eccMm = DegreesToRetinalEccentricityMM(eccDegrees,[species],[method],[eyeLengthMm])
Convert eccentricity in degrees to retinal eccentricity in mm. By
default, this takes into account a simple model eye, rather than just
relying on a linear small angle approximation.
eccDegrees – retinal eccentricity in degrees
species – what species
‘Human’ – Human eye [default]
‘Rhesus’ – Rhesus monkey
method – what method
‘DaceyPeterson’ – formulae from Dacey & Peterson (1992) [default]
‘Linear’ – linear, based on small angle approx
eyeLengthMm – Eye length to assume for linear calculation, should be
the posterior nodal distance. Defaults to the default values returned
by function EyeLength for the chosen species.
The Dacey and Peterson formulae are based on digitizing and fitting
curves published by
1) Drasdo and Fowler, 1974 (British J. Opthth, 58,pp. 709 ff., Figure 2,
2) Perry and Cowey (1985, Vision Reserch, 25, pp. 1795-1810, Figure 4,
for rhesus monkey.
These curves, I think, were produced by ray tracing or otherwise solving
The default eye length returned by EyeLength for Human is currently the Rodiek value of
16.1 mm. Drasdo and Fowler formulae are based on a length of about this,
so the linear and DaceyPeterson methods are roughly consistent for small
angles. Similarly with the Rhesus default. Using other EyeLength’s will
make the two methods inconsistent.
The Dacey and Peterson equations don’t go through (0,0), but rather
produce a visual angle of 0.1 degree for an eccentricity of 0. This
seems bad to me. I modified the formulae so that they use the linear
approximation for small angles, producing a result that does go through
(0,0). This may be related to the fact that there is some ambiguity in
the papers between whether the center should be thought of as the fovea
or the center of the optical axis. But I think this difference is small
enough that the same formulae would apply across such a shift in origin.
I digitized Drasdo and Fowler Figure 2 and compared it to what
DegreesToRetinalEccentricity produces. I’d call agreement so-so, but
considerably better than what the linear approximation produces. One
could probably do better, but my intuition is that the deviations are
small compared to eye to eye differences and differences that would be
produced by different model eyes, so that juice isn’t worth the squeeze.
I pasted my digitization at the end of DegreesToRetinalEccentricity if
anyone wants to fuss with this. But probably if you’re going to do that,
you should do the whole ray tracing thing with our best current model
I have not checked the fit to the Perrry and Cowey curve for Rhesus
against a digitization of that figure.
6/30/2015 dhb Wrote it.