Lattice-Based $n$-Point Time-Sequential Sampling and Two-Stage Process Control for Maintaining Tone Consistency of Xerographic Processes

Abstract

This paper proposes: 1) a lattice based time-sequential sampling approach that requires the printing and measuring of the smallest number of tonal samples to characterize the high-dimensional tone reproduction curve (TRC) at each print cycle, and 2) based on this characterization, the design of a two-stage control strategy to maintain tone consistency of a xerographic printing process. The printer's TRC maps the desired tones to the actual printed tones and it is high dimensional due to the large number of desired tones. To avoid using many sensors, the measurement of the TRC is achieved by sampling it time-sequentially and by reconstructing the TRC from the samples via a Kalman filter. In time-sequential sampling, only a few distinct <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> tones are printed and measured at each print cycle. Using a lattice-theoretic framework, an optimal time-sequential sampling sequence with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n=1$</tex></formula> is designed. This is then extended to the case of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n&gt;1$</tex></formula> to enable the tradeoff between sampling time and sampling resources. With the reconstructed time-varying TRC, a two-stage control strategy uses both the physical xerographic and the image processing processes to compensate for the TRC variations from the desired TRC. Simulations and experiments show that the proposed TRC stabilization system is effective for practical implementation. By stabilizing all the cyan, magenta and yellow primaries of the color xerographic print system, color consistency can be maintained. Furthermore, the proposed time-sequential sampling approach with <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$n=1$</tex></formula> exceeds the capability of conventional three-fixed-point sampling (light, middle, and dark tones) approach while requiring three times fewer samples.