Annex D (INFORMATIVE) ILLUSTRATIONS FOR ACHIEVING CONFORMANCE WITH THE GRAYSCALE STANDARD DISPLAY FUNCTION

The following sections illustrate how conformance with the Grayscale Standard Display Function may be achieved for emissive (soft-copy) Display Systems as well as systems producing image presentations (hard-copies) on transmissive and reflective media. Each section contains four sub-sections on 1) a procedure for measuring the system Characteristic Curve, 2) the application of the Grayscale Standard Display Function to the Luminance Range of the Display System, 3) the implementation of the Grayscale Standard Display Function, and 4) the application of the conformance metrics as proposed in Annex C.

It is emphasized that there are different ways to configure a Display System or to change its performance so that it conforms to the Grayscale Standard Display Function. In fact, conceivably, a Display System may calibrate itself automatically to maintain conformance with the Standard. Hence, the following three illustrations are truly only examples.

Luminance of any Display System, hard-copy or softcopy, may be measured with a photometer. The photometer should have the following characteristics:

- be accurate to within 3% or less of the absolute Luminance level across its full range of operation;

- have a relative accuracy of at least two times the least significant digit at any Luminance level in its range of operation;

- maintain this accuracy at Luminance levels that are one-tenth of the minimum measured Luminance of the Display System;

- have an acceptance angle that is small enough to incorporate only the measurement field without overlapping the surrounding background.

Note: The photometer may be of the type that attaches directly to the display face (with a suction cup) or of the type that is held away from the display face. If of the latter type, the photometer should be well baffled to exclude extraneous light sources, including light from the background area of the test pattern.

For a film Display System the photometer may be appropriately used to measure the background Illuminance and the Luminance of the light-box on which the film will be displayed. The Luminance characteristics of the film Display System may be measured directly with the photometer or indirectly using measured optical density of the film and the values for the measured background Illuminance and the light-box Luminance.

D.1 Emissive Display Systems

D.1.1 Measuring the system Characteristic Curve

Before the characteristic Luminance response of the emissive Display System is measured, it is allowed to warm up as recommended by the manufacturer and is adjusted such that it conforms to the manufacturer’s performance specifications. In particular, adjustment procedures for setting the black and white levels of the display should be obtained from the Display System manufacturer. The goal is to maximize the dynamic Luminance Range of the display without introducing artifacts, resulting in the highest possible number of Just-Noticeable Differences (JNDs).

Note: A simple test that the system is set up properly can be performed by viewing the 5% and 95% squares in the SMPTE pattern. The perceived contrast between the 5% square and its 0% surrounding should be equal to the perceived contrast between the 95% square and a white square.

Measurement of the Characteristic Curve of the Display System may be accomplished using a test pattern (Fig. D.1-1) consisting of:

a square measurement field comprising 10% of the total number of pixels displayed by the system positioned in the center of the display;

a full-screen uniform background of 20% of maximum Luminance surrounding the target.

Note: With a measurement field of 10% of the total number of displayed pixels and a surrounding set to 20% of maximum Luminance, internal light scatter in the monitor causes the Luminance Range to be typically comparable to that found in radiographs, such as a thorax radiograph, when displayed on the CRT monitor.

[pic]

Figure D.1-1. The test pattern will be a variable intensity square in the center of a low Luminance background area.

Notes: 1. For example, on a 5-megapixel Display System with a matrix of 2048 by 2560 pixels, the target would be a square with 724 pixels on each side.

2. Ideally, the test pattern should fill the entire screen. Under certain windowed operating environments, it may be difficult to eliminate certain user-interface objects from the display, in particular, menu bars at the top of the screen. In this case, the background should fill as much of the screen as possible.

The Characteristic Curve of the Display System may be determined by

- turning off all ambient lighting (necessary only when a suction cup photometer is used or when a handheld photometer casts a shadow on the display screen);

- displaying the above test pattern;

- setting the DDL for the measurement field to a sequence of different values, starting with 0 and increasing at each step until the maximum DDL is reached;

- using a photometer to measure and record the Luminance of the measurement field at each command value.

As discussed in Annex C, the number and distribution of DDLs at which measurements are taken must be sufficient to accurately model the Characteristic Curve of the Display System over the entire Luminance Range.

Notes: 1. If a handheld photometer is used, it should be placed at a distance from the display screen so that Luminance is measured in the center of the measurement field, without overlapping the surrounding background. This distance can be calculated using the acceptance angle specification provided by the photometer manufacturer.

2. The exact number and distribution of DDLs should be based both on the characteristics of the Display System and on the mathematical technique used to interpolate the Characteristic Curve of the system. It is recommended that at least 64 different command values be used in the procedure.

3. Successive Luminance measurements should be spaced in time such that the Display System always reaches a steady state. It may be particularly important to allow the system to settle before taking the initial measurement at DDL 0.

As stated in the normative section, the effect of ambient light on the apparent Characteristic Curve must always be included when configuring a Display System to conform with the Grayscale Standard Display Function.

If a handheld photometer that does not cast a shadow on the display screen is used to measure the Characteristic Curve, then the Luminance produced by the display plus the effect of ambient light may be measured simultaneously.

When a suction cup photometer is used to take the Luminance measurements or when a handheld photometer casts a shadow on the display screen, all ambient lighting should be turned off while measuring the Characteristic Curve. The effect of ambient light is determined separately: The Display System is turned off, the ambient light is turned on, and the Luminance produced by scattering of ambient light at the display screen is measured by placing the photometer at a distance from the display screen so that its acceptance angle includes a major portion of the screen and that the measurement is not affected by direct illumination from areas outside the display screen. The Luminance related to ambient light is added to the previously measured Luminance levels produced by the Display System to determine the effective Characteristic Curve of the system.

Note: Changes in ambient lighting conditions may require recalibration of the display subsystem in order to maintain conformance to this standard.

In the following, an example for measurements and transformation of a Display Function is presented. The Display System for this example is a CRT monitor with display controller. It is assumed that the display controller allows a transformation of the DDLs with 8-bit input precision and 10-bit output precision.

The Luminance is measured with a photometer with a narrow (1o) acceptance angle. The ambient light level was adjusted as low as possible. No localized highlights were visible.

1) The maximum Luminance was measured when setting the DDL for the measurement field to the value that yielded the highest Luminance and the DDL of the surrounding to the middle DDL range. From this measurement, the Luminance - 20% of the maximum Luminance - for the surrounding of the measurement field was calculated.

2) The ambient light was turned off. With the photometer centered on the measurement field of the test pattern of Fig. D.1-1, the Luminance was measured when varying the input level Dm in increments of 1 from 0 to 255. The transformation operator of the hypothetical display controller linearly mapped 8 bits on the input to 10 bits on the output. The measured data represent the Characteristic Curve L = F(Dm) for the given operating conditions and this test pattern.

3) Next, the CRT was turned off and the ambient light turned on. The photometer was placed on the center axis of the CRT sufficiently far away so that it did not cast a shadow on the CRT face and its aperture intercepted light scattered from a major portion of the CRT face. The measured Luminance of 0.3 cd/m2 produced by the ambient light on the CRT face was added to the measured Luminance values of the Characteristic Curve without ambient light. The result is listed in Table D.1-1 and plotted in Fig. D.1-2.

[pic]

Figure D.1-2. Measured Characteristic Curve with Ambient Light of an emissive Display System

Table D.1-1 Measured Characteristic Curve plus Ambient Light

DDL Luminance DDL Luminance DDL Luminance DDL Luminance
0 0.305 1 0.305 2 0.305 3 0.305
4 0.305 5 0.305 6 0.305 7 0.305
8 0.305 9 0.305 10 0.305 11 0.307
12 0.307 13 0.307 14 0.307 15 0.307
16 0.307 17 0.307 18 0.307 19 0.307
20 0.307 21 0.307 22 0.310 23 0.310
24 0.310 25 0.310 26 0.310 27 0.320
28 0.320 29 0.320 30 0.330 31 0.330
32 0.340 33 0.350 34 0.360 35 0.370
36 0.380 37 0.392 38 0.410 39 0.424
40 0.442 41 0.464 42 0.486 43 0.512
44 0.534 45 0.562 46 0.594 47 0.626
48 0.674 49 0.710 50 0.750 51 0.796
52 0.842 53 0.888 54 0.938 55 0.994
56 1.048 57 1.108 58 1.168 59 1.232
60 1.294 61 1.366 62 1.438 63 1.512
64 1.620 65 1.702 66 1.788 67 1.876
68 1.960 69 2.056 70 2.154 71 2.248
72 2.350 73 2.456 74 2.564 75 2.670
76 2.790 77 2.908 78 3.022 79 3.146
80 3.328 81 3.460 82 3.584 83 3.732
84 3.870 85 4.006 86 4.156 87 4.310
88 4.456 89 4.608 90 4.766 91 4.944
92 5.104 93 5.268 94 5.444 95 5.630
96 5.864 97 6.050 98 6.238 99 6.438
100 6.610 101 6.820 102 7.024 103 7.224
104 7.428 105 7.644 106 7.872 107 8.066
108 8.298 109 8.528 110 8.752 111 8.982
112 9.330 113 9.574 114 9.796 115 10.060
116 10.314 117 10.560 118 10.820 119 11.080
120 11.340 121 11.620 122 11.880 123 12.180
124 12.460 125 12.700 126 13.020 127 13.300
128 13.720 129 14.020 130 14.360 131 14.640
132 14.940 133 15.300 134 15.600 135 15.900
136 16.240 137 16.560 138 16.920 139 17.220
140 17.600 141 17.940 142 18.240 143 18.640
144 19.120 145 19.460 146 19.800 147 20.260
148 20.560 149 20.920 150 21.360 151 21.760
152 22.060 153 22.520 154 22.960 155 23.300
156 23.700 157 24.080 158 24.600 159 24.980
160 25.520 161 26.040 162 26.480 163 26.700
164 27.380 165 27.620 166 28.040 167 28.580
168 28.980 169 29.400 170 29.840 171 30.540
172 30.800 173 31.380 174 31.880 175 32.400
176 33.060 177 33.400 178 34.040 179 34.400
180 34.840 181 35.360 182 35.900 183 36.400
184 37.060 185 37.400 186 38.300 187 38.420
188 39.160 189 39.760 190 39.980 191 40.840
192 41.540 193 41.900 194 42.800 195 43.060
196 43.620 197 44.520 198 44.620 199 45.500
200 46.100 201 46.380 202 47.400 203 47.600
204 48.320 205 49.060 206 49.380 207 50.320
208 50.920 209 51.600 210 52.420 211 52.680
212 53.520 213 54.220 214 54.620 215 55.420
216 56.100 217 56.600 218 57.400 219 57.820
220 58.660 221 59.320 222 59.800 223 60.720
224 61.520 225 62.240 226 63.040 227 63.480
228 64.460 229 65.020 230 65.500 231 66.500
232 66.960 233 67.840 234 68.600 235 68.980
236 70.040 237 70.520 238 71.420 239 72.180
240 72.900 241 73.980 242 74.580 243 75.320
244 76.200 245 76.540 246 77.720 247 78.220
248 79.200 249 79.880 250 80.420 251 81.560
252 81.960 253 83.140 254 83.720 255 84.340

D.1.2 Application of the Standard Formula

The section of the Grayscale Standard Display Function for the Luminance Range of the CRT monitor Display System is shown in Figure D.1-3. Minimum and maximum Luminance levels correspond to JND indices of JNDmin = 32.54 and JNDmax = 453.85, respectively. Thus, there are theoretically about 420 just-noticeable Luminance differences for the Standard Target (see Normative Section 6). Obviously, with 8-bit input digitization resolution, at best 256 noticeable Luminance increments can be realized.

D.1.3 Implementation of the Standard

The measured Characteristic Curve is interpolated for the available output levels Doutput , in this case, yielding 1024 Luminance levels LI,m . The Grayscale Standard Display Function is also interpolated between JNDmin and JNDmax ( (JND = [ JNDmax - JNDmin ]/1023 = [453.85 - 32.54]/1023) yielding 1024 Standard Luminance levels LI,STD . Interpolations can be performed by a variety of techniques. Here, a cubic spline technique was employed.

For every LI ,STD , the closest L J,m is determined. The data pair I , J defines the transformation between D input and Do utput (Table D.1-2) by which the Luminance response of the Display System is made to approximate the Grayscale Standard Display Function.

Table D.1-2Look-Up Table for Calibrating Display System

Input Output Input Output Input Output Input Output
0 0 1 118 2 131 3 140
4 148 5 153 6 160 7 164
8 169 9 173 10 178 11 182
12 185 13 189 14 191 15 194
16 198 17 201 18 204 19 207
20 210 21 214 22 217 23 219
24 222 25 225 26 228 27 231
28 234 29 237 30 240 31 243
32 245 33 248 34 251 35 253
36 255 37 257 38 260 39 263
40 265 41 268 42 271 43 274
44 276 45 279 46 282 47 284
48 287 49 290 50 292 51 295
52 298 53 301 54 303 55 306
56 308 57 311 58 314 59 317
60 319 61 320 62 323 63 326
64 329 65 331 66 334 67 336
68 339 69 342 70 345 71 347
72 350 73 353 74 356 75 359
76 361 77 364 78 367 79 370
80 372 81 375 82 378 83 381
84 383 85 385 86 388 87 391
88 393 89 396 90 399 91 402
92 405 93 407 94 410 95 413
96 416 97 419 98 422 99 425
100 428 101 431 102 434 103 437
104 440 105 443 106 445 107 448
108 450 109 452 110 456 111 459
112 462 113 465 114 468 115 471
116 474 117 477 118 480 119 483
120 486 121 490 122 492 123 495
124 499 125 502 126 505 127 509
128 511 129 513 130 516 131 519
132 522 133 526 134 529 135 532
136 535 137 539 138 542 139 545
140 549 141 552 142 555 143 559
144 562 145 565 146 569 147 572
148 575 149 578 150 581 151 585
152 588 153 591 154 595 155 599
156 602 157 605 158 609 159 613
160 616 161 619 162 623 163 627
164 631 165 633 166 637 167 640
168 643 169 646 170 650 171 655
172 657 173 663 174 666 175 669
176 674 177 678 178 682 179 684
180 688 181 693 182 696 183 700
184 703 185 706 186 711 187 714
188 719 189 723 190 727 191 731
192 735 193 738 194 743 195 745
196 752 197 754 198 758 199 764
200 766 201 769 202 775 203 777
204 783 205 787 206 789 207 796
208 799 209 805 210 808 211 811
212 818 213 821 214 827 215 830
216 834 217 838 218 841 219 848
220 851 221 856 222 861 223 864
224 870 225 874 226 880 227 883
228 889 229 893 230 897 231 901
232 905 233 911 234 915 235 922
236 925 237 931 238 935 239 941
240 945 241 951 242 955 243 960
244 964 245 969 246 975 247 979
248 985 249 991 250 995 251 1002
252 1006 253 1012 254 1016 255 1023

D.1.4 Measures of Conformance

The FIT and the LUM metrics proposed in Annex C are applied to determine the macroscopic and microscopic approximation of the L J,m to the L I,STD . Figure D.1-3 shows the perceptually linearized Display Function superimposed on the Grayscale Standard Display Function and Figure D.1-4 summarizes the results of the two metrics. A good global fit was achieved as demonstrated by the nearly horizontal-line fit as best fit obtained with the FIT metric. The RMSE is acceptable. All 255 P-Value intervals lead to JNDs on the transformed Display Function for the Standard Target.

[pic]

Figure D.1-3. Measured and interpolated Characteristic Curve, Grayscale Standard Display Function and transformed Display Function of an emissive Display System. The transformed Display Function for this Display System matches the Grayscale Standard Display Function and the two curves are superimposed and indistinguishable.

[pic]

Figure D.1-4. LUM and FIT measures of conformance for a the transformed Display Function of an emissive Display System

D.2 Transparent hardcopy devices

D.2.1 Measuring the system Characteristic Curve

A transparent hardcopy device is exemplified by a laser printer (including processor) which prints (exposes and processes) one or more images on a sheet of transparent film (typically a 14” x 17” film). This film is eventually placed over a high Luminance light-box in a darkened room for viewing.

The Characteristic Curve for such a transparent hardcopy device is obtained by printing a test image consisting of a pattern of n bars, each bar having a specific numeric value (DDL). The optical density of each printed bar is then measured, using a transmission densitometer, for each of the printed bars.

To accurately define a printer’s Characteristic Curve, it is desirable that n be as large as possible (to capture as many points as possible on the Characteristic Curve). However, the limitations on absolute quantitative repeatability imposed by the printer, processor, or media technologies may dictate that a much smaller value of n be used (to prevent a conformance metric which is sensitive to differences from becoming unstable and meaningless, as the density differences between adjacent bars become “in the noise” as the number of bars becomes large).

One example of a test image is a pattern of 32 approximately equal-height bars, spanning the usable printable region of the film, having 32 approximately equi-spaced DDLs as follows:

[pic]

Figure D.2-1. Layout of a Test Pattern for Transparent Hardcopy Media

To define a test pattern with n DDLs for a printer with an N-bit input, the DDL of step # i can be set to

DDLi = (2 N -1) (D.2-1)

rounded to the nearest integer.

The tabulated values of DDLi and the corresponding measured optical densities ODi constitute a Characteristic Curve of the printer.

D.2.2 Application of the Grayscale Standard Display Function

The films which are produced by transparent hardcopy printers are often brought to a variety of locations, where they may be viewed on different light-boxes and under a variety of viewing conditions. Accordingly, the approach of PS 3.14 is to define, for hardcopy transparent printers, what densities (rather than Luminances) should be produced, and to provide here a method of applying the Grayscale Standard Display Function to the transparent hardcopy case, based on parameters which are typical of the expected range of light-box Luminances and other viewing parameters.

The specific parameters which are used in the following example are as follows:

L0 (Luminance of light-box with no film present): 2000 cd/m2

La (ambient room light reflected by film): 10 cd/m2

Dmin (minimum optical density obtainable on film): 0.20

Dmax (maximum optical density desirable on film): 3.00.

The process of constructing a table of desired OD values from the Grayscale Standard Display Function begins with defining the Luminance Range and the corresponding range of the Just-Noticeable Difference Index, j. The minimum and maximum Luminance values are given respectively by

L min = L a + L o 10 -Dmax = 12.0 cd/m2 (D.2-2)

L max = L a + L o 10 -Dmin = 1271.9 cd/m2 (D.2-3)

Next, calculate the corresponding Just-Noticeable Difference Index values, jmin and jmax. For the current example, we obtain

j min = 233.32 (D.2-4)

j max = 848.75 (D.2-5)

This gives us the range of j-values which the printer should cover. The printer should map its minimum input (P-Value = 0) to jmin and the corresponding Lmin. It should map its maximum input (P-Value = 2N-1 where N is the number of input bits) to jmax and the corresponding Lmax. At any intermediate input it should map its input proportionately:

j (PV) = j min + (j max -j min ) [pic] (D.2-6)

and target values for the Luminance given by the Standard’s formula: L(j(P-Value)). This “targeting” consists of producing an optical density OD for this P-Value which will give the desired Luminance L(j(P-Value)) under the conditions of L0 and La previously defined. The required density can thus be calculated as follows: .

[pic] [pic] (D.2-7)

D.2.3 Implementation of the Grayscale Standard Display Function

Carrying this example into the even more specific case of a printer with an 8-bit input leads to the following table, which defines the OD’s to be generated for each of the 256 possible P-Values.

Table D.2-1 Optical Densities for Each P-Value for an 8-Bit Printer

P-Value Optical Density (OD) P-Value Optical Density (OD) P-Value Optical Density (OD) P-Value Optical Density (OD)
0 3.000 1 2.936 2 2.880 3 2.828
4 2.782 5 2.739 6 2.700 7 2.662
8 2.628 9 2.595 10 2.564 11 2.534
12 2.506 13 2.479 14 2.454 15 2.429
16 2.405 17 2.382 18 2.360 19 2.338
20 2.317 21 2.297 22 2.277 23 2.258
24 2.239 25 2.221 26 2.203 27 2.185
28 2.168 29 2.152 30 2.135 31 2.119
32 2.103 33 2.088 34 2.073 35 2.058
36 2.043 37 2.028 38 2.014 39 2.000
40 1.986 41 1.973 42 1.959 43 1.946
44 1.933 45 1.920 46 1.907 47 1.894
48 1.882 49 1.870 50 1.857 51 1.845
52 1.833 53 1.821 54 1.810 55 1.798
56 1.787 57 1.775 58 1.764 59 1.753
60 1.742 61 1.731 62 1.720 63 1.709
64 1.698 65 1.688 66 1.677 67 1.667
68 1.656 69 1.646 70 1.636 71 1.626
72 1.616 73 1.605 74 1.595 75 1.586
76 1.576 77 1.566 78 1.556 79 1.547
80 1.537 81 1.527 82 1.518 83 1.508
84 1.499 85 1.490 86 1.480 87 1.471
88 1.462 89 1.453 90 1.444 91 1.434
92 1.425 93 1.416 94 1.407 95 1.398
96 1.390 97 1.381 98 1.372 99 1.363
100 1.354 101 1.346 102 1.337 103 1.328
104 1.320 105 1.311 106 1.303 107 1.294
108 1.286 109 1.277 110 1.269 111 1.260
112 1.252 113 1.244 114 1.235 115 1.227
116 1.219 117 1.211 118 1.202 119 1.194
120 1.186 121 1.178 122 1.170 123 1.162
124 1.154 125 1.146 126 1.138 127 1.130
128 1.122 129 1.114 130 1.106 131 1.098
132 1.090 133 1.082 134 1.074 135 1.066
136 1.058 137 1.051 138 1.043 139 1.035
140 1.027 141 1.020 142 1.012 143 1.004
144 0.996 145 0.989 146 0.981 147 0.973
148 0.966 149 0.958 150 0.951 151 0.943
152 0.935 153 0.928 154 0.920 155 0.913
156 0.905 157 0.898 158 0.890 159 0.883
160 0.875 161 0.868 162 0.860 163 0.853
164 0.845 165 0.838 166 0.831 167 0.823
168 0.816 169 0.808 170 0.801 171 0.794
172 0.786 173 0.779 174 0.772 175 0.764
176 0.757 177 0.750 178 0.742 179 0.735
180 0.728 181 0.721 182 0.713 183 0.706
184 0.699 185 0.692 186 0.684 187 0.677
188 0.670 189 0.663 190 0.656 191 0.648
192 0.641 193 0.634 194 0.627 195 0.620
196 0.613 197 0.606 198 0.598 199 0.591
200 0.584 201 0.577 202 0.570 203 0.563
204 0.556 205 0.549 206 0.542 207 0.534
208 0.527 209 0.520 210 0.513 211 0.506
212 0.499 213 0.492 214 0.485 215 0.478
216 0.471 217 0.464 218 0.457 219 0.450
220 0.443 221 0.436 222 0.429 223 0.422
224 0.415 225 0.408 226 0.401 227 0.394
228 0.387 229 0.380 230 0.373 231 0.366
232 0.359 233 0.352 234 0.345 235 0.338
236 0.331 237 0.324 238 0.317 239 0.311
240 0.304 241 0.297 242 0.290 243 0.283
244 0.276 245 0.269 246 0.262 247 0.255
248 0.248 249 0.241 250 0.234 251 0.228
252 0.221 253 0.214 254 0.207 255 0.200

Plotting these values gives the curve of Figure D.2-3.

[pic]

Figure D.2-3. Plot of OD vs P-Value for an 8-Bit Printer

D.2.4. Measures of Conformance

As an example, a bar pattern with 32 optical densities was printed on transmissive media (film). Beforehand, the printer had been set up to print over a density range from 0.2 (Dmin) to 3.0 (Dmax) and had been pre-configured by the manufacturer to use the Grayscale Standard Display Function, converted by the manufacturer into the table of target density values vs. P-Values described earlier.

The test pattern which was used for this was an 8-bit image consisting essentially of 32 horizontal bars. The 32 P-Values used for the bars were as follows: 0, 8, 16, 25, 33, 41, 49, 58, 66, 74, 82, 90,99, 107, 115, 123, 132, 140, 148, 156, 165, 173, 181, 189, 197, 206, 214,222, 230, 239, 247, 255.

For a given film, the 32 bars' optical densities were measured (near the middle of the film), converted to Luminances (using the standard parameters of light-box Luminance and reflected ambient light described earlier),and converted to Just-Noticeable Difference Indices by mathematically computing j(L) from L(j), where L(j) is the Grayscale Standard Display Function of Luminance L as a function of the Just-Noticeable Difference Index j. For each of the 31 intervals between consecutive measured values, a calculated value of "JNDs per increment in P-Values" was obtained by dividing the difference in Just-Noticeable Difference Index by the difference in P-Values for that interval. (In these calculations, density, L, and j are all floating-point variables. No rounding to integer values is done, so no truncation error is introduced.)

In this example, the film's data could be reasonably well fit by a horizontal straight line. That is, the calculated "JNDs per increment in P-Values was essentially constant at 2.4. A mathematical fit yielded a slight non-zero slope (specifically, dropping from 2.5 to 2.3 as the P-Value went from 0 to 255), but the 0.2 total difference was considerably smaller than the noise which was present in the 31 individual values of "JNDs per increment in P-Value" so is of doubtful significance. (The "noise" referred to here consists of the random, non-repeatable variations which are seen if a new set of measured data (e.g., from a second print of the same test pattern) is compared with a previous set of measurements.)

No visual tests were done to see if a slope that small could be detected by a human observer in side-by-side film comparisons.

Incidentally, if one considers just the 32 original absolute measured densities (rather than differential values based on small differences), one finds, in this case, quite reasonable agreement between the target and measured optical densities (within the manufacturer's norms for density accuracy, at a given density). But if one uses any metric which is based on differential information over small intervals, the results must be considered more cautiously, since they can be strongly affected by (and may be dominated by) various imperfections which are independent of a device's "true" (or averaged over many cases) characteristic behavior.

D.3 Reflective Display Systems

This last example illustrates how conformance with the Grayscale Standard Display Function may be achieved for a thermal-dye-transfer paper printer/office-light system. The thermal-dye-transfer printer produces black-and-white grayscale prints on a semi-glossy 8-inch x 10-inch heavy-gauge paper. The print is illuminated uniformly by fluorescent lamps so that the minimum reflective density produces a Luminance of 150 cd/m2. The hypothetical transformation operator is assumed to have equal input and output digitization resolution of 8 bits.

D.3.1. Measuring the system Characteristic Curve

A print with a 64-step grayscale tablet was printed for DDLs 4, 8, 12, ...,248, 252, 255. The reflection optical densities (from 0.08 to 2.80) were measured with a densitometer. The Luminance levels corresponding to the measured optical densities and illumination conditions are plotted in Fig. D.3-1.

[pic]

Figure D.3-1 Measured and interpolated Characteristic Curve and Grayscale Standard Display Function for a printer producing reflective hard-copies

D.3.2. Application of the Grayscale Standard Display Function

This last example illustrates how conformance with the Grayscale Standard Display Function may be achieved for a thermal-dye-transfer paper printer/office-light system. The thermal-dye-transfer printer produces black-and-white grayscale prints on a semi-glossy 8-inch x 10-inch heavy-gauge paper. The print is illuminated uniformly by fluorescent lamps so that the minimum reflective density produces a Luminance of 150 cd/m2. The hypothetical transformation operator is assumed to have equal input and output digitization resolution of 8 bits.

D.3.3 Implementation of the Grayscale Standard Display Function

The measured Characteristic Curve is interpolated for the available DDLs yielding 256 Luminance levels L I,m . The Grayscale Standard Display Function is also interpolated between JNDmin and JNDmax ( DJND = [ JND max - JND min ]/255) yielding 256 Standard Luminance levels L I,STD .

For every L I,STD , the closest L J,m is determined. The data pair I , J defines the transformation between D input and D output (Table D.3-1 and Fig. D.3-2) by which the Luminance response of the Display System is made to approximates the Grayscale Standard Display Function.

[pic]

Figure D.3-2 Transformation for modifying the Characteristic Curve of the printer to a Display Function that approximates the Grayscale Standard Display Function

Table D.3-1 Look-Up Table for Calibrating Reflection Hardcopy System

P-Value DDL P-Value DDL P-Value DDL P-Value DDL
0 6 1 9 2 12 3 15
4 18 5 20 6 27 7 29
8 30 9 31 10 31 11 32
12 33 13 33 14 34 15 36
16 38 17 40 18 41 19 42
20 43 21 44 22 45 23 59
24 60 25 61 26 62 27 62
28 63 29 63 30 64 31 64
32 65 33 65 34 65 35 66
36 66 37 67 38 67 39 68
40 70 41 74 42 75 43 76
44 78 45 84 46 85 47 86
48 87 49 87 50 88 51 89
52 89 53 91 54 92 55 94
56 95 57 96 58 97 59 97
60 98 61 99 62 99 63 100
64 101 65 102 66 103 67 104
68 105 69 106 70 107 71 108
72 109 73 110 74 112 75 114
76 116 77 118 78 119 79 120
80 121 81 122 82 122 83 123
84 123 85 124 86 125 87 125
88 126 89 126 90 127 91 127
92 128 93 129 94 130 95 131
96 133 97 134 98 135 99 136
100 136 101 137 102 138 103 138
104 139 105 139 106 140 107 141
108 143 109 145 110 147 111 148
112 149 113 150 114 151 115 152
116 153 117 154 118 154 119 155
120 156 121 156 122 157 123 158
124 159 125 160 126 160 127 162
128 163 129 164 130 165 131 166
132 167 133 168 134 169 135 170
136 170 137 171 138 172 139 172
140 173 141 174 142 175 143 175
144 176 145 177 146 178 147 179
148 179 149 180 150 181 151 182
152 182 153 183 154 184 155 184
156 185 157 186 158 186 159 187
160 187 161 188 162 188 163 189
164 189 165 190 166 190 167 190
168 191 169 191 170 192 171 192
172 192 173 193 174 194 175 194
176 195 177 195 178 196 179 197
180 198 181 199 182 199 183 200
184 200 185 201 186 202 187 202
188 203 189 203 190 204 191 204
192 205 193 205 194 206 195 207
196 207 197 208 198 209 199 210
200 211 201 212 202 213 203 214
204 214 205 215 206 216 207 216
208 217 209 218 210 219 211 219
212 220 213 220 214 221 215 222
216 222 217 223 218 223 219 224
220 224 221 225 222 226 223 226
224 227 225 228 226 228 227 230
228 231 229 232 230 234 231 235
232 236 233 238 234 238 235 239
236 240 237 241 238 242 239 242
240 243 241 244 242 245 243 246
244 247 245 248 246 249 247 250
248 250 249 251 250 251 251 252
252 252 253 253 254 253 255 254

D.3.4 Measures of Conformance

The FIT and LUM metrics as proposed in Annex C are applied to determine the macroscopic and microscopic approximation of the LJ,m to the LI,STD . Fig. D.3-3 shows the perceptually linearized Display Function superimposed on the Grayscale Standard Display Function and Figure D.3-4 summarizes the results of the two metrics. FIT provides as best fit of the JNDs/Luminance interval a straight line almost perfectly parallel to the horizontal axis indicating good global fit of the transformed Display Function with the Grayscale Standard Display Function. The RMSE computed by LUM is relatively large indicating more pronounced local deviations from the Grayscale Standard Display Function as, for example, with the soft-copy Display System illustrated in Section D.1. At least in part, the larger RMSE is due to the fact that the input and output digitization resolution for the transform are equal. The transformation table (Table D.3-1) and Fig. D.3-2 show that several P-Values lead to the same Luminance levels on the transformed Display Function. In fact, only 205 of the 255 Luminance intervals lead to JNDs for the Standard Target.

[pic]

Figure D.3-3. Transformed Display Function and superimposed Grayscale Standard Display Function for a reflective hard-copy Display System. The transformed Display Function for this Display System matches the Grayscale Standard Display Function and the two curves are superimposed and indistinguishable.

[pic]

Figure D.3-4 Measures of conformance for a reflective hard-copy Display System with equal input and output digitization resolution of 8 bits