Note: Descriptions are shown in the official language in which they were submitted.
' ` 1169140
¦ Title of the Invention
AND ~PPARATUS FOR MEASURING A~D
CO~TROLLING THE COLOR OF A MOVING WE~
Field of the Invention ~.
5 ~ Thi~ invention relates to a method and apparatus
for meaqur~ng and controlling color and, especially, to
. a method and apparatus for measuring and controlling the
color of a moving web.
Backg~ound of the IDvention
In general, systems o~ the prior art ~or controlling
the dyeing o a moving web operate by measuring the tristimu-
lus value~ X, Y and Z o~ l~ght réflected from a moving por-
tion o~ the web. The tristimulus values, which are roughly
¦ equiv~lent to the "red," "green" and "blue" ComponentJ, ~.
15 1 respectively, o the reflccted light, are either measured
slmultaneously by different detectors, as in De Rcmlgis
¦ U. S. Patent No. 3,936,189, or successively using a fllter
¦ wheel or the like as in Lodzinski U. S. Patent No. 4,019,819,
The trist~mu1us values X, Y and Z are either used directly
20 ¦ or control purposes or are ~irst converted to other coordin-
2tes such as Hunter coordinates L, a and b.
. ~
While three- or our-filter colorimeters o the type
do3cribcd above are common ln the art and are adoquate or
., I .
. ~ -2-
r/, '
69140
! ordinary control applications, they suffer serious drawbacks.
Fisat, tho X, Y and Z tri~tlmulus outputs are only ind~ica-
tive of the perceived color of the web under the illuminant
u~ed in the colorimeter. A color "match" obtained in ter~
of tristimulu~ values using a standard illuminant aoes not
neces3arily lndicate a match with an illuminant having a
- dif~erent spectral composition, and, in general, it i~
impossible to predict the color properties of a mater~al
with a given illuminant if only it~ tristimulus values X,
10l Y and Z are known. Further, if the actual spectral curves
of the illuminant or detector used in the colorimeter differ
from those for which the filters were designed, the tristlmu-
lu~ values obtained will not necessarily even indicatc the
color properties of the material under a standard illum~nant.
While LodzinsXi does suggest, as an alternative, using a
relatively large number of narrow-band filters so as to
approximate an abridged spectrophotometer, he suggests no
practical implementation of this proposal in an on-line system.
Another defect of control ~ystems of the prlor art
arises from the nonlinearLty of the relationship betwecn
the tristimulus values X, Y and Z and the dye concentratlons
to be controlled. While this nonlinearity is relatively
insignificant at low dye concentrations, it increases wLth
dye concentration so that, when relatively saturated color3
are being sought, the nonlinearity is substantial. As a
result, in practical systems, the relationship between X, Y
and Z and the dye concentrations must be linearized about
~ome nominal setpoint to maXe the computation tractable.
_3_
1 ~69 ~40
This need for linearization is obviously disadvantageou~,
since not only does the operating point vary about the
setpoint, but the setpoint itself is often changed, necessi-
tating a recomputation of the linearized equation.
Mccarty ~. S. Patent No. 3,601,589 disclose~ a
system for selecting pigments to match a given surface
coating in which an in~tial pigment formulation is generated
in advance of actual mixing by selecting those concentrations
which minimize the total square error between the measured
reflectance of the coating being matched and the computed
reflectancc of the pigment formulation. ~owever, the actual
mixing proccss itself is controlled by sampling the mixture
with a colorimeter and using L, a and b coordin~tes computed
from the colorimeter output to correct the ~nitial pigment ~ -
formulation.
Summa_y_of the Inventio_
One object of my invention is to provide a color
measurement and control system which insures a color match
under an arbitrary illuminant.
Anothcr object of my invention is to provido a
color measurement and control system which does not roquire
matching of the spcctral curvcs of its variou~ optical com-
ponents .
116g~0 '
Still another object of my invention is to provide
a color measurement and control system which ~s relatively
insensitive to changes in opcrating point.
A further object of my invention is to provide a
5 color measurement and control system which permits the
independent control of four or more dyes.
Other and further objects will be apparent from
tho following description.
In one aspect, my invention contemplates apparatus
10 for measuring the optical reflectance of a surface such
as that of a moviny web in which a first predetermined
optical path couples a portion of the surface to a light
sourcc of predetermined spectral content whlle a second
predetermined optical path couples the same surface portion
15 to a detactor. Disposed in at least one of the paths i5
a bandpass filter hDving a passband varying subitantially
continuously through the cptical spectrum with the point of
incidence of the optical path on the filter. Varying the
point of incidence of the optical path on the filter produce~
20 an output from the datcctor which scans tho optical spcctrum. c
Preferably, the resolution of the optical system ~n such as
to permit successive dotector outputs representing about 180
differcnt wavolengths oach spaced about 1.7 nanometers apDrt.
Preferably the continuous filter is a circular variable filtor
25 which inters~cts thc optical path at an off-center location
1169140
and which is rotated to scan periodically the optical
spectrum.
In another aspect, my invention contemplates an '~
on-linc system for controlling the application of a
plurality of colorants to a continuously formed material
in which the reflectance of a portion of the material
containing the colorants is measured at a plurality of
wavelengths. The flow of the colorants to the material is
then adjusted so as to minimi7e the sum of the squares of the
deviations of the measured reflectances from predetermined
desired réflectances. Preferably the reflectance measurements
of the material are obtained by using a circular variable
; bandpass filter in the manner described in the preceding
paragraph.
lS Brief Descri~tion of the Drawinqs
In the accompanying drawings to which reference
i3 made in the instant specification and in wh~ch like
reference characters are used to indicate like parts in
the various views:
FIGURE 1 is a sid~ elevation, with parts shown
in section, of the sensing head of my color measurement
and control system.
~ 1~9140
.:
FIGURE 2 is an o~lique view of the circular variable
filter used in the head shown in FIGURE l.
FIGURE 3 is a fragmentary section of the head shown
in FIGURE l, takcn along linc 3-3 thereof.
FIGURE 4 is a schematic view of a tristimulus color
measurement system incorporating the head shown in FIGURE l.
FIGURE 5 is a flowchart of a program for controlling
the operation of the system shown in FIGURE 4.
FIGURE 6 is a schematie view of a eolor control
10 system incorporating the head shown in FIGURE 1.
FIGURES 7a and7b are a flowchart of a program for
controlling the operation of the system shown in FIGURE 6.
FIGURE 8 is a graph illustrating the matching of the
individual dye absorption spectra to the ~eb reflectance spec-
15 trum measured by the system shown in FIGURE 6.
Descri~tion of the Preferred Embodiments
Referring now to thc drawings, the sensor portion
of my syqtem, indicatcd generally by tho referenee
character lO, is adapted to measure the color of a web 12
20 of paper or the like. The sonsor portion 10 includes an C
optical sensing head, indicatcd generally by the reference
character 14, disposcd above thc web 12 and an optical shoo,
indicated generally by the reference character 16, disposed
--7--
1169~40
,
below the head. Any suitable me2ns (not ~hown) may be
provided for mounting the head and shoe for movement out of
associated relationship with the web 12.
Thc optical sensing head 14 includes a housing 18
to which a top plate 20 is secured by any suitable means
such as by screws 22 into sealing engagement with a gasket
24 extending around the top of the housing. Top plate 20
carries a mounting stud 26 adapted to be secured to tha
head support ~not shown). I provide the housing 18 with
respective access openings 28 and 30 normally closed by
covers 32 and 34 which cngage gaskets 36 to seal the access
openings 28 and 30.
The base 38 of tho housing 18 i8 provided with
an opening 40 over which a window 42 is secured. For example,
a framo 44 carrying the window is adapted to be threaded
onto a flange on the bottom 38 around opening 40 and into
sealing engagement with a gasket 46.
The scnsing hcad 14 includcs a light-integrating
spherc, indicated generally by the roference character 48,
located inside housing 18 and made up of a lowcr half 50,
formed with an opening 52 which registers with the wlndow
42, and with an upper half 54 secured in operative rolation-
ship with the lowor half in any suitablo manner.
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1 ~69 140
I secure rospective bulb-mounting tubes 56 over
openings in the upper sphere half 54. Caps 58 assembled
on the tubes 56 hold bulbs 60 and 62 and their associated
mounts in position in the tubes 56 to direct light into
thc interior of the sphere 48. I provide the lower sphare
half 50 with a pair of light deflectors 64 and 66 and pro-
vide the upper sphere half 54 with light deflectors 68 and
70 for ensuring proper distribution of light from the sources
60 and 62 within the sphere while at the same time preventing
the detector to be described hereinbelow, from being directly
illuminated by the sources 60 and 62. While any suitable
sources may be employed, preferably I employ two 50-watt
tungsten-filament quartz-iodine lamps supplied by a constant-
current xource for the lamps 60 and 62.
I form an opening 72 in the upper sphere half 54
through which reflected light from a spot portion of the
web 12 ix directed onto a detector. More specifically, a
lens 76 disposed inside a tube 7~, the lower end of which
adjoins the opening 72, focuses light from the spot portion
20 of the web 12 onto 3 pho~odetector 78 positioned at the
upper end of the tubc 74. In~erposed betwcen thc detector
7a and the upper end of the tube 74 i~ a circular variable
filter indicated gcncrally by thc refercncc numeral 30.
As shown in FIGURE 2, filter 80 comprises a substratu 82
t~9~
.:~
having an interference filter coating 84 on one side thereof.
In a manner known in the art, the thickness of the inter-
ference filter coating 84 that is applied to the substrate
82 varies with angular displacement about the axis of the
filter 80. As a result, there is a corresponding angul~r
dependence of the center wavelength that is passed by any
particular angular segment of the filter coating 84. Thus,
in the embodiment shown, the th;cXness to of the thinnest,
or 0 , coating segment is such as to pass a wavelength of
about 400 nanometers, while the thickness of the 360 segment
(not shown in FIGURE 2) is such as to pass a wavelength of
about 700 nanometers. ~etween these two extremes, the _,
thickness - and hence passband wavelength - vary linearly
with angular displacement, the thickness tl80 of the 180
scgment, for example, being such as to pass a wavelength
of about 550 nanometers.
Filter 80 is mounted on a shat 86 of a suitable
motor such as a stepper motor 88 which rotates the filter
80 to vary the wavelength transmittcd to the detector 78.
A posltion encodcr 90 coupled to the motor shaft 86 provides
a parallel digital output L on a line or channel 108
indicating the particular two-degree angular segment of the
filter 80 that intercepts the optical axis. Prcferably, to
limit the circumferential extent of the f~lter 80 that is
~r~
1 ~691~0
.
"seen" by the detector 78 at any particular instant, an
optical slit-for~ing member 92 is disposed between the
filter 80 and detector 78. Preferably the width d of the
slit is such as to subtend about 2 at its average spacing
r from the axis of the filter 80.
Shoe 16, which supports the web 12 as it moves
past the head 14, comprises a housing 104 within which i8
disposed a rotatable block 102. Normally, during the color
measurement or control phase of operation, block 102 ls 80
oriented within housing 104 as to position a suitable stand-
ard reflecting surface 94 beneath the web 12. Block 102
also supports three additional rcflecting surfaces 96, 98 _ .
and 100 which are rotated into position beneath the web 12
during calibration. These surfaces 96, g8 and 100 may com-
prise, for example, a standard "white" reflecting surface,
a standard "black" reflecting surface and an additional
reflecting surface for calibrating the response of the
detector 78.
Referring now to FIGURE 4, I show a system,
indicated generally by thc refercnce numeral 105, in which
scanning head 14 supplies inputs to a computer whlch
generates and displays the X, Y and Z tristimulus values
of thc light reflcctad from the web 12. More particularly,
a digital computer 1~0 of any suitable type known to the
1 169 :~4~
.
art, such as a genoral purpose microcomputer~ receives
one data input from line 108, which carrics thc signal L
indicating the angular position of the filter 80. A line
106 from the head 14, carrying the detector output IREFL
which is proportional to the reflected light intensity,
feeds an additional data input to computer 110 through an
analog-to-digital converter ~ADC) 112. Computer 110 provides
a suitable digital output to an X display 114, a Y display
116 and a Z display 118. Displays 114, 116 and 118 may be
of any suitable type known to the art such as, for example,
segmental digital displays, strip chart recorders, or thc
like. In addition, the X, Y and Z outputs appear on respec-
tiva lines 113, 115 and 117, whlch may provide inputs to a
suitable control system (not shown) for regulatlng the
application of dyes to the web.
Referring now to ~IGURE 5, I show a program which
may bc uscd by the computer 110 to generate tristimulus
values X, Y and Z from the outputs L and IREFL of the
scanning head 14. The program shown may typically be a sub-
routine that is repeatedly entercd during the mcasuromentphase of operation between poriods of calibration. More
particularly, after tho subroutine i3 entered at block 120,
an index K representing the number of completa revolutions
of the filter 80 por averaging period is initializcd at zcro
~block 122). Aftar the tristimulus values X, Y and Z are
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1 ~69 1'10
:~
also initialized at zero tblock 124), the index K i8
incremented by 1 (block 126) while a second index I, indicat-
ing the particular 2 angular segment of the filter 80, is
initialized at 7.ero (block 128).
S The index I is then incremented by 1 (block 130),
and the position encoder signal L is interrogated to
determine if it s equal to the index I (blocks 132 and
134), the motor 88 being either run continuously or stepped.
2 each traverse of blocks 132 and 134. The subroutine
waits nntil the position signal L matches the index I and
then interrogates the detector output IREFL (block 136).
The subroutine then uses the signal REFL to update
the tristimulus values X, Y and Z by adding to the pre-
viously stored value3 quantitie3 proportional to the
product of the detector output IREFL and tho particular
tristimulus value of the wavelength corresponding to
the index I (blocks 138, 140 and 142). The subroutine
continues along blocks 130 to 142 for each value'of tho
index I until the index reaches 180, at which point the
subroutine leaves the loop (block 144) and test~ whether
tha index K has reachod a predotermined value, in this ,^.
caso 10 (block 146). If the index K is less than 10, the
subroutine returns to block 126 where it incroments K by
1 and updato3 the tristimulus values X, Y and Z for another
revolution of the filter 80. This process is continued
until K reache3 10, at which ppint the subroutine feeds
the finally computed tristimulus values X, Y and Z to the
:l t69 1~0
displays 114, 116 and 118 (bloc~ 146). The subroutine then
returns (block 150) to the main program (not shown), which
typically may immediately re-entcr the subroutine shown
in FIGURE 5.
Referring now to FIGURE 6, I show an embodiment
of my invention in which the absorption spectra of the dyes . .
are fitted by the method of least squares to the measured
spectrum of the web to generate flow correction signals.
In this system, indicated generally by the reference numeral
152, I use a computer 54 which may be similar or identical
to the computer 110 shown in PIGURE 4. Computer 154 receives
the position signal L from the head 14 directly through a
suitable input port. An analog multiplex circuit 156
receiving the IREFL signal from head 14 as one analog input ~ -
provides a selected analog input to analog-to-digital con-
verter (ADC) 158 in accordance with an address signal pro-
vided by the computer 154. ADC 158 provides a multi-bit
digital output to an additional input port of computer 154.
Computer 154 provides flow control signals FCl,
FC2 and FC3 via respectivo channels 160, 162 and 164 to
digital-to-analog converters 166, 168 and 170. Converters
166, 168 and 170 control respective pumps 172, 174, and 176
controlling raspective dye lines 178, 180 and 182 leadlng
from die supplies 184, 186 and 188. Lines 178, 180 and 182
. .
-14-
1 169~0
., ,
feed a single spray head 190 which applies the dye from the
supplies 184, 186 and 188 to the web 12 moving past the
head 190. Head 190 is, of course, located upstream from
measuring head 14 to permit the head 14 to measure changes
effected by adding dye to the web 12. Respecti~e fl~w meters
192, 194 and 196 in dye lines 178, 180 and 182 provide
measured flow inputs E1, F2 and F3 to the analog multiplex
circuit 156 via respective lines 198, 200 and 202.
The re)ationship between the measured reflectance
Ri of the web 12 at a given wavelength ~ i and the
respective dye concentrat~ons cl, c2 and C3 as indicated
by the dyc flows Fl, F2 and F3 is closely approximated by
the followlng equation: ;
Ri ' Irefl/IOi
= ROi/eXP ~Xilcl + Xi2C2 + Xi3 C3 + ei)
where i is an index ranging from 1 to 180, Irefl ls the
measured intensity of reflected light from the web 12 a~
indicated by the ~ignal IREFL; Io~ is the previously
determined intensity of light incident on the same wob por-
tion at wavelength ~it Roi is the reflectance of theundyed sheet at wavclength ~ i ; Xil , Xi2 ~3
predetcrmined constants; and ei is a random ~arror term
reflecting such factors as deviations in actual undyed sheot
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.
1 169:~40
reflectance, deviations in actual aye strength or composition,
and the like.
Equation tl) may be restated in terms of
the following equation:
Yi = -ln (~i/ROi)
= Xilc1 + Xi2C2 + Xi3C3 + ei (2)
Equation (2) may be re-expressed in matrix notation as
follows:
Y = Xc + e (3)
10 wherc Y i8 a column vector with clemcnts Yl, Y2, ... Y180;
C i5 a column vector with elements el, e2, ... el80;
c is a column ve~ctor with elemcnts cl, c2, ci and
x i~ a 180 x 3 matrix with elements Xij .
Standard regression theory tells us that an
"estimatea" or "effective" dye conccntration vector c~,
that is, the quantity that minimizes the square crror
(Y - Xc~)'(Y - Xc) (4)
where ~Y - Xc)' is the transpose of (Y - Xc), i3
given by the expresRion
.. ,
-16-
I :1~169~40
. .
C ~ lx~x)~lx~Y ~s~
Or, more simply, the concentration vector Ce
can be expressed as
~ Ce ~ AY ~6)
5 1 where
~X'X)~ ~' ~7)
¦ In the system contemplated, the "effective~ dye
concentrations obtained in thia manner are compared with
1I previously determined desired concentrations to establlsh ,,
10 ~¦ concentration "errors" due to the factors mentioned above.
The re~pective actual dye concentratlons as ind$cated by
the dye flow meters are then offset by amounts equal to
¦ those concentration errors to generate corrected concen-
¦ trations of dyes to be applied to the web. These correctedlS , dye concentrations minimize the total square error between
¦ the measured reflectance spectrum and the des1red reflec-
¦ tance spectrum of the web.
~o see that this 18 the case, let u~ deflne cd as
! a three-dimensional column vector of the theoretical
zo I donirod dyo concnntrationn, ann~ming no orror voctor o
-17-
1 1 6 9 1 4 O
e as the quantity defined by the equation
~c = Ce ~ Cd t8)
and ck as the quantity defined by the equation
Ck = c - ~c (9)
where e, as stated before, represents the actual
dye concentrations corresponding to the dye flows
Pl, F2 and F3.
If we now change the actual dye coneentrations to
Ck, then the new value of Y is given by the exprsssion
10Yk = Xek + a tl0)
On the other hand, tho theoret~eal desired coneentrations
Cd would, assuming an error voctor e of zero,
result in a "desired" value of Y of
. Yd Xed tll)
' 15The difference, or error, between theso two
; quantitles is
Yk - Yd = XCk ~ e - XCd tl2) ~.
Applying equations t3), t8) and t9), this reduces to
Yk Yd Xe ~ e - Xee
20= Y - Xee tl3)
-18-
1 169 14~
,
where Y is the value obtained with the original actual
concentrations c. Since, however, we have already
minimized the square o the right-hand side of equation
(13) by our selection of Ce , we have minimized the square
of the "error" expression on the left side as well.
Referring now to FIGURES 7a and 7b, I shcw a
program for controlling the application of dye from
supplies 184, 186, 188 in accordance with the color of
the dyed web 12 as sensed by the head 14. LiXe the progra~
~hown in FIGURE 5, the program shown in FIGURES 7a and 7b
may typically be rcpcatedly entered as a subroutine between
successive calibrations of the system 152. After entry
at block 204, the subroutine initializes to zero an indax
~ indicatlng the numbcr of revolutions of the filter 80
lS (blocX 206), as well as the quantities C~l), C~2), and
C~3) corresponding to the components of the "effective" dye
concentration vector Ce ~blocX 2Q8). The subroutine then
increments K by 1 ~blocX 210) and initializes the index I,
corrosponding to the index i in equations ~1) to ~13)
20 ~blocX 212). Next, tho subroutinQ 'ncrements the index ~,
I by 1 ~blocX 214) and waits ~blocks 216 and 218) until
the position signal L from the head 14 matches the indcx I.
When this occurs, thc subroutine suitably addrcsscs the
Iq , .
1 169 1'10
multiplex ci~cuit 15G to input the measured light
intensity IREFL (block 220).
After it has obtained the reflected light
intensity signal IREFL, the subroutine divides this
5 quantity by a previously stored value IO(I) (corresponding
to Ioi) indicating the incident light intensity at that
wavelength to generate a signal R(I) (corresponding to Ri)
indlcating the reflectance of the web 12 at the wavelength
indicated by the index I (block 222). The subroutine
10 divides the quantity R(I) by a previously stored quantity
RO(I) ~corresponding to Roi) indicating the reflectance of
an undyed web portion at that wavelength and takes the nega- _,
tive logaritl~ of the quotient to obtain a quantity Y~II
~corresponding to Yi) that varles linearly with dye concen-
tration (block 224). The subroutine then enters a loop
~blocXs 226 to 232) in which it revises the previou~ly
stored quantities C(l), C~2) and C~3) by adding to the~
terms proportional to the computed quantity Y~I). In
block 230, the quantity A(I,J) corresponds to tho element
20 Aij of the least-square optimization matrix dafinod in
equatlon ~7). c
The subroutine next interrogates I to determino
whether it has reachcd 180 and, if not, returns to block 214
to obtain and proccss the measurcd light intensity IREFL at
1 1691~
the next wavelength I, the subroutine reiterating
blocks 214 to 234 for each value of the index I. When
this loop has been traversed for all values of the $ndex
up to 180, the subroutine leaves the loop (blocX 234) and
interrogates the index K to determine whether it has
reached a predetermined quantity, for example 10 (block 236).
If not, the subroutine returns to block 210 and repeats
the éntire sequence (blocks 210 to 236~ for another revolu-
tion of the filter 80.
After a suitable averaging interval of ten
filter revolutions in this case (block 236), the
subroutine initializes a timer (not shown) internal to the
computer 154 to define a time interval for the control oper-
ation (block 238). During thi~ period, the subroutine
first genarates respective concentration error signals CEl,
CE2 and CE3 corresponding to the components of the error
vector ~c by subtracting from the respective estimated
concentrations C(l), C(2) and C(3) the quantities C01, C02
and C03 corresponding to the elements of the des$red concen-
tration vector cd (block 240). The subroutine then gener-
ates respective flow control signals FCl, FC2 and FC3 by
multiplying the concentration error signals CEl, CE2 and
CE3 by previously determined coefficient~ -Gl, -G2 and -G3
~block 242). After th$s, the subroutine generates a suitable
address signal to obtain the flow inputs Fl, F2 and F3
(block 244) and generates respective target flow values FlT~
1169~Q
F2~, and F3T by adding to the respective measured flow
signals Fl, F2 and F3 the respcctive flow correction
signals FCl, FC2 and FC3 ~block 246 ) .,
The subroutinc then entars a loop (blocks 248 to
254) in which it continually interrogates the measured flcw
values Pl, F2 and F3 and generates flow-control signals
FCl, FC2 and FC3 on the basis of the difference between
the measured flow values and the target flow values previously
generated. These continually recomputed correction signals
FCl, PC2, and FC3 are provided to the digital-to-analog con-
verters 166, 168 and 170 controlling the pumps 172, 174 and
176. ~t the end of the interval determined by the timer in _, .
block 238, at a point when t~le mcasured flow values Fl, F2
: and F3 have convcrged upon tar~et flow values FlT, F2T and
F3T, the ~ubroutine leaves the loop (block 254) and returns~block 256) to the program (not shown) calling the subroutine.
As mentioned above, typically the cubroutine shown in
EIGURES 7a and 7b is repeatedly re-entered between succes-
sive calibration periods of tho apparatu~ 152.
In the system shown in FIGURE 6, the flow
correction signals FCl, FC2 and FC3 are generated by fit-
ting the dye absorption spectra to thc measurcd wcb reflec-
tance spectrum to obtain the "cffectivc" dye concentrations
C(l), C(2) and C(3). Ilowever it will bc apparent to those
2,~ .
1 :169 1 ~ O
skilled in the art that the computational steps involved
are commutative and that one could alternatively compare
the measured rcflcct~nce spectrum with a desired spectrum
and then fit the dye absorption spectra to the error spes:-
5 trum thus obtained.
Referring now to FIGURE 8, I show a graph
illustrating the matching of the individual absorption
spectra of the dyes to the measured reflectance spectrum of
the dyed web 12. In FIGURE 8, the abscissa represents the
10 wavelength in nanometers while the ordinate represents the
negative of the logarithm of the measured reflectance, as it
i8 this quantity which i9, to a first approximation, linearly
dependent on the dye co ncentration. In FIGURE 8, curve
258 corresponds to thc measured reflectance of the dye of
lS dyed wob 12, while curve~ 260, 262 and 264 correspond re-
spectively to thc absorption spectra of the individual
dyes, weighted by the estimated dye concentrations C(l),
C ~2) and C (3) obtained by the subroutine shown in FIGURES
7a and 7b~, In thi~ graph, it i5 assumed that the reflect-
20 ancc of an undyed web is independent of the wavelength )~
80 that the spcctrum corrcspond~ng to the sum of the curves
260, 262 and 264 rcpresents a least-squarc approximation
of the actual reflectance curve 258.
Whilc thc system 152 shown in FIGURE 6 omploy~
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~ 69~
three dyeq, it should be emphasized that my sy~tem i~
¦ readlly adaptable to control the simultaneous application
of a greater number of dyes if more accurate color match~ng
I is desired. Indeed, one of the ~alient advantages of my
5 ' dye control ~ystem employing lea~t-square optimization is
¦I that it is not limited to only throe dyes as are systems
based on measurement of the tristimulus values X, Y and Z.
In my system, for example, a color mi6match occurring over
one portion of the visible spectrum can be correctea by
1~ I using an additional dye that is selectively ab~orptive in
that portion of the spectrum without affect~ng the color
match elsewhore.
It will be seen that I have accomplished the
¦ object~ of my invention. My color measurement and control
lS I system doe~ not require matching of the spectral curve~ of
I it~ various optlcal component~, and i9 relatively in~ensi-
¦l tive to changes in operating point. Finally, my system por-
mit~ the independent control of four or more dyes.
It will be understood that certain feature3 and
20 ¦ subcomblnations are of utillty and may be employed without
reference to other features and subcombination~. ~hi3 1~
' contemplated by and is within the scope of my clalms. It 18
further obvious that various changes may be made in dotalls
within the scope of my claims without departing fr~m
-24_
' 1.1~91~ .
~
the spirit of my invention. It ~B, therefore, to be
understood that my invention is not to be limited to the -.
~peclfic details shown and described.
t~a*ing thu~ described my invention what I s:laim 18:
