A new model is proposed for predicting the apparent dot area of simulated halftone prints on coated paper surface without requiring printing. It is based on Hotelling’s multivariate T2 statistic which is shown to provide a measure of lateral light scattering. The T2 statistic is computed from colorimetric coordinates obtained from of a knife shadow image response on the paper surface. The proposed method offers superior prediction of halftone dot area compared to current light scattering models. A method for characterising peaks on the coated paper surface is introduced in this work. The effect of the paper coating layer thickness and the surface peak height on lateral light scattering and printed dot size are shown.
© 2016 Optical Society of America
This paper is aimed at predicting the apparent dot area of halftone prints from lateral light scattering on coated paper and board grades. Such a model can be useful in controlling paper making process variables that contribute to the lateral light scattering and limit costly rejections during downstream halftone print reproduction.
Apparent dot area is fractional coverage of the printed halftone dots, relative to unprinted paper, measured in terms of optical density. (Optical density is defined as the logarithmic ratio of the ink film reflectance to the paper surface reflectance, ISO – 5 −1 ). When photons enter the surface of paper in between printed halftone dots they may emerge from under the halftone dot at a distance away from the point of incidence due to lateral scattering within the body of the material. This well-known phenomenon increases the optical density (and hence the apparent dot area) of halftone areas printed on the paper.
Optical dot gain in halftone prints was demonstrated by Yule et. al.  using the classical edge spread function (ESF), derived from micro reflectance measurements across a knife edge shadow projection on paper surface. This approach was further developed for directly estimating lateral light scattering from a modulation transfer function (MTF) derived by taking discrete Fourier transformation of the ESF . Wakeshima and Kunishi  used a small pencil of light, Inoue et al.  used a sinusoidal pattern, Rogers  and Arney et al.  employed a bar target and Ukishima et al.  used an octagonal pencil of light by closing the iris of a microscope.
Indirect methods for MTF estimation use Kubelka–Munk equations and Monte Carlo simulation. Engeldrum and Pridham  concluded that K-M theory did not fit the MTF data for coated paper. Monte Carlo simulation was first proposed by Hainzl et al.  and further developed by Coppel et. al.  and Linder et. al.  adopting an isotropic single scattering model; however since this approach involves substantially more parameters that are difficult to measure, its practical application is limited. An alternative to the MTF approach for characterizing apparent dot area increase is based on probability functions of photon behaviour on the paper, first suggested by Huntsman  and further developed by Arney . They concluded that the same probability function cannot distinguish the photon behaviour for different halftone patterns. Namedanian  proposed yet another indirect method for MTF estimation employing microscopic image histogram (MIH) analysis of printed samples, which does not model the halftone dot area from the unprinted paper surface.
Although a large body of work is reported focusing on paper surface’s lateral light scattering measurement, its efficacy in characterising halftone prints is sparsely represented in the literature. As in Bhattacharya et. al. , we use Hotelling’s multivariate T2 statistic computed from a knife edge shadow projection to model lateral light scattering of the paper surface. A development of the previous T2  method is proposed in this work by reducing the impact of undesired surface reflection and by improved optical focusing. Another contribution of this work is the quantification of apparent dot area from simulated halftone printing for de-convolution of the paper surface’s optical contribution to halftone dot area from other factors.
The micro-structure of paper coating has been reported to affect the light scattering, gloss, and homogeneity of prints [16–20]. Roughness measured by conventional air leakage methods lacks the sensitivity to determine micro roughness relevant to halftone printing [21, 22]. Non-contact optical methods can address this concern, and allow superior characterization of coated paper surface structure for halftone printing . However, the previous work does not clearly establish which parameters of the paper coating layer affects light scattering behaviour and the apparent dot area of halftone prints.
A new micro roughness measurement method using confocal laser scanning microscopy of the paper surface is introduced in this work for quantifying surface peak height on the coated paper surface. An analysis of lateral light scattering and surface peak height is presented here in relation to paper coating layer thickness for modelling halftone dot reproduction.
Forty different coated paper and board samples were chosen for this study. These samples represented a wide selection of coated substrate types which included virgin CTMP fibre based folding box boards (FBB), virgin fully bleached chemical fibre based solid bleached sulphate boards (SBS), recycled fibre based white line chip boards (WLC) and virgin fully bleached chemical fibre based lightweight coated papers (LWC). The sample set also provides the opportunity to study paper samples over a wide range of paper surface roughness levels as indicated by the Parker Print Surf – PPS H10 roughness  (see Table 1 below). More details about the different type of substrate chosen for this study can be found in Table 1.
2.1 Lateral light scattering estimation
Traditional MTF approaches characterize lateral light scattering from the paper surface in terms of the reflection intensity distribution around the boundary of a blurred shadow projection image. This approach has been evaluated in the current work and its performance in modelling halftone dot area is found to be relatively poor (see Fig. 7 below). An explanation of this behaviour could be that variation in local intensity of objects under indirect illumination can make it difficult to discriminate the boundaries of the shadow from that of the object boundaries. The classifications of shadow boundaries can be improved from the evaluation of spectral components of reflected light from an object located under a shadow, since the variation in spectral distribution is much lower than the variation in intensity . It is also reported that micro-roughness structure of paper surface increases the reflection intensity resulting in an over-prediction of subsurface light transport by the MTF approach .
We propose an alternative method that addresses the concerns associated with MTF approach. As in Bhattacharya et al , we use the concept of the Hotelling observer [26,27] to characterize subsurface light transport from spatial distances between the spectral components of reflected light near the boundary of a shadow projection on the paper surface.
An imaging system comprising optical microscope (Olympus BX50) equipped with a CCD digital camera (QImaging, RoHS CE, Imaging Corp) is used to obtain a microscopic image of the knife edge shadow projection on the paper surface. A sharp lancet knife is placed into the incident light path of the imaging system to project the knife edge shadow on paper surface. In contrast to Bhattacharya et al  we use two polarizing filters in the imaging system, one in front of the incident light and the other in front of the camera for minimizing the undesired impact of surface reflection. The imaging setup also features a movable lens placed into the incident light path for improving the focus of the knife edge projection on the paper surface. The imaging system in the current work has a 0°:0° geometry (i.e. both incident beam and sensor are normal to the surface) as it is advantageous for adjusting the focus of the camera and of the projected shadow.
The CCD digital camera has a maximum resolution of 4008 x 2672 pixels, and a dynamic range of 12 bits. The light source was a 6V 30W tungsten halogen lamp. The measurements were carried out inside a dark room with the surround being covered with matt grey curtains to avoid stray light in the imaging setup. A schematic view of the knife edge imaging system is shown in Fig. 1.
The CCD camera in the imaging system records RGB reflectance data of the microscopic image. An example of the knife edge shadow image recorded by the imaging system is shown in Fig. 2.
The blurring of the edge image is influenced by the lateral light scattering on the paper surface as well as by Fresnel diffractions at the knife edge in the imaging setup. Similar to Ukishima  and Happel et. al.  we use a reference material to compensate for the optical distortions of the imaging setup. The reference material used here is an experimental grade 1.6 mm thick front surface (FS) mirror which has an average reflectance of 95%. The FS mirror is aluminized on the surface nearest to the incident light to minimize sub surface lateral light transport.
The RGB data is acquired across a set of colinearly paired lines around the boundary of knife edge shadow image (see Fig. 2(a) above). Following colorimetric characterization of the imaging system, camera RGB data was transformed to CIE XYZ values, relative to a perfect reflecting diffuser. Each of the two lines in the image is thus comprised of reflectance values for a large number of pixels. In the line matrix for each of the lines, the pixels are row-wise and X, Y & Z, colorimetric values for each pixel are column-wise. The distance between the two lines and their individual lengths are chosen to be 1mm for characterising the paper surface’s light scattering at this scale, since the detection threshold of human visual system to print density variations at typical viewing distances is approximately 1 mm .
Data acquisition was performed in this manner for each of the forty paper samples. The degree of lateral light scattering on the paper surface was estimated from Hotelling’s Multivariate T2 value which is arrived at using the following equation :
T2 measurements were made at five different locations on each of the forty paper samples, which were digitally marked to enable reproducible imaging. The repeatability of the T2 measurement over the sample sets was estimated from the measurement variance as a percentage of the total variance and is denoted equipment variability (EV%) . The EV% was found to be 1.06%, indicating excellent repeatability of the proposed method.
T2 measurements were also made on the FS mirror surface using the same imaging setup in an identical manner. The ratio between the paper surface’s and the reference material’s T2 values is used to characterize paper surface’s edge spread behaviour. The T2 ratio is referred by the acronym “BBG” in the rest of the work.
The monochromatic intensity values for the same set of lines were used to compute the MTF metric kp, which was introduced by Arney et. al.  and is considered to be a direct measure of the extent of lateral light transport on paper surface. The MTF was also measured by an alternative method proposed by Ukishima , which considers the ratio between the reflection intensity of the paper samples and a perfect specular reflector, providing a compensation for the MTF of imaging system. The kp values are then deduced from the MTF curves. The MTF constant was also derived from the CIE Y value alone independent of the X and Z colorimetric values for the same set of lines. The Y value represents the reflectance of the knife edge shadow projection, weighted by the achromatic response of the human visual system. The efficacy of the proposed T2 method is compared to the MTF based approaches in characterising halftone dot area from surface light scattering.
2.2 Halftone print simulation
To determine the optical contribution of the paper surface alone towards halftone dot area in the print, a simulation of halftone printing is performed. The simulation is achieved by physically contacting the paper surface to a transparent photographically-developed positive-working film imaged with a 133 line 40% halftone screen. A vacuum printing down frame is used for promoting contact uniformity between the halftone film and the paper surface. This film contact method for print simulation has been previously used for visual estimation of halftone print uniformity [5,17].
The non-destructive nature of the simulated printing method avoids the variability associated with ink penetration into paper that occurs when making a halftone print using conventional offset printing. Therefore this approach isolates the optical effects from other variables. Simulated printing coupled with digital marking of samples is also advantageous for making repeatable measurements of lateral light scattering at identical locations on the sample set.
It has been suggested that the film contact method leads to increased light scattering due to multiple Fresnel reflection at the paper surface - film – glass top and - air interfaces due to their different refractive indices, leading to an overestimation of halftone area in the simulated prints. We address this concern by illuminating the film contact setup with polarized light at the Brewster incidence angle of 57° .
Poor contact between the halftone film and paper surface can also limit the performance of this method, and a validation test of contact uniformity is therefore necessitated. Pressure sensitive films composed of a set of pigmented donor and receiver sheet were used for this purpose. Upon separation of contact a pressure map is obtained on the receiver sheet, which was then digitally imaged for quantitative assessment of contact uniformity. The use of a compressible rubber backing plate beneath the paper sample promotes contact uniformity by allowing the halftone film to fully conform to the coated paper surface structure. The film used for simulated halftone printing has a thickness of 100 µm, and was exposed using a film image setter  to obtain extremely sharp halftone dot edges. The dark opaque areas of the film exhibit an optical density of 4.0 whereas the clear film has a density of 0.05. The halftone dot area on the film is 40%, calculated from the transmission densities of the solid and the halftone areas on the film using Murray-Davies (MD) equation .
Simulated halftone printing was carried out for each of the forty paper samples using the film contact setup discussed above. The CCD camera of the optical microscope used for imaging the knife edge shadow is also used for imaging simulated prints. The apparent dot area was calculated from the reflection intensities of the solid and the halftone areas on the simulated print image using the MD equation.
The agreement between proposed simulated halftone printing and a real halftone print was determined for the same set of samples. Printing of 133 line 40% halftone dots was performed using a Prufbau printability tester, and the same CCD camera was used for imaging the Prufbau halftone print strips. The apparent dot area was calculated from the reflection intensities of the solid and the halftone areas on the Prufbau print image using the MD equation as above. A statistical two sample T-test was performed to estimate the 95% confidence interval for mean differences in apparent dot area of simulated and real halftone prints. The interval end points are −1.285 and 0.877 respectively. The test statistic for the hypothesis testing is 0.708 indicating very good agreement between the simulated and real halftone printing.
Illustration of the film, vacuum printing down frame, Prufbau printability tester and digital images of simulated and Prufbau prints are shown in Fig. 3.
The repeatability of simulated printing using the film contact setup was evaluated from the halftone print density measurements for the sample set. The equipment variability EV% for the halftone print density measurement for the simulated printing is found to be 1.96% indicating excellent repeatability of the proposed method.
2.3 Micro roughness measurement
The presence of distinctive peak facets are known to affect surface light scattering due to refractive index mismatch at the boundary between the air and the surface layer . The widely used Parker Print Surf (PPS)  roughness technique classifies paper surface peak height at scales ranging from 51 to 13,500 μm . As the diameter of individual halftone dots varies at a much smaller and narrower band ranging from 20 to 60 μm, the PPS roughness measure cannot uniquely characterise paper surface peak height relevant to halftone printing, while non-contact optical methods like confocal laser scanning microscopy (CLSM) techniques are able to do so. CLSM offers significant advantages over the conventional methods in the three-dimensional surface mapping of planar surfaces owing to its superior recognition of details by the defocussing effect . Several previous researchers have used CLSM for charactering coated paper surface micro roughness and ink penetration behaviour, while the classification of paper surface peak height in relation to halftone printing is sparsely represented in the literature [36–39].
We propose here a new surface peak height measurement method employing confocal microscopy since CLSM offers superior depth discrimination of planar surfaces . A confocal laser scanning microscope from Carl Zeiss (LSN 710) was used for this study and the following parameters were selected for CLSM imaging: mode = reflection; laser power = 15 mW; pinhole diameter = 35 μm; digital zooms = 0.6; scanning area = 1414.22µm X 1414.22µm; scanning pixel format = 512 X 512; Z-step = 2µm; and excitation wavelength = 543 nm. Each of the forty samples was scanned using these settings on the CLSM.
Point probing of the entire paper sample by the CLSM rendered three-dimensional reflection intensity maps. The topography module of the software integrated with the CLSM imaging system was used to convert the reflection intensity to the surface height distribution. Characterization of surface peak above the mean surface micro roughness is the main interest here. For this purpose we use the concept of a material ratio curve, also commonly known as an Abbott-Firestone curve . It is defined as the total percentage of material above a certain height on the surface and is derived by taking the integral of the amplitude distribution function of the surface height . Surface peaks above the mean surface micro roughness were calculated from best fitting of the 40% segment of the least squares mean plane in the material ratio curve, based on the principles described in ISO 13565-2:1996 . The surface peak height is denoted by Spk in terms of microns (µm). Larger Spk values imply that the paper surface is composed of a larger number of peaks, which may significantly impact the intensity of scattered radiation.
A schematic representation of three-dimensional surface height map and the corresponding material ratio curve used for calculating Spk is shown in Fig. 4.
Examples of CLSM three-dimensional surface height maps for two different types substrates are shown in Fig. 5(a) and 5(b) below.
Sample coordinates were again digitally resolved for CLSM surface imaging so that the Spk and BBG measurements coincide with each other. The equipment variability (EV%) for the Spk measurement is 2.35%, indicating excellent repeatability of the proposed method for coated paper surface peak height characterization.
2.4 Coating thickness measurement
The coated paper surface structure is dependent upon the spatial distribution of the coating layer on the base paper. Scanning electron microscopy (SEM) coupled with digital image analysis of cross- sectioned surfaces is the most intuitive method of defining this distribution reported in the literature .
Similar to Rune , we use a scanning electron microscope in the back scattering mode for coating layer thickness estimation. The choice of back scattering mode improves the visualization of heavier coating pigment particles. Prior to SEM imaging, the paper samples were vapor stained with crystalline Osmium Tetroxide (OsO4) for 24 hours at 23 °C for preferential staining of the coating latex binder and improved visibility. The stained samples were then impregnated in an epoxy resin to enhance image contrast by filling the paper coating pores. Cross sectioning of the paper samples was performed, employing a CO2 laser cutting using a gas mixture of CO2:N2:He in the ratio 1:4:10. Sectioning of paper samples by laser cutting reduces the mechanical stress and provides distortion free edge artefacts suited for SEM imaging . The laser cutting process being computer guided is also advantageous in resolving the sample coordinates for cross sectioning at identical locations to where BBG, Spk and halftone dot area of simulated prints are measured. Finally the cross-sectioned paper samples are gold sputtered for 30 seconds to make the surface electrically conductive for SEM imaging.
Scanning electron microscopy from Carl Zeiss (Merlin) was used in the current study. The following parameters are selected for cross section SEM imaging: accelerating voltage = 5 kV; working distance = 8 mm; magnification = 250X; spatial resolution = 1280 X 960 pixels and pixel resolution = 0.37 μm/pixel.
The scanning length for each SEM image is 0.5 mm. In order to estimate the paper coating thickness over a sample length of 1mm, two SEM images were joined together using Adobe PhotoshopTM software for each sample. The SEM images were then processed with image analysis software for noise removal with a 3x3 median filter. Thresholding of the processed SEM images yielded binary images of the white coating layer against a black background. The area of the white portions was then divided by the overall sample length to obtain the mean coating layer thickness. Paper coating thickness is quantified in microns (µm) in this manner for each of the paper samples, and it is denoted by Ct.
Figure 7 shows the lateral light scattering measures for the different types of coated paper and board samples. The subsurface light transport data obtained from the proposed BBG method is presented in Fig. 7(a). Figure 7(b) shows the MTF constant kp values derived from three different methods, where kp-A denotes Arney’s method , kp-U denotes Ukishima’s method  and kp-Y donates the MTF constant derived from the Y value.
The BBG and kp values were correlated to the apparent dot area of 40% halftone screen for the simulated prints over the sample set. The linear least square regression models for the BBG versus dot area and kp versus dot area can be assessed from Figs. 8(a) and 8(b) below.
Figure 9 shows the 95% confidence intervals of mean dot area for two different sets of simulated prints. In one of the sets the simulated prints were imaged by illuminating the film contact setup with a polarized incident light directed at an angle of 57° and the corresponding reflectance values normal to the sample plane were recorded. Apparent dot area for these set of simulated prints is mentioned as “Polarized-57/0” in Fig. 9. While the second set of simulated prints were imaged by illuminating the film contact setup with an unpolarised incident light at diffused angle and the corresponding reflectance values normal to the sample plane were recorded. Apparent dot area for the second set of simulated prints is mentioned as “Unpolarised-d/0” in the Fig. 9. A statistical two sample T-test was performed to estimate the 95% confidence interval for mean differences in apparent dot area obtained from the two different setups used for imaging the simulated halftone prints. The interval end points for the mean difference are −2.852 and −0.633 respectively and the test statistic for the hypothesis testing is 0.002. The results indicate the use of unpolarised incident light and d:0° optical measurement geometry in the film contact setup leads to significantly higher apparent dot area of simulated prints.
Figure 10 below shows the apparent dot area in relation to the conventional paper surface roughness measures, PPS and the proposed surface peak height measure, Spk.
Coating layer thickness is shown in relation to apparent dot area in Fig. 11 above.
Homogeneity of fibre source seems to have limited influence over the extent of lateral light scattering in the coated paper grades, as the heterogeneous recycled fibre based WLC and virgin fibre based FBB samples exhibited significantly lower BBG values than the homogenous virgin fibre based LWC and SBS samples. This behaviour is consistent with respect to the MTF constant kp values also. A constant bias with marginally higher kp values is seen with Arney’s model than the Ukishima’s model (Fig. 7(b)). This can be explained by the fact that both the models uses the same edge spread response data for arriving at the MTF constant kp, with the exception that Ukishima’s model provides a compensation for the imaging system MTF using a reference perfect specular reflector. The MTF constant kp derived using the Y tristimulus data yields identical values to Arney’s model as both these models use the reflectance from the paper surface under knife edge shadow projection to compute the MTF.
The dot area measurement over the simulated halftone prints demonstrates extremely good correlation with the BBG data, while on the other hand the MTF constant kp shows inferior correlation to the apparent dot area (Fig. 8). This appears to validate the fact that classifications of shadow boundaries can be improved by considering spectral variability as opposed to just the monochromatic variation in reflected light near the boundary of knife edge shadow.
The results from two different imaging setups for the simulated prints shows that the use of diffused unpolarised illumination led to an overestimation of the dot area (Fig. 9). The model is improved by polarising the light so as the incident light’s electric field oscillates only perpendicularly to the incidence plane, and at a 57° incidence the angular reflection is zero.
It can be inferred from Fig. 10 that the surface peak analysis employing the proposed Spk method provides a better estimation of apparent dot area, compared to the traditionally used PPS method. The classification of different types of coated substrates from Spk analysis corresponds well to the lateral light scattering behaviour. The SBS and LWC samples demonstrate significantly larger Spk values, while the WLC samples exhibit the lowest Spk values. It is evident that presence of surface peaks augments surface light scattering.
The model presented in Fig. 11 shows a strong inverse relationship between the paper coating layer thickness and the apparent dot area. This behaviour can be attributed to the fact that the surface micro-roughness increases at lower coating thicknesses due to the poor levelling of a thin coating layer on top of base fibres. As a consequence surface light scattering may be increased due to greater refractive index mismatch between the thin coating layer and the fibres lying just beneath the coating, leading to a higher apparent dot area in the halftone prints on the paper surface.
This paper presented a light scattering measurement method referred to as the BBG model, which is based on the multivariate T2 statistic of paper surface reflectance under a knife edge projection. The proposed BBG model is shown to successfully predict the apparent dot area of a 40% halftone screen on different paper substrates, without the need for printing. The estimate of fractional dot area using this approach with test samples with varying degrees of surface micro-roughness is shown to be better than alternative MTF approaches, which tend to overestimate dot area on rougher surfaces.
A film contact setup was evaluated for simulating halftone printing and estimating the apparent dot area of virtual prints. This setup comprises a polarizing filter in front of an illumination source and a 57°:0° optical measurement geometry for minimizing the unwanted impact of multiple surface reflections at the paper surface – film - glass top and air interfaces due to refractive index mismatch.
We also presented an approach to quantify micro-roughness in terms of surface peak height above the mean surface plane from the analysis of three dimensional surface reflection intensity maps obtained from confocal microscopic imaging of coated paper surface. This approach is shown to provide good estimates of surface peak height, and the influence of this micro-roughness over lateral light scattering and halftone dot reproduction is demonstrated.
Finally this work shows that paper coating layer thickness exhibits an inverse relationship to the halftone dot area. A thicker coating layer yields a surface featuring lower degree of surface peak features, which minimizes the surface light scattering and consequently reduces apparent dot gain in halftone prints.
The methods proposed in this work can serve as an in situ quality control and development tool during the manufacturing of coated paper grades on paper machines.
In future work we plan to test the ability of the proposed methods to predict printed dot area over the full tonal range.
The support provided by ITC Limited for this research is gratefully acknowledged by the authors.
References and links
1. ISO 5 −1, “Photography and graphic technology—Density measurements—Part 1: Geometry and notation,” (2009).
2. J. Yule and W. Neilsen, “The penetration of light into paper and its effect on halftone reproduction,” TAGA Proceedings3, 65–67 (1951).
3. J. Arney, C. D. Arney, M. Katsube, and P. G. Engeldrum, “An MTF analysis of papers,” J. Imaging Sci. Technol. 40, 19–25 (1996).
4. H. Wakeshima, T. Kunishi, and S. Kaneko, “Light scattering in paper and its effect on halftone reproduction,” J. Opt. Soc. Am. 58(2), 272–273 (1968). [CrossRef]
5. S. Inoue, N. Tsumura, and Y. Miyake, “Measuring MTF of paper by sinusoidal test pattern projection,” J. Imaging Sci. Technol. 41(6), 657–661 (1997).
7. M. Ukishima, H. Kaneko, T. Nakaguchi, N. Tsumura, M. Hauta-Kasari, J. Parkkinen, and Y. Miyake, “A simple method to measure mtf of paper and its application for dot gain analysis,” IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 92(12), 3328–3335 (2009). [CrossRef]
8. P. G. Engeldrum and B. Pridham, “Application of turbid medium theory to paper spread function measurements,” TAGA Proceedings1, 339–352 (1995).
9. R. Hainzl, Light and Paper—A New Light Scattering Model for Simulating the Interaction between Light and Paper (Acreo, 1999).
12. J. R. Huntsman, “A new model of dot gain and it application to a multilayer color proof,” J. Imaging Sci. Technol. 13(5), 136–145 (1987).
13. J. S. Arney, “A probability description of the Yule-Nielsen effect,” J. Imaging Sci. Technol. 41(6), 633–636 (1997).
14. M. Namedanian, “Characterization of halftone prints based on microscale image analysis,” Dissertation No: 1548, Department of Science and Technology, Linköping University, ISBN 978-91-7519-499-8, 36–38 (2013).
15. A. Bhattacharya, S. Bandhyopadhyay, and P. Green, “Characterizing unprinted paperboard surface for predicting optically induced halftone mottle,” Nord. Pulp Paper Res. J. 30(3), 497–510 (2015). [CrossRef]
16. A. O. Pino, J. Pladellorens, and J. F. Colon, “Method of measure of roughness of paper based in the analysis of the texture of speckle pattern,” Proc. SPIE 7387, 73871W (2010).
17. D. Smith, M. D. Williams, J. P. Salminen, W. G. Welsch, W. Heeschen, R. N. Nicholas, and S. J. Arney, “Definition and model for primary grey scale mottle as a variation in the Yule-Nielsen Effect in offset printed coated paper, ” TAPPI Proceedings (2009).
18. A. Andersson and K. Eklund, “A study of oriented mottle in halftone prints,” Department of Science and Technology, Linkoping University, ISRN: LITH-ITN-MT-EX-07/024—SE, 38–52 (2007).
19. H. Hägglund, O. Norberg, and P. Edström, “Prediction of optical variations in paper from high resolution measurements of paper properties,” Nord. Pulp Paper Res. J. 28(4), 596–601 (2013). [CrossRef]
20. J. Aspler, L. Cormier, and T. Manfred, “Linerboard surface chemistry and structure affect flexographic print quality,” Proceedings of: International printing and graphic arts conference, Montreal, Canada. Montreal: PAPTAC, 167–177 (2004).
21. G. G. Barros, C. M. Fahlcrantz, and P. A. Johansson, “Topographic Distribution of UnCovered Areas (UCA) in Full Tone Flexographic Prints,” TAGA Proceedings 2(1), 43–57 (2005).
22. R. Xu, P. D. Fleming, and A. Pekarovicova, “The effect of inkjet paper roughness on print gloss,” J. Imaging Sci. Technol. 49(6), 660–666 (2005).
23. TAPPI T555, “Roughness of paper and paperboard (Print-Surf Method),” TAPPI (1999).
24. C. M. Fahlcrantz, On Evaluation of Print Mottle, PhD, KTH, School of Computer Science and Communication (2005).
26. L. Caucci, H. H. Barrett, N. Devaney, and J. J. Rodríguez, “Application of the Hotelling and ideal observers to detection and localization of exoplanets,” J. Opt. Soc. Am. A 24(12), B13–B24 (2007). [CrossRef] [PubMed]
28. M. Fairchild, Color Appearance Models (Addison Wesley Longman Inc., 1998).
29. H. Hotelling, “The Generalization of Student’s Ratio,” Ann. Math. Stat. 2(3), 360–378 (1931). [CrossRef]
30. B. L. Barrentine, Concepts of R&R studies, 2nd ed. (ASQ, 2003), Chap. 2, pp. 5–10.
31. N. Pauler, Paper Optics (AB Lorentzen and Wettre, 2002), Chap. 2, pp. 16.
32. H. Kipphan, Handbook of Print Media (Springer, 2001), Chap. 3, pp. 460- 473.
33. A. Murray, “Monochrome reproduction in photoengraving,” J. Franklin Inst. 221(6), 721–744 (1936). [CrossRef]
34. L. G. Coppel, P. Edström, and M. Lindquister, “Open source Monte Carlo simulation platform for particle level simulation of light scattering from generated paper structures,” in Proc. Papermaking Res. Symp., E. Madetoja, (2009).
35. G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy II: The micro and macro irregularities,” Meas. Sci. Technol. 11(3), 315–329 (2000). [CrossRef]
36. A. Goel, E.S. Tzanakakis, S. Huang, S. Ramaswamy, S.W. Hu, D. Choi and B.V. Ramarao, “Confocal laser scanning microscopy to visualize and characterize the structure of paper,” in AIChE Forest Products Symposium, Fundamentals and Numerical Modelling of Unit Operations in the Forest Products Industries (1999), pp. 75–79.
37. J. Vyorykkä, T. Vuoinen, and D. W. Bousfield, “Confocal Raman microscopy: A nondestructive method to analyze depth profiles of coated and printed papers,” Nord. Pulp Paper Res. J. 19(2), 218–223 (2004). [CrossRef]
38. Y. Ozaki, D. W. Bousfield, and S. M. Sharer, “Observation of the ink penetration in the coated paper by confocal laser scanning microscope,” TAGA Proceedings (2005)
39. Y. Ozaki, D. W. Bousfield, and S. M. Sharer, “Three dimensional observation of coated paper by laser scanning confocal microscopy,” Tappi J. 5(1), 1 (2006).
40. E. J. Abbott and F. A. Firestone, “Specifying surface quality: a method based on accurate measurement and comparison,” Mech. Eng. 55, 569–572 (1933).
41. ISO 13565–2, Height characterization using the linear material ratio curve (1996).
42. A. R. Dickson, “Quantitative analysis of paper cross-sections,” Appita J. 53(4), 292–295 (2000).
43. R. Holmstad, C. Antoine, P. Nygård, and T. Helle, “Quantification of the three dimensional paper structure: Methods and potential,” Pulp Paper Canada 104(7), 47–50 (2003).