Virtual electro-photographic printer model

Rochester Institute of Technology

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12-1-2002

Virtual electro-photographic printer model

Sunadi Gunawan

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VIRTUAL ELECTO-PHOTOGRAPHIC PRINTER MODEL

by

Sunadi P. Gunawan

B.s. Imaging Science

(2001)

A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in the Chester F. Carlson Center for Imaging Science

of the College of Science Rochester Institute of Technology

December 2002

Signature of the Author _

H

Rhd

/2/°7/2002.-Accepted by e_nry---=-_ _o--=..y _

CHESTER F. CARLSON CENTER FOR IMAGING SCIENCE

COLLEGE OF SCIENCE

ROCHESTER INSTITUTE OF TECHNOLOGY ROCHESTER, NEW YORK

CERTIFICATE OF APPROVAL

M.S. DEGREE THESIS

The M.S. Degree Thesis of Sunadi P. Gunawan has been examined and approved by the

thesis committee as satisfactory for the thesis requirement for the

Master of Science degree

Dr. Jonathan S. Arney, Thesis Advisor

Dr. Peter G. Anderson

Dr. Roy S. Berns

THESIS RELEASE PERMISSION ROCHESTER INSTITUTE OF TECHNOLOGY

COLLEGE OF SCIENCE CHESTER F. CARLSON CENTER FOR IMAGING SCIENCE

Title of Thesis: VIRTUAL ELECTO-PHOTOGRAPHIC PRINTER MODEL

I, Sunadi P Gunawan, hereby grant permission to the Wallace Memorial Library ofR.I.T. to reproduce my thesis in whole or in part. Any reproduction will not be for commercial use of profit.

Signature: _

VIRTUALELECTO-PHOTOGRAPHIC PRINTERMODEL

by

Sunadi P. Gunawan

Submittedto the

Chester F. Carlson

Center for_Imaging Science College ofScience

inpartial fulfillmentoftherequirements

fortheMasterofScience Degree

ABSTRACT

A halftone image inthecomputerisa_bitmap matrixthatcontains either0 or 1,

where0meanstheprinter willnotdeposit_anytoneronto apaperand 1 means theprinter

will depositsomeamount oftoneronto apaper. The amountoftoner thatisput_bythe

printer onto apaperfora given inputsignal patternischaracterized. The hypothesis was

thatthedistributionoftonermassonthepaperfora given inputmatrix pattern canbe

modeledwith atonerpoint spread_function,atoner transfer_{efficiency function,} anda

noise function.

Inorderto _studytonermassdistributionprinted on_paper,it is necessaryto

develop an analyticaltechnique_{for measuring}thedistributionoftonermass. The

analyticaltechnique usedinthis thesisis anopticalanalysisbasedonlighttransmitted

through the printedsample. This analyticaltechniquewascalibratedagainst a

gravimetric analysis. Linearrelationbetweentheoptical analysis andgravimetric

analysisindicatesthatthetechnique canbeused for measuringspatialdistributionof

printedtonermass on a micro-scale.

Guided_byexperimentalmeasurementsoftonermass_{distribution,} aquantitative

model ofthe threeprinter_functions,thespread_function,the toner_{deliveryfunction,} and

thenoise _function,werecharacterized. These functionswere usedto construct a printer

functionthatwas usedtocomparethe_efficiencyofdifferent halftonepatterns. Theresult

oftheprinter model wasextendedtoincludetheoptical point spreadfunctionofthe

paper. Thisprovided a complete_printingmodelthat simulatedbothphysical and optical

Acknowledgement

IwishtoacknowledgeDr. Jonathan S. _Arneyfor hisadvice and guidancewhich made

thisprojecttobecome a reality.

Iwouldliketo thankDr. Peter S. Anderson for his support and advice sothatIwasable

togenerate variousdifferenttestsamples easily.

Iwouldliketo thankDr. _RoyS. Bernsfor hisparticipation on _mycommittee.

Iwouldliketo thankHewlett-Packard _{Corporation for sponsoring}thisproject.

Table Of Content

Chapter 1: Introduction 1

Chapter2: Background 5

2. 1 BasicHalftone_Theory 5

2.1.2 _Murray-DaviesModel 5

2.1.2 Yule-Nielsen Model 6

2.2 Optical PropertiesofColorantsonPaper 9

2.2. 1 Beer Lambert Law 9

2.2.2 Kubelka-Munk Law 11

2.3 The Electrophotographic Process (Laser Jet_Printing) 13

2.4 _Halftoning 15

2.4.1 Cluster Dot 15

2.4.2 Dispersed Dot 17

2.4.3 Error Diffusion 18

2.4.4 Linear Pixel _Shuffling 21

Chapter 3: Analytical Technique for Toner Mass Analysis 22

3.1 Instrumental Design 22

3.2 CancelingThe Paper Transmittance Pattern 24

3.3 _CalibratingtheOptical Analysis 28

3.4 _TestingtheInstrumentfor Experimental Artifacts 31

3.4. 1 The Instrument Configuration 32

3.4.2 Lens Flair Characteristic oftheInstrument 35

3.4.3 Instrument_Stability Over Time 38

Chapter 4: Analysis ofToner Mass Distribution on Printed Samples...41

4. 1 Relative Toner Mass Distribution (Optical_Analysis) 42

4.2 TestoftheMultiple Reflection Hypothesis 46

4.3 Histogram AnalysisofToner Mass Distribution 49

4.3.1 InterpretationofCoverage Histograms 50

4.3.2 _InterpretingtheHistogramin Figure 4.6 53

4.4 Toner MassVersus Nominal Dot Area Fraction 54

4.5 _SummaryoftheAnalytical Technique 55

Chapter5: The Virtual Printer Model 57

5.1 Virtual Printer Model Function 57

5.2 _Calibrating The Virtual Printer Model 60

5.3 OptimumParameters fortheHP LaserJet 4500 Printer 64

Chapter 6: TestoftheVirtual Printer Model 69

6. 1 Virtual Printer Model _Testing 69

6.2 Printer FigureofMeritandToner Mass Calculation 71

6.3 _ConvertingToner Mass DistributiontoReflectance Image 72

6.3. 1 _CalculatingToner Extinction Coefficient 74

6.4 Virtual Printer Model Performance 74

Illustrations ofComparisons ofReflectance Images 79

Conclusions and Suggestions 86

List Of Figures

Figure 1.1: Illustrationofa_BitmapPatternandIdeal Result 1

Figure 1.2: Real Printed Image Captured_byCCDCamera 2

Figure 2.1: Printer Tone Transfer Function for Ideal Halftone 6

Figure 2.2: Physical DotGain Illustration 7

Figure 2.3: _Scattering ofLightinthePaper 8

Figure 2.4: Illustration ofBeer-LambertCase in_ImagingLayer 10

Figure 2.5: Illustration ofKubelka-Munk Casein_ImagingLayer 11

Figure 2.6: The Steps inanElectrophotographic Process 14

Figure 2.7: 6 x6 Cluster Dot Halftone Mask 16

Figure 2.8: Exampleof6x6 Cluster Dot_Gray Scale Images 17

Figure 2.9: Exampleof

Bayer'

sOptimum Dispersed Dot 18

Figure 2.10: IllustrationofRaster_ProcessingwithError Diffusion 19

Figure 2.11: Floyd-_Steinberg Error Filter 20

Figure 2.12: Example of a_{Floyd-Steinberg}Error Diffusion_GrayLevelofFn=0.3....20

Figure 2.13: ExampleofLinear Pixel_{Shuffling Gray} Scale Images 21

Figure3.1: IllustrationofPossible Light_Traveling 23

Figure 3.2: InstrumentalDesign 24

Figure 3.3: Cyan Toner Image in RedandInfrared Light

(Irradianceis in_{ArbitraryUnit)} 25

Figure3.4: Cyan Toner Spectral Transmittance_Densityat_Fn= ₁

Figure 3.5: _RelationshipBetween Optical Analysisand GravimetricAnalysis

For Cyan Toner Mass Printed_Using 600 dpi Hewlett Packard 4500 30

Figure 3.6: Instrumental Design Illustration for_TestingtheInstrument 32

Figure 3.7: Diagramof_ProcessingTransmittance Image Captured CCD Camera 33

Figure 3.8: IllustrationofHistogramofaFlat-Fielded

Transmittance ImageofPaperwithBlack Tape 34

Figure 3.9: IllustrationofLens Flair 36

Figure 3.10: Experimental Design for_TestingLens Flare 37

Figure 3.11: Lens Flare Experimental Result 38

Figure 3.12: Light SourceandCCD Camera_TestingConfiguration 39

Figure 3.13: Light SourceandCCD Camera_Stability 39

Figure 3.14: RedandInfrared Filter_Testing 40

Figure3.15: _TestingResultfor Red andInfrared Filter 40

Figure 4.1: Relative Cyan Toner Mass Distribution 42

Figure4.2: Scan LineofCyan Toner Mass Distribution Image 45

Figure 4.3: Multiple ReflectanceofLight between TonerandPaper 47

Figure 4.4: Multiple ReflectanceofLight between TonerandPaper Configuration...48

Figure 4.5: MultipleReflectanceofLight Between Inkand PaperResult 49

Figure4.6: Cyan Toner Mass Distributionwith_{Fn=0.3, Fn=0.5,}andFn=0.7 50

Figure 4.7: Histogram AnalysisoftheIdeal Toner Mass Distribution 51

Figure4.9: Figure 5.1: Figure 5.2: Figure 5.3: Figure 5.4: Figure 5.5: Figure 5.6: Figure 6.1: Figure 6.2: Figure 6.3: Figure 6.4: Figure6.5:

Relative Cyan Toner Mass Coverage Measured

OpticallyversusDot AreaFraction, Fn. (HP Laserjet4500) 55

DiagramofVirtual Printer Function 59

5x Super_SamplingoftheInput Image Files 62

Toner Point Spread FunctionandToner Transfer_EfficiencyFunction

for 600 dpi Hewlett-Packard Color Laser Jet 4500 Printer 65

RelationshipbetweentheMeasuredandtheSimulated Toner Mass

Distribution Metrics 66

HistogramofToner Mass DistributionImage

( )Measured & _{( )} Simulated. .66

Visual Comparisonbetweenthe MeasuredandtheSimulated Toner Mass

Distribution 68

TestofThe Printer Model 70

Calculating Printer FigureofMerit 72

Relative Toner Mass Correlation betweentheMeasuredand

Simulated Samples 76

Printer Figure Of Merit CorrelationbetweentheMeasuredandthe

Simulated Samples 77

CorrelationbetweentheMeasuredandthe Simulated Samples forVarious

List Of Table

Chapter 1: Introduction

Ahalftoneimage inacomputerisamatrixthatcontainsa patternof0and 1

values. Thispatternis senttoaprinter andtheprinterwilltranslate the signalfor 1 as

some amount oftonermasstobe depositedonto apaper. Thesignalvaluefor0

translatesintheprinter asa commandtodepositno toner. Figure 1.1 isanillustrationof

a matrixpatterninacomputer andthe_{corresponding}imageprinted_byanidealprinter.

An_{ideal resulting image}fromaprinterisa perfect squaredoton_topof a_paper,which

doesnothave physicaland optical dotgain effects.[7]

1 0 1 0 1 0 1

0 0 0 0 0 0 0

1 0 1 0 1 0 1

0 0 0 0 0 0 0

1 0 1 0 1 0 1

Matrix Pattern

PRINTER

Figure 1.1: Illustration ofa_BitmapPatternandIdeal Result

Figure 1.2 showstheresult of_printingtwo differentmatrix patternson a600 dpi

Hewlett-Packard 4500 colorprinter. The CDintheappendix ofthis thesiscontainsthe

composed of one addressable printerdotand pattern_(B)produces one dotcomposed of

fouraddressable printer dots.

(A)

111

Figure 1.2: Real Printed Image Capture _byCCD Camera

Figure 1.2 showsthat theprinteddotsarenotperfect squaredots, buttheyhave

some shapewithsomedistributionand noise. Itisalso clearthat the amount oftonerin

eachprinterdot depends strongly onthechosen pattern. The individualprinterdots in

Figure 1.2 (A)areverydifficultto seeatall,andthe2x2clustersinfigure 1.2(B)arenot

printedas clusters of_discretelyresolved printerdots. Theeffects ontonereproduction

are_clearly important. In_{the past, the terms}"physical dotgain"

has beenusedtodescribe

tonereproduction effectscaused_bytonermassdistributionssuchasthoseillustrated in

densitometrytechniquecapable of_measuringtonermassdistributions, andtousethe

results oftheanalysisto_developa quantitative modelfortonermassdistributionin laser

electro-photographicprinting.

Themodelthatwasdevelopedcontainedapoint spreadfunction (PSF).

However,thepointspreadfunctionusedinthismodel was not anoptical_PSF,commonly

usedtomodel optical dotgain[13' 23,

29\

An_interestingobservationin Figure 1.2 isthatastheprinter printsfourdots

together(2x2 _clusters),theprinterseemsto put moretonerontothepaper. _Bylooking

visuallyattheimagesonFigure 1.2heldat armslength,pattern(A)image looks brighter

thanpattern _(B)imageeventhough thenominaldotarea_{fraction, Fn,} senttotheprinteris

thesame. Macroscopicmeasurements ofimage_densityconfirmthisobservation. This

phenomenon cannotbe described_bythepointspreadfunctionoftonerbecausethepoint

spread function only describesthe_waytonermassis distributed. Itdoesnotdescribethe

total tonermassthatis delivered. _Therefore,an additionalfunction isneededinthe

printermodel inordertodescribethe tonermassthatis delivered.

The modelwastestedand calibrated_bycomparisonwith measurementsoftoner

mass distributionsmadewith an_especially developedmicro-densitometer. This

analyticaltoolusesoptical_{micro-densitometry}tomeasure thedistributionof printed

tonermass onthepaper. The opticalanalysis oftonermass was calibratedagainst an

micro-densitometricanalysis oftonermassdistributionwas usedtomeasurethespatial

distributionof printedtonermass asaguideto thedevelopmentoftheprinter model.

Theprinter model developed inthis thesiswas usedtocalculate severalfiguresof

meritforcomparison ofdifferent halftonepatterns. Themodelhas been incorporatedas

part ofother projects underthedirectionofProfessor P.G. AndersonandJ.S. _Arneyto

Chapter 2: Background

Thischapter providesbriefbackgroundoverviewsoffourtopicsthatare

importanttoan_{understanding}ofthecurrentthesis. Thebasic halftone_theoryis

described insection2.1. Theoptical_theoryofcolorantsis describedinsection2.2.

Section 2.3 describesthebasicmechanism of electrophotographic_printingprocess.

Finally,section2.4 describesfour_{very different kinds}of_halftoning methods usedinthis

thesis to testthe_reliability oftheprinter model.

2.1 Basic Halftone _Theory

2.1.1 Murray-Davies Model

Thefirstprintermodel usedtopredictoutput reflectanceofan_{image, R,}from

input dot areafractionsenttoa_printer,Fn, wastheMurray-Davies Modelshownin

equation(2.1).[1]

R=

F_-Rk+

(1-F_)-RB

Thereflectance values _Rkand _Rgrepresentthereflectancevalues oftheimageat_Fn= ₁

(solid_ink)and_Fn =

equation_2.1,then thepredicted reflectance willbe_linearlyrelatedto theinputdotarea

fraction. This isillustratedin figure 2.1.

Figure 2.1: Printer Tone Transfer Functionfor Ideal Halftone

2.1.2 Yule-Nielsen Model

It is_{experimentally} observedthat themeasured reflectance is darkerthan the

reflectance predicted_byequation_2.1,andthebiggest differenceoccursnear50%dot

areafraction. Dotgainisthe termusedtodescribethisphenomenon. Therearetwo

typesofdotgain; that_is,physicaldotgain and opticaldotgain.[7]

Becausethemeasured reflectance valueisdarkerthan thepredicted reflectance

value, itis generallyassumedthatdotsgetbiggerinthe_printingprocess. This isthe

reasonthephenomenoniscalleddotgain. Figure 2.2 illustratesphysicaldotgain. In

dotarea_{fraction, Fn,} usedinequation2.1 is _clearlynotthecorrectdotareafractionvalue

ifthesize ofthedots increases.

Ideal _Dot,Fn

Paper

Dot Spreadout, F

Figure 2.2: Physical Dot Gain Illustration

Theactual dotareafraction, F,in a printedhalftone may bemeasured_by

micro-densitometrictechniques.[9] Onemight expectthat_byusingtheactualdotareafraction,

F,inequation2.1 insteadof _Fn,onewould predictthecorrectimage _reflectance,R.

However,themeasured reflectancevalueis stilldarkerthan thepredicted reflectance

value. ' _Therefore,thereisanother effectthatcauses_{this observation,} whichiscalled

optical dotgain. Thecause of optical dotgainisthe_scatteringoflight inthepaperJ '

Arney,et_al,modeledtheopticaldot gaineffect asillustratedin Figure 2.3.[10'"'

12' 13]

Light enteringthepaperasshownin figure 2.3 can reflectbackoutfromthepaper

(I) oritcan scatterand reflectbackoutthroughthe ink (II). Ontheother_hand, light

Paper

Figure 2.3:_{ScatteringofLight in}thePaper

oritcan scatter and reflectbackoutthrough thepaper(IV). The lightpathin figure 2.3

(IV) causes reflectance of paperbetweenthedotstogetdarker. Theamountoflighton

pathIV isthesame as onpathII. _Therefore,theoverall measuredreflectance willbe

darkerthan thepredicted reflectance.

In _1951,Yule andNielsenmodifiedtheMurray-Daviesmodel as shownin

equation2.2.[8] _They addedthe 1/npowerfactorinordertocorrectforphysicaland

opticaldotgain sothat theprinterswouldbeabletopredictthemeasured reflectance

fromthedotareafractionsentto theprinter. Equation 2.2describestheYule-Neilson

model.

R=Fn.R

+(l-Fn).R _(2.2)

Thenfactorisanempirical constantfor_fittingtheexperimentaldata.[9J _By

findingthebest fitof nvaluefora particularsystem,oneis abletopredicttheoutput

Aswill beshown_later,thelateral _scatteringoflightandtheeffects of optical dot

gain cause a problemintheoptical analysis oftonermassdistribution. Thenature ofthe

problem andthe_{way it}was overcome will_{be described}subsequently.

2.2 Optical Properties ofColorants on Paper

Inanidealcontinuous_{imaginglayer,} onecan_applytheBeer-Lambert Law for

predictingtheoutputirradiance from input irradiance after_travelingsomethickness of

imaginglayerwitha given colorant absorption coefficient and concentration ofthat

colorant. _However, ifthelightscattersinthe_layer,Kubelka-Munk_theorycanbeused.

Inorderto_developan optical analysisoftonermasson_{paper, the}absorption and

scatteringpropertiesofboththetonerandthepapermustbeunderstood. Thereaderis

referredtoKubelka-Munk_(1931), Allen_(1980), andBerns₍₂₀₀₀₎foradetailed

discussionofthesetheories.[3'24'25]

2.2.1 Beer Lambert Law

Consideran_imaginglayeras shown onfigure_2.4, whichdoesnot scatterlight.

The lightenters an _{imaginglayer, I0,}andtravelssome xdistance. The layerhascolorant

at concentration c. Thecoloranthasan absorptioncoefficient, s. Lightthatcomes out

fromthe_{layer, I,}canbedescribed_bytheBeer-Lambert Lawas showninequation2.3.

The Beer-Lambert Lawsaysthat the _{irradiance decreases exponentially}with_increasing

ImagingLayer,c,e

I

Figure 2.4: Illustration ofBeer-Lambert Case inImagingLayer

Equation 2.3 showsthat

-In'P

y\j

is_directlyproportionaltoc. Theproducte.c.x isalso

calledabsorbance,A. Theterm

-In

'I"*

J.J

iscalledtransmission_{density, Dt,}so_density is

proportionaltocolorant concentrationinaBeer-Lambertsystem.

D. =-ln =_{s.c.x (2.3)}

TheproductC=

e ciscalledthecolorantcoverage. Ingeneralitiseasier

experimentally tomeasure _{coverage, C,}thantheseparate values of andc. Inthework

2.2.2 Kubelka-MunkLaw

Many imaginglayers,such as paper and_pigment, scatterlight. _Scatteringoflight

inthe_imaging layer is _veryimportanttobetakenintoconsideration. For_instance,

scatteringoflightinthepaper can causetheprintedimagetobe darkerthanpredicted.

Therefore,scattering and absorptionoflight inthe_imaginglayeraffecttheoptical

properties ofimages.

?

Io J

i_

J(x)

1 I(x) r

1 I

r

dx

Figure 2.5: Illustration ofKubelka-MunkCasein_ImagingLayer

Consideran_imaginglayeras showninfigure 2.5thatscatters and absorbs light.

Ifthe_imaging layerdoesnot scatter_light,then the changein input_{irradiance, I0,} will

followtheBeer-Lambert Law. _Thus, equation2.4canbe writtentodescribethechange

dI=-KI-dx (2.4)

whereKistheabsorption coefficient(theproductof extinction_{coefficient, e,} and

concentration,c, withreciprocal_unit,e.g. mm"1). _{However, scattering}also decreasesthe

irradiance,I, inthedown direction. Kubelka-Munk suggestedthatthe _scattering

phenomenon couldbedescribedas afirstorderphenomenon. _Therefore, equation2.4

canbeexpandedtoincludethe_scatteringphenomenon,andthisisshowninequation2.5.

dl=- KI-dx-S-1-dx+S- J-dx

(2.5)

where S is_scatteringcoefficient andhasthesameunitas absorption_coefficient,andJ

represents irradiance inthe_{up direction. A} seconddifferentialequationisneededin

ordertodescribetheirradiance inthe_{up direction}thatwillalsobeaffected_bythe

scatteringoflight. The irradiance inthe_{up direction}is described _byequation2.6.

dJ =- K- dx- S-

J-dx+S- 1-_dx

(2.6)

Lateral scatteringoflight inthe_imaging layerisignoredinthisanalysis. The

a=^> (2.7)

S

b=Va2-1 _(2.8)

1-R _{[a-b-coth(b-S-x)]}

R= s _(2.9)

a-R+_{b-coth(b-S-x)}

T =

(2.10)

a- sinh(b-

S-x)+ b-cosh(b-

S-x)

whereRandTarereflectance andtransmittanceofthe_imaginglayerrespectively,and_Rg

is backgroundreflectance.

2.3 The Electrophotographic Process (Laser Jet _Printing)

Figure 2.6 shows sixbasicsstepsoftheelectrophotographic process. ' The first

step, asshownin figure_2.6-(I),istochargethephotoconductor. Afterthe

photoconductorhas been_{charged, the}laser isusedtoexposethecharged photoconductor.

The laser light dischargesthecharged photoconductor. Thisprocessis illustrated in

figure 2.6-(II). Theareawherethephotoconductordischargedwillbe developedinto a

realimage withtonerparticles. Tonerparticles are chargedparticlesthatwillbeattracted

to the dischargedphotoconductor. _Therefore,inthedevelopment step,shownin figure

2.6-(III),the tonerparticles willbeattractedto thedischargedareas ofthe

accomplished_bychargingthepaper sothatthepaperhaslargeenough electricfield for

breakingthebond betweenthephotoconductor andtoner. This isshownin figure

2.6-(IV).

Photon

(I) Charge P h

oto-C onductor

(II)

'"I

I

il

+ + + + + + + + + + +

Photo-Conductor Photo-Conductor

C h arge 'Loner Particle N / -* _{High Voltage}

(III)

^-*^>^

(' v ) + + + _I B Paper

^^J

+ + + + + + +

Photo-C onductor

o +oo

+ + + + ooo+ + 8

Photo-C onductor

TFT IW? (VI)

(V)

o +oo

+ + + + coo+ + 8

Paper

Cleaning Brush

+ +v

+ + + +

Photo-C onductor

Figure2.6: The Steps inanElectrophotographic Process

Oncethetonerhas beentransferred tothe_{paper, the}tonerparticles arefusedto

create apermanentimage. Thisfusingstateisaccomplished_{by heating}the toneras

showninfigure2.6-(V). The last step intheelectrophotographic processistoclean_up

2.4

Halftoning

Fora review of_halftoningtechniques andhalftone_theory,thereaderisreferredto

Ulichney (1987) and_Kang (1999).[7,26] The_followingis a_summaryof_keypointsabout

halftoningusedinthecurrentthesis.

2.4.1 Cluster Dot

Clustered Dot_halftoningis alsocalledamplitudemodulated _(AM)halftoning.

The AM_halftoningmethodisaconventional_halftoningmethod wherethe_spacing

distance betweenthehalftone dots isconstant andthesize ofthedots isnot constant. In

anAM_halftone,thedotarea_{fraction, F,}is controlled_{by controlling}thesizeofthedots.

An AMtypehalftone isproduced_{digitally byusing}ahalftonemaskwithaclustered

arrangementofthresholdvalues. The individualelements ofthemaskcorrespondto

individual addressable units oftheprinter. Themask as awhole correspondstoasingle

AMhalftone_dot,andthemaskis usedtoconstructahalftone dotateachhalftone

locationintheimage.

Figure2.7 illustrates a6x6clustered dot halftonemaskwith36threshold levels

ranging from 1 to36. A digitalalgorithm comparesthesethresholdvaluesto the _gray

levels oftheoriginal continuoustoneimage inordertodeterminewhetherinkshouldbe

deliveredatthatlocationor not. Thethresholdprocess producesa0fortheprint

command"deliverno

toner"

ora 1 fortheprint command "delivertoner". In_{this way,} a

sequential arrangement ofthe thresholdvalues causes the 1 valuestogrowina

contiguous cluster asthe_{image becomes darker. Figure 2.8} showsseveral 6x6cluster

dot_gray scale imagesattheredifferent dotareafraction.

21 22 23 24 25 26 20 7 8 9 10 27

19 6 1 2 11 28

18 5 4 3 12 29

17 16 15 14 13 30

36 35 34 33 32 31

Figure 2. 7: 6x6 Cluster Dot Halftone Mask

Thetermofdpi (dotsper_inch)isoften usedto describethe_{spacingfrequency} of

theaddressable unitsofa_{printing device. It is} alsothe_{spacingfrequency}oftheelements

inahalftonemask. The_frequencyofthe halftone dot is lessthan the_frequency ofthe

printer. Forexample, ifa600 dpiprinterisusedtoproduceAMclustereddothalftones

byusinga6x6 halftonemask, as shownintheaboveexample, theresultwill bea 100

LPI (linesper_inch) halftoneimage. Thehigherthe_frequencyofthehalftone_image,the

smoother animagewill appear. _Thus,a printer withhigher addressibilityisneededin

6x6 Cluster Dot

Fn=

0.3 Fn=

0.5 Fn=

0.7

Figure 2.8: Example of6x6 Cluster DotGrayScale Images

2.4.2 Dispersed Dot.

There are_many differentwaysthethresholdvaluescanbearrangedina clustered

dot halftonemask,and each produces anAMhalftonewithdifferentproperties.[7] Also,

thearrangement ofthreshold valuesinthehalftonemaskdoesnotneedto beclustered

andregular. _Manytechniqueshave beenpublishedfor_dispersingthethresholdvalues

throughout themaskinrandomor quasi random patterns^ ' ' '

Theresultiscalled a

disperseddothalftone,also calledanFMhalftone. Figure 2.9 shows severalillustration

of constanthalftone gray scaleimagesproduced with adisperseddot halftonepattern

Bayer'sDispersed Dot Patterns

Fn=

0.3 Fn=

0.5

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..."...-..".-..."....v.

x-x-x-x-x-x-x-x-:-X x-x-x-x-x-x-x-x-:-X x-x-x-x-x-x-x-x-:-X x-x-x-x-x-x-x-x-:-XXX X X X X

X XXX X X X X X X -&*:-*::-:V*-#X

XXX XX X X XXX ::x:::::x:::x:::::::x:::

XX XXXX XXX X .:::.::::$:=.$.

xxxxxxxxxx _{:SS...::SH.$i}

xxxxxxxxxx _{:::SS...$::::SS.} xxxxxxxxxx x-x-x-x-x-x-x-x.-: xxxxxxxxxx

Fn=_0.7

xxxxxxxxx:-Figure 2.9: Example ofBayer's Optimum Dispersed Dot

2.4.3 Error Diffusion.

Error diffusion isapopulardigital halftonealgorithmfor preparingimagestobe

printed onlowresolution printers. Errordiffusionwasdeveloped_by Floydand _Steinberg

in 1976as amethod of_preparing animageforcomputerdisplay. 7' Error diffusiondoes

not_rely on ahalftonemask. _Instead,thefirstprinter pixelintheimageiscomparedtoa

thresholdvalueof x=

0.5. Ifthereflectance oftheoriginal, continuoustoneimage(0<

R< _{1)is higher}thanthis_threshold, theprinter command"0" isusedtoprint no ink.

Otherwise,theprintercommandis"1" andinkisprinted. Thisresultsina_{gray level}

errorE= (0

-R)orE=₍₁

-R) atthatparticularlocation. Inordertocompensateforthis

error,thenextlocationuses athresholdvaluethatisadjustedtowithsome_amount,k, of

the error, x= 0.5

-k'E. This newthreshold iscomparedtoRandink isnotprintedif R

>_x,otherwise ink isprinted. Theresultis still an_error, E=₍₀

-R)orE=₍₁

-R),sothis

Theerror propagationtechnique_generallypropagates somefractionof_{the error,}

kE,toseveral_{neighboring locations,}asillustrated inFigure2.10. The locationsmarked

"x"

have been_processed, andink hasbeenprinted or notprinted. The locationmarked

"?"

isthelocationwherethealgorithmis intheprocessof_makingaprint-or-not

thresholddecision. TheresultwillleadtoerrorE=₍₀

-R)orE= ₍₁

-R),andafraction

ofthaterrorkiEwillbesubtractedfromthethresholdvalueofthepixelto theright of

the "?" location. Three other pixelsthathavenot yetbeenprocessedare alsogivena

fractionoftheerrorto adjusttheirrespectivethresholdvalues. Thevaluesofthe

fractions, kithrough_{1_4,}sumtounity. Eachpixellocationintheimagecan accumulate

errorfromas_many asfourthresholdoperationsin neighboringpixels.

Printer locations (printer pixels) x x x x x x x x x x x

i#ft

J_!

Figure2.1 1 istheerrordiffusion kernelmost_commonly usedinthishalftone

process. Thevalues ofthefractionski through_{1_4}are_actuallycalculated as7/(7+3+5+1)

through 1/(7+3+5+1). Figure 2.12 shows an example ofconstant_{gray level}producedby

Floyd-Steinberg errordiffusion. Error diffusiontechniques_typicallyproducehalftone

imageswithindividualprinterdots distributed inaquasi random way. Theresultisan

FMtypeofhalftonepatterninwhich dot fractionvaries withthe_frequencyofoccurrence

of printeddots.

?

7

3

5

1

(1/16)

Figure2.11:_{Floyd-Steinberg}ErrorFilter

mm

2.4.4 Linear Pixel_Shuffling

Linear Pixel _Shufflingisan algorithmdeveloped_byAnderson[20]

thatisuseful for

generating halftone imageswitha_varietyof properties. Linear Pixel _Shufflingcanbe

usedtogeneratedispersedthreshold masksfor dispersed dot_halftoningorfor_dispersing

theorderof raster_{processing in}errordiffusion halftoning. Amajor advantageofLinear

Pixel _Shufflingisthatit isadeterminantprocesswith quasi-randomproperties. Thatis,

itisa_wayto scrambletheorder ofthingsina_waythatis_{mathematically}reversible.

Digitalhalftonesproduced_byLinear Pixel _Shufflinghave a_varietyofdesirable

propertiesfortonecontrol andforcontrol of spatial_frequencycontent. Themathematical

detailsofLinear Pixel _Shufflingcanbe seenintheliterature.[20'21'22] Figure2.13 shows

some Linear Pixel_{Shufflinggray} scale images_{byusingFloyd-Steinberg}errorfilter.

Linear Pixel_Shufflingwith_{Floyd-Steinberg}Error Filter

Fn=

0.3 Fn=_0.5

Fn=_0.7

MiP

*

an

r

Chapter 3: Analytical Technique for Toner Mass Analysis

Inordertocharacterizethe tonerpoint spread_function,the tonermasstransfer

function,and noise_function,itwas_necessaryto _developan analyticaltoolthatcould

measure_opticallytheamountoftonermassdepositedonto a paper. _Therefore,thefirst

focusofthe thesiswasto_developandto testan analyticaltool_{for measuring}the spatial

distributionof printedtonermass on a micro-scale.

3.1 Instrumental Design

Amonochrome CCDcamerawithmicroscope optics wasused inordertocapture

the tonermassinformationonprintedsamples. Imageswere capturedfor images

illuminatedwithdifferentwavelengthbandsoflightinordertoextractthe tonermass

distribution basedon spectral characteristicsofthe toner.

Illumination oftheprintedsample fromthecamera sideofthesample results in

animagemadeofreflectedlight. _However,a reflectionimageisnot abletodistinguish

spatially betweenregions ofthepaperthathavetonerand regionsthatdonothavetoner.

Thisisbecauseofthe_{lateral scattering} oflightwithin_{the paper,} asillustratedin Figure

3.1. Thisisthe samelateral scatteringeffectthatcausestheso-called opticaldotgain

fromabarepaper region oftheimage (pathIVinFig. _3.1) itstill carriesthe spectral

signature ofthe toner. _Thus, spectral analysis of a reflectionimagecaptured witha

microdensitometer wouldindicatethat tonerexistsinthetoner-freeregions ofthepaper.

ReflectanceMode

Io

l^II

Transmittance Mode

Dot

Paper Paper

Figure 3.1: Illustration ofPossible LightTraveling

Inordertoavoidtheproblemof_{lateral scattering}andthe_resultingspatial

scrambling ofthetonerspectral_{signature, the}sampleis illuminated fromtherear as

illustratedontherightside ofinFigure 3.1 andin Figure 3.2. In_{this configuration,}light

scatters inthepaperbefore itencountersthe toner_dots, solight_{emerging from}the

printedsamplecarries spectralinformationaboutthe toner_{only in}regions wherethereis

toner. Thedeviceillustrated in Figure 3.2was constructedtoallowfilterstocontrol

illuminationovertherangeof_sensitivityofthecamera. Thecamera usedinthis thesis

CCDCamera

_____________ Sample

_____________ Filter(RedorInfrared)

v

7LightSource

Figure 3.2: Instrumental Design

Althoughtransmittedilluminationremovestheproblemof_{spatiallyscrambling}

the toner_information, it introducesanother problem. The spatial variationinthepaper

transmittance,knownas"paper_{formation"[17],} is introducedintothemeasurement.

3.2

Canceling

Inordertocancelthenoise ofpaper_formation,anindependentmeasure ofpaper

transmittance isneeded. A preliminary study demonstratedthatcyan, magenta,and

yellowtonerswere notdetectableinimagesmade withnearIRradiation. Figure 3.3

illustratesthe_preliminaryexperimentforthecyantoner. The CD intheappendix ofthis

thesiscontainsthe_{high quality images}usedinthisfigure. Theprintedblockofcyan was

clearlyobservedinred_light, as _expected,butwas notdetectable inthenearIR. This

Cyan Tonerwith

RedLight Scan Line (Red_Light)

^0.5 ~

200 400

Pixel Position 600

Cyan Tonerwith

Infrared Light

Scnn Line

200 400

PixelPosition

600

Figure3.3: Cyan Toner Image in RedandInfrared Light

(Irradiance is in_{Arbitrary Unit)}

The camera usedinthis_studyproduced pixelvaluesthatwere_directly

proportionaltotheradiance ofthesample. SincetheimagecapturedinthenearIR

carriedinformation only aboutthe transmittancepattern of_{the paper,}it was usedto

cancelthepapertransmittancefromimagescapturedwithvisible light. Equation 3.1

showsthefunctionforthepixelvalues,P, intheimageatlocations_(x,y)as afunctionof

Pred(x,y)=

kred(x,y)-Sred(x,y).I(x,y)-Tfred-Tp(x,y)-Ttred(x,y) (3.1)

where_Pred(x,y) ispixel value ofthecaptured_image,k(x,y) isa collectiveconstant

representingsystem optical effects such asthelensaperture and cosinelens fall-off,

Sre_(x,y)iscamera_sensitivitytored_light,I(x,y)is irradiance distributionforthe light

source,Tfre_isthefilter_{transmittance, Tp(x,y)} isthepapertransmittance_{distribution,} and

Ttredistoner transmittance.

Equation 3.2 canbewritten whenthesameimageis captured withInfrared light.

PIR(x,y)=kIR(x,y)-SIR(x,y)-I(x,y)-TfIR-Tp(x,y)-l

(3.2)

where subscriptIRindicatestheinfrared filter is_beingusedfor_{the analysis,}andthe

transmittanceofthetoneris _Tt(x,y)= ₁

.0intheIR. Weassumethe transmittanceofthe

paper,Tp(x,y), is governed_{onlybyscattering}sothatitthesamein both images. _Then,

dividingequation3.1 by 3.2 leadstoequation3.3. This cancels outthepaper

Pred(x,y) = kred

(x,y) Sred(x,y) _Tfred

Jt _(3J)

PiR(x,y) kIR(x,y)-S1R(x,y)-TfIR

Asampleoftheunprintedpaperisthenplaced infrontofthecamera and

illuminated_exactlyasdone fortheprintedsample. Imagesare capturedinredlightand

in IR exactlyasdescribedabove. Thisresultsin images described_byequations3.4 and

3.5. These equations areidenticaltoequations3.1 and3.2exceptthat the toner

transmittancein bothredlightandintheIRare_Tt(x,y)=1.0.

Ppred(x,y)=

kred(x,y) Sred(x,y) I(x,y) Tfred Tp(x,y) (3.4)

PPm(x,y)=

k^(x,y) Sm(x,y) I(x,y) Tfm Tp(x,y) (3.5)

Bydividingequation3.4_{by 3.5,}equation3.6 isobtained

Ppre_(x,y) kred.Sred(x,y).Tf,red

PPiR(x,y) km.S1R(x,y)-TfIR

Finally,rationingequation3.3 with equation3.6results intoner transmittance

informationonly,asshownonequation3.7.

Freddy)/

Ppred(x,y)/

C ;

/PPm(x,y)

Thetransmission_densityis thencalculated as_Dt(x,y)=

-log(T(x,y)), andDtis

proportional_{to toner coverage, C,}at each_location, (x,y).

3.3

Calibrating

Supposethe tonerobeystheBeer-Lambertlawanddoesnotscatterlight.

Therefore,the_{irradiance entering in}thetoner_{decreases exponentially}with_increasing

tonerconcentration and itsthickness. _Byusingthis_assumption, itis_verysimpleto

measuretherelative amount of printedtonermass onpaper_{optically because}the

Transmittance

Density

400 550 650 700

Wavelength,nm

Figure 3.4: Cyan Toner Spectral Transmittance_Densityat_Fn = _I

Figure 3.4 showsanillustrationof spectraltransmittance _densityforcyantoner

whentheprinterprints 100 % cyantonercoverageontothepaper. Forthisgiven

condition, therelative concentration of cyantoner, Cc,isequalto _1.00, andthe

corresponding densityisDc. Thenthedensityat_any otherrelative_{concentration,Cc,} is

given_byequation3.8 asDt(650).

Dt(650)=

Dc-Cc (3.8)

Therefore,by measuringand_calibratingDcat 100%_{toner coverage,}we can calculatethe

relative concentration of printed cyantoner,Cc,by knowingthemeasuredtoner

law. Inorderto testwhether or not equation_(3.8)is applicable, theresultsoftheoptical

analysis were comparedto theresults of anindependentgravimetric analysisoftoner

mass on paper.

Gravimetric analysis was performed_byprintingwhole sheetsofpaperwith cyan

toner and_weighingtheprinted sheets. Sheetswere printed withhalftonepatternsof

differentnominaldotareafractionsfrom 0 to 1. Theprinted cyantoner area was8 x 10.5

inches on8.5x 1 1 inchespapersize. The averagemass of10 differentpaper samples

was subtractedfromthe totalmass of printedcyantoneron a piece of papertogive a

printedtonermass. The gravimetricanalysisresult wasthenplotted againsttherelative

concentration oftonermass determined opticallyas shownin figure 3.5.

H 2a_(0.024)

2ct(1.66 grams/m2)

0 0.5 1

RelativeCyan Toner Concentration

(Optical_Analysis)

Figure 3.5:_RelationshipBetween Optical AnalysisandGravimetric Analysis

The primary cause of variationinthegravimetricanalysis wasthevariationof

paper weight. The standarddeviationfor 10 differentpaper'sweightis0.83 gram/m2.

Nevertheless, Figure 3.5 indicatesalinear relationship betweenthegravimetric analysis

andthe optical analysis. Thegravimetric analysis shows alow levelofprecision

primarilybecauseoftheintrinsic_variability ofpaper. Thegravimetric analysisisalso

not abletoresolvetonermass_spatially atthemicroscopiclevel. _However,the

gravimetric analysis andfigure3.5 provide a calibration constantfor_convertingthe

opticalanalysis of relativetonermasstoreal unitsof gram/m2. _Thus,theproposedthesis

wasbasedonthe optical analysis oftoner.

3.4 _Testing the Instrumentfor ExperimentalArtifacts

Thetransmissionmicro-densitometer shownin Figure 3.2 wastestedfortwo

experimentalproblemsthatoften compromisethe_accuracyof a micro-densitometer.

Theseproblemsarelensflairandtemporal stability. Inordertoevaluatetheextentto

whichtheseproblems contributeto themeasurements madewiththe_instrument,the

3.4.1 TheInstrument Configuration

Figure3.6 shows anillustrationoftheconfigurationoftheinstrumentusedfor

testingtheinstrument for lens flairandforstability. In Figure 3.6, it isshownthatthe

printedpaper sampleissandwichedbetweentwo clear glass plates.Thepurposeof_using

twoclear glass platesistomaintainthesample at aconstantdistance fromthecamera

andthelightsource inordertoholdthefocusofthe camera constantandtoholdthe

illuminationofthesample constant. For_testingthe_instrument, itwasdecidedtousethe

redfilteronly.

)Sample

H Red Filter

C

^

Figure 3.6:InstrumentalDesignIllustration for _TestingtheInstrument

Transmittanceimagesoftest samples,T(x,y),were captured withtheCCD

reference_{imageof an unprinted piece of paper. Inthesetests,variability} causedbythe

paperformation_{pattern was not a significantfactor,} aswillbe illustrated.

T,(_.,)= ^.y)-mean[dark(x,y)1

meanMx>y)_dark(x>y)]

ret_(x,y)

-mean|dark(x,y)J

(3.9)

Following imagecapture and _{flat-fielding,}histogramanalysis was performed.

The general experimental sequenceis illustrated inFigure3.7.

CameraOutput

Transmittance Image

T(x,y)

Flat-Field

TransmittanceImage

Tf(x,y)

Figure_{3. 7: Diagram ofProcessing}Transmittance ImageCaptured CCD Camera

Thetestsamples used inthisseriesofexperiments consistedofthereference

paperwitha_stripofblackvideo cassettetapeplaced overthepaper. Thefractionofthe

paper covered_bytheblacktapewasadjustedtosimulate printed samples withdifferent

dotareafractions. A histogramofaflat-fielded imageof oneofthese samplesis

1

(\l Threshold,Fi r

fee

/

\

___

V

y

Pi

Transmittance

Pixel Value

255

Figure 3.8: Illustration ofHistogram ofaFlat-Fielded Transmittance Image ofPaperwithBlack Tape

Thehistogram_clearlyallows a separation ofthepixels_{corresponding}topaper

fromthepixels_{corresponding}toblacktape. Themeanpixel_{values, Pi}and_Pp,were

selected asthepeaksofthe_{distributions,} asillustrated. _Also,thearea_{fraction, Fj,}ofthe

darktapewasestimated_{by selecting}atransitionpixel value asillustratedin Figure 3.8.

Thepaperandtapepixel values weretranslatedintotransmittancevalues_byusing

equation 3.10and equation3.11.

X =

mean[ref(x,y)

-dark(x,y)]

(3.10)

y P y

p

mean[ref(x,y)

-dark(x,y)]

Theratio_{( Pp/mean[ref-dark] )is} expectedtobe 1 +/-_{experimental variability.} Thetransmittanceof paper_{reference,TPjref,} wasmeasured_{independently}withaMacbeth

TR-1224densitometry. This densitometerapproximatesan_integratingspherefor measurement of_scatteringsamples.

3.4.2 Lens FlairCharacteristics oftheInstrument

"Lens flair" isa generaltermusedinthis thesis tomean_{any stray light}thatcauses

inaccuracy inthemeasuredtransmittancevalues_usingtheinstrumentshownin Figures

3.2 and3.6. Lightscatteredwithinthe_lens,as illustrated in Figure 3.9-c,resultsinan

overall additionoflightto theentireCCDarray. Anothercommon sourceof_straylight

is lightthatcomesfroma region ofthesamplethatis outsidethefield of view ofthe camera. Thisis illustratedin Figure 3.9_by light frompointbthatcomestofocusat point

b'

insidetheoptical system whereitshouldbeabsorbed. _However, a small amount of

scattered reflection can occurattheblackwall oftheopticalsystem,andthisscattered

aT al'

Camera

SamplePlane

Figure_{3.9: Illustration ofLens Flair}

Inorderto testthe significance of_straylight,a sample of paperwasmasked_bya

pieceofblackvideo cassettetapeas illustratedin Figure 3.10. Themaskedregion

coveredbothregions withinthecamerafieldof viewand regionswelloutsidethecamera

fieldof view. Imageswere captured withthe tapepositionedtoproduce different

fractionsofcoveredpaper,F. Thevalueof Fwasmeasured_bythehistogramanalysis

Ill

1

n

Increasing

H

Field OfView

Black Tape

?Plain Paper

Figure 3.10: Experimental Design for_TestingLensFlare

Iftheinstrumentsuffersfromsignificant_straylight, thenthemeasured valuesof

X,and_Tpfromequations 3.10and 3.11 will_vary withthepaperarea_fraction, F.

However, iftheinstrument lensflareis negligible, thevalues of_Xand_Tpwillbe

independentofthearea_fraction,F. Theresults shownin Figure 3.11 indicatethat_stray

lightisnegligible withintheprecisionofthemeasurement. _Therefore,theCCD camera

Lens Flare Test_(StrayLight) 0.4 -S 0.2 E -0.2

-1 1 1 1 1

.

ou o o o

--CT o t

1 oo o o o

1 u 1 o S 1 1 =c-^ 1 Transmittanceof Paper Transmittanceof Black Tape

0.2 0.4 0.6 0.8

PaperArea Fraction

Figure 3.11: Lens Flare Experimental Result

3.4.3 Instrument_StabilityOver Time

Anotherimportantcharacteristicfortheinstrument designisthe _stabilityofthe

instrument. The lightsource, CCDcamera, andthecolorfiltersusedintheinstrument

have tobestableovertime. _Otherwise, thevariation oftheinstrument_{may be}mistaken

foravariationintoner. The firsttestofinstrument stability involvedthecamera andthe

CCD Camera

i -J Plain Paper Sample

V _yLight Source

Figure 3.12: Light SourceandCCD Camera_TestingConfiguration

Thetransmittanceof a plainpaper_sample,Tp,was measuredseveraltimesover a

ten-minuteperiod oftimewith_{approximately}one-minute increments. _{The resulting}

measurements are showninfigure3.13. Itisclearthat themeasuredtransmittance ofthe

paperis constantoverten-minutes. _Thus,thelightsourceandtheCCDcamera are stable

enoughfor measuringthespatialdistributionoftonermass.

s 0.4

e

E

V. a

i-H 0.2

_ ti ed

Oh

o o o o o o o o e i

10

Period_(Minutes)

Secondtestwasto test the_stabilityoftheredandthe infrared filterused fortoner

mass analysis. Thistestinvolvedthesystem as showninFigure 3.14. Thetransmittance

values of paper inthered andinfraredregionwere_measured,andtheresultsare shownin

Figure 3.15. It isclearthat the twofilters usedintheexperimentare stable over a

10-minute period oftime. _Therefore, these twofilterscanbeusedtobuildtheinstrument for

measuringthe spatialdistributionoftonermass.

CCD Camera

_l Plain Paper Sample __RedorInfrared Filter

C PLightSource

Figure3.14: RedandInfrared Filter_Testing

Test forRed Filter

S0.4 c I

H0.2

-1 1

V u

1 1

TestforIRfilter

T"

10

s- _0.2

-5 10

Period(Minutes) Period(Minutes)

Chapter 4: Analysis ofToner Mass Distribution

on Printed Samples

Experimentalsamples were printed with aHewlett-Packard Laser Jet 4500color

printer. Sampleswere printed_usingcyantoneronly. Differentdotpatternswereprinted

forthis analysis. Thetoner_{transmittance,Ttre_(x,y),}was calculatedforeach pixelinthe

image,usingequation3.7. Thistransmittance_mapwas usedtocalculatea relativetoner

coverage, C(x,y),at eachpixellocation. Therelative coverage canbetranslatedinto

absolute

grams/m2

asdescribed inChapter 3. _However, most oftheanalysiswasdonein

relative units.

Inordertoobservethedistributionoftonermass_{visually, the}calculatedtoner

mass_{distribution, C(x,y)}wasconvertedintoa viewable image_{by applying}equation4.1.

Pc(x,y)=

[l-0.8C(x,y)]255 _(4.1)

Onthe average, thehighestrelativetonermassis 1.00. _However,experimental and

printingvariations resultin localcoveragethataredistributed aroundC=l. Thus,the factorof0.8 inequation_(4.1)was selectedto_keepvaluesbetween0and 1. Thenthe

values weresubtractedfrom 1.00,multiplied_by255,and roundedto thenearestinteger.

Thisproduced viewablepixelvalues_linearlyrelatedto tonermass. A perfectlywhite

Tonermass_{images, Pc(x,y),were usedonly forillustration}purposes. Actualtonermass

calculations were performed onthe datamatrices C(x,y).

TheCD intheappendix ofthis thesiscontains all oftheillustrationsusedinthis

thesis since printed and copiedillustrationsare not always_easily observed. The readeris

referredto these illustrationsforthebest illustrationoftheexamplesdiscussed inthe

remainderofthis thesis.

4.1 Relative Toner Mass Distribution (Optical Analysis).

Figure 4.1 showsrelative cyantonermassdistribution_{images, Pc(x,y),}forthree

differentinput dotpatterns withthesamenominaldotarea _fraction,Fn=

0.25, sentto the

printer. Theseprintedillustrationsofthetonermassimagesarenot ofhigh_quality, so

thereaderis referredto theCD intheappendix ofthis thesisforclearillustrations.

(I) (!!)

(III)|

|

|

t.m m-m 1

'ik^A^m,M>^ \ & & iH i

Relative Toner Mass=_{0.185 Relative Toner Mass}=_0.191

Relative Toner Mass=_0.257

F=_{0.25 F}=_0.25

Fn=_0.25

Thethreeoriginal dotpatternsineach experiment showninFigure 4.1 were

formedas clusters of_{2x2, 3x3,}and4x4_pixels,where each pixelmapped 1:1 onto printer

addressable units. The printer was a600 dpiHewlett-Packard 4500 color_printer,so each

addressable unitis 1/600_inches,or0.0423 millimeters.

Thetotalrelativetonermass on each printed samplewasfound_bysummingthe

massineachlocationin_{C(x,y),according}toequation4.2.

Relative Toner Mass=

f

fc(x,

k

xy

The constant,k,inthisequationis defined as_follows,

k=jJCso.,d(x,y)dxdy (4.3)

where_Csoiid(x,y)isa sample ofthecyantonerprinted at adotareafractionof1.00. Since

theaverage value of _{Csoii_(x,y)}=

1,thismeansk=

N,whereNisthenumberof pixelsin

theconcentration_map,C(x,y). Inother_{words, the} relativetonermassis_simplythemean

value ofthematrixC(x,y).

Theidealprinter should printarelativetonermass of0.25 foreachdotpatternin

lessthan theidealamount oftoner. _Thus,it isclearthattheamount of cyantoner that the

printer_{deposits depends}ontheinput halftonepattern. Inthisexample, the_efficiencyof

toner_deliveryto the paperdeclines asthesize oftheclustereddot declines. Thisis

consistent withthe_earlyvisual observationsdescribedintheintroductionto this thesis.

Anotherobservation we canmakefrom figure 4.1 isthatsometonermassappears

tobe deposited_bytheprinterinbetweenthedots. Therefore, ascanline analysisoftoner

massdistributionwascarriedoutasillustrated in Figure 4.2. The scanlinewas

performed_byaveragingtherelativetonercoverage,C, inthey-directionfor everyx

position. _Bylookingat point_(A)in figure_4.2, itappearsthat thereissometonermass

deposited in betweenthedots. Thiswas a_surprisingresult. Itwas expectedthatthere

wouldn'tbe anytonermassdeposited_bytheprinterbetweenthe_{dots especially}for

_>

b ST

s-_>

>

<

mm me

t

i

_&___i_l_--ie-i a n _t

^^^^^^^^^^P ^r IW *_F 1^

ii * * * *

M'iuik.

20 40 60

Pixel Position

Figure 4.2: Scan Line ofCyan Toner Mass Distribution Image

Itwashypothesizedthatthenon-zerovalue at point_(A)in Figure 4.2 mightbean

experimental artifact. A stray light_artifact,for_example,might resultinan apparent non

zero valuefortonerbetweenthedots. _However,as illustratedintheprevious_section, a

stray lightartifactdoesnot seemtobea problem withtheinstrument.

Itwasalsohypothesizedthatsomekindof multiple reflection processbetweenthe

paper andthetonermightintroducean optical artifact ofsomekindand cause an errorin

theanalysisoftoner mass. _Thus, aneffortwasmadetoreproduce such an effectinorder

tosee ifafalse_readingmightbe inducedto showtonermassbetweenthedotsas seenin

4.2 Test ofthe _{Multiple Reflection} Hypothesis

Considertwocases in figure_4.3,where inone case wehave_onlypaper andinthe

other case wehavepaper with sometonerdepositedonit. Figure 4.3-1shows some

possible lightpaths_{for scattering light}through thepaper. The lightcantravel_laterally

while_making its_waythrough thepaper. For_example, infigure_4.3-1, light AandB

travel _laterally forgreaterlateral distancesinpapercompareto thelightC. Now,ifthere

issome amount oftonerprinted on_topofthepaperas showninfigure4. 3_-II,multiple

reflectance oflightmightoccurbetweentonerand paper. Forexample, asshown in

figure_4.3-II, lightAandBmightbe reflectedback intothepaper_bythetoner. Onthe

other_hand, light Ctravelsonthesamelightpathin bothcases. Lightreflectedbackinto

thepaperhasanother_opportunitytoscatterto thebackofthepaper andbelost. _Thus,

reflectance atthepaper/tonerinterfacemightbeexpectedtodecreasethetotalamount of

lightthatgetsthrough the sample. Thiswouldresult,intheopticaltonermass_analysis,

inan over-estimate ofthe totaltonerintheimage. Thiscouldrationalizetheobserved

(I)

_i

Air

1

1

A

>

Paper Paper

Figure4.3: MultipleReflectance _{ofLight between Toner}andPaper

Anexperiment wasdesignedtotestwhether multiplereflectance oflight between

toner and paperintransmittancemode could explainthisobservation. Aphotographic

transparency filmwithprintedlinesatvarious different line frequencies (0-10

cycles/mm)wasusedfor simulatingtonermaterial. Figure 4.4showstheinstrumental

design for_testingthe interaction betweentonerand paper. _First,thefilmanda piece of

paper were placed incontactas showninfigure4.4-1. Thisconfiguration was intendedto

simulate printedtoneron paper with a maximum likelihoodof multiple reflectionsthat

couldreturnlight intothepaper. Thesecond_{configuration,} showninfigure_4.4-II, is

identical to thefirstexceptthat thepaperis3 cmbelowthefilmimage. In_{this case,} no

(I) (II)

CCD Camera

^^Film

if' _{PlainPaper 4}

CCD Camera Film

_] Film

3cm

3 _{Plain Paper}

V

-7LightSource CVLight Source

Figure 4.4: Multiple Reflectance ofLight between TonerandPaper Configuration

Thecapturedtransmittanceimages in bothcases wereflat-fieldedagainstthe

imagescaptured withthefilmremoved. Thetransmittanceofinkandpaperwere

calculated_bydoing histogramanalysis. Figure 4.5 showsthe_relationship of

transmittanceofinkandpaperbetweenthetwo cases. Thetransmittancevalues_vary

significantlyacrossthefilm becauseofvariations inthefilmandbecause of variationsin

theinkthickness. _However,whenthetransmittance values are compared point-by-point

onthefilmforthe twoexperimentalconfigurations, thelinear relationshipofFigure 4.5

is _clearlyevident. _Therefore,these datawereunableto _{detect any} significantdifference

that couldberelatedtodifferentamountsofmultiple reflectancebetweenthepaper and

theinklayeronthepaper. Althoughtheabsenceof proofisnotthesame as a proof of

contributeto theexperimentalobservations. _Thus,itappearsthatthe tonermass

measured_{in Figure4.2at point (A)isanactualindication}oftonermassbetweenthedots.

-a ts S3 CL

0)

8-Oh

_-,

Transmittance

ofInkon.Paper

Transmittance of

Paper

0.1 0.2

Film & Paper in Contact

Figure 4.5: Multiple Reflectances ofLight Between InkandPaperResult

4.3 Histogram AnalysisofTonerMass Distribution.

Figure4.6 showsseveralcyantonermassdistribution_{images, Pc(x,y),}andtheir

corresponding coveragehistogramsfromthecoverage_matrix, C(x,y). Theimageswere

printed_usingaclustereddot halftonewith a6x6halftone cell. Thethreesamples were

printedatnominaldotareafractions ofFn=

0.3, 0.5, and0.7. Thesamples were printed

using aHewlett Packard 4500 Color Laser Jetprinter. Froma visual inspectionofthe

coverage _images,thereis nodoubtthat the totalamount oftoneris_verymuchlarger in

increaseas_{the total tonerconcentrationincreases. However,theareasinthese three}

histogramsare _{approximately}thesame. This apparentparadoxis_easily explained_by

considering inmore detailthe_meaningofthecoveragehistogram.

/|\ **_.*i_t,**<

.tf*a*jt*4#<NH

N *1? #**##*!

It#**####<*?.

r###**# _MM

(II) >++*+***++? 4* an) |.. if l.|f.i _a._-S__-_-*U_A*___*_ o s 1 1

Fn=_0.3

Paper

w Toner

^1 -_ i

u

Z 0.02

c

l i

Fn=_0.5

a

a"

u Paper Toner

0 0.5 1 1

Relative MassConcentration,c

0 0.5 1

Relative MassConcentration,c Relative MassConcentration,c

Figure 4.6: Cyan Toner Mass Distributionwith_{Fn=0.3, Fn=0.5,} andFn=0. 7

4.3.1 Interpretation ofCoverage Histograms

Considertwoideal tonermassdistributionsas shownin figure 4.7. Thefirst_case,

figure_4.7-1,consists of three tonermass_piles,eachwithapileheightof x. Thesepiles

aredistributedon_topof atransparentlayerthatdoesnot absorb_anylight. The second

case,Figure4.7-II, consists ofthesame amountoftoner. _However,the toneris stacked

toadepthof3xina singlepile. The histograms forthese twocases areillustrated in

Thus,thehistogrampeak atthelowtonercoveragehasa relative areaof3. However,the

histogram forthe second case showspeakofheight 1 since_onlyone "pixel"iscovered.

Thelocationofthepeak showsthatitrepresents acoveragethatisthreetimesasmuchas

thefirsthistogram.

(I)

Toner_? f~n

| | ' "| x

Transparent Layer

(U)

It

H 3x

Toner _{? |||\}

/ Transparent Layer o [--, L 1 o G 0.2 Relative Concentration

r. , -6

Relative

Concentration

Figure 4. 7: Histogram_{Analysis of}theIdeal TonerMass Distribution

The histogramfunction, H(C), is a_{probability density}function fortoner_coverage,

C. Inordertofindtheaverage coverageof_{the sample, ^coverage, the}firstmoment ofthe

probability densityfunctionmustbecalculated,as showninequation(4.4).

ltcoverage = JH(C)-CdC

For example,in Figure_4.7,theproduct oftheheighttimesthecoverageis 0.6 inboth

casesillustrated. Thismeansthe totalamount oftonerintheexperimentalfieldof view

forthe twocases isthesame. _Onlythedistributionis different. Nevertheless, theareas

underthehistogramsare quitedifferent.

Figure4.8 shows anidealclustereddot halftoneandtheidealcoveragehistogram

fortheimage at adotareafractionof_Fn=

0.5. Distributionof_toner,coupled with

experimental_variability,will resultin histogrampeaksthatare muchbroaderthan the

ideal. _{Moreover,blurring}ofthe tonerimage_by variousspreadfunctionsinthe_printing

process will spreadthe tonerout, resulting intonerbetweenthedotsanda shiftofthe

histogrampeakfromzero coveragetosome valuesgreaterthanzero.

Cluster Dot Fn=

0.5

(6x6 Halftone _Cell)

0.5

Paper Toner

0 0.5 1

Relative Mass Concentration

4.3.2 _InterpretingtheHistogramsin Figure 4.6

Alltheeffectsdescribedaboveare _clearlyevidentintheexperimental histograms

of_{Figure 4.6. In particular, thepeak}

representingthepaperbetweenthedots_clearly

showsthata small amount oftonerhasbeendepositedbetweenthedots. _Thus, thepeak

labeled "paper"

inthehistogram for_Fn=

0.3 is located slightlyabove zero. Asthe

nominaldot fraction_increases,thepeaksfor bothtonerand"paper" shift _{significantly}

towardhighercoverage. Theterm"paper" nowdoesnotmean paperthatis_completely

withouttoner. Thereisno area ofthesample withouttoner. Thebi-modaldistribution

that _visuallylooks like dotsandpaperbetweenthedots_{is really}twodistinctcoverage

populations oftoner.

Noticethat the coveragehistogramof sampleIinfigure4.6 hasthetonerpeak

value at_{approximately 0.7,}whereasthe tonermasshistogram ofsample IIIhas atoner

peakvalueat_{approximately 1}.2. Itis becausetheopticalanalysis was calibrated with

respecttoa cyan sampleprinted at 1 00 %nominaldotarea_fraction,anditwas assigned

tohave arelativecyan massconcentration ofone. Itisevidentthat theheightoftoner

pile at adifferentnominaldot areafractioncanbe quitedifferent from 1.00. The

distributionoftonercanleadtopileheights insome areasthatare muchlargerthan1.00

and somethat are much shorter.

A significant observationfromtheexperimental resultsin figure 4.6 isthat the

peak_{corresponding}topaperbetweenthedots shiftsfromzero at_Fn=

0tohigher

observedisthat there couldbean optical artifactintheanalysis. However,asdiscussed

previously,the instrumentdoesnot sufferfrom_straylight_problems, andthereisno

evidence fora significant contributionfrom internalreflectionsbetweenthe tonerandthe

paper. _Thus,theobservedincreaseoftonermass onthepaperbetweenthedotsappears

tobea real phenomenon and notanexperimental artifact.

4.4 Toner Mass Versus Nominal Dot Area Fraction

Alargenumber ofsamplesof cyantonerwereprintedatdifferent dotarea

fractions_usingthe 6x6clusteredhalftoneillustrated in Figure 4.6. The opticalanalytical

techniquewas usedtodeterminetheaveragetonercoverage, u.Coverage, foreachsample at

eachnominaldotareafraction,Fn. Figure4.9showstheresults. The dotted linewas

sketched ontothegraphtohighlighttheapparent shape ofthe_{relationship between}the

delivered tonermass and_{the signal, Fn,} sentto theprinter. Thepointat_Fn= ₁

isthe

reference point. That_is, therelativetonermassis 1.00bydefinitionatF

= ₁

. This

clearlyshowsthat the total tonermassdelivered forFn=

0.95 is _{significantly}greaterthan

themassdelivered at_Fn= ₁

0.2 0.4 0.6 0.8 1

Nominal Dot AreaFraction,Fn

Figure 4.9: Relative Cyan Toner Mass Coverage Measured

OpticallyversusDot AreaFraction, Fn. (HP Laserjet₄₅₀₀₎

4.5

Summary

Theoptical analysisoftonermassdistributionhas been demonstratedtobea

reliable experimentaltechniquefortheanalysisoftonermass. Itis _{significantly}more

precisethangravimetric _analysis,anditcanberesolved_spatiallytoshowthe

micro-distributionofthe tonermass.

Close examinationofthedatadescribedabove suggeststhree significant

observations. First,thehalftonepatternsentto theprinteris blurred_duringthe_printing

process. This is_certainly notsurprising. _However, thesignificance ofthisobservation is

that the_printingprocessinvolves apoint spreadfunction (atleast_one)thatisa point

spreadfunctionintermsof_{toner mass,} PSFm(x,y). Printersare often modeled with

printerMTF orPSF functions,buttheseare_generallyexpressedintermsofthereflected

non-linearityof printers. _Thus, intheprintermodel described_below, aPSFinter