## ComputePhotopigmentBleaching

##### >Psychtoolbox>PsychColorimetric

[fractionBleached] = ComputePhtopigmentBleaching(irradiance,[receptorType],[units],[source],[initialFraction],[timeUnits])

Compute fraction of photopigment bleached, given irradiance of light

reaching the eye.

There are two distinct uses, controlled by the value of initialFraction.

Usage 1 - If initialFraction is not passed or is empty, the steady state

fraction of pigment bleached is returned for each irradiance in the

passed input irradiance.

Usage 2 - If initialFraction is passed as a scalar, this is taken as the

time zero fraction bleached, and inputirradiance is taken to be the time

variying irradiance, with fractionBleached the time varying fraction

bleached.

When time varying signals are handled, the unit of time is as specified

by the timeunits argument (default, msec).

As far as I can tell, the fundemantal measurements of the half-bleach

constant for human cones were made by Rushton and Henry (1968, Vision Research,

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. This

is the number you get here if you specify ‘Boynton’ as the source for the

cone bleaching data.

Elsewhere in the same paper, Rushton and Henry use another method and

come up with 29167 td) as the half-bleach constant. You can get this

number by specifying ‘RushtonHenryAlt’ as the source for the cone

constants. If you use isomemerizations here, the constant is scaled up

from the one derived above by the ratio (29167/(10^4.3)).

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 irradiance 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)/3 = 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 to compute the bleaching constant

expressed in terms of isomerizations, 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 paper

Burkhardt, D. A. “Light adaptation and photopigment

bleaching in cone photoreceptors in situ in the retina

of the turtle.” Journal of Neuroscience 14.3 (1994):

1091-1105.

provides a half bleach constant for turtle cones of 5.57 expressed

in log10 R*/um2/sec, which could with some work be converted to

isomerizations/cone/sec for turtle cones. But it’s not

clear you want to use that number unless you are studying turtle.

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- cones.

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).

irradiance – retinal irradiance specified as determined by units. If

initialFraction is empty, this is a single number and

steady state bleaching fraction is returned. If

initialFraction is a number, then this is a time series

of irradiance versus time, and fraction bleached for the

same times is returned.

receptortype

‘cones’ – computations for cones. [Default]

‘rods’ – computations for rods. Currently only implemented for

recovery kinetics. Need to find and enter half-bleach

constant for rods in scotopic trolands and/or

isomerizations to do steady state of full kinetic

calculations for rods.

units – units of irradiance

‘trolands’ input irradiance 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.

source – source of underlying data

‘Boynton’ Boynton and Kaiser, Human Color Vision, 2nd edition,

pp. 211 and following. See intro text above. [Default]

‘RushtonHenryAlt’ - Rushton and Henry’s other half-bleach constant.

Only available for ‘cones’.

initialFraction – fraction of input bleached at time zero. If

empty, steady state fraction bleached is

returned. Default is empty.

timeUnits – units for time step on input and output

‘sec’ seconds

‘tenth’ tenths of seconds

‘hundredth’ hundredths of seconds

‘msec’ millseconds [Default]

‘tenthmsec’ tenths of milliseconds

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.

12/18/18 dhb Modify header comments for possibility of passing time

varying signal. This breaks old usage that allowed

computing steady state bleaching for a set of vector

inputs, but I think that is OK.

08/19/19 dhb Added some information about Burkhardt (1994) to header

comment, and inserted a stub to use that information if

someone does the work to put the number from it into the

right units.

dhb Reorganized some code relative to source switch statement. Because

there was only one case this didn’t matter, but now I think it

is right if more cases.

01/09/21 dhb Finish off adding kinetics.

01/12/21 dhb Add in the alternate Rushton & Henry half-bleach constant

for cones.

`Psychtoolbox/PsychColorimetric/ComputePhotopigmentBleaching.m`