Proc. of 35 Int. Conf. of IARIGAI, Valencia (Spain), 2008, pp. 347-357.
Yuri V. Kuznetsov, Denis E. Zheludev
North-West Institute of Printing of the St. Petersburg State University of Technology and Design
MTF, screening, distortion, halftone
For objective quantitative measurement of the image fine detail distortion involved by screening the Screening Distortion Factor (SDF) is proposed. It comprises the norm of an error evaluated by superimposing of the original and halftone resolution pattern bitmaps and counting the normalized sum of microdots, which changed their polarity (from black to white and from white to black) as result of screening. The losses in an image high spatial frequency component are illustrated by plotting the SDF curves via line test pattern frequency for variety of such screening process parameters as screen ruling, screening factor, screen and dot geometry, screening algorithm, etc.
Unlike the other imaging systems the specific process of graphic industry is to transform the continuous tone original to a bi-level print comprised of the plurality of small inked and blank elements. As far as the resulting amount of ink transferred to a print and, hence, the basic quality issues of the latter such as color, definition, tone rendition, sharpness, etc. are fundamentally dependent on these elements area, form and geometry of placement the screening has always comprised the actual, cornerstone R&D issue of illustrative printing. As result, many dozens of currently available, announced or upcoming, patented and trade marked screening techniques are currently pretending on their approbation and practical use.
In such situation the demand arises for correct, quantitative comparison of various screening techniques efficiency with the other important factors involved to the process being, if possible, kept the same . The generalized approach to the halftone print quality evaluation was formulated in  on the basis of comparing not the original and its halftone copy themselves but the image metaphors of the both produced by the HVS model. So, this approach embraces the whole great number of halftone print quality parameters which can be subdivided on two groups. Parameters, related to the first of them, characterize the reproduced color, contrast or tone range, the number and distribution of the grey levels within the latter, the uniformity of vast image areas, etc. Along with the visual estimation, these quality indices of reproduction can be objectively and separately measured by colorimeter and densitometer with the use of corresponding test wedges, which results, for example, in plotting of the so called TCRs (Tone Reproduction Curves), color gamuts, tone deviation distributions, etc.
Given research is, however, related to the parameters of the second group which are responsible for reproduction of the high spatial frequency content of an image, i.e. for its sharpness and definition. The evaluation of just this kind of parameters is needed for estimation of those digital screening techniques, which have no any effect on the first mentioned kind of parameters as compared to the other screening technologies
The Modulation Transfer Function (MTF) is commonly used to model the frequency response of an imaging system [2, 3]. Micro photometric measuring of profiles or contrasts across the lines and gaps of the reproduced variable spatial frequency bar pattern can be applied, for example in photography, to verify the correlation of a modeled MTF to an experimental results. However, this micro photometric method isn’t efficient to estimate the halftone reproduction of such a pattern because the micro structure of the latter stays bi-level, i.e. similar to the structure of an original test image. The only difference is in that instead, for example, of solid lines and clean gaps of a test target the structure of its halftoned version comprises the scattered halftone dots or just parts thereof filling both the lines and gaps of a pattern in the manner dependant on specific of a screening method used in reproduction (Fig. 1).
Figure 1. The bit maps of enlarged fragment of resolution test pattern (a) and its halftone reproduction (b)
Therefore, the facility of certain screening technology to preserve the sharpness and definition of an original continuous image is mostly judged by the visual evaluation of resolution test patterns. Such practice doesn’t make possible the objective comparison of various screening techniques efficiency in relation of these important image quality issues because of the difficulty of providing the multiple of other imaging conditions exactly the same. So, the need exist in a quantitative method allowing for evaluation of effect of various imaging parameters (volume of a scanned/input image data, printer resolution, type of printing, etc.) and of various screening settings (screen and dot geometry, screen ruling and angle, screening algorithm, etc.) on halftone picture quality at different spatial frequencies and contrasts, as well as, along the whole chain of reproduction stages.
The method and measurement procedures
We have measured the norm of an error to quantitatively estimate the fine detail distortion involved by screening. This norm is evaluated by superimposing of the original and halftone pattern bitmaps and counting some normalized sum of the microdots, which changed their polarity (from black to white and from white to black) as result of screening. With the use of such a norm the Screening Distortion Factor (SDF) can be calculated according to the equation
where and are correspondingly the bi-level values in A and B matrixes of an original and screened patterns, while M and N denoting the number of lines and columns in a matrix.
In this approach the initial test with resolution pattern of full or intermediate contrast is concerned as a detail of continuous tone original to be reproduced with the use of screening. The method of such test processing comprises, as is shown on Fig. 2, the following steps:
- formation the high resolution bitmap of a test resolution pattern (Fig. 2a);
- capturing and encoding of this test by a scanner at the predetermined screening factor and contrast settings with providing the multilevel CT (byte-map) image file (Fig. 2b);
- creating the PostScript file at predetermined settings of tone value percent for white and black levels (Fig. 2c);
- screening the PostScript image file in a RIP or some custom software with providing the halftone bitmap (Fig. 2d);
- superimposing the initial and final bitmaps to calculate the SDF according to above equation (Fig. 2e).
Figure 2. The sequence of resolution test pattern processing steps for SDF calculation
The predetermined quantization levels of 8-bit code emulating some intermediate contrast of an original pattern or taking into account certain artistic considerations are assigned to b/w levels of an input image at the first step (Fig. 2b). Nevertheless, if even the extreme values of , for example, 0 and 255 are used, as indicated on the same figure, the intermediate values appear in encoded image version due to the aperture distortion of scanning or, in the other words, due to the averaging the tone value over an image sampling area at detail boundaries. Such important variable of halftoning procedure as the sampling or screen factor (SF) comprising the ratio of image scanning and screening frequencies is also set at this step.
When the picture is further prepared for printing the new codes should be assigned to black and white corresponding to minimal and maximal, for example, 10% and 90% halftone dot area appropriate to the technology being used for given kind of a print job (Fig. 2c).
The use at the last of these steps of a bit map produced by screening program undermines the SDF evaluation in relation to some idealistic image copy. However, the superimposing a high resolution scanned bit map of a halftone transparency, plate or print may also be used here allowing for evaluating the share of distortion added by the corresponding further stage of printing technology.
The graphs of such a factor, plotted along the pattern ruling values, should comprise some equivalent of MTFs and allow for comparing the various screening methods efficiency in relation of the reproduction of high spatial frequency content of an image.
For testing this method working ability the MATLAB facilities  were used to create resolution test patterns at 3600 dpi, process them with analytically defined (Fig. 3) weight function, calculate and plot the SDF curves. Test image scanning and encoding were emulated in Photoshop.
Figure 3. Examples of “screen hills” produced with the use of analytically defined (by analogy with ) screen function for three halftone frequencies
Testing and preliminary discussion of the method workability
The first graphs produced by the above described method (Fig. 4) allowed for some discussion of proposed Screening Distortion Factor representativeness.
The SDF value equal to 1.0 relates to the case of facsimile reproduction when all the input pixels remained unchanged. Such situation takes place for an input test of full contrast scanned at maximal SF, i.e. at as high resolution as that of the printer and assigning to its white and black levels correspondingly of the 0% halftone dot and ink solid. The screening process has no place in this case, the halftone dot generator working as a simple Boolean repeater and SDF curve comes on a graph parallel to abscissa as shown on figure 8.
Zero value of SDF corresponds, according its formula, to opposite case of some virtual, theoretical presentation of an original by its negative (Fig. 5c) as result of screening by reversing the sign of all the bits of an input test.
The SDF value of 0.5 corresponds to the case in which the half of bits of both dark and light lines of an input test-pattern has changed their sign as result of screening, as, for example, shown on figure 5b. So, all the SDF values lower than 0.5 may be considered non-representative. Small fluctuation of SDF curve near this value can be explained by some deviation from 50/50 relationship of black and white within resolution pattern patches of different frequencies.
However, the SDF level of 0.5 doesn’t completely correlate with visual estimation of resolution pattern halftone copy because of aliasing which arises at some lower frequency of an input pattern than that corresponding to SDF = 0.5. Such aliasing appears due to the interference between pattern and screen frequencies. The peak on lower curve of figure 6 demonstrates the result of such interference at about 28 lines per mm () of an input line pattern when the 20 l/cm orthogonal screen is used at 45 degrees angle. The number of such peaks increases (Fig. 4a) when the lines of a pattern are vertical and the screen isn’t turned.
From the other hand, the use of the pattern comprised of circular lines, as the graph on figure 4b shows, gives estimations which are less disturbed by the interference due to some compensation of its effect on calculated SDF value. Anyway, the SDF graphs properly reflect the visually perceived definition at the level which is somewhat higher of 0.5. Nevertheless, the plots coming down to 0.5 SDF level may be advised to be used as far as the certain tendencies of the other factors influence on fine detail distortion are demonstrated by more extended graphs. Such different trends can be seen on graphs presented on figures 6 – 9 and calculated for the number of variables.
Figure 4. Screening Distortion Factor (SDF) plotted along the resolution test pattern frequencies for two geometries of a pattern: concentric (a) and parallel lines (b)
Figure 5. Examples of the input test halftone copies for SDF values of 1.0 (a), 0.5 (b), 0.0 (c)
Figure 6 shows the screening distortion at different screen rulings at fixed SF of 2.0 and full contrast of an input test while figures 7 and 8 are plotted correspondingly for variable test contrast and screening factor. At the same time, the combination of four of these graphs on figure 9 allows to see how two above variables may compensate each other in relation of fine detail distortion involved by the screening process.
Such estimation can be performed starting from the idealistic, bitmap presentation of a screened pattern in a RIP according to above listed steps, and up to the use of a bitmap produced by the high resolution scanning and bi-level encoding of a final, i.e. printed, resolution test. So, the method allows for independent and comparative quantitative estimation of the additional share of low pass image frequency filtration introduced in computer-to-film and computer-to-plate techniques at various output resolutions as well as with the use of various types of plates in conventional platemaking. Being applied to silk printing it makes possible the objective evaluation of the effect of various silk screen parameters on sharpness and definition of the halftone image. The same kind of investigation can be related to the similar effects of anilox roller parameters in flexography. At last, the method stays helpful to practically evaluate the halftoning facilities of those digital printing devices where the screened bitmaps aren’t available and the method of screening is unknown due to the closed architecture of such devices.
The methodology and results of comparative evaluation are demonstrated for different screening techniques and also at such halftone process variables as screen ruling, screening factor, screen and dot geometry, etc.
, the proper geometry of a test pattern has in this method the great influence on providing the representative and stable results. Figure 3 (a) shows the peaks on curve provided with the use of a pattern of parallel lines. The reason of this fluctuation is in the interference of these lines frequency with that of an orthogonal screen. From the other hand, the curve on figure 3(b) tells that this is not such a problem for the test pattern comprised of concentric circles.
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