Document NNenZKrp4b97V69K1DbkJyapy
CONFIDENTIAL DU PONT TECHNICAL INFORMATION REPORT PE-67-1;
A STUDY OF SHADING PROCEDURES
FOR SATURATED COLORS (P-57)
BY: S. W. REMENTER - 10/10/67
DUPONT
MARSHALL LABORATORY LIBRARY
CONFIDENTIAL DU PORT TECHNICAL HTFOBMATIOH
REPORT HO. PE-ffM
E* I. DU POST HE IMOURS & ^wiuu, ao . FABRICS & FINISHES DEPARTMENT PRODUCTION DIVISION
DIVISIONAL PROCESS ENGINEERING GROUP COLOR OPERATIONS SECTION
A STUDY OF SHADING PROCEDURES FOR SATURATED COLORS
By: S. W. Repeater Date Issued: October 10, 1967
Project: P-57* General Technical Support
ABSTRACT An investigation of saturated colors is undertaken to supply more practical shading corrections by taking advantage of less stringent color tolerances for saturated color space.
DUP030002349
G
A STUDY OF SHADING PROCEDURES FOR SATURATED COLORS
TABLE OF COBTEKTS
MS
I. SUMMARY
Introduction ......... ...................................... ..............
1
Results ..........
1
Conclusions ......................................
2
Recommendations...................................
2
O II. DISCUSSIOR
Background ................................
3
Modified Instrumental Shading Technique ........... h
Weighting of (&&} and (Ah) Tolerances ..................
17
`>
DUP030002350
IHTR0DUCT10N
Visual color shading depends on a man's ability to distinguish color differences;, and his shading experience to correctly discern the colorants needed for an acceptable color match. Since the eye is the final arbitrator of all color matching 9 instrumental color definition should parallel visual definition as closely as possible. Recent and continuing studies describing the instrumental measurement of visually accepted color matches indicate that visual tolerances, though tight and nearly symmetrical about the standard for products of moderate saturation, become less strict as saturation increases. Visual tolerance zones become elongated in the saturation direction and offset from the standard center point*
Saturated colors pose special problems to instrumental shading that were not presented to the visual shader. Computerized vector shading attempts to provide a numerically perfect color match in all regions of color space. This need not be accomplished for a good visual match of saturated colors, and production efficiency is cut when it is attempted. Unrealistically large additions of colorant are often necessary to achieve instrumental color agreement when a fraction of this amount is needed for visual agreement.
This study was initiated to present possible methods of assimilating visual appraisal into instrumental shading of saturated colors.
RESULTS
1. A 780-line yellow and a 780-line red were successfully shaded by manual calculations involving only lightness and hue from on-load positions significantly more saturated than the product standard. The colorant additions (hits) calculated this way reduced the amount of colorant needed for shading to quantities closely approximating visual experience. Proper on-load positioning is important for the successful operation of this method. Conventional vectors should be used when the batch is not sufficiently saturated with respect to standard. The hits made in this manner are termed two-dimensional or planar hits.
2. Readings were encountered for which no solutions were obtainable because no combination of colorant gave the needed prescribed movement.
3. Ho successful shading technique that would decrease hit size was found for saturated oranges.
h. Hits calculated by analog computer could be reduced in size by removing colorants with high shading concentrations that provided vector movement approximated by another colorant from the shading scheme* Under these circumstances the analog computer gave hits very similar to those calcu lated manually, if the vector card were modified to show only the lightness and hue effects of the remaining colorants.
5. The planar hits without redundant colorants did not always provide better hits than with these colorants since maneuverability (the vector schemers ability to provide shading corrections for any on-load position) was sometimes hampered greatly.
DUP030002351
CQHCKJSI0H3 1. Specific planar functions numerically describing color differences by
incorporating only lightness and hue may be used in specialized cases to more elosely approximate visually prescribed hits for saturated yellows and reds. This method will not shade saturated oranges to visually acceptable positions. 2. Many large hits may be reduced by removing redundant colorants from the shading scheme. 3. Bach problem product must be examined independently to ascertain if either or both of the above methods will aid in providing Production with useable hits. b. The Job of shading may be made easier by formulation that considers the needs of instrumental shading. Providing balanced colorants giving nearly equalateral vector movement and formulation that takes into account the offset tolerances of saturated colors may help. RSCOMMEMATiOMS 1. Continued study of visual-instrumental tolerance correlations. 2. Problem products be studied to find and remove any high concentration colorants that give redundant vector displacement. Care must be exercised so that maneuverability is not greatly reduced. 3o Emergency degenerate vectors may then be established, if necessary, to handle cases requiring further consideration of the hit size.
DUP030002352
3-
DISCUSSIOH
She Modified Adams Color Coordinate System describes a point in color space by the set of orthogonal axes; lightness (L), Red-Green (a), and Yellow-Blue (b). Matching a color standard is accomplished by constructing a like coordinate system about the product standard. Each colorant in the product is described by a rector (Ah, Aa, Ab) anchored at the origin.
At the present time, instrumental shading by vector movement simultaneously controls each axis equally until the batch is within a nearly cubical tolerance range centered on the product standard, This can be described as shading to minimise the function E * (Ah2 + Aa2 * Ab2)*/2. Studies of saturated yellows, oranges, and red indicate that it ia not necessary to control all coordinates within the same tolerances for a good visual match.
Saturated yellows must be controlled for lightness (AL) end Red-Green hue (Aa) but have a wide (Ab) tolerance as illustrated by the passing delta values of the following. Greater positive (Ab) variation, or increased saturation, can be tolerated visually than can negative (Ab) variation, or desaturation.
Sflte
Product Code
Ah Aa Ab
A78Q-1226
+0.05
+0.16
+3.60
0-780-75306
-0,05 +0,03
-0.22 -0,11
*0.89 +0.46
116-1346
+0.16
-0.06
+0.79
247-3404
+0.12
-0.19
-1.20
253-52422
-0,24 .
-0.22
+0,83
I.797-78068
+0.12 +0,35
+0.16 -0.10
-0.47 -1.07
*8l-26545
+0,15 +0.50
+0.32
--0.38 -0.34 --0.56
+3*38 +3.62
+5.37
83-2684l
-0,17
+0.34
+1.14
The visual tolerance range, though nearly cubical for products of moderate saturation, becomes elongated perpendicular to the lightness-hue plane as specified saturation increases.
Du Pont Registered Trademark
**Data by G, C. Cline, S.S.F,, "Zone Charts for Yellow, Orange and Red *Dulu#'", letter to W, H. Edwards, February 8, 196$*
DUP030002353
Saturated Reds follow much the seine patters as the Yellows, Reds need to he controlled more for lightness (AL) and Yellow-Blue hue (Ah), than for (Aa). Again, it is more difficult to perceive too much Red (increased saturation) than too little Red (desaturation) in a saturated Red. The following passing
panels indicate the lesser importance of controlling (Aa) compared to (AL) and (Ah).
Red
Product Code AT80-59758
AL
-0.02 -0.02
ML-
8-2.17 I.h6
Ab
1.6l 0.18
86M913Q 868-98138 93-2*Ul8
-0.12
-0.22
-0.06 -0.28
0,68
0.5*8
1.16 +2ol6
-0.03
*0,37
0,30 0,62
93-2l0}kO
-0.56 -0.61
-0.88 -0.72 -0.12 -0.56
+0,11 2.80 +1.86
2.3* 1,*5 1.2*8
-0.38
0,37 0.07 0.1*8 0.80 0.07
There is greater restriction on lightness variations than either (Aa) or (Ah) for orangeso The tolerance none may he elongated parallel to a line passing through the absolute origin of color space and the point in color space marking the product standard.
Orange
Product Code
AL Aa
Ab
2*83 92029 A78O-O82 83-190*85
0.30
-0.18
0.00 +0,10
0.51
0.70
0.62 1.10
+0.58
1,29
0,78 O.tS
Modified Instrumental Shading Techniques
Saturated Reds and Yellows often require unrealistically large additions of colorant, and the corresponding mount of resin, to achieve an acceptable instrumental color match by minimising E. A significant decrease in the amount of colorant necessary for shading can be had by taking advantage of the less stringent visual tolerance zones of the saturated region of color space. Specific planar functions will permit shading to a visually acceptable point providing the on-load delta values insure against visually perceptible desaturatioa
at negligible hue variation.
DUP030002354
5
The planar function for saturated Yellows deletes the (Ah) effect and shades by minimizing (AL2 + Aa2)*/2, Comparisons to conventional shading for
A780-1226 indicate the effectiveness of this method for different on-load positions.
I. On-load
AL *1.53 da * *2.15 Ah a *4.09
Conventional Bit
Ca l 2 * Aa2)^2
24.035 0.1235 0.01635
42-687 42-622 42-224
0.7935 0.0336
743-123 42-224
24.1435 Total
0,8236
Total
3*4j6 of conventional hit
Computed Outcome (CiO.)
C.O.
AL a 000 Aa * 000 Ah * +C.06
AL *0.01 Aa m .000 Ah *o 86
12. On-load
AL * 1-0.42 Aa m *0.49
Ah * *1.52
Conventional Bit
15.235 0.1135
42-687 42-622
15.3156
Total
C.O.
AL * *0.24 Aa * --0.10 Ah -0.36
Ca l 2 * Aa2)1^2
0.00936
42-224
0.0635 of conventional hit
C.O.
AL * -0.02 Aa " -0.02 Ah +0,86
DUP030002355
6
IIIo On-Load
Conventional Hit
0.28$
3,90$
0.09$
743-123 lt2-687 42-622
4.27$
Total
AL +0.42 Aa m -0.49 Ab +1.52
C.O.
AL * -0,01 Aa * +0,02 Ab +0,03
CAL2 + Aa2)*^2
. $0.06$
0 002 0.062$
42-622 42-224
Total
1.9$ of conventional hit
C.O.
AL * +0,02 Aa * +0.01 Ab +0.82
IV. Qn-Load
Conventional git
1.56$ 1,2$ 0,01$
743-123 42-687 42-622
2,77$
Total
C0Q0
AL * 0,01 Aa * 000 Ab * +0.05
AL * -0,42 Aa * +0,49 Ab +1.52
(AL2 + Aa2)^2
1.54$
743-123
55.6$ of conventional hit
C.O.
AL * +0.02 Aa * +0.01 Ab w +0.26
DUP030002356
V. On-Load.
Conventional Hit
2.42? 5.953? 0.10?
8.47?
0.0.
743-123 42-686 42-622
ota
a l * -0.01 A& +0.07
Ab +0.03
VI. On-Load
Conventional Hit
11.4? 0.05?
11.45?
42-687 42-224
Total
C.Sj .
AL * 000 Aa 000 Ab +0.10
YXX. On-Load
Conventional Bit
1.04?
0.05? 0.02?
42-687
42-622 42-224
10.47?
Total
C.O.
AL 0 +0.02 Aa +0.01
Ab * +0.10
7
AL -0.42 Aa -0.49 Ab - +1.52
CAL2 * &a2)l/2
8.00? .04?
42-686 42-622
8.04?
Total
94.9? of conventional hit
C.O.
AL * -0.03 Aa -0.03 Ab * +2.36
AL +1.-92 Aa +3.62 Ab +4,30
CAL2 * Aa2)^2
2.68? 0.05?
743-123 42-224
2o73?
Tbtal
23.8? of conventional bit
C.O.
AL ** --0.01 Aa +0.09 Ab * -1.4l
AL * +1.20 Aa * +I.69 Ab +2.94
Ca l 2 + Aa2)^2
0.65? 0.028?
743-123 42-224
0.68?
Total
6.5? of conventional bit
C.O.
AL " 000 Aa * -0.02 Ab " +0.36
DUP030002357
YHI. On-Load
Conventional Hit
o.**2 3.32
J.-XL
13.**2
7*3-123 *2-686 *2-687
Total
Cq O
AL * Aa Ab
-0.15 000
+0.01
IX. On-Load
Conventional Hit
l.l2
<5,5*
0.062
7.66$
7*3-123
*2-686
*2-622
Total
C.Oo
AL -0.1* Aa * -0.08 Ab +0.02
8 AL =0,57 Aa a +0.96 Ab +0oQ*
AL -0,,53 Aa ** -OolO Ab B --0.09
. (AL2 + Aa2)^2
.3.**2
Jj M
3.*72
*2-686 *2-22*
Total
25.92 of conventional hit
Cj O^
AL * +6.0* Aa a +0.01 Ab w -2.83
(AL2 + Aa2)*^2
7.722
*2-686
100.82 of conventional hit
m AL -0.11 Aa * 000 Ab +1.01
In all tests but IX the hit size was reduced at least slightly. Test VI and
Yin predict end points that may he too desaturated to be acceptable.
DUP030002358
9
The following datum shows how closely the hit minimising (AL2 + Aa2)s^2 matches the visually prescribed hit for rr97?8o63s fellow with on-load fibres.
AL -K).80 Aa a ->1.29 Ab -0.21}
Conventional Computer Hit
C.O.
5.3% 0.1TJI 0.019%
5.49%
42-686 42-622 42-224
Total
CAL2 + Aa2)^2 Hit
0.015%
42-224
0.27$ of conventional hit
Visually Prescribed Hit
0.01%
42-224
giving an acceptable visual match.
*L " +0.44 An * +0.39 Ab * +0,09
C.O.
AL -0,01 Aa +0.01 Ab * -1.52
Actual End Point AL +0,12 Aa m +0.16 Ab * -0.4T
The planar function for the Bed portion of the color solid would be (AL2, + Ab2)*^2.
Again the batch should he loaded sufficiently Red to standard to Insure against visually perceptible desaturation at the end point. The following tests for ATo O-59758, Red0 indicate the effectiveness of this formula for varying starting points.
On-Load
AL * +0.73 Aa +4.24 Ab * +2.81
Conventional Bit
2.76% 0,36% 0.07%,
743-655 743-123 42-224
3,19%
Total
C.O.
(AL2 + Ab^J^^
0.38% 0.06%
743-123 42-224
0.44%
Total
13.8% of conventional hit C.O.
AL -0.07 Aa +0.09 Ab " -0.05
AL +0.03 Aa a +0.91 Ab a -0.02
DUP030002359
n. On-Load
Conventional Hit
3,65 ' 0.25? 0.025
743-655 743-123 42-224
3.875
Total
C.O.
AL * -0.04 &a m *0.05 Ab * -0.02
h i. On-Load
Conventional Bit
0.205
743-123
10 fil. -0.64 fia <= +0.54 fib * -0.14
fiL -0.19 fia * -0.07 fib +0.49
C.O. fill ,8 -0,01 fia -0.40 fib *0.18
IV. On-Load
Conventional Hit
1.715 0.205 0.015
1.925
743-655 743-123 42-224
Total
C.O.
fiL " -0.01 fia * +0.01 fib * 000
fill --0.43 fia +O.65 fib * +0.35
,
i(AL2 + Ab2)3^2
1.555 0.255
1,805
743-655 743-123
Total
46,55 of conventional hit C.O.
AL * -0.07 fia +0.61
fib -0.10
(AL2 + fib2)3/*
0.215
743-123
105.05 of conventional hit
C.O.
Ah +0.07 fia -0,30 fib * +0.02
Ca l 2 + fib2)3/2
0.575 0.195
743-655 743-123
0.765
Total
39.65 of conventional hit
C.O.
AL a +0,03 fia +0.54 fib * 4-0.07
DUP030002360
V.
On-Load
Ax, +0.54
4a a# -0,40
&b -0,34
Conventional Hit
2.95% 3,60%
743-655 743-300
6.55%
Total
11 -
Sj E
4L - +0.01 4a -0.07 4b * +0.02
(AL2 + Ab2)l/2
3.04% 4,07%
743-655 743-300
7,11%
Total
108.5% of conventional hit
C.o.
AL * 000 As -0.16 Ab +0.05
VI.
On-Load
AL +0.75
Aa * +1.51
Ab -0.65
Conventional Hit
6.35% 2.40% 0.04%
743-655 743-300 42-224
8.79%
Total
(AL2 + Ab2)1/2
4.26% 5.40%
743-655 743-300
9.66%
Total
109.9% of conventional hit
AL +0,01 Aa +0,01 Ab -0.01
AL - +0.09 Aa " +2.02 Ab ** -0.02
Batches of this material that are light and blue to standard present a problem as there la no vector movement out of that quadrant.
The planar functions are useful only in the sections of color space near the +a or +b axes, where one absolute coordinate Is larger than the other. They are of no use for shading orange where a and b are more or less equal.
In most instances, saturated products are shade variations of a single pigment, or two similar pigments. Similar pigments require high concentrations for relatively small vector movements when letdown In each other. Saturated yellows may be mostly W-686 and/or W-687. Oranges may be mostly W-622, and reds mostly W-655 and/or W-300. For example, 42-687, used in A78Q-1226, requires a concentration of 24.9% for a vector movement of 2.53 N.B.S. units. 743-123, also used in this product, moves into the same octant, (+,-,-), as 42-687 and requires a concentration of only 1.72%. The largest movement of 42-687 (Aa ** 2.12) can be duplicated by 743-123 with a 40% saving of material. There is no great loss in maneuverability since the product has four remaining component colorants. The following points were calculated by computer for A780-1226 without using 42-687 for shading purposes. The percentage of the conventional hit (previously given) follows each calculation.
DUP030002361
I, On-Load
Hit
1.4% 0.025% ,0.03%
743-123 42-622 42-224
1.43% total
fiL * +1,53 da " +2.15 db +4.09
11. On-Load
Hit
0.78% 0.02% 0.009%
743-123 42-622 42-224
0.81%
total
dL +0.42
da m +0.49 db ** +1.52
111.
On-Load
Hit
1.58%
743-123
dL --0*42 da +0.49 db +1.52
IV. On--Load
Hit
0.73% 0.02% 0.002%
743-123 42-622
42-224
0.75%
Total
V. On-Load
Kit
- 1.78% 43% 0.06%
743-123 42-686 42-622
dL * +0.42 da -0.49 db +1.52
dL -0.42 da -0.49 fib - +1.52
Computed Outcome dL +0.02 da * +0.03 db +0.16
5.9% of conventional hit
C.O. dL * 000 da " 000 db +0.04
5.3% of conventional hit
C.O. dL ** +0.08 da * --0.05 fib +0,09 57.0% of conventional hit
C.O, fiL " +0.03 fia * +0.04 fib * +0.04
18% of conventional hit
CaO* L -0.01 fia a -0,01 fib w -0,07 72.4% of conventional hit
DUP030002362
13-
VI. On-Load AL +1.92 da +3,63
O Ab +4.30
Hit
C.O.
0.03%
42-224
AL -0.11 Aa - +0.40 Ab -0.06
VII,
On-Load
AL - -0.57 Aa +0.96 Ab +0.04
0.76% of conventional hit
Hit
1.0% 9.1% 0.01%
743-123 42-686 42-224
C.O.
AL -0.05 Aa * +0.19 Ab. --0.02
75.2% of conventional hit
VIII.
On-Load
AL * -0.53 Aa -0.10 Ab -0.09
Hit
0.32% 2.5%
743-123 42-686
2.82%
Total
C.O.
AL * -0.28 Aa * -0,15 Ab m +0.06
36.8% of conventional hit
All bits ware Improved by at least 251 of the conventional hit. This
la not a planar method and does not require proper on-load positioning for use.
Once the extraneous 42-687 is removed from the vector card the com puter is capable of assimilating the planar method* Only the lightness and hue components are recorded on the shading card. It will again be necessary to have correct on-load positioning for effective use.
Examples
X,
On-Load
AL +1.53
Aa +2.15
Ab +4.09
Hit
0.721 0.02%
0.74%
743-123 42-224
Total
C.O.
AL +0.04 Aa - 000 Ab +0.86
DUP030002363
II.
On-Loed
AL m +0.42
Aa * +0.49
Ab - +1.52
Hit c.o.
0*0072
42-224
AL +0.04 Aa +0.04 Ab * +0.93
III,
On-Load
AL +1,92 Aa - +3.63 Ab +4,30
Hit C.O.
1.82% 0.8% 0.03%
743-123 42-686 42-224
AL -0.05 Aa -0.02 Ah * -1.36
2.65%
Total
IV.
On--Load
AL * +1.20
Aa - +1.69
Ab +2.94
m
0,4% 0.02%
743-123 42-224
C.O.
AL m -0.02 Aa 000 ih m +0.42
If 42-687 were not removed, tests I and II would not change, tests III and IV, however, would change to;
III. Hit
13.2% jum
13.22%
42-687 42-224
Total
AL +0.05 Aa +0.04 Ah +0,35
IV. Hit
SsSa.
2,5% 0.02%
42-687 42-224
hSk_____Mi
& +0.05 Aa - +0,04 &> -*0.87
Conventional hits for A-780-59758 can he improved hy removing 743-300 from shading use. 743-300 moves to the same octant as 42-224 and has 275 times the concentration of 42-224, Maneuverahility is hampered in this case, as only three vectors remain for shading. Teats I, IV and V were not satisfactorily
shaded.
I. On-Load
AL +0.73 Aa " +4,24 Ah " +2,81
DUP030002364
II. III. IV. V.
33
Hit
0.282 0.06%
0.34%
743-123 42-224
Total
On-Load
Hit
1.9% 0.22% 0.01%
2.13%
743-655 743-123 42-224
Total
Ott-Load
m 0.11%
743-123
On-LOad
Hit 0.19%
743-655
On-Load
m .06%
743-123
C.O.
AL *0.40 Aa -0.65 Ah *0.32
10.7% of conventional hit
AL 10 --0.64 Aa - *0.54 Ab m --0.14
C.O.
AL * -0.08 Aa +0,15 Ab ** --0,07
55% of conventional hit
AL -0.19 Aa * -0.07 Ab - *0.49
C.O.
AL --0.02 Aa -0.23 Ab +0.16
55% of conventional hit-
AL - +0.54 Aa --0.40 Ab m -0.34
C.O.
AL *0, 58 Aa " -0.34 Ab -0.23
2.9% of conventional hit
AL a --0,43 Aa -0.65 Ab *0.35
C.O.
AL -0.32 Aa -0.74 4b *0.17
11% of conventional hie
DUP030002365
16
VI. On-load
AL -0.43 4a pi +0.65 4b - +0.35
Sit
1.71% 0.21% 0.01%
743-655 743-123 42-224
Ss Pj s.
AL 000 4a - +0,01 4b 000
1.92%
Total
100% of conventional hit
The majority of itests calculating . planar solutions by computer gave
better solutions when 743-300 was included in the shading scheme.
Planar sole-
tloas excluding 743-300 closely followed the manually computed solutions. Only in
the first test did removing 743-300 improve the hit.
I. On-Load 4L m +0.73 4a +4.24 4b 2.81
A with 743-300
C.O.
611% 0.94%
7.04%
743-300 743-123
Total
4L -0.02 4a ** +2.13 4b +0.04
220,7% of conventional hit
B v/o 743-300
C.O.
0.28% 0.05%
0.33%
-743-123 42-224
Total
AL 000 4a +0.89 4b 000
10.3% of conventional hit
XI.
On-Load
AL +1.14
4a * +2.03
4b +0.79
A with 743-300
0,81% 2.81%
3.62%
743-655 743-300
Total
AL * 000 Aa - +1.57 Ab 000
104,9% of conventional hit
R w/o 743-300
C.O.
5.02% 0.07%
5.09%
743-655 42-224
Total
AL +0.08 Ab - -1.55 fib * -0.11
146,4% of conventional hit
DUP030002366
IT
XIX.
On-Load
AL 40.54 Aa -0.40 Ab -0.34
A with 743-300
C.O.
2.17% 2.43%
,r
4.60%
743-655 743-300
Total
AL - +0.01 Aa -0.06 Ab * --0.01
70.2% of conventional hit
B w/o 743-300
C.O.
6.76% .06%
6,82%.
743-655 42-224
Total
,
AL +0.06 Aa -2,98 Ab -0.03
104*4% of conventional hit
XV.
On-Load
AL ** +0.86
Aa * -0.32
Ab - +1.01
A with 743-300
C.O.
8.
2.84% 0.03%
2.87
743-300 743-123
Total
Aa -0.50 Ab 000
90.25% of conventional hit
JLzls. 743-300
C.O.
3.72% 0.06%
3.78%
743-655 42-224
Total
AL - -0.11 Aa -3.37 Ab +0.07
118.9% of conventional hit
These tests make it evident that, although the modifications may help to shade certain problem products, no set method for all saturated colors is forthcoming* It seems that 42-687 cm be removed from shading consideration for A-780-1226 with no harmful effects. Maneuverability is not restricted, and a useable planar function is obtained. A-780-59758 does not lend itself as readily to the preceding methods. Removing 743-300 restricts shading from some positions to an undesirable degree. Hit size is increased as often as it is decteased by using planar methods. Only in certain cases will vector card modifications achieve the desired objective. Each problem product will have to be investigated to determine if these methods, either singularly or in com bination, will aid in providing more useable hits.
A correlation may be formed between the absolute color coordinates A and B and the visual tolerance region for a given product. Weights for (Aa) and (Ab) can be calculated as a function of saturation and the perpendicular color coordinate. The factor Wa for (Aa) would be -
DUP030002367
M-
such'that
wa
(Ka B2 . C) S)
(Ka i?2 .
1, Ka is an experimentally determined constant giving the ratio of Wa + u W1 (the lightness factor). Ifs for example (Ah), (ha) and <Ab) .must be equally controlled for an orange with A a B, then Wa 1.0. Neglecting C/S* Ka would equal 1.0.
2 a8 % TW 1.0
If (Aa) and (Ah) tolerances were twice the (AL) tolerance for this orange Ka (and Kb) equals one.
2. C is an experimentally determined constant to increase the weight as saturation decreases causing the tolerances to equalise.
As Vx (x a,b) goes to zero* the necessity of close control for axis x decreases
The weights show a pattern for A-780-1226f A-780--59758 and 0-780-98166*
a saturated orange, that follows the tolerances presented earlier in this dis cussion.
1. Let VL 1.0 2. Ka % 1,0 3. C *> 0
A-780-1226
A m 0.14B wa b -
B2 (aa4B>2 + 'W -
(0.14B)2 (0.1AB)4> B*
0.98 0,02
A-780-59758
A 1.9IB
Wa" (1.91BF
* 0.22
% fenk + 82 0.79
e. A-780-98166
A 0.9B
B2
Vra TMfX'
- 0.55
V
ts2 - 45
DUP030002368
These weights do not account for the offset of visual acceptance toward increased saturation. They do help to reunite the yellow, orange and red portions of color space, partitioned "by considering the planar shading solutions which are applicable only in regions near the absolute color axes.
DUP030002369
DISTRIBUTION LIST
C. F. KALB F, Ho BEADLES
- WXLM. Fo k F. ) 11 * " f TURK
K* E* ACKL353T
- SO. SAW FRA.
F* S, BAKER
- TUCKS?
Wo H. BEUTEL
PHILADELPHIA
B. Ao DE WALL
- CHICAGO
J. F. MO GETTIGAIf - PARLIJT
P. 0, PEASES?
- WERETT
C. W. STAHL
- TOLEDO
H. B. STINE
- FLINT
Co H. THOMPSON - POST MADISON
Wo Ho EDWARDS
- PHILADELPHIA
Bo H. FINING
- PHILADELPHIA
PROOFS EHGIHEEBIHC- FILS COPIES
c o p y io0 1
2 3 is 5 6 7 8 9 10 U 12 13-So
DUP030002370