Eye-pupil displacement and prediction: effects on residual wavefront in adaptive optics retinal imaging

Abstract

This paper studies the effect of pupil displacements on the best achievable performance of retinal imaging adaptive optics (AO) systems, using 52 trajectories of horizontal and vertical displacements sampled at 80 Hz by a pupil tracker (PT) device on 13 different subjects. This effect is quantified in the form of minimal root mean square (rms) of the residual phase affecting image formation, as a function of the delay between PT measurement and wavefront correction. It is shown that simple dynamic models identified from data can be used to predict horizontal and vertical pupil displacements with greater accuracy (in terms of average rms) over short-term time horizons. The potential impact of these improvements on residual wavefront rms is investigated. These results allow to quantify the part of disturbances corrected by retinal imaging systems that are caused by relative displacements of an otherwise fixed or slowy-varying subject-dependent aberration. They also suggest that prediction has a limited impact on wavefront rms and that taking into account PT measurements in real time improves the performance of AO retinal imaging systems.

Keywords: (070.2025) Discrete optical signal processing; (110.1080) Active or adaptive optics; (120.0120) Instrumentation, measurement, and metrology; (170.4470) Ophthalmology.

Fig. 1

Pupil-Tracker (PT): acquisition (left) and system’s description

Fig. 2

Example of pupil position measurements for one of the subjects in our sample (dashed lines delimit saccades zones).

Fig. 3

Example 1: PT measurements during fixation for the same subject at different instants (top and bottom). The time unit is Δt = 12.5 ms. Signal is a mixture of saccades, drift, tremor, blink and small head movements. Noise measurement (3σ) is 20 μm.

Fig. 4

Statistics of displacements as a function of the delay between PT measurements. The unit delay is Δt = 12.5 ms. The curves represent the displacement values δ p^m under which we have 99%, 95% and 90% (dashed, dot-dashed and dotted lines, respectively) of the data, when the delay between two successive positions varies from Δt to 6Δt. The average value calculated considering all data is also shown (solid line).

Fig. 5

Comparison of predictors for Δt and 2Δt, in a good improvement case. Solid line: measurements; dashed line: predictions.

Fig. 6

Comparison of predictors for Δt and 2Δt, in a case without improvement. Solid line: measurements; dashed line: predictions.

Fig. 7

Statistics of phase screens generated from real and synthetic Zernike coefficients. The latter shows a more concentrated distribution, while the histogram generated from real data exhibits a large scattering. Dashed lines denote median values.

Fig. 8

Impact of random displacements of the pupil on the residual rms. The difference between reference and shifted phase screens are piston and tip-tilt subtracted before the computation of the rms values. The curve represents the average value and the error bars are the standard deviations calculated from 500 realizations (a number of 50 randomly selected phase screens were used here, and 10 random directions used for each displacement amplitude).

Fig. 9

Residual wavefront error (in rms, piston/tip/tilt removed) as a function of the PT frame rate. The curves correspond to upper limits considering all 99%, 95% and 90% smallest absolute value of the one-step displacements (dashed, dot-dashed and dotted lines). The mean and median computed over all one-step displacements are shown as circles and stars, respectively. The red and green lines represent the linear fits as explained in the text. The arrow shows the current WFS rate.

Fig. 10

Residual wavefront errors obtained from prediction models, expressed in rms (nm), for a prediction delay of Δt. The dashed line denotes the median value of the histogram.