For transmissive hardcopy printing, the relationship between luminance, L, and the printed optical density, D, is:

where:

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: