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.