The films that 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 PS3.14 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 that are typical of the expected range of light-box Luminances and other viewing parameters.

The specific parameters that are used in the following example are as follows:

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

Next, calculate the corresponding Just-Noticeable Difference Index values, j_min and j_max. For the current example, we obtain

This gives us the range of j-values that the printer should cover. The printer should map its minimum input (P-Value = 0) to j_min and the corresponding Lmin. It should map its maximum input (P-Value = 2N-1 where N is the number of input bits) to j_max and the corresponding L_max. At any intermediate input it should map its input proportionately:

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 that will give the desired Luminance L(j(P-Value)) under the conditions of L₀ and L_a previously defined. The required density can thus be calculated as follows: