Direct Color Consistency Control for Xerographic Printing

The digital color printing process can be described by the color reproduction characteristics (CRC) function that maps the input color to the output color. The CRC map is high dimensional in that there are potentially high number of output colors that a digital color printing process can reproduced. To maintain color consistency, it is desirable to have the CRC to match the desired CRC map at all times. In this paper, we first propose an effective sparse sensing approach known as time-sequential sampling to retrieve the time-varying CRC using small number of color samples at each print cycle. The availability of this information enables formulation of a 2-STAGE process level control system: STAGE-I is a curve fitting robust control that makes best use of the xerographic actuators and STAGE-II is a image feedforward compensation scheme. The key contribution of this paper is in proposing direct CRC control(full closed loop) for maintaining color consistency, as opposed to stabilizing the TRC of all the primary color separations (i.e. Cyan, Magenta, Yellow and Black) in previous works. Effective CRC stabilization is demonstrated using the proposed approach while requiring small number of color samples. Introduction An important performance criterion in digital xerographic printing is that any desired colors in the desired customer image(s) are faithfully reproduced at all times. Achieving good color consistency is difficult because the marking process is subject to many disturbances including temperature, humidity, material age and variations, etc. These factors contribute to prints that look different from one print to the next and from the desired customer image. In this paper we propose a direct color control approach to maintain color consistency of xerographic printing process. Notice that, unlike the control objective for most processes which is to control or regulate the output of the process, the color control problem consists of maintaining the process itself to be constant and stable. The difference is because every customer image to be printed can contain many and any possible colors which the xerographic printer must reproduce correctly all at once. Moreover, xerographic printers are often used in an on-demand manner in which consecutive customer images are different. By ignoring the spatial dimension (such as lines and textures) of print quality for the moment and focusing on the issue of consistent color reproduction only, a color xerographic printer can be represented by the color reproduction characteristics(CRC) function CRC(t) : C → C ,xdesired 7→ yprinted (1) where C is any consistent 3-dimensional colorspaces e.g. CIE L∗a∗b∗, CMY, etc. An ideal printer is the one in which the CRC matched the desired CRC map. In order to motivate the need for direct CRC control for maintaining color consistency, a brief description of the digital xerographic printer is in order. A digital xerographic color printer generates colors by printing and overlaying the Cyan, Magenta, Yellow and blacK (CMYK) separations. The printing of each color separation is characterized by the tone reproduction curve (TRC), T RC : T → T , τdesired 7→ τprinted , where the tone, τ of the separation is the solidness of the primary toner color. Hence, the control problem can be formulated for the printing of each color separation. In this case, the control objective is to maintain and stabilize the tone reproduction curve (TRC) for each separation. However in this approach, the output colors are consistent only if the manner in which the primaries are combined is stable and constant i.e. there is no disturbances in the color mixing process. The color mixing is a complex process that is dictated by possibility of mis-registration of the different primary layers and disturbances in the color fusing process(typically through heating). Therefore, variations of colors can occur despite having all the primary TRCs stabilized. Hence, direct CRC control that enable full feedback color control system will likely be more effective. However, the color control formulation poses significant problems for sensing and control. The color print sensing involves multi-dimensional time-varying spatial signal (1 temporal dimension and 3 spatial/color dimensions) using only small number of n color samples. In this paper, this sensing issue is addressed using time-sequential sampling as reported previously in [1]. The color print control involves control of potentially high number of reproducible colors using limited actuation authorities. In this paper, a 2-STAGE process level control is used to maintain color consistency. STAGE-I control makes use of the limited xerographic actuators to stabilize the print process in a least squares sense. Residual variations can then be compensated using STAGE-II by continuously updating a software profile in the image processing process. Time-Varying CRC The time-varying CRC map given in (1) is potentially infinite dimensional because ideally any specified colors can be reproduced. This map is made up of three main processes : image processing (software), xerographic marking (hardware) and human perception (psychophysics). Hence, CRC(t) := fpercept } {{ } human ◦ fcomb ◦ fmark } {{ } printer ◦ fhtone ◦ fsep } {{ } image processing (2) where fsep separates the image into primary color planes1, fhtone performs half-toning on each color separations, fmark prints these 1The separation process is typically achieved by using the inverse map of the actual printing process. To improve the print quality, in current printing system this inverse map is periodically updated through the device characterization methods i.e. the ICC profile [2]. half-tones separations, fcomb forms a composite image from the printer separations, and fpercept models the human color perception. In both sensing and control for maintaining color consistency, it is convenient to take the input colorspace as the CMY colorspace (i.e. taking fsep as an identity map) and the output colorspace as the CIE L∗a∗b∗ colorspace. The CMY colorspace is used as the input colorspace because it is the colorspace where colors are specified in typical digital color printers(corresponding to C,M,Y,K print engines). The CIE L∗a∗b∗ colorspace is used as the output colorspace because it is a perceptually uniform deviceindependent colorspace that enables meaningful formulation of print quality requirements. Henceforth, CRC(t) is defined with input CMY colorspace(denoted by CCMY) and output CIE L∗a∗b∗ colorspace(denoted by CL∗a∗b∗ ), unless stated otherwise. Uniformly discretizing the CMY colorspace domain, typically given by CCMY = [0,1)3 ⊂ R3, by M1, M2 and M3 points in each of the C, M, Y coordinates respectively, the CRC can be adequately approximated by its response at a finite number of Mt = M1M2M3 color combinations. Thus, the xerographic color control process at time t = kT ∈R+ where T is the inter-sampling time can be represented by: CRC(k)= [ L∗ 1(k), . . . ,L ∗ Mt (k),a ∗ 1(k), . . . ,a ∗ Mt (k),b ∗ 1(k), . . . ,b ∗ Mt (k) ]T