The dot technology is the basic way to reproduce continuous tone images. In lithography and letterpress printing, which are commonly used at present, in principle, the ink film thickness on the ink dot-dot is fixed, and the tone and color of the image are expressed by changing the size (area ratio) of the dot on the color separation plate. , The so-called halftone technique. The characteristic of the traditional screening technology is that the interval of the dots is fixed (determined by the number of screens), the ink dots are concentrated in the center of the grid, and the area size (equivalent to the strength or amplitude of the carrier signal in the electronic system) is a function of the tone information Therefore, it is called amplitude modulation screening (AMS—AmplitudeModulationScreening). Over the past 100 years, amplitude modulation screening has experienced the development of glass screens, contact screens, and dot generator screens, and has formed screening technologies such as rational grid, irrational grid, and composite grid. The amplitude modulation screening technology is basically mature. Due to the regular distribution of dots, it is easy to produce interference fringes in multi-color overprinting when amplitude modulation screening is used. The screen angle of the color separation version must be strictly controlled. The tone jump occurs at the middle tone due to the angle of the dots. Loss of image details, these shortcomings restrict the development of color reproduction technology.
FM screening is a brand-new technology that was researched in the early 1980s and introduced to the market in the 1990s. It is characterized by inked dot particles in a unit area (grid) equivalent to an amplitude modulation dot (currently the name is not uniform, this article It is called dot element) with the same size and randomly distributed positions, and the degree of density of its distribution, that is, the spatial distribution frequency is a function of image tone information, so it is called frequency modulation screening (FMS—FrequencyModulationScreening). In the FM screened image, there are only a certain number of randomly distributed point elements in the unit grid, and the traditional "net point" cannot be seen on the whole. The point element distribution is irregular, so there is no screen angle problem , The interference fringe is eliminated fundamentally, and there is no mid-level gradation jump phenomenon, and the gradation reproduction is even and beautiful. Because the dot elements are very small, the resolution and clarity of the image are greatly improved. The subtle levels of the high-resolution amplitude modulation network can be obtained with low resolution. The dot elements at high-profile overlap less, which can increase the chroma of the printed product. Because there is no concept of mesh angle, on the contrary, the requirement of overprinting accuracy of printing equipment is not high, which provides the possibility for ordinary printing factories to print high-quality color prints with mid-range laser imagesetters and printing machines. Due to its outstanding advantages, FM screening technology has attracted people's attention as soon as it appeared. In the past few years, it has developed rapidly. Companies such as AGFA, Linotype-Hell, UGRA / KOHAN, and Japan Screen have successively launched their own FM screening technology, which has excellent development prospects in the fields of offset printing, flexographic printing, and news printing. However, due to the small dots of FM screening, the requirements on the suitability of paper, ink and equipment are high, and there are difficulties in the promotion and application. Research and development of FM screening theory and technology suitable for general printing conditions, and promotion and application in production, is an urgent task for the printing industry in China.
1. Principle of random distribution of point elements
Figure 1 is a schematic diagram comparing the structure of AM dots and FM dots when the gray value is 24 (the number of dots is 8 × 8, and the number of gray levels is 64 + 1). When the laser electronic screening system is used to realize amplitude modulation screening, the gray value of the input image pixels is compared with the screening threshold in the dot model memory (SPM). If the former is greater than or equal to the latter, the laser beam is exposed to produce Inked, otherwise it will not be exposed. The screening thresholds are regularly arranged in the cell grid, and from the center of the grid to the edge of the grid, the screening thresholds gradually increase from small to large, so as to ensure that the dots formed by the pixel gray value from small to large The center of the grid expands around until it covers the entire grid. It can be seen that the key to making the dots scattered randomly in the grid is to break the threshold distribution rule in the dot model memory, so that several dots determined by the pixel gray value of the input image are in the unit network. Random and uniformly spread out in the lattice, that is, to establish a random number sequence that allocates point elements within the unit grid. The right side of Figure 1 shows the distribution order of FM plus dot elements implemented according to an algorithm. However, in order to avoid the same dot distribution of the same gray value, it is generally not made into a fixed dot model memory in FM screening. Even if the pixel gray value is the same and the number of dot elements is the same, the distribution order can be different, so as to achieve Random screening.
The generation of true random numbers generally requires the use of physical methods, such as the use of radioactive materials or the inherent noise of electronic computers. However, such a random number sequence cannot be realized repeatedly, the program cannot be recalculated, and verification is difficult. And it is expensive to add additional equipment such as random number generator and circuit connection. Therefore, in practice, mathematical recursion formulas are used, for example, for a given initial value ξ1, ξn + 1 (n = 1, 2, ...) is determined. This method is semi-empirical and can only be approximated by random numbers, so it is called pseudo-random numbers. There are two major problems in using pseudo-random numbers: first, after the recursive formula and the initial value are determined, the entire random number sequence is also uniquely determined, that is, it cannot meet the requirement that the random numbers are independent of each other; second, the resulting random number exists Cyclic phenomenon. Therefore, when the pseudo-random method is used to achieve random screening, the recursive formula for generating pseudo-random numbers must be properly selected to strive to improve the independence of the pseudo-random numbers and be evenly distributed within the grid range. Greater than the total number of point elements in the grid.
2. Multiply congruence pseudo-random screening method
Since the primary goal of this study is to explore the basic techniques for implementing FM screening in a DTP system, a detailed comparative study of the recursive formula is left for later. Therefore, of the mathematical methods for generating pseudo-random numbers, I prefer the statistical properties that are better, the convenience of generating random numbers, and the wider use of the congruent method. The recursive formula is Xi + 1 = AXi (modM) (2), that is, the next random number is obtained by multiplying the previous random number by A to M, so it is called the multiplication congruence method. In the multiplicative congruence method, how to select the three parameters X0, A, and M is the key to determine whether the random number sequence that meets the requirements can be quickly generated. According to the literature, it is usually M = 2l A = 8q ± 3X0 = 2t + 1 (3) where l, q and t are all positive integers, and M and X0 are primed, and X0 and A are primed. M in formula (3) is actually the period of random numbers that can be generated. The required random number period is smaller than the period of random numbers that can be generated. Generally, the required random number period is M / 4, and the coefficient A is generally Take the value closest to A 2l / 2 while satisfying the formula A = 8q ± 3. For random screening, the dot matrix structure is usually 16 × 16, and the random number is required to be between 1 and 256, so we take M = 256 × 4 = 1024, that is l = 10. And 2l / 2 = 210/2 = 32, take A = 35, 29, 43, 37, 27, 21 (that is, q is 4, 5, 3 respectively), take X0 = 1, the result of experience calculation is shown in Table 1. Show. If a random number greater than 256 is used to take the remainder of 256, then each random number appears recoded 4 times. The result of X0 taking other odd numbers is the same, and the cycle T becomes smaller when taking even numbers. This shows that the parameters cannot be selected in this way. Literature [4] pointed out that taking M = 2l, where l is the word length at the end of a number on a digital computer, and the maximum possible period for generating random numbers at this time is T = 2l-2. Theoretical analysis and statistical tests show that when the value of A is too small or the 0 and 1 in its binary form are regularly arranged, a random number sequence with ideal statistical properties cannot be generated. Especially for the multiplicative congruence method: A = 52s + 1 (4)
It can be seen from Table 2 that although the maximum number of cycles is T = 2l-2 as mentioned in the literature, the number of random numbers between 1 and 256 is 64, and the rest cannot be used directly. Secondary code, so the parameters can not use this method.
After repeated experiments, the author found that when M takes a prime number around 2l, for example, M = 1021, 1019, 1033, A takes an appropriate positive integer (even or odd), and the maximum period of the generated random number is T = M- 1. There are exactly 256 random positive integers less than 256 (the proof of the mathematical principle of sufficient and necessary conditions for any prime number M to make the maximum period of the pseudo-random number generated equal to M-1, discussed in another article). [next]
3. Random screening experiments and results
The experimental process flow using multiply congruent pseudo-random screening is shown in Figure 2. Raster image processor (abbreviated as RIP) is the core of the color desktop publishing system. Its main role is to interpret the image, graphics, and text information in the page file described by the page description language, convert it into dot matrix information, and control the printer or The imagesetter records dot matrix information on paper or film. RIP is divided into hardware RIP and software RIP, generally for amplitude modulation screening. The original image is scanned and collected by the scanner, and then processed by image processing software (photoshop) for color correction, gradation adjustment, color separation, etc., and then the frequency modulation and screening are carried out by the multiply congruence pseudo-random method. The screened image is assembled into the required layout by the grouping software (PageMaker), and then sent to the RIP after proper processing to control the output of the imagesetter, and the purpose of borrowing the existing RIP to complete the frequency modulation and screening can be achieved. The results of the study confirm that this is feasible, which opens the way for frequency modulation and screening using the hardware and software of the existing DTP system. In the study, novaRIP (a software RIP) was used. Its advantage is that it can predict the result of the screening and find that the problem can be revised repeatedly.
(Picture 2 Multiply congruence pseudo-random screening experiment process flow chart)
For simplicity, first try to randomly screen the grayscale image. Figure 3 is a sample image output on a laser printer with an output resolution of 600dpi. In color printing, large areas of spot color with the same tone and level are difficult to replicate. We tried this in the Air Force Xi'an Printing Factory, and achieved satisfactory experimental results.
(Figure 3 gray-scale image randomly screened output results)
When randomly screening, the texture will appear when the gray value is high. We think that the main reason for this phenomenon is that when there are a large number of pixels with the same gray value in the image, due to the use of the same pseudo-random number sequence distribution, the distribution rules among each other are the same, thus forming a texture, as shown in Figure 4a Show. In this regard, as long as measures are taken, when pixels of the same gray value are screened, different sequence starting points are used in the same random number sequence, or different random number sequences are used to make their distribution rules different from each other, thereby avoiding texture The phenomenon occurs, as shown in Figure 4b.
4. Conclusion
A pseudo-random function is used to randomly screen the image, and the amplitude and screening RIP is used to interpret and convert the graphic text information, and the laser phototypesetting machine is controlled and driven to realize the frequency-modulated screen output of the image in the ordinary DTP system, and the CMY color is printed. Spot color proofs have opened the way for frequency modulation and screening using the existing hardware and software of the DTP system.
The experiment proves that it is convenient and fast to generate pseudo-random number sequence by multiply congruence method, and it is used successfully in FM screening. For random screening, the appropriate parameters X0, A, and M must be selected to ensure that a random number sequence with a number less than or equal to the number of dots and a number equal to the number of dots is generated in the shortest period, thereby accelerating the screening process.
When there is a large area with the same pixel gray value in the image, as long as the pixels of the same gray value are used in the same random number sequence with different sequence starting points or different random number sequences, Make them distributed differently from each other, so as to avoid the occurrence of texture phenomena. The future research topic is to use different pseudo-random functions for FM screening, compare its advantages and disadvantages, discuss and establish an evaluation system for the uniformity and independence of the element distribution of random screening points; from screening before the group version to group version Post-screening, study the suitability of plate making, printing and printing of FM screening, especially the rule of dot expansion and its compensation method, and explore the commercialization and practical ways of FM screening software.
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