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.

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.

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 JND_min and JND_max (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 Figure D.3-2) by which the Luminance response of the Display System is made to approximates the Grayscale Standard Display Function.

The FIT and LUM metrics as 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.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.