D Illustrations for Achieving Conformance with the Grayscale Standard Display Function (Informative)
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# D Illustrations for Achieving Conformance with the Grayscale Standard Display Function (Informative)

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 (Figure 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.

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

### Note

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.

### Note

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 (1°) 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 Figure 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/m2produced 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 Figure D.1-2.

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 LJ,m is determined. The data pair I,J defines the transformation between Dinput and Doutput (Table D.1-2) by which the Luminance response of the Display System is made to approximate the Grayscale Standard Display Function.

Table D.1-2. Look-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,mto 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.

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.

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

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