A mathematical analysis of an electronic dot generating scanner for dot resolution and tone reproduction

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Title: A mathematical analysis of an electronic dot generating scanner for dot resolution and tone reproduction
Author: Waechter, Frederick K.
Abstract: An electronic dot generating scanner is a complex machine. This complexity is based in the photographic methods which the scanner is designed to duplicate. This study addresses the mathematical principles of the entire scanner system. This paper was intended to provide an improved understanding of the scanner system. The hypothesis states that a mathematical analysis with experimental verification can be developed to accurately model the internal optics, tone reproduction, and output dot characteristics of an electronic dot generating scanner. The analysis begins with a functional block diagram, which shows the information flow through the scanner. This diagram breaks the process into its smaller components and provides the framework for the mathematical analysis. The diagram has an accompanying word description for each section of the scanner. The basic function of the scanning optics, data compression, gradation, color correction, digitization, halftone screening, and film exposure is discussed for the scanner system. The system characterization develops a mathematical analysis based on the functional block diagram. It details the theory behind each section of the scanner. Fourier optics, electrical engineering, and photographic tone reproduction theories are applied to the various scanner functions. The scanning optical system is analyzed using Fourier transform techniques to describe the effect of the imaging system on image transmission. Modulation Transfer Functions (MTFs) are used to show the output frequency spectrum of the scanning aperture. The electronic unsharp masking is modeled by using an optically equivalent process. The photomultiplier and associated data compression's effect on the reproduction of shadow detail is demonstrated graphically. The improvement in the photomultiplier response is noted due to logarithmic compression. The flexibility of the gradation processing is demonstrated through a graphical representation of the treatment of a typical signal. The gradation selection provides the operator with the ability to tailor the output to the reproduction requirements of each transparency. This flexibility is a great advantage, if properly utilized, because it allows customization of each separation. The color computer is described in general terms. The subjective manner, which color correction is determined is not addressed in this paper. Digitization is described with its associated compromises in signal integrity. The sampling and quantization processes are detailed. The screening computer and linearization together effectively transform a digitized gray level into a dot on film. The linearization sets up the scanner for its processing environment. The output signal from the screening computer drives a laser modulator, which controls the light traveling through the fiber optic cables to expose the film. The film is developed to produce the final separation. An experimental tone reproduction curve was produced. The type of curve produced versus the expected is discussed. The input/output characteristics are examined through the scanning of a UGRA resolution wedge. The UGRA wedge input and separation film output is analyzed using microphotographic methods to examine structure. This hypothesis was not proven because of the many assumptions required by the scope of this project, which made the prediction of overall systems results not possible. Although, each function (minus color correction) of the scanner is analyzed. This model of the entire scanning system from input optics through the final film exposure can be utilized to improve understanding of the entire scanner system.
Record URI: http://hdl.handle.net/1850/10436
Date: 1987-10

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