Physical foundations of moire. See what "Moire" is in other dictionaries Moire in offset printing and elimination
A moire pattern is observed when different parts of tulle curtains are superimposed on each other.
The concept of "moire" comes from the fabric moire, in the decoration of which this phenomenon was used.
A moiré pattern occurs in digital photography and scanning of reticulated and other periodic images if their period is close to the distance between the light-sensitive elements of the equipment. This fact is used in one of the mechanisms for protecting banknotes from counterfeiting: a wave-like pattern is applied to banknotes, which, when scanned, can be covered with a very noticeable pattern that distinguishes a fake from the original.
Digital Image Processing
Moiré appearance during scanning
Most often in Everyday life moiré appears when scanning printed images. This is because the scanner re-rasterizes an image that already has the original raster. It can be more simply represented as follows: if you take a tracing paper with one ornament and put it on a tracing paper with the same ornament, but depicted at a different angle, then the resulting ornament will differ from both the first and the second. If you impose them so that they coincide, then the first ornament will coincide with the second.
The round rosettes at the intersection of the two rectangles result in the distortion of the image seen in the first image.
The appearance of moiré in the screening process
"Divers". The sky is filled with uneven horizontal lines, and at low resolutions moiré is obtained.
Moire can also occur due to incorrect setting of the angles between the lines of the primary colors when screening. Both are, in fact, the interference of two sets of raster lines. There are several types of moire rosettes, by the appearance of which you can often find out the cause of the moire.
Physical basis for the appearance of moiré
Scanning, in fact, is the modulation of signals at the nodes of the scanner grid by the brightness of the nodes of the typographic raster. AT general view the product of two modulated sinusoids (grids) with a different period of spatial oscillations is obtained. One harmonic may have a larger period equal to the sum of the periods of both gratings, which causes moiré. The second one always has a period equal to the modulus of the grating period difference and disappears because it cannot be realized at a given scanning resolution.
Paints that affect moiré
When printing with any set of inks, the most intense (dark) ink, which has a value of 30 to 70% over a large area, can give moiré. That is, if we have CMYK photos. The raster rotation angle between the most problematic channels should be as close to 45° as possible.
When printing with “solids” (i.e., with >95% infill), the concept of “screen tilt angle” practically disappears (even if we are talking about photography).
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Synonyms:Books
- Moiré of the Lost Sands…, Elza Popova, The title of this book speaks for itself. A small selection of verses on oriental themes, which I would like to highlight separately. … Category:
Quality printed matter- the main question of concern to customers. To achieve a clear image, many factors are taken into account - from the skill level of the printers to the printing process and the correct selection of paper and colors. However, the plot itself, chosen by the customer, can also cause poor-quality printing.
Moiré is an optical effect that occurs when closely related structures that have almost the same frequency are superimposed. On the image, it looks like dots or spots. The complexity of this defect lies in the fact that in most cases it can be detected only on the finished print. However, knowing the reasons for its appearance, you can reduce the likelihood of moiré in the image.
Causes of the defect
Moire can occur for several reasons, of which the most common are:
- Incorrect rotation angles of raster structures;
- Object moiré can occur if other printing objects are used, in which the contrast between the background and the object is minimal;
- When printing objects with a clearly defined structure: fabric, shading;
If the selected scene contains extremely saturated tones, the quality of their reproduction may also give errors.
How to avoid moiré?
- In order to prevent the appearance of a defect with an incorrectly selected angle of rotation of the raster structures, this color separation model for 3 colors is turned at an angle of 30 ° relative to each other. If a 4-colour image is used, application angles of 0° for yellow ink, 45° for black and 15° and 75° for magenta and cyan are used for them;
- Increase the contrast between the background and the object on it;
- Object moiré is quite difficult to get rid of. In some cases, the image sharpness is reduced, but the print quality may be reduced.
If the reason for the appearance of moire lies not in the unskilled work of the printing staff, this defect should not be considered as a defect, but as a small defect due to the selection of the original with a clearly defined structure.
Rice. 12.13 a. Periodic structures (b) in variants A-E placement the same number of elements in a 3 x 3 matrix (a); tone differences in the same structures when printed (c) Rice. 12.13, b. Periodic structures (b) c options A-E placing the same number of elements in a 3 x 3 matrix (a); tone differences in the same structures when printed (c)
As a result of the interference interaction of regular raster gratings of color-separated images superimposed on each other when receiving a print, a secondary pattern arises - moiré of multi-color printing.
A special type is a subject moiré, resulting from a similar interaction of a periodic fine-structured pattern - texture (if any on the original itself) with one or more of the spatial sampling frequencies in the reproduction process.
Monochromatic background areas of prints are also characterized to some extent by a pronounced low-frequency pattern, which is referred to as own or "internal" (internal) moiré. It arises as a result of the interaction of the orthogonal synthesis grating with the raster formed in it.
The last two varieties of moire are already present in black and white reproductions. In color tone printing, they are, as it were, additional and their visibility can be either enhanced or weakened by the main moiré, which to a certain extent complicates the theoretical analysis and visual assessment of this phenomenon as a whole.
Two oscillations can weaken or strengthen each other to varying degrees, depending on the phase of their superposition (see Fig. 12.1, a, b 
). If they are also characterized by different periods, then the resulting fluctuation inevitably contains the so-called. difference frequency, the value of which is less than the initial one and can be arbitrarily low. This phenomenon, known in the art as "frequency beat", is illustrated graphically in Fig. 12.2 
, illustrating the appearance of the frequency f/6 in the spectrum of the signal obtained as a result of the addition of harmonic oscillations with frequencies f/2 and f/3.
Below, we confine ourselves to a qualitative consideration of the process of moiré formation.
The relationship between the moiré period and the mutual orientation of the gratings can be easily established by rotating two raster photoforms folded together relative to each other and examining them through the light. For two linear rasters, monotonous changes in the moiré period and its pattern are repeated after 180°, and for orthogonal and hexagonal dotted rasters, respectively, after 90° and 60°. The mechanism of formation of periodic clusters that generate moiré and rarefaction of printed elements during pairwise alignment of linear and orthogonal gratings of the same lineature at a certain small angle is explained in Fig. 12.4 
, and the nature of the change in the moire period in connection with the angle of coincidence is illustrated by the graphs in Fig. 12.5 
in relation to raster structures of various geometry.
When the gratings coincide (the angle is 0° and the angles are multiples of the periods of the graphs in Fig. 12.5), the moiré period, tending to infinity, exceeds the physical dimensions of the illustration. Even with a slight deviation from these angles, only one vacuum or a bunch of printed elements is placed on it. In the first case, the raster dots of two images are located side by side, forming the largest printed area, and overlapping in the second, freeing the largest gap area from paint. However, a slight, half a lineature step, register instability of the printed sheet leads to a sharp change in the nature of the autotype synthesis (spatial mixing or overlaying of paint layers) throughout the image and deviations in the overall color and tone in the print run - color imbalance.
As the angle increases further, the sizes of bunches and discharges decrease, and their frequency increases. Some critical angles of pairwise alignment of raster gratings equal to 90°, 45° and 30° (extrema of the graphs in Fig. 12.5) correspond to the final, minimum values of the moiré period and its extremely high frequency. Printed elements of different colors form specific indistinguishable figures. This is rosette moire.
Moiré contrast is determined by the tone or relative area of the printed elements of the combined areas of color separations. You can verify this by aligning a pair of raster transparencies of a continuous or stepped tone scale on a viewing device at an angle of 5-10 °. The contrast of moiré spots monotonously weakens from areas of midtones to shadows and highlights. The predominant factor here is the ratio of the relative areas of the substrate, sealed in bunches and discharges of raster dots. Therefore, for an approximate assessment of the relationship between the moiré contrast and the tone of the image, the following assumptions are appropriate, which are quite consistent with general principle autotype synthesis of halftones:
- the optical density of the print is determined only by the relative printed area and does not increase as a result of the overlap of two or more ink layers;
- the spectral and optical properties of the layers of compatible paints are identical.
These assumptions imply a difference in clumps and rarefaction of moiré pattern points only in terms of their lightness, but not chromaticity, and simplify the simulation of moiré by superimposing one-color raster fields.
In the case of double overlay, the maximum contrast occurs when each image is represented by a checkerboard field of halftone dots, i.e. relative area 50%.gif" border="0" align="absmiddle" alt="(!LANG:
Where the bitmap dots of one image cover the spaces of another, i.e..gif" border="0" align="absmiddle" alt="(!LANG:
where K is the overall contrast of the printing process, estimated by the ratio of reflections of unprinted paper formula "src="http://hi-edu.ru/e-books/xbook438/files/ro-T.gif" absmiddle" alt="(!LANG:..gif" border="0" align="absmiddle" alt="(!LANG:
It is obvious that, taking into account the same assumptions, any other values of the areas of points of two combined images other than 50% will give a moire of less contrast.
For a triple overlay in the ratio under consideration, the most critical is the equality of the pixel areas of each of the images 33.3%..gif" border="0" align="absmiddle" alt="(!LANG:\u003d K - 0.33 (K - 1) \u003d 0.66 K, and therefore the most moirogenic halftones with values of the relative area of \u200b\u200bdots 30-35%. For four colors, a similar reasoning indicates an even greater, about 0.75K, contrast value and maximum muarogenicity of fields with the same and equal to 25% dot area.
These approximate general conclusions about the relationship between the moiré contrast and the tone of the combined raster fields, given already in L. 2.2, are fully confirmed by the results of a later theoretical analysis.
Taking into account the role of black ink in multicolor printing, it can be assumed that the exclusion of one of the color inks from the process at large volumes of UCC somewhat reduces the muarogenicity. When synthesizing a color of the binary + black type, the greatest contrast should be expected in fields obtained by combining fields with 33% cyan, magenta and black inks. Combinations similar in percentage with the participation of yellow paint give a less noticeable moiré due to its greater lightness. The same circumstance, as will be shown below, is effectively used in choosing the screen orientation for yellow ink in the most common moiré correction methods.
Going beyond the above assumptions, one can also discuss the contrast due to color differences in the clots and rarefaction of the printed elements of the moiré pattern. If in the first case subtractive prevails in the formation of the resulting color, then in the second their spatial mixing, which gives, as indicated in Section 9, not the same results, which differ the more, the more the ink capture differs from 100%.
In essence, the approach used for the correction of muap is divided into three groups:
- alignment of raster gratings of color separations;
- rotation of raster gratings relative to each other;
- irregular placement of printed and white space elements.
In the first two of them, the moire frequency is affected, trying to get it as low as possible or, conversely, as high as possible. The latter option excludes the very periodicity of the raster grating as a potential source of moiré.
In this method, the spatial moiré frequency is attempted to be made so low that in its period, which exceeds the size of the illustration itself, clots or rarefaction of raster dots do not have time to repeat. This is achieved by a particularly accurate registration of a paper sheet in the so-called. dot to dot printing. As can be seen from fig. 12.4, such registration must satisfy the condition
def"> ..gif" border="0" align="absmiddle" alt="(!LANG:(see figure 2.5). If at the same time the printed elements of some color inks are located in the gaps of others, if possible excluding their mutual imposition, then the largest color gamut for this paper-ink system is provided.
In addition to the high accuracy of angular registration, careful parallel alignment of the printed sheet with the form is also necessary. A parallel shift of two gratings of color-separated images by half a raster step leads to a color imbalance, which in this case will be the largest at a relative dot area, for example, 50%. On one of the prints, the resulting color is formed only by the imposition of ink layers of printed elements, and on the other, only by spatial mixing of light fluxes from elements located isolated from each other (see Fig. 8.4).
Deviations of prints in circulation in terms of lightness and color can be very significant, especially when printing "on wet", due to differences in ink perception (see expression 8.6). For example, for a combination of cyan and magenta colors, it reaches 20 and 38 color difference units, respectively. !LANG: link to literature sources" onclick="showlitlist(new Array("8.7. Rhodes W. L., Hains Ch. M. The Influence of Halftone Oi ientation on Color Gamut and Registration Sensivity. Recent Progress in Digital Halftoning. - IST, 1994. - P. 117-119. - (англ.).",""));">].!}
Print "dot to dot" found in last years practical use in those digital printing and proofing systems where all inks are applied to the substrate in a single ink pass. The structures of the color separation images are rigidly tied to each other, for example, in some inkjet systems with a compact arrangement of four inking units in one printing section. Deviations in angular or parallel registration lead only to a shift of the entire illustration on the print, and moiré and instability of tone and color are excluded.
In conclusion, we note that in terms of its frequency-contrast characteristics, printing with the same orientation and geometry of raster gratings is inferior to methods in which each of the raster has its own slope. Due to the different orientation of the gratings, the final spatial discretization, due to screening, is carried out for each of the color-separated images according to its own law. If the rasters are not rotated relative to each other, then, for example, with an unfavorable phase, illustrated in Fig. 5.5 (c, d), the strokes of the original are not equally reproduced in all four colors. However, if the rasters of other color separations have a different orientation, then it is obvious that the depth of modulation of their dot sizes by these strokes will be different from zero. Therefore, arguments about the advantages of the above method in relation to the quality of illustrations seem to be quite controversial. Higher register accuracy, which is mandatory for dot-to-dot printing, favorably affects the quality of reproduction of the original drawing in all other cases, i.e. regardless of the characteristics of the raster process used.
The most common correction method is to minimize the moiré spatial period. They strive to make its frequency as high as possible so that it is not noticeable due to the continuous perception of tone and color fluctuations averaged by the visual analyzer with a relatively short repetition period of rosettes.
As follows from the graphs in Fig. 12.5, in two-color printing, the moire period is minimal when two linear, orthogonal, or hexagonal screens are rotated relative to each other by 30°, 45°, and 30°, respectively. The shape of the graphs also shows that deviations from these angles due to non-registration or inaccurate mounting of photoforms are fraught with a significantly smaller increase in the moiré period and, consequently, its visibility than with zero angular alignment, which corresponds to areas asymptotic to their ordinates in these graphs.
The raster image structure of the third ink added to the first two already printed with such a mutual orientation interacts with each of them. Therefore, an acceptable compromise for it is the angles of 45°, 22.5° and 15°, respectively, for each of the three specified raster geometries. Similarly, the angles of 135°, 67.5° and 45° remain within the periods of these graphs to place the raster of the fourth color.
The spacing of the lines of the raster dots of four orthogonal structures by the same angle equal to 22.5° is explained in Fig. 12.6(a) 
. However, this combination of angles, which was used at the initial stage of development of multi-color printing, has now been replaced by the second option (see Fig. 12.6, b). In it, rasters of contrasting, "drawing" (black, cyan and magenta) colors form a moire of a smaller period, because spaced apart by 30°. The yellow paint raster, located at an angle of 15 ° with respect to two of them, gives a lower frequency, but at the same time less noticeable moiré due to its relatively low contrast. In the hexagonal structure, this option corresponds to the angles 0°, 10°, 20° and 40°.
In both of these options, the diagonal orientation (45° angle in the orthogonal grid) belongs to black, the most contrasting ink in accordance with the provisions set out in subsection 6.4, and the lightest yellow is printed at 0°. The entire system of angles is sometimes slightly shifted to one side or the other by 7.5 °, so, for example, that the lines of printed elements and yellow paint, being close to the horizontal or vertical, do not create noticeable stepped distortions at the edges of the image. A similar shift may also be due to features of specialty printing, such as the presence of a fifth periodic structure on the anilox roll (flexo) or on the mesh (screen printing), as well as the orientation of the squeegee (gravure printing).
In some cases, in order to expand the color gamut of printing synthesis, in addition to cyan, magenta and yellow inks, inks are used whose colors are complementary to the colors of the printing triad, i.e. red (orange), green and blue (purple). New problems with the formation of moiré in this case do not arise if the rasters of these colors are located at the corners of the colors of the corresponding primary colors, i.e. red (orange) uses the angle for cyan, green for magenta, and blue (violet) for yellow. In this technology, as shown, for example, in Fig. 8.4, orange ink is printed on those areas where magenta is completely absent or removed by the UCC procedure. To adjust the saturation of the orange color itself, it is enough to use black paint.
Rasters of paints of complementary colors can also be placed at the same angle, for example, 30° or 60° (between cyan and black or between black and magenta in Fig. 12.6, b), since their simultaneous presence in any color area of the image is excluded by the the idea of printing on the principle of HiFi Color.
In the optical method, any orientation of the raster is provided by its rotation by a given angle in the camera. The contact rasters were produced in sets of four rectangular sheets, on each of which the dot structure was oriented in a certain way. Very inconvenient, but fundamentally possible to achieve the same result, is to rotate the original in the scanner upon receipt of each color separation image. Therefore, obtaining raster structures of different orientations in scanning systems was a technical problem, some of the solutions to which are discussed below.
With the exception of tg0° and tg45°, the tangents of all the other angles mentioned above cannot be represented by ratios of integers and are therefore irrational numbers. It is in this connection that such screen rotation angles, screening processes, screen structures, etc. in recent years, sometimes not quite correctly denoted by the term irrational.
The presence of such angles in the representation system of color-separated images turned out to be fundamental for electronic screening systems that use a static grid of line-by-line and element-by-element decomposition in image synthesis. Any straight line passing at an angle with an irrational tangent can intersect only one node of such a lattice. And this means, for example, that during electronic engraving of a plate cylinder, it is necessary not only to shift the phase of immersion of the cutter into the plate material with each subsequent pass, but also to make the total number of passes, lines or revolutions of the cylinder equal to the number of printed elements in the entire image, which does not have technical sense. In practice, the dots of the raster are located on a straight line passing at an arbitrary angle, only with an accuracy determined by the grating pitch or the frequency of controlling the inclusion of the exposure spot in the output device.
In systems for generating points from smaller elements, a raster can be rotated according to the coordinate rotation equations by changing the addresses of a table-defined raster function. In contrast to the case described in subsection 7.6.3.1, the displacement of points from the centers of some initial, non-expanded raster occurs in this case over the entire image field. Rice. 12.7 
explains the procedure for calculating new addresses:
formula" src="http://hi-edu.ru/e-books/xbook438/files/264-1.gif" border="0" align="absmiddle" alt="(!LANG:
The v coordinate within the line is also unchanged, i.e..gif" border="0" align="absmiddle" alt="(!LANG:- measure number from the beginning of the line. So
formula" src="http://hi-edu.ru/e-books/xbook438/files/264-5.gif" border="0" align="absmiddle" alt="(!LANG:these equations can be written as
selection">Fig. 12.10 
), the lineature values of the color separations differ in the icon" src="http://hi-edu.ru/e-books/xbook438/01/files/litlist.gif" alt="(!LANG: link to literature" onclick="showlitlist(new Array("12.2. Delabastita P. A. Moire in Four Color Printing / TAGA Proceedings. - 1992. - Р. 44-65. - (англ.).",""));"> условию подобное различие пространственных частот растровых решеток компенсирует неоптимальность их ориентации относительно друг друга. Лишь форма розеток оказывается несколько ассиметричной, в отличие от присущей рассмотренной выше общепринятой системе.!}
This approach to moiré correction received a new life with the development of computer publishing systems, where the implementation of angles with irrational tangents turned out to be less acceptable due to the large amount of calculations. According to the same principle as in the DC 300 Chromograph, here, in some cases, angles close in their values to 7.5°, 15°, 30°, etc. are provided. The only difference, however, is that the period of the raster function or the bitmaps of the characters of the raster alphabet represent supercells much larger than shown in Fig. 6.10 and fig. 12.10, size. Examples of the exact values of the angles corresponding to such cells and their rational tangents are given, for example, in L. 12.11.
Moire is hardly noticeable if the raster structures are in a certain way deployed relative to each other. However, even in this case, the complete constancy of the geometry of the microsections printed by the elements of color divided images is not ensured from print to print. As in the parallel screen registration described above, the phase change (shift) of the superimposed rotated screen gratings, as a result of minor deviations in registration, causes some differences in tone and color reproduction. In this regard, two "micromoire" geometries are distinguished, most pronounced when the phase is shifted by half the lineature step. The first of them is characterized by hollow (open) rosettes that do not contain printed elements inside the ring formed by multi-colored raster dots. AT closed outlet in the center of a slightly larger ring there is a clot of ink formed by the imposition of several printed elements (see Fig. 12.11 
).
Results of the theoretical spectral analysis, given in L. 12.12, reveal and quantitatively confirm a number of patterns inherent in these two types of moiré. Their essence is as follows:
- if the greatest visibility of the micromoire formed by open rosettes is shifted to the area of shadows, then on the print with closed rosettes it is more easily detected in lighter colors;
- if the relative areas of the points of the three superimposed structures are equal, open rosettes give a smaller total printed area and, accordingly, are distinguished by greater lightness (the value of the L * coordinate in the CIE Lab system);
- the color of neutral, gray fields reproduced by hollow rosettes is shifted to the green area (the values of the a* coordinate are relatively small), and for closed rosettes to a purple tone (the values of the b* coordinate are relatively large);
- in a three-color overlay, the largest, about seven units, color difference occurs at a relative dot area of about 75%.
As a comparison base for the second and third of these conclusions, a random order of filling the print area with differently colored printed elements is assumed, which is inherent in irregular raster structures, and also underlies the probabilistic estimate of the relative area printed by the base colors of autotype synthesis, in calculating the resulting color in accordance with the equations 8.1 and 8.2, taking into account the probabilistic Demichel coefficients. Therefore, the color separation and color correction parameters set in the prepress process can be considered uniquely implemented only when printing with an irregular raster.
It is possible to increase the stability of tone and color reproduction in a regular raster system by directional violation of the geometry of rosettes in those parts of the tone range where it is most pronounced. With this chain in L. 12.12, for example, it is envisaged to shift the raster dots from their centers according to a random law, and, as was suggested by L. 12.13, to put the magnitude of the random shift depending on the tone of the reproduced area. Such a problem is solved, for example, by referring to an asymmetric threshold function, characterized by the top of the "raster hill" offset from the center of the base. Similar measures are used, in particular, in the raster system Balanced Screening of Agfa.
The third of the previously listed approaches to correcting the moire of multi-color printing is based on the irregular placement of printed elements on the image.
Prints with an irregular structure were obtained in the printing industry long before the introduction of electronic or computer reproduction methods into widespread practice. In some cases, for example, in phototype, the raster process is absent as such. The irregular structure was due to the technology of mold preparation itself, and not the need to correct the moiré. Numerous later non-raster printing methods provided either high definition or artistic effects, expressed mainly in the original image texture. The latter purpose is also served by special varieties of contact rasters.
Random processes, as can be judged from the above material, are widely used in modern reproduction technologies to varying degrees. In a number of electronic screening methods, the overall increase in the printed area as the reproduced tone intensifies is accompanied by a pseudo-random change in the shape, size and frequency of placement of printed elements and spaces.
A correct (based on the observance of all other conditions being equal) comparison of the capabilities of irregular raster systems with their traditional counterparts allows us to single out the following as more or less indisputable among the many advertised advantages:
- the absence of a rosette structure and less visibility of the raster at low print resolution;
- no imbalance in color reproduction due to register deviations;
- an increase in the clarity of prints adequate to an increase in the resolution of the reader when screening by the error diffusion method.
The first of these advantages is relevant, for example, for color printing of newspapers, taking into account low values lineatures and frequencies of rosette moiré of traditional rasters.
In other respects, and, in particular, in terms of the number of reproducible gradations, as well as the smoothness of tone reproduction, irregular systems are rather less suitable for printing. The irregular shape of printed elements and their larger total perimeter with the same printed area as in a regular screen reduce the stability and unambiguity of transferring the value of this area to the print, starting from the process of recording photoforms, and also lead to significant dot gain in a wider range of halftones.
Even if the minimum elements of the structure, for example, frequency screening, are chosen to be reliably reproducible and stable, it is practically impossible to provide a 50% printed area with a checkerboard field of such elements. Due to dot gain, this field will have almost the same optical density as a solid ink layer. The additional colorful zones shown in Section 8 arise when elements in such a structure are touched randomly and in the entire effective interval of the printed area, which, as a result, is almost halved compared to the traditional geometry raster.
Another fundamental drawback is the very irregularity of the geometry of such raster systems. In Section 3, the property of a regular raster to be ignored (filtered) in the process of viewing (in terms of radio engineering - demodulation) was noted, despite the distinguishability of its relatively low spatial frequency. For an irregular raster, this process is complicated by the fact that vision must decide how to perceive one or another random clot or rarefaction of printed elements: as image information or as a component of an auxiliary grating that carries it.
Such parameters as the clarity and sharpness of prints, as well as the geometric accuracy of reproduction of small details and contours, as already shown, depend on the values of a number of spatial frequencies involved in the reproduction process. The indicated advantages of frequency screening are provided only with an increased resolution of reading originals compared to that adopted for regular screens and, as it should, a larger volume of processed files. Therefore, for a correct comparison of raster systems in relation to such parameters, it is necessary to take into account the volume of the used video signal.
The development of irregular screening for mass production is accompanied, as practice shows, by at least a stricter normalization of all technological stages following the creation of the rasterized file. Often, these measures result in a reduction in the inherent noise level of the process, from increasing the resolution when recording photoforms, the accuracy of their copying on printing plates, and ending with the use of smoother papers. And all this, if we take into account what is stated in Section 4, makes it possible, even with the usual regular screening, not only to increase the lineature, but to improve the whole complex of quality indicators of illustrations.
Thus, in relation to the Dimon Screening system, for example, printing plates are recommended that are suitable for traditional screening with a lineature of 240 lines / cm, i.e. three to four times higher than those used in general practice.
One of the most common irregular screens, initiated mainly by incorrect advertising, is the myth about the lack of alternatives for their use in printing with six or seven colors using the already mentioned HiFi Color technology.
The appearance of an additional moire after applying orange, green or purple paint to the print only indicates the futility of the corresponding ink run. So, if this happens after printing green with the same screen angle as for magenta, then this indicates an incomplete subtraction (volume of UCC) of the latter and, thus, a decrease in the saturation of the area of the illustration, the spectral purity of which was originally supposed to be enhanced. A similar error in color separation is also indicated by moiré as a result of the interaction of additional colors with each other, when they are all printed at the same angle. In any chromatic area, these paints, in accordance with the basic provisions set out in section 9.1, mutually exclude each other.
The first four-color images, obtained by the method of electronic screening and having a pseudo-random raster structure that excluded moiré, were demonstrated by the Problem Laboratory of the LEIS. prof. M.A. Bonch-Bruevich at the international insert "Inpoligraphmash-69" back in 1969.
It was shown that for complete suppression of moiré, the centers of the raster elements of the original regular raster can randomly occupy only two or three discrete positions within half the lineature step. In systems with continuous spatial modulation of the area of the printed (blank) element, for example, in electronic engraving, this is easily achieved by pseudo-random change in the phase of raster pulses (see Fig. 12.12, in 
). If at the same time the original regular structure is oriented to the direction of the lines at an angle with a rational value of arctg greater than 3, then the random effect on the raster geometry can be one-dimensional. The moiré contrast from the interaction of scanning lines of color-separated images is insignificant due to the small number of dots in the rows coinciding with the lines (see Fig. 12.12, a, b).
The raster of at least one of the color separations, for example "drawing" black ink, can remain regular. From the same experiments, the need for greater homogeneity of each of the resulting structures, excluding noticeable clusters and rarefaction of points, became obvious. This problem is solved by introducing a number of restrictions on the random law of displacement of printed elements. The creators of the first frequency screening systems also faced a similar problem of the formation of unwanted clots and vacuum in an attempt to eliminate the directional structures inherent in this method with the help of such a displacement. For the same purpose, it was later proposed to eliminate the redundancy of a random signal adaptively, i.e. taking into account the moirogenicity of the reproducible section of the original in terms of its parameters such as tone, color and spatial frequency, as well as directed influence on the frequency spectrum of a random signal, suppressing low-frequency harmonics in it.
As a means of eliminating moiré, screening with pseudo-random dot shift is currently used in some digital printing and proofing devices.
A random structure can also be obtained using a raster alphabet, the individual characters of which are represented by bitmaps or matrices, with a random arrangement of elements or their weight values. Used by analogy with the technique of modulating electrical signals, the term frequency screening does not accurately characterize the process occurring in such systems. If in the signs of light tones (see Fig. 2.2, b) the elements are located mainly in isolation and the tone is actually enhanced on the print by an increase in their number, then after filling it by 20-30%, the addition of each new element is inevitably accompanied by its contact with the previously established ones. The display of a further increase in tone occurs on the print for the most part by increasing the area of printed elements with a constant or even decreasing number of them. After filling more than half, the tone transfer occurs at first by reducing the areas of randomly located gaps, and only then, in deep shadows, by reducing their number.
Separate elements of the matrix, which participated, for example, in its filling for lighter gradations, may be absent for a somewhat darker tone. Therefore, a raster system of this type is usually represented not by a random distribution of weight values, but bitmap alphabet- a set of bitmaps in combination with a threshold function that relates the number of the character of the alphabet with the tone value . Taking into account the additional areas formed when adjacent elements touch (see Section 8), the number of characters that provide a scale of equally contrasting tone steps in such an alphabet can significantly exceed the dimensions of the matrices (bitmaps) themselves. So, if in a 4 x 4 matrix the “hill” of weight values gives 16 + 1 far uneven (theoretical) gradations, then additional manipulation of the placement of elements in the same matrix allows you to get more than 25 equally contrasting values. The effect of placing the same number of elements in a 3 x 3 matrix on the tone of a raster field illustrates rice. 12.13, a As in traditional screening, the creation of such an alphabet takes into account the following main restrictions: It is quite difficult to satisfy the totality of such requirements using small-sized matrices, while their increase reduces the system's response to sharp changes in the tone of the original, worsens the clarity and sharpness of the image. Therefore, in a number of ways, to obtain additional gradations and suppress directional structures, several relatively small matrices are used for each tone level, placing them on the background areas in a random order. This is consonant with the quantization error diffusion principle, the application of which to the raster process is commented below. The raster process as a task of processing a digital video signal is the transformation of an array of multilevel samples of an optical parameter into a binary array. Abstracting from the technological aspects discussed above, related to the geometry of the resulting bitmap, the shape and orientation of the clusters formed by its ones and zeros, etc., this process can be considered stochastic, since the resulting binary image must correspond to the original one with a probability determined by the value itself its multilevel reference. If the area printed on some area of the print, covering 16 x 16 synthesis elements, in the initial array is specified by the 57th level of quantization of an eight-bit signal, then the bitmap of this area should contain 57 ones and 256 - 57 = 199 zeros. The raster generator generates the same number of synthesis elements within the area as dark and light, respectively. Two-level quantization of multilevel values according to a given threshold is accompanied by an error in the form of a difference between the quantized and the threshold values. The redistribution (diffusion) of this error between the initial values of the surrounding counts gave the name and formed the basis of one of the directions for obtaining pseudo-grayscale images, a priori characterized by an irregular structure. It does not use the predefined raster functions or alphabets described above. Initially intended for fine scan / fine print reproduction, error diffusion screening assumes such a spatial encoding frequency of the original that provides an independent multi-level value of its tone for each element of the future bitmap. Thanks to element-by-element tracking of changes in the tone of the original, the frequency-contrast characteristics of images are not limited by the frequency of the raster function or the size of the matrix, and with the same amount of data used, as already mentioned, can be, in principle, higher than in matrix methods. In a more practical coarse scan / fine print mode (see section 7.6) this method is implemented in conjunction with the interpolation-replication of the values of coarse readings to all elements of the synthesis proposed in L. 6.5. However, in this case as well complicated procedure calculations significantly slows down the work of the raster processor. For this reason, the error diffusion method is more often used only for calculating and loading predefined alphabets in a number of the irregular screening methods mentioned above. The simplest algorithm for converting an eight-bit value is the formula :according to a predetermined threshold h, the formula "src="http://hi-edu.ru/e-books/xbook438/files/a-ij.gif" border="0" align="absmiddle" alt=" (!LANG: + 1: icon" src="http://hi-edu.ru/e-books/xbook438/01/files/litlist.gif" alt="(!LANG:link to literature sources" onclick="showlitlist(new Array("12.26. Ulichney R. System for producing dithered images from continuous-tone data. Пат. заявка ф. Digital Equipment Corp. WO 88/07306 от 22.09.1988 (PCT/ US 88/00875 англ.).","","12.27. Anastassiou D., Kollias S. Progressive half-toning of images // Electronic Letters. - 1988. - Vol. 24, № 8. - P. 489-490.","","12.28. Peli E. Halftone Imaging method and apparatus utilizirg pyramidal error convergence. Пат. Retina Foundation, US 5109282, заявл. 20.06.1990. - (англ.).",""));">] применяют следующие меры:!} In some cases, for example, in the one described in L. 12.29, in light and dark colors, an almost regular arrangement of elements is achieved, which gives a less pronounced printed structure on a single-color image, but at the same time still suppresses low-frequency moiré on a multi-color print. The more uniform diffusion achieved by such measures entails blurring of contours, loss of contrast of fine details and other distortions. Therefore, to improve clarity and sharpness, algorithms are used, the so-called. "forced averaging" with dynamic threshold adjustment, taking into account the values of the surrounding samples, the local level and gradient of the optical parameter, local contrast, etc. False patterns (moire) are the result of the interference interaction of regular spatial structures involved in the reproductive process. The visibility of false patterns depends on their contrast and spatial frequency. The moire frequency is determined by the mutual orientation of regular gratings and the ratio of their frequencies. The ratio of the resulting areas, printed by different colors of the triad in clots and rarefaction of raster dots, determines the contrast of the moiré. Areas of a color original may be moirogenic to a greater or lesser extent, depending on how close to the critical ratio the corresponding amounts of triad inks in color separations are. Printing with raster registration gives a worse study of fine details than with their different orientations on color separations. At the largest angles from each other (30 °) the screens of cyan, magenta and black colors are spaced, while the screen of yellow paint is placed at an angle of only 15 ° to two of them, given that the larger moiré spots formed with its participation are of low contrast and therefore less noticeable. With register fluctuations within half the raster step, the placement of colors of color-separated images either in superimposed on each other or in adjacent raster dots leads to color deviations in the print run - color imbalance. The ratio of the area printed by raster dots superimposed on each other and located next to each other is different in open and closed sockets. In systems of raster rotation by angles with rational tangents, the non-optimality of the values of these angles is compensated by the difference in the lineatures of the color-separated images. The rotation of the raster by an angle with an irrational tangent in the lattice of the finite step is accompanied by fluctuations in the position, geometry and area of the raster dots, which depend on the resolution and addressability of the synthesizing device. Irregular raster systems have inherent limitations in tone transfer due to the random formation of additional printed area when adjacent printed elements are in contact. If a regular raster limits the frequency-contrast characteristics of the image, then the structures obtained by the error diffusion method with a sufficient amount of the original signal use the print resolution to a greater extent. 12.1. As a result of the interference interaction of raster structures of color-separated images, the following occurs: a) subject moiré; b) moire of multicolor printing; 12.2. Subject moire occurs as a result of interference: a) raster structures of color-separated images; b) original texture and raster structure; c) raster structure and sampling lattice of the image recording device. 12.3. The moiré frequency is at its maximum for two images aligned at 30° when their raster structures are: a) linear; b) orthogonal; c) hexagonal; d) irregular. 12.4. Multi-color printing moiré has the greatest contrast in: a) average; b) light; c) dark tones of the image. 12.5. When the relative area of the printed elements of one of the two color separations combined at a certain angle is 50% and the other is 100%, moiré: a) has maximum contrast; b) absent; c) has some average contrast value. 12.6. The moiré period of multi-color printing tends to be minimal: a) combining rasters of color-separated images; b) placing rasters of color-separated images at a certain angle to each other; c) irregularly placing printed elements and spaces on the image. 12.7. The best study of small details of the original takes place when printing color illustrations: a) with the combination of rasters of color-separated images; b) with the maximum possible use of the fourth (black) paint (binary + black); c) with a turn of raster gratings of color-separated images relative to each other. 12.8. In four-color printing, a raster structure is oriented at an angle of 15 ° with respect to the other two: a) blue; b) purple; c) yellow; d) black paint. 12.9. The raster structure of the fifth, green, paint can be oriented on the image at the same angle as the raster: a) blue; b) purple; c) yellow paint. 12.10. The raster structure of the sixth, purple, paint can be oriented on the image at the same angle as the raster: a) blue; b) purple; c) yellow paint. 12.11. The raster structure of the seventh, orange, paint can be oriented on the image at the same angle as the raster: a) blue; b) purple; The quality of printing reproduction depends on many different factors: photography and prepress, printing equipment and the qualifications of the printing house employees, etc. But no less significant factor is the plot itself that we are going to print. The quality of the print directly depends on it. There are stories that, no matter how hard you try, you still won’t print well. Conventionally, they can be divided into three groups: With the first two groups, everything is pretty clear, but with texture objects, the situation is more complicated. Many do not even imagine what problems may arise when working with them and what will happen in the end. It is known that the superimposition of two regular structures with the same or close frequency can cause an optical effect called moire: when superimposed, a pattern that does not exist in any of the textures appears (Fig. 1). Rice. 1. The appearance of moiré when two regular structures are superimposed The raster structure, which all printing images are printed with, has a certain shape, frequency, size, etc., and, in fact, is a texture (Fig. 2). And in any image there are four such structures (one for each base color). Now imagine that we are going to print an image, for example, the texture of a fabric. If the texture is fine enough and its frequency or size is close to the lineature of the raster with which we are going to print images, then the occurrence of moiré is almost inevitable. Moreover, the probability of its occurrence is higher, the closer the texture frequency is to the raster lineature. On fig. 3 shows some examples of the occurrence of plot moiré. WAYS TO SOLVING THE PROBLEM It is not yet possible to completely get rid of the plot moire, you can only reduce the visual effect. In addition, moiré appears only on the print run! This means that it is impossible to find out in advance about its presence and take any steps to eliminate it. Only a few analog proofs or a very experienced imager can accurately predict moiré appearance. However, if there is a suspicion that moire will occur, you can do the following. It is important to understand that moiré is not a printing or prepress defect, and the contractors are not to blame for this. It's just such a law of physics. The solution to the problem is to use other images that do not contain complex textures. If this is not possible and you need to print exactly the “dangerous” image, then you need to be prepared for the fact that defects may appear on the print. In general, the problem of moiré is not new. Even in Soviet times, the illustration departments of publishing houses carefully monitored this and tried to prevent images containing complex textures from being printed. Professional print photographers are also aware of this problem and strive to prepare their subjects in such a way as to avoid it. With the proliferation of computers and affordable photography (primarily digital), prepress (from creative to layout) has become easy for almost anyone with even a little knowledge of it. Unfortunately, not all of them know about the problem of plot moiré. The problem is also exacerbated by the fact that the print quality has improved, many other complexities have been eliminated, and the plot moiré is now much more noticeable. Therefore, in conclusion, we repeat once again: plot moire is not a defect in printing reproduction, but rather an error at the stage of selecting images or simply imperfection modern technologies, and that will have to be dealt with. After all, they put up with black and white television, although it was clear that all objects on the screen were originally colored.
