1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
|
% 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');
|
