D.3 Reflective Display Systems
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## 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 Figure D.3-1.

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 LI,m. The Grayscale Standard Display Function is also interpolated between JNDmin and JNDmax (DJND = [JNDmax - JNDmin]/255) yielding 256 Standard Luminance levels LI,STD.

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

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. Figure 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 Figure 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.

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.

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

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