Enrique Gambra

Accommodative lag and fluctuations when optical aberrations are manipulated

We evaluated the accommodative response to a stimulus moving from 0 to 6 D following a staircase function under natural, corrected, and induced optical aberrations, using an adaptive-optics (AO) electromagnetic deformable mirror. The accommodative response of the eye (through the mirror) and the change of aberrations were measured on 5 subjects using a Hartmann-Shack wavefront sensor operating at 12.8 Hz. Five conditions were tested: (1) natural aberrations, (2) AO correction of the unaccommodated state and induction (over 6-mm pupils) of (3) +1 microm and (4) -1 microm of spherical aberration and (5) -2 microm of vertical coma. Four subjects showed a better accommodative response with AO correction than with their natural aberrations. The induction of negative spherical aberration also produced a better accommodative response in the same subjects. Accommodative lag increased in all subjects when positive spherical aberration and coma were induced. Fluctuations of the accommodative response (computed during each 1-D period of steady accommodation) increased with accommodative response when high-order aberrations were induced. The largest fluctuations occurred for induced negative spherical aberration and the smallest for natural and corrected aberrations. The study demonstrates that aberrations influence accommodative lag and fluctuations of accommodation and that correcting aberrations improves rather than compromises the accommodative response.

Influence of adaptive-optics ocular aberration correction on visual acuity at different luminances and contrast polarities.

We evaluated the visual benefit of correcting astigmatism and high-order aberrations with adaptive optics (AO) on visual acuity (VA) measured at 7 different luminances (ranging from 0.8 to 50 cd/m(2)) and two contrast polarities (black letters on white background, BoW, and white letters on black background, WoB) on 7 subjects. For the BoW condition, VA increased with background luminance in both natural and AO-corrected conditions, and there was a benefit of AO correction at all luminances (by a factor of 1.29 on average across luminances). For WoB VA increased with foreground luminance but decreased for the highest luminances. In this reversed polarity condition AO correction increased VA by a factor of 1.13 on average and did not produce a visual benefit at high luminances. The improvement of VA (averaged across conditions) was significantly correlated (p = 0.04) with the amount of corrected aberrations (in terms of Strehl ratio). The improved performance with WoB targets with respect to BoW targets is decreased when correcting aberrations, suggesting a role of ocular aberrations in the differences in visual performance between contrast polarities.

Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging

We present an optimization method to retrieve the gradient index (GRIN) distribution of the in-vitro crystalline lens from optical path difference data extracted from OCT images. Three-dimensional OCT images of the crystalline lens are obtained in two orientations (with the anterior surface up and posterior surface up), allowing to obtain the lens geometry. The GRIN reconstruction method is based on a genetic algorithm that searches for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens. Computer simulations showed that, for noise of 5 μm in the surface elevations, the GRIN is recovered with an accuracy of 0.003 and 0.010 in the refractive indices of the nucleus and surface of the lens, respectively. The method was applied to retrieve three-dimensionally the GRIN of a porcine crystalline lens in vitro. We found a refractive index ranging from 1.362 in the surface to 1.443 in the nucleus of the lens, an axial exponential decay of the GRIN profile of 2.62 and a meridional exponential decay ranging from 3.56 to 5.18. The effect of GRIN on the aberrations of the lens also studied. The estimated spherical aberration of the measured porcine lens was 2.87 μm assuming a homogenous equivalent refractive index, and the presence of GRIN shifted the spherical aberration toward negative values (-0.97 μm), for a 6-mm pupil.

Visual performance with real-life tasks under adaptive-optics ocular aberration correction.

We measured the effect of the correction of the natural aberrations of the eye by means of adaptive optics on the subjects performance on three different visual tasks: subjective sharpness assessment of natural images, familiar face recognition, and facial expression recognition. Images were presented through a dedicated psychophysical channel and viewed through an electromagnetic deformable mirror. Experiments were performed on 17 normal subjects. Ocular aberrations (astigmatism and higher order aberrations) were reduced on average from 0.366 +/- 0.154 to 0.101 +/- 0.055 mum for a 5-mm pupil diameter. On average, subjects considered to be sharper 84 +/- 14% of the images viewed under AO correction, and there was a significant correlation between the amount of corrected aberrations and the percentage of images that the subject considered sharper when observed under AO-corrected aberrations. In all eyes (except one), AO correction improved familiar face recognition, by a factor of x1.13 +/- 0.12 on average. However, AO correction did not improve systematically facial expression recognition.

In vivo human crystalline lens topography

Custom high-resolution high-speed anterior segment spectral domain optical coherence tomography (OCT) was used to characterize three-dimensionally (3-D) the human crystalline lens in vivo. The system was provided with custom algorithms for denoising and segmentation of the images, as well as for fan (scanning) and optical (refraction) distortion correction, to provide fully quantitative images of the anterior and posterior crystalline lens surfaces. The method was tested on an artificial eye with known surfaces geometry and on a human lens in vitro, and demonstrated on three human lenses in vivo. Not correcting for distortion overestimated the anterior lens radius by 25% and the posterior lens radius by more than 65%. In vivo lens surfaces were fitted by biconicoids and Zernike polynomials after distortion correction. The anterior lens radii of curvature ranged from 10.27 to 14.14 mm, and the posterior lens radii of curvature ranged from 6.12 to 7.54 mm. Surface asphericities ranged from −0.04 to −1.96. The lens surfaces were well fitted by quadrics (with variation smaller than 2%, for 5-mm pupils), with low amounts of high order terms. Surface lens astigmatism was significant, with the anterior lens typically showing horizontal astigmatism (Z22 ranging from −11 to −1 µm) and the posterior lens showing vertical astigmatism (Z22 ranging from 6 to 10 µm).

Combining coma with astigmatism can improve retinal image over astigmatism alone

We demonstrate that certain combinations of non-rotationally symmetric aberrations (coma and astigmatism) can improve retinal image quality over the condition with the same amount of astigmatism alone. Simulations of the retinal image quality in terms of Strehl Ratio, and measurements of Visual Acuity under controlled aberrations with adaptive optics were performed, varying defocus, astigmatism and coma. Astigmatism ranged between 0 and 1.5D. Defocus ranged typically between -1 and 1D. The amount of coma producing best retinal image quality (for a given relative angle between astigmatism and coma) was computed and the amount was found to be different from zero in all cases (except for 0D of astigmatism). For example, for a 6mm pupil, in the presence of 0.5D of astigmatism, a value of coma of 0.23mum produced (for best focus) a peak improvement in Strehl Ratio by a factor of 1.7, over having 0.5D of astigmatism alone. The improvement holds over a range of >1.5D of defocus and peak improvements were found for amounts of coma ranging from 0.15mum to 0.35mum. We measured VA under corrected high order aberrations, astigmatism alone (0.5D) and astigmatism in combination with coma (0.23mum), with and without adaptive optics correction of all the other aberrations, in two subjects. We found that the combination of coma with astigmatism improved decimal VA by a factor of 1.28 (28%) and 1.47 (47%) in both subjects, over VA with astigmatism alone when all the rest of aberrations were corrected. Nevertheless, in the presence of typical normal levels of HOA the effect of the coma/astigmatism interaction is considerably diminished.

Distortion Correction of OCT Images of the Crystalline Lens: Gradient Index Approach

Purpose. To propose a method to correct optical coherence tomography (OCT) images of posterior surface of the crystalline lens incorporating its gradient index (GRIN) distribution and explore its possibilities for posterior surface shape reconstruction in comparison to existing methods of correction. Methods. Two-dimensional images of nine human lenses were obtained with a time-domain OCT system. The shape of the posterior lens surface was corrected using the proposed iterative correction method. The parameters defining the GRIN distribution used for the correction were taken from a previous publication. The results of correction were evaluated relative to the nominal surface shape (accessible in vitro) and compared with the performance of two other existing methods (simple division, refraction correction: assuming a homogeneous index). Comparisons were made in terms of posterior surface radius, conic constant, root mean square, peak to valley, and lens thickness shifts from the nominal data. Results. Differences in the retrieved radius and conic constant were not statistically significant across methods. However, GRIN distortion correction with optimal shape GRIN parameters provided more accurate estimates of the posterior lens surface in terms of root mean square and peak values, with errors <6 and 13 &mgr;m, respectively, on average. Thickness was also more accurately estimated with the new method, with a mean discrepancy of 8 &mgr;m. Conclusions. The posterior surface of the crystalline lens and lens thickness can be accurately reconstructed from OCT images, with the accuracy improving with an accurate model of the GRIN distribution. The algorithm can be used to improve quantitative knowledge of the crystalline lens from OCT imaging in vivo. Although the improvements over other methods are modest in two dimension, it is expected that three-dimensional imaging will fully exploit the potential of the technique. The method will also benefit from increasing experimental data of GRIN distribution in the lens of larger populations.

Static and dynamic crystalline lens accommodation evaluated using quantitative 3-D OCT

Custom high-resolution high-speed anterior segment spectral domain Optical Coherence Tomography (OCT) provided with automatic quantification and distortion correction algorithms was used to characterize three-dimensionally (3-D) the human crystalline lens in vivo in four subjects, for accommodative demands between 0 to 6 D in 1 D steps. Anterior and posterior lens radii of curvature decreased with accommodative demand at rates of 0.73 and 0.20 mm/D, resulting in an increase of the estimated optical power of the eye of 0.62 D per diopter of accommodative demand. Dynamic fluctuations in crystalline lens radii of curvature, anterior chamber depth and lens thickness were also estimated from dynamic 2-D OCT images (14 Hz), acquired during 5-s of steady fixation, for different accommodative demands. Estimates of the eye power from dynamical geometrical measurements revealed an increase of the fluctuations of the accommodative response from 0.07 D to 0.47 D between 0 and 6 D (0.044 D per D of accommodative demand). A sensitivity analysis showed that the fluctuations of accommodation were driven by dynamic changes in the lens surfaces, particularly in the posterior lens surface.

Dynamic accommodation with simulated targets blurred with high order aberrations.

High order aberrations have been suggested to play a role in determining the direction of accommodation. We have explored the effect of retinal blur induced by high order aberrations on dynamic accommodation by measuring the accommodative response to sinusoidal variations in accommodative demand (1-3D). The targets were blurred with 0.3 and 1mum (for a 3-mm pupil) of defocus, coma, trefoil and spherical aberration. Accommodative gain decreased significantly when 1-mum of aberration was induced. We found a strong correlation between the relative accommodative gain (and phase lag) and the contrast degradation imposed on the target at relevant spatial frequencies.

Experimental Test of Simulated Retinal Images Using Adaptive Optics

Ocular degradation is frequently assessed convolving images with the ocular point-spread-function, estimated from the wave-aberration. Comparisons of visual acuity measured using aberrated targets (viewed through adaptive-optics corrected aberrations) and under natural aberrations reveal consistent discrepancies.