# ASTM E1682-08 (Reapproved 2013)

Designation: E1682 − 08 (Reapproved 2013)Standard Guide forModeling the Colorimetric Properties of a CRT-Type VisualDisplay Unit1This standard is issued under the fixed designation E1682; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.INTRODUCTIONThis guide provides directions and mathematical models for deriving the relationship betweendigital settings in a computer-controlled visual display unit and the resulting photometric andcolorimetric output of the display unit. The accurate determination of this relationship is critical to thegoal of accurate, device-independent color simulation on a visual display unit.1. Scope1.1 This guide is intended for use in establishing theoperating characteristics of a visual display unit (VDU), suchas a cathode ray tube (CRT). Those characteristics define therelationship between the digital information supplied by acomputer, which defines an image, and the resulting spectralradiant exitance and CIE tristimulus values. The mathematicaldescription of this relationship can be used to provide a nearbydevice-independent model for the accurate display of color andcolored images on the VDU. The CIE tristimulus valuesreferred to here are those calculated from the CIE 1931 2°standard colorimetric (photopic) observer.1.2 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:2E284 Terminology of AppearanceE1336 Test Method for Obtaining Colorimetric Data From aVisual Display Unit by SpectroradiometryE1455 Practice for Obtaining Colorimetric Data from aVisual Display Unit Using Tristimulus Colorimeters3. Terminology3.1 Definitions of appearance terms in Terminology E284are applicable to this guide.3.2 Acronyms:3.2.1 CRT, n—an abbreviation for the term cathode ray tube,a device for projecting a stream of electrons onto a phosphor-coated screen in such a way as to display characters andgraphics.3.2.2 DAC, n—an abbreviation for the term digital to analogconverter, a device for accepting a digital computer bit patternand translating it into an analog voltage of a prescribed value.3.2.3 LUT, n—an abbreviation for the term look up table, aprocess in which input and output values are mapped in ann-dimensional table such that, for a given input value, theappropriate output value is “looked-up” from the table.3.2.4 VDU, n—an abbreviation for the term visual displayunit, a device interfaced to a computer for displaying text andgraphics.3.2.4.1 Discussion—A CRT is one type of VDU.4. Summary of Guide4.1 Every color stimulus generated on a VDU is realized bythe linear (additive) superposition of the spectral power distri-bution of three primaries. Test Method E1336 describes how tomeasure the spectral power distributions and reduce them toCIE tristimulus values. Practice E1455 describes how tomeasure the CIE tristimulus values of the primaries directly.An exact characterization of the VDU would require measure-ment of the spectral power distribution at all possible combi-nations of primary settings. Modern, computer-controlledVDUs will provide 256 or more levels of each of the threeprimaries. This results in more than 16 777 000 uniquesettings, which is far too many combinations to be measuredpractically (see Note 1). Instead, a characteristic function1This guide is under the jurisdiction of ASTM Committee E12 on Color andAppearance and is the direct responsibility of Subcommittee E12.06 on ImageBased Color Measurement.Current edition approved Oct. 1, 2013. Published October 2013. Originallyapproved in 1995. Last previous edition approved in 2008 as E1682 – 08. DOI:10.1520/E1682-08R13.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1relating the radiant output of the screen to the digital inputsfrom the computer must be derived. Procedures are outlined forderiving a characteristic function for a computer-controlledVDU, using a minimum number of spectral radiometric mea-surements while maintaining near optimum accuracy. Ex-amples of deriving and testing such models are given inAppendix X1.NOTE 1—Different primary settings do not necessarily produce percep-tibly different colors. For VDUs with a large number (for example,16 777 000) of different primary settings, the number of perceptiblydifferent colors will be less than the number of primary settings.5. Significance and Use5.1 The color displayed on a VDU is an important aspect ofthe reproduction of colored images. The VDU is often used asthe design, edit, and approval medium. Images are placed intothe computer by some sort of capture device, such as a cameraor scanner, modified by the computer operator, and sent on toa printer or color separation generator, or even to a paintdispenser or textile dyer. The color of the final product is tohave some well-defined relationship to the original. The mostcommon medium for establishing the relationship betweeninput, edit, and output color (device-independent color space)is the CIE tristimulus space. This guide identifies the proce-dures for deriving a model that relates the digital computersettings of a VDU to the CIE tristimulus values of the coloredlight emitted by the primaries.6. Models6.1 The models are based on eight basic assumptions. First,at each pixel location on the VDU, the radiant exitance(emitted light per unit area) attributable to one primary type(red, green, or blue) is invariant with the radiant exitances ofthe other primary types. Second, the radiance exitance at onespatial location is invariant with the radiant exitance at otherspatial locations. Third, the relative spectral radiant exitance ofa primary is invariant with excitation level. Fourth, there is nointer-reflection of light between pixel locations. Fifth, theoutput of the digital-to-analog conversion process is linear.Sixth, there is no ambient glare (flare) from the screen into theobserver’s eyes. Seventh, the refresh rate of the image is rapidenough to produce temporal fusion (no noticeable flicker) forthe normal observer. Eighth, the pixel pitch is fine enough toproduce spatial fusion for the normal observer. Each of theeight basic assumptions should be tested and either verified,noted, or corrected before deriving a characteristic model.6.1.1 Assumption 1, independence of the primaries, is testedby measuring the radiometric output at several levels, asdescribed by Cowan and Rowell.3If the departures are small,they may be neglected or a LUT correction applied. If thedepartures are significant and maximum reproduction accuracyis required, only a full table look-up method can be used tocreate the RGB to XYZ transform.6.1.2 Assumption 2, spatial invariance, can be tested bymeasuring the center of a dark display and then repeating themeasurements with pixels near the edge of the display illumi-nated fully. The display may have to be considered unusablefor critical applications if this assumption is not met. Theamount of spectral variance will be a function of both positionand intensity of both the area of interest and the integrated areaof pollution. While such models can be derived, they may betoo complex to justify their use.6.1.3 Assumption 3, level invariance, is tested by measuringthe chromaticity of a primary at several different levels. Itshould be noted that care must be taken to maintain the signalto noise value of the color measuring instrument as theluminance of the primary is reduced. As the signal level of acolorimeter approaches the optical/electrical zero, the apparentchromaticity approaches that of neutral black.6.1.4 Assumption 4, absence of inter-reflections, is oftenviolated on CRT-type displays without high efficiency antire-flection (HEA) coatings on the face plate gloss.This is detectedin the same manner as spatial invariance. Again, models forthis can be derived, but the complexity may not be worth theeffort.6.1.5 Assumption 5, linearity of the DAC, can be tested witha calibrated, high-precision oscilloscope. A doubling of thedigital counts should produce a doubling of the output signal.It should be noted that RS-170 voltage levels are from −0.286V to +0.714 V with the range from 0 V to 0.714 V being usedfor signal level and 0 V to −0.286 V being used for synchro-nization during the blanking interval on a CRT-type display.Other types of visual display units may have their own uniquevoltage ranges as well. In general, the setting of the drivevoltage requires the simultaneous alignment of many opera-tional parameters, the specification of which are beyond thescope of this guide. It is assumed that the signal generator andthe receiver are adjusted to be within their unique operationalspecifications before the linearity test is performed.6.1.6 Assumption 6, ambient glare, can be tested with atelephotometer, measuring the luminance and chroma of eachprimary in a dark and ambient environment. If the two readingsdiffer by an unacceptable amount, either the display must beoutfitted with light shields or its operation restricted to a darkenvironment.6.1.7 Assumption 7, flicker rate, is a function of the displayelectronics and display type. Chromatic flicker ceases atfrequencies above 30 Hz. Brightness flicker ceases for mostpeople above 60 Hz, although some people continue toexperience the sensation of flicker up to 70 Hz. Most moderngraphics displays operate at refresh rates above 60 Hz. Broad-cast displays may operate at rates as low as 30 Hz. Low-ratedisplay electronics interfaced to a high-rate display may resultin an unacceptable appearance.6.1.8 Assumption 8, pixel density, is a characteristic of thedisplay and a function of the application.Alow-density displaymay be adequate for displaying solid patches of color but notfor detailed drawings or renderings.6.2 Examples of using the LUT method are also given inthis guide for completeness. There are three possible ap-proaches to modeling the relationship between the digitalcounts and the VDU tristimulus values. The first requires theuser to adjust the video gain and offset manually such that the3Cowan, W. B., and Rowell, N., “On the Gun Independence and PhosphorConstancy of Colour Video Monitors,” Color Research and Application, Vol 11,1986, pp. S35–S38.E1682 − 08 (2013)2black level and the offset cancel each other.The second methodtries to approximate the gain and offset by trial and error. Thethird method, the one used most commonly commercially,ignores the physical origins of the signals and collects mea-surements of the VDU output at a large number of points,sampling each primary channel between the minimum andmaximum counts. The unmeasured data values are determinedby interpolation, and a LUT is formed such that all possiblecombinations of primary settings can be found in the table. Therecommended procedure in this guide conforms most closely tothe second method, using statistical methods to determine theoptimum parametric values for the gain, offset, and gamma ofeach primary while requiring the smallest number of calibra-tion patches.This, then, linearizes the output of the system, anda linear transformation is applied to convert the linear RGBprimary values to CIE tristimulus values.6.3 The model parameters for the red primary are related tothe operational variables as follows:Mλ,r5 Mλ,r,maxFkg,rSdr2N2 1D1ko,rGγ(1)where:Mλ,r= the spectral exitance of the (r)ed primary,Mλ,r,max= the maximum spectral exitance of the (r)edprimary,dr= the digital setting of the (r)ed primary,2N− 1 = the number of digital states generated by thedisplay driver,kg,r= the system (g)ain coefficient for the (r)ed primary,ko,r= the system (o)ffset coefficient for the (r)edprimary, andγ = the system gamma coefficient.Similar expressions can be derived for the green and blueprimaries.6.3.1 Following the procedures given in Test MethodE1336, the spectroradiometer will measure the spectral radi-ance (Lλ) of an extended diffuse source, such as a VDU. Thespectral radiance is related to the spectral exitance as follows:Lλ5Mλπ(2)6.3.2 The radiance for each primary can be described asfollows:Lλ,r5 RLλ,r,max, Lλ,g5 GLλ,g,max, Lλ,b5 BLλ,b,maxThe scalars R, G, and B can be thought of as the displaytristimulus values. From Test Method E1336, we obtain therelationship between the measured spectral radiance and theCIE tristimulus values, in luminance units as follows:Xr5 683 *360830Lλ,rx¯λdλ 5 683R *360830Lλ,r,maxx¯λdλ (3)Yr5 683 *360830Lλ,ry¯λdλ 5 683R *360830Lλ,r,maxy¯λdλZr5 683 *360830Lλ,rz¯λdλ 5 683R *360830Lλ,r,maxz¯λdλ6.3.3 The linear superposition of the red, green, and bluetristimulus values yield the following:X 5 683 *360830~Lλ,r1Lλ,g1Lλ,b!x¯λdλ (4)5RXr,max1GXg,max1BXb,maxY 5 683 *360830~Lλ,r1Lλ,g1Lλ,b! y¯λdλ5RYr,max1GYg,max1BYb,maxZ 5 683 *360830~Lλ,r1Lλ,g1Lλ,b!z¯λdλ5RZr,max1GZg,max1BZb,maxIn matrix notation, these equations can be reduced to thefollowing:FXYZG5FXr,maxXg,maxXb,maxYr,maxYg,maxYb,maxZr,maxZg,maxZb,maxGFRGBG(5)where R, G, and B are defined as follows:R 5FmaxHkg,rSdr2n2 1D1ko,r,0JGγ(6)G 5FmaxHkg,gSdg2n2 1D1ko,g,0JGγB 5FmaxHkg,bSdb2n2 1D1ko,b,0JGγBeing linear, Eq 5 can be solved for R, G, B. Thus theinverse is given, in matrix notation, as follows:FRGBG5FXr,maxXg,maxXb,maxYr,maxYg,maxYb,maxZr,maxZg,maxZb,maxG21FXYZG(7)and in like manner,dr5S2n2 1kg,rD~R1γ2 ko,r! for 0# R #1 (8)dg5S2n2 1kg,gD~G1γ2 ko,g! for 0# G #1db5S2n2 1kg,bD~B1γ2 ko,b! for 0# B #17. Procedure7.1 Analytical Method:7.1.1 Once the display unit is warmed up and stabilized, it isnecessary to display the test patches over a constant neutralbackground of approximately 18 % of the maximum lumi-nance. Measure the color of the patches following the proce-dures contained in Test Method E1336 or Practice E1455. Thecalculated or measured tristimulus values are used to estimatethe optimum set of values for the model parameters and thecoefficients of the XYZ to RGB conversion matrix. The patchesshould be as small as practical and distributed in a square orE1682 − 08 (2013)3hexagonal pattern. Readings from each of the patches will beaveraged together to constitute a measurement. Display thefollowing sets of patches and measure with at least five neutralpatches, (dr=dg=db) with DAC settings of 32, 96, 128, 192,and 255, the three primaries at maximum DAC setting (255 foreight-bit display drivers). An alternate