## RetinalEccentricityMMToDegrees

##### >Psychtoolbox>PsychColorimetricData

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.

Input:

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,

for human.

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

model eyes.

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

eye.

I have not checked the fit to the Perrry and Cowey curve for Rhesus

against a digitization of that figure.

See also: EyeLength, DegreesToRetinalEccentricityMM, DegreesToRetinalMM, RetinalMMToDegrees

6/30/2015 dhb Wrote it.

`Psychtoolbox/PsychColorimetricData/RetinalEccentricityMMToDegrees.m`