Integrated analysis of industrial limitations and image quality: an end-to-end design approach.

There is a trend in optical system design toward explicitly considering real-world industrial demands in the metrics to be optimized, from which emerges a cost-performance trade-off. Another relevant recent tendency is the so-called end-to-end design, where the design metric is an expected quality index of the final image, after digital restoration. We propose an integrated approach for analyzing the cost-performance trade-off in end-to-end designs. We exemplify it with a simple optical model where the cost is determined by the inclusion of an aspherical surface. We show that the resulting optimal trade-off configurations when applying an end-to-end design are substantially different from a conventional design. Such differences, as well as the increase in performance, are especially significant for lower-cost configurations.

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.

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.

Effects of a Regular Endurance Training Program on Running Economy and Biomechanics in Runners.

A regular endurance training program may elicit different adaptations compared to an isolated training method. In this study, we analyzed the effects of 8 weeks of a regular endurance training program on running economy (RE), particularly neuromuscular and biomechanical parameters, in runners of different athletic abilities. Twenty-four male runners were divided into two groups: well-trained (n=12) and recreational (n=12). Both groups completed a 4-min running bout at 13 and 17 km·h-1, respectively, for the recreational and well-trained group, and a 5-jump plyometric test pre-post intervention. During the training program, participants completed low-intensity continuous sessions, high-intensity interval training sessions, and auxiliary strength training sessions. RE, measured as oxygen cost and energy cost, decreased by 6.15% (p=0.006) and 5.11% (p=0.043), respectively, in the well-trained group. In the recreational group, energy cost of running, respiratory exchange ratio, and leg stiffness decreased by 5.08% (p=0.035), 7.61% (p=0.003), and 10.59% (p=0.017), respectively, while ground contact time increased by 3.34% (p=0.012). The maximum height of the 5-jump plyometric test decreased by 4.55% (p=0.018) in the recreational group. We suggest that 8 weeks of regular endurance training leads to an improvement of ~5% in RE in recreational and well-trained runners with different physiological adaptations between groups and few changes in biomechanical and neuromuscular parameters only in recreational runners.

Acute effects of combined cycling and plyometrics on vertical jump performance in active males.

The aim of this study was to analyze the acute effects of high vs low-intensity cycling efforts, combined with plyometrics, on vertical jump performance. Twenty-four physically active men (mean ± SD: 23 ± 2 years, 72.1 ± 10.1 kg, 1.73 ± 0.07 m) were randomly divided into two groups: experimental group (EXP, n = 16) and control group (CON, n = 8). EXP competed 2 experimental trials in a random order: (a) short high-intensity interval exercise (HI + Plyo) [5 × 10 s of cycling ("all-out")/50 s active rest] or (b) low-intensity continuous exercise (LO + Plyo) [5 min of cycling at 75% of the HRmax)], along with 3 × 10 plyometric bounds (drop jumps)/1 min rest between sets. CON used a preconditioning activity of 13 min of low intensity cycling at ~60% of HRmax. Both EXP interventions significantly increased (p ≤ 0.05) the countermovement jump (CMJ) height at 1 min, 3 min, 6 min and 9 min compared to baseline, while the CON remained unchanged. There were no significant differences in CMJ performance enhancement between HI + Plyo (largest 11.2% at 9 min) and LO + Plyo (largest 15.0% at 3 min) at any time-point, suggesting that the plyometric component may be most important, with HR recovery taking slightly longer following HI + Plyo. The findings suggest that CMJ performance can be enhanced following high or low-intensity cycling combined with plyometric preconditioning activities in active males, the optimum recovery period likely to be individual-specific.

Multifocal wavefronts with prescribed caustics in axially symmetric optical systems.

Multifocal and/or extended depth-of-focus designs are widely used in many optical applications. In most of them, the optical configuration has axial symmetry. A usual design strategy consists of exploring the optimal wavefronts that emerging out of the optical system would provide the desired multifocal properties. Those properties are closely related to light concentration on caustic surfaces. We present a systematic analysis of how to obtain those multifocal wavefronts given some prescriptions on the locations of caustics. In particular, we derive several multifocal wavefronts under archetypical prescriptions in the sagittal caustic alone, or combined with the tangential one at certain points, with some emphasis on visual optics applications.

Catastrophe optics theory unveils the localised wave aberration features that generate ghost images.

Monocular polyplopia (ghost or multiple images) is a serious visual impediment for some people who report seeing two (diplopia), three (triplopia) or even more images. Polyplopia is expected to appear if the point spread function (PSF) has multiple intensity cores (a dense concentration of a large portion of the radiant flux contained in the PSF) relatively separated from each other, each of which contributes to a distinct image. We present a theory that assigns these multiple PSF cores to specific features of aberrated wavefronts, thereby accounting optically for the perceptual phenomenon of monocular polyplopia. The theory provides two major conclusions. First, the most likely event giving rise to multiple PSF cores is the presence of hyperbolic, or less probably elliptical, umbilic caustics (using the terminology of catastrophe optics). Second, those umbilic caustics formed on the retinal surface are associated with certain points of the wave aberration function, called cusps of Gauss, where the gradient of a curvature function vanishes. However, not all cusps of Gauss generate those umbilic caustics. We also provide necessary conditions for those cusps of Gauss to be fertile. To show the potential of this theoretical framework for understanding the nature and origin of polyplopia, we provide specific examples of ocular wave aberration functions that induce diplopia and triplopia. The polyplopia effects in these examples are illustrated by depicting the multi-core PSFs and the convolved retinal images for clinical letter charts, both through computer simulations and through experimental recording using an adaptive optics set-up. The number and location of cores in the PSF is thus a potentially useful metric for the existence and severity of polyplopia in spatial vision. These examples also help explain why physiological pupil constriction might reduce the incidence of ghosting and multiple images of daily objects that affect vision with dilated pupils. This mechanistic explanation suggests a possible role for optical phase-masking as a clinical treatment for polyplopia and ghosting.

Smooth multifocal wavefronts with a prescribed mean curvature for visual optics applications.

Multifocal lenses comprising progressive power surfaces are commonly used in contact and intraocular lens designs. Given a visual performance metric, a wavefront engineering approach to design such lenses is based on searching for the optimal wavefront at the exit pupil of the eye. Multifocal wavefronts distribute the energy along the different foci thanks to having a varying mean curvature. Therefore, a fundamental step in the wavefront engineering approach is to generate the wavefront from a prescribed mean curvature function. Conventionally, such a thing is done by superimposing spherical wavefront patches and maybe adding a certain component of spherical aberration to each spherical patch in order to increase the depth-of-field associated with each focus. However, such a procedure does not lead to smooth wavefront solutions and also restricts the type of available multifocal wavefronts. We derive a new, to the best of our knowledge, mathematical method to uniquely construct multifocal wavefronts from mean curvature functions (depending on radial and angular coordinates) under certain numerically justified approximations and restrictions. Additionally, our procedure leads to a particular family of wavefronts (line-umbilical multifocal wavefronts) described by 2 conditions: (1) to be smooth multiplicative separable functions in the radial and angular coordinates; (2) to be umbilical along a specific segment connecting the circle center with its edge. We provide several examples of multifocal wavefronts belonging to this family, including a smooth variant of the so-called light sword element.

Using a Portable Near-infrared Spectroscopy Device to Estimate The Second Ventilatory Threshold.

A breakpoint in a portable near-infrared spectroscopy (NIRS) derived deoxygenated haemoglobin (deoxy[Hb]) signal during an incremental VO2max running test has been associated with the second ventilatory threshold (VT2) in healthy participants. Thus, the aim was to examine the association between this breakpoint (NIRS) and VT2 in well-trained runners. Gas exchange and NIRS data were collected during an incremental VO2max running test for 10 well-trained runners. The breakpoint calculated in oxygen saturation (StO2) and the VT2 were determined and compared in terms relative to %VO2max, absolute speed, VO2, and maximum heart rate (HRmax). There were no significant differences (p>0.05) between the breakpoint in StO2 and VT2 relative to %VO2max (87.00±6.14 and 88.28 ± 3.98 %), absolute speed (15.70±1.42 and 16.10±1.66 km·h-1), VO2 (53.71±15.17 and 54.66±15.57 ml·kg-1·min-1), and%HRmax (90.90±4.17 and 91.84±3.70%). There were large and significant correlations between instruments relative to%VO2max (r=0.68, p<0.05), absolute speed (r=0.86, p<0.001), VO2 (r=0.86, p<0.001), and %HRmax (r=0.69; p<0.05). A Bland and Altman analysis of agreement between instruments resulted in a mean difference of - 1.27±4.49%, -0.40±0.84 km·h-1,-0.90±3.07 ml·kg-1·min-1, and - 0.94±3.14 for %VO2max, absolute speed, VO2, and %HRmax, respectively. We conclude that a portable NIRS determination of the StO2 breakpoint is comparable with VT2 using gas exchange and therefore appropriate for use in determining exercise training above VT2 intensity. This is the first study to analyze the validity with the running mode using a NIRS portable device.

Admissible surfaces in progressive addition lenses.

Progressive addition lenses (PALs) contain a surface of spatially varying curvature, which supplies variable optical power for different viewing areas over the lens. We derive complete compatibility equations providing the exact magnitude of a cylinder along lines of curvature on any arbitrary PAL smooth surface. These equations reveal that, contrary to current knowledge, the cylinder and its derivative depend not only on the principal curvature and its derivatives along the principal line but also on the geodesic curvature and its derivatives along the line orthogonal to the principal line. We quantify the relevance of the geodesic curvature through numerical computations. We also derive an extended and exact Minkwitz theorem restricted only to be applied along lines of curvature, but excluding umbilical points.

Foveal vision power errors induced by spectacle lenses designed to correct peripheral refractive errors.

PURPOSE: Radial Refractive Gradient (RRG) spectacles are lenses specifically designed to minimize peripheral hyperopic defocus typically found in conventional spectacles. Our goals were: (1) to demonstrate a method to design such lenses; and (2) to quantify the exact foveal vision power errors induced by them. METHODS: The design procedure was based on a point-by-point sequential surface construction algorithm that designs a front aspheric surface (back surface is spherical) to achieve a given overall tangential focal length of the lens. A peripheral refraction model was built based on average peripheral refractive errors from a set of eyes. We designed four negative lenses with optical powers: -2.5, -5.0, -7.5 and -10.0 D, so that the tangential focal length of the lens matches the retinal conjugate surface. RESULTS: The lenses induce very small sagittal power errors in a wide range of off-axis field angles (30°), solving the problem of peripheral hyperopic defocus. However, such designs introduce non-negligible mean power errors (above 0.25 D from 7°, 6.8°, 7.1° and 7.8° for the -2.5, -5.0, -7.5 and -10.0 D lenses, respectively) for foveal vision in a rotating eye. CONCLUSION: Our results show the unavoidable errors introduced by RRG spectacles when used for dynamic foveal vision. The described method offers valuable information towards determining the best trade-off between controlling power errors for peripheral and foveal vision.

Simulating real-world scenes viewed through ophthalmic lenses.

We present a comprehensive procedure to simulate real-world scenes viewed through ophthalmic lenses. Such a method enables us to anticipate the effects on image formation of the following combined undesired optical defects typically found in ophthalmic lenses: blur, distortion, and chromatic aberration. Additionally, it helps in comparing the expected scenes seen with different lens designs. The procedure is based on the following steps: (1) to calculate the distortion and local dioptric matrix associated with a set of different gaze directions; (2) to estimate point spread functions (PSF) associated with these matrices; (3) to compute the joint action of distortion, chromatic aberration, and PSF field on the scenes. We illustrate this procedure with two +5D spherical lenses: a moderately good performance lens and a highly degrading one. The method is suitable to evaluate ophthalmic lenses in a virtual reality framework.

The relationship between dioptric power and magnification in progressive addition lenses.

PURPOSE: Non-uniform magnification (distortion) and dioptric blur are two major undesired optical defects affecting vision when looking through progressive addition lenses (PALs) and studying them is potentially very valuable for PAL design. The major purpose of this paper is to analyse the relationship between dioptric power and magnification and, additionally, to evaluate the expected values of distortion and dioptric blur typically present in PALs. This has not been carefully and rigorously analysed to date. METHODS: We computed the local dioptric and magnification matrices (using a two-ray differential method) for different gaze directions in an archetypical model of a PAL. We used four different maps: scalar magnification and anamorphic distortion, to describe magnification, and mean power and astigmatism, to describe dioptric power. RESULTS: There is a good correlation between scalar magnification and mean power on the one hand, and anamorphic distortion and astigmatism on the other hand. Changes of 1 D in mean power are associated with variations in scalar magnification of around 3%. Also, 3% of anamorphic distortion is associated with increasing astigmatism up to 1 D. The directions of maximal power and maximal magnification are quite similar, though not equal (differences up to ± 1.5°). These directions strongly change from close to isotropic at the intermediate corridor to around 45° of oblique inclination for a few degrees of horizontal eye rotation. In typical PALs the level of distortion, which is unavoidably present when dioptric blurring appears, is small for usable vision zones (below 1 D of astigmatism). CONCLUSION: The combined analysis of dioptric power and magnification in PALs helps to understand their limitations as a visual aid. On the one hand, the potentials of including distortion magnitude as a target in the metric function being optimised in the PAL design are reduced; on the other hand, it seems worthwhile to explore adding the degradation orientation as an additional target.

Geometrical interpretation of dioptric blurring and magnification in ophthalmic lenses.

Blur and non-uniform magnification are two related undesired effects affecting vision when looking through eyeglasses. We propose a geometrical framework to study the relationship between both effects. Magnification and blur are locally characterized by dioptric and magnification matrices, respectively, which we compute here by using a novel two-ray numerical method. We propose a set of geometrical entities associated with the dioptric and magnification local matrices, which are analyzed in several examples. We prove that there is a strong correlation between such entities (e.g., astigmatism and anamorphic distortion), which, to a certain extent, is maintained even in highly asymmetric lenses. We also show the somewhat anti-intuitive result that the axis of maximal blurring is sometimes close to orthogonal to the axis of maximal distortion. The results provide useful clues for ophthalmic lens design.

The concept of geodesic curvature applied to optical surfaces.

PURPOSE: To propose geodesic curvature as a metric to characterise how an optical surface locally differs from axial symmetry. To derive equations to evaluate geodesic curvatures of arbitrary surfaces expressed in polar coordinates. METHODS: The concept of geodesic curvature is explained in detail as compared to other curvature-based metrics. Starting with the formula representing a surface as function of polar coordinates, an equation for the geodesic curvature is obtained depending only on first and second radial and first order angular derivatives of the surface function. The potential of the geodesic curvature is illustrated using different surface tests. RESULTS: Geodesic curvature reveals local axial asymmetries more sharply than other types of curvatures such as normal curvatures. CONCLUSION: Geodesic curvature maps could be used to characterise local axial asymmetries for relevant optometry applications such as corneal topography anomalies (keratoconus) or ophthalmic lens metrology.

Wavefront reconstruction from tangential and sagittal curvature.

In a previous contribution [Appl. Opt.51, 8599 (2012)], a coauthor of this work presented a method for reconstructing the wavefront aberration from tangential refractive power data measured using dynamic skiascopy. Here we propose a new regularized least squares method where the wavefront is reconstructed not only using tangential but also sagittal curvature data. We prove that our new method provides improved quality reconstruction for typical and also for highly aberrated wavefronts, under a wide range of experimental error levels. Our method may be applied to any type of wavefront sensor (not only dynamic skiascopy) able to measure either just tangential or tangential plus sagittal curvature data.

Multifocal intraocular lens providing optimized through-focus performance.

A widespread type of multifocal intraocular lens (MIOL) is based on expanding the depth of focus with specific amounts of spherical aberration. However, knowing the optimal wavefront aberration for multifocality does not directly provide a MIOL geometry. To overcome this issue, we present a new strategy to design MIOLs. The method optimizes directly the IOL surface geometries (aspheres with aspherical coefficients up to tenth order) using a multisurface pseudophakic eye model and a multiconfiguration approach, where the merit function jointly considers the optical quality at different object plane locations. An example of MIOL [22 diopters (D) far distance correction] was designed. For this design, the ocular modulator transfer function (MTF) at 50 cycles per millimeter remained above 0.47 for all object locations. The design provides high optical quality performance for far and intermediate distances and peak optical performance at near distances (MTF>0.57). Additionally, the design shows good performance against pupil changes (3-5 mm pupil diameter range). Finally, when the MIOL was tested on pseudophakic eye models with corneal spherical aberrations within a typical population range, the high multifocal performance was maintained in almost 40% of potential patients (ignoring asymmetric aberrations effects).

Effects of the Nike ZoomX Vaporfly Next% 2 shoe on long-interval training performance, kinematics, neuromuscular parameters, running power and fatigue.

We analysed the effects of the Nike ZoomX Vaporfly (VPF) on long-interval training performance, kinematic parameters, running power and fatigue compared to a traditional running shoe. Twelve well-trained men (mean ± SD: 32.91 ± 7.50 years; 69.29 ± 7.55 kg and 172.73 ± 5.97 cm) performed two long-interval training sessions (5 × 1000 m with 90s recovery period) 7 days apart, with the VPF shoe or a traditional running shoe (CON) in random order. The countermovement jump (CMJ) height was measured before and after the training sessions and heart rate, spatiotemporal parameters, running power and leg stiffness was measured during training sessions. Running-related pain was assessed prior and post-24 h of each training session. Long-interval training performance improved 2.4% using the VPF shoe compared to CON (p = 0.009; ES = 0.482). Step length, contact time and leg stiffness were higher (p < 0.05; ES = 0.51, ES = 0.677, ES = 0.356) while flight time was lower (p < 0.001; ES = 0.756) when using VPF. Running power decreased in a similar way in both conditions throughout the training session. Vertical power was significantly higher in the VPF condition (p = 0.023, ES = 0.388). CMJ height decreased in both conditions after training (4.7 vs. 7.2%, for the VPF and control, respectively, p < 0.001; ES = 0.573). Finally, the perceived muscle pain was influenced by the shoe model condition (chi-square 5.042, P = 0.025). VPF shoes improved the long-interval training performance with similar running power, heart rate and neuromuscular fatigue, and reduced subjective perceived muscle pain compared to regular training shoes.HighlightsVPF shoe may improve long-interval training performance in trained runners with the same running power and heart rate.Lower subjective perceived muscle pain is found with VPF compared to the regular training shoes.This type of footwear may be used in high-intensity training sessions aiming to increase the training volume at higher intensities with lower associated fatigue.

Acute effects of interval training on running kinematics in runners: A systematic review.

BACKGROUND: Interval training (IT) is influenced by several variables and its design. However, there is no consensus about the acute effects of this type of training on running kinematics and gait patterns due to the variety of session designs. RESEARCH QUESTION: The aim of this systematic review was to determine the acute effects of IT on gait patterns and running kinematics in endurance runners depending on the characteristics of the training sessions. METHODS: A systematic search on four databases (Pubmed, WOS, Medline, and Scopus) was conducted on February 22, 2022. After analyzing 655 articles, studies were included if they met the inclusion criteria developed according to the PICO model. Nine studies were finally included. RESULTS: Only two of these studies measured kinematics changes during IT bouts while seven measured pre-post changes of these parameters. The quality scores of the included studies in the review averaged 5.44 (good quality) points using the modified PEDro scale. The observed changes in running kinematics during IT sessions were an increase in stride frequency, contact time and vertical displacement of center of mass. SIGNIFICANCE: Regarding the type of IT, anaerobic and short aerobic interval sessions (200-1000 m) should include long recovery periods (2-3 min) to avoid the increase of stride frequency, contact time and vertical oscillation of the center of mass as a results of muscle fatigue. For long aerobic interval sessions (>1000 m), a short recovery (1-2 min) between bouts do not induce a high level of muscle fatigue nor modifications in gait patterns. Coaches and athletes must consider the relative intensity and recovery periods of IT, and the type of IT, to prevent excessive fatigue which can negatively affect running kinematics.

Influence of Running Shoe Longitudinal Bending Stiffness on Running Economy and Performance in Trained and National Level Runners.

INTRODUCTION/PURPOSE: Previous results about shoe longitudinal bending stiffness (LBS) and running economy (RE) show high variability. This study aimed to assess the effects of shoes with increased LBS on RE and performance in trained and national runners. METHODS: Twenty-eight male runners were divided into two groups according to their 10-km performance times (trained, 38-45 min and national runners, <34 min). Subjects ran 2 × 3 min (at 9 and 13 km·h -1 for trained, and 13 and 17 km·h -1 for national runners) with an experimental shoe with carbon fiber plate to increase the LBS (Increased LBS) and a control shoe (without carbon fiber plate). We measured energy cost of running (W·kg -1 ) and spatiotemporal parameters in visit one and participants performed a 3000 m time trial (TT) in two successive visits. RESULTS: Increased LBS improved RE in the trained group at slow (11.41 ± 0.93 W·kg -1 vs 11.86 ± 0.93 W·kg -1 ) and fast velocity (15.89 ± 1.24 W·kg -1 vs 16.39 ± 1.24 W·kg -1 ) and only at the fast velocity in the national group (20.35 ± 1.45 W·kg -1 vs 20.78 ± 1.18 W·kg -1 ). The improvements in RE were accompanied by different changes in biomechanical variables between groups. There were a similar improvement in the 3000 m TT test in Increased LBS for trained (639 ± 59 vs 644 ± 61 s in control shoes) and national runners (569 ± 21 vs 574 ± 21 s in control shoes) with more constant pace in increased LBS compared with control shoes in both groups. CONCLUSIONS: Increasing shoe LBS improved RE at slow and fast velocities in trained runners and only at fast velocity in national runners. However, the 3000 m TT test improved similarly in both levels of runners with increased LBS. The improvements in RE are accompanied by small modifications in running kinematics that could explain the difference between the different levels of runners.