## DegreesToRetinalEccentricityMM

##### >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 eyeLengthMm parameter does not affect what this method

does.

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 this

routine 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, RetinalEccentricityMMToDegrees, DegreesToRetinalMM, RetinalMMToDegrees

6/30/2015 dhb Wrote it.

`Psychtoolbox/PsychColorimetricData/DegreesToRetinalEccentricityMM.m`