Jacobi-Fourier phase masks as ophthalmic elements to correct presbyopia.

PURPOSE: Investigations into the correction of presbyopia have considered lens design, clinical implications and the development of objective metrics such as the visual Strehl ratio. This study investigated the Jacobi-Fourier phase mask as an ophthalmic element in the correction of presbyopia. The goal was to develop a contact or intraocular lens whose performance was largely insensitive to changes in pupil diameter. METHODS: Numerical simulations based on Fourier optics were performed to evaluate three different Jacobi-Fourier polynomials, with the aim of providing a range of clear vision (1 Dioptre (D)). Performance was evaluated for three pupil sizes (6, 4 and 2 mm), while polychromatic images were simulated using three different wavelengths (656.3, 587.6 and 486.1 nm). The Neural Transfer function was included in the simulation. To validate the method and results, we used the Visual Strehl combined objective metric (VSCombined) currently used in visual optics. This metric gives more weight to the phase transfer function and is more suitable for non-symmetrical phase functions. RESULTS: Numerical validation showed the suitability of the Jacobi-Fourier phase masks for extending the range of clear vision of presbyopic eyes, providing a visual acuity of at least 0.10 logMAR (6/7.5 Snellen) at all distances between 1 and 6 m. The results show a range of clear vision of 1D was not affected by changes in pupil size, an increase in retinal image contrast accompanied by image artefact reduction by increasing the radial order of the Jacobi-Fourier phase mask and a reduction of wavelength dependence of the retinal images. These results are supported by simulated images and the objective criterion VSCombined. CONCLUSIONS: The use of Jacobi-Fourier phase masks as ophthalmic elements for presbyopic correction show promising results, with a good range of clear vision and reduced dependence on pupil size and chromatic aberration.

Towards a wavefront-preservation X-ray crystal monochromator for high-repetition-rate FELs.

The wavefront preservation of coherent X-ray free-electron laser beams is pushing the requirement on the quality and performance of X-ray optics to an unprecedented level. The Strehl ratio can be used to quantify this requirement. In this paper, the criteria for thermal deformation of the X-ray optics are formulated, especially for crystal monochromators. To preserve the X-ray wavefront, the standard deviation of the height error should be sub-nm for mirrors and less than 25 pm for crystal monochromators. Cryocooled silicon crystals combined with two techniques can be used to achieve this level of performance for monochromator crystals: (1) using a focusing element to compensate the second-order component of the thermal deformation; (2) introducing a cooling pad between the cooling block and silicon crystal and optimizing the effective cooling temperature. Each of these techniques allows the thermal deformation in standard deviation of the height error to be reduced by an order of magnitude. As an example, for the LCLS-II-HE Dynamic X-ray Scattering instrument, the criteria on thermal deformation of a high-heat-load monochromator crystal can be achieved for a 100 W SASE FEL beam. Wavefront propagation simulations confirm that the reflected beam intensity profile is satisfactory on both the peak power density and focused beam size.

The Effect of the Position Determination Error for Flexible Linear Array Elements on the Tomogram Focusing.

In the article, the study of the quality of tomogram focusing during the inspection of objects with curved surfaces by flexible acoustic array was described. The main goal of the study was theoretically and experimentally define the acceptable deviation limits of the elements' coordinates values. The tomogram reconstruction was performed by the total focusing method. The Strehl ratio was chosen as a criterion for assessing the quality of tomogram focusing. The ultrasonic inspection procedure were simulated and validated experimentally by means of convex and concave curved arrays. In the study, it was proven that the elements coordinates of the flexible acoustic array were determined with an error of no more than 0.18λ and the tomogram image was obtained in sharp focus.

Sensitivity of remote focusing microscopes to magnification mismatch.

Remote focusing (RF) is a technique that greatly extends the aberration-free axial scan range of an optical microscope. To maximise the diffraction limited depth range in an RF system, the magnification of the relay lenses should be such that the pupil planes of the objectives are accurately mapped on to each other. In this paper we study the tolerance of the RF system to magnification mismatch and quantify the amount of residual spherical aberration present at different focusing depths. We observe that small deviations from ideal magnification results in increased amounts of residual spherical aberration terms leading to a reduction in the diffracted limited range. For high-numerical aperture objectives, the simulation predicts a 50% decrease in the diffracted limited range for 1% magnification mismatch. The simulation has been verified against an experimental RF system with ideal and nonideal magnifications. Experimentally confirmed predictions also provide a valuable empirical method of determining when a system is close to the ideal phase matching condition, based on the sign of the spherical aberration on either side of focus.

Visual interaction of 2nd to 5th order Zernike aberration terms with vertical coma.

PURPOSE: In order to better understand the optical consequence of residual aberrations during conventional rigid contact lens wear in keratoconus, this study aimed to quantify the visual interaction between positive vertical coma (C(3, -1)) and other individual 2nd to 5th radial order Zernike aberration terms. METHODS: The experiment proceeded in two parts. First, two levels of C(3, -1) (target term) were simulated. Individual Zernike aberration terms from the 2nd to 5th radial orders (test terms) were combined in 0.05-µm steps a) from -2.00 µm to +2.00 µm with +1.00 µm of C(3, -1) and b) from -1.00 µm to +1.00 µm with +0.50 µm of C(3, -1). The resulting combinations were used to calculate the logarithm of the visual Strehl ratio (logVSX) and predict the relative beneficial or deleterious impact of the interaction. Second, for test terms where an interaction was predicted to provide more than a 0.25 logVSX benefit compared to C(3, -1) alone, high contrast logMAR acuity charts were constructed (simulating the manner in which the test + target term combinations would impact the retinal image of the chart), and randomly read by three well-corrected, typically-sighted individuals through a 3.0-mm diameter artificial pupil. RESULTS: When combined with positive C(3, -1), C(3, -3), C(4, -4), C(5, -5), C(5, -3), and C(5, -1) exhibited better visual image quality compared with C(3, -1) alone. Ratios of the test terms to target term providing maximal benefit remained constant for both +0.50 µm and +1.00 µm of C(3, -1). C(3, -3) and C(5, -1) had the largest predicted beneficial effect, with the maximal effect for +1.00 µm of C(3, -1) occurring with +0.35 µm of C(5, -1) and -1.00 µm of C(3, -3). When individuals read letter charts convolved with the point spread function derived from C(3, -1) combined with C(3, -3) and C(3, -1) combined with C(5, -1), the maximal beneficial effect was 0.27 logMAR (13.5 letters) for C(3, -3) and 0.36 logMAR (18 letters) for C(5, -1). CONCLUSIONS: While most interactions reduced visual image quality, combinations of C(3, -3) (vertical trefoil) and C(5, -1) (vertical secondary coma) provided a clinically relevant beneficial effect in the presence of C(3, -1) (vertical coma) which was demonstrated in both through-focus simulation and chart reading tests. Future work will examine whether these effects persist in the presence of the entire spectrum of residual aberrations seen in the eyes of individuals with keratoconus.

Optimal STEM Convergence Angle Selection Using a Convolutional Neural Network and the Strehl Ratio.

The selection of the correct convergence angle is essential for achieving the highest resolution imaging in scanning transmission electron microscopy (STEM). The use of poor heuristics, such as Rayleigh's quarter-phase rule, to assess probe quality and uncertainties in the measurement of the aberration function results in the incorrect selection of convergence angles and lower resolution. Here, we show that the Strehl ratio provides an accurate and efficient way to calculate criteria for evaluating the probe size for STEM. A convolutional neural network trained on the Strehl ratio is shown to outperform experienced microscopists at selecting a convergence angle from a single electron Ronchigram using simulated datasets. Generating tens of thousands of simulated Ronchigram examples, the network is trained to select convergence angles yielding probes on average 85% nearer to optimal size at millisecond speeds (0.02% of human assessment time). Qualitative assessment on experimental Ronchigrams with intentionally introduced aberrations suggests that trends in the optimal convergence angle size are well modeled but high accuracy requires a high number of training datasets. This near-immediate assessment of Ronchigrams using the Strehl ratio and machine learning highlights a viable path toward the rapid, automated alignment of aberration-corrected electron microscopes.

Utility of the optical quality analysis system for decision-making in cataract surgery.

BACKGROUND: A cataract is a common cause of vision impairment that requires surgery in older subjects. The Optical Quality Analysis System (OQAS, Visiometrics SL, Terrassa, Spain) assesses the optical quality of the eye in cataract patients. This study shows the role of the optical quality evaluation system for decision-making in cataract surgery. We investigated the clinical utility of the OQAS for decision-making in cataract surgery. METHODS: Sixty-seven eyes from 67 patients undergoing cataract surgery and 109 eyes from 109 control subjects were compared. The best corrected visual acuity (BCVA) was measured. The objective scatter index (OSI), modulation transfer function (MTF), Strehl ratio, predicted visual acuity (PVA) 100%, PVA 20%, and PVA 10% were measured using the OQAS. The sensitivity and specificity of the different parameters were analyzed using the receiver operating characteristic (ROC) curve. The main parameters measured were sensitivity and specificity. RESULTS: The BCVA, OSI, PVA 100%, PVA 20%, and PVA 10% were higher in the cataract group compared to those in the control group, while the MTF and Strehl ratios were lower (p <  0.001 for all). ROC analysis showed that the OSI had the largest area under the curve and that the sensitivity and specificity of the OSI were 83.9 and 84.6%, respectively, at the optimal cut-off point of 2.35. CONCLUSION: The MTF, OSI, Strehl ratio, PVA 100%, PVA 20% and PVA 10% may be useful parameters for preoperative decision-making in cataract surgery. The OSI appears to be the most effective parameter for this purpose.

In vitro comparative optical bench analysis of a spherical and aspheric optic design of the same IOL model.

BACKGROUND: To analyse objective optical properties of the spherical and aspheric design of the same intraocular lens (IOL) model using optical bench analysis. METHODS: This study entailed a comparative analysis of 10 spherical C-flex 570 C and 10 aspheric C-flex 970 C IOLs (Rayner Intraocular Lenses Ltd., Hove, UK) of 26 diopters [D] using an optical bench (OptiSpheric, Trioptics, Germany). In all lenses, we evaluated the modulation transfer function (MTF) at 50 lp/mm and 100 lp/mm and the Strehl Ratio using a 3-mm (photopic) and 4.5-mm (mesopic) aperture. RESULTS: At 50 lp/mm, the MTF values were 0.713/0.805 (C-flex 570 C/C-flex 970 C) for a 3-mm aperture and 0.294/0.591 for a 4.5-mm aperture. At 100 lp/mm, the MTF values were 0.524/0.634 for a 3-mm aperture and 0.198/0.344 for a 4.5-mm aperture. The Strehl Ratio was 0.806/0.925 and 0.237/0.479 for a 3-mm and 4.5-mm aperture respectively. A Mann-Whitney U test revealed all intergroup differences to be statistically significant (p < 0.01). CONCLUSION: The aspheric IOL design achieved higher MTF values than the spherical design of the same IOL for both apertures. Moreover, the differences between the two designs of the IOL were more prominent for larger apertures. This suggests that the evaluated IOL provides enhanced optical quality to patients with larger pupils or working under mesopic conditions.

Optimal orientation for angularly segmented multifocal corrections.

PURPOSE: Evaluate the importance of orientation of multifocal lens designs with angular increments of addition. METHODS: Optical properties of one monofocal and three multifocal designs were analysed with the visual Strehl ratio (VSOTF) metric through-focus (-1 to 5 D). Designs were tested in combination with the higher-order aberrations (HOAs) of 782 subjects (1564 eyes). Simulations included one monofocal, one bifocal (eight orientations), one trifocal (four orientations), and a 4-foci design (four orientations). Monocular and binocular performances of all designs were assessed by computing the area under the through-focus VSOTF plots, the through-focus range of acceptable optical performance, and, for binocular combinations, optical disparity between left and right eyes. RESULTS: Under monocular conditions, bifocal designs generated larger areas under the through focus VSOTF than trifocal designs and 4-foci designs. Specifically, bifocal designs divided vertically were optimal for 48% of eyes. Trifocal designs and 4-foci designs offered longer intervals of acceptable through-focus vision. Coma and spherical aberration values were correlated with the optimal orientation of multifocal corrections. The best binocular combination was achieved with a monofocal and a trifocal lens. The orientation of a multifocal design with angular areas affected the final optical properties of the combination (lens plus eye). CONCLUSIONS: The optical aberration distributions for our population of physiologically normal eyes demonstrated improved performance for some lens design orientations (i.e., left-right segments for 2-zone bifocals). Taking into account the HOAs of healthy patients, with special attention to coma and spherical aberration, will increase the optical quality of angularly divided multifocal solutions.

Comparison of postoperative visual performance between trifocal intraocular lens and monofocal intraocular lens.

OBJECTIVES: To compare the subjective and objective visual quality more comprehensively after surgery of the commonly used multifocal intraocular lenses (IOL) and monolocal IOL implants through long-term systematic clinical observation, providing reference and basis for clinical application. METHODS: Non-randomized controlled trial. A total of 91 (138 eyes) patients between June 2020 and December 2020 were implanted trifocal IOL or monofocal IOL after phacoemulsification in a tertiary class hospital in Wuhan. Monocular testing 3 months after surgery included best-spectacles corrected and uncorrected visual at distant, intermediate, and near vision; spherical equivalent (SE); defocus curve; modulation transfer function (MTF); dysfunctional lens index (DLI); Strehl ratio (SR); mesopic contrast sensitivity function; quality-of-life, spectacles independence, visual disturbance, and surgical satisfaction surveys 3 months post-surgery. RESULTS: There was statistically better uncorrected vision acuity with trifocal IOLs in all range, while monofocal IOL had statistically better mesopic contrast sensitivity at specific spatial frequencies and statistically worse defocus curves, spectacles independence, and surgical satisfaction. The trifocal IOL performed better in subjective quality of vision and life and spectacles independence questionnaires, and the objective quality of vision had no statistical significance. CONCLUSION: Compared to monofocal IOL, trifocal IOL could provide a full range of clear vision for the majority of patients with simple cataracts, improve the rate of spectacles independence and patient satisfaction. And the objective quality of vision did not show any difference.

Effect of postoperative residual astigmatism on visual outcomes after trifocal intraocular lens implantation.

Purpose: The aim of this study was to evaluate the effect of residual astigmatism on postoperative visual outcomes after trifocal intraocular lens implantation. Methods: In this prospective observational study, we divided 156 eyes into two groups according to postoperative astigmatism measured by subjective optometry and followed them up for 3 months. Visual acuity, modulation transfer function (MTF) curves, Strehl ratio (SR), Visual Function Index-14 scores, and photic phenomena were compared. Results: Linear regression analysis revealed a weak correlation between residual astigmatism and uncorrected distance visual acuity (UDVA) (r = 0.190, P = 0.016) at 3 months and a significant between-group difference at 1- and 3-month postoperative UDVA (P = 0.038, P = 0.018, respectively). MTF curve values and SR (MTF-10 total, MTF-10 cornea, MTF-30 total, MTF-30 cornea, SR Total, and SR cornea) were significantly worse (P < 0.001), and the Visual Function Index-14 scores were lower in the 0.5 < astigmatism ≤ 1.25 D group (P < 0.05) than in the astigmatism ≤ 0.5 D group. No significant differences were found in the frequency, severity, and bothersomeness of photic phenomena (P > 0.05). Conclusion: Postoperative residual astigmatism affects the UDVA of the trifocal intraocular lens-implanted eyes. Although we found no significant differences in uncorrected intermediate and near visual acuity, both objective and subjective visual quality were affected, suggesting the need for surgical planning when the anticipated postoperative astigmatism is >0.5 D.

Comparison of Corneal Optical Quality After SMILE, Wavefront-Optimized LASIK and Topography-Guided LASIK for Myopia and Myopic Astigmatism.

Purpose: To compare visual outcomes and corneal optical quality after small incision lenticule extraction (SMILE), wavefront-optimized (WFO) FS-LASIK, and topography-guided customized ablation treatment (TCAT) FS-LASIK for myopia. Methods: This prospective case-series study included 283 eyes of 283 myopic patients who underwent SMILE or FS-LASIK. There were 102, 100, and 81 eyes in the SMILE group, WFO group and TCAT group, respectively. The tomography system (Sirius) was used to measure corneal aberrations and optical quality. Results: At postoperative 1 and 6 months, there were no significant differences in uncorrected distance visual acuity and corrected distance visual acuity among the three groups (P > 0.05). Postoperative manifest refractive spherical equivalent was similar among the groups (P > 0.05). There was statistically significant difference in cylinder at 1 month among the three groups, with the highest mean value in TCAT group (P < 0.05). The corneal optical path difference, root mean square of corneal astigmatism and strehl ratio were the most superior in the TCAT group at postoperative 1 and 6 months (P < 0.05). Conclusion: SMILE, WFO FS-LASIK, and TCAT FS-LASIK provided similar visual results. The corneal visual quality after TCAT FS-LASIK was the best.

One-year effect of wearing orthokeratology lenses on the visual quality of juvenile myopia: a retrospective study.

OBJECTIVE: To study the one-year effect of wearing orthokeratology (OK) lenses on the visual quality of juvenile myopia. METHODS: The right eyes of 36 juvenile myopias were retrospectively studied in this work. Q-value, e-value, corneal curvature, strehl ratio (SR), modulation transfer function (MTF) and wavefront aberration (WA) were compared before and at 1, 3 and 12 months after wearing OK lenses. The SR, MTF and WA of cornea, internal optic and ocular were analyzed separately. The spherical and cylinder diopter, vision acuity, compensating factor (CF) and compensative rate (CF%) were compared before and at 12 months after wearing OK lenses. RESULTS: (1) The vision of LogMAR increased and the corneal curvature decreased significantly after wearing OK lenses. There was no significant difference for the e-value before and after wearing OK lenses. The Q-value increased at 1 month but decreased at 3 and 12 months remarkably. (2) The ocular and internal optic SR and MTF increased significantly at 1 month and then remained stable. The MTF in different spacial frequencies increased after wearing OK lenses. There was no significant difference for the corneal SR before and after wearing OK lenses, and the corneal MTF decreased significantly after wearing OK lenses. (3) For the ocular, the total higher order aberration (HOA), spherical, coma and trefoil aberrations increased, and the total aberration, total lower order aberration (LOA) and defocus aberration decreased obviously except astigmatism. The corneal aberrations increased significantly after wearing OK lenses except astigmatism. For the internal optic, the total aberration, total LOA and defocus aberration decreased, and the total HOA, coma and trefoil aberration increased significantly except the astigmatism and spherical aberrations. (4) The CF and CF% of total aberration, total LOA, total HOA and coma aberrations increased, and those of astigmatism and spherical decreased at 12 months. CONCLUSIONS: Orthokeratology is effective in correcting the refractive error and improving the vision quality of juvenile myopia over the one-year follow-up period.

Critical band masking reveals the effects of optical distortions on the channel mediating letter identification.

There is evidence that letter identification is mediated by only a narrow band of spatial frequencies and that the center frequency of the neural channel thought to underlie this selectivity is related to the size of the letters. When letters are spatially filtered (at a fixed size) the channel tuning characteristics change according to the properties of the spatial filter (Majaj et al., 2002). Optical aberrations in the eye act to spatially filter the image formed on the retina-their effect is generally to attenuate high frequencies more than low frequencies but often in a non-monotonic way. We might expect the change in the spatial frequency spectrum caused by the aberration to predict the shift in channel tuning observed for aberrated letters. We show that this is not the case. We used critical-band masking to estimate channel-tuning in the presence of three types of aberration-defocus, coma and secondary astigmatism. We found that the maximum masking was shifted to lower frequencies in the presence of an aberration and that this result was not simply predicted by the spatial-frequency-dependent degradation in image quality, assessed via metrics that have previously been shown to correlate well with performance loss in the presence of an aberration. We show that if image quality effects are taken into account (using visual Strehl metrics), the neural channel required to model the data is shifted to lower frequencies compared to the control (no-aberration) condition. Additionally, we show that when spurious resolution (caused by π phase shifts in the optical transfer function) in the image is masked, the channel tuning properties for aberrated letters are affected, suggesting that there may be interference between visual channels. Even in the presence of simulated aberrations, whose properties change from trial-to-trial, observers exhibit flexibility in selecting the spatial frequencies that support letter identification.

Accounting for the phase, spatial frequency and orientation demands of the task improves metrics based on the visual Strehl ratio.

Advances in ophthalmic instrumentation have allowed high order aberrations to be measured in vivo. These measurements describe the distortions to a plane wavefront entering the eye, but not the effect they have on visual performance. One metric for predicting visual performance from a wavefront measurement uses the visual Strehl ratio, calculated in the optical transfer function (OTF) domain (VSOTF) (Thibos et al., 2004). We considered how well such a metric captures empirical measurements of the effects of defocus, coma and secondary astigmatism on letter identification and on reading. We show that predictions using the visual Strehl ratio can be significantly improved by weighting the OTF by the spatial frequency band that mediates letter identification and further improved by considering the orientation of phase and contrast changes imposed by the aberration. We additionally showed that these altered metrics compare well to a cross-correlation-based metric. We suggest a version of the visual Strehl ratio, VScombined, that incorporates primarily those phase disruptions and contrast changes that have been shown independently to affect object recognition processes. This metric compared well to VSOTF for letter identification and was the best predictor of reading performance, having a higher correlation with the data than either the VSOTF or cross-correlation-based metric.