Standards for Reporting the Optical Aberrations of Eyes

Associations between refractive error components and higher-order aberrations in simple myopia and compound myopic astigmatism

Aim

To investigate associations between refractive error components and higher-order aberrations (HOAs) in adult myopic subjects.

Methods

A total of 1370 myopia right eyes, aged 18-40, were included in a cross-sectional study. Subjective cycloplegic refractions and distance aberrometry measured with a Shack-Hartmann device were analyzed. Zernike components of horizontal coma (Z3 1), vertical coma (Z3 -1), oblique trefoil (Z3 3), vertical trefoil (Z3 -3), spherical aberration, and total root-mean-square (RMS) wave-front error for 6 mm pupil were analyzed. Pearson's correlations were calculated between sphero-cylindrical components and HOAs based on vector analysis for the astigmatism axis. Total subjects were divided into two subgroups: simple myopia (SMY, 648 eyes) and compound myopic astigmatism (CMA, 722 eyes). HOAs were compared between the two subgroups.

Results

Total RMS wave-front error correlates with spherical equivalent myopia (r = -0.1, P<0.05) and J45 (r = 0.1, P<0.001). J0 correlates positively with vertical coma (Z3 -1) (r = 0.1 p <0.001) and negatively with oblique trefoil (Z3 3) and vertical trefoil (Z3 -3), (r = -0.1, p < 0.001; r = -0.1, P < 0.05). The total RMS wavefront-error was larger in the CMA (|0.37| ± 0.18 µm) compared to the SMY (|0.34| ± 0.16 µm, P <0.001). The mean values of vertical coma (Z3 -1), vertical trefoil (Z3 -3), and oblique trefoil (Z3 3) differed between the two subgroups.

Conclusion

Total RMS wave-front error increases with increasing myopia and astigmatism. Increasing myopia power does not show a systematic correlation with HOAs components. A weak systematic correlation is suggested between astigmatism direction and third-order aberrations.

Design concepts for advanced-technology intraocular lenses [Invited]

An intraocular lens (IOL) replaces the natural crystalline lens during cataract surgery, and although the vast majority of implants have simple optics, "advanced technology" IOLs have multifocal and extended depth of focus (EDOF) properties. Optical concepts are evaluated here, with image contrast, focal range, and unwanted visual phenomena being the primary concerns. Visual phenomena with earlier bifocal diffractive lenses led to alternative diffractive designs (trifocals, etc.) and also to exploring increasing the depth of focus for monofocal IOLs using refractive methods, where although the defocus range might be more modest, visual phenomena are much less obvious. The designs cover a range of possibilities that might provide the best overall vision for patients with differing motivations, needs, and sensitivity to visual side effects.

Optical characterization of a manual tunable lens for eye-care applications

The popularity of focus tunable lenses has increased in the last decade. In this study we present an experimental optical characterization of a commercially available manually tunable lens to describe its behavior regarding optical aberrations, expressed in terms of Zernike coefficients, under different laboratory conditions. Measurements were performed by using a Shack-Hartmann aberrometer, and four different experiments were carried out in order to assess 1) the lens stability in time for a given temperature, 2) the temporal response of the lens, 3) the behavior of the lens when changing the room temperature, and 4) the possible influence of gravity on the lens performance according to its mounting orientation. The main conclusion we outlined states that the properties of the tunable lens stay steady over time as long as room temperature remains constant, making it a good option for ophthalmologic and optometric eye-care applications.

Linearized wavefront sensing model for aberration retrieval from low-frequency Fourier coefficients

This paper proposes and demonstrates a linearized model for phase diversity wavefront sensing, facilitating real-time processing and much less data required for training. Specifically, we find that the low-frequency Fourier coefficients of point spread function images are linearly proportional to pupil aberration coefficients under certain conditions. Simulation and experimental results show that the model can greatly reduce the processing time to several milliseconds by merely requiring hundreds of training samples while maintaining a comparatively high accuracy with state-of-the-art methods.

Motion onset VEPs can see through the blur

Motion-onset visual evoked potentials (MO VEPs) are robust to dioptric blur when low contrast and low spatial frequency patterns are used for stimulation. To reveal mechanisms of MO VEPs robustness, we studied whether the resistance to defocus persists even when using a high-contrast checkerboard using digital defocus in the emmetropic eyes of 13 subjects (males 20-60 years). We compared the dominant components of MO VEPs to pattern-reversal VEPs (PR VEP), which are sensitive to the blur. For stimulation, we used checkerboard patterns with 15´ and 60´ checks. To defocus the checkerboard, we rendered it with a second-order Zernike polynomial ( Z 2 0 ) with an equivalent defocus of 0, 2, or 4 D. For PR VEP, the checkerboards were reversed in terms of their contrast. To evoke MO VEP, the checkerboard of 60´ checks moved for 200 ms with a speed of 5 or 10 deg/s in the cardinal directions. The MO VEP did not change in peak time (P ≥ 0.0747) or interpeak amplitude (P > 0.0772) with digital blur. In contrast, for PR VEP, the results showed a decrease in interpeak amplitude (P ≤ 6.65ˑ10-4) and an increase in peak time (P ≤ 0.0385). Thus, we demonstrated that MO VEPs evoked by checkerboard, structure containing high spatial content, can be robust to defocus.

Topography-guided photorefractive keratectomy combined with accelerated corneal collagen cross-linking versus cross-linking alone for progressive keratoconus: a long-term prospective cohort study

Purpose

To comprehensively compare the long-term outcome of the combined topography guided photorefractive keratectomy (TG-PRK) with accelerated corneal cross-linking (ACXL) and ACXL alone in eyes with progressive keratoconus. The analysis focused on the changes in the detailed corneal aberrometric values.

Methods

This single-center, prospective cohort study included 28 patients (30 eyes) of the TG-PRK plus ACXL group and 14 patients (15 eyes) of the ACXL alone group. The mean duration of the follow-up was 44 ± 10.18 months (ranged from 31 to 65 months). The preoperative data and the postoperative measurement data at the last follow-up visit, including demographic data, uncorrected distance visual acuity (UDVA), corrected distance visual acuity (CDVA), manifest refraction, corneal topography, pachymetry, aberrometry and densitometry were analyzed.

Results

The CDVA significantly improved in the TG-PRK plus ACXL group at the last follow-up visit (p = 0.006), while no significant improvement was found in the ACXL alone group (p = 0.432). The maximal keratometry of the anterior corneal surface (Kmax) of both groups significantly decreased at the last follow-up visit (p < 0.05). Compared with the ACXL alone group, the Kmax of the TG-PRK plus ACXL group showed a greater decline (p = 0.008). The total corneal aberrations, the corneal lower-order aberrations (LOAs), the corneal higher order aberrations (HOAs), the vertical coma and the spherical aberration (SA) at the 4.0 mm and 6.0 mm zone of the TG-PRK plus ACXL group significantly decreased at the last follow-up visit (all p < 0.05). The declines of the total corneal aberrations, the corneal LOAs, the corneal HOAs and the vertical coma at the 4.0 mm and 6.0 mm zone of the TG-PRK plus ACXL group were significantly higher than those in the ACXL alone group (p < 0.001).

Conclusion

Compared with ACXL alone, combined TG-PRK with ACXL procedure had a significantly higher reduction in the corneal HOAs and better CDVA, while providing a similar long-term stability and safety. For progressive keratoconus patients with adequate corneal thickness, the combined procedure might be a recommended treatment option.

Wide Dynamic Range Digital Aberration Measurement and Fast Anterior-Segment OCT Imaging †

Ocular aberrometry with a wide dynamic range for assessing vision performance and anterior segment imaging that provides anatomical details of the eye are both essential for vision research and clinical applications. Defocus error is a major limitation of digital wavefront aberrometry (DWA), as the blurring of the detected point spread function (PSF) significantly reduces the signal-to-noise ratio (SNR) beyond the ±3 D range. With the aid of Badal-like precompensation of defocus, the dynamic defocus range of the captured aberrated PSFs can be effectively extended. We demonstrate a dual-modality MHz VCSEL-based swept-source OCT (SS-OCT) system with easy switching between DWA and OCT imaging modes. The system is capable of measuring aberrations with defocus dynamic range of 20 D as well as providing fast anatomical imaging of the anterior segment at an A-scan rate of 1.6 MHz.

Effects on Wavefront Aberration after Short-term Wear of Senofilcon A Photochromic Contact Lens

BACKGROUND

To assess the variability in wavefront aberrations with short-term wear of photochromic senofilcon A contact lenses in both its activated and inactive states.

METHODS AND MATERIAL

In this cross-sectional study, 20 participants who had previously used soft contact lenses were enrolled. Corneal aberrometry measurements were performed on each subject, without contact lenses, using Sirius Scheimpflug-Placido topography. The photochromic lenses were illuminated using a blue-violet light (λ max = 420 nm) so as to provoke an activated state, and measurements were taken with the lenses inserted, in both states. The root mean square (RMS) of the aberrations was calculated, and the higher- and lower-order aberrations, astigmatism, coma, spherical aberration, and trefoil measurements were evaluated using a 5.0-mm pupil diameter.

RESULTS

The average contact lens sphere power was - 2.33 ± 1.07 D. The mean refractive errors with contact lens wear were 0.07 ± 0.18 D for the sphere and - 0.26 ± 0.15 D for the cylinder. The mean RMS values for all the corneal aberrations showed no statistically significant differences with and without contact lenses (p > 0.05). In a bivariate correlation analysis, there was a positive correlation between contact lens sphere power and coma (vertical and horizontal) in the activated state (r = 0.455, p = 0.44 and r = 0.495, p = 0.27, respectively).

CONCLUSION

The photochromic contact lenses did not influence ocular aberration during short-term wear, even when the photochromatic additive was activated. This property may help to provide more comfortable vision with lens wear. This finding needs to be verified by further studies.

Evaluation of Higher-Order Aberrations After the Smooth Incision Lenticular Keratomileusis (SILKTM) Procedure Using the ELITATM Femtosecond Platform for Correction of Myopic and Astigmatic Refractive Errors

Purpose

To evaluate the changes of higher-order wavefront aberrations following the Smooth Incision Lenticular Keratomileusis (SILKTM) procedure for correction of myopic refractive errors with and without astigmatism, using the ELITATM Femtosecond Platform.

Methods

This prospective study included 24 eyes that underwent SILK procedure using one ELITA femtosecond laser system for the correction of myopic refractive errors with and without astigmatism. Preoperative and postoperative 1-day, 1-week, 1-month, 3-month, and 9-month eye exams were measured with a commercial wavefront aberrometer (iDESIGN ® Refractive Studio, Johnson & Johnson Surgical Vision, Inc). Wavefront aberrations up to the 6th order Zernike coefficients, including coma Z(3, -1) and Z(3, 1), spherical aberration Z(4, 1), and the wavefront error of all higher-order aberrations (HOAs RMS), were evaluated across a 6 mm pupil.

Results

The mean manifest refractive spherical equivalent changed from the preoperative refractions -3.82 ± 1.26 D (range -6.00 to -2.25 D) to the postoperative refractions -0.20 ± 0.15 D (range -0.50 to 0.00 D) at the 9-month follow-up. Compared to baseline preoperative HOAs, the mean postoperative HOAs were significantly increased at the 1-day follow-up. On average, at the 9-month postoperative assessment the vertical coma Z(3, -1) was -0.054 ±0.186 µm, horizontal coma Z(3, 1) was 0.016 ± 0.124 µm, spherical aberration Z(4, 0) was 0.046 ± 0.163 µm, and HOAs RMS was 0.363 ± 0.115 µm across a 6 mm pupil. There is no significant difference in the mean HOAs starting at 1-week follow-up for the horizontal coma (P = 0.346) and spherical aberration (P = 0.095).

Conclusions

The visual outcomes demonstrated that the SILK procedure for refractive lenticule extraction using ELITA femtosecond laser system is effective and predictable for the correction of myopic refractive errors with and without astigmatism. The ELITA femtosecond laser system induced minimal HOAs in surgical eyes following the SILK procedures. These results demonstrate fast corneal recovery starting at 1-week follow-up, and spherical aberration was not induced.

Statistical optimal parameters obtained by using clinical human ocular aberrations for high-precision aberration measurement

PURPOSE

Compared to Shack-Hartmann wavefront sensor (SHWS), the parameters of virtual SHWS (vSHWS) can be easily adjusted to obtain the optimal performance of aberration measurement. Its current optimal parameters are obtained with only a set of statistical aberrations and not statistically significant. Whether the above parameters are consistent with the statistical results of the optimal parameters corresponding to each set of aberrations, and which performance is better if not? The purpose of this study was to answer these questions.

METHODS

The optimal parameters to reconstruct 624 sets of clinical ocular aberrations in the highest accuracy, including the numbers of sub-apertures (NSAs) and the expansion ratios (ERs) of electric field zero-padding, were determined sequentially in this work. By using wavefront-reconstruction accuracy as an evaluation index, the statistical optimal parameter configuration was selected from some possible configurations determined by the optimal NSAs and ERs.

RESULTS

The statistical optimal parameters are consistent for normal and abnormal eyes. They are different from the optimal parameters obtained with a set of statistical aberrations from the same 624 sets of aberrations, and the performance using the former is better than that using the latter. The performance using a fixed set of statistical optimal parameters is even close to that using the respective optimal parameters corresponding to each set of aberrations.

CONCLUSION

The vSHWS configured with a fixed set of statistical optimal parameters can be used for high-precision aberration measurement of both normal and abnormal eyes. The statistical optimal parameters are more suitable for vSHWS than the parameters obtained with a set of statistical aberrations. These conclusions are significant for the designs of vSHWS and also SHWS.

Allowable movement of wavefront-guided contact lens corrections in normal and keratoconic eyes

PURPOSE

The goal was to use SyntEyes modelling to estimate the allowable alignment error of wavefront-guided rigid contact lens corrections for a range of normal and keratoconic eye aberration structures to keep objectively measured visual image quality at or above average levels of well-corrected normal eyes. Secondary purposes included determining the required radial order of correction, whether increased radial order of the corrections further constrained the allowable alignment error and how alignment constraints vary with keratoconus severity.

METHODS

Building on previous work, 20 normal SyntEyes and 20 keratoconic SyntEyes were fitted with optimised wavefront-guided rigid contact lens corrections targeting between three and eight radial orders that drove visual image quality, as measured objectively by the visual Strehl ratio, to near 1 (best possible) over a 5-mm pupil for the aligned position. The resulting wavefront-guided contact lens was then allowed to translate up to ±1 mm in the x- and y-directions and rotate up ±15°.

RESULTS

Allowable alignment error changed as a function of the magnitude of aberration structure to be corrected, which depends on keratoconus severity. This alignment error varied only slightly with the radial order of correction above the fourth radial order. To return the keratoconic SyntEyes to average levels of visual image quality depended on maximum anterior corneal curvature (Kmax). Acceptable tolerances for misalignment that returned keratoconic visual image quality to average normal levels varied between 0.29 and 0.63 mm for translation and approximately ±6.5° for rotation, depending on the magnitude of the aberration structure being corrected.

CONCLUSIONS

Allowable alignment errors vary as a function of the aberration structure being corrected, the desired goal for visual image quality and as a function of keratoconus severity.

Risk Factors for Corneal Monochromatic Aberrations and Implications for Multifocal and Extended Depth-of-Focus Intraocular Lens Implantation

PURPOSE

To discuss factors influencing corneal aberrations that might influence the optical quality after intraocular lens (IOL) implantation.

METHODS

PubMed and Scopus were the main resources used to search the medical literature. An extensive search was performed to identify relevant articles concerning factors influencing the level of corneal aberrations as of August 27, 2023. The following keywords were used in various combinations: corneal, aberrations, defocus, astigmatism, spherical aberration, coma, trefoil, quadrafoil, intraocular lens, and IOL.

RESULTS

Conclusive evidence is lacking regarding the correlation between age and changes in corneal aberrations. Patients with astigmatism have greater corneal higher-order aberrations than those with minimal astigmatism, particularly concerning trefoil and coma. Increased levels of corneal higher-order aberrations are noted following contact lens wear, in patients with dry eye disease, and with pterygium. Increased higher-order aberrations have been reported following corneal refractive surgery and for 3 months following trabeculectomy; regarding intraocular lens surgery, the results remain controversial.

CONCLUSIONS

Several factors influence the level of corneal higher-order aberrations. Multifocal and extended depth-of-focus IOLs can share similarities in their optical properties, and the main difference arises in their design and performance with respect to spherical aberration. Preoperative evaluation is critical for proper IOL choice, particularly in corneas with risk of high levels of aberrations. [J Refract Surg. 2024;40(6):e420-e434.].

Cell-TIMP: Cellular Trajectory Inference based on Morphological Parameter

Cellular morphology, shaped by various genetic and environmental influences, is pivotal to studying experimental cell biology, necessitating precise measurement and analysis techniques. Traditional approaches, which rely on geometric metrics derived from stained images, encounter obstacles stemming from both the imaging and analytical domains. Staining processes can disrupt the cell's natural state and diminish accuracy due to photobleaching, while conventional analysis techniques, which categorize cells based on shape to discern pathophysiological conditions, often fail to capture the continuous and asynchronous nature of biological processes such as cell differentiation, immune responses, and cancer progression. In this work, we propose the use of quantitative phase imaging for morphological assessment due to its label-free nature. For analysis, we repurposed the genomic analysis toolbox to perform trajectory inference analysis purely based on morphology information. We applied the developed framework to study the progression of leukemia and breast cancer metastasis. Our approach revealed a clear pattern of morphological evolution tied to the diseases' advancement, highlighting the efficacy of our method in identifying functionally significant shape changes where conventional techniques falter. This advancement offers a fresh perspective on analyzing cellular morphology and holds significant potential for the broader research community, enabling a deeper understanding of complex biological dynamics.

Algorithm and software for field distortion correction in a commercial SD-OCT for corneal curvature assessment

Accurate assessment of corneal curvatures using frequency domain optical coherence tomography (OCT) with galvanometer scanners remains challenging due to the well-known scan field distortion. This paper presents an algorithm and software for correcting the distortion using only two simple measurements in which a readily available standard sphere is positioned in different depths in front of the OCT scanner. This offers a highly accessible and easily reproducible method for the field distortion correction (FDC). The correction was validated by measuring different spherical phantoms and conducting corneal curvature measurements of ex vivo porcine corneas using a commercial spectral-domain OCT system and a clinically approved swept-source OCT as a reference instrument. Thus, the error in radius measurements of spherical phantoms was reduced by >90% and astigmatism by >80% using FDC. In explanted porcine eyes, the error in astigmatism measurements with the Telesto was reduced by 75% for power and 70% for angle. The best fitting sphere radius was determined up to a deviation of 0.4% from the Anterion. This paper describes a correction algorithm for OCT immanent distortion that is applicable to any scanning OCT setup and enables precise corneal curvature measurements. The MATLAB software for the FDC is publicly available on GitHub.

Fourier Ptychographic Neural Network Combined with Zernike Aberration Recovery and Wirtinger Flow Optimization

Fourier ptychographic microscopy, as a computational imaging method, can reconstruct high-resolution images but suffers optical aberration, which affects its imaging quality. For this reason, this paper proposes a network model for simulating the forward imaging process in the Tensorflow framework using samples and coherent transfer functions as the input. The proposed model improves the introduced Wirtinger flow algorithm, retains the central idea, simplifies the calculation process, and optimizes the update through back propagation. In addition, Zernike polynomials are used to accurately estimate aberration. The simulation and experimental results show that this method can effectively improve the accuracy of aberration correction, maintain good correction performance under complex scenes, and reduce the influence of optical aberration on imaging quality.

Spherical Aberration and Scattering Compensation in Microscopy Images through a Blind Deconvolution Method

The optical quality of an image depends on both the optical properties of the imaging system and the physical properties of the medium the light passes while travelling from the object to the image plane. The computation of the point spread function (PSF) associated to the optical system is often used to assess the image quality. In a non-ideal optical system, the PSF is affected by aberrations that distort the final image. Moreover, in the presence of turbid media, the scattering phenomena spread the light at wide angular distributions that contribute to reduce contrast and sharpness. If the mathematical degradation operator affecting the recorded image is known, the image can be restored through deconvolution methods. In some scenarios, no (or partial) information on the PSF is available. In those cases, blind deconvolution approaches arise as useful solutions for image restoration. In this work, a new blind deconvolution method is proposed to restore images using spherical aberration (SA) and scatter-based kernel filters. The procedure was evaluated in different microscopy images. The results show the capability of the algorithm to detect both degradation coefficients (i.e., SA and scattering) and to restore images without information on the real PSF.

Improving iconic memory through contrast detection training with HOA-corrected vision

Iconic memory and short-term memory are not only crucial for perception and cognition, but also of great importance to mental health. Here, we first showed that both types of memory could be improved by improving limiting processes in visual processing through perceptual learning. Normal adults were trained in a contrast detection task for ten days, with their higher-order aberrations (HOA) corrected in real-time. We found that the training improved not only their contrast sensitivity function (CSF), but also their iconic memory and baseline information maintenance for short-term memory, and the relationship between memory and CSF improvements could be well-predicted by an observer model. These results suggest that training the limiting component of a cognitive task with visual perceptual learning could improve visual cognition. They may also provide an empirical foundation for new therapies to treat people with poor sensory memory.

Potential vision tester using adaptive optics, Maxwellian view, and small pupil

We demonstrate a free-space, trolley-mounted potential vision tester (PVT), designed to study and improve the accuracy of visual acuity (VA) measurements in the aging eye. Key features include a high-resolution visual display presented in Maxwellian view, a 3 mm pupil to limit wavefront (WF) aberrations, and a moderate cost deformable mirror to induce or correct higher order optical aberrations. The visual display supported accurate measurement of visual acuities down to 20/5. The moderate cost, piezo deformable mirror induced seven nominal aberrations, calibrated as 0, -0.32, -0.23, + 0.27, and +0.39 microns spherical aberration; + 0.49 microns Y coma; and -0.51 microns X coma. A custom Hartmann Shack (HS) calibration (HSc) system demonstrated that induced aberrations were repeatable and stable. A Badal optometer provided the coarse focus. WF aberrations were measured for five normal subjects with a commercially available HS device (HSP) (OCULUS Pentacam AXL Wave), providing estimates of WF errors for 3 mm and other pupil sizes. VA was measured using four alternative forced-choice for a single black on white E stimulus in each trial. Using the method of constant stimuli yielded robust standard deviation measurements. The 50% fit for VA plotted against induced aberration resulted in linear functions for each subject for the range of our positive and negative spherical aberration data. Subjects differed, but higher order terms were unnecessary to describe data across spherical aberrations.

Extended-depth-of-focus wavefront design from pseudo-umbilical space curves

Designing extended-depth-of-focus wavefronts is required in multiple optical applications. Caustic location and structure analysis offer a powerful tool for designing such wavefronts. An intrinsic limitation of designing extended-depth-of-focus wavefronts is that any smooth surface, with a non-constant mean curvature, unavoidably introduces a separation between caustic sheets, which is proportional to the ratio of change of the mean curvature along a curve embedded in the wavefront. We present a method to obtain extended-depth-of-focus wavefronts where the mean curvature variation ratio is reduced thanks to using a long circle-involute space curve effectively filling the wavefront surface. Additionally, we present a variant of the method in which the wavefront is modified within a small tubular neighborhood of the circle involute in order to partially meet the umbilical condition along that tubular region. Finally, we provide some numerical results showing the potential of our method in an application example.

Optical simulations of the impact of vault increase in scleral contact lenses in healthy eyes

PURPOSE

To investigate by using computational simulations the optical impact of the change in the vault of two geometries of scleral contact lenses (SCLs).

METHODS

Ray-tracing simulations were performed using specialized software in three eye models with different levels of primary SA (6 mm pupil). Two different geometries of SCL were used in such simulations characterized by the conic constants of the anterior surface of the lens (K1, -0.1 and -0.3). Likewise, the fitting of the SCL was simulated for different vaults (50-250 µm). The impact on the quality of the images through the eye models was assessed by analyzing the modulation transfer function (MTF) at different spatial frequencies (10 Lp/mm, 30 Lp/mm, and 50 Lp/mm). This impact was not only simulated for a distant object, but also for intermediate and near objects (vergence demands from 0.00 to 3.00 D). All these optical simulations were performed assuming a centered SCL, but also assuming a downward vertical decentration of 0.5 mm.

RESULTS

The thinnest vault (50 µm) provided the best ocular optical quality in all three eye models for low vergence demands. For medium and high vergence demands, Lens 1 (K1 = -0.3, K2 = -0.4) resulted in a considerable improvement in optical quality in Eye 2 (C40 = -0.078 µm), while for eyes 1 (C40 = 0.408 µm) and 3 (C40 = -0.195 µm), this improvement only tended to happen for medium vergence demands. Overall, all the aberrations increased after lens fitting. Lens decentration did not cause significant variations in the results obtained with the well-centered lenses.

CONCLUSIONS

Changes in the vault of a SCL have an impact on the optical quality achieved for different vergence demands independently on the level of SA of the eye in which it is fitted. The clinical relevance of such impact should be investigated further.

The Strehl ratio as a phase histogram

It is shown that the Strehl ratio can always be written as an integral over an apodization-weighted phase histogram. The corresponding mathematical formalism, based on Federer's co-area formula, is enumerated, and a practical numerical method to quickly and accurately calculate apodization-weighted phase histograms is detailed and compared with similar methods. Conditions for expressing the Strehl ratio as a product S=S 1 S 2 are investigated.

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.].

Generalization of learned Fourier-based phase-diversity wavefront sensing

Proper initialization of the nonlinear optimization is important to avoid local minima in phase diversity wavefront sensing (PDWS). An effective neural network based on low-frequency coefficients in the Fourier domain has proved effective to determine a better estimate of the unknown aberrations. However, the network relies significantly on the training settings, such as imaging object and optical system parameters, resulting in a weak generalization ability. Here we propose a generalized Fourier-based PDWS method by combining an object-independent network with a system-independent image processing procedure. We demonstrate that a network trained with a specific setting can be applied to any image regardless of the actual settings. Experimental results show that a network trained with one setting can be applied to images with four other settings. For 1000 aberrations with RMS wavefront errors bounded within [0.2 λ, 0.4 λ], the mean RMS residual errors are 0.032 λ, 0.039 λ, 0.035 λ, and 0.037 λ, respectively, and 98.9% of the RMS residual errors are less than 0.05 λ.

Rendering algorithms for aberrated human vision simulation

Vision-simulated imagery-the process of generating images that mimic the human visual system-is a valuable tool with a wide spectrum of possible applications, including visual acuity measurements, personalized planning of corrective lenses and surgeries, vision-correcting displays, vision-related hardware development, and extended reality discomfort reduction. A critical property of human vision is that it is imperfect because of the highly influential wavefront aberrations that vary from person to person. This study provides an overview of the existing computational image generation techniques that properly simulate human vision in the presence of wavefront aberrations. These algorithms typically apply ray tracing with a detailed description of the simulated eye or utilize the point-spread function of the eye to perform convolution on the input image. Based on the description of the vision simulation techniques, several of their characteristic features have been evaluated and some potential application areas and research directions have been outlined.

Comparison of Ocular Wavefront Aberration Measurements Obtained Using Two Hartmann-Shack Wavefront Aberrometers

OBJECTIVES

To assess agreement between measurements of ocular wavefront aberrations obtained using the Pentacam AXL Wave (Oculus Optikgeräte GmbH) (Aberrometer A) and KR-1W (Topcon Corp) (Aberrometer B), both of which are based on the Hartmann-Shack principle.

METHODS

In this prospective case-control study, ocular wavefront aberrations measurements were obtained using both aberrometers in patients with keratoconus (KC) and control participants. Ocular wavefront aberrations were measured through the natural pupil without dilation using both devices in a dark room. For both aberrometers, accommodation was inhibited by automatically adding fogging. The individual Zernike coefficients from the second to fourth order were compared between the two aberrometers for a 4-mm pupil diameter.

RESULTS

Twenty-six KC and 29 control eyes were assessed. Statistically significant correlations ( P <0.05) were observed for all Zernike coefficients, except for Z 4-2 in the control group. Bland-Altman analysis indicated good agreement between aberrometers and no statistically significant differences in the control group. However, in the KC group, patterns of proportional error were observed in vertical coma Z 3-1 (r=0.338, P =0.008), trefoil Z 4-4 (r=0.701, P =0.003), secondary astigmatism Z 4-2 (r=0.348, P =0.025), and spherical aberrations Z 40 (r=0.407, P =0.012).

CONCLUSIONS

The Zernike coefficient values measured by the two aberrometers were well correlated in the control and KC groups. However, in eyes with KC, Aberrometer B tended to present greater values in several Zernike coefficients than Aberrometer A, suggesting that wavefront measurements obtained using the two aberrometers are not interchangeable in patients with KC.

From mouse to human: Accessing the biochemistry of vision in vivo by two-photon excitation

The eye is an ideal organ for imaging by a multi-photon excitation approach, because ocular tissues such as the sclera, cornea, lens and neurosensory retina, are highly transparent to infrared (IR) light. The interface between the retina and the retinal pigment epithelium (RPE) is especially informative, because it reflects the health of the visual (retinoid) cycle and its changes in response to external stress, genetic manipulations, and drug treatments. Vitamin A-derived retinoids, like retinyl esters, are natural fluorophores that respond to multi-photon excitation with near IR light, bypassing the filter-like properties of the cornea, lens, and macular pigments. Also, during natural aging some retinoids form bisretinoids, like diretinoid-pyridiniumethanolamine (A2E), that are highly fluorescent. These bisretinoids appear to be elevated concurrently with aging. Vitamin A-derived retinoids and bisretinoidss are detected by two-photon ophthalmoscopy (2PO), using a new class of light sources with adjustable spatial, temporal, and spectral properties. Furthermore, the two-photon (2P) absorption of IR light by the visual pigments in rod and cone photoreceptors can initiate visual transduction by cis-trans isomerization of retinal, enabling parallel functional studies. Recently we overcame concerns about safety, data interpretation and complexity of the 2P-based instrumentation, the major roadblocks toward advancing this modality to the clinic. These imaging and retina-function assessment advancements have enabled us to conduct the first 2P studies with humans.

Robust numerical solution to the Levi-Civita wavefront coupling problem via level set computation of the point characteristic function

The Levi-Civita wavefront coupling problem consists of, given two prescribed wavefronts, obtaining a refractive or reflective surface coupling them. We propose a robust numerical method to solve Levi-Civita's problem, whose rationale is to consider that Levi-Civita's solutions are level surfaces of the point characteristic function established between points of incoming and outgoing wavefronts. The method obtains both surface data points and their normals, enabling a more robust surface reconstruction. We carry out a detailed error analysis of our method by means of comparing the surface data estimation with nominal surfaces obtained in reference tests offering analytical solutions to Levi-Civita's problem. The method offers, in computer simulations, highly accurate results with moderate computational cost.

Direct retrieval of Zernike-based pupil functions using integrated diffractive deep neural networks

Retrieving the pupil phase of a beam path is a central problem for optical systems across scales, from telescopes, where the phase information allows for aberration correction, to the imaging of near-transparent biological samples in phase contrast microscopy. Current phase retrieval schemes rely on complex digital algorithms that process data acquired from precise wavefront sensors, reconstructing the optical phase information at great expense of computational resources. Here, we present a compact optical-electronic module based on multi-layered diffractive neural networks printed on imaging sensors, capable of directly retrieving Zernike-based pupil phase distributions from an incident point spread function. We demonstrate this concept numerically and experimentally, showing the direct pupil phase retrieval of superpositions of the first 14 Zernike polynomials. The integrability of the diffractive elements with CMOS sensors shows the potential for the direct extraction of the pupil phase information from a detector module without additional digital post-processing.

Influence of rigid lens decentration and rotation on visual image quality in normal and keratoconic eyes

PURPOSE

To investigate whether the movement of a rigid sphero-cylindrical contact lens has a greater impact on the visual image quality in highly aberrated eyes than in normal eyes.

METHODS

For 20 normal and 20 keratoconic SyntEyes, a previously determined best sphero-cylindrical rigid lens was permitted to shift by up to ±1 mm from the line of sight and rotate up to ±15°. Each of the 52,111 lens locations sampled was ray-traced to determine the influence on the wavefront aberration. In turn, the logarithm of visual Strehl ratio (log10 [VSX]) was calculated for each aberration structure and was used to estimate the associated changes in logMAR visual acuity. Finally, contour surfaces of two-letter change in visual acuity were plotted in three-dimensional misalignment space, consisting of decentrations in the x and y directions and rotation, and volumes within these surfaces were calculated.

RESULTS

The variations in image quality within the misalignment space were unique to each eye. A two-letter loss was generally reached with smaller misalignments in keratoconic eyes (10.5 ± 4.7° of rotation or 0.27 ± 0.13 mm of shift) than in normal eyes (13.4 ± 1.8° and 0.39 ± 0.15 mm, respectively) due to larger cylindrical errors. For keratoconic eyes, on average, 14.4 ± 14.9% of misalignment space saw VSX values above the lower normal VSX threshold, well below the values of normal eyes of 48.5 ± 18.5%. In some eyes, a specific combination of lens shift and lens rotation away from the line of sight leads to a simulated improvement in visual image quality.

CONCLUSION

Variations in visual image quality due to the misalignment of rigid sphero-cylindrical contact lens corrections are larger for keratoconic eyes than for normal eyes. In some cases, a specific misalignment may improve visual image quality, which could be considered in the design of the next generation of rigid contact lenses.

Comparison of wavefront aberrations in the object and image spaces using wide-field individual eye models

Wavefront aberrations in the image space are critical for visual perception, though the clinical available instruments usually give the wavefront aberrations in the object space. This study aims to compare the aberrations in the object and image spaces. With the measured wavefront aberrations over the horizontal and vertical ±15° visual fields, the in-going and out-going wide-field individual myopic eye models were constructed to obtain the wavefront aberrations in the object and image spaces of the same eye over ±45° horizontal and vertical visual fields. The average differences in the mean sphere and astigmatism were below 0.25 D between the object and image spaces over the horizontal and vertical ±45° visual fields under 3 mm and 6 mm pupil diameter. The wavefront aberrations in the object space are a proper representation of the aberrations in the image space at least for horizontal visual fields ranging from -35°to +35° and vertical visual fields ranging from -15°to +15°.

Local aberration control to improve efficiency in multiphoton holographic projections

Optical aberrations affect the quality of light propagating through a turbid medium, where refractive index is spatially inhomogeneous. In multiphoton optical applications, such as two-photon excitation fluorescence imaging and optogenetics, aberrations non-linearly impair the efficiency of excitation. We demonstrate a sensorless adaptive optics technique to compensate aberrations in holograms projected into turbid media. We use a spatial light modulator to project custom three dimensional holographic patterns and to correct for local (anisoplanatic) distortions. The method is tested on both synthetic and biological samples to counteract aberrations arising respectively from misalignment of the optical system and from samples inhomogeneities. In both cases the anisoplanatic correction improves the intensity of the stimulation pattern at least two-fold.

Prediction of manifest refraction using machine learning ensemble models on wavefront aberrometry data

PURPOSE

To assess the performance of machine learning (ML) ensemble models for predicting patient subjective refraction (SR) using demographic factors, wavefront aberrometry data, and measurement quality related metrics taken with a low-cost portable autorefractor.

METHODS

Four ensemble models were evaluated for predicting individual power vectors (M, J0, and J45) corresponding to the eyeglass prescription of each patient. Those models were random forest regressor (RF), gradient boosting regressor (GB), extreme gradient boosting regressor (XGB), and a custom assembly model (ASB) that averages the first three models. Algorithms were trained on a dataset of 1244 samples and the predictive power was evaluated with 518 unseen samples. Variables used for the prediction were age, gender, Zernike coefficients up to 5th order, and pupil related metrics provided by the autorefractor. Agreement with SR was measured using Bland-Altman analysis, overall prediction error, and percentage of agreement between the ML predictions and subjective refractions for different thresholds (0.25 D, 0.5 D).

RESULTS

All models considerably outperformed the predictions from the autorefractor, while ASB obtained the best results. The accuracy of the predictions for each individual power vector component was substantially improved resulting in a ± 0.63 D, ±0.14D, and ±0.08 D reduction in the 95% limits of agreement of the error distribution for M, J0, and J45, respectively. The wavefront-aberrometry related variables had the biggest impact on the prediction, while demographic and measurement quality-related features showed a heterogeneous but consistent predictive value.

CONCLUSIONS

These results suggest that ML is effective for improving precision in predicting patient's SR from objective measurements taken with a low-cost portable device.

Prediction of Subjective Refraction From Anterior Corneal Surface, Eye Lengths, and Age Using Machine Learning Algorithms

Purpose

To develop a machine learning regression model of subjective refractive prescription from minimum ocular biometry and corneal topography features.

Methods

Anterior corneal surface parameters (Zernike coefficients and keratometry), axial length, anterior chamber depth, and age were posed as features to predict subjective refractions. Measurements from 355 eyes were split into training (75%) and test (25%) sets. Different machine learning regression algorithms were trained by 10-fold cross-validation, optimized, and tested. A neighborhood component analysis provided features’ normalized weights in predictions.

Results

Gaussian process regression algorithms provided the best models with mean absolute errors of around 1.00 diopters (D) in the spherical component and 0.15 D in the astigmatic components.

Conclusions

The normalized weights showed that subjective refraction can be predicted by only keratometry, age, and axial length. Increasing the topographic description detail of the anterior corneal surface implied by a high-order Zernike decomposition versus adjustment to a spherocylindrical surface is not reflected as improved subjective refraction prediction, which is poor, mainly in the spherical component. However, the highest achievable accuracy differs by only 0.75 D from that of other works with a more exhaustive eye refractive elements description. Although the chosen parameters may have not been the most efficient, applying machine learning and big data to predict subjective refraction can be risky and impractical when evaluating a particular subject at statistical extremes.

Translational Relevance

This work evaluates subjective refraction prediction by machine learning from the anterior corneal surface and ocular biometry. It shows the minimum biometric information required and the highest achievable accuracy.

RESUMEN

Objetivo

El desarrollo de un modelo de regresión de aprendizaje automático prescripción refractiva subjetiva a partir de las características mínimas de la biometría ocular y la superficie corneal.

Métodos

Los parámetros de la superficie corneal anterior (coeficientes de Zernike y queratometría), además de longitudes axiales y de cámara anterior, edades y las refracciones subjetivas no ciclopléjicas de 355 ojos se dividieron en un conjunto de entrenamiento (75%) y otro de test (25%) y se entrenaron diferentes algoritmos de regresión de aprendizaje automático mediante validación cruzada 10 veces, se optimizaron y se probaron sobre el conjunto test.

Resultados

Los algoritmos de regresión del proceso gaussiano proporcionaron los mejores modelos con un error absoluto medio fue de alrededor de 1.00 D en el componente esférico y de 0.25 D en los componentes astigmáticos.

Conclusiones

Los pesos normalizados mostraron que la refracción subjetiva puede predecirse utilizando únicamente la queratometría, la edad y la longitud axial como características. El aumento del detalle de la descripción topográfica de la superficie corneal anterior que supone una descomposición de Zernike de alto orden frente al ajuste a una superficie esferocilíndrica realizado por queratometría no se refleja en una mejora de la predicción de la refracción subjetiva, que es pobre, en cualquier caso, principalmente en el componente esférico. Sin embargo, la máxima precisión alcanzada difiere en sólo 0,75 D de la de otros trabajos con una descripción más exhaustiva de los elementos refractivos del ojo. De todos modos, el aprendizaje automático y los datos masivos aplicados a la predicción de la refracción subjetiva pueden ser arriesgados y poco prácticos cuando se evalúa a un sujeto concreto en los extremos estadísticos, aunque los parámetros elegidos puedan no haber sido los más ineficaces.

Relevancia Traslativa

El trabajo evalúa la predicción de la refracción subjetiva mediante aprendizaje automático a partir de la superficie corneal anterior y la biometría ocular, mostrando la mínima información biométrica requerida y la máxima precisión alcanzable.

Dynamic wavefront distortion in resonant scanners

Dynamic mirror deformation can substantially degrade the performance of optical instruments using resonant scanners. Here, we evaluate two scanners with resonant frequencies >12kHz with low dynamic distortion. First, we tested an existing galvanometric motor with a novel, to the best of our knowledge, mirror substrate material, silicon carbide, which resonates at 13.8 kHz. This material is stiffer than conventional optical glasses and has lower manufacturing toxicity than beryllium, the stiffest material currently used for this application. Then, we tested a biaxial microelectromechanical (MEMS) scanner with the resonant axis operating at 29.4 kHz. Dynamic deformation measurements show that wavefront aberrations in the galvanometric scanner are dominated by linear oblique astigmatism (90%), while wavefront aberrations in the MEMS scanner are dominated by horizontal coma (30%) and oblique trefoil (27%). In both scanners, distortion amplitude increases linearly with deflection angle, yielding diffraction-limited performance over half of the maximum possible deflection for wavelengths longer than 450 nm and over the full deflection range for wavelengths above 850 nm. Diffraction-limited performance for shorter wavelengths or over larger fractions of the deflection range can be achieved by reducing the beam diameter at the mirror surface. The small dynamic distortion of the MEMS scanner offers a promising alternative to galvanometric resonant scanners with desirable but currently unattainably high resonant frequencies.

The random walk of accommodation fluctuations

The focusing distance of the eye fluctuates during accommodation. However, the visual role of these accommodation fluctuations is not yet fully understood. The fluctuation complexity is one of the obstacles to this long standing challenge in visual science. In this work we seek to develop a statistical approach that i) accurately describes experimental measurements and ii) directly generates randomized and realistic simulations of accommodation fluctuations for use in future experiments. To do so we use the random walk approach, which is usually appropriate to describe the dynamics of systems that combine both randomness and memory.

Digital ocular swept source optical coherence aberrometry

Ocular aberrometry is an essential technique in vision science and ophthalmology. We demonstrate how a phase-sensitive single mode fiber-based swept source optical coherence tomography (SS-OCT) setup can be employed for quantitative ocular aberrometry with digital adaptive optics (DAO). The system records the volumetric point spread function at the retina in a de-scanning geometry using a guide star pencil beam. Succeeding test-retest repeatability assessment with defocus and astigmatism analysis on a model eye within ± 3 D dynamic range, the feasibility of technique is demonstrated in-vivo at a B-scan rate of >1 kHz in comparison with a commercially available aberrometer.

Hybrid FPGA-CPU pupil tracker

An off-axis monocular pupil tracker designed for eventual integration in ophthalmoscopes for eye movement stabilization is described and demonstrated. The instrument consists of light-emitting diodes, a camera, a field-programmable gate array (FPGA) and a central processing unit (CPU). The raw camera image undergoes background subtraction, field-flattening, 1-dimensional low-pass filtering, thresholding and robust pupil edge detection on an FPGA pixel stream, followed by least-squares fitting of the pupil edge pixel coordinates to an ellipse in the CPU. Experimental data suggest that the proposed algorithms require raw images with a minimum of ∼32 gray levels to achieve sub-pixel pupil center accuracy. Tests with two different cameras operating at 575, 1250 and 5400 frames per second trained on a model pupil achieved 0.5-1.5 μm pupil center estimation precision with 0.6-2.1 ms combined image download, FPGA and CPU processing latency. Pupil tracking data from a fixating human subject show that the tracker operation only requires the adjustment of a single parameter, namely an image intensity threshold. The latency of the proposed pupil tracker is limited by camera download time (latency) and sensitivity (precision).

Comparing the CamBlobs2 contrast sensitivity test to the near Pelli-Robson contrast sensitivity test in normally-sighted young adults

PURPOSE

Contrast sensitivity (CS) has been proposed as a potential method for patients to assess their vision at home. The CamBlobs2 contrast sensitivity test is meant to be performed easily in the clinic or at home. The purpose of this study was to determine the intra-visit coefficient of repeatability of the CamBlobs2 compared with the near Pelli-Robson test, and the limits of agreement between these two tests on normally-sighted subjects.

METHODS

Twenty-two normally-sighted subjects (mean age 28 ± 4 years) completed two trials of the near Pelli-Robson and CamBlobs2 contrast sensitivity tests within a single visit. Tests were performed monocularly on each eye in random order. Pelli-Robson tests were scored as 0.05 logCS for each letter read correctly after deducting the first triplet. CamBlob2 tests were scored as the highest line where two or fewer blobs were marked correctly. The coefficient of repeatability was determined as 1.96 times the standard deviation of the difference between the two measurements using the same type of chart on the same eye. The limits of agreement between the two tests were evaluated using Bland-Altman analysis.

RESULTS

The mean difference between intra-visit measurements for both the near Pelli-Robson and CamBlobs2 was less than 0.05 logCS and the coefficient of repeatability was within ±0.20 log CS for both left and right eyes. The mean ± standard deviation differences between near Pelli-Robson and CamBlobs2 scores was -0.08 ± 0.08 (limits of agreement: -0.24 to 0.09) for right eyes and -0.05 ± 0.10 (limits of agreement: -0.23 to 0.14) logCS for left eyes based on average measurements.

CONCLUSIONS

The intra-visit repeatability of CamBlobs2 was consistent with the near Pelli-Robson contrast sensitivity test (±0.20 logCS). With a 0.05 correction, the CamBlobs2 scores showed excellent agreement with the near Pelli-Robson contrast sensitivity test.

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.

Optimization of Virtual Shack-Hartmann Wavefront Sensing

Virtual Shack–Hartmann wavefront sensing (vSHWS) can flexibly adjust parameters to meet different requirements without changing the system, and it is a promising means for aberration measurement. However, how to optimize its parameters to achieve the best performance is rarely discussed. In this work, the data processing procedure and methods of vSHWS were demonstrated by using a set of normal human ocular aberrations as an example. The shapes (round and square) of a virtual lenslet, the zero-padding of the sub-aperture electric field, sub-aperture number, as well as the sequences (before and after diffraction calculation), algorithms, and interval of data interpolation, were analyzed to find the optimal configuration. The effect of the above optimizations on its anti-noise performance was also studied. The Zernike coefficient errors and the root mean square of the wavefront error between the reconstructed and preset wavefronts were used for performance evaluation. The performance of the optimized vSHWS could be significantly improved compared to that of a non-optimized one, which was also verified with 20 sets of clinical human ocular aberrations. This work makes the vSHWS’s implementation clearer, and the optimization methods and the obtained results are of great significance for its applications.

Joint effect of defocus blur and spatial attention

Defocus blur and spatial attention both act on our ability to see clearly over time. However, it is currently unknown how these two factors interact because studies on spatial resolution only focused on the separate effects of attention and defocus blurs. In this study, eleven participants performed a resolution acuity task along the diagonal 135˚/315˚ with horizontal, at 8˚ eccentricity for clear and blurred Landolt C images under various manipulations of covert endogenous attention. All the conditions were interleaved and viewed binocularly on a visual display. We observed that attention not just improves the resolution of clear stimuli, but also modulates the resolution of defocused stimuli for compensating the loss of resolution caused by retinal blur. Our results show, however, that as the degree of attention decreases, the differences between clear and blurred images largely diminish, thus limiting the benefit of an image quality enhancement. It also appeared that attention tends to enhance the resolution of clear targets more than blurred targets, suggesting potential variations in the gain of vision correction with the level of attention. This demonstrates that the interaction between spatial attention and defocus blur can play a role in the way we see things. In view of these findings, the development of adaptive interventions, which adjust the eye's defocus to attention, may hold promise.

Short-term effect of atropine on higher-order aberrations in myopic children

BACKGROUND

This study aimed to investigate the short-term effect of cycloplegia on higher-order aberrations (HOAs) in school-age myopic children who received 0.25% atropine for cycloplegic refraction.

METHODS

We performed a retrospective chart review of 24 myopic children between the ages of 5 and 15 years, who had received one topical drop of 0.25% atropine for three consecutive nights before undergoing cycloplegic refraction. Auto-refraction, visual acuity, and HOAs measured with the iTrace aberrometer were compared before and after atropine use. To account for the effect of cycloplegia, the amount of HOAs under matching scanning sizes was compared.

RESULTS

There were statistically significant differences in the spherical equivalent, with a hyperopic shift after atropine use (p < 0.001). Corrected visual acuity and spherical aberrations showed no significant change under the respective pupil and scanning sizes before and after atropine use. Under identical scanning sizes, there was a significant change in total spherical aberration (from 0.03 to 0.06 μm, p = 0.044) and internal spherical aberration (from -0.10 to -0.05 μm, p = 0.049) after atropine use. Differences in corneal spherical aberration were insignificant.

CONCLUSION

The positive shift of spherical aberration induced by the inhibition of accommodation in myopic children may have a possible effect against myopic progression. Future studies can focus on the long-term effect on HOAs and impact on visual quality with lower concentrations of atropine.

Neural network model assisted Fourier ptychography with Zernike aberration recovery and total variation constraint

SIGNIFICANCE

Fourier ptychography (FP) is a computational imaging approach that achieves high-resolution reconstruction. Inspired by neural networks, many deep-learning-based methods are proposed to solve FP problems. However, the performance of FP still suffers from optical aberration, which needs to be considered.

AIM

We present a neural network model for FP reconstructions that can make proper estimation toward aberration and achieve artifact-free reconstruction.

APPROACH

Inspired by the iterative reconstruction of FP, we design a neural network model that mimics the forward imaging process of FP via TensorFlow. The sample and aberration are considered as learnable weights and optimized through back-propagation. Especially, we employ the Zernike terms instead of aberration to decrease the optimization freedom of pupil recovery and perform a high-accuracy estimation. Owing to the auto-differentiation capabilities of the neural network, we additionally utilize total variation regularization to improve the visual quality.

RESULTS

We validate the performance of the reported method via both simulation and experiment. Our method exhibits higher robustness against sophisticated optical aberrations and achieves better image quality by reducing artifacts.

CONCLUSIONS

The forward neural network model can jointly recover the high-resolution sample and optical aberration in iterative FP reconstruction. We hope our method that can provide a neural-network perspective to solve iterative-based coherent or incoherent imaging problems.

Adaptive optics for high-resolution imaging

Adaptive optics (AO) is a technique that corrects for optical aberrations. It was originally proposed to correct for the blurring effect of atmospheric turbulence on images in ground-based telescopes and was instrumental in the work that resulted in the Nobel prize-winning discovery of a supermassive compact object at the centre of our galaxy. When AO is used to correct for the eye's imperfect optics, retinal changes at the cellular level can be detected, allowing us to study the operation of the visual system and to assess ocular health in the microscopic domain. By correcting for sample-induced blur in microscopy, AO has pushed the boundaries of imaging in thick tissue specimens, such as when observing neuronal processes in the brain. In this primer, we focus on the application of AO for high-resolution imaging in astronomy, vision science and microscopy. We begin with an overview of the general principles of AO and its main components, which include methods to measure the aberrations, devices for aberration correction, and how these components are linked in operation. We present results and applications from each field along with reproducibility considerations and limitations. Finally, we discuss future directions.

An Alternative Wavefront Reconstruction Method for Human Eyes

PURPOSE

To expand upon and clinically demonstrate the results of a new polynomial decomposition method.

METHODS

To discuss the theoretical considerations comparing the qualitative and quantitative information produced by the Zernike coefficients and a new polynomial decomposition basis, in a comparative series of theoretical and clinical case studies.

RESULTS

These comparative studies validate the novel polynomial basis that decomposes the wavefront, with clear segregation of the higher and lower aberrations. There is no artifactual reduction of some of the higher order aberration coefficients, providing a more clinically relevant retinal image quality prediction.

CONCLUSIONS

Some of the inherent limitations of the Zernike polynomials in clinical ophthalmic applications can be solved by a novel set of polynomials forming an alternative higher order basis. The new basis provides a clear separation between modes containing lower order terms versus higher order terms and offers clinicians a more clinically realistic wavefront analysis. [J Refract Surg. 2020;36(2):74-81.].

Corneal wavefront aberrations and subjective quality of vision after small incision lenticule extraction

PURPOSE

To analyse in depth the associations between objectively measured corneal higher-order aberrations (HOAs) and subjectively perceived visual quality after small incision lenticule extraction (SMILE) as quantified with the standardized and clinically validated quality of vision (QOV) questionnaire.

METHODS

This cross-sectional study included patients after bilateral simultaneous SMILE for the treatment of myopia and/or myopic astigmatism with plano target refraction. Scheimpflug imaging (Pentacam HR; Oculus Optikgeräte GmbH, Wetzlar, Germany) was used to objectively quantify corneal HOAs. The standardized and validated QOV questionnaire was employed to gauge patients' subjectively perceived visual quality regarding frequency, severity and bothering effect of visual disturbances.

RESULTS

A total of 394 eyes of 197 patients with a mean age of 32.4 ± 7.7 years and a mean postoperative follow-up of 24.3 ± 14.1 months were included. SMILE induced a statistically significant (p < 0.001) increase in spherical aberration (0.074 ± 0.131 µm), coma (0.142 ± 0.179 µm), trefoil (0.018 ± 0.067 µm) as well as in total HOAs (0.191 ± 0.176 µm). Surgically induced and postoperative levels of HOA showed no correlation with the three QOV scores representative of overall visual symptom frequency, severity and bothering effect (all R² values ≤ 0.016). In addition, the associations between specific visual symptoms (e.g. starburst) and singular HOA terms (e.g. haloes) were very weak (all Rho values ≤ 0.164).

CONCLUSIONS

Small incision lenticule extraction induced significant amounts of corneal HOAs that, however, showed no clear relationships to patient-reported QOV or specific long-term visual symptoms.

A Toolbox for Isophase-Curvature Guided Computation of Metrology Hologram

We describe the algorithmic foundations of an open-source numerical toolbox, written in the Octave language, for the creation of computer-generated binary and multi-level holograms used in interferometric form error measurements of complex aspheric and free-form precision surfaces and wavefronts. In a typical measurement setup for this type of surface, a hologram is used to generate a test wavefront that has the design shape of the surface, which is then compared to a fabricated part using an imaging laser interferometer. The optical function of the hologram in the measurement is generally modeled with optical ray-tracing software and it can be encapsulated by a scalar optical phase function φ : R2 →R. The toolbox converts phase functions into equivalent binary holograms that generate the desired test wavefronts for an interferometric form error measurement. The algorithms in this toolbox take advantage of the relationship between the local properties of phase functions and the local geometry (curvature) of isophase lines. It forms the core of an effcient algorithm for the computation of optical holograms. Holograms are created in a format that can be processed by most laser-or e-beam lithography systems. While the toolbox is chiefy aimed at the creation of hologram layouts needed for measurements of precision surfaces and wavefronts, we show that the isophase-following algorithm is easily extended to phase functions with singularities and discontinuities. Such phase functions result in holograms with zone bifurcation and they can be used to generate helical wavefronts. Light beams with helical wavefronts have applications beyond surface and wavefront metrology. The toolbox also includes a family of functions for the effcient estimation and evaluation of Zernike polynomials, which are widely used in optical applications.

Wavefront Aberration Sensor Based on a Multichannel Diffractive Optical Element

We propose a new type of a wavefront aberration sensor, that is, a Zernike matched multichannel diffractive optical filter, which performs consistent filtering of phase distributions corresponding to Zernike polynomials. The sensitivity of the new sensor is theoretically estimated. Based on the theory, we develop recommendations for its application. Test wavefronts formed using a spatial light modulator are experimentally investigated. The applicability of the new sensor for the fine-tuning of a laser collimator is assessed.

Noninvasive imaging of the tree shrew eye: Wavefront analysis and retinal imaging with correlative histology

Tree shrews are small mammals with excellent vision and are closely related to primates. They have been used extensively as a model for studying refractive development, myopia, and central visual processing and are becoming an important model for vision research. Their cone dominant retina (∼95% cones) provides a potential avenue to create new damage/disease models of human macular pathology and to monitor progression or treatment response. To continue the development of the tree shrew as an animal model, we provide here the first measurements of higher order aberrations along with adaptive optics scanning light ophthalmoscopy (AOSLO) images of the photoreceptor mosaic in the tree shrew retina. To compare intra-animal in vivo and ex vivo cone density measurements, the AOSLO images were matched to whole-mount immunofluorescence microscopy. Analysis of the tree shrew wavefront indicated that the optics are well-matched to the sampling of the cone mosaic and is consistent with the suggestion that juvenile tree shrews are nearly emmetropic (slightly hyperopic). Compared with in vivo measurements, consistently higher cone density was measured ex vivo, likely due to tissue shrinkage during histological processing. Tree shrews also possess massive mitochondria ("megamitochondria") in their cone inner segments, providing a natural model to assess how mitochondrial size affects in vivo retinal imagery. Intra-animal in vivo and ex vivo axial distance measurements were made in the outer retina with optical coherence tomography (OCT) and transmission electron microscopy (TEM), respectively, to determine the origin of sub-cellular cone reflectivity seen on OCT. These results demonstrate that these megamitochondria create an additional hyper-reflective outer retinal reflective band in OCT images. The ability to use noninvasive retinal imaging in tree shrews supports development of this species as a model of cone disorders.