the wavelength dependence of the yule-nielsen factor joseph m. janiak* and dr. jon arney rochester...

The Wavelength Dependence of the Yule-Nielsen Factor

Joseph M. Janiak* and Dr. Jon ArneyRochester Institute of Technology

Overview

• Background

• Experimental Design

• Results

Optical Dot Gain

• Caused by the lateral scattering of light in a paper substrate.

• Another name for optical dot gain is the Yule-Nielsen effect.

Paper

LightLight Scatters

in Paper

Dot

R = F Ri + (1 - F)Rp

Ri and Rp

are functionsof F.

Paper CrossSection

R = F Ri + (1 - F)Rp

A special case of the Law ofConservation of Energy.

Dot Fraction, F

R

00 1

1

The Image is Darker Due to Dot Gain

R

00 1

1

Dot Fraction, F

“Dot Gain”

0.5 10

0.5

0

1

R

Dot Fraction, F

n is the Yule-NielsenDot Gain Parameter

)/1()/1()/1( )1( npo

nio

n RFRFR

Yule-Nielsen Equation

• R = Reflectance of Image

• Fo = Dot Area Fraction

• Ri = Reflectance of ink patch

• Rp = Reflectance of paper

)/1()/1()/1( )1( npo

nio

n RFRFR

What Affects n?

• Optical scattering power of paper

• Halftone pattern

• Sharpness of the edge on dots

• Opacity of the dot

Yule-Nielsen Factor, n

• When n = 1 there is no diffusion or spreading

• The theoretical limit of n is 2

Research Objective

• Five variables were looked at to determine which variable was most important in controlling the wavelength dependence of n.

1. Color of Ink

• Cyan

• Magenta

• Yellow

2. Color of Paper

• Cyan

• White

3. Paper Substrate

• Ink jet paper

• Copier paper

Paper Substrate(cont.)

• When ink jet paper is used, ink will penetrate the paper less.

• Physical dot gain is reduced when inkjet paper is used.

4. Opacity of Colorant

• Laser Jet 5TM printer

• Offset printer

Opacity(cont.)

• Laser Jet 5TM uses opaque toner.

• Offset printers use transparent ink.

• Scattering within the absorbing layer should be more intense when opaque toner is used.

Ink Jet/Offset vs. Laser

Ink Jet/Offset Laser

5. Halftone Pattern

• FM halftone

• AM halftone

AM Halftones

• Clustered dot halftone

• Dots are printed at fixed distances from each other.

• Grayscale is controlled by varying size of dots.

FM Halftones

• Error diffused halftone

• Dots are the same size throughout the halftone.

• Grayscale is controlled by varying the distance between the dots.

Halftone Comparison

Clustered Dot(AM Halftone)

Error Diffused(FM Halftone)

25% Dot AreaF = 0.25

Rp

Ri

Halftone Sample

)/1()/1()/1( )1( npo

nio

n RFRFR

Experimental Method

• First created series of samples via computer and printer.

• Found sample area where dot area fraction was roughly 50% and took precsise measurement with microdensitometer.

• Found reflectances of 100% dot area region,50% dot area region, and 0% dot area region via spectrophotometer.

Experimental Method(cont.)

• Placed the known values of R,Ri,Rp, and Fo into Yule-Nielsen equation and solved for the value of n.

• Generated plots of n versus wavelength and absorbance spectra of samples.

Results Wavelength vs. n

1

1.25

1.5

1.75

2

400 425 450 475 500 525 550 575 600 625 650 675 700

Wavelength(nm)

n

Magenta ink - Yellow paper

Magenta ink - White inkjet paper

Magenta ink - White copier paper

Magenta ink - Offset printer

Magenta ink - Clustered dot halftone

Magenta ink - Error diffused halftone

Magenta ink - Blue paper

Wavelength vs. n

1

1.25

1.5

1.75

2

400 425 450 475 500 525 550 575 600 625 650 675 700

Wavelength(nm)

n








- n was larger when electrophotography was used compared to when offset was used.- n was larger when a clustered dot halftone was used.

Results(cont.)

Wavelength vs. Absorbance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

400 425 450 475 500 525 550 575 600 625 650 675 700

Wavelength(nm)

Ab

so

rban

ce








Results(cont.)Wavelength vs. n

1

1.25

1.5

1.75

2

400 425 450 475 500 525 550 575 600 625 650 675 700

Wavelength(nm)

n




Cyan ink - Offset printer

Cyan ink - White inkjet paper

Cyan ink - White copier paper

Yellow ink - Offset printer

Yellow ink - White inkjet paper

Results(cont.)

Wavelength vs. n

1

1.25

1.5

1.75

2

400 425 450 475 500 525 550 575 600 625 650 675 700

Wavelength(nm)

n









- again n was larger when electrophotography was used compared to when offset was used.

Results(cont.)Wavelength vs. Absorbance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

400 425 450 475 500 525 550 575 600 625 650 675 700

Wavelength(nm)

Ab

so

rba

nc

e



Magenta ink - White copierpaper






Results Summary - Effect on n

• Color of Ink- Proved to be similar to the absorbance spectra. As absorbance increased, n increased. This is different that what has been seen in past research.

• Opacity- When electrophotography was used n values appeared to be larger.

Results Summary - Effect on n

• Halftone-When clustered dot halftones were used(AM halftones) n values were larger, compared to when error diffused halftones were used(FM halftones).

• After the conclusion of this experiment it was seen that the Yule-Nielsen effect was not only a function of scattering but also absorbance.

the wavelength dependence of the yule-nielsen factor joseph m. janiak* and dr. jon arney rochester...

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