The Wavelength Dependence of the Yule-Nielsen Factor Joseph M. Janiak* and Dr. Jon Arney Rochester 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 Light Light Scatters in Paper Dot R = F R i + (1 - F)R p R i and R p are functions of F. Paper Cross Section

R = F R i + (1 - F)R p A special case of the Law of Conservation of Energy. Dot Fraction, F R

The Image is Darker Due to Dot Gain R Dot Fraction, F “Dot Gain”

R Dot Fraction, F n is the Yule-Nielsen Dot Gain Parameter

Yule-Nielsen Equation R = Reflectance of Image F o = Dot Area Fraction R i = Reflectance of ink patch R p = Reflectance of paper

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 5 TM printer Offset printer

Opacity(cont.) Laser Jet 5 TM 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/OffsetLaser

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 Area F = 0.25 RpRp RiRi Halftone Sample

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

- 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.)

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

Results(cont.)

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.