[T_quantalAbsorptionsNormalized,T_quantalAbsorptions,T_quantalIsomerizations,adjIndDiffParams,params,staticParams] = …
Function to compute normalized cone quantal sensitivities
from underlying pieces, as specified in CIE 170-1:2006.
IMPORTANT: This routine returns quantal sensitivities. You
may want energy sensitivities. In that case, use EnergyToQuanta to convert
T_energy = EnergyToQuanta(S,T_quantal’)’
and then renormalize. (You call EnergyToQuanta because you’re converting
sensitivities, which go the opposite direction from spectra.)
The routine also returns two quantal sensitivity functions. The first gives
the probability that a photon will be absorbed. The second is the probability
that the photon will cause a photopigment isomerization. It is the latter
that is what you want to compute isomerization rates from retinal illuminance.
See note at the end of function FillInPhotoreceptors for some information about
convention. In particular, this routine takes pre-retinal absorption into
account in its computation of probability of absorptions and isomerizations,
so that the relevant retinal illuminant is one computed without accounting for
those factors. This routine does not account for light attenuation due to
the pupil, however. The only use of pupil size here is becuase of its
slight effect on lens density as accounted for in the CIE standard.
This standard allows customizing the fundamentals for
field size, observer age, and pupil size in mm.
To get the Stockman-Sharpe/CIE 2-deg fundamentals, use
fieldSizeDegrees = 2;
ageInYears = 32;
pupilDiameterMM = 3;
and don’t pass the rest of the arguments.
To get the Stockman-Sharpe/CIE 10-deg fundamentals, use
fieldSizeDegrees = 10;
ageInYears = 32;
pupilDiameterMM = 3;
and don’t pass the rest of the arguments.
Although this routine will compute something over any wavelength
range, I’d (DHB) recommend not going lower than 390 or above about 780 without
thinking hard about how various pieces were extrapolated out of the range
that they are specified in the standard. Indeed, the lens optical
density measurements only go down to 400 nm and these are extropolated
to go below 400.
This routine will compute from tabulated absorbance or absorbance based on a nomogram, where
whichNomogram can be any source understood by the routine PhotopigmentNomogram. To obtain
the nomogram behavior, pass a lambdaMax vector. You can then also optionally pass a nomogram
source (default: StockmanSharpe)). This option (using shifted nomograms) is not part of the
CIE standard. See NOTE below for another way to handle individual differences
The nominal values of lambdaMax to fit the CIE 2-degree fundamentals with the
Stockman-Sharpe nomogram are 558.9, 530.3, and 420.7 nm for the LMS cones respectively.
These in fact do a reasonable job of reconstructing the CIE 2-degree fundamentals, although
there are small deviations from what you get if you simply read in the tabulated cone
absorbances. Thus starting with these as nominal values and shifting is one way to
produce fundamentals tailored to observers with different known photopigments.
If you pass lambaMax and its length is 4, then first two values are treated as
the peak wavelengths of the ser/ala variants of the L cone pigment, and these
are then weighted according to LserWeight and (1-LserWeight)). The default
for LserWeight is 0.56. After travelling it for a distance to try to get better
agreement between the nomogram based fundamentals and the tabulated fundamentals
I (DHB) gave up and decided that using a single lambdaMax is as good as anything
else I could come up with. If you are interested, see FitConeFundamentalsTest.
NOTE 1: When we first implemented the CIE standard, adding this shifting feature
seemed like a good idea to allow exploration of individual differences in photopigments.
But, with 0 shift, none of the nomograms exactly reproduce the tabulated photopigment absorbance
spectral sensitivities, and this is not so good. We are phasing out our
use of this feature in favor of simply shifting the tabulated
photopigment absorbances, and indeed in favor of adopting the method
published by Asano, Fairchild, & Blonde (2016), PLOS One, doi: 10.1371/journal.pone.0145671
to tailor the CIE fundamentals to individual observers. This is done by
passing the argument indDiffParams, which is a structure as follows.
indDiffParams.dlens - deviation in % from CIE computed peak lens density
indDiffParams.dmac - deviation in % from CIE peak macular pigment density
indDiffParams.dphotopigment - vector of deviations in % from CIE photopigment peak density.
indDiffParams.lambdaMaxShift - vector of values (in nm) to shift lambda max of each photopigment absorbance by.
indDiffParams.shiftType - ‘linear’ (default) or ‘log’. ‘linear’ gets the Asano et al. behavior
You also can shift the absorbances along a wavenumber axis after you have
obtained them. To do this, pass argument lambdaMaxShift with the same
number of entries as the number of absorbances that are used.
The adjIndDiffParams output is a struct which is populated by ComputeRawConeFundamentals.
It contains the actual parameter values for the parameters adjusted using the indDiffParams
input. It contains the following fields:
adjIndDiffParams.mac - the adjusted macular pigment transmittance as a function of wavelength
as calculated in line 151 of ComputeRawConeFundamentals.
adjIndDiffParams.lens - the adjusted lens transmittance as a function of wavelength as calculated
in line 41 of ComputeRawConeFundamentals.
adjIndDiffParams.dphotopigment - 3-vector of the adjusted photopigment axial density for
L, M and S cones (in that order), as calculated in lines
200-202 of ComputeRawConeFundamentals; or rods, as calculated
in line 216 of ComputeRawConeFundamentals if params.DORODS is true.
adjIndDiffParams.absorbance - Photopigment absorbance as given in line 188 of ComputeRawConeFundamentals
adjIndDiffParams.absorptance - Photopigment absorptance as given in line 230 of ComputeRawConeFundamentals
For both adjIndDiffParams.mac and adjIndDiffParams.lens, the wavelength
spacing is the same as in the S input variable of this function.
The params and staticParams outputs are the argument strucutures that
were passed to ComputeRawConeFundamentals by this routine to do the work.
These can be useful if you’d like, say, to susequently use
ComputeRawConeFundamentals to produce estimates for (e.g.) melanopsin or
the rods, where you keep everything else as consistent as possible to
what this routine does. Note that this is all a bit klugy for historical
reasons, as there is redundancy between what you can/might do with
adjIndDiffParams and with these two return outputs. In particular, these
two return outputs would let you call ComputeRawConeFundamentals and get
adjIndDiffParams directly from there.
This function also has an option to compute rod spectral sensitivities, using
the pre-retinal values that come from the CIE standard. Set DORODS to true on
call. You then need to explicitly pass a single lambdaMax value. You can
also pass an optional rodAxialDensity value. If you don’t pass that, the
routine uses the ‘Alpern’ estimate for ‘Human’/’Rod’ embodied in routine
PhotopigmentAxialDensity. The default nomogram for the rod spectral
absorbance is ‘StockmanSharpe’, but you can override with any of the
others available in routine PhotopigmentNomogram. Use of this requires
good choices for lambdaMax, rodAxialDensity, and the nomogram. We are
working on identifying those values more precisely.
Finally, you can adjust the returned spectral sensitivities to account for
the possibility that some of the pigment in the cones is bleached. Pass
a column vector with same length as number of spectral sensitivities beingt
computed. You need to estimate the fraction elsewhere.
Relevant to individual differences, S & S (2000) estimate the wavelength difference
between the ser/ala variants to be be 2.7 nm (ser longer).
NOTE 2. The CIE standard is specified for field sizes between 1 and 10
degrees. Our code will extrapolate using the given formulae to larger
field sizes without complaining. We think this is reasonable; see
CIEConeFundamentalsFieldSizeTest and its header comments, but be aware
that you have sailed into little charted territory if you do this.
See also: ComputeRawConeFundamentals, CIEConeFundamentalsTest, CIEConeFundamentalsFieldSizeTest,
FitConeFundamentalsTest, FitConeFundamentalsWithNomogram, StockmanSharpeNomogram,
8/13/11 dhb Wrote it.
8/14/11 dhb Clean up a little.
12/16/12 dhb, ms Add rod option.
08/10/13 dhb Test for consistency between what’s returned by FillInPhotoreceptors and
what’s returned by ComputeRawConeFundamentals.
05/24/14 dhb Add fractionPigmentBleached optional arg.
05/26/14 dhb Comment improvements.
02/08/16 dhb, ms Add lambdaMaxShift argument.
ms Don’t do two way check when lambdaMax is shifted.
02/24/16 dhb, ms Started to implement Asano et al. individual difference model
3/30/17 ms Added output argument returning adjusted ind differences
8/1/17 dhb, ms Added return of params and staticParams.