% CIEConeFundamentalsFieldSizeTest
%
% Look at how the quantities in the CIE standard that depend on field size vary with
% field size, particularly for field sizes greater than 10-degrees, which
% is the outer limit of what the standard sanctions.
%
% My conclusions are
% 1. that since we know macular pigment is declining towards zero with
% field size (see refs below) and the CIE expoential formula has this
% property, it is resonable to use the CIE formula for macular pigment
% density for field sizes greater than 10-degrees.
% 2. the CIE formula for pigment optical density asymptotes to a constant
% as one extends past 10-degrees. Whether this is true in the retina or
% not, I am not sure. But as field size gets larger, using this formula
% is going to be no worse than simply using the 10-degree values, since
% they are the same.
% 3. one needs to take any estimate of the CMFs for large field sizes
% with a grain of salt. There is going to be variation across the field,
% so any point estimate is likely to be wrong somewhere. The CIE
% formulae, extended using the formulae past their bounds, are a good
% first guess for the mean field properties, but being aware that there
% is variation within the field, as well as individual variation around
% the CIE estimates, is important when considering things like the effect
% of inadvertant stimulation of cones when one tries to isolate
% melanopsin using silent substitution. Note in particular that the CIE
% formula is trying to capture large field color matches where subjects
% are instructed to ignore the center of the field as best they can. In
% a threshold experiment, this might not be how subjects were instructed
% and would in any case be rather hard to do. And if you used annular
% stimuli, you'd be a bit off and might want to think about how to
% estimate the fundamentals from the annulus. Studying the Moreland and
% Alexander paper below in detail might help with thinking on that.
%
% Refs:
% Mooreland & Alexander (1997). Effect of macular pigment on color
% matching with field sizes in the 1 deg to 10 deg range. Doc. Opth.
% Proc. Ser., 59, 363-368.
% Moreland and Alexander make color matches for annuli and for
% circular fields, and develop a formula for the equivalent macular
% pigment density for color matches of various field sizes. In
% these matches, observers are instructed to to ignore the central
% Maxwell?s spot, I am pretty sure. M&A say the data are consistent
% with the idea that obsevers look near the edge of the field but
% not quite at it. Their data are for field sizes of 10 degrees,
% and the estimates are fit with exponentials. M&A used these data
% together with measurements of macular pigment density by Moreland
% & Bhatt (1884) to develop an equivalent (for uniform fields)
% macular pigment density to be used in predicting color matches
% out to 10 degrees. The formula is an exponential decay.
% Something like this made it into the CIE standard, although it
% may have been tweaked to make sure the color matching data are
% consistent with the 10-deg and 2-deg CMFs. I have not thought
% hard about the underlying calculations.
%
% Moreland, J.D. and Bhatt, P. (1984). Retinal distribution ofmacular
% pigment. In: Verriest, G. (ed.), Colour Vision Deficiencies VII. Doc.
% Ophthalmol. Proc. Ser. 39: 127-132. W. Junk, The Hague.
% Uses color-matching data for field sizes out to 18 deg (I think)
% to develop estimates of macular pigment density as a function of
% eccentricity. Key feature of the data is that density estimates
% decline according to an exponential and reach zero at
% eccentricity (radius) of about 7 degrees. This paper also
% reviews earlier estimates and they all look like decaying
% exponentials.
%
% Putnam and Bland (2014). Macular pigment optical density spatial
% distribution measured in a subject with oculocutaneous albinism.
% Journal of Optometry, 7, 241-245.
%
% See ComputeCIEConeFundamentals, CIEConeFundamentalsTest.
%
% 5/25/16 dhb Wrote it.
% 6/1/16 dhb Polished it up a bit, and added to PTB distribution.
% Initialize and clear
clear; close all;
%% Generate field sizes
fieldSizesDegrees = 1:1:60;
S = 460;
%% Macular pigment transmittance
%
% This looks like it matches Figure 5.1 (p. 17) of the CIE 2006 standard
% between 1 and 10 degrees.
for ii = 1:length(fieldSizesDegrees)
% This is the CIE formula, and presumably gives some sort of effective
% macular pigment density over the field, with some sort of exclusion
% of the center for 10 degrees. I think this because presumbably these
% values are chosen to make the color matching functions produced using
% spatially uniform macular pigment density come out right. I believe
% this formula comes from Mooreland & Alexander (1997).
[macTran(ii),macDen(ii)] = MacularTransmittance(S,'Human','CIE',fieldSizesDegrees(ii));
% Isetbio has a function that provides macular density as a function of
% eccentricity. This is probably a different function than the above,
% since I believe the above comes from an "equivlent" density
% appropriate for a uniform field. But we can at least look at this
% too. The original data are in Putnam & Bland (2014).
if (exist('macularDensity','file'))
macDenIsetbio(ii) = macularDensity(fieldSizesDegrees(ii));
end
end
macFig = figure; clf; hold on
plot(fieldSizesDegrees,macDen,'ro','MarkerSize',8,'MarkerFaceColor','r');
plot(fieldSizesDegrees,macDen,'r');
% This is what the isetbio function returns. Not clear it is really
% comparable in exact form. Here multiplicatively scaled to have the
% same max as the CIE function, but not clear that is the right thing
% to do. When you compare, this falls off faster than the CIE formula,
% but this makes a certain amount of sense since the CIE formula is trying
% to express an equivalent macular pigment density over a uniform field
% (but excluding the very center, which subjects are instructed to ignore
% in making large field color matches).
if (exist('macularDensity','file'))
plot(fieldSizesDegrees,max(macDen(:))*macDenIsetbio/max(macDenIsetbio(:)),'bo','MarkerSize',8,'MarkerFaceColor','b');
plot(fieldSizesDegrees,max(macDen(:))*macDenIsetbio/max(macDenIsetbio(:)),'b');
end
ylim([0 1]);
xlabel('Field Size (Degrees)');
ylabel('Macular Pigment Density (460 nm)');
%% Photopigment optical density
for ii = 1:length(fieldSizesDegrees)
% This is the CIE formula, and presumably gives some sort of effective
% macular pigment density over the field, with some sort of exclusion
% of the center for 10 degrees. I think this because presumbably these
% values are chosen to make the color matching functions produced using
% spatially uniform macular pigment density come out right. I believe
% this formula comes from Mooreland & Alexander (1997).
[LPhotopigmentOpticaDensity(ii)] = PhotopigmentAxialDensity('LCone','Human','CIE',fieldSizesDegrees(ii));
[SPhotopigmentOpticaDensity(ii)] = PhotopigmentAxialDensity('SCone','Human','CIE',fieldSizesDegrees(ii));
end
photopigFig = figure; clf; hold on
plot(fieldSizesDegrees,LPhotopigmentOpticaDensity,'ro','MarkerSize',8,'MarkerFaceColor','r');
plot(fieldSizesDegrees,SPhotopigmentOpticaDensity,'bo','MarkerSize',8,'MarkerFaceColor','b');
plot(fieldSizesDegrees,LPhotopigmentOpticaDensity,'r');
plot(fieldSizesDegrees,SPhotopigmentOpticaDensity,'b');
ylim([0 1]);
xlabel('Field Size (Degrees)');
ylabel('Photopigment Density');
legend({'L & M cones','S cones'},'Location','NorthWest');