Replicated multi-channel sensors for decucing ink thicknesses in color printing devices

Abstract

A method and computing system are proposed for deducing ink thickness variations from solid-state multi-sensor measurements performed online on a printing press or printer. The computed ink thickness variations enable controlling the ink deposition and therefore the color accuracy. Ink thickness variations are expressed as ink thickness variation factors incorporated into an ink thickness variation and sensor response enhanced spectral prediction model. The ink thickness variation computing system comprises multi-channel sensor devices (e.g. red, green, blue, near infra-red), a processing module, and a computing system. The multi-channel sensor devices are replicated over the width of the print sheet. Preferably embodied by Single Photon Avalanche Diodes (SPADs), due to their high-speed acquisition capabilities, they provide responses according to the reflectance of small area segments within a print sheet. The processing module accumulates the digital sensor responses and forwards them to the computing system, which deduces the ink thickness variations.

Description

The present patent application is a continuation-in-part of U.S. patent application Ser. No. 10/631743, Prediction model for color separation, calibration and control of printers, inventors R. D. Hersch, P. Emmel, F. Collaud, filed Aug. 1, 2003.

BACKGROUND OF THE INVENTION

The present invention relates to the field of color printing and more specifically to the control of color printer actuation parameters. It discloses a new concept of non-expensive replicated illuminating and sensor devices placed on the printer in face of the moving paper sheets as well as a spectral prediction model extension adapted to the proposed set of illuminating and sensor devices.

Color control in printing presses is desirable in order to ensure that effectively printed colors correspond to the desired colors, i.e. the colors expected by the prepress color separation stage. Color consistency is desirable both across consecutive sheets of a multi-sheet print job and also from print job to print job.

In the prior art, densitometers were often used to control the amount of ink of single ink printed patches. The densitometer measures the optical density, which is an approximate measure of the ink thickness. In the prior art, the control of print actuation parameters affecting the printed output such as the ink thickness is generally performed by an operator or by an apparatus measuring the density of solid ink or of halftone ink patches, see U.S. Pat. No. 4,852,485 (Method of operating an autotypical color offset machine, Inventor F. Brunner, issued Aug. 1, 1989). Special patches are usually integrated along the borders of printed sheets and serve as a means to measure their density. These special patches need however to be subsequently cut out.

U.S. Pat. No. 6,230,622 (Image data-oriented printing machine and method of operating the same, to P. Dilling, issued May 15, 2001) teaches a method for operating a printing machine with an expert system which determines the effect of the interaction of a large number of print parameters and acts on some of these parameters in order to reach a high print quality. The proposed method relies only on density measurements. Due to the large number of parameters which need to be taken into account, this solution seems complex and costly.

U.S. Pat. No. 5,903,712, Ink separation device for printing press ink feed control, to X. X. Wang, and R. J. Nemeth, filed Oct. 5, 1995, issued May 11, 1999, teaches an ink separation device or process where red, green, blue and infra-red scalar reflection values within a printed sheet are measured and converted into cyan, magenta, and yellow dot size values according to a previously initialized transfer function. By comparing the so-obtained dot size values with reference dot size values, a dot size ratio is derived to adjust the ink feed rate of the press. The transfer function is a multi-variable polynomial of order 6. It comprises about 80 different coefficients which need to be regressed for each combination of paper and ink set. A specially printed test form with hundreds of patches is needed to enable these regressions. In that invention, the relationship between 4 channel sensor responses and the ink dot sizes is considered to be unknown, i.e. a black box whose behavior is modeled by the multi-variable high-order polynomial. Such high order polynomials are known to oscillate between the known values of input/output variables and therefore do not always provide a correct mapping between sensor input variables and ink dot size output variables. In contrast, in our invention, we rely on a physically-based spectral prediction model describing the interaction of light, ink halftones and paper, as well as the ink spreading phenomenon. The model we propose is therefore robust and each of its elements (paper reflectance, ink transmittances, effective surface coverages) is separately characterized from spectral reflectance or from multi-channel sensor response measurements.

U.S. Pat. No. 6,684,780, Ink control in printing press, filed Jan. 21 2003, issued Feb. 3, 2004, to Y. Shiraishi, teaches a method for ink key aperture control by using a color difference between an original image and an RGB CCD camera image of the print. By using a conversion table, color differences are converted into corresponding desired density corrections, which, through a second conversion table, are converted into ink key aperture correction values. Since these two conversion tables are deduced from experiments which may have been performed under different printing conditions (temperature, settings of the press, etc.), the control of the ink aperture is not precisely adapted to the current operating conditions of the press. In addition, experience shows that it is very difficult to control the ink feed of 4 inks (c,m,y,k) with a 3-sensor system only. Experience also shows that using a spectral prediction model incorporating explicitly the ink thickness terms provides more robustness than a pure colorimetric approach.

U.S. Pat. No. 6,611,357, Method of stipulating values for use in the control of a printing machine, to K. Wendt and P. Schramm, filed Jan. 26, 2001, issued Aug. 26, 2003, teaches a method for controlling printers by determining according to the surface coverages of individual inks within an original image element the predicted (desired) color spectrum, and achieving that color spectrum by varying the actual area coverages of the individual inks by multiplicative factors deduced from spectra predictions. Spectra are predicted according to a weighted average of the reflection spectra of the inks, the weights being determined by the respective surface coverages of the inks. The reflectance spectra of ink superpositions are not considered. It is known in the art that no accurate spectral or color predictions can be made without considering explicitly the reflectance of superposed inks.

U.S. Pat. No. 6,679,169, Ink control model for controlling the ink feed in a machine which processes printing substrates, filed Oct. 24, 2002, issued Jan. 20, 2004, to Anweiler, Gateaud, Hauck and Mayer teaches a method for controlling the ink feed in a printing press by deducing the ink feed rate from stored physical properties of inks and paper. That method does not consider controlling the ink feed rate according to sensor responses of illuminated polychromatic halftones.

U.S. Pat. No. 4,975,852, Process and apparatus for the ink control of a printing machine, to G. Keller and H. Kipphan, filed Jan. 5, 1989, issued Dec. 4, 1990, U.S. Pat. No. 5,182,721, Process and apparatus for controlling the inking process in a printing machine, to H. Kipphan, G. Loffler, G. Keller and H. Ott, filed Sep. 28, 1990, issued Jan. 26, 1993, and U.S. Pat. No. 6,041,708, Process and apparatus for controlling the inking process in a printing machine, to H. Kipphan, G. Loffler, G. Keller and H. Ott, filed Aug. 22, 1994, issued Mar. 28, 2000 teach methods to derive ink layer thickness variations from spectral reflectance differences of specially printed test patches by converting these differences to CIELAB differences and by multiplying these differences by the inverse of a matrix whose components are derivatives of the CIELAB components in respect to the cyan, magenta and yellow ink thicknesses. The elements of the matrix are dependent on the area coverage of the inks and need therefore to be calibrated for each considered test patch.

U.S. Pat. No. 6,564,714, Spectral color control method, to D. Brydges and E. Tobiason, Jul. 26, 2001, issued May 20, 2003, teaches a method to derive ink layer thickness correction values from spectral reflectance differences of specially printed test patches. Ink layer thickness differences are obtained by multiplying the spectral reflectance difference vector with a correction matrix expressing the derivatives of the ink layer thicknesses in respect to each of the monochromatic reflectance values. The elements of the correction matrix are dependent on the area coverage of the inks and need therefore be calibrated for each test patch. In contrast, our invention provides a single computation model for deriving ink thickness variations from halftone prints. It does not require halftone area coverage dependent calibrations to be performed.

U.S. Pat. No. 7,077,064, Methods for measurement and control of ink concentration and film thickness, to D. Rich, filed Apr. 19, 2005, issued Jul. 18, 2006, teaches a method to deduce ink thickness as well as ink concentration from red, green and blue responses of a camera, using a variant of the Kubelka-Munk model. It is known that the Kubelka-Munk model only works on uniformly diffuse layers and is therefore not applicable to halftones. In contrast, our invention deduces ink thickness variations from halftones.

US parent patent application Ser. No. 10/631743 (Prediction model for color separation, calibration and control of printers, inventors R. D. Hersch, P. Emmel, F. Collaud, filed Aug. 1, 2003) teaches a method to deduce the ink thicknesses for a color patch printed with 2, 3 or 4 inks. The method works for deducing the ink thicknesses on single ink patches, on two ink patches and on 3 ink patches. But due to the uncertainty between joint variations in the ink thicknesses of cyan, magenta, and yellow and a variation in thickness of black, the method does not work well for the set of cyan, magenta, yellow and black inks. In addition, that method does not teach how to calibrate the prediction model with halftones that are an integral part of a printed document page delivered to a customer. The present invention improves upon that application by introducing a 4^th infra-red sensor to separate ink thickness variations of black from joint ink thickness variations of cyan, magenta and yellow. In addition, the present invention clearly separates the calibration process into an offline calibration with spectral measurement devices on specially printed patches and an online calibration with multi-sensor responses on halftones located within a normal printed page.

U.S. patent application Ser. No. 10/698667 (Inks Thickness Consistency in Digital Printing Presses, to Staelin et al., filed Oct. 31, 2003) teaches a model for estimating ink thickness control parameters such as the developer voltage in case of an electrographic printer. This model takes as input values measurements of the internal state of a digital printing press as well as of the densities of monochrome patches. This patent application does neither teach how to obtain ink thickness control parameters from polychromatic halftone patches nor from halftones being part of the actual printed document pages.

U.S. Pat. No. 7,000,544, (Measurement and regulation of inking in web printing, to Riepenhoff, filed 1^st Jul. 2002) teaches a process for measuring the mean spectrum integrated over a stripe of the printed sheet. It also teaches a device for regulating the ink density by predicting the mean reflection spectrum along a stripe thanks to a correspondence function between image data located along the stripe and the resulting reflection spectrum. That correspondence function does not incorporate an explicit ink thickness variable, nor does it make the distinction between nominal surface coverages and effective surface coverages. It therefore does not account for the ink spreading phenomenon.

U.S. Pat. No. 7,252,360, Ink thickness variations for the control of color printers, filed 25^th Oct. 2005, issued 7^th of Aug. 2007, to R. D. Hersch (also inventor in the present patent application), P. Amrhyn and M. Riepenhoff, teaches a spectral prediction model for deducing ink thickness variations working with a single head spectrophotometer located on the running printing press, for acquiring halftones or mean reflection spectra over stripes (spectral acquisition averaged over the length of a print). The present invention improves upon U.S. Pat. No. 7,252,360, by replacing the single moving head spectrophotometer by a sensing system formed by non-moving multiple-channel solid-state high-speed acquisition sensor devices replicated over the width of the printer (printed sheet width). Solid state sensor devices, especially when embodied by Single Photon Avalanche Diodes, provide a cheaper solution, compared with a moving head spectrophotometer. In addition, in the present invention, the high-speed sensor response enables sensing small halftone area segments which do not incorporate much paper white and exhibit therefore less noise. Furthermore, the new online calibration steps are performed on the running press and do not require specially printed uniform color patches or control stripes.

The present disclosure provides a robust means of deducing online and in real time ink thickness or ink volume variations of cyan, magenta, yellow and black on a running printing press or color printer, without needing at print time specific solid or halftone patches within the printed sheet. In addition, due to an optional online calibration, the deduced ink thickness variations are accurate in respect to the current printing device operating conditions (temperature, settings of the printing device, etc. . . . ).

SUMMARY

The present invention proposes a method and a computing system for deducing ink thickness variations from multi-channel sensor responses acquired online during print operation of a printing press or a printer. Acquiring the ink thickness variations online and in real-time enables regulating the ink deposition process during normal print operation. Real-time online control of the ink deposition process enables keeping a high color accuracy from print sheet to print sheet and from print job to print job. This is especially important if the ink deposition process is not stable when working in open loop mode.

Ink thickness variations are expressed as ink thickness variation factors incorporated into an ink thickness variation and sensor response enhanced spectral prediction model. The method for computing ink thickness variations comprises both calibration and ink thickness variation computation steps. The calibration steps comprise the measurement and adjustment of paper reflectance, possibly the calculation of internal paper reflectance, the calculation of ink transmittances from measured reflectances, the computation of scalar ink thicknesses of solid superposed inks and, in order to account for ink spreading, the computation of effective surface coverages of single ink halftones in different superposition conditions. By interpolation, we obtain the effective surface coverage curves mapping nominal to effective surface coverages of single ink halftones in different superposition conditions. The calibration steps can be divided into offline and online calibration steps. The offline calibration steps require specially printed patches such as solid ink and solid ink superposition patches on which spectral reflectance measurements are performed. From these spectral reflectance measurements, the internal reflectance of paper and the transmittance of the inks are obtained. The optional online calibration steps improve the calibration in case of changes in the printer operating conditions, e.g. a change in temperature, a change of paper, or a new set of inks which differs from the previous set. Online calibration steps are performed only with multi-channel sensor responses from printed area segments located within the printed sheet. They may comprise the recalibration of the paper reflectance, and possibly the calibration or recalibration of the effective surface coverage curves. They may also comprise deducing reference thickness variations which are then used to compute thickness variations normalized in respect to these reference thickness variations.

In respect to the ink thickness variation computation steps, the thickness variation and sensor response enhanced spectral prediction model comprises as solid colorant transmittance of two or more superposed solid inks the transmittance of each of the contributing superposed ink raised to the power of a product of two variables, one variable being the superposition condition dependent ink thickness and the other variable being the ink thickness variation factor. The ink thickness variations are fitted by minimizing a distance metric between predicted multi-channel sensor responses and acquired multi-channel sensor responses, the predicted multi-channel sensor responses being computed according to the ink thickness variation and sensor response enhanced spectral prediction model.

With one of the multi-sensor channels also operating in the near infra-red region, for black inks absorbing in the near infra-red region, the ambiguity between ink thickness variations of the black ink and joint ink thickness variations of the cyan, magenta, and yellow inks is resolved.

In case that the area sensed by the multi-sensor devices comprises significantly different colors, the obtained sensor response is a mean value over sensor responses across several nearly uniform color sub-areas. Corresponding predicted sensor responses can be computed by predicting sub-areas sensor responses and by performing a weighted average over these sub-area sensor responses, the weights corresponding to the respective surface coverages of the sub-areas.

If the nominal surface coverages of the halftone area segment on which thickness variations are to be performed are unknown, it is possible, in addition to the calibration of the transmittances and the thicknesses of the inks, to measure sensor responses from a reference print under reference settings and to deduce with the thickness enhanced spectral prediction model the corresponding reference effective surface coverages. The sensor responses are then predicted with the deduced reference effective surface coverages. Ink thickness variations are computed by minimizing a distance metric between predicted sensor responses and measured sensor responses. The computed ink thickness variations represent ink thickness variations in respect to the reference print.

The disclosed ink thickness variation computing system computes ink thickness variations online and in real time. It comprises multi-channel sensor devices, a processing module, and a computing system. The multi-channel sensor devices are replicated over the width of the print sheet. The multi-channel sensor devices respond at different spectral sensibility ranges within the visible and near infra-red wavelength range. The multi-channel sensor devices, due to their high-speed acquisition capabilities, provide responses according to the reflectance of small areas within a print sheet. The processing module accumulates the digital sensor responses and forwards them to the computing system, which according to an ink thickness variation and sensor response enhanced spectral prediction model deduces the ink thickness variations.

In a preferred embodiment, the sensor devices are Single Photon Avalanche Diodes, which create a pulse upon arrival of a photon. With pulse dead times in the order of 20 ns to 50 ns it is possible to have a maximal photon count between 20000 and 50000 pulses per millisecond. This allows to have both low sensor acquisition times (e.g. 0.2 ms to 1 ms) and a high signal to noise ratio. At a printer speed of 10 m/s, the area segment length passing underneath a sensor has a corresponding length of 2 mm to 10 mm. In a possible layout, there may be one colored, respectively infra-red, LED in front of each sensor with the light of the LED being directed towards the print and being reflected into the corresponding sensor. The colored and infra-red LED's may also be replaced by a white LED followed by a corresponding colored, respectively infra-red, filter. To avoid specular reflection, the incident light may be oriented towards the print at 45 degrees and read out at zero degrees. Alternately, to discard specular reflections, it is also possible to have a first polarizer on the incident light path and second polarizer turned by 90 degrees in respect to first one on the reflected light path.

In a further possible layout of the illumination and sensing system, the sensing system may be formed by the multi-channel sensors located within a single integrated circuit. The illumination may be produced by a white LED whose light is directed towards the print. The reflected light is for example filtered by specific filters each located in front of its respective sensor.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a schematic view of an ink thickness variation computation model embodiment, where ink thickness variations dr_C, dr_M, dr_Y are deduced from known nominal surface coverages of cyan (c), magenta (m), and yellow (y) inks and from sensor responses q_r, q_g, q_b;

FIG. 2 illustrates a generalization of the ink thickness variation computation model of FIG. 1, for a set of 4 inks with nominal input surface coverages c₁, c₂, c₃, c₄, 4-channel sensor responses q_α, q_β, q_γ, q_δ and output ink thickness variations dr₁, dr₂, dr₃, dr₄;

FIG. 3A shows a sensing system comprising 4-channel illuminating/sensor devices replicated over the width of the printed sheet and their corresponding input and output signals;

FIG. 3B shows a sensor processing module comprising a multiplexer, a counter, fast logic (FL) and a microcontroller (μC);

FIG. 4A shows a 4 channel illuminating/sensing device set and its corresponding input and output signals;

FIG. 4B shows one integrated circuit comprising a 4 channel sensing device set, pulse counters and a multiplexer;

FIG. 5A shows an embodiment of a single illuminating/sensing device with an incident angle of 45° and a light capture angle of 0°;

FIG. 5B shows a further embodiment of a single illuminating/sensing device comprising a light-emitting diode (LED), a polarizing filter 514 on the incident light path, a beam splitter 510 and a second polarizing filter 511 on the reflected light path;

FIG. 5C shows a further embodiment with a white diffuse illumination 534 illuminating the print sheet 537 and a sensing device 533 whose focalizing lens 531 is coated with a filtering substance 530.

FIG. 6 shows a possible embodiment of blue, green, red and infra-red sensor sensibilities;

FIG. 7 shows an ink thickness variation computing system comprising a sensing system 708, a computing system 701 and a print actuation parameter driving module 709; and

FIGS. 8A and 8B illustrate respectively examples of deduced normalized ink thickness variations of the magenta, respectively the black ink in many different print trials, where the ink feed of one or of several inks has been increased or decreased.

DETAILED DESCRIPTION OF THE INVENTION

The present invention proposes models, a computing system as well as methods for deducing ink thickness variations from sensor responses obtained on a printer or printing press, online and in real-time. The computed ink thickness variations enable controlling the ink deposition and therefore the color accuracy, in the case of high-speed printing presses, of network printers and desktop printers. The ink thickness variations can be directly used for the real-time control of the print actuation parameters which influence the ink deposition, such as the ink feed in the case of an offset press.

The proposed method and computing system rely on a spectral prediction model incorporating as input parameters the responses from multi-channel sensors, as internal parameters the ink thicknesses and as output parameters ink thickness variation factors. Hereinafter, such a model is called “thickness variation and sensor response enhanced spectral prediction model”. Ink thickness variations are deduced by an “ink thickness variation computation model”. When the ink thickness variation computation model is embodied by a computing system, it becomes an “ink thickness variation computing system”. By deriving from the thickness variation computation model a series of processing steps, we obtain a thickness variation prediction method.

In the present invention, unknown variables are fitted by minimizing a distance metric (also called difference metric) between a measured reflection spectrum, respectively sensor responses, and a reflection spectrum, respectively sensor responses predicted according to a spectral reflectance prediction model. The preferred distance metric is the sum of square differences between the corresponding measured and predicted reflection density spectra, respectively sensor density responses, with reflection density spectra, respectively sensor density responses, being computed according to formula (2a), respectively (2b). Minimizing a distance metric can be performed, for example with a software package such as Matlab or with a program implementing Powell's function minimization method (see W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Fetterling, Numerical Recipes, Cambridge University Press, 1st edition, 1988, section 10.5, pp. 309-317).

The present invention deals with deducing ink thickness variations from sensor responses of illuminated halftones with color inks. The substrate on which the inks are printed is paper in the general case. But in other cases, the substrate can be another diffusely reflecting substrate such as a polymer. In the present invention, the term “paper” is meant in a generic sense and designates any diffusely reflecting substrate.

Once printed, the physical size of the printed dot generally increases, partly due to the interaction between the ink and the paper, and partly due to the interaction between successively printed ink layers. This phenomenon is called physical (or mechanical) dot gain or ink spreading. Therefore, “nominal surface coverages” (or simply “nominal coverages”) are initially specified amounts of inks and “effective surface coverages” (or simply “effective coverages”) are physical surface coverages inferred from the spectral or sensor response measurements of the printed patches according to the considered spectral prediction model.

Halftones which are printed with multiple, partly superposed inks are called polychromatic halftones. A solid ink patch is a patch printed with 100% surface coverage. A halftone is a printed area, e.g. a small rectangle within a printed sheet, where at least one ink layer is printed in halftone. Halftones may form an integral part of a printed document page delivered to a customer, i.e. they may be located within color images, within gray or colored bars separating different parts of a printed document page, or they may form the gray or colored background of advertisements.

A calibration halftone patch is a uniform color patch where one ink is printed as a halftone at a specified nominal surface coverage value, for example 25%, 50% or 75%. This halftone may be printed alone on paper or printed in superposition with other solid inks. Note that since one of the goals of the present invention is to avoid printing special control stripes or halftone patches at the borders of a printed document page, the disclosed online calibration does not require calibration halftone patches.

A printed area segment may be located within a printed page. The printed area segment is a rectangle whose length corresponds to a small displacement of a print page location under a sensor. The width of the rectangle corresponds to the width of the sensor.

The considered inks are usually the standard cyan, magenta, yellow and black inks. But the disclosed ink thickness variation computation model may also be applied in a straightforward manner to inks of other colors. For example, the set of inks may comprise the standard cyan, magenta and yellow inks plus one or several additional inks such as orange, red, green and blue. The term “ink” is used in a generic sense: It may comprise any colored matter that can be transferred onto specific locations of a substrate (e.g. offset inks, ink-jet inks, toner particles, liquid toner, dye sublimation colorants, etc. . . . ).

In the present invention, the multi-channel sensors replicated over the width of the printed sheet comprise for each channel an illuminating and sensor device, also called “illuminating/sensor device”. In the case of multiple channels, we have a “set of illuminating/sensor devices” or simply an “illuminating/sensor set”. When such an illuminating/sensor set is replicated over the width the print, it is called “illuminating/sensor array”. An illuminating/sensor set may comprise one illuminating device and several sensors.

Throughout the application the expressions “printing device”, “printer” and “printing press” are used interchangeably, i.e. the disclosure with respect to one is equally applicable with respect to the other. The invention is advantageous for computing ink thickness variations or equivalently, ink colorant concentration variations by a computing system which regulates the print actuation parameters controlling the amount of deposited colorant substance or ink, such as the ink feed (ink volume), the ink thickness, or the ink colorant concentration.

The present invention also enables controlling the ink deposition in printers, such as electro-photographic printers, ink-jet printers, solid-tone printers, liquid-toner printers, dye sublimation printers and thermal transfer printers. In such printers, there is often the possibility of varying the size of the individual printed dot. The number of available dot sizes depends on the printer technology, and may range from 3 to 255 different dot sizes. Increasing, respectively decreasing, the amount of ink can also be achieved by increasing, respectively decreasing, the individual printed dot size.

For a printing press (e.g. a web-offset press), deducing ink thickness variations from sensor responses enables the automatic regulation of the thickness (or volume) of the deposited inks by acting on the print actuation parameters such as the ink feed. For a digital printer hooked onto a computer network or for a desktop printer, deduction of ink thickness variations enables adjusting the printer settings by acting on the print actuation parameters, such as the droplet ejection mechanism in the case of an ink-jet printer, the electronic charge and discharge mechanism as well as possibly the fusing mechanism in the case of an electrophotographic printer, and the head element temperature profiles in the case of thermal transfer or dye sublimation printers.

Deducing the thickness variations of the inks from sensor responses of illuminated halftones is achieved thanks to an enhanced spectral reflectance prediction model which has an explicit representation of the wavelength-dependent ink transmittances, of the wavelength-dependent reflectance of paper, of the wavelength-dependent sensibilities of each of the multi-channel sensor devices, of wavelength-independent ink thicknesses, and of wavelength-independent ink thickness variations. This ink thickness and sensor response enhanced spectral reflectance prediction model takes into account ink spreading, i.e. the mapping from nominal to effective dot surface coverages under different ink superposition conditions.

The embodiment of the disclosed ink thickness variation computation model presented here uses as base spectral prediction model either the Clapper-Yule spectral reflection prediction model or the Yule-Nielsen modified spectral Neugebauer model, see D. R. Wyble, R. S. Berns, A Critical Review of Spectral Models Applied to Binary Color Printing, Journal of Color Research and Application, Vol. 25, No. 1, 4-19, 2000, hereinafter referenced as [Wyble and Berns 2000].

The Clapper-Yule model, see F. R. Clapper, J. A. C Yule, “The effect of multiple internal reflections on the densities of halftone prints on paper”, Journal of the Optical Society of America, Vol. 43, 1953, 600-603, hereinafter referenced as [Clapper53], takes simultaneously into account halftone patterns and multiple internal reflections occurring at the interface between the paper and the air and assumes a relatively high screen frequency. In a recent extension, the Clapper-Yule model has been combined with a Saunderson corrected spectral Neugebauer model which gives assumes a low screen frequency, see R. D. Hersch and al, “Spectral reflection and dot surface prediction models for color halftone prints”, R. D. Hersch, et. al., Journal of Electronic Imaging, Vol. 14, No. 3, August 2005, pp. 33001-12, incorporated in the present disclosure by reference, hereinafter referenced as [Hersch05A]. The weighting factor b indicates the relative weight of the Saunderson corrected Neugebauer model component. For four ink prints, this composed Clapper-Yule Saunderson corrected Neugebauer spectral reflection prediction model, hereinafter referenced as “CYSN spectral prediction model” is formulated as follows: $\begin{array}{cc}R\left(\lambda \right)=K*r_s+\left(1-r_s\right)*r_g\left(\lambda \right)*\left(1-r_i\right)·\left[\begin{array}{c}b·\sum _{j=1}^{16}\frac{a_j*{t_j\left(\lambda \right)}^2}{1-r_g\left(\lambda \right)*r_i*t_j^2\left(\lambda \right)}+\\ \left(1-b\right)·\frac{{(\sum _{j=1}^{16}{a}_j*t_j\left(\lambda \right))}^2}{1-r_g\left(\lambda \right)*r_i*\sum _{j=1}^{16}{a}_j*t_j^2\left(\lambda \right)}\end{array}\right]& \left(1a\right)\end{array}$
where K is the fraction of specular reflected light reaching the spectrophotometer (for a 45/0 degrees measuring geometry, K=0), r_s is the surface reflection at the air paper coating interface, r_g is the paper substrate reflectance, r_i is the internal Fresnel reflection factor obtained by integrating the Fresnel reflection factor over all orientations, a_j represents the fractional surface coverage of a colorant j, t_j represents the transmittance of a colorant j, and R(λ) is the predicted reflection spectrum. The b weighting factor is fitted for a giving printing process by minimizing on a subset of halftones a difference metric between predicted reflection spectrum and measured reflection spectrum. At a screen frequency (screen ruling) above 120 lpi (lines per inch), experience shows that b tends to zero, i.e. the Clapper-Yule component of the model is sufficient and provides a high enough accuracy.

Instead of using the Clapper-Yule Saunderson corrected Neugebauer model (CYSN) as base spectral reflectance model, one may equally well use the Yule-Nielsen modified spectral Neugebauer model (YNSN) extended with effective coverages in different superposition conditions (see R. D Hersch and al, “Improving the Yule-Nielsen modified spectral Neugebauer model by dot surface coverages depending on the ink superposition conditions”, IS&T/SPIE Electronic Imaging Symposium, Conf. Imaging X: Processing, Hardcopy and Applications, January 2005, SPIE Vol. 5667, 434-445, incorporated by reference) where reflection spectra of the colorants R_j are expressed by colorant transmittance spectra t_i and the paper reflectance R_g, as expressed in Eq. (1b).

For 4 inks, the corresponding Yule-Nielsen modified Spectral Neugebauer reflectance is $\begin{array}{cc}R\left(\lambda \right)={\left(\sum _{j=1}^{16}{a}_j·{R_j\left(\lambda \right)}^{\frac{1}{n}}\right)}^n;\mathrm{with}& \left(1b\right)\\ R_j\left(\lambda \right)={t_j\left(\lambda \right)}^2*R_g\left(\lambda \right)& \left(1c\right)\end{array}$
where the Yule-Nielsen scalar n-value is fitted for a giving printing process by minimizing on a subset of halftones a difference metric between predicted reflection spectrum and measured reflection spectrum. Reflectances R_j (λ) are measured reflectances of paper (R_g), of solid inks and of solid ink superpositions printed on paper. In the YNSN model, there is no need to derive an internal paper reflectance from a measured paper reflectance.

The reflection density spectrum D(λ) is deduced from the reflectance R(λ) according to the following well known formula
D(λ)=−log₁₀(R(λ))   (2a)

Equations (1a), (1b) define respectively two different embodiments of base spectral prediction models. For each embodiment, either the reflection spectrum R(λ) or the reflection density spectrum D(λ) can be predicted.

In the present invention, instead of a spectral acquisition device (spectrophotometer), we consider for online use sensor acquisition devices such as blue, green, red and near-infra-red sensors. The CYSN or YNSN spectral prediction models given above can be extended to predict the response of the sensors.

In the case of 4 α, β, γ, δ illuminating and sensor devices having respective illuminant spectra I_α, I_β, I_γ, I_δ, and spectral sensitivities S_α, S_β, S_γ, S_δ, the responses of the α, β, γ, δ sensors expressing the amount of light reflected by the sample of spectral reflectance R can be described by Equations (3). In these equations, all spectral values are discrete values, distributed across the wavelength range of interest, e.g. between 380 nm and preferably 900 nm for the visible wavelength and near infra-red wavelength range. The differences in sensibility between channels α, β, γ, δ may be due to different illuminations (e.g. blue, green, red, and infra-red illuminations expressed by I_α, I_β, I_γ, I_δ) or due to filters located in the pathway of the light to the sensors, expressed as combined filter and sensor sensibilities S_α, S_β, S_γ, S_δ. $\begin{array}{cc}{q}_{\alpha }=\sum _i{S}_{\alpha i}{R}_i{I}_{\alpha i}/\sum _i{S}_{\alpha i}{I}_{\alpha i}{q}_{\beta }=\sum _i{S}_{\beta i}{R}_i{I}_{\beta i}/\sum _i{S}_{\beta i}{I}_{\beta i}{q}_{\gamma }=\sum _i{S}_{\gamma i}{R}_i{I}_{\gamma i}/\sum _i{S}_{\gamma i}{I}_{\gamma i}{q}_{\delta }=\sum _i{S}_{\delta i}{R}_i{I}_{\delta i}/\sum _i{S}_{\delta i}{I}_{\delta i}& \mathrm{Equation}\left(3\right)\end{array}$

By plugging the predicted reflectance R(λ) of Eq. (1a) or (1b) as discrete reflectance vector components R_i into equations (3), the sensor responses q_α, q_β, q_γ, q_δ, are predicted as a function of the surface coverages a_j of the colorants. One may also consider converting the sensor responses q_k into sensor densities responses D_k according to the equation
D_k=−log₁₀(q_k)   (2b)

The well known Demichel equations (4) yield the colorant (also called Neugebauer primaries) surface coverages a_i as a function of the ink surface coverages c₁, c₂, c₃, and c₄ of the inks i₁, i₂, i₃, and i₄.
i₁ alone: a₁=c₁(1−c₂)(1−c₃)(1−c₄)
i₂ alone: a₂=(1−c₁)c₂(1−c₃)(1−c₄)
i₃ alone: a₃=(1−c₁)(1−c₂)c₃(1−c₄)
i₄ alone: a₄=(1−c₁)(1−c₂)(1−c₃)c₄
i₁ and i₂: a₅=c₁ c₂(1−c₃)(1−c₄)
i₁ and i₃: a₆=c₁(1−c₂)c₃(1−c₄)
i_i and i₄: a₇=c₁(1−c₂)(1−c₃)c₄
i₂ and i₃: a₈=(1−c₁)c₂ c₃(1−c₄)
i₂ and i₄: a₉=(1−c₁)c₂(1−c₃)c₄
i₃ and i₄: a₁₀=(1−c₁)(1−c₂)c₃ c₄
i₁, i₂ and i₃: a₁₁=c₁ c₂ c₃(1−c₄)
i₂, i₃ and i₄: a₁₂=(1−c₁)c₂ c₃ c₄
i_i, i₃ and i₄: a₁₃=c₁(1−c₂)c₃ c₄
i_i, i₂ and i₄: a₁₄=c₁ c₂(1−c₃)c₄
i₁, i₂, i₃ and i₄: a₁₅=c₁ c₂ c₃ c₄
substrate white: a₁₆=(1−c₁)(1−c₂)(1−c₃)(1−c₄).   Equations (4)

For more information on the computation of the colorant surface coverages from ink surface coverages, see [Wyble and Berns 2000].

Let us consider the Clapper-Yule based spectral prediction model. By inserting the relative amounts of colorants a_i and their transmittances t_i into Equation (1), we obtain a predicted reflection spectrum of a color patch printed with given surface coverages of cyan, magenta, yellow and black. Both the specular reflection r_s and the internal reflection r_i depend on the refraction indices of the air (n₁=1) and of the paper (n₂=1.5 for paper). According to the Fresnel equations (see E. Hecht, Schaum's Outline of Optics, McGraw-Hill, 1974, Chapter 3), for collimated light at an incident angle of 45°, the specular reflection factor is r_s=0.05. With light diffusely reflected by the paper (Lambert radiator), the internal reflection factor is r_i=0.6 (see D. B. Judd, Fresnel reflection of diffusely incident light, Journal of Research of the National Bureau of Standards, Vol. 29, November 42, 329-332). To put the model into practice, we deduce from Equation (1a) the internal reflectance spectrum r_g of a blank paper by setting all the ink surface coverages different from white as zero $\begin{array}{cc}{r}_g=\frac{R_g-K*r_S}{1+\left(1-K\right)*r_i*r_S+r_i*R_g-r_S{r}_i}& \left(5\right)\end{array}$
where R_g is the measured unprinted paper reflectance.

We then calculate the transmittance of each individual solid colorant (solid inks and solid ink superposition) t_c, t_m, t_y, t_k, t_cm, t_cy, t_ck, t_my, t_mk, t_yk, t_cmy, t_myk, t_cyk, t_cmk, t_cmyk, t_w by inserting into Eq. (1a) the measured solid colorant reflectance R_i and by setting the appropriate colorant surface coverage a_i=1 and all other colorant coverages a_j≠i=0. The transmittance of solid colorant i becomes $\begin{array}{cc}{t}_i=\sqrt{\frac{R_i-K*r_S}{r_g*r_i*\left(R_i-K*r_S\right)+r_g*\left(1-r_i\right)*\left(1-r_S\right)}}& \left(6\right)\end{array}$

We should also take ink spreading into account, i.e. the increase in effective (physical) dot surface coverage. We can fit effective surface coverages either by minimizing a distance metric either between measured and predicted reflection spectra or between measured and predicted multi-channel sensor responses.

During an initial calibration, for each ink u, we fit according to the selected spectral prediction model (CYSN, Eq. (1a) or YNSN, Eq. (1b), with a_j=u being fitted and a_j≠u=0) the unknown effective surface coverages f_u(c_u) of the measured single ink patches at nominal coverages c_u of e.g. 25%, 50%, 75%, 100% by minimizing a distance metric between predicted and measured reflection spectra or multi-channel sensor responses.

Similarly, we fit the unknown effective surface coverages f_u/v(c_u) of single ink halftones of ink u printed in superposition with a second solid ink v at nominal surface coverages c_u (e.g. at 25%, 50% and 75%) with the selected spectral prediction model, Eq. (1a) or (1b), with halftone surface coverage f_u/v(c_u)=a_u being fitted, a second solid ink a_v=1 and all other colorant surface coverages a_{(j≠u,j≠v)}=0, by minimizing a distance metric between predicted and measured reflection spectra, respectively multi-channel sensor responses. The same procedure is applied for fitting the unknown effective surface coverages f_u/vw(c_u) of single ink halftones a_u printed in superposition with two solid inks, Eq. (1a) or (1b), with halftone surface coverage f_u/vw(c_u)=a_j=u being fitted, a second solid ink a_v=1, a 3^rd solid ink a_w=1 and 4^th ink surface coverage a_{(j≠u,j≠v,j≠w)}=0. The same procedure is also applied for fitting the unknown effective surface coverages f_u/vwz(c_u) of single ink halftones of ink u printed in superposition with three solid inks, Eq. (1a) or (1b), with halftone surface coverage f_u/vwz(c_u)=a_j=u being fitted, a second solid ink a_v=1, a 3^rd solid ink a_w=1 and a 4^th solid ink a_z=1. Each set of fitted effective surface coverages (e.g. at nominal surface coverages c_u=25%, 50% and 75%) maps nominal surface coverages to effective surface coverages for that superposition condition. For a given superposition condition, by interpolating between the known mappings between nominal to effective surface coverages, we obtain a function mapping between nominal to effective surface coverages. This function is called “effective surface coverage curve” or “effective coverage curve”.

In order to obtain the effective surface coverages c₁, c₂, c₃ and c₄ of a color halftone patch from their nominal coverages c_1n, c_2n c_3n, and c_4n and then, with the Demichel equations (4), to obtain the corresponding effective colorant surface coverages a_j to be inserted in the spectral prediction model equation (1a), or respectively (1b), it is necessary to weight the contributions of the corresponding effective coverage curves. The weighting functions depend on the effective coverages of the considered ink alone, of the considered ink in superposition with a second ink, of the considered ink in superposition with the two other inks and of the considered ink in superposition with the three other inks. For the considered system of 4 inks i₁, i₂, i₃ and i₄ with nominal coverages c_1n c_2n, c_3n and c_4n and effective coverages c₁, c₂, c₃ and c₄, assuming that inks are printed independently of each other, e.g. according to the classical screen angles 15°, 45°, 75° and 0°, by computing the relative weight, i.e. the relative surface of each superposition condition, we obtain the system of equations (7) published in [Hersch05A]. $\begin{array}{cc}{c}_1=f_1\left(c_{1n}\right)\left(1-c_2\right)\left(1-c_3\right)\left(1-c_4\right)+f_{1|2}\left(c_{1n}\right)c_2\left(1-c_3\right)\left(1-c_4\right)+f_{1|3}\left(c_{1n}\right)\left(1-c_2\right)c_3\left(1-c_4\right)+f_{1|4}\left(c_{1n}\right)\left(1-c_2\right)\left(1-c_3\right)c_4+f_{1|23}\left(c_{1n}\right)c_2{c}_3\left(1-c_4\right)+f_{1|24}\left(c_{1n}\right)c_2\left(1-c_3\right)c_4+f_{1|34}\left(c_{1n}\right)\left(1-c_2\right)c_3{c}_4+f_{1|234}\left(c_{1n}\right)c_2{c}_3{c}_4{c}_1=f_2\left(c_{2n}\right)\left(1-c_1\right)\left(1-c_3\right)\left(1-c_4\right)+f_{2|1}\left(c_{2n}\right)c_1\left(1-c_3\right)\left(1-c_4\right)+f_{2|3}\left(c_{2n}\right)\left(1-c_1\right)c_3\left(1-c_4\right)+f_{2|4}\left(c_{2n}\right)\left(1-c_1\right)\left(1-c_3\right)c_4+f_{2|13}\left(c_{2n}\right)c_1{c}_3\left(1-c_4\right)+f_{2|24}\left(c_{2n}\right)c_1\left(1-c_3\right)c_4+f_{2|34}\left(c_{2n}\right)\left(1-c_1\right)c_3{c}_4+f_{2|134}\left(c_{2n}\right)c_1{c}_3{c}_4{c}_3=f_3\left(c_{3n}\right)\left(1-c_1\right)\left(1-c_2\right)\left(1-c_4\right)+f_{3|1}\left(c_{3n}\right)c_1\left(1-c_2\right)\left(1-c_4\right)+f_{3|2}\left(c_{3n}\right)\left(1-c_{}\right)c_2\left(1-c_4\right)+f_{3|4}\left(c_{3n}\right)\left(1-c_1\right)\left(1-c_2\right)c_4+f_{3|12}\left(c_{3n}\right)c_1{c}_2\left(1-c_4\right)+f_{3|14}\left(c_{3n}\right)c_1\left(1-c_2\right)c_4+f_{3|24}\left(c_{3n}\right)\left(1-c_1\right)c_2{c}_4+f_{3|124}\left(c_{3n}\right)c_1{c}_2{c}_4{c}_4=f_4\left(c_{4n}\right)\left(1-c_1\right)\left(1-c_2\right)\left(1-c_3\right)+f_{4|1}\left(c_{4n}\right)c_1\left(1-c_2\right)\left(1-c_3\right)+f_{4|2}\left(c_{4n}\right)\left(1-c_1\right)c_2\left(1-c_3\right)+f_{4|3}\left(c_{4n}\right)\left(1-c_1\right)\left(1-c_2\right)c_3+f_{4|12}\left(c_{4n}\right)c_1{c}_2\left(1-c_3\right)+f_{4|13}\left(c_{4n}\right)c_1\left(1-c_2\right)c_3+f_{4|23}\left(c_{4n}\right)\left(1-c_1\right)c_2{c}_3+f_{4|123}\left(c_{4n}\right)c_1{c}_2{c}_3.& \mathrm{Equation}\left(7\right)\end{array}$

This system of equations requires the acquisition of 32 effective coverage curves (all f functions). In the case of cyan, magenta, yellow and black inks, this system of equations may be simplified by assuming that any halftone printed on the solid black ink results anyway in a color very close to black and does not modify the ratio between the weights of the effective surface coverage curves of that halftone. For black ink halftones however, the surface coverage curves depend on the different superposition conditions and are therefore kept intact. We therefore obtain for cyan, magenta, yellow and black inks the simplified set of effective surface coverage equations (8), mapping nominal surface coverages c_n m_n, y_n and k_n to effective surface coverages c, m, y and k. $\begin{array}{cc}c=f_c\left(c_n\right)\left(1-m\right)\left(1-y\right)+f_{c|m}\left(c_n\right)m\left(1-y\right)+f_{c|y}\left(c_n\right)\left(1-m\right)y+f_{c|\mathrm{my}}\left(c_n\right)mym=f_m\left(m_n\right)\left(1-c\right)\left(1-y\right)+f_{m|c}\left(m_n\right)c\left(1-y\right)+f_{m|y}\left(m_n\right)\left(1-c\right)y+f_{f|\mathrm{cy}}\left(m_n\right)cyy=f_y\left(y_n\right)\left(1-c\right)\left(1-m\right)+f_{y|c}\left(y_n\right)c\left(1-m\right)+f_{y|m}\left(y_n\right)\left(1-c\right)m+f_{y|\mathrm{cm}}\left(y_n\right)cmk=f_k\left(k_n\right)\left(1-c\right)\left(1-m\right)\left(1-y\right)+f_{k|c}\left(k_n\right)c\left(1-m\right)\left(1-y\right)+f_{k|m}\left(k_n\right)\left(1-c\right)m\left(1-y\right)++f_{k|y}\left(k_n\right)\left(1-c\right)\left(1-m\right)y+f_{k|\mathrm{cm}}\left(k_n\right)cm\left(1-y\right)+f_{k|\mathrm{cy}}\left(k_n\right)c\left(1-m\right)y+f_{k|\mathrm{my}}\left(k_n\right)\left(1-c\right)my+f_{k|\mathrm{cmy}}\left(k_n\right)cmy.& \mathrm{Equation}\left(8\right)\end{array}$

Here, only 20 effective surface coverage curves need to be acquired. This system of equations can be solved by first assigning the nominal surface coverages c_n m_n, y_n and k_n to the corresponding effective surface coverages c, m, y and k and then by performing several iterations, typically 5 iterations, until the system converges.

This reduction in the number of surface coverage curves and simplification of the ink spreading equations will be published on the 29^th of Jan. 2008 in a paper by T. Bugnon, R. D. Hersch, Simplified ink spreading equations for CMYK prints, in SPIE Vol. 6807.

Scalar Initial Thicknesses

The accurate computation of ink thickness variations requires an explicit expression of ink transmittances. Transmittances may be deduced from measured reflectances with any spectral prediction model, in which the ink transmittances are explicitly expressed.

In most printing processes, there is trapping, i.e. the respective ink thicknesses of superposed inks are modified (generally reduced). The disclosed ink thickness variation computation model takes care of trapping by computing the internal transmittances t_ij of colorants obtained by the superposition of two inks, of three inks t_ijk and of four inks t_ijkl from the internal transmittance of the individual inks t_c, t_m, t_y, t_k and from their respective fitted reduced thicknesses. For each superposition of solid inks we compute their respective thicknesses, called “initial thicknesses”.

For each solid ink contributing to a superposition of solid inks, called “solid colorant”, each solid ink wavelength-dependent spectral transmittance has an initial scalar thickness. Since we perform computations with relative thickness values, the initial thickness of a single ink is one. For two superposed inks i and j, two initial thicknesses d_Ij and d_iJ for the inks i and j respectively are fitted, by starting from a unit thickness. The same applies for 3 inks or for 4 inks. In Eqs. (9) below, for example, the initial thickness d_iJk expresses the initial thickness of ink j, when superposed with inks i and k. The initial thickness d_ijK expresses the initial thickness of ink k, when superposed with inks i and j. Similar denominations apply for the other initial thicknesses.
t(λ)_ij={circumflex over (t)}_i(λ)^dIj*{circumflex over (t)}_j(λ)^d_iJ
t(λ)_ijk={circumflex over (t)}_i(λ)^dIjk*{circumflex over (t)}_j(λ)^diJk*{circumflex over (t)}_k(λ)^dijK
t(λ)_ijkl={circumflex over (t)}_i(λ)^dIjkl*{circumflex over (t)}_j(λ)^diJkl*{circumflex over (t)}_k(λ)^dijKl*{circumflex over (t)}_l(λ)^dijkL  Equations (9)
where {circumflex over (t)}_i(λ),{circumflex over (t)}_j(λ),{circumflex over (t)}_k(λ),{circumflex over (t)}_l(λ) are respectively the initially computed wavelength-dependent transmittances of single solid inks i, j, k, l of the calibration patches, calculated according to Eq. (6). By inserting the colorant transmittances t(λ)_ij, t(λ)_ijk, t(λ)_iklj of Eqs. (8) for all ink superposition conditions into Eq. (1a), or respectively (1b), the underlying spectral prediction model becomes an ink thickness enhanced spectral prediction model.

Ink Thickness Variation Factors

The introduction of ink thickness variation factors within the spectral prediction model allows the deduction of ink thickness variations from spectral light reflectance, respectively the multi-channel light reflectance sensor response of halftones. Such halftones are generally present at specific locations within a printed page (e.g. within a reproduced color image). We introduce the ink thickness variations into Eqs. (9) by multiplying each initial ink thickness with a scalar ink thickness variation factor (also simply called “ink thickness variation”). There is one ink thickness variation factor per contributing ink and it does not depend on the superposition condition, i.e. with which other ink (or inks) the considered ink is superposed. The transmittances of single ink, two ink, three ink and four ink solid colorants are expressed by ink transmittances (symbol: {circumflex over (t)}) initial ink thicknesses (symbol: d) and ink thickness variation factors (symbol: dr), see Eqs. (10).
t(λ)_i={circumflex over (t)}_i(λ)^dri
t(λ)_ij={circumflex over (t)}_i(λ)^dIj*^dri*{circumflex over (t)}_j(λ)^diJ*^drj
t(λ)_ijk={circumflex over (t)}_i(λ)^dijk*^dri*{circumflex over (t)}_j(λ)^diJk*^drj*{circumflex over (t)}_k(λ)^dijK*^drk
t(λ)_ijkl={circumflex over (t)}_i(λ)^dIjkl*^dri*{circumflex over (t)}_j(λ)^diJkl*^drj*{circumflex over (t)}_k(λ)^dijKl*^drk*{circumflex over (t)}_l(λ)^dijkL*^drl  Equations (10)
where the thickness variation factor of ink i is dr_i, of ink j is dr_j, of ink k is dr_k and of ink l is dr_l.

In the case of cyan, magenta, yellow and black inks, we express the 16 colorant transmittances as follows.
t_C={circumflex over (t)}_C^drC; transmittance of solid colorant cyan
t_M={circumflex over (t)}_M^drM; transmittance of solid colorant magenta
t_Y={circumflex over (t)}_Y^drY; transmittance of solid colorant yellow
t_K={circumflex over (t)}_T^drK; transmittance of solid colorant black
t_CM={circumflex over (t)}_C^dCm*^drC*{circumflex over (t)}_M^dcM*^drM; transmittance of solid colorant cyan+magenta (blue)
t_CY={circumflex over (t)}_C^dCm*^drC*{circumflex over (t)}_Y^dcY*^drY; transmittance of solid colorant cyan+yellow (green)
t_CK={circumflex over (t)}_C^dCm*^drC*{circumflex over (t)}_K^dcK*^drK; transmittance of solid colorant cyan+black
t_MY={circumflex over (t)}_M^dMy*^drM*{circumflex over (t)}_Y^dmY*^drY; transmittance of solid colorant magenta+yellow (red)
t_MK={circumflex over (t)}_M^dMk*^drM*{circumflex over (t)}_K^dmK*^drK; transmittance of solid colorant magenta+black
t_YK={circumflex over (t)}_Y^dMk*^drY*{circumflex over (t)}_K^dyK*^drK; transmittance of solid colorant yellow+black
t_CMY={circumflex over (t)}_C^dCmy*^drC*{circumflex over (t)}_M^dcMy*^drM*{circumflex over (t)}_Y^dcmY*^drY; transmittance of cyan+magenta+yellow
t_MYK={circumflex over (t)}_M^dMyk*^drM*{circumflex over (t)}_Y^dmYk*^drY*{circumflex over (t)}_K^dmyK*^drK; transmittance of magenta+yellow+black
t_CYK={circumflex over (t)}_C^dCyk*^drC*{circumflex over (t)}_Y^dcYk*^drY*{circumflex over (t)}_K^dcyK*^drK; transmittance of cyan+yellow+black
t_CMK={circumflex over (t)}_C^dCmk*^drC*{circumflex over (t)}_M^dcMk*^drM*{circumflex over (t)}_K^dcmK*^drK; transmittance of cyan+magenta+black
t_CMYK={circumflex over (t)}_C^dCmyk*^drC*{circumflex over (t)}_M^dcMyk*^drM*{circumflex over (t)}_Y^dcmYk*^drY*{circumflex over (t)}_K^dcmyK*^drK; transmittance of cyan+magenta+yellow+black
t_W={circumflex over (t)}_W; transmittance of unprinted paper, by definition equal to 1 at all wavelengths.  Equations (11)

In the solid colorant transmittances above (Eqs. 11), the superposition dependent initial thicknesses are calibrated during the calibration phase according to equations (9). At printing time, the ink thickness variation factors are the fitted unknowns. For cmyk inks, the thickness variation factors of cyan, magenta, yellow and black are respectively dr_C, dr_M, dr_Y and dr_K. The ink thickness variation computation model now consists of Eqs. (1a) or (1b, 1c), and (3) in which transmittances t₁ to t₁₆ are expressed by the 16 transmittances present in Eqs. (11), which in the case of 4 inks are a function of the 4 ink thickness variation factors.

The spectral ink thickness variation computation model enables obtaining the ink thickness variations of a printing system (a) on specially defined test patches, (b) on freely chosen print image locations and (c) with sensor responses over an area segment (i.e. along a thin rectangle of a short length, e.g. 1 mm×2 mm or 2 mm×2 mm) within the printed sheet. Only nominal surface coverages, as defined by the prepress system, need to be known. Accurate ink thickness variation factors can be fitted thanks to the ink thickness variation computation model once the initial ink thicknesses are fitted and the effective coverage curves have been established (either during offline initial calibration or during online calibration). With the effective surface coverage curves, nominal surface coverages of inks are mapped into effective surface coverages of inks, from which the effective surface coverages a_j of the colorants are computed according to the Demichel equations (4) and inserted into respectively Eq. (1a) or Eq. (1b).

As an example, FIG. 1 shows a diagram of the ink thickness variation computation model for the three inks cyan, magenta and yellow. It comprises respectively the input nominal surface coverages of c, m, and y 101, the operation 102 of weighting the surface coverages curves 112 according to the surface coverages of the underlying colorants in order to obtain the effective surface coverages c′, m′, and y′ 105, the computation 103 of the effective colorant coverages according to the Demichel equations, the ink thickness and sensor response extended spectral prediction model 104, which receives as input 109 measured sensor responses (e.g. q_r, q_g, q_b) or sensor density responses. Initially calibrated parameters comprise the ink transmittances 106, and the initial ink thicknesses 107 for each ink in each possible ink superposition (colorant). Parameters calibrated or recalibrated at the beginning of the print session comprise the paper or substrate reflectance r_g 108 and possibly the effective coverage curves for each useful superposition condition 113. The output of the model are the cyan, magenta, and yellow ink thickness variation factors 110 dr_C, dr_M, and dr_Y. In FIG. 1, the initial thicknesses 107 are labeled d_i for the initial thickness of a single ink, d_Ij for the initial thickness of one ink i superposed with another ink j, and d_Ijk for the initial thickness of one ink i superposed with two other inks j and k. Ink layers I, j, and k are different one from another and are placeholders for every of the 3 possible inks of the considered printing system.

FIG. 2 is a generalization of the ink thickness variation computation model shown in FIG. 1, for a freely chosen set of four different inks I₁, I₂, I₃, I₄ of surface coverages c₁, c₂, c₃, c₄ (201). Box 211 represents the connections between input nominal ink surface coverages 201 and their corresponding mappings 212 to effective surface coverages f_i(i), f_i/j(i), f_i/jk(i), f_i/jkl(i) in the different superposition conditions i alone, i superposed with j, i superposed with j and k, and i superposed with j, k and l, where i,j, k and l are placeholders for any of the inks and are different one from another. Surface coverages 213 are weighted 202 according to the underlying colorants to yield after a few iterations the effective surface coverages c₁′, c₂′, c₃′, c₄′ (205). Thanks to the colorant computation equations 203 (Demichel in case of independently printed ink layers, Eqs, (4)), one obtains the effective surface coverages a₁′, to a₁₆′ (214). The ink thickness variation extended spectral prediction model 204 fits the ink thickness variations 210 dr₁ of ink I₁, dr₂ of ink I₂, dr₃ of ink I₃ and dr₄ of ink I₄ by minimizing a difference metric between predicted sensor responses and measured sensor responses 209 q_α, q_β, q_γ, q_δ or possibly by minimizing the sum of such differences for several measurements performed at different locations of the printed sheet. Parameters deduced either from initial offline or from online calibration comprise the ink transmittances 206, the initial ink thicknesses 207 for each ink superposed with any other combination of inks (different colorants) and the paper reflectance 208 (R_g). One possible embodiment of the ink thickness variation computation model of FIG. 2 is a printing system printing with cyan, magenta, yellow and black inks.

The ink thickness variation computation model shown in FIG. 2 can be extended in several ways.

(A): Instead of having 4 sensors with spectral sensibilities in different parts of the considered wavelength range (visible and near infra-red), one may introduce 5, 6 or more sensors.

(B): Since some printing systems employ more than 4 inks (examples of possible additional inks: orange, dark blue, light cyan, light magenta, etc.), the ink thickness variation computation model can be correspondingly extended by introducing as many nominal 201 and effective 205 ink surface coverages as inks, as many transmittances 206 as inks, as many effective surface coverage curves 212 and initial ink thicknesses 207 as used superpositions of inks and as many ink thickness variations 214 as inks.

Calibration of the Ink Thickness Variation Computation Model

We distinguish between an off-line initial calibration for a given class of printers, papers and inks and an optional online calibration (or recalibration) for further tuning the calibration according to the current printing conditions (current paper, currently used set of inks, current temperature, etc.). The off-line calibration may be performed once (e.g. in the factory) by the manufacturer of the printer, respectively printing press, and delivered or made available for download as a computer file, called “initial calibration data”.

The initial calibration of the ink thickness variation computation model comprises the deduction of the transmittances of the inks and possibly an initial set of effective surface coverage curves. During the initial calibration, the spectral reflectances of unprinted paper and of all solid ink and solid ink superpositions are measured by a spectral measurement device. The Clapper-Yule internal reflectance of paper r_g(λ) is deduced by equation (5). Ink and colorant transmittances are deduced according to Eq. (6) or respectively according to Eq. (1c). For 4 inks (e.g. cmyk), 16 spectral measurements are needed. Initial thicknesses are fitted according to equations (9), by minimizing a distance metric between predicted colorant transmittance spectra and transmittance spectra deduced from colorant measurements.

Initial surface coverage curves can be obtained for the relevant superposition conditions by measuring single halftone patches (e.g. at 50% nominal surface coverages), deducing the corresponding effective surface coverages and creating the effective surface coverages curves by interpolation. According to Equations (8), for creating 20 surface coverage curves, one needs 60 measurements in the case of 3 different surface coverages per curve or 20 measurements in the case of a single surface coverage measurement per curve. For deducing effective surface coverages during the initial calibration, one may measure halftone reflectance spectra and fit the effective surface coverages by minimizing a distance metric between reflection spectra predicted according to Equation (1a) or (1b) and measured reflection spectra. Alternately, for example during online calibration, one may measure the sensor responses q_α, q_β, q_γ, q₆₇ and, according to Equations (1a) or (1b) and (3), fit the surface coverages by minimizing a distance metric between predicted and measured sensor responses.

The online calibration (when applicable also called recalibration) of the paper reflectance (from which in the case of the CYSN model the internal paper reflectance is derived) and of the surface coverage curves is performed on the running printer or press, once the prints match the desired quality. The recalibration of the paper reflectance R_g(λ) according to the current print sheet paper is performed by replacing the paper reflectance R_g′(λ) measured during the initial calibration by a scaled paper reflectance R_g(λ)=R_g′(λ)s_g+o_g, where s_g is a scaling factor and o_g is an offset, both fitted by minimizing a difference metric between sensor responses predicted according to Eq. (3) for white paper and corresponding measured sensor responses. To reduce the impact of noise, it is preferable to minimize the sum of such difference metrics for several paper locations.

The online calibration (or recalibration) of the effective surface coverage curves is performed as follows. Sensor response predictions for a number of area segments are made on the running press, by considering the effective surface coverage curves as free variables and by fitting these effective surface coverage curves so as to minimize the sum of a difference metric between measured sensor responses and predicted sensor responses at different printed sheet locations. A surface coverage curve may be given as a corresponding dot gain curve, where dot gain is defined as the effective surface coverage minus the nominal surface coverage. The dot gain curve may be given by a single quadratic Bézier spline through the points (0,0), (0.5, dot gain at 50%), (1,0). In a preferred implementation, this dot gain curve, and therefore the corresponding surface coverage curve are fitted by fitting the dot gain at 50% surface coverage.

Layout of Illuminating and Sensing Devices

Since there may be variations of ink thicknesses across the printed sheet, compact elements comprising the illuminating and sensing devices (FIG. 3, 308) may be repeated along the width 321 of the printed sheet 301, or in the case of a printing press, at the location of each ink zone. These elements are positioned on the path way of the printed paper. In a preferred embodiment (FIG. 5A), each sensor of a 4-channel sensor device may have its own illumination, either white light including infra-red components or light formed by a light emitting diode (LED) emitting within a given spectral wavelength range. In a possible embodiment, the light 505 is guided by a waveguide 503 (or by an optical fiber) to hit the print surface 501 at an angle of approximately 45 degrees. In the case of white light, a corresponding red, green, blue or infra-red filter 509 is placed in the light path of the light, e.g. at the entry of the waveguide. Optionally, the waveguide for the incident light may be terminated by a lens (possibly Fresnel lenses) 506 which focus the light onto the print surface. In alternative embodiments, the filters may be integrated into the lens by diffusing a partially absorbing layer at its surface or by creating the lens with a partially absorbing substance. In a further alternative, the waveguide may also be conceived to filter light at a given wavelength range.

To avoid capturing specular reflections, the reflected light is captured perpendicularly to the print surface, e.g. by being focused by a lens 507 in front of an optional waveguide 508. The sensor 504 may either be directly in front of the print, or hooked onto the waveguide 508 transmitting the light which is perpendicularly reflected from the print surface. The sensor 504 is generally an integrated circuit bonded onto an electronic circuit board 502.

A compact embodiment (FIG. 5B) may comprise a light source embodied by a LED 513 emitting in the blue, green, red or respectively in the near-infra-red wavelength range, a polarizing filter 514 polarizing the incident light according to a given orientation, a waveguide 515 guiding the light to a beam splitter 510 which directs the incoming polarized light perpendicularly into the print surface 517. The part of incident polarized light specularly reflected at the surface of the print is discarded by a second polarization filter 511 located on the reflected light path. This output polarization filter is rotated by 90 degrees in respect to the input polarization filter 514, located within the incident light path. Light crossing the print interface 517 is transmitted onto the print substrate (e.g. paper), is scattered within the substrate and becomes depolarized. It is reflected by the substrate, reaches the light guide, possibly through a focusing lens, traverses the beam splitter in the reverse direction, traverses the polarization filter 511 and strikes the sensor 512, in the present embodiment, the SPAD (see next section). The two polarizing filters discard specular reflections, which may be high when the ink is still wet on the printed sheet. Many different variants equivalent to the present embodiment may be considered, such as using white light filtered by the input polarization filter and further filtered by blue, green, red or infra-red filters instead of a LED followed by the input polarization filter. As previously, the sensor 512 is an integrated circuit located on a printed circuit board 518 and the LED 513 is also connected 519 to the printed circuit board.

In a further embodiment (FIG. 5C), the white light source 534 may have a certain length and illuminates the print sheet parallel to the paper (537) moving orientation, along the multi-channel sensing devices (530, 531, 532, 533). Alternately, the elongated white light source may be positioned over the full length of the printed sheet width and create the illumination for many or all sensing devices. In both cases, each sensing device may comprise a coating 530 with a filtering substance on the focalizing lens 531. An optional waveguide 532 connects the lens to the sensor 533. These elements can be fixed on a printed circuit board 538.

Each of the 4 illuminating/sensor devices (FIGS. 3 and 4A, 304, 305, 306, 307) may be placed at successive positions within the path of the moving paper. For example, by placing them one or several millimeters apart one from another, reflected light captured by one sensor device does not contribute to the light captured by its neighbor device.

In order to capture ink thickness variations across the full sheet width, 4-channel illuminating/sensor sets 308 may be placed at regular intervals across the paper width, perpendicularly to the paper displacement orientation. In the case of offset presses, it is advisable to place at least one set of 4-channel illuminating/sensor devices within each ink zone.

Processing of the Sensor Outputs

In the considered embodiment, the electronic signal (FIG. 4A, 401, 402, 403, 404) emitted by each of the 4 sensors according to the illumination and the reflectance of the underlying sensed area of the printed sheet depends on the sensor technology. The preferred technology is the Single Photon Avalanche Diode (SPAD), see S. Cova, et. al., Avalanche photodiodes and quenching circuits for single-photon detection, Applied Optics, Vol. 35, Issue 12, pp. 1956-1976 (April 1996) as well as E. Charbon, Techniques for CMOS Single Photon Imaging and Processing, 6^th Intl. Conf. on ASIC, IEEE ASICON 2005, pp. 1163-1168, referenced as [Charbon05], hereby incorporated by reference. Other technologies, such as Charged Coupled Devices (CCDs), or CMOS may also be used as sensors. The advantage of SPADs is their ability of counting single photon events, i.e. the possibility of very short sensor response acquisition times, between hundreds of nanoseconds to a few milliseconds and to provide a high signal to noise ratio, and therefore a high effective dynamic range.

A set of multi-channel sensors may also be integrated within a single integrated circuit (FIG. 4B, 440). In the embodiment of FIG. 4B, a quadruplet of SPAD sensors 414, 415, 416, 417 comprise their own pulse counters 424, 425, 426, 427 and counter output lines 434, 435, 436, 437. The counter output lines may be multiplexed by an internal multiplexer 438, whose output is connected for example via a communication bus 460 to the sensing system microcontroller 470. Such integrated multi-channel sensors may be replicated over the width of the print sheet. An example is the replicated multi-sensor integrated circuit 450, also connected to the sensing system microcontroller 470 through the communication bus 460.

In the case of paper printed at a speed of for example 2 meter per second (m/s), a sensor response acquisition time (also called sensor active time or sensor aperture time) of one. millisecond, counting the photons captured by the SPAD during 1 ms, corresponds to a displacement of the paper by 2 mm, i.e. a sensed area segment length of 2 mm. Within a printed sheet, many area segments of this size have a nearly uniform color, i.e. are composed of color pixels varying one in respect to an other by less than CIELAB ΔE₉₄=6.

At a speed of 10 m/s, the sensed area segment length is 10 mm. Within a printed sheet either a close to uniform color area segment of that size can be located within the printed sheet and in the region of interest (e.g. an ink zone), or a non uniform area segment is selected, and subdivided into parts. For predicting its multi-channel sensor response, the multi-channel response of each part is separately predicted. The predicted multi-channel sensor response for the whole area segment is the weighted average of the separately predicted parts, the weights corresponding to the respective relative surfaces of these parts.

In the preferred SPAD embodiment, the sensing devices are connected to a sensor processing module (FIGS. 3A and 3B, 320) which comprises a multiplexer 310, a counter 311, fast logic (FL) 312 and a microcontroller (μC) 316. The signal lines 309 arriving from the individual SPAD sensors transmit serially the pulses corresponding to photon counts to a multiplexer (FIG. 3B, 310), which selects the sensor which must be currently read out. The output of the multiplexer 314 is forwarded to the counter (CTR) 311 which is enabled 316 by the fast logic 312 to count the pulses during the desired active time of the SPAD, i.e. during the passage of a desired paper area segment beneath the corresponding sensor. The output of the counter 315 giving the sensor response in term of intensity is stored in the sensing system microcontroller 313 responsible for the control of the present sensing system. The sensor devices 308 as well as the elements of the sensor processing module 320 may be attached to a same printed circuit board 303.

The sensing processing module microcontroller 313 connected to the main computing system (FIG. 7, 701) by a communication link 317 (FIGS. 3A and 3B), e.g. USB (Universal Serial Bus), receives from the main computing system timing information about the location of the area segments whose sensor responses need to be read out. The sensing processing module microcomputer communicates 324 with the fast logic 312, for example embodied by a field programmable gate array (FPGA), and initializes it to create the signals 318 (FIGS. 3A, 3B and 4A) driving the sensor enabling inputs, the signals driving the multiplexor 319, and the signals resetting 325 and enabling 316 the counter 311. The sensing processing module microcontroller 313 transmits the sensor responses to the main computer. Thanks to the sensor responses, the main computing system (FIG. 7, 701) computes the ink thickness variations, and if necessary, applies corresponding corrections to the printer actuation variables such as the amount of deposited ink. For a printing press, deduction of ink thickness variations enables automatically regulating the ink flow by acting on the print actuation parameters such as the feed of ink.

In the case of sensors embodied by SPADs, one may conceive an illuminating/sensing device where (a) all sensors continuously provide pulses according to the incoming photons, (b) the multiplexor 310 selects the currently active sensor and the fast logic 312 defines the acquisition time and period by activating the reset signal 325 of the counter before the acquisition and by activating the counter's count enable signal 316 during the acquisition period (few hundreds of nanoseconds to a few milliseconds).

According to [Charbon05], the duration of a full photon detection cycle called dead time (tD) is between 20 ns and 50 ns, depending on the implementation of the SPAD. The maximal number of detected photons during the sensor active time t_A, called max photon count (N_max), is N_max=t_A/t_D. For example, with a sensor active time t_A of 1 ms, and a dead time of t_D of 50 ns, the largest number of detected photons is 20,000. The Poisson noise yields a number of pulses N_Poisson≈√{square root over (N_max)}. Without accounting for the dark count rate which is negligible in the present case (about 300 pulses per second, i.e. less than one pulse per millisecond on average), we obtain a signal to noise ratio
SNR=20 log(N_Max/√{square root over (N_Max)})=20 log √{square root over (N_Max)}  (12)

In the example above, the signal to noise ratio is SNR=20 log √{square root over (20000)}=43 dB.

This signal to noise ratio is high since, with an SPAD, pulses are directly converted into TTL or CMOS compatible pulses and counted. There is no need for an amplifier, a sampler and an A/D converter which introduce additional noise. With a maximal signal √{square root over (N_max)} times higher than the noise, it becomes possible to build high-speed sensors capable of sensing very low reflectances in the range between 1/100 and 1/1000, i.e. corresponding to reflectance densities between 2 and 3.

The maximal photon count N_max defines the size of the counter (FIG. 3, 311) in terms of its number of bits. For N_max=20000, a 15 bits counter is sufficient. It is however easy to reach N_max=100,000 with a 17 bits counter or N_max=1,000,000 with a 24 bits counter.

Spectral Sensibilities of the Sensing System

If the illuminating device is white light, red, green, blue or infra-red filter is placed within the light path, before the corresponding sensor. In one embodiment, the red, green, and blue filters have similar spectral sensibilities as the sensibilities used for building densitometers, which are specified by DIN standard 16536-2. The infra-red sensibilities should cover a part of the near-infra-red spectrum, for example between 730 nm and 900 nm.

FIG. 6 shows the blue (B: 601), green (G: 602) and red (R: 603) normalized sensitivities according to DIN standard 16536-2 used for deriving the densities of the corresponding cyan, magenta and yellow ink patches. These sensitivities correspond to the multiplication of the sensibilities of filters in front of the sensors and the own sensitivity of the sensors. In a possible embodiment, these sensitivities, together with the near infra-red sensitivity (IR: 604) can be used for the presently proposed 4 sensor sensing system.

If the illuminating devices are LEDs, then the light of the chosen red, green blue and infra-red LEDs should be directed to the print surface, be reflected and sensed by the corresponding sensor. The sensor sensibilities should be known, and should provide a positive response at the wavelengths of the blue, green, red and infra-red LEDs, preferably located respectively between 380 nm and 480 nm, between 500 nm and 600 nm, between 620 and 720 nm and between 750 nm and 900 nm. In the case that the sensibility of the sensor is not given by the sensor manufacturer, it can be deduced experimentally by irradiating the sensor with light at narrow wavelengths, e.g. at each 10 nm between 380 nm and 900 nm, and by measuring the corresponding responses.

Thickness Variations Deduced from Area Segments within a Printed Sheet

The present invention aims at deducing ink thickness variations at print time. Since during the print operation the printed paper is moving forward at a given speed, we measure the sensor responses over an area segment of the print along the paper movement orientation. The position of the paper in respect to the sensors is known at any time. The sensor acquisition logic may acquire the sensor responses at regular time intervals. The sensor responses from area segments known to be nearly uniform are memorized and forwarded to the computing system which deduces the ink thickness variations. As an alternative, by interacting with the microcontroller 313 which drives the sensor acquisition logic (FIG. 3B, 312), the software running on the computing system may launch the sensor acquisition at a location on the print where the area segment is nearly uniform.

When acquired from nearly uniform area segments, the sensor responses integrated over an area segment are considered to be the sensor responses of a uniform halftone patch whose nominal surface coverages are the mean of the nominal surface coverages (e.g. nominal c,m, y, and k values) of the corresponding area segment pixels within the prepress sheet image.

The ink thickness variations, expressed by the ink thickness variation factors, for the considered area segment are obtained by minimizing a distance metric between the predicted area segment sensor responses and the measured area segment sensor responses, for example by minimizing the sum of square differences between the predicted area segment sensor density responses and the measured area segment sensor density responses. Accurate results which reduce the impact of noise are obtained by measuring the sensor responses at several area segment locations and by minimizing the sum of these distances between predicted and measured sensor responses at these locations.

In the case of the cyan, magenta, yellow and black inks, in order to create for each ink an independent absorption wavelength range, we consider wavelengths incorporating both the visible wavelength range (380 nm to 730 nm) and the near-infra-red wavelength range (e.g. 740 nm to 900 nm). In the near-infra-red wavelength range, the cyan, magenta and yellow colorants do not absorb light. Only the pigmented black ink absorbs light. An ink thickness variation model with a wavelength range from 380 nm to 900 nm, i.e. with the visible and near-infra-red wavelength ranges, enables computing ink thickness variations for the cyan, magenta, yellow and black inks. FIG. 2 gives a schematic view of the ink thickness variation computation system, for 4 inks I₁, I₂, I₃, and I₄, which may represent the cyan, magenta, yellow and black inks.

Normalized Ink Thickness Variation Computation

In the case of small variations between the calibration and the printer operating conditions (e.g. the ink density during calibration differs slightly from the ink density during normal printing operation) more accurate results may be obtained by computing normalized ink thickness variations.

Normalized ink thickness variation computation requires establishing reference ink thickness variations dr₁′, dr₂′, dr₃40 , dr₄′ (FIG. 2, 214) on a reference print under reference settings of the printing device. In order to create the reference settings, the printed color pictures are observed and verified (e.g. compared with a soft proof on a calibrated display) by a print operator. Alternately, it may be possible to use another print verification system (see “Background of the invention”). As soon as the current print result meets the desired quality criteria (e.g. a color picture close to the desired color picture or ink densities within a given tolerance range), the reference ink thickness variations are deduced by measuring the area segment sensor responses at different area segment locations, by predicting the area segment sensor responses at these locations, by deriving at each location according to a difference metric the distance between measured and predicted area segment sensor responses and by fitting the ink thickness variations so as to minimize the sum of the computed distances across the considered area segment locations. The fact that several color area segments contribute to the computation of the reference ink thickness variations reduces the impact of noise present within the individual area segments.

From now on, ink thickness variation computations are normalized in respect to these recorded reference thickness variations dr₁′, dr₂′, dr₃′, dr₄′, i.e. the ink thickness variation computing system computes the normalized ink thickness variations dr₁, dr₂, dr₃, dr₄ in respect to the initial ink thicknesses multiplied by the corresponding reference ink thickness variations. FIG. 8A illustrates normalized ink thickness variations 804 (axis 801) deduced from polychromatic halftones present in printed sheets of the magenta ink 801, and of the black ink (FIG. 8B, 814, axis 811) for many different print trials, where the ink feed of one or of several inks has been increased or decreased. In FIGS. 8A and 8B, print trials 802 are characterized by a variation of the amount of deposited ink. C+, M+, Y+, K+ indicate respectively a higher ink feed of the cyan, magenta, yellow and black inks and C−, M−, Y−, K− indicate respectively a lower ink feed of the cyan, magenta, yellow and black inks. The labels “+”, “−”, “0” indicate respectively an increment, a decrement or a constant value of the ink feed for the considered ink (FIG. 8A: magenta ink, FIG. 8B: black ink). In order to provide a comparison with the real amount of deposited ink, the black triangles, placed according to the vertical axis on the right of FIGS. 8A (803) and 8B (813), indicate the corresponding measured relative scalar density values, i.e. the solid ink density values measured on special patches located on the trial print sheet divided by the solid ink density values measured on the reference print sheet without any ink feed increase or decrease. The reference print trial is located at the leftmost position. The gray bars in FIGS. 8A and 8B indicate the range of values where no significant ink thickness variations occur.

Ink Thickness Variation Computation in Respect to Reference Settings

In a further embodiment, the system may track ink thickness variations at print time without knowing the nominal surface coverages of inks, but after having performed reference settings of the print control parameters of the printing press (e.g. ink feed) by an operator and/or by another print calibration system. Under the reference settings, sensor responses (e.g. q_α′, q_β′, q_γ′, q_δ′, FIG. 2, 215) are measured from within specific area segments of a printed sheet. Then, ink thickness variations occurring when printing that sheet can be deduced by the ink thickness variation computing system.

The reference effective surface coverages and possibly reference thickness variations are deduced from the reference sensor responses and recorded. Then, while printing the same print sheet, or when printing the same print sheet again in a new print session, the corresponding sensor responses are measured. The ink thickness variation computing system then computes the ink thickness variations occurring in respect to the reference settings. In the present embodiment, the ink thickness variation computing system does not depend on the knowledge of nominal surface coverages. It depends only on the initial calibration of ink transmittances, of initial ink thicknesses and on the measured sensor responses. Since only the effective surface coverages are used, calibration is simplified by avoiding the need to establish the effective surface coverage curves.

Ink Thickness Variation Computation

The method for computing ink thickness variations comprises the step of calibration of a thickness variation and sensor response enhanced spectral prediction model by (a) measuring the paper reflectance, if applicable, deducing the internal paper reflectance and deducing spectral ink transmittances from spectral measurements, (b) computing the scalar ink thicknesses of the superposed inks forming a solid colorant and (c) computing the effective coverage curves for halftones in different superposition conditions. Steps (b) and (c) can be performed either by spectral measurements of by sensor responses.

In order to adapt an initial calibration to the current print conditions (state of the printer, temperature, paper, inks), the ink thickness variation computation method also comprises the optional step of recalibrating at printing time the paper reflectance and the effective surface coverage curves.

It further comprises the step of fitting, during print operation, according to the thickness variation and sensor response enhanced spectral prediction model, for each contributing ink, the corresponding ink thickness variation factors. This is performed by minimizing a distance metric such as the sum of square differences between the predicted sensor responses and the measured sensor responses. In the case of cyan, magenta, yellow and black inks, the presently disclosed ink thickness variation computation method works simultaneously within the visible and the near-infra-red wavelength range domain.

In order to even better adapt the initial calibration to the current print conditions (state of the printer, temperature, paper, inks), an optional reference thickness variation computation step enables computing reference thickness variations which are used for computing normalized ink thickness variations during print operation.

A further ink thickness variation computation method variant also comprises, during online calibration, the step of measuring reference sensor responses from specific locations of the print, of deducing corresponding reference effective surface coverages and of computing ink thickness variations by minimizing a distance metric between the sensor responses predicted according to the thickness variation enhanced spectral prediction model and the measured sensor responses. This method does not need as calibration data the effective surface coverage curves, but relies on the reference sensor responses recorded under reference settings to compute the reference effective surface coverages (see section “Ink thickness variation computation in respect to reference settings”).

Ink Thickness Variation Computing System

An ink thickness variation computing system is shown in FIG. 7, 710. It comprises a computing system 701 and a sensing system 708. The sensing system is made of an array 702 of illuminating 703 and sensor devices 704 located on the pathway of the printed paper and of a processing module 706 for selecting, computing, storing and delivering the sensor responses to the computing system 701. The processing module receives from a subset of the lines 705 the output of the sensor devices and optionally transmits through another subset of the lines 705 sensor acquisition synchronization signals. The sensing system's processing module 706 is connected to the computing system 701 by a digital link 707, for example an USB link.

According to the sensor responses, the computing system 701 computes the ink thickness variations by performing the steps described in section “ink thickness variation computation”. The computing system can also perform the online calibration or recalibration step of adapting the paper reflectance and the surface coverage curves (see Section “Calibration of the ink thickness variation computation model”) according to the sensor responses.

When connected to a print actuation parameter driving module 709, the ink thickness variation computing system 710 becomes an online print parameter regulation system which regulates actuation parameters such as the ink feed or the volume of deposited toner per unit of time according to the current ink thickness variations.

Specific Advantages of the Present Disclosure

Specific advantageous features of the presently disclosed methods and systems are:

1. The internal use of a spectral prediction model incorporating explicitly ink thickness variations but without the need of expensive online spectral reflectance measuring devices. The only required spectral measurements are off-line one-time initial calibration measurements for obtaining the paper reflectance and the ink transmittances for a class of similar papers and inks. This can be performed in the factory manufacturing the printing device. During the print sessions, the only online measurements are the sensor responses (or equivalently, the sensor density responses), performed with non-expensive solid-state sensor devices.

2. The multi-channel sensor devices, for example 4 sensor devices, are preferably embodied by Single Photon Avalanche Diodes (SPADs). They allow building high-speed acquisition sensors with a short active time (also called aperture time), typically between a few hundreds of nanoseconds to a few milliseconds. They induce only very low noise and require only simple digital electronics for accumulating and counting the photon pulses in order to obtain the reflected intensity.

3. Due to the low price of the illuminating/sensor devices, multi-channel sensors can be replicated over the width of the printed sheet, allowing the acquisition of accurate ink thickness information within the full printed sheet. In addition, their low price enables using them within cheap mass product printers, such as low cost ink-jet, dye-diffusion, thermal transfer and electro-photographic printers, for the automatic regulation of print activation parameters. Furthermore, since the presently disclosed sensing system does not require any moving part, it is also cheap for maintenance.

4. Due to the short sensor acquisition times, in the order of hundreds of nanoseconds to a few milliseconds, sensor responses from short area segments (length: e.g. one to ten millimeters) can be acquired, which incorporate a color halftone and no paper white. This avoids the relatively important noise present in the paper white reflectance and provides more robust results than accounting for color variations within long stripe parts (long thin lines along the length of the sheet) as proposed by U.S. Pat. No. 7,252,360 to Hersch et. al.

5. In the present disclosure, we use the ink thickness and sensor response enhanced spectral prediction model within a single continuous wavelength range covering both the visible and the near infra-red wavelength range. There is no need for two separate applications of the model, one in the visible wavelength range and one in the near infra-red wavelength range, as taught by U.S. Pat. No. 7,252,360 to Hersch et. al. By operating over the visible and near infra-red wavelength range, the sensor-based thickness variation computation system can unambiguously compute simultaneous thickness variations of the cyan, magenta, yellow and black inks.

6. The effective surface coverage curves expressing the functions mapping nominal surface coverages into effective surface coverages in the different superposition conditions, combined with the spectral prediction model incorporating explicit transmittances for all solid inks and with the formula modeling the sensor responses from reflection spectra and from illuminating device spectra (Equations 3) provide accurate sensor response predictions.

7. The calibration effort can be reduced in the case of cyan, magenta, yellow and black inks by considering that the superposition of an ink halftone and solid black yields black and therefore does not have a direct impact on the mapping between nominal and effective surface coverage of that ink halftone. This allows reducing the number of curves mapping nominal to effective surface coverages from 32 to 20.

8. The ink thickness variation prediction model provides improved thickness variation predictions thanks to the introduction of an optional online refined calibration of the paper reflectance and of the effective surface coverage curves performed during print operation (running printer or printing press). The online calibration is performed with multi-sensor responses on halftones located within normal printed document pages.

9. More accurate ink thickness variations are obtained by measuring the sensor responses at several area segment locations and by minimizing the sum of the differences (according to a difference metric) between predicted and measured sensor responses at these locations.

10. When predicting ink thickness variations, we assume that a small increase in the amount of ink does not change the ink surface coverages. Therefore, fitting ink thickness variations from sensor responses is the same as fitting ink volume variations. However, in some printers, an increased ink thickness also yields an increase of the corresponding effective surface coverages. Under these conditions, with the methods described in the present disclosure, we fit ink volume variations instead of ink thickness variations. We may consider the deduced ink volume variations as a multiplication of a pure ink surface variation factor and a pure ink thickness variation factor. If we want to obtain the pure ink thickness variation factor we may apply a function to the ink volume variation factor, for example a square root function. But in the general case, we can use directly the deduced ink volume variations to regulate the print actuation parameters such as the ink feed.

General Advantages

In addition to the specific advantages described above, the invention has also similar advantages as taught by U.S. Pat. No. 7,252,360 to Hersch et. al.:

1. The ink thickness variations which have been introduced into the spectral prediction model are exactly the variables needed to control the ink deposition process within a printing press or a printer.

2. The fact that ink thickness variations of the contributing inks can be computed from sensor measurements at various locations within the printed document pages enables avoiding printing special patches or control strips at the border of the printed sheet and therefore also avoids the need to cut these elements out after printing.

3. In case that the calibration conditions deviate slightly from the normal print operating conditions, a recorded set of reference ink thickness variations enables deducing during print operation normalized ink thickness variations with an improved precision.

4. Ink thickness variations may also be computed, when the nominal surface coverages of the target halftone area segment are unknown, by measuring under reference settings, for a halftone area segment, reference sensor values, by deriving a corresponding set of reference effective surface coverages and by computing for the same halftone area segment in the following printed sheets, the ink thickness variations by minimizing a distance metric between the sensor values predicted according to the reference effective surface coverages and the currently measured sensor values.

The disclosed simple and non-expensive solid device sensing system make ink thickness variation prediction and therefore the regulation of print actuation variables applicable to many different kinds of printing devices, from expensive large format printing devices to small and cheap printing devices.

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Claims

1. A method for computing ink thickness variations for the control of printing devices, the method being based on an ink thickness variation and sensor response enhanced spectral prediction model, said method comprising calibration steps and, during print operation, online ink thickness variation computation steps, where the calibration steps comprise the calculation of ink transmittances, and where the ink thickness variation computation steps comprise fitting of ink thickness variations by minimizing a distance metric between predicted multi-channel sensor responses and acquired multi-channel sensor responses, said predicted multi-channel sensor responses being computed according to the ink thickness variation and sensor response enhanced spectral prediction model, and said. acquired multi-channel sensor responses being generated by light reflected on a print sheet.

2. The method of claim 1, where the print sheet is moving and the multi-channel sensor devices, due to their high-speed acquisition capabilities, provide responses according to the reflectance of small area segments within the print sheet, and where the calibration steps also comprise, in order to account for ink spreading, fitting of effective surface coverage curves mapping nominal to effective surface coverages of single ink halftones in different superposition conditions.

3. The method of claim 1, comprising also during said print operation online calibration steps, said online calibration steps comprising a step of fitting effective surface coverage curves mapping nominal to effective surface coverages of single ink halftones in different superposition conditions by acquisition of sensor responses from polychromatic halftones.

4. The method of claim 1, where the thickness variation and sensor response enhanced spectral prediction model comprises as solid colorant transmittance of at least two superposed solid inks the transmittance of each of the superposed inks raised to the power of a product of variables, one variable being the superposition condition dependent ink thickness and the other variable being the ink thickness variation factor.

5. The method of claim 1, where the inks are the cyan, magenta, yellow, and black inks and where the thickness variation and sensor response enhanced spectral prediction model operates simultaneously in the visible and near infra-red wavelength range domain.

6. The method of claim 1, where the ink thickness variation computation steps also comprise the step of online recording of reference thickness variations and where the computed ink thickness variations are ink thickness variations normalized in respect to the reference ink thickness variations.

7. The method of claim 1, where, in addition to the calibration and recalibration steps, the step of acquiring during print operation reference sensor responses from a reference print under reference settings and of deducing corresponding reference effective surface coverages is performed, where the sensor responses are predicted with the deduced reference effective surface coverages, and where the computed ink thickness variations represent ink thickness variations in respect to the reference print.

8. The method of claim 1, where said multi-channel sensor devices are based on single photon avalanche diodes (SPADs) which capture during print operation light reflected by said small area segments within the print page.

9. The method of claim 8, where light emitting diodes (LEDs) emit light that is directed towards the print sheet, where part of said light penetrates the print sheet, is reflected by the sheet's substrate and captured by said SPAD sensor devices.

10. An ink thickness variation computing system for the control of printers, respectively printing presses operable for the online computation of ink thickness variations during print operation, said ink thickness variation computing system comprising multi-channel sensor devices, a processing module, and a computing system, where the multi-channel sensor devices respond at different spectral sensibility ranges within the visible and near infra-red wavelength range, where the multi-channel sensor devices, due to their high-speed acquisition capabilities, provide responses according to the reflectance of small area segments within a print sheet, where the processing module receives the responses from said multi-channel sensor devices and forwards them to the computing system, which according to an ink thickness variation and sensor response enhanced spectral prediction model deduces said ink thickness variations.

11. The ink thickness variation computing system of claim 10, where said multi-channel sensor devices are based on single photon avalanche diodes (SPADs) which capture light reflected by said small area segments within the print sheet.

12. The ink thickness variation computing system of claim 11, where single photon avalanche diodes photon count acquisition times range between 200 nanoseconds and 10 milliseconds.

13. The ink thickness variation computing system of claim 11, where the processing module comprises a multiplexer, a fast logic, a pulse counter and a microcontroller, where the multiplexer is operable for selecting the SPAD whose pulses are counted, where the pulse counter is operable for counting the pulses received from the SPADs and where the microcontroller is operable for storing the resulting pulse count and for transmitting it to the computing system.

14. The ink thickness variation computing system of claim 11, where light emitting diodes (LEDs) emit light that is directed towards the print sheet, where part of said light penetrates the print sheet, is reflected by the sheet's substrate and captured by said SPAD sensor devices.

15. The ink thickness variation computing system of claim 11, where white light is filtered by filters having different spectral sensibilities within the visible and near infra-red wavelength range and directed towards the print sheet, where part of said filtered light penetrates the print sheet, is reflected by the print sheet's substrate and captured by said SPAD sensor devices.

16. The ink thickness variation computing system of claim 11, where white light illuminates an area segment of said print sheet, is reflected by said area segment, is filtered by filters having different spectral sensibilities within the visible and near infra-red wavelength range and is captured by said SPAD sensor devices.

17. The ink thickness variation computing system of claim 11, where one input and one output polarizing filters discard part of said light that is specularly reflected at the surface of said moving print sheet.

18. The ink thickness variation computing system of claim 10 forming together with an additional print actuation parameter driving module an online ink regulation system operable for controlling according to the deduced ink thickness variations the amount of ink deposited onto a substrate.

19. The ink thickness variation computing system of claim 18, where controlling the amount of ink deposited onto a substrate is performed in case of a printed press by ink feed, in case of an ink jet printer by a function selected from the set of droplet ejection control and droplet count, in case of an electrophotographic printer by a function selected from the set of toner transfer and fusing and in case of a thermal transfer, respectively dye sublimation printer, by controlling head element temperature profiles.

20. The ink thickness variation computing system of claim 10, where the inks are the cyan, magenta, yellow, and black inks and where said thickness variation and sensor response enhanced spectral prediction model operates in the visible and near infra-red wavelength range.

21. The ink thickness variation computing system of claim 10, where said computing system also performs an online refined calibration of said thickness variation and sensor response enhanced spectral prediction model by deducing paper reflectances of said print sheets and by fitting according to the multi-channel sensor responses effective surface coverage curves mapping nominal to effective surface coverages of single ink halftones in different superposition conditions.

22. The ink thickness variation computing system of claim 10, where said computing system also records reference thickness variations and where the computed ink thickness variations are ink thickness variations normalized in respect to the reference ink thickness variations.

23. The ink thickness variation computing system of claim 10, where said computing system also records reference sensor responses from a reference print under reference settings, deduces corresponding reference effective surface coverages, and predicts sensor responses with the deduced reference effective surface coverages and where the computed ink thickness variations represent ink thickness variations in respect to the reference print.