DICOM PS3.14 2019b - Grayscale Standard Display Function |
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For reflective hardcopy printing, the relationship between luminance, L, and the printed optical density, D, is:

If film is to be printed with a density ranging from D_{min} to D_{max}, the final luminance will range between
and
and the j values will correspondingly range from j_{min} = j(Lmin) to j_{max} = j(L_{max}).

If this span of j values is represented by an N-bit P-Value, ranging from 0 for j_{min} to 2N-1 for j_{max}, the j values will correspond to P-Values as follows:

and the corresponding L values will be L(j(p)).

Finally, converting the L(j(p)) values to densities results in

DICOM PS3.14 2019b - Grayscale Standard Display Function |
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