D.2.2 Application of the Grayscale Standard Display Function
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### D.2.2 Application of the Grayscale Standard Display Function

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:

- 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

Equation D.2-2.

Lmin= La + L010-Dmax = 12.0 cd/m2

Equation D.2-3.

Lmax= La + L010-Dmin = 1271.9 cd/m2

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

Equation D.2-4.

jmin = 233.32

Equation D.2-5.

jmax = 848.75

This gives us the range of j-values that 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:

Equation D.2-6.

j(PV) = jmin + (jmax-jmin)

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 La previously defined. The required density can thus be calculated as follows:

Equation D.2-7.

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