Printing System Models - Control of Color Imaging Systems: Analysis and Design - page 587

p 0 (g) is the measurable front surface re ectance (FSR) (function of gloss as

described in Ref. [32])
p 1 (n 1 , n 2 , i) is the total FSR (function of refractive indices n 1 , n 2 , and incident
angle i)
R s ( l ) is the substrate re ectance (function of paper type)

t ) is the transmittance from air through toner to paper (function of TMA

and toner spectral transmittance)
t 0 (m i ;

(m i ; l

) is the return transmittance from paper through toner to air (again,
function of TMA and toner spectral transmittance)

l

The physical process considered here is fairly simple (see also Figure 10.29
and Ref. [32]). Essentially, incident light hits the surface of the paper and a portion
of it, namely, p 1 , the so-called total FSR, gets re ected. This is the total amount of

light re ected, which is assumed to be constant and independent of gloss. It depends

only on the ratio of the refractive indices of the two surfaces and the angle of
the incident light. This is captured by the well-known Fresnel equations (see also
Ref. [32]) given by

2 3

q

n 2 = n 1

2

2 i

cos i ð Þ sin

4 5

p k ¼ q

n 2 = n 1

( 10 : 55 a)

2

2 i

cos i þ ð Þ sin

Measurement device
(e.g., Xrite-938)

(1-ρ 1 )τ R s τ΄

ρ 0

Toner
layer

ρ 1

Paper

FIGURE 10.29 Visualization of the physical process considered by the color model.