Renfeng Xu

Impact of primary spherical aberration, spatial frequency and Stiles Crawford apodization on wavefront determined refractive error: a computational study

We tested the hypothesis that pupil apodization is the basis for central pupil bias of spherical refractions in eyes with spherical aberration.

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

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

Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality

To examine the separate and combined influences of zone geometry, pupil size, diffraction, apodisation and spherical aberration on the optical performance of concentric zonal bifocals.

Modelling the effects of secondary spherical aberration on refractive error, image quality and depth of focus

To examine the role of Zernike secondary spherical aberration and its component terms on refraction, image quality and depth of focus.

IURead: a new computer‐based reading test

To develop a computer‐based single sentence reading test especially designed for clinical research enabling multiple repeat trials without reusing the same sentences.

Effect of Target Luminance on Optimum Pupil Diameter for Presbyopic Eyes.

Purpose To quantify the optimum pupil diameters for presbyopic eyes when environmental light levels vary from high photopic to low mesopic. Methods We computed the white light visual Strehl ratio from the polychromatic optical transfer function (VSOTF). The impact on image quality of retinal illuminance and the accompanying changes in photon noise were reflected in changing neural contrast sensitivity. VSOTF was calculated for focused and −2D defocused images, over a wide range of photopic and mesopic target luminances, and for pupil diameters ranging from 1 to 7 mm. We compare these modeling data to logMAR visual acuity measured under the same conditions. Results Optimum pupil depends on the relative gain of optical factors (diffraction and aberrations) and neural thresholds (photon noise effect). When light levels are reduced from 1000 to 2 cd/m2, the pupil size that optimizes VSOTF for a well-focused presbyopic eye model also maximizes visual acuity and it increases from 2.5 to 4 mm. A 1-mm-diameter pupil maximizes VSOTF at all light levels when −2D of defocus are included, but at 2 cd/m2 the optimum pupil diameter for acuity increases slightly to 1.4 mm. At 0.2 cd/m2, the pupil size that optimizes VSOTF remains 4 and 1 mm for a focused and −2D defocused eye, respectively, but significantly larger pupils are needed for maximal visual acuity. Reducing pupils to 30% of their natural size is beneficial for distance and near image quality and visual acuity at all light levels, producing more gains for near than for distance. Conclusions A fixed 2- to 3-mm small pupil or a 30% pupil miosis can both produce near visual acuity gains without significant losses to distance acuity or image quality, and therefore can be considered as optimal for a presbyope experiencing a wide range of light levels.

The Effect of Light Level and Small Pupils on Presbyopic Reading Performance

Purpose To examine the impact of small pupils and light levels on reading performance of distance-corrected presbyopes. To determine whether small pupils would enable presbyopes to read at near even at low light levels. Methods To establish the lower range of text luminances, we quantified the space-averaged luminance of text in nine different artificially lit interior environments, and examined the impact of the text characters on space-averaged luminance of electronic and printed displays. Distance and near reading speeds of 20 presbyopes (ages 40-60 years) were measured while viewing through artificial pupils (diameters 1-4.5 mm), natural pupils, or with a multifocal contact lens. Space-averaged text luminance levels varied from 0.14 to 140 cd/m2 (including the range of measured environmental text luminances). Results Adding black text to a white computer display or paper reduces luminance by approximately 15% to 31%, and the lowest encountered environmental text luminance was approximately 2 to 3 cd/m2. For both distance and near reading performance, the 2- to 3-mm small pupil yielded the best overall reading acuity for space-averaged text light levels ≥ 2 cd/m2. The 2- to 3-mm artificial pupils and the multifocal contact lenses both enabled maximum or near-maximum reading speeds for 0.5 logMAR characters at distance and near, but with natural pupils, reading speeds were significantly reduced at near. Conclusions Although photon noise at low luminance reduces the visual benefits of small pupils, the benefits of 2- to 3-mm artificial pupils are sufficient to enable >80% of distance-corrected presbyopes to read proficiently at near, even at the lowest text luminances found in interior environments.

Reducing starbursts in highly aberrated eyes with pupil miosis

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

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

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

The effect of spherical aberration on visual performance and refractive state for stimuli and tasks typical of night viewing

Purpose The aim of this work was to examine the impact of Seidel spherical aberration (SA) on optimum refractive state for detecting and discriminating small bright lights on a dark background. Methods An adaptive-optics system was used to correct ocular aberrations of cyclopleged eyes and then systematically introduce five levels of Seidel SA for a 7-mm diameter pupil: 0, ± 0.18, and ± 0.36 diopters (D) mm−2. For each level of SA, subjects were required to detect one or resolve two points of light (0.54 arc min diameter) on a dark background. Refractive error was measured by adjusting stimulus vergence to minimize detection and resolution thresholds. Two other novel focusing tasks for single points of light required maximizing the perceived intensity of a bright points core and minimizing its overall perceived size (i.e. minimize starburst artifacts). Except for the detection task, luminance of the point of light was 1000 cd m−2 on a black background lower than 0.5 cd m−2. Results Positive SA introduced myopic shifts relative to the best subjective focus for dark letters on a bright background when there was no SA, whereas negative SA introduced hyperopic shifts in optimal focus. The changes in optimal focus were −1.7, −2.4, −2.0, and −9.2 D of focus per D mm−2 of SA for the detection task, resolution task, and maximization of cores intensity and minimization of size, respectively. Conclusion Ocular SA can be a significant contributor to changes in refractive state when viewing high-contrast point sources typically encountered in nighttime environments.