Luis Diaz-Santana

Aberrations of the Human Eye in Visible and Near Infrared Illumination

Purpose. In most current aberrometers, near infrared light is used to measure ocular aberrations, whereas in some applications, optical aberration data in the visible range are required. We compared optical aberration measurements using infrared (787 nm) and visible light (543 nm) in a heterogeneous group of subjects to assess whether aberrations are similar in both wavelengths and to estimate experimentally the ocular chromatic focus shift. Methods. Ocular aberrations were measured in near infrared and visible light using two different laboratory-developed systems: laser ray tracing (LRT) and Shack-Hartmann. Measurements were conducted on 36 eyes (25 and 11 eyes, respectively), within a wide range of ages (20 to 71 years), refractive errors (−6.00 to +16.50), and optical quality (root mean square wavefront error, excluding defocus, from 0.40 to 9.89 &mgr;m). In both systems, wave aberrations were computed from the ray aberrations by modal fitting to a Zernike polynomial base (up to seventh order in laser ray tracing and sixth order in Shack-Hartmann). We compared the Zernike coefficients and the root mean square wavefront error corresponding to different terms between infrared and green illumination. Results. A Student’s t-test performed on the Zernike coefficients indicates that defocus was significantly different in all of the subjects but one. Average focus shift found between 787 nm and 543 nm was 0.72 D. A very small percentage of the remaining coefficients was found to be significantly different: 4.7% of the 825 coefficients (25 eyes with 33 terms) for laser ray tracing and 18.2% of the 275 coefficients (11 eyes with 25 terms) for Shack-Hartmann. Astigmatism was statistically different in 8.3% of the eyes, root mean square wavefront error for third-order aberrations in 16.6%, and spherical aberration (Z40) in 11.1%. Conclusions. Aerial images captured using infrared and green light showed noticeable differences. Apart from defocus, this did not affect centroid computations because within the variability of the techniques, estimates of aberrations with infrared were equivalent to those measured with green. In normal eyes, the Longitudinal Chromatic Aberration of the Indiana Chromatic Eye Model can predict the defocus term changes measured experimentally, although the intersubject variability could not be neglected. The largest deviations from the prediction were found on an aphakic eye and on the oldest subject.

Benefit of higher closed-loop bandwidths in ocular adaptive optics

We present an ocular adaptive optics system with a wavefront sampling rate of 240 Hz and maximum recorded closed-loop bandwidth close to 25 Hz, but with typical performances around 10 Hz. The measured bandwidth depended on the specific system configuration and the particular subject tested. An analysis of the system performance as a function of achieved bandwidth showed consistently higher Strehl ratios for higher closed-loop bandwidths. This may be attributed to a combination of limitations on the available technology and the dynamics of ocular aberrations. We observed dynamic behaviour with a maximum frequency content around 30 Hz.

Repeatability of ocular wavefront measurement

Purpose. To assess the repeatability of measurements of ocular aberrations using wavefront sensing in a small group of observers and to assess the potential effect of measurement error on custom corneal correction due to this variability. Method. A Shack-Hartmann wavefront sensor was used to measure the ocular wavefront in nine eyes. Head position was stabilized using a dental bite bar, and the pupil was centred using a cathode ray tube monitor and circular grating. Twenty Shack-Hartmann images were collected for each measurement. Each observer had three sets of measurements taken; the first and the second after careful alignment and the final after regrasping the bite bar in the same position as for the second measurement, but without pupil realignment. The modulation transfer functions for each set were calculated, and the effect of best-aligned custom treatments on the modulation transfer function was estimated. Results. There were highly statistically significant differences in a large number of Zernike modes between the three sets of measurements. The modulation transfer functions calculated for the residual wavefronts after aligned custom treatment were below the diffraction limit. The root mean square wavefront errors were consistently better for the residual wavefronts obtained using the realigned data than using data taken without pupil realignment. Conclusions. Sequential measurement of ocular aberrations shows statistically significant differences in a large number of Zernike modes. If aberrations determined by a single measurement are to be used in a custom correction, the resulting modulation transfer function is likely to remain below the diffraction limit. Pupil realignment is critical in reduction of the residual root mean square wavefront values to a minimum.

Ocular aberrations with ray tracing and Shack-Hartmann wave-front sensors: Does polarization play a role?

Ocular aberrations were measured in 71 eyes by using two reflectometric aberrometers, employing laser ray tracing (LRT) (60 eyes) and a Shack-Hartmann wave-front sensor (S-H) (11 eyes). In both techniques a point source is imaged on the retina (through different pupil positions in the LRT or a single position in the S-H). The aberrations are estimated by measuring the deviations of the retinal spot from the reference as the pupil is sampled (in LRT) or the deviations of a wave front as it emerges from the eye by means of a lenslet array (in the S-H). In this paper we studied the effect of different polarization configurations in the aberration measurements, including linearly polarized light and circularly polarized light in the illuminating channel and sampling light in the crossed or parallel orientations. In addition, completely depolarized light in the imaging channel was obtained from retinal lipofuscin autofluorescence. The intensity distribution of the retinal spots as a function of entry (for LRT) or exit pupil (for S-H) depends on the polarization configuration. These intensity patterns show bright corners and a dark area at the pupil center for crossed polarization, an approximately Gaussian distribution for parallel polarization and a homogeneous distribution for the autofluorescence case. However, the measured aberrations are independent of the polarization states. These results indicate that the differences in retardation across the pupil imposed by corneal birefringence do not produce significant phase delays compared with those produced by aberrations, at least within the accuracy of these techniques. In addition, differences in the recorded aerial images due to changes in polarization do not affect the aberration measurements in these reflectometric aberrometers.

Sampling geometries for ocular aberrometry: A model for evaluation of performance

The purpose of this work is to outline a simple model to assess the relative merits of different sampling grids for ocular aberrometry and illustrate it with an example. While in traditional Hartmann-Shack setups the sampling grid geometries have been somewhat restricted by the geometries of the available microlens arrays, other techniques such as laser ray tracing or spatially resolved refractometry allow for a greater freedom of choice. For all available setups, including HS, it is worth studying which of these choices perform better in terms of accuracy (closeness of the obtained results to the actual ones) and precision (uncertainty of the obtained results). Whilst the mathematical model presented in this paper is quite general and it can be applied to optimise existing or new aberrometers, the numerical results presented in the example are only valid for the particular aberration sample used and centroiding algorithms studied, and should not be generalised outside of these boundaries.

New methodology to measure the dynamics of ocular wave front aberrations during small amplitude changes of accommodation

We present a methodology to measure the systematic changes of aberrations induced by small changes in amplitude of accommodation. We use a method similar the one used in electrophysiology, where a periodic stimulus is presented to the eye and many periods (epochs) of the stimulus are averaged. Using this technique we have measured changes in higher order aberrations from 0.006 mum to 0.02 mum and correlated them with amplitude changes of accommodation as small as 0.14D. These small changes would have been undetectable without epoch averaging. The correlation coefficients of Zernike terms with defocus were calculated, demonstrating higher values of correlation for epoch averaging. The accurate monitoring of defocus at the start of the accommodation response has shown some interesting trends that may be related with the mechanisms behind accommodation.

Temporal dynamics and statistical characteristics of the microfluctuations of accommodation: dependence on the mean accommodative effort.

Microfluctuations of accommodation have been the subject of many studies. New technological developments now permit us to study the dynamics of the microfluctuations with unprecedented resolution and accuracy. We aim to characterise their temporal statistics for different levels of accommodative effort, using a custom-built aberrometer. We conducted 46 s long measurements on the dominant eye of 9 young, healthy subjects. The ocular wavefront was sampled every 250 microm across the 3.9 mm measured pupil, at a frame rate of 173 Hz. This enabled us to obtain high resolution estimates of the Power Spectral Density (PSD). Results show that the shape of the estimated PSD for a 4 D effort is distinct from the shape for the two extrema of the accommodation range. The autocorrelation function of the increments of the accommodation signal is also affected by the level of effort, regardless of the refractive error of the subject.

Wavefront curvature sensing for the human eye

In this paper we present a curvature wavefront sensor for the eye. The layout proposed is novel, whilst the algorithm used has been adapted from previously published work [Roddier, F.; Roddier, C. Appl. Opt. 1991, 30, 1325–1327]. The design of the set-up incorporates two field lenses that, together with a beam separator, define the distance Δz between the two sampled planes. We present a feasibility study to use this particular combination of optical configuration and retrieval algorithm in the eye. We present calibration curves and results from three real eyes.

Centroid displacement statistics of the eye aberration

We discuss a method for the study of the spatial statistics of the ocular aberrations, based on the direct use of the Hartmann-Shack centroid displacements, avoiding the wavefront reconstruction step. Centroid diagrams are introduced as a helpful aid to visualize basic properties of the aberration datasets, and slope-related second-order statistical functions are applied to check the compatibility between the experimental data and different models for the aberration statistics. Preliminary results suggest that no single power-law spectrum (e.g., Kolmogorovs) is able to represent the whole range of spatial statistics of individual eye fluctuations and that more elaborated models, including at least the contribution of a relevant defocus fluctuation term, are required. This centroid-based approach allows for an easier intercomparison of results between laboratories and avoids the bias and information loss associated with the estimation of a reduced number of Zernike coefficients from a much wider slope data set.

Translational and rotational pupil tracking by use of wavefront aberration data and image registration techniques

We present a methodology with which to evaluate translations and rotations of wavefront aberration measurements of systems in which the exit pupil suffers displacements and rotations with respect to the reference frame of the measuring device. We propose to use image registration techniques to account for rotations, translations, and scale changes of the pupil. We present a proof of principle, using an artificial eye in addition to computer simulations. The method is software based and requires no additional hardware.