Modeling of Toner Coverage in Laser Printers

Publication Date


Type of Culminating Activity


Degree Title

Master of Science in Electrical Engineering


Electrical and Computer Engineering

Major Advisor

Elisa H. Barney Smith


Paper documents, whether printed by laser printers, FAX, copier, typesetting, or typewriter, contain distortions. When the document is scanned into a computer, these distortions can lead to errors during Optical Character Recognition (OCR). The goal of this research is to create a mathematical model that is a representation of the distortion caused by the xerographic machines. The model can be used with the OCR to improve the character recognition.

A mathematical model for the density of toner on paper that leads to the average coverage on paper was formulated. The density function represents the shape that the laser beam creates on the photoconductor. The intensity profile of the laser beam is a Gaussian distribution.

The coverage equation has parameters that represent the number of toner particles, the size of tone particles, and the standard deviation of the spread of the toner particles. A simplistic document was created to measure the range of parameters in the coverage equation. A range of values corresponding to printed samples were measured and noted.

Simulations that represented placing toner on paper were done using functions in the Matlab program. First, the number of simulations needed to be averaged to produce an error less than 10 percent was found. To narrow the range of parameters used in the coverage equation for the experiment, pixel images were simulated varying the number of toner particles, the size of the toner particles, and the spread of the toner particles. The simulated images were compared with the magnified single pixel images. The parameter values corresponding to the simulated single pixel image that best represented the laser printed image were then used in the remaining simulations or experiments.

For different shapes, the theoretical coverage equation was tested with the average simulated images. The number of simulations created and averaged for each shape was 100,000. The comparison between the theoretical coverage and the average simulated image was less than 10 percent error in all cases. Therefore, the coverage equation is a good representation of the average toner placed on paper through the xerographic printing process.

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