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«Lawrence A. Taplin B.S. University of Delaware (1996) A thesis submitted in partial fulfillment of the requirements for the degree of Master of ...»

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Spectral Modeling of a Six-Color Inkjet Printer

Lawrence A. Taplin

B.S. University of Delaware

(1996)

A thesis submitted in partial fulfillment of the requirements

for the degree of Master of Science in Color Science

in the Chester F. Carlson Center of Imaging Science

of the College of Science

Rochester Institute of Technology

December 2001

Signature of the Author

Accepted by Dr. Roy S. Berns,

Coordinator, M.S. Degree Program

CENTER FOR IMAGING SCIENCE

ROCHESTER INSTITUTE OF TECHNOLOGY

ROCHESTER, NEW YORK

CERTIFICATE OF APPROVAL

M.S DEGREE THESIS

The M.S. Degree Thesis of Lawrence A. Taplin has been examined and approved by two member of the Color science faculty as satisfactory of the thesis requirement for the Master of Science degree Dr. Roy S. Berns, Thesis Advisor Dr. Jonathan S. Arney

CENTER FOR IMAGING SCIENCE

ROCHESTER INSTITUTE OF TECHNOLOGY

ROCHESTER, NEW YORK

THESIS REPRODUCTION PERMISSION STATEMENT

Title of thesis: Spectral Modeling of a Six-Color Inkjet Printer I, Lawrence A. Taplin, hereby grant permission to the Wallace Library of the Rochester Institute of Technology to reproduce my thesis in whole or in part. Any reproduction will not be for commercial use or profit.

Date: ____________ Signature of Author: _____________________________

Spectral Modeling of a Six-Color Inkjet Printer Lawrence A. Taplin B.S. University of Delaware (1996) Acknowledgement My sincerest thanks go out to my advisor Roy, my family and friends.

Spectral Modeling of a Six-Color Inkjet Printer Lawrence A. Taplin B.S. University of Delaware (1996) A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Color Science in the Chester F. Carlson Center of Imaging Science of the College of Science Rochester Institute of Technology

ABSTRACT

After customizing an Epson Stylus Photo 1200 by adding a continuous-feed ink system and a cyan,magenta,yellow,black,orange and green ink set, a series of research tasks were carried out to build a full spectral model of the printers output. First, various forward printer models were tested using the fifteen two color combinations of the printer. YuleNielsen-spectral-Neugebauer (YNSN) was selected as the forward model and its accuracy tested throughout the colorant space. It was found to be highly accurate, performing as well as a more complex local, cellular version. Next, the performance of nonlinear optimization-routine algorithms were evaluated for their ability to efficiently invert the YNSN model. A quasi-Newton based algorithm designed by Davidon, Fletcher and Powell (DFP) was found to give the best performance when combined with starting values produced from the non-negative least squares fit of single-constant Kubelka-Munk.

The accuracy of the inverse model was tested and different optimization objective functions were evaluated. A multistage objective function based on minimizing spectral RMS error and then colorimetric error was found to give highly accurate matches with low metameric potential. Finally, the relationship between the number of printing inks and the ability to eliminate metamerism was explored.

TABLE OF CONTENTS

1. INTRODUCTION

2. MATERIALS

HARDWARE

Epson Stylus Photo 1200

MIS Associates Continuous Feed System

Pigmented ink set

Paper

Spectrophotometer

SOFTWARE

Mathworks MATLAB 5.3

Metrowerks CodeWarrior 6

Numerical Recipes in C

Solaris based printer driver

Halftone Algorithm

SYSTEM FLOW CHART

3. TWO-COLOR MODEL EVALUATION

HALFTONE MODELS

Neugebauer Model

Theoretical and Effective Area Coverage

Yule-Nielsen Spectral Neugebauer Model

Determination of Yule-Nielsen n-value

Cellular Neugebauer Models

CONTINUOUS TONE MODELS

Single-Constant Kubelka-Munk

Cellular Kubelka-Munk

EXPERIMENTAL

RESULTS AND DISCUSSION

Neugebauer Model

Yule-Nielsen Spectral Neugebauer Model

Cellular Neugebauer Model

Cellular Yule-Nielsen Spectral Neugebauer Model

Single Constant Kubelka-Munk Model

Cellular Kubelka-Munk Model

CONCLUSIONS

4. SIX-COLOR FORWARD MODEL

SIX-COLOR YULE-NIELSEN-SPECTRAL-NEUGEBAUER (YNSN).................4-36 Conversion from digital count to effective area coverage

Yule-Nielsen n-value

SIX-COLOR CELLULAR YNSN

EXPERIMENTAL

vi Printed Samples

RESULTS AND DISCUSSION

CONCLUSIONS

5. OPTIMIZING MODEL INVERSION

INTRODUCTION

Evaluation Targets

Objective Function

Optimization in MATLAB

Numerical Recipes in C

Starting Value Sensitivity

RESULTS AND DISCUSSION

Downhill Simplex - AMOEBA

Single constant Kubelka Munk - KS

Multidimensional Search - POWELL

Conjugate gradient method – FRPR





Variable-Metric/Quasi-Newton method - DFP

CONCLUSIONS

6. SIX-COLOR INVERSE MODEL EVALUATION

OBJECTIVE FUNCTIONS

Spectral RMS Error

Spectral RMS Error with Spectral Weighting

Multistage Objective Function

EVALUATION TARGETS

NGA Pigment Target

GretagMacbeth ColorChecker

GretagMacbeth ColorChecker DC

Vrhel Object Colors

Random Printed Samples

RESULTS AND DISCUSSION

Comparison with Di-Yuan Tzeng’s results

CONCLUSIONS

7. METAMERIC POTENTIAL

INTRODUCTION

RESULTS AND DISCUSSION

CONCLUSIONS

8. CONCLUSIONS

Two-Color Model Evaluation

Testing of the Six-Color Forward Model

Optimizing Model Inversion

Six-Color Inverse Model Evaluation

Metameric Potential

Closing Thoughts on Future Research

REFERENCES vii APPENDIX A. SPECTRAL PRINT SAMPLES

APPENDIX B. MATLAB CODE

CIE HELPER FUNCTIONS

xyz.m

lab.m

illD.m

deltaEab.m

deltaE94.m

deltaE00.m

meta_idx00.m

pcorrect.m

PRINTED IMAGE UTILITIES

patch_image.m

epson_image.m

CHARACTERIZATION TARGETS

neugpatches.m

one_ink_ramps.m

INK SET STRUCTURE INITIALIZATION

init_model.m

init_inkset6.m

COLORANT SPACE TRANSFORMATIONS

dc2eff.m

eff2dc.m

inv_murr.m

YULE-NIELSEN-SPECTRAL-NEUGEBAUER (FORWARD MODEL)................ B-9 neug.m

INVERSE MODEL OPTIMIZATION

inverse6.m

sep1_obj_RMS.m

RMS.m

SPECTRAL, COLORIMETRIC AND METAMERIC REPORTING

reportstats00.m

APPENDIX C. RESEARCH SOURCE CODE IN C

neugdemo.c

wrappers.h

wrappers.h

munsell.h

munsell.c

–  –  –

Traditional imaging systems take advantage of the fact that the human visual system is trichromatic. These systems record and reproduce a wide range of visual stimuli using just three channels of information. In most applications this works quite well.

However, three-color reproductions systems are insufficient if printed reproductions from these systems are viewed under a range of lighting conditions. For several years research efforts within the Munsell Color Science Laboratory (MCSL) have been focused on the spectral reproduction of color.1-60 If the spectral characteristics of the original are recorded and reproduced across all wavelengths of the visual spectrum, differences in the appearance of the reproduction will be eliminated even when the observer or lighting are changed. Practically, exact spectral reproduction through conventional inkjet printing cannot be obtained. However, the colorimetric redundancy within a six-color inkjet system can be exploited to minimize metamerism in the final print while maintaining a high level of colorimetric accuracy.

The current research effort described in this thesis is the direct continuation of the work begun by Di-Yuan Tzeng in creating a complete spectral color-output system.

Tzeng presented his research in the form of a doctoral dissertation and a series of papers at the annual Color Imaging Conference.23,27,37,44 The current research initiative included several stages. First, a six-color inkjet printing system, around which the research would be conducted, was assembled. The next stage involved selecting an appropriate mathematical model to transform between digital counts and printed spectra. Next, the effectiveness of this model in predicting the six-ink output from the printing system was tested. Research into methods for inverting

–  –  –

counts best reproducing them were tested next. The accuracy of the inverse model was tested and optimization objective functions leading to the best spectral matches were explored. Finally, the relationship between the number of inks used in the printing system and the degree of metamerism in the matches was explored.

The completed printing system fits into the broader spectral color reproduction research being conducted at MCSL as the output stage of a full end-to-end spectral capture, archiving and output system (Figure 1-1).

–  –  –

The following section details the hardware and software components that were assembled into the completed printing system.

Hardware Epson Stylus Photo 1200 The Epson Stylus Photo 1200, a consumer class desktop inkjet printer was selected based on its high resolution, low cost and six-color capacity. The printer, shown below in Figure 2-1, was modified by changing the ink set and adding a continuous-feed inksupply system. The printer has an advertised resolution of 1440x720dpi; however, it was only used at a resolution of 720x720dpi.

–  –  –

A continuous feed ink supply system was installed into the printer so that a large number of prints could be made before the ink needed to be replenished. This was important in limiting the number of times the printer required characterization.

–  –  –

The feed system is shown in Figure 2-2. Ink drawn out through the bottom of the cartridges by the vacuum from the print head causes additional ink to be drawn in through the tubes at the top that are connected to the vent holes. The free ends of the tubes rest at the bottom of the four-ounce ink bottles.

Pigmented ink set At the time the printing system was assembled, there were several CMYK ink sets to choose from. Archival-pigmented CMYK inks from MIS Associates were selected but additional ink colors were not yet available. Green and Orange ink from a Roland Hi-Fi jet printer was used to fill the fifth and six positions in the printer. Since the printer had already been used with regular Epson inks, it was necessary to flush out the print head before installing the new inks. This was accomplished by printing many pages of a dense test target using special cleaning cartridges also purchased from MIS Associates. The

–  –  –

system. Patches of each ink were printed and measured to produce the plot of reflectance spectra shown in Figure 2-3. By inspection, it is clear that the green and orange inks cannot be reproduced spectrally by combinations of cyan, magenta yellow and black.

–  –  –

Paper After visually assessing output on various high quality inkjet papers, Lumijet Classic Velour was selected for use in the printer characterization and modeling reseach. The paper, manufactured by Luminos, is a heavyweight (310gsm) matte paper with a velvety finish. With only minimal bleeding, the paper was able to absorb the ink from patches printed at maximum area coverage for all six channels.

–  –  –

Spectrophotometer A GretagMacbeth SpectroScan spectrophotometer was used to make all the spectral measurements in this research. The SpectroScan is a 45°/0° spectrophotometer with a 4mm aperture mounted on a motorized X/Y positioning table. The device was controlled using a software package called SpectraChart that helped automate the measurement of the large number of samples from each printed target. The manufacturer specifications for the instrument state an inter-instrument agreement of 0.3∆E*ab (D50,2°) based on 12 BCRA tiles with a maximum of 0.8 ∆E*ab. Short-term repeatability is stated as 0.03 ∆E*ab based on 10 measurements of white spaced out ten seconds apart. Further testing of the instrument within MCSL has confirmed a high level of precision and accuracy. As shown in Figure 2-5, printed samples were measured against the dark background of the SpectroScan’s top surface.

–  –  –

Software Mathworks MATLAB 5.3 Initial testing and development of the various models and algorithms was conducted using MATLAB, an environment that combines mathematical computing and visualization tools with a high level programming language. The final code makes use of the image processing and optimization toolboxes. The project source code as well as descriptions for each module are included at the end of this thesis as Appendix B.

Metrowerks CodeWarrior 6 One drawback of evaluating the model in MATLAB was the slow speed of execution. To improve performance, much of the research was recoded in C using Metrowerks CodeWarrior 6 cross platform (PC/Mac) compiler. C source code for the project is

–  –  –

Many of the algorithms needed for this research were already compiled together into one source, the book and CD, “Numerical Recipes in C”.61 Redistribution of the source code for the algorithms is strictly controlled by a license agreement and therefore the code is not included in an appendix. However, the code was used nearly unmodified and the routines need to interface to it are included in Appendix C. The only modifications made were to change the exit conditions of some routines to better handle error conditions.



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