Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
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TXTL~
Three Direction Measurement For Characterization
Of a Surface Containing Metallic Particles
BACK~ROUND OF THE INVE~TION
5In the ~anufacture of pigmented f inishes one
rarely if ever achieves a ~atisfactory color match
versus ~ color standard without an adjustment process
known as shading~ Shading usually involves a
rela~ively minor but cri tical ~anipulation of the
10 formula pigment composition, correcting for the
cumul~tive effects of manu~acturing variables on
pigment dispersions.
Traditionally, the shading process has been
c:arried out by highly skilled and tr~ined personnel
15 who require extensiv~ on-the-job experience to
achieve proficiency in their craft. Since visual
shading at best is an art, effective adrninistration
of the process was difficult.
In more recent years, such visual shading
20 has been supplemented by the use of apparatuses for
instrumentally characterizing ~ paint or pigment
composi tion . Colorimeters and spectropho~ometers are
well-known in the art and ~re used to measure certain
optical properties of various paint films which have
2S been c3ated over test panels. A typical
spectrophotometer provides for the measurement of the
amount of light reflected at varying light wavelength
in the visible spectrum by a painted panel that is
held at a given angle relative to the di rection of an
incident source of light. The reflectance factor of
the paint en abl es pa i nt chem i s ts to cal cul at e col or
values by which to characteri~e variou~ paint
colors. For a paint containing no light-reflecting
flakes or platelets (i.e., non-met~llic paints), the
reflectance factor will not vary with the angle of
,,
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the panel relative to the direction of incident light
except at the gloss (specular ) ~ngle. Consequently,
a single cpectrophota~etric reading at any specif ied
an~le will produce a reflectance value by which to
5 accur ately characteri ze the pai nt .
EIowever, the paint industry of ten util izes
light reflecting flakes in pain~s (i.e., met~llic
paints) ~o obtain pleasing aesthetic effects~ Paints
containing Iight-reflecting flakes of such materials
10 as al~nin~o, bronze, ~oated mica and the like are
charac~erized by a ~two-tone" or ~flip-flop" effect
whereby the apparent o~lor of ~he paint changes at
different viewing ~ngles. This effect is due to the
orientation of the flakes in the paint film. 5ince
15 the e:olor of such met~llic paints will apparently
vary as a func:tion of the angle of ill~nination and
viewing, a s~ngle spectropho~canetric reading is
inadequate to ~ccurately characterize the pain~.
Although measurement studies have chown th~t visual
color differences existing between two metallic
paints were detectable at an infinite n~nber of
angles, it is obvlous that practical reasons preclude
the collection of reflectance factors for an infinite
number of vi.ewing angles. E~owever, previous studies
have also indicated tha~ measurement of the optical
properties of a metallic paint at only two specified
angles can provide useful characterization. See, for
example, U.S. Patent No. 3,690,771, issued
September 12, 1972 to Armstrong, Jr., Edwards, Laird,
~nd Vining.
The present invention relates to the
discovery that unexpectedly improved op~i~al
characterization of metallic paint~ results when
measure~ents are taken at three specif ied angles .
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S UMM;~ R Y OF T ~ I NVE NT I O~
-
There is provided by the present invention
an improved method for instr~nentally characterizing
the optical properties of a surface containing
5 metallic particles such as paint-containing metallic
par t i cl es or f l akes by us i ng mul ti angul ar
spectrophotometri~ or colorimetric measurelT ents to
derive color constarl~s for the paint, wherein th
improvement comprises using three multiangular
10 measurements.
~RIEF D~S CRIPrrION OF DRA~INGS
FIGo 1 is a graphic representation of the
angul ar dependence of tristimulus v~lues.
FIG. 2 is a schematic represen~ation of a
preferred spectrophotometric system embodying the
~ethod of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
_ .
In optically characterizing surfaces
containing metallic particles such as ~etallic paints
20 and f ilms t it was recognized that directional
reflectance had to be considered~ Metallic paints
contain light-reflecting flakes or platelets of such
materlal as al~ninum, bronze, coated mica and the
like. These flakes or platelets function much like
25 little mirrors, reflecting light directionally rather
than in a diffuse manner. The directional
reflectance characteristic of ~ metallic paint f ilm
result~ in a phencmenon known as goniochr~xnatism,
which is def ined as the variation in ~:olor of a paint
30 film as a function of the directions of illumination
~nd viewing. This phenomenon is also sometimes
descri~ed as ~two-tone", ~flop", ~flip-flop~,
" flash", " side-tone", etc . In sum, the color of a
~net all ic pai nt will appe ar d i f ferent at d i f f er ent
35 viewing angles.
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To account for this directional or angular -
reflectance, i.e, goniochromatism,
spectrophotcmetrically determined reflec~ance factors
must be taken multiangularly. The reflectance factor
5 of a paint f ilm is the ratio of the light flux
reflected from the film sample to the light flux
reflected frcm a perfect reflecting diffuser when the
sample and perfect diffus er are identically
irradiated. A per~ect white reflector has a value of
1. A perfect black nonreflector has a value of 0.
The reflectance factors are used to
calculate color descriptor values used to specify
color and color difference. The tristimulus values
(X, Y, Z) of a color are calculated ~y combining the
15 reflectance factor data (R) with data on the
sensitivity of the human eye ~x, y, z~ and the
irradiance o~ ~ light source ~E) all as f unctions of
wavelength (~) in the visible spectrum. The def ining
equations f or t r i s timul us val ues 2~r e:
X =360J R (~.) E (A~ x (~) dA
y I R (~1 E (~.) y ~A) d~
z =3~;0~ R (~.) E ~) æ (~ ) dA
25 ~he tristimulus values can be used to ca:Lculate color
descriptors which relate to visual perception o~
color and color difference. One of many sets of
descriptors which can be used are the CIELAB
perceptual color scales recommended by the
30 International Commission on Illumination
l"Recommendations on Uniform Color Spaces, Color
Diff erence Equations , Psychanetric Color Terms",
Supplement No. 2 To CIE Publication No. 15 (El.3.1)
1971/CTtl.3) 1978. Bureau Central De La CIE, 52,
35 Boulevard Malesherbes 750û8, Paris, France).
.
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Transformations of the tristimulus values
can be used to calculate perceptual color values
describing ligh~ness (I.*), redness/gr eenness (a~),
yell~ness/blueness (b*), saturation ~C) or hue (H).
5 A color can be canpletely descri~ed by a set of L, a,
b or L, C, ~ values. The following equations which
have been specif ied by the I nternational Commi ttee on
Ill~nination relate the tristimulus values to I.*, a~
and b*
L* - 116 (Y/Yc) 1/3 -16
a* s ~oo ~ (x/xo)l/3_(y/yo)lJ3
b* ~ 20~ ~ (y/yo)l/3-(z/zo)l/
where
Xo, Yo and Zo are the tristimulus values of
15 the perfect white for a given illuminant;
X, Y and Z are the tristimulus values for
the color.
The s at uration (C) and hue (~) descriptors
are related to the a* and b* values as follows:
C _ (a*2 + b*2~1/2
~ - ~an 1 (b~/a~1
Of~en it i5 necessary to compare a color
such ~s a sample batch of paint to a standard color
and determine the difference and then adjust ~he
~5 sample with appropriate additives to bring the sample
within tolerance values of the standard. The
difference in col~r between 8 color standard and a
batch sample is described as f ollows:
~L* = L* (batchl - L* (standard)
aa* = a* (batch) - a* (standard)
ab* = b* (batch) - b* (standard~
The resultant values agree with the visual
assessments of differences in lightness t~L*),
redness/greenness (aa*3 and yellowness~blueness (ab*~.
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Further discussion will e~ploy the
tristimulus values (X, Y, Z) and perceptual color
values (L*, a*, b*, C, ~) to quantify the influence
of changing conditions of illumination and viewing on
measurement of goniochromatic color. The specific
color descriptors employed are only one of many
possible choices o transformations of tristimulus
values which could be employed in this task.
The tristimulus values, anfl hence the L*,
a*, b* values as well, for a metallic paint vary in a
regular manner with regular variation in the angle of
viewing the paint film. In FIG. 1, the directional
color behavior of a solution lacquer medium red
metallic color is shown. The sample was prepared by
conventional air atomized spray onto an aluminum
substrate followed by a 155C bake fnr 30 minutes.
Reflectance factor measurements relative to a
standard white (BaS~4) were made in six sets of
irradiation and viewing directions using a reflection
spectrophotometer specif ically designed to measure
reflection properties with Yariable measurement
geometry. This instrument is esser.tially a standard
spectrophotometer consist;ng of a lightsource,
monochrometer, variable measurement geometry module,
light detector and associated control and readout
elect ron i cs . The reflectance factor for each
measurement geometry was used to calculate
tristimulus val ues as previously described. In
FIG. 1, the angular dependence of tristimulus values,
Xt Y and Z is illustrated. The angle is measured
from the specular (or ~mirr2r~) angle.
The val~es used for FIG. 1 are as follows:
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Meas ur ement
Angle Fran
the Specular
A~ 'C ' l T r i s t i m u 1. us V al ue s
X Y
67.6 57.2 46.
~1.2 17.3 13.3
~5 12.9 10.3 7.7
8~4 6.7 4.
7~ 5.0 3.9 2.6
3.6 2.8 1.9
An al ys i s of the an gu 1 ar de pe n de n ce pl ot of
FIG. 1 reveals three things:
(1) Tristimulus values are not constant with
angle variatiQn, hence values frcxn multiple angle
measurements are necessary to accurately describe
the color behavior of the sample;
(23 The plots are monotonically decreasing
funct;ons as the angle from specular increases,
therefore a simple mathematical model should
describe the curve; and
(3) The plots are curYed such that the
~athematical model should probably be one higher
than of the ~irst ordee (linear).
Similar angular dependence plots have been
25 obtained for a wide variety of metallic colors and
all show si~ilar results. The significance of these
results is that they define the metallic color
characteri zation and specif ication problem. Since
all metallic colors show similar curved,
monotomically decreasing tristimulus values as
f unctions of the measurement di rection f rom the
specular angle, there is A systematic angular color
behavior for which ~ simple measurement strategy can
be developed. Multiple measurements will be required
35 to adequately characterize this behavior.
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Since L~, a*, and b~ are the color values
usually employed to characterize the color of paint
f ilms, it is of prime importance ~Lo determine the
number of measuremen~s neecled to satisfactorily
5 characteri ze the angular dependence of these values .
Plots of all three variables are adequately similar,
~o ~hat it is reasonable to ass~ne that a
mathematical characterization that fit a plot of the
angular dependence of L~ would also fit a plot of the
10 angular dependence of a* and b*.
The optimum f it of various mathematical
models to a lightness (L*) angular dependence curve
is of the seoond order, which requires three
measurements.
This can be shown by considering the mean
residual error in L* value at six sets of ~easuring
directions as predicted by various prediction models
employing subsets of the six measuring directions.
The reflectance factors in 6 measurement
geometries for 37 solution lacquer metallic colors
was de~ermined and the lightness values, L~, for
these geometries calculated. The samples were
prepared and measured as previously described. The
objective is to define a metallic ~olor
characterizatiQn system which provides optimum
informat on for minimum effort. This is done by
considering whether subsets of the ~ measurement
geometry data are adequate to predict the color
lightness behavior at all 6 geometries. A linear
metallic color chara~terization model are developed
based on a first order equation. S~ch equations for
the angular dependence of metallic lightness have the
form:
~L al + a2~
where L* is lig'ntness, ~ is angle from the specular
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ansle and al and a2 are constants specif ic to
each color which are fit frcm measurements uslng at
least two different measurement directions.
Similarly, a q~adratic (second order~ equation is
5 used havi ng the f orm:
*L = al + a2 ~ + a3~
where the variables are the same as in the linear
example with the addition of another constant a3.
A minim~n of three measurement directions are now
required. Table I indicates the mean sum o~ squares
residual for 6 measurement geometries with 37
metallic colors with several metallic
characteri zation models. When the mean sum at
squares residual is low, a model which describes the
color dependence of metallic color on measurement
direction has been formed.
TABLE
Influence of measurement direction
selection on metallic color lightness prediction.
Number of Mean Sum of Squares
Model ~easurement Residual for 6 Measurement
(OrderL Directions_ Directions.
Linear (1) 2 529.3
Quadratic (2) 3 12.5
2 5 n 4
~j 8.5
Addition of just one more measurement, taken
nearer to the specular angle, decreases the sum of
the squares error of prediction from 529.3 ~o 12.5 in
L* units. This indicates that the metallic color
lightness behavior at any direc~ion can be well
predicted from measureme~ts at 3 selected directions.
~ igher accuracy can be achieved by adding
more measure~ent angles or by going to a higher order
3~ equation with more measurement angles, but no such
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move will lead to the dramatic and ~urprisin~
increase in accuracy at~ainable by u~ ing a ~econd
order m~del incorporating ~ust on~ mOe angle
measurement than in the ~-angle ~ystem. Th~c is,
5 three properly selected measurement diect.ions are ~n
optimized ~election ~o give m~xim~n information on
metallic color fol minim~n measurement efort. The
example da~a ~escribe the optir~i ~atiion results for
lightness values. Si~ilar results are o~tained for
10 tristimulus value~ ~X, Y, Z~, perceptual ccllor ~ralues
S~*? b~ , El) f color difference values 5~L*t ~a*l
~b*) or other transformation fxom tristimulus ~alues.
In oollecting dat~ on the opti csl
characterlzation of ~ paint film, e ~rariety of
15 measur~nent techni~ues can be used. One technique is
object modulated reflectance (O~) wherein the light
source and viewer or detector reference point are
f ixed and the object position i5 varied. This
techni~ue is exemplified in U.~. Patent No.
20 .3,712,745, issued January 23, lg73 to Armstrong, Jr.,
E dwar ds, and Yi ni ng.
Two other techniques are Detector P~odulated
Reflectance IDMR3 and Illuminant Modulated
Re~lectance (IMR). In ~ he detector is varied
while the light source and object are fixed. And in
IM~r ~he lll~inant or light source i~ varied, while
detector and object remain ~ixed.
As discussed earlier, analysis o~ data
tcollected by use of DMR) ~ndic~ted that the optimum
30 set of ~neasurements to characterize the
goniochrosnati~ effect in metallic paint f ilms
~onsists of measurements Saken at three angles: tl)
near the ~pecular angle; (2) ~bout 4S fraTI the
ular angle; and (3) f ar f rom the specular angle .
35 In gener~l, f~r a ~yp~cal metallic color~ the angular
~0
853
11
dDpendence of L*, C, H values is of the second order
for any set of anqles varying regularly from near
specular to far from specular/ whether measured by
OMR, DMR, IMR or some co~bination of these~ Hence,
5 whether OMR, DMR, or IMR is utili zed, three
measurements can optimally characterize the L*, ~, H
angular dependence curves.
FIG. ~ represents a preferred embodiment of
the invention wherein DMR i5 utilized. The incident
10 light source is positioned a'c an angle of 45
relative to the paint f ilm. Three detectors are
positioned in order to take optical property
measurements at three different angles (as measured
f rom the specular angle):
15 (1~ Detector No. 1 - 15 (near spec~lar);
(2) Detector No. 2 - 45 (perpendicular to the
paint f ilm surface); and
(3) Detector No. 3 - 110D (far from specular).
While the same angles may not be chosen for
20 a syste}n utilizing IMR or. O~, suitable angles ccsuld
be easily determined by one skilled in the art.
The improved method of this invention can be
used to characterize not only metallic pain~ films
but any surface containing metallic particles, such
25 as plastics containing reflective metallic flakes.
The improved method is part~cularly usef ul in shading
paint wherein the L*, ~ and b* values are determined
for a standard. ~hen a batch of pain~ is
manuactured according to a given formula; a painted
panel of the batch is made and the L*, a~ and b~
values are determined. Often the batch of paint,
even if carefully made, does not match the standard
because of variations in pigments and color drift of
pigment dispersions. The ~L*, ~a* and ~b* values of
the batch are calculated and if outside ~f an
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acceptable l:olerance value, calculatlons are made for
the addi~ion of pigments in the form of mill bases
and the mill bases added to ~che batch and a second
panel prepared and values are measured as above. The
5 process is repeated until there is ~n acce~table
color match ~etween the standard and the batch of
pai nt .
