Page 165 - Computational Colour Science Using MATLAB

152 CHARACTERIZATION OF PRINTERS

x = linspace(0,1,101);
y = polyval(p,x);
hold on
plot(x,y,’k-’)
end

The built-in MATLAB function polyfit is then used to fit a third-order
polynomial between the actual and target coverage areas and the coefficients of
this fit are returned in the matrix p. The full syntax for gettrc is

function [p] = gettrc(dig,R,w,solid,n,graphs)

where dig is a 16r matrix of target area coverages, R is an r6m matrix of
measured reflectance values, w is a 16m matrix of reflectance for the white
substrate, solid is a 16m matrix of reflectance for the solid ink, n is a 161 matrix
containing the free parameter [see Equation (9.5)] to determine the non-linearity,
r is the number of target coverage areas, m is the number of wavelengths
(usually 31) at which the reflectance data are measured and graphs ¼ ‘on’
causes a plot of the actual versus target areas to be generated. Once the
characteristics of the tone-reproduction curve have been established using gettrc
any target coverage can be converted to the actual coverage using the polyval
command:

actual = polyval(p,target)

where target and actual are 161 matrices that hold the target and actual area
coverage values and p is the output of the gettrc function. Figures 9.4 and 9.5
show the result of the gettrc function for n ¼ 1 and n ¼ 20, respectively, for each
of the three inks.
The optimum value of n may be found to give the lowest prediction error
for the reflectances of the inks printed on their own at various coverage
areas and in mixture with other inks. For this example application, a value
of n ¼ 20 was found to be optimum. The tone reproduction curves allow the
target areas to be converted to actual areas and these may be used with
the n-modified Neugebauer equations to predict the spectral reflectance
for combinations of inks. For a single ink, and measurements at 31
wavelengths between 400 and 700 nm, the colour difference between the
predicted reflectance and the measured reflectance is predicted using the
following code: