Adaptive optics data for the human point spread function


Using adaptive optics, a group led by Thibos collected many different wavefronts in the human eye for a range of pupil sizes. The data are summarized using a simple statistical model of the Zernicke polynomial coefficients. The data were published in

 "Retinal Image Quality for Virtual Eyes Generated by a Statistical
 Model of Ocular Wavefront Aberrations" published in Ophthalmological
 and Physiological Optics (2009). Thibos, Ophthalmic & Physiological

The data and a sample program are onlineat the bottom of the online article in Supporting Information.

We retrieved the data and implemented a version of the calculations in the Wavefront toolbox. This script calculates the PSF for example subjects.

See also: VirtualEyesDemo and wvfLoadHuman

Copyright Wavefront Toolbox Team, 2012


Initialize ISET

Set the largest size in microns for plotting Set the pupil diameter in millimeters

maxUM = 40;
pupilMM = 4.5;
ISET 4, Matlab 7.13
Copyright ImagEval Consulting, LLC, 2003-2012
Session iset-20120520T232050
No Scenes.
No optical images.
No Sensors.
No Processed images.

White point for Scene/OI rendering set to ep

Load the statistical wavefront properties

The Zernike coefficients describing the wavefront aberrations are each distributed as a Gaussian. There is some covariance between these coefficients. The covariance is summarized in the variable S. The mean values across a large sample of eyes measured by Thibos and gang are in the variable sample_mean.

[sample_mean S] = wvfLoadHuman(pupilMM);

Plot the means and covariance (not)


plot(sample_mean,'--o'); grid on
xlabel('Zernike polynomial number')
ylabel('Coefficient value')
title('Mean coefficient');

axis image,
colormap(hot); colorbar
title('Coefficient covariance')

% Calculate sample eyes using the multivariate normal distribution Each
% column of Zcoeffs is an example person. Each row of R is a vector of
% Zernike coeffs
N = 10;
Zcoeffs = ieMvnrnd(sample_mean,S,N)';

% Plot the random examples of coefficients
plot(Zcoeffs); grid on
xlabel('Zernike polynomial number')
ylabel('Coefficient value')
title('Example coefficients')

Examine a single PSF for the subject at the sample mean

% Allocate space and fill in the lower order Zernicke coefficients
z = zeros(65,1);
z(1:13) = sample_mean(1:13);

% Create the example subject
thisGuy = wvfCreate;                                  % Initialize
thisGuy = wvfSet(thisGuy,'zcoeffs',z);                % Zernike
thisGuy = wvfSet(thisGuy,'measured pupil',pupilMM);   % Data
thisGuy = wvfSet(thisGuy,'calculated pupil',pupilMM); % What we calculate
thisGuy = wvfSet(thisGuy,'measured wl',550);
thisGuy = wvfSet(thisGuy,'wavelength',[450 100 3]);     % SToWls format
thisGuy = wvfComputePSF(thisGuy);

Plot the PSFs of the sample mean subject for several wavelengths

These illustrate the strong axial chromatic aberration.

wave  = wvfGet(thisGuy,'wave');
nWave = wvfGet(thisGuy,'nwave');
for ii=1:nWave
    wvfPlot(thisGuy,'image psf space','um',ii,maxUM);
    title(sprintf('%d nm',wave(ii)));

Calculate the PSFs from the coeffcients

Here we illustrate the variance between different subjects.

% Choose example subjects
whichSubjects = 1:3:N;
nSubjects = length(whichSubjects);
z = zeros(65,1);     % Allocate space for the Zernicke coefficients

% Create the example subject
thisGuy = wvfCreate;                                % Initialize
thisGuy = wvfSet(thisGuy,'measuredpupil',pupilMM);  % Data
thisGuy = wvfSet(thisGuy,'calculatedpupil',pupilMM);% What we calculate

for ii = 1:nSubjects

    % Choose different coefficients and compute for each subject
    z(1:13) = Zcoeffs(1:13,whichSubjects(ii));
    thisGuy = wvfSet(thisGuy,'zcoeffs',z);              % Zernike
    thisGuy = wvfComputePSF(thisGuy);

    wvfPlot(thisGuy,'image psf space','um',1,maxUM);
    title(sprintf('Subject %d\n',ii))