As an example, we find the optimal gray levels by solving Equation 9.134 for spatial TRC data. The quality of TRCs derived from equispaced levels is compared with the quality derived from levels determined by using the optimal gray level method. A system is assumed with a small number of gray levels (32, rather than 256) to make the demonstration tractable with a reasonable amount of effort and a small number of test prints and measurements.

A first printing is performed using all of the 32 gray levels in a calibration target where a gray strip for each level spans across the page (Figure 9.53a). Measurements are taken of the spatial nonuniformity using a scanner for each gray level to obtain spatial TRC data. These first printing and measurement results are used to 1. Derive TRC eigenvector matrix that characterize the system. In our example, a reduced set of two basis vectors is selected as the system characterization. Prior experience shows that this number is adequate when significant drift in the print engine response is not present. More basis vectors can be included depending on the level of accuracy needed.

2. Derive the optimal gray levels for future calibration updates. Optimal gray levels are derived for three separate cases: 2 levels, 4 levels, and 8 levels.

A second printing of the 32 levels is performed and used for the following steps:

1. Complete print engine state (spatial TRCs) is measured for t>0. These measurements serve as a reference for comparison of TRCs derived from subsets of gray levels.

2. TRCs are generated using several equispaced subsets of gray levels, namely 2, 4, and 8 levels.

3. TRCs are generated using the optimal levels derived above.

4. Derived TRCs are compared to the fully measured TRCs