The term, photoelectric colorimetry, is commonly employed to designate both photoelectric tristimulus colorimetry, used to evaluate the appearance of materials, and abridged spectrophotometry, often used to assist in chemical analyses. This paper is devoted to the first type of measurement. For a photoelectric tristimulus colorimeter, it is desired to find three or more source-filter photo-cell combinations of such spectral character that they duplicate the standard I.C.I. observer for colorimetry. With an instrument having these combinations, tristimulus values would be obtained by direct measurement. Although no one has duplicated the I.C.I. observer perfectly, several investigators have obtained source-filter photo-cell combinations suitable for the measurement of color differences between spectrally similar samples. To measure color differences as small as those which the trained inspectors of paint, textile, plastic, paper, and ceramic products can see, an instrument must have high precision. If the needed precision is available, a photoelectric tristimulus colorimeter may be used to measure: (1) I.C.I. colorimetric values, x, y, and Y, relative to those of a spectrally similar, calibrated standard; (2) relative values of α and β, components of the chromaticity departure from neutral in a new uniform-chromaticness-scale mixture diagram for representing surface colors; (3) amounts of color difference between pairs of spectrally similar samples; (4) amounts of color change accompanying fading; and (5) whiteness of white and near-white surfaces. In giving examples of the measurement of some of these different properties and in describing the errors of color measurement to which the tristimulus method is subject, reference is made to operations with the author’s recently developed multipurpose photoelectric reflectometer.
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Designation of the surface color by a set of tristimulus values for it; X, Y and Z; A, G and B; or other.
The perceived surface color
The separate attributes of the surface color, and the perceived surface color
Luminous apparent reflectance Aθi,θυ (chiefly designated below by Y), the lightness index L.
Dominant wave-length Λ, or hue angle ϕ
Purity p, or saturation index S
Lightness
Hue
Saturation, or “strength”
(2 and 3 combined) Chromaticity, indicated either by Λ and p, ϕ and S, or by a pair of trilinear coordinates, x and y, α and β, etc.
(2 and 3 combined) Chromaticness
Table II
Spectral character of the individual components and of the source-filter photo-cell combinations used for photoelectric tristimulus colorimetry with the multipurpose reflectometer [18].
Wavelength (mμ)
Spectral transmissions (Corning filters)
s Spectral response of G.E. cell No. 55 (in microamperes per milliwatt)
TA (Amber filter of No. 330 yellow glass and No. 978 green glass)
TG (Green filter of No. 428 green glass and No. 330 yellow glass)
TB (Blue filter of No. 554 blue glass and No. 038 yellow glass)
EI Relative spectral irradiance of source at 3100°K [44]
Spectral specification of the three source-filter photo-cell combinations.(Each value of k has been chosen so that the sum of the column is 100,000.)
EITAskA (amber)
EITGskG (green)
EITBskB (blue)
380
0.010
0.000
0.1188
94.5
31
90
.010
.000
.1425
101.5
39
400
.011
.000
.1688
107.8
56
10
.011
.020
.1979
113.9
70
337
20
.012
.298
.2294
119.5
92
6,109
30
.013
.443
.2634
124.7
120
10,885
40
.017
.478
.2998
129.7
185
13,901
450
.023
.482
.3383
134.2
291
16,368
60
.035
.445
.3790
138.8
514
17,511
70
.050
.338
.4215
143.0
842
15,237
80
.077
.195
.4658
147.2
1,476
10,001
90
0.004
.107
.090
.5114
151.3
96
2,315
5,208
500
.010
.138
.045
.5582
155.5
269
3,350
2,922
10
.020
.173
.015
.6061
159.1
596
4,664
1,082
20
.038
.209
.003
.6548
162.3
1,248
6,210
239
30
.063
.235
.000
.7040
164.9
2,258
7,628
40
.095
.249
.7536
167.0
3,695
8,763
550
.128
.251
.8033
168.4
5,351
9,496
60
.164
.243
.8531
168.7
7,291
9,778
70
.196
.222
.9025
167.4
9,148
9,378
80
.224
.193
.9516
162.9
10,727
8,366
90
.237
.163
1.0000
156.3
11,443
7,125
600
.238
.135
1.0476
147.5
11,363
5,833
10
.227
.109
1.0945
135.4
10,393
4,516
20
.206
.086
1.1403
117.3
8,511
3,216
30
.181
.067
1.1850
97.7
6,472
2,170
40
.153
.053
1.2284
79.1
4,594
1,440
650
.122
.040
1.2704
60.8
2,910
864
60
.099
.032
1.3111
43.7
1,752
512
70
.077
.025
1.3503
28.5
914
268
80
.057
.020
.000
1.3880
18.0
439
140
90
.043
.017
.002
1.4240
11.9
226
81
25
700
.030
.014
.003
1.4584
8.8
117
50
28
10
.022
.012
.004
1.4912
7.2
74
36
32
20
.016
.010
.004
1.5223
6.1
46
25
28
30
.011
.009
.005
1.5517
5.8
31
22
34
40
.008
.008
.004
1.5793
5.7
22
20
27
750
.005
.007
.004
1.6055
5.5
12
17
26
Σ
99,998
99,999
100,000
Table III
The uses of photoelectric tristimulus measurements.
Quantities computed from settings
Equations used
Uses of results
The coordinates, x, y, and Y of the I.C.I. standard system
x ≐ (0.80A +0.18B) /Σ
To find whether sample meets color requirements specified by x, y, and F.
y ≐ G/Σ
Σ = 0.80A+G+1.36B
To represent colors in the standard I.C.I. system.
To measure the amount of color difference between two surface colors in N.B.S. units.
To find whether a sample differs from a standard by more or less than a specified color tolerance.
To measure the amount of color change resulting from exposure, change of composition, change of method of preparation, or other treatment of the sample.
The coordinates α′, β′, and L′ of a uniformly-spaced surface-color solid
To designate a white or near-white surface with a number on a scale of whiteness which gives an MgO surface a value of 1.00 and a black surface a value of zero.
To give a white or near-white surface a number which indicates degree of yellowness if positive, degree of blueness if negative.
Table IV
Values of α and β, computed according to Eqs. (7), of spectrum colors at 10-millimicron intervals.
Wave-length in millimicrons
α
β
380
+0.0731
−0.3604
90
+.0725
−.3608
400
+.0718
−.3612
10
+.0705
−.3617
20
+.0679
−.3622
30
+.0613
−.3611
40
+.0484
−.3579
450
+.0265
−.3528
60
−.0095
−.3430
70
−.0729
−.3146
80
−.1876
−.2361
90
−.3373
−.0977
500
−.4440
+.0446
10
−.4651
+.1317
20
−.4166
+.1661
30
−.3387
+.1688
40
−.2605
+.1641
550
−.1793
+.1557
60
−.0924
+.1451
70
+.0001
+.1330
80
+.0952
+.1204
90
+.1879
+.1082
600
+.2688
+.0974
10
+.3320
+.0891
20
+.3754
+.0833
30
+.4035
+.0796
40
+.4229
+.0769
650
+.4352
+.0753
60
+.4423
+.0744
70
+.4458
+.0740
80
+.4483
+.0736
90
+.4501
+.0734
700 to 780 inc.
+.4506
+.0733
MgO under I.C.I. illuminant C
.0000
.0000
Table V
Values of k1, the proximity factor, suggested by Judd [28, p. 425].
Conditions of observation giving equivalent visual estimates of color difference
k1
Samples separated by a very narrow or non-existent dividing line
120
Samples separated by a contrasting, but narrow dividing line
90
Samples separated by a broad patterned area different from the areas being compared
40
Samples evaluated for whiteness without visual reference to other samples
20
(Convenient value for use when samples are separated by narrow line)
100
Table VI
Amounts of change in chromaticity and color difference introduced by changes in instrument settings of 0.001.
For a white surface reflecting 80%
For a yellow surface reflecting 35%
If settings of the instrument should be
A
0.800
0.500
G
.800
.350
B
.800
.050
But instead the instrument gives
A
.801
.501
G
.799
.349
B
.801
.051
Changes of the following magnitudes will result
in x
+.00024
+.00049
in y
−.00054
−.00182
in α.
+.00062
+.00160
in β
−.00025
−.00064
in
.00067
.00172
in ΔE (maxi-mum, N.B.S. units)
±.45
±.94
in W
−.0025
Table VII
Errors in measured chromaticity differences which result from substitution of photoelectric tristimulus combinations for the I.C.I. standard observer.
Specimens compared
Size of the chromaticity difference
Error in the photoelectrically measured chromaticity difference
Actual
Relative to size of difference (percent)
Munsell BPB 8/2 and MgO
0.0229
0.0013
6
BG 6/4 and BG 7/4
.0150
.0018
12
Yellow Y1 and Yellow Y2
.00187
.00043
(23)
Gray G1 and Gray G2
.0160
.0061
(38)
Table VIII
Changes in measured chromaticity difference which would result from the substitution of one photo-cell for another of the same type, but of different spectral response.
Specimens compared
Measured size of the chromaticity difference (with cell 55)
Change in the measured chromaticity difference with substitution of cell
Actual
Relative to size of difference (percent)
Munsell BPB 8/2 and MgO
0.0261
0.0016
6
BG 6/4 and BG 7/4
.0136
.0004
3
Yellow Y1 and Yellow Y2
.00224
.00035
(16)
Gray G1 and Gray G2
.0184
.0024
(13)
Table IX
Percentage errors in computed values of color difference from using the suggested short-cuts.
Short cut
Errors in percent of total difference
For 2 pairs of white samples
For 2 pairs of blue samples
For 2 pairs of orange samples
ΔE = 1.8
ΔE = 6.6
ΔE = 1.0
ΔE = 7.6
ΔE = 1.4
ΔE = 6.0
Scale corrections omitted
0.6
1.1
0
4.1
4.2
4.8
Use of instrument values of A, G, and B having only relatively correct magnitudes
0
0
1.0
2.9
26.6
6.3
Use of 0.5 and 0.1 instead of true neutral-filter factors
—
—
3.9
3.6
7.7
1.0
Combination of above 3 short-cuts
0.6
0.3
0
8.7
27.3
4.8
Table X
Advantages and disadvantages of photoelectric tristimulus colorimetry.
Advantages
Disadvantages
1.
Small number of settings required for each sample.
1.
Errors resulting from the inaccurate spectral response of the source-filter photo-cell combinations used.
2.
Small number of computational steps required to obtain x, y, and Y, or α, β, and Y.
2.
The necessity for working standards which are spectrally similar to the samples measured.
3.
Simplicity and inexpensiveness of apparatus.
3.
The necessity for special precautions to attain the high precision required if the tristimulus method is to equal the eye in power to discriminate colors.
4.
Opportunity to convert settings rapidly to numbers giving size and character of color difference perceived between samples.
4.
Failure of tristimulus measurements to provide the physical description of a color stimulus such as is given by a spectrophotometric curve.
5.
Correspondence between values of α, β, and Y, and positions of points representing colors in the uniformly spaced surface-color solid.
Example 1
Measurement of the I.C.I. values, x, y, z, and Y of four white painted plaques (see Eqs. (5) and (6), and Fig. 10).Purpose—To test samples for compliance with color requirements given in Federal Specification TT-P-23a, [8] namely:
x
y
z
Y
Minimum
—
—
0.355
0.85
Maximum
0.324
0.331
—
—
Computational short-cut—Scale corrections omitted.Working standard—Vitrolite No. 1 (A =0.906, G = 0.909, B = 0.890)
Specimen
Standard
No. 1
No. 2
No. 3
No. 4
Blue settings
0.8985
0.8480
0.7900
0.7810
0.7080
.8955
.8450
.7880
.7790
.7070
Mean
.8970
.8465
.7890
.7800
.7075
.8398
.7828
.7739
.7020
Amber settings
.9055
.8785
.8720
.8420
.8530
.9030
.8770
.8680
.8400
.8520
Mean
.9042
.8778
.8700
.8410
.8525
.8795
.8717
.8427
.8542
Green settings
.9100
.8770
.8620
.8340
.8320
.9070
.8740
.8585
.8320
.8310
Mean
.9085
.8755
.8602
.8330
.8315
.8760
.8607
.8335
.8320
0.18 B
.1512
.1409
.1393
.1264
1.18 B
.9910
.9237
.9132
.8284
0.80 A+0.18 B
.8548
.8383
.8135
.8098
Denom (G+0.80 A+1.36 B)
2.7218
2.6227
2.5602
2.4702
.3141
.3196
.3177
.3278
y ≐ G /Denom
.3218
.3282
.3256
.3368
z ≐ 1.18/Denom
.3641
.3522
.3567
.3354
Result of test
pass
fail (x)
fail (Y)
fail (all)
Example 2
Measurement of the change of α and β of three painted plaques with exposure (see Eqs. (8) and Fig. 11).Purpose—To follow the chromaticity changes of panels of the same paint exposed out of doors and in two machines which accelerate the changes produced by weathering.Note—Only one of the many sets of computations used to obtain values of α and β is reproduced below. Computational short-cut—Scale corrections omitted. Working standard—Pink plaque (A = 0.7058, G = 0.606, B = 0.4714).
Specimen
Standard
Roof (4 days)
Machine 1 (43 hours)
Machine 2 (41 hours)
Blue settings
0.4995
0.300
0.685
0.597
.501
Mean
.5002
.2827
.6453
.5626
Amber settings
.704
.510
.7075
.675
.704
Mean
.704
.5113
.7093
.6767
Green settings
.620
.424
.708
.656
.619
Mean
.6195
.4148
.6926
.6417
A–G
+.0965
+.0167
+.0350
G–B
+.1321
+.0473
+.0791
0.4(G–B)
+.0528
+.0189
+.0316
B+A + 2G = Denom
1.6236
2.7398
2.5227
α ≐ (A–G)/Denom
+.0594
+.0061
+.0139
β ≐ 0.4(G–B)/Denom
+.0325
+.0069
+.0125
Example 3
Measurement of the amount of color difference ΔE between a standard and each of four similarly colored brown automobile pile fabrics (see Eq. (13)).Purpose—To find which fabrics comply with the requirement that they differ from the standard by no more than one N.B.S. unit of color difference.Computational short-cut—No calibrated standard used. kl = 100, fg = 1.00.
Compute
for standard and for any samples for which the value of Y differs from that of the standard by more than 10 percent. For the latter samples, use the mean of the two values of
; for others, use the value for the standard.
Example 4
Measurement of the hue-difference estimate, ΔH′, the saturation-difference estimate, ΔS′, and the lightness-difference estimate, ΔL′, between an actual earth sample and two modified earths (see Eqs. (17)).Purpose—To find how the modified earths differ in color from the actual earth.Computational short-cuts—Scale corrections omitted, no calibrated standard used, and the factor 0.5 used instead of the actual transmissions of the neutral filter.ki = 100, fg = 1.00.
Values which are average for the two specimens being compared should be entered in those rows marked by an asterisk.
Example 5
Measurement of the whiteness W of one new and two laundered sheeting specimens (see Eq. (19)). Purpose—To measure the effect of repeated laundering on the whiteness of new sheeting material.Computational short-cut—Scale corrections omitted.kl, = 20,fg = 1.00.Working standard—Vitrolite No. 1 (A = 0.906, G = 0.909, B = 0.890).
Specimen
Standard
New
1L
20L
Blue settings
0.898
0.837
0.845
0.765
.892
.850
.852
.787
Mean
.895
.8435
.8485
.776
.8388
.8438
.7717
Amber settings
.9085
.892
.912
.826
.906
.904
.912
.836
Mean
.9072
.898
.912
.831
.8968
.9108
.8299
Green settings
.9055
.884
.900
.812
.903
.894
.900
.824
Mean
.9042
.889
.900
.818
.8937
.9048
.8223
A–G
.0031
.0060
.0076
2.5 (A–G)
.0078
.0150
.0190
G–B
.0549
.0610
.0506
α ≐ 2.5 (A–G)/10G
.0009
.0017
.0023
β ≐ (G–B)/10G
.0061
.0067
.0062
.0062
.0069
.0066
.186
.207
.198
1.00−G
.106
.095
.178
WL = (1.00−G)/2
.053
.048
.089
.193
.213
.217
W = 1 − above
.807
.787
.783
Example 6
Measurement of the yellowness of four near-white porcelain-enamel specimens (Eq. (20)).Purpose—To find which of several enamel specimens are yellowish (+ values) and which are bluish (− values).Computational short-cut—Scale corrections omitted.Working standard—Vitrolite No. 1 (A = 0.906, G = 0.909, B = 0.890).
Designation of the surface color by a set of tristimulus values for it; X, Y and Z; A, G and B; or other.
The perceived surface color
The separate attributes of the surface color, and the perceived surface color
Luminous apparent reflectance Aθi,θυ (chiefly designated below by Y), the lightness index L.
Dominant wave-length Λ, or hue angle ϕ
Purity p, or saturation index S
Lightness
Hue
Saturation, or “strength”
(2 and 3 combined) Chromaticity, indicated either by Λ and p, ϕ and S, or by a pair of trilinear coordinates, x and y, α and β, etc.
(2 and 3 combined) Chromaticness
Table II
Spectral character of the individual components and of the source-filter photo-cell combinations used for photoelectric tristimulus colorimetry with the multipurpose reflectometer [18].
Wavelength (mμ)
Spectral transmissions (Corning filters)
s Spectral response of G.E. cell No. 55 (in microamperes per milliwatt)
TA (Amber filter of No. 330 yellow glass and No. 978 green glass)
TG (Green filter of No. 428 green glass and No. 330 yellow glass)
TB (Blue filter of No. 554 blue glass and No. 038 yellow glass)
EI Relative spectral irradiance of source at 3100°K [44]
Spectral specification of the three source-filter photo-cell combinations.(Each value of k has been chosen so that the sum of the column is 100,000.)
EITAskA (amber)
EITGskG (green)
EITBskB (blue)
380
0.010
0.000
0.1188
94.5
31
90
.010
.000
.1425
101.5
39
400
.011
.000
.1688
107.8
56
10
.011
.020
.1979
113.9
70
337
20
.012
.298
.2294
119.5
92
6,109
30
.013
.443
.2634
124.7
120
10,885
40
.017
.478
.2998
129.7
185
13,901
450
.023
.482
.3383
134.2
291
16,368
60
.035
.445
.3790
138.8
514
17,511
70
.050
.338
.4215
143.0
842
15,237
80
.077
.195
.4658
147.2
1,476
10,001
90
0.004
.107
.090
.5114
151.3
96
2,315
5,208
500
.010
.138
.045
.5582
155.5
269
3,350
2,922
10
.020
.173
.015
.6061
159.1
596
4,664
1,082
20
.038
.209
.003
.6548
162.3
1,248
6,210
239
30
.063
.235
.000
.7040
164.9
2,258
7,628
40
.095
.249
.7536
167.0
3,695
8,763
550
.128
.251
.8033
168.4
5,351
9,496
60
.164
.243
.8531
168.7
7,291
9,778
70
.196
.222
.9025
167.4
9,148
9,378
80
.224
.193
.9516
162.9
10,727
8,366
90
.237
.163
1.0000
156.3
11,443
7,125
600
.238
.135
1.0476
147.5
11,363
5,833
10
.227
.109
1.0945
135.4
10,393
4,516
20
.206
.086
1.1403
117.3
8,511
3,216
30
.181
.067
1.1850
97.7
6,472
2,170
40
.153
.053
1.2284
79.1
4,594
1,440
650
.122
.040
1.2704
60.8
2,910
864
60
.099
.032
1.3111
43.7
1,752
512
70
.077
.025
1.3503
28.5
914
268
80
.057
.020
.000
1.3880
18.0
439
140
90
.043
.017
.002
1.4240
11.9
226
81
25
700
.030
.014
.003
1.4584
8.8
117
50
28
10
.022
.012
.004
1.4912
7.2
74
36
32
20
.016
.010
.004
1.5223
6.1
46
25
28
30
.011
.009
.005
1.5517
5.8
31
22
34
40
.008
.008
.004
1.5793
5.7
22
20
27
750
.005
.007
.004
1.6055
5.5
12
17
26
Σ
99,998
99,999
100,000
Table III
The uses of photoelectric tristimulus measurements.
Quantities computed from settings
Equations used
Uses of results
The coordinates, x, y, and Y of the I.C.I. standard system
x ≐ (0.80A +0.18B) /Σ
To find whether sample meets color requirements specified by x, y, and F.
y ≐ G/Σ
Σ = 0.80A+G+1.36B
To represent colors in the standard I.C.I. system.
To measure the amount of color difference between two surface colors in N.B.S. units.
To find whether a sample differs from a standard by more or less than a specified color tolerance.
To measure the amount of color change resulting from exposure, change of composition, change of method of preparation, or other treatment of the sample.
The coordinates α′, β′, and L′ of a uniformly-spaced surface-color solid
To designate a white or near-white surface with a number on a scale of whiteness which gives an MgO surface a value of 1.00 and a black surface a value of zero.
To give a white or near-white surface a number which indicates degree of yellowness if positive, degree of blueness if negative.
Table IV
Values of α and β, computed according to Eqs. (7), of spectrum colors at 10-millimicron intervals.
Wave-length in millimicrons
α
β
380
+0.0731
−0.3604
90
+.0725
−.3608
400
+.0718
−.3612
10
+.0705
−.3617
20
+.0679
−.3622
30
+.0613
−.3611
40
+.0484
−.3579
450
+.0265
−.3528
60
−.0095
−.3430
70
−.0729
−.3146
80
−.1876
−.2361
90
−.3373
−.0977
500
−.4440
+.0446
10
−.4651
+.1317
20
−.4166
+.1661
30
−.3387
+.1688
40
−.2605
+.1641
550
−.1793
+.1557
60
−.0924
+.1451
70
+.0001
+.1330
80
+.0952
+.1204
90
+.1879
+.1082
600
+.2688
+.0974
10
+.3320
+.0891
20
+.3754
+.0833
30
+.4035
+.0796
40
+.4229
+.0769
650
+.4352
+.0753
60
+.4423
+.0744
70
+.4458
+.0740
80
+.4483
+.0736
90
+.4501
+.0734
700 to 780 inc.
+.4506
+.0733
MgO under I.C.I. illuminant C
.0000
.0000
Table V
Values of k1, the proximity factor, suggested by Judd [28, p. 425].
Conditions of observation giving equivalent visual estimates of color difference
k1
Samples separated by a very narrow or non-existent dividing line
120
Samples separated by a contrasting, but narrow dividing line
90
Samples separated by a broad patterned area different from the areas being compared
40
Samples evaluated for whiteness without visual reference to other samples
20
(Convenient value for use when samples are separated by narrow line)
100
Table VI
Amounts of change in chromaticity and color difference introduced by changes in instrument settings of 0.001.
For a white surface reflecting 80%
For a yellow surface reflecting 35%
If settings of the instrument should be
A
0.800
0.500
G
.800
.350
B
.800
.050
But instead the instrument gives
A
.801
.501
G
.799
.349
B
.801
.051
Changes of the following magnitudes will result
in x
+.00024
+.00049
in y
−.00054
−.00182
in α.
+.00062
+.00160
in β
−.00025
−.00064
in
.00067
.00172
in ΔE (maxi-mum, N.B.S. units)
±.45
±.94
in W
−.0025
Table VII
Errors in measured chromaticity differences which result from substitution of photoelectric tristimulus combinations for the I.C.I. standard observer.
Specimens compared
Size of the chromaticity difference
Error in the photoelectrically measured chromaticity difference
Actual
Relative to size of difference (percent)
Munsell BPB 8/2 and MgO
0.0229
0.0013
6
BG 6/4 and BG 7/4
.0150
.0018
12
Yellow Y1 and Yellow Y2
.00187
.00043
(23)
Gray G1 and Gray G2
.0160
.0061
(38)
Table VIII
Changes in measured chromaticity difference which would result from the substitution of one photo-cell for another of the same type, but of different spectral response.
Specimens compared
Measured size of the chromaticity difference (with cell 55)
Change in the measured chromaticity difference with substitution of cell
Actual
Relative to size of difference (percent)
Munsell BPB 8/2 and MgO
0.0261
0.0016
6
BG 6/4 and BG 7/4
.0136
.0004
3
Yellow Y1 and Yellow Y2
.00224
.00035
(16)
Gray G1 and Gray G2
.0184
.0024
(13)
Table IX
Percentage errors in computed values of color difference from using the suggested short-cuts.
Short cut
Errors in percent of total difference
For 2 pairs of white samples
For 2 pairs of blue samples
For 2 pairs of orange samples
ΔE = 1.8
ΔE = 6.6
ΔE = 1.0
ΔE = 7.6
ΔE = 1.4
ΔE = 6.0
Scale corrections omitted
0.6
1.1
0
4.1
4.2
4.8
Use of instrument values of A, G, and B having only relatively correct magnitudes
0
0
1.0
2.9
26.6
6.3
Use of 0.5 and 0.1 instead of true neutral-filter factors
—
—
3.9
3.6
7.7
1.0
Combination of above 3 short-cuts
0.6
0.3
0
8.7
27.3
4.8
Table X
Advantages and disadvantages of photoelectric tristimulus colorimetry.
Advantages
Disadvantages
1.
Small number of settings required for each sample.
1.
Errors resulting from the inaccurate spectral response of the source-filter photo-cell combinations used.
2.
Small number of computational steps required to obtain x, y, and Y, or α, β, and Y.
2.
The necessity for working standards which are spectrally similar to the samples measured.
3.
Simplicity and inexpensiveness of apparatus.
3.
The necessity for special precautions to attain the high precision required if the tristimulus method is to equal the eye in power to discriminate colors.
4.
Opportunity to convert settings rapidly to numbers giving size and character of color difference perceived between samples.
4.
Failure of tristimulus measurements to provide the physical description of a color stimulus such as is given by a spectrophotometric curve.
5.
Correspondence between values of α, β, and Y, and positions of points representing colors in the uniformly spaced surface-color solid.
Example 1
Measurement of the I.C.I. values, x, y, z, and Y of four white painted plaques (see Eqs. (5) and (6), and Fig. 10).Purpose—To test samples for compliance with color requirements given in Federal Specification TT-P-23a, [8] namely:
x
y
z
Y
Minimum
—
—
0.355
0.85
Maximum
0.324
0.331
—
—
Computational short-cut—Scale corrections omitted.Working standard—Vitrolite No. 1 (A =0.906, G = 0.909, B = 0.890)
Specimen
Standard
No. 1
No. 2
No. 3
No. 4
Blue settings
0.8985
0.8480
0.7900
0.7810
0.7080
.8955
.8450
.7880
.7790
.7070
Mean
.8970
.8465
.7890
.7800
.7075
.8398
.7828
.7739
.7020
Amber settings
.9055
.8785
.8720
.8420
.8530
.9030
.8770
.8680
.8400
.8520
Mean
.9042
.8778
.8700
.8410
.8525
.8795
.8717
.8427
.8542
Green settings
.9100
.8770
.8620
.8340
.8320
.9070
.8740
.8585
.8320
.8310
Mean
.9085
.8755
.8602
.8330
.8315
.8760
.8607
.8335
.8320
0.18 B
.1512
.1409
.1393
.1264
1.18 B
.9910
.9237
.9132
.8284
0.80 A+0.18 B
.8548
.8383
.8135
.8098
Denom (G+0.80 A+1.36 B)
2.7218
2.6227
2.5602
2.4702
.3141
.3196
.3177
.3278
y ≐ G /Denom
.3218
.3282
.3256
.3368
z ≐ 1.18/Denom
.3641
.3522
.3567
.3354
Result of test
pass
fail (x)
fail (Y)
fail (all)
Example 2
Measurement of the change of α and β of three painted plaques with exposure (see Eqs. (8) and Fig. 11).Purpose—To follow the chromaticity changes of panels of the same paint exposed out of doors and in two machines which accelerate the changes produced by weathering.Note—Only one of the many sets of computations used to obtain values of α and β is reproduced below. Computational short-cut—Scale corrections omitted. Working standard—Pink plaque (A = 0.7058, G = 0.606, B = 0.4714).
Specimen
Standard
Roof (4 days)
Machine 1 (43 hours)
Machine 2 (41 hours)
Blue settings
0.4995
0.300
0.685
0.597
.501
Mean
.5002
.2827
.6453
.5626
Amber settings
.704
.510
.7075
.675
.704
Mean
.704
.5113
.7093
.6767
Green settings
.620
.424
.708
.656
.619
Mean
.6195
.4148
.6926
.6417
A–G
+.0965
+.0167
+.0350
G–B
+.1321
+.0473
+.0791
0.4(G–B)
+.0528
+.0189
+.0316
B+A + 2G = Denom
1.6236
2.7398
2.5227
α ≐ (A–G)/Denom
+.0594
+.0061
+.0139
β ≐ 0.4(G–B)/Denom
+.0325
+.0069
+.0125
Example 3
Measurement of the amount of color difference ΔE between a standard and each of four similarly colored brown automobile pile fabrics (see Eq. (13)).Purpose—To find which fabrics comply with the requirement that they differ from the standard by no more than one N.B.S. unit of color difference.Computational short-cut—No calibrated standard used. kl = 100, fg = 1.00.
Compute
for standard and for any samples for which the value of Y differs from that of the standard by more than 10 percent. For the latter samples, use the mean of the two values of
; for others, use the value for the standard.
Example 4
Measurement of the hue-difference estimate, ΔH′, the saturation-difference estimate, ΔS′, and the lightness-difference estimate, ΔL′, between an actual earth sample and two modified earths (see Eqs. (17)).Purpose—To find how the modified earths differ in color from the actual earth.Computational short-cuts—Scale corrections omitted, no calibrated standard used, and the factor 0.5 used instead of the actual transmissions of the neutral filter.ki = 100, fg = 1.00.
Values which are average for the two specimens being compared should be entered in those rows marked by an asterisk.
Example 5
Measurement of the whiteness W of one new and two laundered sheeting specimens (see Eq. (19)). Purpose—To measure the effect of repeated laundering on the whiteness of new sheeting material.Computational short-cut—Scale corrections omitted.kl, = 20,fg = 1.00.Working standard—Vitrolite No. 1 (A = 0.906, G = 0.909, B = 0.890).
Specimen
Standard
New
1L
20L
Blue settings
0.898
0.837
0.845
0.765
.892
.850
.852
.787
Mean
.895
.8435
.8485
.776
.8388
.8438
.7717
Amber settings
.9085
.892
.912
.826
.906
.904
.912
.836
Mean
.9072
.898
.912
.831
.8968
.9108
.8299
Green settings
.9055
.884
.900
.812
.903
.894
.900
.824
Mean
.9042
.889
.900
.818
.8937
.9048
.8223
A–G
.0031
.0060
.0076
2.5 (A–G)
.0078
.0150
.0190
G–B
.0549
.0610
.0506
α ≐ 2.5 (A–G)/10G
.0009
.0017
.0023
β ≐ (G–B)/10G
.0061
.0067
.0062
.0062
.0069
.0066
.186
.207
.198
1.00−G
.106
.095
.178
WL = (1.00−G)/2
.053
.048
.089
.193
.213
.217
W = 1 − above
.807
.787
.783
Example 6
Measurement of the yellowness of four near-white porcelain-enamel specimens (Eq. (20)).Purpose—To find which of several enamel specimens are yellowish (+ values) and which are bluish (− values).Computational short-cut—Scale corrections omitted.Working standard—Vitrolite No. 1 (A = 0.906, G = 0.909, B = 0.890).