[fractionBleached] = ComputePhtopigmentBleaching(intensity,units,source)
Compute fraction of photopigment bleached, given some measure of
the intensity of light reaching the eye.
As far as I can tell, the fundemantal measurements of the half-bleach
constant for cones were made by Rushton and Henry (1968, Vision Reserch, 8, 617-631).
This fact I learned from CVRL (http://www.cvrl.org/database/text/intros/introbleaches.htm).
I am pretty sure that the Rushton and Henry measurements were made for 560 nm
light, and they give (see their Figure 2) a half-bleach constant of 4.3 log10 trolands (20,000 td).
This number is also given in Boynton and Kaiser, Human Color Vision, 2nd edition,
pp 211 and following.
It’s probably fine to compute bleaching for L and M cones given retinal illuminance
in trolands, given that these are effects that matter over log10 units. But trolands
are not going to help much for the S-cones. According to CVRL there aren’t good
measurements for the half-bleaching constant for S cones because putting enough short-wavelength
light onto the retina to bleach the S cones is not good for the eyes.
None-the-less, it seems nice to have this routine written so that it will return a number
if you give it intensity either in trolands or in isomerizations/cone-sec. For 560 nm
light and the CIE 10 deg fundamentals, I compute that 1 td is 137 isomerizations/cone-sec
for L cones and 110 isomerizations/cone-sec for M cones. Take the weighted average value
of (2*L + 1*M) = 128 and multiply by (10.^4.3) to get a half-bleach constant in
isomerizations/cone-sec of 2.55e+06 (6.4 log10 isomerizations/cone-sec).
[Computations done 6/2/14 using IsomerizationsInEyeDemo and setting the fundamentals to ‘CIE10deg’ and wavelength to 560 nm
by hand in the code. These are for the ‘Boynton’ source.]
[ASIDE: I used 10 deg fundamentals because I figure that Rushton’s measurements are based
on a fairly large field. Because the macular pigment absorbs a fair amount of light,
this matters. If I compute instead with 2-deg fundamentals, I get that 1 td is 23.7
L cone isomerizations/cone-sec and 19.5 M cone isomerizations/cone-sec. These two
numbers are ballpark consistent with Rodiek page 475 who gives 18.3 and 15.9 for a
monochromatic 540 THz light (555 nm)].
This routine will do the computation either on the basis of input in trolands or input
in isomerization/cone-sec, using the appropirate constant as above. Note that the
computation of isomerizations takes into account lens and macular pigment, while the
troland value is the straight troland value. A second advantage of using units of
isomerizations/cone-sec is that you can compute this for other regions of the visual
field and presumably the numbers will be about right. You can also compute for S-cones
on the assumption that the half-bleach constant is the same for S-cones as for L- and M-
As far as I can tell, the computations and analysis of bleaching do not take into account
changes in isomerization rate that occur because of change in spectral sensitivity of cones
with bleaching. That is, the measurements are simply of steady state pigment density and are
modeled with a formula that assumes monochromatic light (see treatment in Boynton).
‘cones’ – computations for cones. [Default]
‘troalands’ – input intensity in trolands. Note that the computation only makes
sense for L and M cones if this is the input. This is photopic trolands
if receptor type is ‘cones’. [Default]
‘isomerizations’ – nominal isomerization rate in isomerizations/cone-sec, comptued
taking into account pre-retinal absorption as well as nominal cone
axial density. But not taking into account any pigment bleaching.
‘Boynton’ – Boynton and Kaiser, Human Color Vision, 2nd edition,
pp. 211 and following. [Default.]
05/23/14 dhb Wrote it.
05/26/14 dhb Clean up.
06/02/14 dhb Take isomerizations number based on 2:1 L:M assumed ratio.