�
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%
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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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