Optimizing tone production on a 300 spot per inch laser printer

Theses

Thesis/Dissertation Collections

1-1-1988

Optimizing tone production on a 300 spot per inch

laser printer

James R. Hamilton

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Recommended Citation

by

James R. Hamilton

Athesissubmittedinpartialfulfillmentofthe

requirements forthedegreeofMasterofScience inthe

Schoolof

Printing

andManagementSciences intheCollegeofGraphic Arts and

Photography

oftheRochesterInstituteof

Technology

January,

1988

School of Printing and Management Sciences

Rochester Institute of Technology

Rochester, New York

CERTIFICATE OF APPROVAL

MASTER'S lHESIS

This is to certify that the Master's Thesis of

James

R.

Hamilton

With a major in Printing Technology

has been approved by the Thesis Committee as

satisfactory for the thesis requirement for the

Master of Science

degree

at the convocation of

January, 1988

Thesis Committee:

Frank Cost

--~~---')=Th::re-s"""'is-A"""""-:-dv--;i"-so-r---Joseph

L. Noga

Graduate

Pro~am Coor~ator

Miles Southworth

OPTIMIZING TONE PRODUCTION

ON A 300 DOT PER INCH LASER PRINTER

I, James R. Hamilton, hereby grant permission to the Wallace Memorial Library, of

R.I.T, to reproduce my thesis in whole or in part. Any reproduction will not be for

commercial use or profit.

Iwouldliketo thank the

following

people:

Prof. Frank

Cost,

whoseinsightandinterest inspiredthisproject

Dr.JosephDeLorenzoandProf. Michael Kleper for

lending

theirexpertisetothis

undertaking

RochesterInstituteof

Technology

professorsJoseph

Brown,

Robert

Chung,

Marie

Freckleton,

C.R.Meyers,

Joseph

Noga,

Michael

Peres,

Bob TompkinsaswellasDavid CohnoftheT&ECenterwho allhelpedinnumerous stages oftheproject

Mark

Curby

andIshmael J. Stevanov-WagneroftheEaton

Peabody

Laboratory

for

answerstotechnicalquestions about_{laser printing}

Betty

GreenawaltandPamelaOriansofBoise

Cascade,

andJohnGorskiand

Judy

Palucki

ofHammermill_{for arranging}paperdonations

Lisa DigginsofData

Recording

Systemsfor providingtranscriptsofDavidSpencer'stalks

Greg

Haddam,

whose_{understanding}ofthe_{Macintosh greatly}aidedthisproject

List ofTables v

ListofFigures vi

Abstract 1

ChapterOne 1

Introduction 1

Footnotes forChapter One 6

Chapter Two 7

Theoretical Basis 7

TheLaser Printer 8

PostScript 9

Footnotes for ChapterTwo 10

Chapter Three 11

Review oftheLiterature 11

Footnotes forChapter Three 13

ChapterFour 14

Hypothesis 14

ChapterFive 16

Methodology

16

TheDevelopmentoftheTests 16

Density

Measurements 21

Testing

oftheDensitometer 21

Testing

oftheLaser Printer 22

Comparing

theStandard Deviations 23

Microscopic Studies 23

Footnotes for ChapterFive 24

Chapter Six 25

Results 25

Tone Production 25

Microscopic Studies 26

PaperTests 29

Maximum

Density

Tests 29

Gray

Production Tests 30

PaperTests 33

Chapter 8 50

Discussion 50

ToneProduction 50

MicroscopicStudies 52

PaperTests 53

Maximum

Density

53

Gray

Production 54

Chapter 9 56

Summary

56

Conclusions 56

Recommendations for Further

Study

57

EquipmentUse 57

Bibliography

59

Appendices 62

A Tone Production Data 63

Condensed 63

Diamond 67

Open 70

B

-Paper Tests 74

Density

-Part One 75

Maximum

Density

- Part Two

. . . . 76

Gray

Production 77

Grading

Grays 78

C

-Consistency

Tests 79

LaserWriter 80

Densitometer 83

D- Bartleson_andBreneman 84

E- Spot Sequence 88

Condensed Dot Form Sequence 89

Diamond Dot Form Sequence 90

Open Dot Form Sequence 91

F - Sample Output- 3x3 Condensed 92

3x3 Condensed 93

Pagenumber

Table 1 - Matrix

size,number of grays possible andlinescreenat300spotsperinch. ..11

Table 2

-Summary

of spots _{in matrix, gray}

level, linescreen,

and screen angle 20

Table 3 - Comparison

oftestsquareswith 50% spots on 26

Table 4 Dot size measurements 27

Table5

-Testing

the _accuracy ofthemicroscopic measurements 28

Table 6 Results ofthe firstpapertest 29

Table 7

-Results ofthe second papertest 29

Table 8 - Results

ofthethirdpapertest 30

Table 9 - Overview

of paper characteristics 31

Table 10

-50%spots onwithinformation concerning areabetweenspots 51

Table 1 1

Pagenumber Figure 1 - 3x3

matrix of squares 3

Figure 2 - Grays

possibleversus linescreen at300 spots perinch 11 Figure 3-

Comparison

of4x4open and condensed matriceswith eight spots on 14 Figure 4 - 3x3

open matrix 18

Figure 5 - 3x3

condensed matrix 18

Figure 6 - 13

spotdiamond matrix ₁₉

Figure 7 - Spot

sequence in 13 spotdiamond matrix 20

Figure 8 - Irregular

nature ofthe dot 27

Figure 9

Illustrating

dotsize ₂₈

Figure 10 Graph of

2x2, 3x3, 4x4,

and 6x6open matrices 35 Figure 1 1 - Graph_of

2x2, 3x3, 4x4,

and 6x6condensed matrices 36 Figure 12 - Graph

of

5,

8, 12,

and24 diamondmatrices 37

Figure 13 - Graph _{of matrices}

containing 25 spots 38

Figure 14- Graph_{of open and condensed} 8x8_matrices (with_column

breaks)

39

Figure 15 Graphofidealtonal scale versus 8x8condensed matrix 40 Figure 16 - Microphoto_ofparallel lines _atfinest_resolution 41

Figure 17 Microphoto of1/25 5x5 open matrix 42

Figure 18 - Microphoto _of6/25 5x5 _{open matrix}

43

Figure 19

-Microphotoof 12/25 5x5 openmatrix 44

Figure 20 - Microphoto_of 13/25 5x5 _openmatrix 45

Figure 21 Microphotoof 18/25 5x5 open matrix ₄₆

Figure 22 - Microphoto_of24/25 5x5 openmatrix 47

Figure23 - Microphoto_of 12/25 5x5 condensed matri 48

Figure 24 - Microphotoof 12/25 25 diamond matrix 49

Digitalhalftonesas output on plain paper arethefocusofthisstudy. Anew

terminology

issuggestedtoallow properdescriptionofdigital halftones. Themost importantofthese termsistheuse of

"addressability"

toreplacetheoften misusedterm "resolution."

Also important istheuseoftheterm"spot" ratherthan"dot" todescribe addressability. Ameans of_properly

describing

digitalhalftonesissuggestedtoavoid confusion with_analog

(ie.,

conventional_{photographic)}halftones.

Halftonepatterns were createdto test the_efficiencyofdifferent designsat300spot perinch addressabilityon alaserprinter.Thepagedescription language PostScriptwas usedtocreatethehalftonepatternswhichweremodeled onthreebasic designs.

Ithasbeenestablishedthat twohalftone dotpatternsconstructed onthesamematrix and_containingthesame number of spots will producedifferent densities ifthe

configuration ofthespotswithinthematrixisdifferent This has beentested

by

_comparing theresults ofthe toneproductioncurves ofthecondensedand openhalftone dot designs. Thesepatterns were output on alaserprinterand measuredfor density. Toneproduction curves weredrawnand compared.Eventhougheachmatrix containsthesame numberof spots,it hasbeenshownthatdifferent densitiesresult.This is solelya consequence ofthe dotdesign.

Microscopicstudies wereconductedtoillustratethenature ofthefilling-in inthe non-image area.Microscopicmeasurements werealso madetoascertainthesize of an individualspotatvarious screen rulings. Itwasfoundthat thespot,whichwas_very irregulartobeginwith,actually begantobreak upasthelinescreenapproached150 lines perinch.

Papertestswere runtogaugethemaximum

density

andthe toneproduction capabilities ofvarious papers.Although theresults were

inconclusive,

they

point out anotherflawofdigital halftoneswhichareoutputon plain paper.Thenumber of grays predictable,givenamatrixsize,isgreaterthanwhatisachievableinpractice.

INTRODUCTION

Theideaof_combiningtextandillustrationswithout

having

tocut and pasteisa conceptthathas intriguedtheauthor sincehis daysas a mechanical artist.

However,

tobe

abletoachievethis goal,both digitaltypeandhalftonesare necessary.Inaddition,a "type-"

or"image-"setterisrequiredthatcan receive and createbothtypesof output

Devicesandtechniqueshave been developedthatcan now achievethesegoals, and what's

more,since

they

output onplain_paper,

they

_mayevenleadto theelimination offilmas a

step intheproduction process.This study investigates digital halftonesandthe_waythese

halftones are output onplainpaper. Suggestionsare madetooptimizethedesignanduse

ofdigital halftones.

Consistency

interminology isstrivedforthroughoutthisproject Someoftheterms

thatare used_repeatedlyare:

addressability

-the

frequency

withwhichthelasermarks thephotoconductive surface

dot- the_{one or more spots}usedtoformthebasicunit of ahalftonepattern

halftone

-atechniqueusedtosimulate continuoustoneimages ina processthatcan

onlyprint or not print at all

latent image- _animagethatis

present,butnot yet visible

(ie.,

beforeapplicationof

toner)

linescreen- _alsoknown_aslineruling; themeasure ofthedistance between halftone

dots inahalftone

linesperinch- theterm_usedtodescribethelinescreenof ahalftone

matrix- _a

groupingof spots

photoconductivity- the

propertyof_{conductingelectricity}uponexposuretolight

orsharpness

spot

-thesmallest mark alaserprinter can make on paper spots perinch- theterm

usedto_{describe addressability}

Toconduct adiscussionoftheissuesinthis_{thesis, it is}oftheutmostimportanceto

maintain_consistencyinterminology. Thereare a number of_{misleading terms which,}

poorly

defined,

haveresultedinmuch confusion.Oneofthemostimportantoftheseterms

is"resolution."

Resolutionisoften

incorrectly

describedintermsofthenumber of marks that thelasercan makein creatinganinchoflatent image. Thislatent

image, however,

is subsequentlytonedandtransferredtopaper, and_{any degradation}oftheimagethatoccurs

inthis processisunaccountedfor. Sincethisdegradationtends tobemuchlargerthanina

photographic_process,itmakestheuseofthe term"resolution" quite misleading. Ifa number valueistobeassigned,the term"addressability" ismore accurate.

Addressability

isthe_capabilityofthelasertomark alatent imageonthephotoconductive surface.This canbedescribedmore_{accurately numerically}thanresolution sincethereisnodegradation

oftheimagetoaccountfor.

Keep

inmindthat_{addressability describes}thelatentimage

whereas resolutiondescribestheimageonpaper.

Unfortunately,

"resolution" isthe term thatismost_commonly usedtodescribethe

imaging

_capabilityof aprinter, andit isoften

described intermsof "dotsper

inch",

another_confusingterm.Printersare accustomedto

theterm"linesperinch" todescribehalftonescreens.

However,

300"dotsperinch" and

300"linesperinch"donotmeanthesamething.Inhalftones a300lineperinch linescreen wouldbeof extremefineness. 300 dotsperinchontheother

hand,

producesimagesthat

are_relativelycrude

(keep

inmindthat72dotsperinchis dotmatrix printer_qualitywhile

1000dotsperinch isthe

beginning

oftypeset_quality.) Theword"dot" alsoisassociated withhalftonescreens,as in "halftone

dot."

Thepotentialforconfusionis

limidess,

and

solelya result of

faulty

terminology.

Tounderstandthisproblemitis_necessary tohavea general_{understanding}ofthe nature ofhalftones.

They

existtoproduceanillusionofgrayness ina processthatcan_only printblackornot print at all.Halftonescanbe describedas

being

_analogordigital. In

using theterm

"analog

halftone"

the dots inch. Confused?Youhavea reasontobeconfused sincetheword "dot"

hastwomeanings withinthelastsentence.First it isusedas"halftonedot" which

may vary insize,andthenit isused as"dot" in dotsperinchwhereitmeanstheminimum markablespot_{(a constant)}inalaser_printingsystem.

Toalleviate some oftheconfusionbetween digitaland_analog

halftones,

itwillbe

necessarytorevise some commonly-used vocabulary. Theterm"addressability" shouldbe

usedwhen_numerically

describing

thecapabilities of a plainpaperprinter.

"Addressability"

and"resolution"which are_{virtually identical in}referencetophotographic processes arein

factquitedifferentwhen usedtodescribeplain paper processes.

Furthermore,

"spotsper inch,"

not"dotsperinch," shouldbethe termusedfor

describing

addressability.Theword "dot"

simply hastoo_manyother connotations."Spotsperinch" willbethe termusedto

describe addressability fortherest ofthisstudy. "Linesperinch" shouldbeused_{solely for}

describing

halftones.

Analog

halftonesare_{adequately described}

by

thetermlinesper

inch;

however,

digital halftonesrequirefurtherexplanation.

Abasic descriptionofadigital halftonewill

help

illustratethepointFigure 1

illustratesa3x3matrixof squares:

X

m

X

X

X

X

X

X

X

Figure 1 - 3x3_{matrixof squares}

Using

this tobuildadigital

halftone,

black,

whiteand eight shades ofgraycanbe

shades of_graythantheexample above. In

fact

it'slaughableto

try

and comparethem. Yet ifthedigital screenisdescribed as a100 linescreen,theimmediateassumptionisthatit is

equivalenttoa100line_analoghalftone.

Therefore,

to_adequatelydescribeadigital

halftone,

itis_necessarytostate not_onlythelinescreenbutalsothe_{addressability}ofthe

outputdevice.

So,

where 100 lines perinch

justly

describesan_analog

halftone,

100lines perinchat300spots perinchwould

justly

describeadigital halftone.

This brings_upanother point.Oneofthecharacteristicsthatcanmake_analog

halftonessuperiortodigitalhalftones isthat

they

are outputonphotographicpaper_which,

ofcourse,hasgreat_sensitivityto_verysubtiedifferences. Whenphotographicpaperis

usedtocapturedigital

halftones,

much moredetailcanbe heldthanifthesamehalftone were outputon plainpaper.Thus ifadigital halftonewereoutput onbothplainand photographic_paper,much moredetailwouldbe heldonthephotographic paper. This seems quite obvious.Butitisalsotrue thataslaserprinters gainhigherandhigher addressabilities(intermsofspotsper

inch),

themain

limiting

factorwillbethepaper,not thenumberof spots perinch.

Theuse ofdigitalhalftones is goingto

increase,

and as a_result,the"look"of

halftoneswillchange.Digitalhalftonesthatarecreatedforoutput ondotmatrix orlaser

printers_alreadystart out at a markeddisadvantageto_{analog halftones:}

they

_{simply fall far} short ofphotographic resolution.Even digitalhalftonesthatare output onlasertypesetters havelowerresolutionas comparedto_{analog halftones.}There is a simple explanationfor

this: thesmallestmarkalaserphototypesettercan createislimited

by

thesizeofthelaser

spotwhile,on theother

hand,

lighton photographicfilmorpaperis limited only

by

the grainsize ofsilverhalidewhichismuchsmallerthan laserspot size(silverhalidecrystals

rangefrom0.05 to2

microns1

whilelaserspot size at300spots perinchis around85

microns.2)Thereisanother complication: thesmallerthelaserspotsize, thelargerthe amount ofinformationtobeencoded,and, thelargerthe amount of

information,

thelarger thecost andtimeinvolved. Forexample, at300spotsper

inch,

90,000

(300x300)

bitsof informationareneededtoencodea squareinchofimage. At 1000spotsper

inch,

1,000,000

(1000x1000)

bits arerequired. Thusthereis atradeoffbetweencost and

addition, there for using digital halftones.

Among

advantages are ease of_{data transmission,}electronic storage of

images,

and electronicdata manipulation.

Itshouldbestressedthatalloftheexperimentationinthis _studywasdoneona

singleAppleLaserWriter. The limitedscope oftheexperimentswillgive someinsight into

thestrengths and weaknesses oflaserprinting;

however,

these tests are notintendedtobe

usedtodrawconclusions about the capabilities of_anymanufacturer'sproduct.Thereis

simplynotenoughdatatosupportthose sorts of claims.Thisisalsotrueofthetestsonthe

X-Rite densitometerandtheHammermillandBoise Cascadepapers. Thesetestshave been

JMcGraw

Hill EncyclopediaofScienceandTechnology. 6thed.S. v.

"Photography,"

by

Vivian K. WalworthandRobert D.

Anwyl,

p.405.

2Author's

calculation:

1/300"

THEORETICAL BASIS

In 1937Chester Carlson inventedthefirstelectrostatic process (latercalled xerography.)1

Thiswas thebirthof part of the

technology

forthelaserprinter.Patents

wereissuedin 1942and

1944,

and

by

1950Xeroxhadthefirstcommercial copieronthe market.The Xerox 914office copier was introducedin

1960,

and since_then,electrostatic copiershavebecomeanintegralpart ofAmericanbusiness life. Inthelate

1950's,

Dr. CharlesTownesandDr. Arthur Schawlow laidthefoundations fortheconstructionforthe

firstlaser.2

The first_{working laser}was constructed

by

Dr. Therodore Maiman in I960.3 The laserhas broadenedtheapplication ofthecopier.The devicecan nowbeusedas an

imagesetter/typesetter. Aprime exampleofthisistheApple LaserWriter.The LaserWriter ismorethanalaser_printer;it isa_{computing device}with 1.5megabytes ofrandomaccess memory.Ithasbeen describedasthemostpowerfulcomputerthatApplemakes.4

And

yeteven withthatamount of_memorytheLaserWriteris limitedtoan_{addressability}of300

spots perinch. This makesitan excellent choicefor business applications,butsubstandard

forthegraphicarts (where 1000spotsperinchis _{arguablythe standard.)}Larger

addressabilityrequires morememory,butthishasnot preventedtherecentintroductionof 400and600spot perinchprinters.Ofcourse,laserphototypesettershave beenused with

great success ataddressabilities of muchhigherthan300spotsperinch

but,

forthemost part,thesesystems usephotographicpaper.5Companiesare anxioustoperfect a plain

papersystemdueto thehighexpense ofphotographicpaper.

Oneofthemost

interesting

developmentshas beenthatofthepagedescription

language PostScript.

Previously,

each

typesetting

manufacturerhaditsown_coding

language fortheirmachinery.Acomputerfile forone manufacturer'stypesetterwouldbe

useless onanother's.

However,

through theuse of

PostScript,

a single computerfilecan berun on anumberofdifferentoutputdevices attheresolutionofthatoutputdevice. This

is what

is

knownas deviceindependence.

PostScript,

thoughnottheonlypagedescription

Sincethelaserprinter and pagedescription languageare ofimportancetothis

project,

they

willbe discussedinthe

following

sections.

The Laser Printer

Tounderstand whatthelaserprinterdoestoproduce an

image,

_{it is necessary}to

havean_{understanding}oftheelectrostatic process.Inthis

discussion,

theelectrostatic

process(ormore_{specifically,}transfer_xerography)willbe describedas atoner-based

system.Theelectrostatic_process,as usedinconventional_{photocopiers,}is_relatively

simple.Adrumor

belt,

often constructed of_selenium,is charged.This surfaceisa

photoconductor whichloses itscharge when exposedto_{light. When oppositely}charged

tonerparticles arebroughtincontact withthesurfaceofthe

drum,

they

adhereto the

charged areas

(ie.,

theareasthathavenotbeenstruck

by

light.)

Inthenext_step,a pieceof

paperisbrought incontactwiththedrumatthesametimethata chargeisappliedto the

backside ofthe_{paper,removing}thetonerfromthedrumand_passingitto thepaper. The

toneristhenfusedto thepaper,_completingtheprocess.7

Considerfora moment a conventional copier.Toobtain acopy,light isreflectedoff

theimagethatis

being

reproduced.Where light fromthenon-image area reflects ontothe

surface ofthe

drum,

thechargewillbe

lost,

andthereforenotonerwillbeattracted.The

reverseistrueintheimagearea;nolightreflectsfromtheblackoftheimageandtherefore

thedrumstays charged and attractstoner.Inalaserprinter,whereyouare not_working

fromreflectioncopy,thelasercanbeused eithertoerasethenon-image areainthe_way

thatlight does in theconventionalcopier,oritcanbeusedtocreate animagearea.Ifthe

laseris usedtoerasethenon-imageareaitisknownas_{whitewriting;}if itcreatestheimage

areait isknownasblackwriting.The

image-creating

part of alaserprinteriscalledthe

"engine."

The CanonengineintheApple LaserWriterusedforthisexperimentis

blackwriting.8

The laser inalaserprinteriscontrolled

by

a polygon-shaped mirrorthat

aimsthelaser beamatthedrum.Thepathofthebeamishorizontalacrossthedrum

surface.The drum in theLaserWriterischargedandthechargesdissipatewhenstruck

by

thelaser. It becomesclearatthispointthatiftoneristhenattractedto thecharged_areas, a

negativeimagewillresult

However,

sincethetonerhas thesame charge asthecharged

areas ofthe

drum,

tonerwill_onlygotonon-chargedareas

(ie.,

wherethe_{laser has struck.)}

Thusthe tonersystemsare quitedifferent betweenblack- and whitewriters.

creating finehalftonea similar problem arises.The halftone

dotscreateslittleislandsoflike-chargethatbegintoaffect each other asthelinescreen

increases.

PostScript

In

1982,

ChuckGeschkeandJohn WarnockformedAdobe

Systems,

Inc. Their product

PostScript

isdescribedas "a_{programming language designed}to_convey a descriptionof_{virtually any}desiredpagetoaprinter."9

PostScript's syntax resembles the

programminglanguage

Forth,

butthereare also similaritiestoLisp10. The PostScript imageoperator was used_{exclusively for}thisproject Adescriptionofhow itwasusedis

containedinthe

Methodology

section,page 16. Forthepurposes ofthisproject,

FOOTNOTES

FOR_{CHAPTER TWO}

-J.J.RheinfrankandL.E.

Walkup,

"Current Status ofElectrostaticReproduction Processes,"

1961 TAGA Proceedings.TechnicalAssociationoftheGraphic

Arts,

Rochester,

NewYork: _n.p.,

1961,

p.114.

2Allen

Maurer,

Lasers - Light Wave

oftheFuture. _{NewYork: Arco}

Publishing, Inc.,

1982,

p.2.

-Ibid., p.39.

4Bruce

Blumberg,

"Page Printersfor LowCost ElectronicPublishing,"

The Fourth

National Print

Quality

Seminar.

Newtonville,

Massachusetts:Datek Information

Services,

Inc., 1985,

p.237.

5One

exceptionistheTegraGenesissystemwhichclaims_{addressability}of1012spotsper

horizontal inchon plain_paper,Tegrapromotional material.

6"...PostScript

hasnow emerged as'the'pagedescriptionlanguage. Atthemoment,

AdobeSystems isalmostina_monopoly

position."

TheSeyboldReporton

Publishing

Systems."Competitors for AdobeSystems," 16

(May

11,

1987): 49.

Encyclopedia

ofPhysicalScienceandTechnology. 1987ed.S. v."Photographic

Materialsand

Processes,"

by

P.S.

Vincent,

pp.484-494.

8Personal

letterfrom Mark

Curby

andIshmael Stevanov-Wagner.

9Adobe

Systems, Inc.,

PostScript Language Tutorial andCookbook.

Reading,

Mass.:

Addison

Wesley Publishing

Co.

Inc., 1985,

p. 1.

10Adobe

Systems, Inc.,

PostScript LanguageReferenceManual.

Reading,

Mass.:

CHAPTER THREE

REVIEWOFTHE LITERATURE

In an articleinthe

February

16,

1987 Seybold Reporton

Publishing

Systems1,

David R.

Spencer,

chairmanofData

Recording

Systems,

uses a charttoillustratea point

aboutthe tradeoffsbetweenshades of_grayandthefinenessoflinescreens. Theresultsfor 300spots perinchare summarizedin Table 1 and shown _{graphically in Figure 2.}

Table 1 - Matrix

size,number of grays possibleandlinescreenat300spotsperinch

MatrixSize 2x2 3x3 4x4 5x5 6x6 8x8 10x10

GraysPossible* _{5 10 17 26 37 65 101}

Linescreen 150 100 75 60 50 37.5 30

?this isatheoreticalcalculationof_grays,

including

blackandwhite

Grays

100-75

-50

-25

-Grays

Possible

vs. Linescreen

at 300 spi

I

90

T

T

n

r

30 60 90 120 150

Linescreen in lines perinch

Figure2showsthat thelargerthenumber of grays_{producible, the}fewerthelines in

thelinescreen. Spencergoes onto_saythatat300spots per

inch,

therejust isnota

satisfying tradeoff; hiscutoffis thepoint at which64shades of_grayare_achievable, and thelinescreenis atleast65linesperinch.In

fact,

thiscombination offactors isnot possible untilthe_{addressability}reaches600spots perinch. StephenRoth2 ,inthe

May

1987issueofPersonal

Publishing

_magazine,makes a similar statement aboutthenumber

of grays producible. Bothauthors haveassumedthat theseprojections arein facttrue.

Whilethelinescreen informationisaccurate, thenumber of grays achievableis debatable

(refertodiscussionon_grayproductioninthepaper_tests,page

54.)

Itisthis

discrepancy

betweenwhatiscalculable and whathappensin_reality thatprovidedtheimpetus forthis thesis.

A good_{understanding}ofdigital

halftoning

isimportantto thisstudy. Some

referencesthatarehelpfulareJarviset al

(1976),

StoffelandMoreland

(1981),

and

AnastassiouandPennington(1982).Morerecently,GoertzelandThompsonofIBM

(1987),

havewrittenaboutdigital halftonesontheIBM4250printer.David Spencer

(1985, 1987)

andAmnon Goldstein

(1985),

bothofData

Recording Systems, Inc.,

have

bothpublished_{thought-provoking}articlesontheissues

involving

print_qualityoflaser

printers.Dr. William White hasalsowritten

lucidly

ontonersand resolutions(ofparticular

notearethemicrophotographs.)His

book,

Laser Printing: The

Fundamentals,

has good

basic informationonlaserprinters.

For informationon

PostScript,

thebooks

by

Adobe Systems Inc. formedthe

startingpointfor_{the programming}necessarytobuildthetestpatterns.PostScripthas been

thefocusof quite alotofinterestrecently,seeDennis Pelli'scontributionto the

Berkeley

Macintosh Users

Group

Newsletter,

Fall

1986,

pp.35-44.For informationabout

numerouspagedescription languagesseetheApril

14,

1986issueoftheSeybold Report

on

Publishing

Systems.

ForinformationonBartlesonandBreneman'sdarknessvalues, referto their

originalarticle

(1967),

andalsothoseofArcher

(1978)

andR. E. Maurer (1982). In

addition,anunpublishedhandout

by

Prof. Robert

Chung

ofRITwas instrumentalin

FOOTNOTESFORCHAPTER THREE

!David

R.

Spencer,

"OutputTechnologiesandHigh

Resolution,"

The Seybold Reporton

Publishing. 16

(February

16 1987):p.5.

CHAPTERFOUR

HYPOTHESIS

Thehypothesisofthisproject canbestated asfollows:

Twohalftonedotpatterns constructed onthesame matrix and_containingthesamenumber

of spots will producedifferent densitiesiftheconfiguration ofthespotswithinthematrix

is different

Togive an_example, a4x4condensed matrix_containingeight spotswillproduce a

different

density

than a4x4open matrix_containingeight spots (see Figure3).

Open

Condensed

Figure 3 - Comparison_of4x4openand condensedmatriceswitheight spots on

The 4x4open matrix_containingeight spotswillproduceadarker

density

becauseofthe

tendency

oftonertofill inthenon-image area.Whatisofimportance here isthatjudicious

designof matrices canbeusedtocontroltoneproduction.

This hypothesiswillbetested

by

_comparingtheresults of condensed versus open dot forms. Thenature ofnon-square matrices willbetestedwith thediamond dot forms. Theeffect ofpaper ontheseprocesses willalsobetested.

Firstand

foremost,

it istheintentofthisprojecttoshowthatwhatmight appearto beachievablewiththelaserprinterisnot always whathappens inpractice.Theconfusion

between300spotsperinchaddressabilityand300spots perinchresolutionis an example

mathematicallypossible,but

they

havenottested theactual outputItis theauthor'sbelief

thatfewergrays are_actuallypossiblethanSpencerandRothestimate.

Testing

how many

gray levelscanbeproduced wouldbeathesisin

itself,

butitwillbeaddressedinsome

CHAPTER FIVE

METHODOLOGY

Abasic method was usedforallthe

testing

inthisproject.

First

aPostScript file wascreated_that,when output onthelaser_printer,would resultinahalftonetestpattern. Thesetestpatternsweremeasured

by

densitometerandtheresults recorded.Inthis

section, thenature ofthecreation ofthe testswillbe

discussed,

aswellastests toascertain

thevariationinthedensitometerandthelaserprinter.

Finally,

thetechniquesusedforthe

microphotographyand microscopic measurementswillbe discussed.

TheDevelopmentoftheTests

The

feasibility

ofthisprojecthingedonthecreationofthevarioustestpatterns.

Prof. FrankCostsuggestedthat thesepatterns couldbecreated on anApple Macintosh personal computer_usingthepagedescription language PostScript Continuedresearch

revealedthatthe"imageoperator"

described inthePostScript CookbookandTutorial1

alongwiththesoftware programsJustTextandSendPostScriptwould allowthecreation of theprogramsandtheir transferto theLaserWriter.Thecreationoftheindividualpatterns wastime-consuming.

First,

thedotpatternhadtobe broken downintoa series oflaser spotsthatcouldberepeatedtoproducetheactualdot.Thisseriesthenhadtobetranslated

intoahexidecimalformat foruseintheimageoperator.

Finally,

thehexidecimalnumbers wereinputontheMacintoshand proofedontheLaserWritertoensurethat thecorrectdot

pattern was produced.

Aportionofatypicalprogramlooks likethis:

150 650translate 69 69scale

288288 1 [288 0 0288

00]

B6DBB6DBB6DBB6DBB6DBB6DBB6DBB6DBB6DB

B6DBB6DBB6DBB6DBB6DBB6DBB6DBB6DBB6DB

FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

>}image

showpage

Thisprogram would create a3x3matrix with one spot on out of nine.The firstcommand,

"translate",

determineswheretheimagewillbeplaced_usingx and_ycoordinates.The

second_command,

"scale",

determinesthata squareimage 69x69units willbeproduced

(thereare72unitstoan

inch.)

Thenext sevenlinesarethe"image" command.The first

threenumbers ofthefirst line indicatethat theimagewillbe 288x288pixels wide and each

pixel willberepresented

by

onebit Thesix numbersinthesquarebracketsscaletheimage

tofittheunitsquaredescribed inthe"scale" command.2

Thenext sixlinesare a

hexidecimalrepresentation of ahalftone.PostScript hexisthereverse of normalhex so

thatF =0000_where0_{represents non-image area.}The_twolines _ofsolidF's (the F's

repeat72

times)

represent onehorizontalscanline.Thesameistrueofthe twolinesof

B's,

6'sandD's. The lasttworows ofF's completethe thirdrow ofthe3x3 matrix.

Whenthatiscompleted, thecycleisrepeateduntiltheunitsquareis filled.Atthatpoint,

theimageis _actuallycreated_usingthecommand

"showpage."

Appendix

F,

page

93,

containsa sampleofa3x3condenseddottestpattern.Note

thatthe 10squares(oneis

blank)

representtheten_{gray levels. The four}smallblackcorner

squares appearin every testimage.

Using

thiskindofprogram,severaldotshapes were produced.

They

are categorized

underthenames

"condensed", "open",

and"diamond".Thefigures thatfollow illustrate

thedifferences inthevariousdotshapes.Theopendotshapedescribesadotthatis

X

X

X

?x?

X

X

X

X

Figure4- 3x3

open matrix

Thecondenseddotshapedescribesadotthatis builtaround a central spot:

Z

1

Figure5 - 3x3

condensed matrix

Thesquare nature oftheseopenandcondenseddotformsmakesitpossibletostackthem

one on

top

ofanother. Thisallows ascreenangle of zero(therows couldbestaggeredto

createscreenanglesotherthan zero;howeverthiswasnotdone inthis_experiment.)

Screenanglebecomesafactor inthediamondclassofdotshapes sincethesedots

are notformedonasquare matrixanddon'tstack_{up neatly like boxes.}

However,

inthe

sensethat

they

buildonacentralspot,

they

are similartocondensed spots.Figure6

X

EX

*P

KN

X

Hxil^

_*<*

i***

Therelationbetweenspotsinthe_matrix,number of_gray

levels,

and screen angleisshown

inthe tablebelow:

Table2

-Summary

of spots_{in matrix, gray}

levels,

_{linescreenand screen angle}

Condensed/Open

2x2

3x3

4x4

5x5

6x6

8x8

Diamond

5

8

12

13

24

25

?includesblackand white(rememberthatthis iswhatis mathematically_possible)

Thespot patternsdescribed inthe chart above canbe described inavisualshorthand

thatdescribesthe_waythedotis formed:

Grays+

Linesperinch ScreenAngle

5 150 0

10 100 0

17 75 0

26 60 0

37 50 0

65 37.5 0

6 134.2 63.4

9 106.1 45

13 83.2 33.7

14 83.2 56.3

25 60 36.9

26 60 36.9

13

7 8 9

12

6

1 2 10

5 4 3

11

Figure7

For informationonthespot sequence of alldot

forms,

seeAppendix

E,

pages 88-91.

Sincethereare so_manypossible combinations ofdot formations_onlyafewcould

bechosenfortesting.Theseparticular condensed and open patterns were chosento

comparetheaffect oftoner_{spreading into}non-image area.Thediamondpattern was

chosentolookattheeffect of anotherdotform(onewitha non-squarematrixandascreen

angle.)Screenangle couldhavebeenisolatedas afactor

by

_creating screen anglesforthe

openand condensed

dots,

butthiswasnotdone inthisstudy.

Density

Measurements

All

density

measurements were madewithanX-Rite 309reflectiondensitometer.

Calibrationwashandledas specified

by

themanufacturer.Measurementswere madeon a

tablesurface with ablanksheet ofpaper

backing

_upthetest.Threemeasurementswere

made on each l"xl"

testsquare.Themeasurementsequencewithinthesquarewas: upper

right_corner,leftcenterandlowerrightcomer. Thesemeasurementswererecorded

direcdy

onthesheetandlateraveraged.Theseaverages wereusedforanalysis.

Thetestsforthisresearch wererunon an_{Apple LaserWriter. When running}a series

of_tests,

they

were rununinterrupted.Paperforthese testshas beensupplied

by

Boise CascadeandHammermill.

They

have been labeled "A-E".

"A"

representsHammermill

Laser

Copy,

"B"representsHammermillLaser

Print,

"C"

representsHammermill Laser

Plus,

"D"representsBoise CascadeLaserPaperand "E"

representsBoiseCascade Cotton

LaserPaper. Paper"C" waschosentobeusedforalltestswhere paper was notthe

variable.

Twoparametersare ofparticularimportanceinthisstudy.The first isthe_abilityof

the densitometer togivereproducibleresultswithinan acceptable_tolerance,andthesecond

isthe_abilityofthelaserprintertoproducethesamepattern(froma sourcecomputer

file)

within reasonabletolerances. Theresultsforthe

following

sections aretobefound in

Appendix

C,

page79.

Testing

ofthe Densitometer

The X-Rite309manual3

statesthatmeasurementofthecalibrated reference check

inthis_study

by

thehalftonenature ofthetestpatterns andthevariationsthatcanoccur

within a giventestpattern.Measurementswere recordedin

density,

notdotarea. Inan efforttomaintainthe_{highest accuracy}while

keeping

theprocedure

feasible,

three measurementshavebeenmade on eachtestsquare.Totest the_{repeatability}of

measurements madein_{this manner,}an experiment wasconducted.Threetestsquares were chosen andmeasured35timeseach.Thefirstsquarehadan average

density

of.26,the

second squarehadan average

density

of.78,andthe thirdsquarehadanaverage

density

of1.13. The standarddeviationsare asfollows: lightpatch _.006,medium patch .010and

solid patch.018.Whatthisimplies isthat thelowerdensities_{are measured more}

accurately

thanthehigherones.

Testing

oftheLaser Printer

AsingleAppleLaserWriterwasusedforall_tests;

initially

itwastestedfor

consistency. The_consistency test(see Appendix

C,

page

80)

showedtheextentof variationpossiblewithinrepetitions ofthesamefile. This testhad

thirty

solidblack

squares(each

l"xl")

infivecolumns of six squares each.Thissamefilewasprintedthree

timeswiththeresults asfollows.

Density

measurements rangedfrom.88to 1.30 (arange

of.42).Thiswide rangeisaccentuated

by

thevariationsin

density

on a givenpage;

however,

ifa squareiscomparedtoa squareinthesamepositiononthe

following

page

thenthevariations went_onlyas highas.26.

Following

inthismanner ofonly comparing

thesame square ondifferentpages showsthat 100%ofthemeasurementsfallwithin.243

ofthemean. Inotherwords,there isastandarddeviationof.081.

Itwasdiscoveredthat thereisa

tendency

fortheprintertoprintdarkerontheleft handside ofthepage(thisis_clearlyshown

by

theaverages of pages

1-3,

Appendix

C,

page

81.)

The

top

was also_{slighdy darker}thanthebottom. Generalobservations revealed

thatsheets were oftenmarked withtracesofapreviousimage. In_addition,adarkimageon

a single sheet could affectthedarknessachievableinother areas ofthesheet.It became clearthatseveral stepswouldhavetobetakentoadjustforthesevariations.

First,

corner testsquares wereincludedoneachimagesothatageneral comparisoncouldbemade

between _any twotestsheets.

Secondly,

thepositioningofthesquares was reconsidered. Greaterspace wasleft betweentest

images,

fewer imageswereincludedon apage, and

testimageswerekept away fromtheedge areas of pages wherevariationwasgreatest.

Thirdly,

whenanumberoflike-tests weretoberun,a

"sample"

the_ghosting effect of a previousimage.Evenwiththese_adjustments,itwas clearthata

certain amount ofvariationwasinherentintheprocess which could notbeavoided.

Comparing

theStandard Deviations

Itfollowsthata comparison canbemadebetweenthedensitometerandthelaser

printer.Thedensitometermeasured a solidtestsquarein35trialswitha standarddeviation

of.018(mean

density

= 1.13). The LaserWritercreatedthesame solidtestsquare90times

witha standarddeviationof.081 (mean

density

_=1.14.) Althoughit istruethatthe

variationcaused

by density

measurementwillbereflectedinthis .081 standarddeviation

forthe

LaserWriter,

it isstill quite clearthat thevariationintheLaserWriterisof amuch

greatermagnitudethaninthedensitometer.

MicroscopicStudies

Themicrophotos were shot_usinganOlympus BH-2microscopewith

Tungsten-Halogen

lamp

and aNikonMultiphotphotographic attachmentThe

magnification was80x (Vonthephotograph = _onthe

original.) Allphotographs

representPaperC. Polaroid Type 55 Positive/Negative Instantsheetfilmwasused.

Exposuretimewasfourminutes anddevelopmentwas handledas prescribed

by

Polaroid.

These4x5negatives werethencontact printedforreproductioninthis thesis.

They

have

beenmounted on a grid

illustrating

thematrix.

Microscopicmeasurementsweretakentodeterminetheactualsize of adot

consistingofonespot.The instrumentused wasaBauschandLomb lightmicroscope

witha lOx

lens,

zoom adjustmentand a_calibratingeyepiece.Theeyepiecewascalibrated

toan etched slidewithdivisionsof.001".Themarkingsintheeyepiece were adjustedto

FOOTNOTESFOR CHAPTERFTVE

1_Adobe

Systems, Inc.,

PostScript LanguageTutorial andCookbook.

Reading,

Mass.:

Addison

Wesley Publishing

Co, Inc., 1985,

p.l1 1-116.

2Surprisingly,

whenthescale was setto72x72and a300x300pixelimagewascreatedthe

resultingtestpatterndisplayed repeatingpatternsthatstreakedthe_{image vertically}

andhorizontally. Trial and errortestsconfirmedthat thecombination of69x69

scalingplus a288x288pixelimageresultedinnon-streakedtestpatterns.288 is a

multiple of72which_{may be why}iteliminates_{the streaking,}althoughno

explanationfora unit square of69x69was everdetermined.

CHAPTERSIX

RESULTS

Besidesthe_consistencytests(referto the

Methodology

_section),a numberof

differenttests were conducted.

They

canbe divided intogroups: _{tone production,}

microscopic_studies,and papertests. Alldata forthe toneproduction and papertestsare

includedintheAppendices.Theresults ofthemicroscopic studies areincludedinthis

chapter(withtheexception ofthe_{microphotographs.)}

Tone Production

Toneproduction curves were producedfor

2x2, 3x3, 4x4, 5x5, 6x6,

and8x8

matrices.Withineach ofthesematrix structurestwodotformswerecompared: open and

condensed.Thesetests were run onPaperC. Thegraphs ofthese testsappearonpages35

to40intheAnalysissection. (Thegraphs record

density

onthey-axisandnumberof

spots ondivided

by

totalspotsinthematrix onthex-axis.)Severaltrends becomeclear.

Thecondenseddot

forms,

Figure

11,

tend toproducea slight s-shaped curvethatbecomes

lessandlessaccentuated as thematrix sizeincreases.

Conversely

theopendot

forms,

Figure

10,

produces an exaggerated s-curvethat_{actually develops}a

hump

nearthe50%

spots on region.

Density

continuesto

drop

untilaround70%. Thiscurvebecomesmore

exaggeratedas matrix sizeincreases.

Toneproductioncurves were alsoproducedforthediamond dot forms. These dot

forms(see Figure

12)

produced curves quitesimilarinshapetothecondenseddotforms

(ie.,slightly

s-shaped.)Themidtones(from_{approximately} 30%to

70%)

are covered

by

lowerandlower densitiesasthenumberof spotswithinthediamondmatrixincreases.

Wheredirectcomparisonispossible(see

below)

itcanbeseenthateventhoughthe

samepercentageof spots are oninthematrix,alarger

density

is achievedwherethematrix

Table 3 Comparisonoftestsquares with50%spots on

Spotson

Density

_Maximum

Density

_AdjustedDensity*

2/4 .71 .93 .76

4/8 .63 .85 .74

6/12 .56 .95 .60

8/16 .49 .89 .55

12/24 .47 .94 .50

18/36 .42 .91 .46

32/64 .45 1.15 .39

?Forthepurpose of_comparison,the

density

isadjustedto themaximum

density

achieved

by

theLaserWriteron a givenday.Allofthedensitieshave beenadjusted

toa maximum

density

of1.00. Inthecase of2/4spots onthismeansthatthe

density,

.71,ismultiplied

by

1.00/.93togive an adjusted

density

of.76.The

assumption madehere isthatifthe

density

had been

1.00,

the_{2/4 step}wouldhave

been.76.Yeteven withoutadjustingthe

density

thereisa gradualdeclinein

density

asthenumber of spotsincreases.

Thedotshapes usedforthis testwerethe

8,

12 and24 diamondshape,andthe

2x2, 4x4,

6x6and8x8condenseddotshapes.Theopendotshapes at

50%,

since

they

are all

checkerboards,are all quite similar.

They

averageat about.82adjusteddensity.

Microscopic Studies

Microscopicmeasurements weremadetodeterminetheactual size ofthedot. The

markingsin theeyepiece were adjustedtobeequalto through theuseofthe zoom

adjustment. Theactualdotsare quiteirregular innature(see

below),

sothesediameter

3 units =

Figure8- Irregular

nature ofthedot

Thecriterion used wasthatthebulkofthedotshouldfallwithinthestated

measurementMeasurements weremade on

2x2, 3x3, 4x4, 5x5, 6x6,

and8x8 matrices

usingthe testsquare where_onlyonespotinthematrix was on.Inthismanner,thevariable

betweenthe testsisthedistancebetweenadjacent spots. Itshould alsobenotedthatasthe

dotscome closer and closer_together,the

irregularity

inthedotshapeincreases. The

measurementsfortheindividualspots are asfollows:

Table 4- Dot

size measurement

Matrix

2x2

3x3

4x4

5x5

6x6

8x8

Diameterofthedot

Ameasurementwas also made ofthe2x2opendot formwheretwoout offourspotsare

oninthematrix.Thischeckerboardpatternhasquite anirregulardotwhichmakesexact

measurement

difficult

howeverthediameterisnogreaterthan.003".

Graphically

thedata

5x5 4x4 3x3 2x2 2x2

*

?

Side

of boxequals

Figure9

-Illustrating

dotsize

(Thesecond2x2matrix representsthe twospots on situation.Ineach case thenearest

adjacentdotsare also_shown.)

The accuracyofthemeasurements wastested

by

_measuringthedistance betweenthe

dotsand_comparingitwiththeknown linescreenvalues:

Table5

-Testing

the_accuracyofthemicroscopic measurements

Distance betweenspots(midpointto midpoint)

Matrix Measured Calculated

2x2

3x3

4x4

5x5

6x6

8x8

Microphotographs weretakentogive avisualillustrationofwhatis

happening

atthe

levelofasinglespot.Thephotos areshownon pages41 to49.

They

have beenmounted

on a gridtoillustratetherelationship between thespot andthematrix. Thephotos were

shot at amagnificationofapproximately80x (one inchonthephotographisequalto

.0125").Thephotos willbe

discussedintheanalysissection,butpleasenotetwo things:

first

therelativesize of anindividual spotandsecond, therelationofthematrixtothe

PaperTests

Twofactors_relatingtopaper weretestedas part ofthisresearch.The firstisthe

ability toachieve ahighmaximumdensity.Thesecondisthe_abilitytoproduceatonal

curvethrough a range of grays.

Maximum

Density

Tests- The

density

testconsisted of_taking

density

measurements

from 12solidblackpatches,aswellas_recordingthe

density

ofthewhite ofthepaper.

Threesheets were runforeach paper sample.Theresults werethenaveragedand shown

below (rankingsareinparentheses):

Table6- Results_ofthefirst_papertest

Paper Dmax Paper White Range St. Dev.

A

1.114(2)

0.089(1)

1.025(2)

.030(5)

B

1.134(1)

0.090(2)

1.044(1)

.034(3)

C

1.102(3)

0.095(4)

1.007(3)

.035(1-2)

D

1.069(5)

0.102(5)

0.967(5)

.035(1-2)

E

1.061(4)

0.093(3)

0.968(4)

.031(4)

Ave. 1.096 0.094 1.002 .043

Thetestwas repeatedat alater datewiththe

following

results:

Table 7- Results_ofthesecond papertest

Paper Dmax PaperWhite Range St. Dev.

A

0.887(4)

0.089(1)

0.798(3)

.033(2-3)

B

0.908(2)

0.096(4)

0.812(2)

.035(1)

C

0.913(1)

0.092(2)

0.821(1)

.033(2-3)

D

0.897(3)

0.103(5)

0.794(4)

.022(5)

E

0.846(5)

0.093(3)

0.753(5)

.025(4)

Ave. 0.890 0.095 0.796

Itis

interesting

tonotethat themaximum

density

achieved onthe

day

ofthefirsttest

is 1.096comparedto0.890onthesecondday. Eachtest_represents,inthecase of maximum

density,

36measurements(gleaned from 108 actual measurements onthe36

squares.)

Gray

Production Test- Totest the

abilityof a papertoproduce grays(andalsoto

gaugetheamount of

filling in)

anothertestwas run. The 5x5open matrixpatternwasrun

threetimeson each paper.

Density

measurements weretakenand averaged. Sincethis

particulardot formationformsa characteristichump-shapedtoneproduction_curve, itwas decidedtocomparethepoints wherethecurve peaks and whereitreachesthebottom. Thesepeaks,bottomsand_{corresponding}spot numbers are recordedbelow:

Table8- Results_ofthethird_papertest

Peak

Density

Bottom

Density

Difference between Paper andSpot # andSpot # PeakandBottom

A .70/12,14 .64/17 .06

B .72/12 .66/16,17 .06

C .69/12 .63/16 .05

D .69/14 .67/16,17 .02

E .69/14 .64/16 .05

Ave. .69/14 .65/17 .04

Thisparticulartestwillbeofimportancenot_{only in}

determining

a paper's_abilityto

reproduceatonecurveaccurately, butalsotoget alookatthenature ofthis hump/bottom

phenomenon. Thisis becausetheaverages oftheresultsof all papersshowthat

steps 14

and 17arethekeysto solvingthepuzzle.Thenatureofthe_grayproduction willbe discussed

by

theuseofseveral methodstogradetheproductionofgrays.Referto the Analysis section,page32 foranexplanationofthesemethods.

Table 9- Overview

of papercharacteristics

A B C D E

Weight(in

lbs.)

20 24 24 20 20

Opacity

87 90 92 86+ 85+

Brightness 89 89 90 85.5 91

Brightness* ₈₉

93 89.5 85 90

?brightnessmeasurements made on aPhotovolt Model 670reflection meter(the

CHAPTER

SEVEN

ANALYSIS

Thissectionis divided intothreeparts: tone_production,microscopic_studies,and

papertests.The datafromtheResultssectioniscontainedintheAppendices.The data has

beenusedtocalculatemeans andstandarddeviations. Theraw

data,

_alongwiththemeans

and standarddeviations isshownintheseAppendices. Graphs havebeen drawnto

illustratesome ofthedata. Thegraphs are on pages35 to40attheend ofthischapter.

ToneProduction

Thebulkofthissection consists ofthegraphical representation oftheResults

section. Figures 10through 15are graphs ofthetoneproduction curves.

Density

is

recorded onthey-axis while percent of spotsoninthe matrixisrecordedonthex-axis.

Percentof spots on inthematrix_simplyisa calculation of spotsondivided

by

spotsinthe

matrix. For_example,one spot onina25spotmatrixyieldsa valueof4%spots oninthe

matrix.Wherecertain curveswithina_category showed great_{similarity (as}is thecaseinthe

diamondmatrixfor_example)onlyone curvewas showntopreservethe_clarityofthe

graph.Forexample, the 12 diamondand 13 diamondare_verysimilar andtherefore_only

the 12diamondisshown on the graph (thesameistruefor 24and

25,

_{only 24 diamond is}

shown.) This adjustmenthas beenmadein figures 10through 12.

Agoodcomparisoncanbemadeofthe25

diamond,

5x5condensed andthe5x5

open matrices since

they

allcontain25 spotswithinthematrix. Forthisreason_theyhave

allbeenshowntogetherin figure 13. Thecurvesinthegraphs havebeen drawnto

representthedatapoints.Itshouldbenotedthatinthematrices_{containing few}spots

(ie.,

2x2, 3x3,

5

diamond)

thismeansthat thecurvehas been drawn using relatively few data

points.Nocurves aredrawn in figure 14. Allthedatapoints are showntoillustratethe

unevennature ofthedata. Column breaksare showntoshowtheeffectthatpagelocation

hasonthetest.Inthe8x8 test, 24testsquaresfiton a pagein fourcolumns of sixsquares

each. Threepageswere requiredtofitalltestsquares. 8x8openisrepresented

by

and8x8condensedisrepresented

by

_{"c's". Where}thevalues arethesame an

"x"

appears.

BartlesonandBrenemanvalues were usedtocreatetheidealtonalscalein Figure

15. Thissystem relateshumanperceptionto

density

values.Inthis_manner,stepsofequal

visualdifferencecanbecreated.

Therefore,

_ifthemaximum

density

ofthe8x8condensed

matrixis 1.

15,

anidealcurve of65steps canbecreated_{using 1}.15as the maximum

density

and0.10astheminimumdensity. See Appendix

D,

page84 forcalculations and

anin-depthexplanation.

MicroscopicStudies

Themicroscopic measurement results are shownintheresults sectionintheir

entirety.No furtheranalysishasbeenperformed onthisdata.

Themicrophotographs have beenmountedongridswhichrepresentthematrices on

which

they

arebuilt The"x's" representthespotswhichare on. Figure 16 includesa

microphotograph of parallellinesattheirfinestresolution(thereisno_underlyingmatrixfor

this.)

Figures 17through22shouldbeviewedas a series.

They

allrepresentthe5x5open

matrix with anywherefromoneto24spots on. Figures 18and21 are remarkablefortheir

similaritythough 18 has six spots on while21 has 18spots on. Figure 23representsthe

12spots on square ofthe5x5condensed matrix.Figure 24represents 12 spots_on,inthis

caseinthe25 spotdiamondmatrix.Both23and24shouldbecomparedtoFigure

19,

sinceineach ofthesecases 12out of25 ofthespots areoninthematrices.

Paper Tests

Appendix

B,

page

74,

givesthefullextent ofdataand calculations.The gray

production part ofthepapertestsrequiresan analysis to_{determine how many}grayswere

produced.Thereare_{certainly many} waystodothiskindof analysis.Theauthorhas developedthreemethods of

doing

thisand eachwillbe lookedat separately.

First,

it is

possibletomeasurethenumberoftimes thatavalueofagiven_stepislessthanor equalto theprevious value.

Certainly

ifavalue inanascending gray scaledoesnotexceedthe

previous valueitcannotbeconsideredaseparategray. ThismethodwillbecalledMethod

One.Anothermethod wouldbetocountthenumberoftimes that thevalue of a givenstep

doesnotexceedthehighestpreviousvalue.Thismethod will accountfor dips ina curve

(likeintheopencurves) where valuesmay be ascending but have actuallybeenexceeded

countingthenumber oftimesthat thevalue of_{anystep in}the testisrepeated.Thismethod

willbereferredtoasMethod Three.Toreview:

MethodOne

-thenumber oftimesthatthevalue ofa given_stepislessthanorequal

to theprevious_step

MethodTwo

-thenumber oftimesthat thevalue of a given_stepis lessthanorequal

to thehighestprevious value

MethodThree- _{the number of}times that the_{value of a}

steprepeats

Thesecalculations havebeenmadenot_{only for}thepaper_tests,butalsoforthe tone

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Figure 10 - Graphof

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Figure 1 1 - Graphof

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Figure 12- Graph_of

5, 8,

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Figure 13 - Graph

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CHAPTEREIGHT

DISCUSSION

Thischapteris divided intothreesections:_{tone production,} microscopicstudies and

papertests.

ToneProduction

Forthisdiscussionplease refertoFigures 10through 15on pages35to40. An

inherentcharacteristic ofthecurves oftheopen matricesbecomesclearin Figure 10. The

curve (of6x6 forexample)reaches aninitialpeakatabout50% spots on andthendrops

until 70%spots on at which pointitincreasesagain.This isapparentin Figures 13and 14

as well.Thecurves ofthecondensed matrices ontheother

hand,

tend towardan s-curve

shapewhichis_{relatively flat in}the midtones.The diamondmatricesare quite similarto the

condensedas a_{group (see}Figure 12).Thethree typesofcurves canbecomparedin

Figure 13.

Clearly

themost_striking aspectofthisgraphisthehumped-shapeofthe5x5

opencurve.Itmightbesurmisedthat theopenmatriceswouldfill in causingtherapidrise

indensitiesshown;howeverit iscuriousthatthedensities decreasepast50%as more

spots are added. Thisquestionisanswered

by

themicrophotographs andwillbe discussed

inthemicroscopic studiessectionofthis chapter.Rememberin

looking

atFigure 13 that

theopenand condensed5x5 matricesdiffer only inthe_waythespots are configured.

Thegeneralshape of open versus condensed curvesiswelldocumented in Figure

14.Inaddition, theinfluenceof pagelocationisindicated

by

themarkingofthecolumn

changes.The datapointsdonotforma_perfecdy smoothcurve.Inpartthisiscaused

by

thecolumn changes.

Note,

inparticular,page

3,

column 1 wherebothopen and condensed

rise

by

considerable amounts.Thesameistruetoa somewhatlesserextentinpage

3,

column2. This emphasizesthepoint madeinthe

Methodology

section, that

is,

thatpage

locationplays alargeroleinthe

density

ofagiventestsquare.

Thefinalgraph,Figure

15,

comparesanideal BartlesonandBrenemancurveto the

facts

shouldbenoted.

First,

the

8x8

condensedmatrix represents alinescreenof37.5

which while

affording

numerous _grays,sacrificesdetail. Secondof_{all, the}8x8curveis

too_{steep in}the

highlight

and_shadow,andtooflatinthemidtone.Thismeansthat the

midtoneareafromabout.3to.6in

density

(

a range of

.3)iscovered

by

moregrays than

theentire rest oftherange(about.75).Lastof_all,duetothedigitalnature ofdigital

halftones,

thefirst few steps are of greater magnitude thantheonesthatfollow. Thevalues

of

0/25,1/25,2/25,3/25

and4/25 are asfollows:

0.10, 0.14,

0.17, 0.19,

and0.20.

Ideally

thesteps mightbe

0.10, 0.12,

0.14, 0.16,

and0.18. Ifthiswerethecase, therewould

notbesuch alarge

jump

fromthepaper whitetothefirstgray.In addition,itwould

facilitatethe_spreadingout oftheflatareainthemidtone.These_conditions,

however,

are

difficulttoachieveinadigitalhalftone.Rememberthat theaddition ofa spotwithinthe

matrix will make a greaterdifference_{if very few}spots are_alreadythere.For_example,

fromoneto twospotsthereis a100% increaseinthenumber ofspots,fromtwo tothree

onlya50% increase and so on.

Pulling

data fromthevariouscurvesthe

following

comparison canbemadebetween

all ofthedatapointsatwhich50%ofthespots are on(see

Results,

page26):

Table 10- 50%_{spots onwith}information concerning_areabetweenspots

Spotson Area betweenspots Docomerstouch? Adjusted

density

2/4 2units Yes .76

4/8 4units Yes .74

6/12 6units Yes .60

8/16 8units No .55

12/24 12units No .50

18/36 18 units No .46

32/64 32units No .39

Eventhoughthesame percent of spots areon,itisclearthatthe

density

increasesas the

areabetweenthespotsincreases.

Why

shouldthisbe? Therearecertainly manyfactorsat

play

here,

twoofthem

being

laserspot size andtheamount of overlap. Onepossible

explanationis thatastheline ruling

increases, toning

willbeless

likely

inthenon-image

Microscopic Studies

Themicroscopicmeasurementsrevealthat thediameterof a_{dot consisting}of a

single spot remains at aconstant untilthematrix sizeisreducedto4x4.Atthatpoint

thedotcontinuestoshrink untilit

becomes

soirregularthatit is difficulttomeasure.This

destruction

oftheunit

building

blockof a

halftone

isof utmost concerntodesignersof

digital

halftones.

Forthe

following

discussionofthemicrophotographsplease refertoFigures 16

through

24,

pages41 to49. Figure 16isa goodillustrationofthemannerinwhichtoner

fillsinthenon-imagearea.ThesearethefinestparallellinesthattheLaserWritercan

create.Ina unit

inch,

onehundredand

fifty

oftheseblacklineswouldbe bordered

by

one

hundredand

fifty

whitelines.Ifitwere possibletooutputthis imagetophotographic paper

thenature oftheimagewouldbemuchdifferentThespread oftonerwould notbea

problem andthedefinitionoftheedge wouldbemuchfiner. Thishigherresolutionis

reflectedinthehighercost of photographic paper andfilm.

Thenext_sequence,Figures 17through

22,

isofinterestforseveral reasons. Note

thedecreaseinspot sizebetween Figure 17and 19. The individualspots are visiblein

Figure 19andhaveshrunken_remarkablyas comparedtoFigure 17. Figures 18and 21

make another

interesting

comparison.Ineffect, six spots (in Figure

18)

dotheworkof18

spots(in Figure21).This isdueto toner

filling

inthenon-image areainFigure 18. Toner

falls intothenon-image_area;however becauseit issurrounded

by

moretonerthathas

alreadymadeits _wayto theimagearea,itcan't makeits_wayoutandis_ultimatelytrapped.

The

hump

shaped curvein Figure 13canbeexplainedwiththe microphotographs.

Figure 19representsthepeakof_{the curve,}Figure 20representsthepoint

immediately

after.Figures 19and20illustratethedecrease in

density

thatoccurs.Notehow Figure 20

appearslighterthanFigure 19eventhoughan extra spothasbeenadded. Whatappearsto

be

happening

hereis that theextra_spot,whichissurrounded

by

fourother_spots,forms a

largecharged areawithitsneighbors.Thischarged areaappearstodrawthetonerfromthe

non-image area

thereby

creatingahigher density. Thisextraspothastheeffect of_cleaning

upthenon-image area of_{stray toner; however}italsoappearstomakeitmoredifficultfor

tonertobeattractedto theimageareasthatareisolated.Thisprocess continuesuntilthis

largecentral charged areahasbecome largeenoughitselftobeginanincreasein

density

(seeFigure

21.)

ItissurprisingthattoreachFigure21 it is necessarytopass through

toeach otherin_sequence, and_{yet, the}central_{dot in Figure 18 virtually decomposes before}

being

built

_upagain _{in Figure 21.}

Figure

_{22represents one spot short of a solidblack.}

Notethat thesize oftheopen

(non-image)

areais quite similarinsizetothatoftheimage

areain Figure 17.

Figures

19,

23 and24make an

interesting

comparison of25 spot matriceswith 12

spotson. _{The resulting densities (.42}

diamond,

.53 condensed,and.88open,referto

Appendix

A)

show a

difference

thatisalso quite visible onthemicroscopiclevel. In Figure

19,

theopen areas betweenspotshave filledintoa great extent In Figure23thegreatest

amount offilling-intakesplace atthepoint wherethehalftone dotsare endtoend. In

Figure24the

halftone

_{dots only}approach each other atthecomers andit isatthesecorners

thatsomefilling-intakesplace.This limited filling-inthat takesplaceinFigure24isa

result ofthescreen anglethatexistsinthe25diamondmatrix. Thisisanimportant factor

to

keep

inmind while

designing

matrices sinceitcanbeusedtocontrolfilling-in. These

microphotographsshowthatconfigurationwithin_{the matrix, and, the}shape ofthematrix

itself_playalargeroleinthe_resultingdensities.

Paper Tests

Maximum

Density

-Achieving

ahighmaximum

density

isimportantintone

productionsinceitallows a greater range of valuestobecovered

by

various grays. Alow

maximum

density

willcompress the_grayscale sothatadjacent graysbecomemore similar.

Theotherfactorinrangeistheminimumdensity. What is

being

comparedinthispapertest

istherangefrommaximumtominimumdensity. Inthefirst_testTable

6,

page 29the

papers are ranked

by

rangeinthe

following

order: Bthen

A,

C, E,

andD. Itwouldbe

statisticallypossibletojudgethe_accuracyofthis_rankinggiventhemeans and standard

deviations.

However,

thesecond_test,Table

7,

page

29,

gives a_rankingofCthen

B, A,

D,

andE. This rankingthrowssomedoubtonto_anyjudgementsof orderthatmightbe

drawn fromtheserankings.Itshouldbenotedthatonthe

day

ofthe_{first test,}theaverage

maximum

density

was 1.096while onthe

day