Adaptive optics data for the human point spread function

s_wvfThibosModel

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
 Optics.
 http://onlinelibrary.wiley.com/doi/10.1111/j.1475-1313.2009.00662.x/full

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

Initialize ISET
Load the statistical wavefront properties
Plot the means and covariance (not)
Examine a single PSF for the subject at the sample mean
Plot the PSFs of the sample mean subject for several wavelengths
Calculate the PSFs from the coeffcients

Initialize ISET

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

s_initISET
maxUM = 40;
pupilMM = 4.5;

ISET 4, Matlab 7.13
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Copyright ImagEval Consulting, LLC, 2003-2012
Session iset-20120520T232050
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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)

vcNewGraphWin([],'tall');

subplot(3,1,1)
plot(sample_mean,'--o'); grid on
xlabel('Zernike polynomial number')
ylabel('Coefficient value')
title('Mean coefficient');

subplot(3,1,2)
imagesc(S);
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
subplot(3,1,3)
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');
vcNewGraphWin([],'tall');
for ii=1:nWave
    subplot(nWave,1,ii)
    wvfPlot(thisGuy,'image psf space','um',ii,maxUM);
    title(sprintf('%d nm',wave(ii)));
end

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

vcNewGraphWin([],'tall');
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);

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