# Illustrate a metameric matching and chromatic aberration

Metamerism is a fundamental insight of color science. The word is used in two different ways, however. In its principal scientific use, two metamers are lights with different spectral power distributions that are visually indistinguishable.

People in industry often use metamerism to refer to the phenomenon that the same surface, scene under two different lights, does not appear the same.

This script describes the scientific analysis of metamers. We simulat a uniform field with D65 spectral power distribution and find a matching (metameric) LCD display output.

The two metameric lights are then used to create a bar pattern. We represent the bar pattern after optical blurring and then encoded by the human cone sensor array.

(c) Imageval Consulting, LLC 2012

## Contents

```ieInit
```

## Create a uniform scene with a D65 spectral power distribution

```uSize = 64;
uS = sceneCreate('uniformd65',uSize);
```

## Create a uniform field with a metameric spectral power distribution

```% The new spectrum is the weighted sum of the primaries of an
% LCD. spectrum.  The weights are chosen so that the LCD has the
% same effect as the D65 on the cones.

% The mean LMS cone values of the original
lms = sceneGet(uS,'lms');
meanLMS = mean(RGB2XWFormat(lms));

% Load a display and use the display primaries as a set of basis
% functions for the metameric light.
d    = displayCreate('lcdExample');
wave = sceneGet(uS,'wave');
displaySPD = displayGet(d,'spd',wave);

% These are the display primaries
vcNewGraphWin; plot(wave,displaySPD)
title('Display primaries')

% Now read the Stockman cone wavelength sensitivities
dW = wave(2)-wave(1);   % Delta Wavelength

% Solve for the weights on the primaries that will produce the
% same absorptions in the cones as the D65 light.  Be careful to
% account for the wavelength sample spacing, dW.
%
%   meanLMS(:) = S'*(displaySPD*w)*dW
%
w = ((S'*displaySPD)\meanLMS(:))/dW;
metamer = displaySPD*w;
```

## Create a new uniform scene with the SPD that is metameric to D65

```% We do this using the sceneSPDScale routine.  This multiplies
% the SPD in the scene by another SPD.  We use the
% metamer/originalSPD as the multiplier.

% Here is the original
oSPD = sceneGet(uS,'mean energy spd');

% Divide by the original, and then multiply by the metamer
uS2 = sceneSPDScale(uS,metamer(:)./oSPD(:),'*',0);
uS2 = sceneSet(uS2,'name','metamer');

% The metamer SPD
mSPD = sceneGet(uS2,'mean energy spd');

% Make a plot comparing the metamer and the original mean energy (mn)
vcNewGraphWin;
plot(wave,mSPD,'-o',wave,oSPD,'--');
legend('Metamer','original')

% Note that the color appearance on the screen differs between these two
% metamers.  That is because I did not implement a rendering algorithm
% based on human vision and the cones.  I used a method that is faster.  I
% am thinking of changing because, well, computers are now faster.
```

## Numerical check

The comparison projects of the SPDs of the metamers onto the Stockman cones. The difference should be zero. It is small, and I am not sure why it is not precisely zero. I could probably do better.

```S'*(mSPD(:) - oSPD(:)) / norm(oSPD,2)
```
```ans =

1.0e-04 *

-0.7756
-0.7939
-0.2283

```

## A spatial pattern with two metamers adjacent.

```% This will enable us to see the effect of optical blurring on the
% different spectral power distributions.

% Retrieve the SPD data from the two different uniform scenes.
height = 64; width = 32;
xwData  = sceneGet(uS,'roi photons',  [8 8 width-1 height-1]);
xwData2 = sceneGet(uS2,'roi photons',[8 8 width-1 height-1]);

% Combine the two data sets into one and attach it to a new scene
cBar = XW2RGBFormat([xwData; xwData2],height,2*width);
barS = sceneSet(uS,'photons',cBar);

% Name it, set the FOV, and show it.
barS = sceneSet(barS,'name','bars');
barS = sceneSet(barS,'h fov',1);
```

## Compute the OI and show the SPD across a line in the image

```% Notice that the optical image spectral irradiance varies across
% the row. The LCD spectra are clearly scene at the positive
% positions.  They are blurred a little onto the left side by the
% optics.
oi = oiCreate('human');
oi = oiCompute(oi,barS);

midRow = round(oiGet(oi,'rows')/2);
title('1 cpd bar');
```

## Compute the sensor response for these half degree bars

```% Although the spd of the OI differs across the image the cone
% absorptions are fairly constant across the horizontal line at
% this spatial resolution.
sensor = sensorCreate('human');
sensor = sensorSet(sensor,'exp time',0.10);
sensor = sensorSetSizeToFOV(sensor,1,uS,oi);
sensor = sensorCompute(sensor,oi);

sz = sensorGet(sensor,'size');
sensorPlot(sensor,'electrons hline',[1,sz(1)]);
```

## Now, reduce the fov so the bars are thinner

```% There is structure in that we see more clearly if we average a
% few rows. Let's do it. S-cone response, higher on the left and
% lower on the right.
barS = sceneSet(barS,'h fov',1/8);

oi = oiCompute(oi,barS);