We have developed a simulation model for monochrome and color laser printers that relies on knowing the physical structure of the halftone dot (including light adsorption and scattering), the nature of the halftone technology (dithered screens, stochastic processes, dot-on-dot and dot-off-dot patterns) and the optical interactions between the toner dots and paper substrate. The model is capable of allowing a system designer to simulate the final halftone and its imaging characteristics, thus allowing for a faster design cycle given the physical data defining the optical characteristics of the toners, paper substrate and toner development curve. The resulting simulations provide dot gain, color, and general tone-scale reproduction for any given, well-defined halftone pattern or method.
This simulation model starts with the creation of something that 'looks' like a real toner dot seen under a low-power microscope. To generate such dots, a 21×21 simulation array is assumed. Each dot location on a photoconductor is illuminated by a scanning laser beam that leaves a residual charge profile that, when passed through a threshold development curve, generates the toner dot. The dots and surrounding clear areas have noise-induced defects based on using a Poisson distribution that combines the fluctuations in light exposure and the point-to-point quantum efficiency of the photoconductor. The resulting halftone patterns look very much like those seen with real halftones under the microscope (see Figure 1
Figure 1. Simulated halftone (top) and real halftone (bottom) based on identical inputs. The paper structure is not simulated by the model.
The next step was to link the optical scattering of light from the paper substrate and any given halftone dot pattern. An optical spread function is assumed (based on measurements) for the paper substrate. Light passing through the toner or directly onto the paper is scattered according to the nature of the optical spread function. The 'scattered' light then passes back through the toner and into the air (to be measured). However, a significant amount of light will be reflected at the paper/toner-air interface back into the paper substrate, and this process continues until the light is totally absorbed or released.
The resulting tone scales were then compared to the ideal, hard-dot model of Murray-Davies1
and, based on this comparison, the dot gain (the amount bigger than intended the dots appear to be) was calculated as was the n
value (another correction factor) of the modified Yule-Nielsen2
model. Both were highly dependent on the range of the optical spread function (with a saturation effect when the average optical scattering equaled the pitch of the dots), the amount of reflected light (more dot-gain for increasing light reflection), and the actual dot patterns (more dot-gain for stochastic halftones than for central dot halftones).
The results agree with an analytical models developed by Rodgers.3,4
Also, due to the nature of our model, it is possible to separate the contributions to dot gain by the physical development and the optical coupling. Comparisons between the model and a well-characterized experimental print engine demonstrated that the monochrome model could predict experimental results. The advantage of this over the outstanding work of Rodgers is that any halftone pattern can be used rather than one constrained by the needs of a complex analytical model.
Figure 2. The small green patch is reproduced by a dot-on-dot (top) and dot-off-dot (bottom) halftone. The yellow layer is nearest the air interface and tends to scatter red light. Placing the yellow layer on top shifts the green to be warmer relative to the original. The dot-off-dot pattern shows the great impact due to scattering: in combination with optical dot-gain, it tends to desaturated the green.
The model was extended to color systems by assuming a given lay-down order for the cyan, magenta, yellow, and black toners. Each was defined by its absorption and the scattering of red, green, and blue light. The toner scattering is assumed to take place at the boundaries between layers. The same multiple reflections discussed above in the monochrome model were used in this one. Any given halftone pattern or mechanism can be used, and the input separations (cyan, magenta, yellow and black) were adjusted based on their respective unwanted adsorptions (of the pigments) and whether a dot-on-dot or dot-off-dot halftone was used.
This model enabled the study of the impact of layer order on color and tone scale reproduction, and clearly demonstrated that it is best to 'bury' a scattering toner closer to the paper substrate rather than allow it to remain near the air interface. The model also clearly demonstrated the change in color reproduction between dot-on-dot and dot-off-dot halftones (see Figure 2
) as well as the impact of stochastic halftones. The amount of dot gain was found to be lower than in the monochrome systems, which may be due to the unwanted absorptions of the various toners (a cyan toner has significant blue density, etc.).
Future work will involve refining the scattering component of the model and going to a spectral version of it. We will also attempt to exploit other model features: the fact that it allows straightforward simulation of the impact of dot placement errors, for instance, and that it can perform the simulation of various halftone properties such as the modulation transfer function, edge raggedness, and the visibility of halftone contours.