Printing System Models - Control of Color Imaging Systems: Analysis and Design - page 596

The compact characterization of a printer as an analytical MIMO system is very
important for applications. However, this is not enough for control. The dot printer
model shown above for electrophotographic printers is meant to represent how a
single rendered dot results into color when produced with four separations. In an
attempt to print a single dot, EP prints may print a light dot or no dot at all depending
on the state of the ROS (raster output scanner) and development process. In a single
dot system, not only do the neighboring dots interact, but they also spread as the
laser beam cannot expose binary pixels perfectly at the micron level. Even if the laser
exposes the dots well, the development process cannot make the toner perfectly
adhere to the exposed dot, thereby injecting nonlinearities in the tone curves. At
least the nonlinearities have to be modeled so that the analytical models presented
above can become useful for developing system-level calibration, pro ling, and

control algorithms.

10.3 MODULATION TRANSFER FUNCTIONS
The MTF approach is used to characterize the spatial response of the printing system
when dots are spread over an entire page to form a color image. This approach is
based on the spatial frequency response of an imaging system. High spatial frequen-
cies correspond to

fine details in the image that are lost or enhanced due to dot spread
caused by laser spreading or developability defects, light scattering, diffusion of light
through the paper, etc. The dot spread and light spread functions can be measured
and incorporated at each step in the EP process.
The exposure step involves generating a laser intensity pro

le for each separ-
ation. The input image consisting of CMYK separations is halftoned prior to expos-
ure. The halftoned separations are exposed on the PR (to form a latent image) using a
Gaussian or sinc 2 beam pro le models the dot gain due to the laser

spreading effect at the micron level. The resulting latent image contains the spatial
frequencies that are not

le. This beam pro

filtered out by the MTF for the exposure station since the
dot spreading produces a low-pass filtering effect on the image. Thus, with this

process, we create the halftoned image using the dot exposure model including the
majority of spatial effects. The schematics in Figure 10.37a and b show the exposure
process and Figure 10.38a and b show the functions used to model the effects of
exposure MTF.
The rotation of the polygon mirror moves the laser beam across the width of the
PR belt, and the transition to the next face on the polygon corresponds to the next
line in the latent image. This direction of motion is termed as the scan direction. The
perpendicular direction that is controlled by the angular rotation of the PR drum is
called the cross scan or process direction.
The image is written on the PR as a series of overlapping envelopes. We consider
the case when the laser exposes the PR in a raster scan format. We assume that the
pixels where the halftone pattern takes a binary '' 1 '' need to be exposed by the laser
and the spreading effect of the laser beam is modeled using a Gaussian beam or a
sinc 2 function (Figure 10.38a and b) or an experimentally measured function.
The main parameter of the laser pro le is the width of the beam at 50% of the

maximum intensity. The beam pro les are obtained as a matrix containing the laser