The robustness of three digital halftoning techniques are simulated for a hypothetical electrophotographic laser printer subjected to dynamic environmental conditions over a copy run of one thousand images. Mathematical electrophotographic models have primarily concentrated on solid area reproductions under time-invariant conditions. The models used in this study predict the behavior of complex image distributions at various stages in the electrophotographic process. The system model is divided into seven subsystems: Halftoning, Laser Exposure, Photoconductor Discharge, Toner Development, Transfer, Fusing, and Image Display. Spread functions associated with laser spot intensity, charge migration, and toner transfer and fusing are used to predict the electrophotographic system response for continuous and halftone reproduction. Many digital halftoning techniques have been developed for converting from continuous-tone to binary (halftone) images. The general objective of halftoning is to approximate the intermediate gray levels of continuous tone images with a binary (black-and-white) imaging system. Three major halftoning techniques currently used are Ordered-Dither, Cluster-Dot, and Error Diffusion. These halftoning algorithms are included in the simulation model. Simulation in electrophotography can be used to better understand the relationship between electrophotographic parameters and image quality, and to observe the effects of time-variant degradation on electrophotographic parameters and materials. Simulation programs, written in FORTRAN and SLAM (Simulation Language Alternative Modeling), have been developed to investigate the effects of system degradation on halftone image quality. The programs have been designed for continuous simulation to characterize the behavior or condition of the electrophotographic system. The simulation language provides the necessary algorithms for obtaining values for the variables described by the time-variant equations, maintaining a history of values during the simulation run, and reporting statistical information on time-dependent variables. Electrophotographic variables associated with laser intensity, initial photoconductor surface voltage, and residual voltage are degraded over a simulated run of one thousand copies. These results are employed to predict the degraded electrophotographic system response and to investigate the behavior of the various halftone techniques under dynamic system conditions. Two techniques have been applied to characterize halftone image quality: Tone Reproduction Curves are used to characterize and record the tone reproduction capability of an electrophotographic system over a simulated copy run. Density measurements are collected and statistical inferences drawn using SLAM. Typically the sharpness of an image is characterized by a system modulation transfer function (MTF). The mathematical models used to describe the subsystem transforms of an electrophotographic system involve non-linear functions. One means for predicting this non-linear system response is to use a Chirp function as the input to the model and then to compare the reproduced modulation to that of the original. Since the imaging system is non-linear, the system response cannot be described by an MTF, but rather an Input Response Function. This function was used to characterize the robustness of halftone patterns at various frequencies. Simulated images were also generated throughout the simulation run and used to evaluate image sharpness and resolution. The data, generated from each of the electrophotographic simulation models, clearly indicates that image stability and image sharpness is not influenced by dot orientation, but rather by the type of halftoning operation used. Error-Diffusion is significantly more variable than Clustered-Dot and Dispersed-Dot at low to mid densities. However, Error-Diffusion is significantly less variable than the ordered dither patterns at high densities. Also, images generated from Error-Diffusion are sharper than those generated using Clustered-Dot and Dispersed-Dot techniques, but the resolution capability of each of the techniques remained the same and degraded equally for each simulation run.
Library of Congress Subject Headings
Electrophotography; Image processing
Department, Program, or Center
Chester F. Carlson Center for Imaging Science (COS)
Nazzaro, Alfonse, "Simulation of an electrophotographic halftone reproduction" (1991). Thesis. Rochester Institute of Technology. Accessed from
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