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

[pic]

where:

L0 is the maximum luminance obtainable from diffuse reflection of the illumination that is present.

If film is to be printed with a density ranging from Dmin to Dmax, the final luminance will range between:

[pic] , [pic]

and the j values will correspondingly range from jmin = j(Lmin) to jmax = j(Lmax).

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

[pic]

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

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

[pic].

Note: Typical values for the parameters used in reflective hardcopy printing areL0 = 150 cd/m2.