�

Gernot Hoffmann

Color RenderingPrintingScanning

Contents

�. Introduction 2

2. ColorRendering 3

3. LaserandOffsetPrinting 6

4. HowmanyPixelsforRasterPrinting? 7

5. HowmanyPixelsforInkjetPrinting? �0

6. HowmanyPixelsforScanning? �2

7. ExampleforScanning �3

2

1. Introduction

Physicalcolorsaredefinedbyspectra:waveswithvaryingintensityforthewavelength.EyeandbraincondensethisinformationtoonlythreevalueswhichwemaycallRed,Green,Blue,thoughthisisalittlesimplified.Atleastweneedonlythreeinformationstodescribeacolor.Acolorprojectorcouldbemadebythreelaserswithred,greenandbluemonochromaticrays.Thearbitrarymixtureoftheserayswithintensitiesfromzerotoonedeliversasetofavailablecolors–thegamutofthedevice.Monitorsdonotusemonochromaticsourcesbut threespectraldistributionsofwaves,butthesearecharacterizedbyequivalentmonochromaticred,greenandbluesourcesR,G,B.Obviously,theresultofthemixturedependsontherealcolorofthe’primaries’R,G,B.ThesearedescribedinabsolutephysicalcoordinatesCIEXYZ,basedontheCIE(�93�)colormatch-ingtheory.CIExyY(nextpage)isaperspectivetransformofthehumangamutinXYZontoaplanex,y.Theluminanceisleftout,thecontentofthehorseshoeshowscolorssymbolically.AnimagecontainsforeachpixelasetofthreenumbersR,G,B,onebyteortwobytesperchannel.EqualvaluesR,G,Bmeangray,everythingfromblacktowhite.Agraycanbered-ishorblue-ish,thereforeawhitepointWhastobedefinedinadditiontheprimariesR,G,B.TheseinformationsarecarriedinanICCprofile,eitheraworkingspaceprofilelikesRGBorAdobeRGB(98)oramonitorprofileorascannerprofile.ThegamutofsuchatristimulussystemappearsinxyYasatriangle.InXYZitisanaffinedistortedcube.

PrintingisdonebyinksCyan, Magenta,YellowandadditionallyBlack(K).Printedinksinteractwiththelightsourcecolorbyreflectance.CabsorbesR,MabsorbesGandYabsorbesB.Forprinting,thefileimagecanbemappedvirtuallyontothepaper.ThisisherecalledsourceRGBimageonthenextpages.Thesourceimagepixelsarenotprinteddirectly,theyhavetobeinterpreted.Offsetandlaserprintersuserastercellstosimulatetheimage.Theinkortonerisclusteredbyordereddithering.Inkjetsusestochasticditheringordiffusionbysmalldrops.Bothtechniqueshaveaverylimitedsetofafewinks,CMYKandeventuallysomeextrainkslikespotcolors(offsetinks)orlightmagenta,lightcyan,orange,green(inkjets,hexachrome).CharacteristicsofprintersaredefinedbyICCprofilesaswell.Thereforeitispossibletocon-vertasourceimagecolorR,G,BintoaphysicalcolorX,Y,Zandthenintoamountsofink,whichcreatesthecorrectimpressionforatleastonespecifiedlightsource.

Altogetherwehaveplentyconversions:

InterpretationofthesourceRGBimagebyphysicalcolors.MappingofsourceRGBpixelstorealorfictitiousrastercells.ConversiontoCMYKcolorswiththesameappearanceonthepaper.Generationofappropriatepatternsofclustersorsingledots.

TheconversionfromawelldefinedRGBspaceintoawelldefinedCMYKspaceisdoneforoffsetprintinginadvance,e.g.byPhotoshop.Fordesktopprinterstheconversionisdonebytheprinterdriverortheprinteritself.

SettingsforAcrobat

Edit/Preferences/General/PageDisplay(sinceversion6)CustomResolution72dpi/Viewbyzoom�00%or200%

Edit/Preferences/General/ColorManagement(fullversiononly)sRGB

EuroscaleCoatedorISOCoatedorSWOPGrayGamma2.2 2

3

Recommendation:1.5 ... 2 Pixels per cell width

The raster frequency in Lpi is e.g. ten times smaller than the printer resolution in dpiThis results in n = (dpi/Lpi)2 +1or n = 101 levels per color

Source pixels Printer halftone cell

Diffuse black and white pointof RGB Source

Gamma CorrectionTone Reproduction Curve

RGB to CIELab Conversion

Black-White Match

Color MappingGamut Compression CIELab to CMYK Conversion

Undercolor Removal UCR/GCRInk limiter for Inkjets

Halftone RenderingUsing Spot Function for Raster PrintUsing Dithering/Diffusion for Inkjet

Scan Conversion

RGB

RGB Linear

Lab

Lab

CMYK

CMYK

CMYK

CMYK

Source RGB Pixels

CMYK space

CMYK space

Separation

Printer Pixels

Diffuse blackand white pointof CMYK-Printer

Gray Component Replacement GCRUndercolor Remo-val UCRc = 1 – R m = 1 – G y = 1 – B k = min (c,m,y)C = c – U(k)M = m – U(k)Y = y – U(k)K = B(k)e.g.U(k)=k B(k)=k

RGB SourceWorking space e.d. sRGB, AdobeRGB(98)or AppleRGB

ICC ProfileRendering Intentperceptualabs.colorimetricrel. colorimetricsaturation

Spot Function

2.1 Color Rendering / Source RGB to Printer CMYK

10 printer pixels per raster cell width

60% K

11% K3% K 12% K 60% K1/ dpi

1/ Lpi

1/ Lpi

Source RGBPrinter CMYK

xCIE xyY Diagram

Gamut Compressiony

SourceRGB:RGBfile,mappedvirtuallyontothepaper

RGB SourceWorking space e.d. sRGB, AdobeRGB(98)or AppleRGB

4

2.2 Color Rendering / Raster Cells

Theexplanationsonthepreviouspageweresimplifiedfortutorialpurposes:actuallythecontentofarastercellisnotanaveragedversionoftheunderlyingsourceimage.Thevaluesfortheprinterpixelsaretakendirectlyfromthemappedsourceimage,usingaso-calledthresholdarray(whichisnotexplainedhere).Thisretainssharpedges.TheclustersinthehalftonecellmaylookfuzzyforlowLpitodpiratios.Theillustrationshowshalftoningbytheauthor‘simplementationforroundspots.

Bestviewzoom200%

5

05%K �5%K

40%K 50%K

60%K 85%K

95%K �00%K

2.3 Spot Function for PostScript Round Dot

Arasterspotisgeneratedbytheintersectionofthespotfunctionz(x,y)=0.5[cos(πx)+cos(πy)]andaplane.Thespotfunctiondefinesthearea,butthespothastobecreatedbyaspiralscan,startinginthemiddle.Fuzzysingledotlinesshouldbeavoided.

5

6

3. Laser and Offset Printing

Rasterfrequency �50 LpiResolutionabout2400 dpiAngle C 75°Angle M �5°Angle Y 0°Angle K 45°

Scanresolution �200 dpi

Zoomfactor 5

Zoombyinterpolation

Rasterfrequency�75 LpiResolutionabout 2400 dpiAngle K 45°

Scanresolution �200 dpi

75°

0.1 inch

AnglesaremeasuredinGermanstandardsclockwise,beginningatthevertical.Inotherstandardstheyaremeasuredcounterclockwise,begin-ningatthehorizontal.

CMYKandK-only

7

It´sobviousfromthepreviouschaptersthatweneedatleastonesourcepixelperrastercell.Therecommendationbelow,Factor(�.5..2),isbasedonpracticalexperiences.Toomanysourcepixelsperrastercellmightmakethedotsfuzzy,butthiscouldnotbeprovedbylaserprintingwith�200dpi/�06Lpi.

4.1 How many Pixels for Raster Printing ?

X

px pixelnumberinwidthdirectionLpi rasterfrequencyinLinesperinch wx widthofimageininchonprint

px = (1.5...2.0) · Lpi · wx

Whathappensiftheppi-valueistoohigh,toomanysourceimagepixels?Itiscommonknow-ledgethatthiscanspoiltheprint.ThisissuewasfurtherinvestigatedinSeptember2005,printingbyanewcolorlaserprinter�200dpi /�20Lpi(nextpages).Thiscanbeconsideredasasimulationforoffsetprinting.

Theguidelinesasabovearestillvalid,butmodernrasterizesdonotspoiltheprintifthesourceimageistoolargebypixels.

Inthetestsonthenextpagesthesourceimagehasalways�20x�20pixels,buteachoneisshownscaledbyadifferentsizeonthepaper.Thisscalingmeans:theoriginalsourceimageissentalwaysasitistoprinter,accompaniedbyPostScriptcommands’bottomleftcorneratx,y’and’edgelengthsa,bonthepaper’.NeitherPageMakernorInDesignmanipulateimages(withtheexceptionofcroppingforprint-ingtoPostScript).

ppi pixelsperinchforthesource image,mappedvirtuallyonto thepaper

ppi = (1.5...2.0) · Lpi

8

120ppi = Factor 1.0

180ppi = Factor 1.5

240ppi = Factor 2.0

300ppi = Factor 2.5

360ppi = Factor 3.0

Which version is the best ?

Is the quality really different ?

Use Acrobat resolution 72dpi and zoom 100% / 200% / 300% / 400%

240ppi 360ppi

120ppi

180ppi

300ppi

The print was scanned as RGB / 1200dpi, downsampled for 600dpi

and converted to RGB gray (below).

The image is always the same, a photo 120x120 pixels, and a circle

as vector graphic. Scaled by PageMaker.

The page was printed by a laser printer 120Lpi /1200dpi.

RGB gray was printed as rich black CMYK.

4.2 How many Pixels for Raster Printing ?

9

4.3 How many Pixels for Raster Printing ?

240ppi 360ppi

120ppi = Factor 1.0

180ppi = Factor 1.5

240ppi = Factor 2.0

300ppi = Factor 2.5

360ppi = Factor 3.0

Which version is the best ?

Is the quality really different ?

Use Acrobat resolution 72dpi and zoom 100% / 200% / 300% / 400%

120ppi

180ppi

300ppi

The print was scanned as RGB / 1200dpi,

downsampled for 600dpi and converted to RGB gray (below)

The image is always the same, a photo 120x120 pixels, and a circle

as vector graphic. Scaled by PageMaker.

The page was printed by a laser printer 120Lpi /1200dpi.

RGB gray was printed as rich black CMYK.

�0

5.1 How many Pixels for Inkjet Printing ?

Inkjetprinterstrytosimulatecolorpatternsbycloudsofinkdotswithoutcreatingartifacts.Itishelpfultoassumeafictitiousrastercell,thoughthecalculationofdotcloudsisdistributedoverthewholeimage(errordiffusion,dithering).Alargecellcanrepresentmanylevelspercolor(heregray),asmallcellshowsthegeometryofthepixelimagemoreaccurately,butthenumberofcolorlevelsissmaller.Thuswehaveexactlythesamesituationasforrasterprinters.AssumingafictitiousLpivalue,thenumberofnecessarypixelscanbecalculated,atleastareasonableguess.

�/Lpi

�/dpi

Thisfictitiousrastercellrepresentsoneormoresourcepixelswithanaverageof20%gray.Thenumberofgraylevelsinonecellisdefinedbyn=(dpi /Lpi)2+�Herewehaven = �0�fordpi/Lpi=�0

InkjetuserscannotchoosethecellsizeLpivalue.Areasonableassumption:Lpi=dpi /�0.Thisallowstheapplicationofthesamerulesasforrasterprinting(previouspages).The’reasonableassumption’isbasedoninformationperarea.Thedotsareinrealityslightlylargerthaninthedraw-ing,e.g.byafactor�.4.�00dropsshouldcoverthecellwidthwithoutgaps.

�0mm

80%K�00%KThisisatestimage:twopatches �0x�0mm,left80%K,right�00%K.

Mutoh6�00,720dpi.Themillimeterscalewasestimatedbytwoavail-ablelines.Theoreticallywehave720/25.4=28.35dotspermillimeter.Thegridwidthis�/720inch.Thedotslookrandomlydistributed.Thisunevenspacingmaybearesultofinaccuratepositioningortimingforthenozzlecontrolsystem.DensityD=0.97,visualdotarea86%.

�mm

A view through the microscope for the 80%Kimage:Pleaseviewbyzoom200%

��

Anexample:aninkjetprintswith720dpi.Thefictitiousrastercellwidthisdefinedby72Lpi.Thisdelivers�0�levels.Thesourceimageshouldhave(�.5...2)·72pixelsperinch,whichmeans�08...�44ppi.Moresourcepixelsdonoharm,thiswasprovedbymanyexperiments.Formorelevelswewillneedlargerfictitiousrastercells.Theseneedlesssourcepixels.Grayimagesneed256levels.Forcolorimageswithoutweakmonochromegradientsthenumberofnecessarylevelsissomewherebetween�20and�80.

RasterprintingiscalledAMorAmplitudeModulation.Thesizeoftheprintedclusterdotisvaried.DiffusionprintingiscalledFMorFrequencyModulation.Thedistanceandthenumberofdropswithequalsizeisvaried(bottomimageonpreviouspage).

OffsetinkcannotbeprintedeasilybyFMbecauseofthehighviscosity.Itcanbehandledbetterbyclusters.Inthelastyearsthetechnicalproblemscouldbesolved.FMseemstobethestandardinfuture.

Somedesktopinkjetsuseafewdifferentdropsizes,buttheprecisionislimited.Largeformatprintersusealwaysthesamesize,buteventuallytwoadditionalcolors,eitherorangeandgreen(bettergamut)orlightmagentaandlightcyan.Withtheselightcolors,thedistanceofmagentaandcyandotscanbereduced-thesameeffectasproducedbysmallerdots.

5.2 How many Pixels for Inkjet Printing ?

�2

6. How many Pixels for Scanning ?

Scanningimagesshouldbeconsideredasaprocesswhichhasprimarilynothingtodowithprinting-scanforimagebanks,applyimageprocessingandsaveforanyapplication.Never-theless,sometimesitisnecessarytoscandirectlyforaprintablepage.Againwehavetogatherenoughpixels.Thereforedefinetheminimumscansizeinpixels.Startwithopticalresolution.Ifthefileistoolargethenreducetheresolution.

px pixelnumberinwidthdirectionLpi rasterfrequencyinlinesperinchwx widthofimageininchonprintws widthofimageininchonsourcesc scalesc = wx/wssrindpi scanresolutionsr= px /ws

px = (1.5...2) · Lpi · wx

Lpi�50wx5ws 3sc�.67srindpi375...500

px = (1.5...2) · 150 · 5 = (1.5...2) · 750 = 1125...1500

Thescanresolutionis sr=(��25...�500)/3=375...500scandotsperinch(dpi).Practicallytheimagecanbescannedby600dpiaswell,ifthefilesizeisaccepted.

Thescannerscansanywaybyopticalresolution600dpior�200dpi,orwhatisavailable.Scanningbyanyvirtualresolution,e.g.500dpi,isperformedbyopticalscanningandinter-polationinadvancetothefilegeneration.

Startingwiththeprintedsize,itisnotnecessarytoknowthescale.WedonothaveanyfixedoraccuraterelationbetweenScanner-dpiandImagesetter-dpi.

Exampleimagesareonthenextpage.

Example

�3�3

7. Example for Scanning

Printedwidth 5 inchLinescreen �50 Lpi Factor 2Image 300 ppiPixelnumber �500Scannedwidth 3 inchScanresolution 500 dpi

5inch

Printedimage

3inch

Scannedimage

GernotHoffmannOctober29/2000–April�3/20�9

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