# 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)