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Moire in printing. Physical foundations of moire

moiré frequency

Color-separated photoforms with regular screening are a regular repeating structure of raster dots that have different sizes and are spaced at an equal distance from each other. The number of such points per unit length is called spatial frequency or raster lineature. In the simplest case, when two raster structures are superimposed on each other, we obtain a new raster structure containing both the total and the difference components of the original raster structures. The moiré frequency is equal to the frequency difference of superimposed structures.

The moiré period is determined by the mutual orientation of the raster gratings. For two linear rasters, monotonous changes in the moiré period and its pattern are repeated after 180°, and for orthogonal and hexagonal dotted rasters, after 90° and 60°, respectively.

When the gratings coincide (angle 0° and angles that are multiples of those indicated above), the moiré period tends to infinity. However, a slight, half the lineature step, register instability of the printed sheet leads to sharp deviations in the overall tone and color in the print run - color imbalance.

square moire

Rosette moire

As the angle increases, the sizes of bunches and discharges decrease, and their frequency increases. That. the critical angles of pairwise alignment of raster gratings 90°, 45°, 30° correspond to the minimum values ​​of the moiré period and its extremely high frequency. In such cases, printed elements different colors form a specific, less noticeable circular structure - rosette moire.

moire contrast

Moiré contrast is determined by the tone or relative area of ​​the printed elements of the combined areas of color separations.

The contrast of moiré spots monotonously weakens from areas of midtones to shadows and highlights. Those. moiré has a maximum of its manifestation in the area of ​​semitones. This is due to the fact that the raster elements that form the difference frequencies have a maximum size at 50% of the raster dot. In the range from 0% to 50%, the raster is formed by increasing spots of ink against a background of lighter paper, and in the range from 50% to 100% by decreasing gaps not filled with ink. And although moiré is present in almost the entire tonal range, it is less noticeable in the highlights and shadows, similar to how the raster structure is less noticeable at 2% and 98% compared to 50%.

Moiré correction methods

In essence, the approach used moiré correction methods are divided into the following groups:

  1. exact alignment of raster gratings of color-separated images;
  2. rotation of raster gratings relative to each other at an angle exceeding 30°;
  3. irregular placement of printed and white space elements.

The first two methods act on the moiré frequency, trying to make it as low as possible or, on the contrary, as high as possible. The third option excludes the periodicity of the raster grating as a potential source of moiré.

Printing with the combination of raster grids

With this method, the spatial moiré frequency is attempted to be made so low that its period exceeds the size of the illustration, and, as a result, clumps or rarefaction of raster dots, as a result, would not have time to repeat.

This is achieved by a particularly precise registration of the paper sheet. So-called dot-to-dot printing. In addition, with this method, careful parallel alignment of the printed sheet with the form is also necessary, since a parallel shift of two gratings of color-separated images by half the raster step will lead to color imbalance. Therefore, in practice, only color posters with a particularly low lineature (8-/12 lines / cm) were previously printed with dot-to-dot printing. The reduction in lineature had the advantage of widening the effective range of densities up to the range of the printing process. In recent years, this type of printing has found application in those systems of digital printing and color proofing, where all the colors are applied to the substrate in a single ink pass. For example, in some inkjet systems with a compact arrangement of four inking units in one printing section. Structures of color-separated images are rigidly tied to each other, as a result of 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 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.

Rotating Color Separation Bitmaps

The most common method of correction is to minimize the spatial moiré period. They strive to make its frequency as high as possible so that the moire is not noticeable due to the fact that with a relatively short period of repetition of rosettes, fluctuations in tone and color begin to merge for the eye.

In two-color printing, the moiré period is minimal when two linear, orthogonal, or hexagonal screens are rotated relative to each other by 90°, 45°, and 30°, respectively. 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.

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, to place the raster of the fourth color inside the periods of these graphs, the angles of 135°, 67.5° and 45° remain.

On the initial stage In the development of multi-color printing, it was practiced to space the lines of raster dots of four orthogonal structures at the same angle, equal to 22.5 °, but by now this combination has been supplanted by another option. In it, rasters of contrasting, “drawing” (black, cyan and magenta) colors form a moiré of a smaller period, since they are separated from each other by 30 °. A raster of yellow paint, 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 (the 45° angle in the orthogonal grid) belongs to black, the most contrasting ink, 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 that the lines of printed elements and yellow ink, being close to the horizontal or vertical, do not create noticeable stepped distortions at the edges of the image.

Irregular rasters

This approach to correcting the moire of multi-color printing is based on the irregular placement of printed elements on the image.

In a number of electronic screening methods, the overall increase in the printed area as the reproduced tone increases is accompanied by a pseudo-random change in the shape, size and frequency of placement of printed elements and spaces.

Advantages of this method:

  • lack of a rosette structure and less visibility of the raster at low print resolution;
  • no imbalance in color reproduction due to register deviations;
  • an adequate increase in the resolution of the reader, an increase in the clarity of prints when screening by the error diffusion method.

The first of these advantages is relevant, for example, for color printing of newspapers, taking into account the low values ​​​​of the lineatures and frequencies of the rosette moiré of traditional screens.

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.

Additional colorful zones appear when touching elements in such a structure randomly and in the entire effective range of the printed area, which, as a result, is reduced by almost half compared to the raster of traditional geometry.

Ways to implement irregular screening:

  • random displacement of points
  • raster alphabet with irregular distribution
  • error diffusion method

Random shift of points

For complete suppression of moiré, the centers of 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

The raster of at least one of the color separations, for example, "drawing" black paint, can remain regular.

As a means of eliminating moiré, screening with pseudo-random dot shift is currently used in some digital printing and proofing devices.

Raster alphabet with irregular distribution

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. The display of tone enhancement occurs on the print mostly due to an increase in 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 due to a decrease in the areas of haphazardly located gaps, and only then, in deep shadows, by reducing their number.

Separate elements of the matrix that participated, for example, in its filling for lighter gradations, may be absent for a slightly 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 conjunction with a threshold function that links the number of the character of the alphabet with the value of the tone.

Taking into account the additional areas formed when adjacent elements touch, 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. 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.

Error Diffusion Method

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, this process can be considered stochastic, since the resulting binary image must correspond to the original one with a probability determined by the very value of its multilevel sample.

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 formed the basis of one of the directions for obtaining pseudo-grayscale images, a priori characterized by an irregular structure.

The error diffusion method is more often used only to calculate and load predefined alphabets in a number of the irregular screening methods mentioned above.

Literature

  • Kuznetsov Yu. V., "Technology of visual information processing". - St. Petersburg: "Petersburg Institute of Printing", 2002
  • Plyasunova T. S., Lapatukhin V. S., On the possibility of reducing moiré in four-color reproduction. Polygraphy, No. 12, 1965, p. 18-22.

see also


Wikimedia Foundation. 2010 .

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 dotted orthogonal and hexagonal 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 suggest that the clusters and rarefaction of the dots of the moiré pattern differ only in their lightness, but not in their chromaticity, and simplify simulation modeling moiré overlay of 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:

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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. Similar percentage combinations 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, exceeding 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 units of color difference, 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 method discussed above 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 are 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, in this case, the complete constancy of the geometry of the micro-sections, sealed by the elements of the color of the 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 "micromoir" 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. V 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 circuit 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 moiré 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 increases 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 the low values ​​of the lineatures and frequencies of the rosette moiré of traditional screens.

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 almost 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 ink 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.

Parameters such as clarity and sharpness of prints, as well as geometric accuracy reproduction of fine 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, with regard 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 vainness 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 indicated by moire 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 colors, 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 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 in this case 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 structures obtained, 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 quite 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 due to an increase in 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 slightly 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 conjunction with a threshold function that links the number of the character of the alphabet with the tone value. Taking into account the additional areas formed when neighboring 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:

  • the minimum printed element and gap should be adequate in size to the level of intrinsic noise of the printing process (in most cases they are formed from several sub-elements, while the high discreteness of the matrix allows you to smoothly control the printed and gap area);
  • the size of the matrix cannot be excessively large in order to ensure the transmission of fine details and textures of low contrast;
  • clumps and rarefaction of printed elements are excluded, as well as the formation of directional structures during mating of matrices in the background areas;
  • each of the colors uses its own alphabet, since the imposition of completely identical irregular structures is fraught with color imbalance due to slight register instability.

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 principle of quantization error diffusion, the application of which in 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 the coarse scan / fine print mode more acceptable for practice (see Section 7.6), this method is implemented in conjunction with the interpolation-replication of coarse sample values ​​to all synthesis elements proposed in L. 6.5. However, even in this case, a relatively complex calculation procedure 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 predetermined 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:!}

  • the error is spread over the numerical array more evenly, bypassing it, for example, with a "serpentine" (from the beginning to the end of one line and from the end of the next to its beginning);
  • distribute the error not only to the next element in the bypass direction, but to the set of neighboring ones, using weight coefficients that take into account the proximity of the neighboring element to the given one;
  • eliminating periodicity in error propagation by pseudo-randomly modifying the process using, for example, "blue" noise or passing a matrix of weight coefficients through a stochastic filter;
  • "pyramidally" distribute the error in several stages with an intermediate stage of forming its array for the entire image.

    • 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 can 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 final 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 printed products is the main issue that concerns customers. To achieve a clear image, many factors are taken into account - from the level of skill 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?

    1. In order to prevent the appearance of a defect with an incorrectly chosen 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;
    2. Increase the contrast between the background and the object on it;
    3. 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.

    moire) - a pattern that occurs when two periodic mesh patterns are superimposed. The phenomenon is due to the fact that the repeating elements of two patterns follow with a slightly different frequency and then overlap each other, then form gaps.

    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, moire appears when scanning images printed in a printing method. 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. V 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 that has large area a value of 30 to 70% may 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” (that is, with >95% infill), the concept of “screen tilt angle” practically disappears (even when it comes to photography).

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    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:

    Moire is not only a polygraphic term. The physical principles that give rise to this phenomenon are much more widespread. In relation to moiré, the terms difference frequency or frequency beat can be applied. The fact is that when summing signals (electrical, optical, etc.), the resulting signal contains, in addition to the sum component, also the difference component of the original signals. And this is directly related to the theme of moiré.

    The roots of moire are at the very heart of modern color separation - screening. Color-separated photoforms with regular screening, which is sometimes called amplitude-modulated, represent a regular repeating structure of raster dots that have different sizes, depending on the content of the image, and are spaced at an equal distance from each other (Fig. 1). The number of such points per unit length is usually called the spatial frequency or raster lineature. In the simplest case, when two raster structures are superimposed on each other, we obtain a new raster structure containing both the total and the difference components of the original raster structures. In polygraphy, moire is understood as a situation when the difference component of the original raster structures becomes visible during printing. In fact, moiré is always present on the print (i.e., in principle), but it can be both clearly expressed and almost imperceptible. Ideally, in a four-color publication, moire, as a result of the interaction of four raster structures, degenerates into an inconspicuous circular structure - a polygraphic rosette (Fig. 2).

    Fig.2. Socket according to DIN16457.

    Moire frequency is of great importance. If it is high, say 62 repetition periods or lines per inch, then there will most likely not be a problem. If the moiré lineature is low and is, for example, 3 lines per inch, then the probability of a printing problem is high.

    Let's do an experiment. Let's output to the phototypesetting machine a photoform that has a screen rotation angle equal to zero (usually this corresponds to a yellow paint photoform), a size of about five by ten centimeters, a lineature of 75 lines per inch and containing a 30% halftone dot. Let's cut the resulting photoform in half and get two photoforms 5 by 5 centimeters in size, which contain raster structures with the same raster rotation angle and spatial frequency. Let's put them on top of each other on a light table or a sheet of paper and rotate one relative to the other.

    0o 5o
    15o 30o
    Fig.3. Moiré view at different overlapping angles of two raster structures.
    45o

    On fig. 3 shows images obtained at various angles of rotation. Those who have encountered the problem of moire will notice that the picture obtained at an angle of 15 degrees exactly repeats the picture of moire, sometimes appearing in flesh or green tones. A legitimate question is why does the difference component appear if the spatial frequencies of the photoforms are equal. This is due to the fact that the rotation of one of the photoforms at a certain angle leads to a relative increase in its spatial frequency relative to the other photoform. In this case, the magnification factor is equal to the reciprocal cosine of this angle. For example, the difference frequency or, what is the same, the spatial frequency of a possible moiré for a 150 lineature and typical rotation angles of 15, 30 and 45 degrees will be 5.3 lpi (150 / cos15-150 = 5.3), 23.2 lpi and 62 lpi respectively.

    Note that at small angles of rotation, the lineature of the difference component also has a small value. Obviously a 45 degree rotation is the best option to prevent moiré, a 30 degree rotation is also acceptable and a 15 degree difference can cause printing problems. Theoretically, the difference component is absent at a zero angle of rotation of the rasters relative to each other. However, it is difficult to implement such a printing mode in practice. Any misalignment of photoforms during printing will result in low-frequency moiré, its worst form (Fig. 3 for the case of 5 degrees).

    Another problem that can arise with this is color shift. The inks applied to the paper act as a filter for the light reflected off the paper. However, due to the imperfect nature of the inks, the resulting color when the dots of different inks are side by side will be different from the color when they are superimposed. When inks are printed with one angle of rotation, even a small error in photoform registration leads to a color shift, since the halftone dots in one case are located side by side, and in the other they are superimposed on each other.

    The visibility of moiré is determined not only by its frequency. Ceteris paribus, it depends on the optical density of the colors and the percentage of the raster point of each of the raster structures. The visibility of the moiré increases with the growth of the optical densities of the colors of the raster structures and is maximum when they are equal. Moiré is most pronounced in the midtone region. This is due to the fact that the raster elements that form the difference frequencies have a maximum size at 50% of the raster dot. With an increase in the half-dot percentage in the range from 0% to 50%, the screen is formed by increasing spots of ink against a background of lighter paper, and in the range from 50% to 100%, the screen is formed by decreasing gaps that are not filled with paint.

    Moire is present in almost the entire tonal range (at 0% and 100% of the raster dot, there is no raster and, accordingly, moiré is impossible), however, in the area of ​​​​highlights and shadows, it is less noticeable, as well as the raster structure is less noticeable at 2% and 98% compared to from 50%.

    With four-color or multi-color printing, four or more raster structures, respectively, interact. This leads to the appearance of many difference components, which, in turn, interact with each other and with the original raster structures, etc. In this case, the main contribution to the formation of moiré is made by the difference frequencies between the original raster structures.

    However, not only screening can cause moiré. If an already rasterized image was used as the original during scanning, then its repeated rasterization is equivalent to superimposing two rasters on top of each other with all the ensuing consequences. When scanning, moiré can occur between scan lines and image structure. In this case, moiré is fortunately visible on the monitor screen.

    If the image or its parts represent a regular structure, such as the texture of fabric or wood, then moiré can also occur. It also appears when printing due to the characteristics of the printing machine or in violation of the printing technology. Each of the listed potential causes requires more careful consideration, so we only note that despite their apparent diversity, the physical basis of the moiré is the same - the difference frequency of two or more regular structures.

    Four color printing

    The recommended arrangement of screen rotation angles with equal lineature of all photoforms for four-color printing, according to DIN16457, is shown in fig. 4. This arrangement of corners is explained as follows. The black paint is the darkest and was placed at a 45 degree angle. It is believed that at 45 degrees the raster structure of the image is most comfortably perceived by the human eye. Two other less dark colors, cyan and magenta, were placed on either side of black at a distance of 30 degrees. Yellow, the lightest paint, was placed at an angle of 0 degrees. It is important to note here that the socket is built on an axis of 90 degrees. If you rotate the image of the outlet (Fig. 2) by 90 degrees, then its appearance will remain the same. In this regard, the angle of 0 degrees is also an angle of 90 degrees. Thus, the yellow ink is located between cyan and magenta at a distance of 15 degrees from each. This is what in most cases is the cause of the screening moiré.

    Yellow paint, although the lightest, but at high intensity, an angle of 15 degrees can lead to the appearance of moiré in flesh or green tones. Raster processor manufacturers use different screening algorithms and, accordingly, give their recommendations for minimizing moiré. Therefore, first of all, you should carefully study the documentation attached to the raster processor, or contact the supplier for advice.

    Here are a few guidelines for preventing moire in four-color printing that Heidelberg Prepress gives to users of its RIPs. It can be assumed, and this is confirmed by practice, that these tips are valid not only for the raster processors of this company.

    • The most important colors from the point of view of the plot should be placed at an angle of at least 30 degrees from each other. For example, if the image contains flesh tones in the most critical parts, then the magenta and black colors should be swapped to prevent moiré between yellow and magenta colors (Fig. 5). It is this arrangement of corners that many companies use by default. This is because skin tones are more critical of moire in terms of human perception than greens. If the most important parts of the image contain green tones, then the cyan and black colors should be interchanged to prevent moiré between yellow and cyan (Fig. 6).
    • When printing in three colors or when the black ink photoform percentage is low, the yellow ink should be positioned at a 45 degree angle.
    • The use of GCR and UCR technologies, which are mainly designed to reduce total paint, also reduces the likelihood of moiré. This is because although the black ink photoform level increases, the percentage of other photoforms decreases to a greater extent as the optical density of the black ink is higher.
    • When scanning rasterized originals, you must use a filter that eliminates the raster structure of the image.

    Compliance with even these simple rules can significantly reduce the likelihood of moiré. The final check of the photoforms for the absence of moiré is an analog color proof directly from the photoforms. In the absence of such a color proof, the appearance of moiré can be predicted by photoforms. To do this, the photoforms are combined on a light table and carefully studied. It is often sufficient to check a pair of photoforms rotated 15 degrees relative to each other. It should be taken into account that printing inks have a significantly lower optical density than photoforms. Therefore, what you will see will be the worst kind of moiré.

    And, of course, you need to know exactly and control the real values ​​\u200b\u200bof angles and lineatures. If these data are not available in the description of the raster processor, then they must be measured for all used resolutions and lineatures. A small PostScript file for making your own lineature and screen rotation meter can be found at the address on the Internet http://init.ekonomika.ru

    Multicolor printing

    If everything is more or less clear with four-color printing, then when printing additional colors or six-color Hexachrome printing, many questions arise. The most acceptable in this case and completely free from moiré is stochastic screening, which is sometimes called frequency modulated. The absence of moire in stochastic screening is explained by the irregular, random nature of the generated raster. Unfortunately, stochastic screening is not yet widely used, so we have to look for ways to print more than four colors without going beyond regular screening.

    So, we have only 90 degrees and five, six or more colors at our disposal. There is a need to return to the issue of printing two colors with the same screen rotation angle. In some cases this is a valid solution.

    Printing of two inks with the same screen rotation angle is possible when the presence of one of the inks in any part of the image completely excludes or minimizes the presence of the other ink. This mode is possible and most acceptable for opposite colors. For cyan, magenta, and yellow, the opposite colors are red, green, and blue, respectively. When printing with six Hexachrome inks, it is recommended, for example, to print orange with the same angle as cyan, and green with magenta.

    Printing with one screen rotation angle is theoretically also possible for photoforms with different lineatures. To clarify, let's do another experiment. We will display on the phototypesetting machine a photoform with a raster rotation angle zero, measuring five by five centimeters, with a lineature of 100 lines per inch and containing a 30 percent dot. Let's put it on a similar lineature with 75 (deduced by us earlier) and rotate it a little. Please note that at a zero angle of rotation of the photoforms relative to each other, the moiré frequency is 25 lines per inch, which exactly corresponds to the difference in the lineatures of the original rasters. When one of the photoforms is rotated, the moire frequency will increase in accordance with the above formulas. From this we can conclude that the increase in the lineature of one of the photoforms from the point of view of moiré prevention is equivalent to its rotation by a certain angle.

    In our example, with a zero angle of rotation of the rasters relative to each other, we have a moiré with a frequency corresponding to a rotation of 41 degrees (ArcCos75/100=41) of photoforms with a lineature of 75. If it is worth using this method, then very carefully. The mechanism of formation of the difference frequency for rasters with different lineatures when changing the angle of their superposition is actually more complicated. It is possible that low-frequency moire will be present at several rotation angles or between photoforms rotated at a sufficiently large angle relative to each other.

    For example, let's place two paints with lineatures of 75 and 100 at an angle of 45 degrees, and place a third paint with a lineature of 75 at an angle of 0 degrees. Between two paints located at an angle of 45 degrees, the difference frequency will be 25 lines per inch, but in this case we get a completely unacceptable low-frequency moiré between ink at 0 degrees and ink at 45 degrees and having a lineature of 100. With a different ratio of lineatures, the result may be quite acceptable. It should also be taken into account that dot gain has a different value for different lineatures. As the lineature increases, the optical dot gain increases. This effect can be considered insignificant with a small difference in lineatures, but otherwise you can get color distortion on the print. The method of minimizing moire by changing the lineature of one or more photoforms is also applicable to four-color printing, and is sometimes used in the "proprietary" screening algorithms of some companies. For example, the screening method RT_Y45_Kfine offered by Heidelberg Prepress places black and yellow inks at the same angle of 45 degrees, but the lineature of the black ink photoform is 1.5 times higher than the lineatures of the other photoforms. exemplary integrated approach to the problem of moiré is the screening method IS classic from Heidelberg Prepress. At the same time, the photoforms have angles that prevent moiré in flesh tones. The photoform of yellow paint contains a lineature enlarged by a factor of 1.06, which expands the effective angle between the yellow and adjacent paints and, accordingly, reduces the likelihood of moiré in green tones. Many years of experience in using this screening method in the RIP60 and Delta Technology screening processors testify to the high degree of protection against moiré.

    Some raster processors allow non-standard 30 and 60 degree angles. When working with arbitrary (not opposite) colors, the use of these angles seems to be more preferable than printing two colors with the same screen rotation angle.

    And the last. It should be understood that the moiré model presented in the article is simplified, although it allows one to explain and sometimes even predict the nature of this phenomenon. Each "proprietary" screening method is based on complex mathematical algorithms and is thoroughly tested, including the minimization of moiré. Therefore, any combination of angles and lineatures other than those recommended by the manufacturer of the raster processor must be checked and the optimal combinations searched for for each particular raster processor, ink set, etc.

    Igor Golovachev- Head of the service center of the company InitPrepress. He can be contacted at: