality and a vision-dependent mechanism in childhood eye growth.

Reliability of Ocular Aberration Measurements in Children with Moderate and Low Myopia under Scotopic Conditions

Purpose

To investigate the reliability of ocular aberration measurement in myopic children under scotopic conditions and to validate the mathematical Zernike pupil scaling-down technique.

Methods

Ocular aberrations of 45 myopic children were examined under scotopic conditions via iTrace aberrometer. The intra- and intersession repeatability was evaluated for both the measured values with the true pupil sizes and the estimated ones that were determined by scaling down the pupil sizes to the largest integer value across all measurements.

Results

The intra- and intersession difference of clinically measured aberration was generally insignificant, and the ICCs for each aberration component exhibited good to excellent reliability (ICCs > 0.4). Similar results were found for the estimated aberration using the scaling-down technique. Although the majority of the estimated Zernike components were comparable with the corresponding measured one, the estimated values of defocus, coma, and the corresponding total aberrations were found significantly smaller than the measured values (all P < 0.01).

Conclusions

The ocular aberration measurements in myopic children under the circumstances described are reliable. The scaling-down technique is a useful option for comparing the results obtained from different pupil sizes, but the estimated Zernike coefficients were not always comparable with the corresponding measured values.

Influence of Refractive Status on the Higher-Order Aberration Pattern After Small Incision Lenticule Extraction Surgery

PURPOSE

To study the effect of myopia on the pattern change in higher-order aberrations after small incision lenticule extraction.

METHODS

Sixty eyes of 60 patients were included: low myopia (≤-3.00 D), moderate myopia (-3.00 D to -6.00 D), and high myopia (≥-6.00 D). Total higher-order aberrations (tHOA), vertical coma ((Equation is included in full-text article.)), horizontal coma ((Equation is included in full-text article.)), and spherical aberration ((Equation is included in full-text article.)) were measured preoperatively and at postoperative 3 months.

RESULTS

At the end of 3 months, tHOA changed significantly compared with the preoperative values (P < 0.05), except for (Equation is included in full-text article.)and (Equation is included in full-text article.)in the low myopia group. The change in (Equation is included in full-text article.), (Equation is included in full-text article.), and (Equation is included in full-text article.)in the moderate group (-0.299, -0.175, and 0.108 μm) was 2.020, 4.861, and 4.696 times higher than the low group (-0.148, -0.036, 0.023 μm) (P = 0.002, 0.001, 0.001), respectively. The value in the high group (-0.331, -0.192, 0.154 μm) was 1.107, 1.097 (P = 0.478, 0.665), and 1.426 times (P = 0.047) higher than the moderate group. The degree of myopia was positively correlated with Δ(Equation is included in full-text article.)(r = 0.447; P < 0.001) and Δ(Equation is included in full-text article.)(r = 0.496; P < 0.001), and negatively correlated with ΔtHOA (r = -0.363, P = 0.004) and Δ(Equation is included in full-text article.)(r = -0.599; P < 0.001).

CONCLUSIONS

The study showed a different pattern of change in ocular aberrations after small incision lenticule extraction in patients with varying degrees of myopia. In patients with low myopia, there was no increase in (Equation is included in full-text article.)or (Equation is included in full-text article.). In high myopia, however, (Equation is included in full-text article.)increased with the degree of myopia, whereas the rising rate of coma was slowing.

Reducing starbursts in highly aberrated eyes with pupil miosis

PURPOSE

To test the hypothesis that marginal ray deviations determine perceived starburst sizes, and to explore different strategies for decreasing starburst size in highly aberrated eyes.

METHODS

Perceived size of starburst images and visual acuities were measured psychophysically for eyes with varying levels of spherical aberration, pupil sizes, and defocus. Computationally, we use a polychromatic eye model including the typical levels of higher order aberrations (HOAs) for keratoconic and post-LASIK eyes to quantify the image quality (the visually weighted Strehl ratio derived from the optical transfer function, VSOTF) with different pupil sizes at both photopic and mesopic light levels.

RESULTS

For distance corrected post-LASIK and keratoconic eyes with a night-time pupil (e.g., 7 mm), the starburst diameter is about 1.5 degrees (1 degree for normal presbyopic eyes), which can be reduced to ≤0.25 degrees with pupil sizes ≤3 mm. Starburst size is predicted from the magnitude of the longitudinal spherical aberration. Refracting the eye to focus the pupil margin also removed starbursts, but, unlike small pupils, significantly degraded visual acuity. Reducing pupil diameter to 3 mm improved image quality for these highly aberrated eyes by about 2.7 ×  to 1.7 ×  relative to the natural pupils when light levels were varied from 0.1 to 1000 cd m^-2 , respectively.

CONCLUSION

Subjects with highly aberrated eyes observed larger starbursts around bright lights at night predictable by the deviated marginal rays. These were effectively attenuated by reducing pupil diameters to ≤3 mm, which did not cause a drop in visual acuity or modelled image quality even at mesopic light levels.

New Objective Refraction Metric Based on Sphere Fitting to the Wavefront

Purpose

To develop an objective refraction formula based on the ocular wavefront error (WFE) expressed in terms of Zernike coefficients and pupil radius, which would be an accurate predictor of subjective spherical equivalent (SE) for different pupil sizes.

Methods

A sphere is fitted to the ocular wavefront at the center and at a variable distance, t. The optimal fitting distance, t_opt, is obtained empirically from a dataset of 308 eyes as a function of objective refraction pupil radius, r₀, and used to define the formula of a new wavefront refraction metric (MTR). The metric is tested in another, independent dataset of 200 eyes.

Results

For pupil radii r₀ ≤ 2 mm, the new metric predicts the equivalent sphere with similar accuracy (<0.1D), however, for r₀ > 2 mm, the mean error of traditional metrics can increase beyond 0.25D, and the MTR remains accurate. The proposed metric allows clinicians to obtain an accurate clinical spherical equivalent value without rescaling/refitting of the wavefront coefficients. It has the potential to be developed into a metric which will be able to predict full spherocylindrical refraction for the desired illumination conditions and corresponding pupil size.

Interaction of aberrations, diffraction, and quantal fluctuations determine the impact of pupil size on visual quality

Our purpose is to develop a computational approach that jointly assesses the impact of stimulus luminance and pupil size on visual quality. We compared traditional optical measures of image quality and those that incorporate the impact of retinal illuminance dependent neural contrast sensitivity. Visually weighted image quality was calculated for a presbyopic model eye with representative levels of chromatic and monochromatic aberrations as pupil diameter was varied from 7 to 1 mm, stimulus luminance varied from 2000 to 0.1  cd/m², and defocus varied from 0 to -2 diopters. The model included the effects of quantal fluctuations on neural contrast sensitivity. We tested the model's predictions for five cycles per degree gratings by measuring contrast sensitivity at 5  cyc/deg. Unlike the traditional Strehl ratio and the visually weighted area under the modulation transfer function, the visual Strehl ratio derived from the optical transfer function was able to capture the combined impact of optics and quantal noise on visual quality. In a well-focused eye, provided retinal illuminance is held constant as pupil size varies, visual image quality scales approximately as the square root of illuminance because of quantum fluctuations, but optimum pupil size is essentially independent of retinal illuminance and quantum fluctuations. Conversely, when stimulus luminance is held constant (and therefore illuminance varies with pupil size), optimum pupil size increases as luminance decreases, thereby compensating partially for increased quantum fluctuations. However, in the presence of -1 and -2 diopters of defocus and at high photopic levels where Weber's law operates, optical aberrations and diffraction dominate image quality and pupil optimization. Similar behavior was observed in human observers viewing sinusoidal gratings. Optimum pupil size increases as stimulus luminance drops for the well-focused eye, and the benefits of small pupils for improving defocused image quality remain throughout the photopic and mesopic ranges. However, restricting pupils to <2  mm will cause significant reductions in the best focus vision at low photopic and mesopic luminances.

Comparison of Measurements and Clinical Outcomes After Wavefront-Guided LASEK Between iDesign and WaveScan

PURPOSE

To compare the measurements of refractive errors and ocular aberrations obtained using iDesign and WaveScan (Abbott Medical Optics, Inc., Santa Ana, CA), and to compare surgical outcomes of wavefront-guided LASEK using ablation profiles based on both aberrometers.

METHODS

Ninety myopic eyes of 45 normal patients were evaluated using both the iDesign and WaveScan to measure spherical and cylindrical errors, spherical equivalents, and Zernike coefficients of ocular aberrations. Wavefront-guided LASEK was performed in a different group of 59 eyes of 30 patients divided into two groups, the iDesign and Wavescan groups. The clinical outcomes between the two groups including uncorrected visual acuity, refractive errors, contrast sensitivity, and ocular aberration were compared at 1, 3, and 6 months postoperatively.

RESULTS

The iDesign produced significantly higher myopic values for refractive errors than the WaveScan, as well as significantly lower levels of total higher order, third, fourth, and fifth order root mean square values and Zernike coefficients of vertical coma and spherical aberration. At postoperative 1, 3, and 6 months, there were no statistically significant differences between the two groups in terms of uncorrected visual acuity and remaining refractive errors. The percentages of patients with spherical equivalents within ±1.00 and ±0.50 diopters of emmetropia were 100% (29 eyes) and 75.9% (22 eyes), respectively, in the iDesign group and 96.7% (29 eyes) and 70.0% (21 eyes), respectively, in the WaveScan group. Mesopic contrast sensitivity values were significantly higher, and the change in root mean square values for spherical aberration was significantly lower in the iDesign group.

CONCLUSIONS

There were significant differences between the iDesign and the WaveScan in the measurements of refraction and ocular aberrations. Wavefront-guided LASEK based on an ablation profile from the iDesign demonstrated comparable refractive predictability with the WaveScan group, resulting in minimal physician adjustment and superior postoperative visual quality.

Higher-order aberrations and best-corrected visual acuity in Native American children with a high prevalence of astigmatism

PURPOSE

To determine whether higher-order aberrations (HOAs) in children from a highly astigmatic population differ from population norms and whether HOAs are associated with astigmatism and reduced best-corrected visual acuity.

METHODS

Subjects were 218 Tohono O'odham Native American children 5-9 years of age. Noncycloplegic HOA measurements were obtained with a handheld Shack-Hartmann sensor (SHS). Signed (z06s to z14s) and unsigned (z06u to z14u) wavefront aberration Zernike coefficients Z(3,-3) to Z(4,4) were rescaled for a 4 mm diameter pupil and compared to adult population norms. Cycloplegic refraction and best-corrected logMAR letter visual acuity (BCVA) were also measured. Regression analyses assessed the contribution of astigmatism (J0) and HOAs to BCVA.

RESULTS

The mean root-mean-square (RMS) HOA of 0.191 ± 0.072 μm was significantly greater than population norms (0.100 ± 0.044 μm). All unsigned HOA coefficients (z06u to z14u) and all signed coefficients except z09s, z10s, and z11s were significantly larger than population norms. Decreased BCVA was associated with astigmatism (J0) and spherical aberration (z12u) but not RMS coma, with the effect of J0 about 4 times as great as z12u.

CONCLUSIONS

Tohono O'odham children show elevated HOAs compared to population norms. Astigmatism and unsigned spherical aberration are associated with decreased acuity, but the effects of spherical aberration are minimal and not clinically significant.

Influence of spherical aberration, stimulus spatial frequency, and pupil apodisation on subjective refractions

PURPOSE

To test competing hypotheses (Stiles Crawford pupil apodising or superior imaging of high spatial frequencies by the central pupil) for the pupil size independence of subjective refractions in the presence of primary spherical aberration.

METHODS

Subjective refractions were obtained with a variety of test stimuli (high contrast letters, urban cityscape, high and low spatial frequency gratings) while modulating pupil diameter, levels of primary spherical aberration and pupil apodisation. Subjective refractions were also obtained with low-pass and high-pass stimuli and using 'darker' and 'sharper' subjective criteria.

RESULTS

Subjective refractions for stimuli containing high spatial frequencies focus a near paraxial region of the pupil and are affected only slightly by level of Seidel spherical aberration, degree of pupil apodisation and pupil diameter, and generally focused a radius of about 1-1.5 mm from the pupil centre. Low spatial frequency refractions focus a marginal region of the pupil, and are significantly affected by level of spherical aberration, amount of pupil apodisation, and pupil size. Clinical refractions that employ the 'darker' or 'sharper' subjective criteria bias the patient to use lower or higher spatial frequencies, respectively.

CONCLUSIONS

In the presence of significant levels of spherical aberration, the pupil size independence of subjective refractions occurs with or without Stiles Crawford apodisation for refractions that optimise high spatial frequency content in the image. If low spatial frequencies are optimised by a subjective refraction, spherical refractive error varies with spherical aberration, pupil size, and level of apodisation. As light levels drop from photopic to scotopic, therefore, we expect a shift from pupil size independent to pupil size dependent subjective refractions. Emphasising a 'sharper' criterion during subjective refractions will improve image quality for high spatial frequencies and generate pupil size independent refractions.

Spherical aberration and the sign of defocus

PURPOSE

Visual sensing of the sign of defocus is important not only for the rapid control of accommodation but also for regulating the slower long-term growth of the eye.

METHODS

We examined the possibility that ocular spherical aberration (SA) elicits a sign of defocus by optical modeling of image formation using the principles of physical optics.

RESULTS

Retinal image contrast, as measured by the area under the visually weighted modulation-transfer function, depends on both the magnitude and the sign of defocus relative to the sign of the SA. Image contrast is greater for hyperopic blur than for myopic blur when SA is positive and vice versa when SA is negative.

CONCLUSIONS

When coupled with Wallman's hypothesis that retinal activity caused by image contrast inhibits eye growth, these results provide a testable hypothesis to account for myopia progression. For example, we suggest that hyperopic blur is a risk factor for myopia progression only when the eye has a negative SA because that is the combination leading to relatively low contrast in the defocused retinal image. Because the likelihood of a negative SA increases with accommodation, avoiding long hours of near work in the presence of accommodative lag may help prevent the onset and progression of myopia.

Estimating the eye aberration coefficients in resized pupils: is it better to refit or to rescale?

In order to work in a consistent way with Zernike aberration coefficients estimated in different pupils, it is necessary to refer them to a common pupil size. Two standard approaches can be used to that end: to rescale algebraically the coefficients estimated in the original pupil or to refit them anew using the wavefront slope measurements available within the new one. These procedures are not equivalent; they are affected by different estimation errors that we address in this work. Our results for normal eye populations show that in case of reducing the pupil size it is better to rescale the original coefficients than to refit them using the measurements contained within the smaller pupil. In case of enlarging the pupil size, as it can a priori be expected, the opposite holds true. We provide explicit expressions to quantify the errors arising in both cases, including the expected error incurred when extrapolating the Zernike estimation beyond the radius where the measurements were made.

Analysis of the impacts of horizontal translation and scaling on wavefront approximation coefficients with rectangular pupils for Chebyshev and Legendre polynomials

Chebyshev and Legendre polynomials are frequently used in rectangular pupils for wavefront approximation. Ideally, the dataset completely fits with the polynomial basis, which provides the full-pupil approximation coefficients and the corresponding geometric aberrations. However, if there are horizontal translation and scaling, the terms in the original polynomials will become the linear combinations of the coefficients of the other terms. This paper introduces analytical expressions for two typical situations after translation and scaling. With a small translation, first-order Taylor expansion could be used to simplify the computation. Several representative terms could be selected as inputs to compute the coefficient changes before and after translation and scaling. Results show that the outcomes of the analytical solutions and the approximated values under discrete sampling are consistent. With the computation of a group of randomly generated coefficients, we contrasted the changes under different translation and scaling conditions. The larger ratios correlate the larger deviation from the approximated values to the original ones. Finally, we analyzed the peak-to-valley (PV) and root mean square (RMS) deviations from the uses of the first-order approximation and the direct expansion under different translation values. The results show that when the translation is less than 4%, the most deviated 5th term in the first-order 1D-Legendre expansion has a PV deviation less than 7% and an RMS deviation less than 2%. The analytical expressions and the computed results under discrete sampling given in this paper for the multiple typical function basis during translation and scaling in the rectangular areas could be applied in wavefront approximation and analysis.

Laser tomography adaptive optics: a performance study

We present an analytical derivation of the on-axis performance of adaptive optics systems using a given number of guide stars of arbitrary altitude, distributed at arbitrary angular positions in the sky. The expressions of the residual error are given for cases of both continuous and discrete turbulent atmospheric profiles. Assuming Shack-Hartmann wavefront sensing with circular apertures, we demonstrate that the error is formally described by integrals of products of three Bessel functions. We compare the performance of adaptive optics correction when using natural, sodium, or Rayleigh laser guide stars. For small diameter class telescopes (≲5 m), we show that a small number of Rayleigh beacons can provide similar performance to that of a single sodium laser, for a lower overall cost of the instrument. For bigger apertures, using Rayleigh stars may not be such a suitable alternative because of the too severe cone effect that drastically degrades the quality of the correction.

Registration tolerance of a custom correction to maintain visual acuity

PURPOSE

To present a predictive model of the registration tolerance for wavefront-guided correction to maintain acuity within fixed limits and demonstrate the potential utility using two typical keratoconic eyes.

METHODS

Change in log visual Strehl was plotted as a function of translation error for a series of rotations of a wavefront-guided correction. Contour lines were added at Δlog visual Strehl levels predicted to induce one- and two-line losses of logMAR visual acuity. The model was validated by regressing measured acuity loss from subjects viewing acuity charts that were degraded by the residual wavefront error resulting from the movement of wavefront-guided correction against the model's predicted acuity.

RESULTS

The model's predicted change in acuity can be substituted for measured change in acuity (R² = 0.91) within measurement error (±0.1 logMAR). Translation and/or rotation of a wavefront-guided correction induced asymmetric optical tolerance to movement. Induced errors depended on the wavefront error being corrected, the wavefront-guided correction design, and the amount of registration error.

CONCLUSIONS

Change in log visual Strehl can be used to determine the registration tolerance necessary to keep the variation in acuity within user-defined limits. This tolerance is unique for each wavefront error and wavefront-guided correction design.