Keywords: frequency modulation screening; amplitude modulation screening; multiplicative congruence; pseudo-random number; raster image processor.
Dot technology is the basic way to reproduce continuous tone images. At present, in the lithography and letterpress printing that are generally used, in principle, the ink film thickness at the ink dot-net is certain, and the tone and color of the image are expressed by changing the dot size (area ratio) of the separation dot. , the so-called halftone technology. The traditional screening technology is characterized in that the dot spacing is fixed (determined by the number of screens), the dot is concentrated in the center of the grid, and its area size (corresponding to the strength or amplitude of the carrier signal in the electronic system) is a function of the tone information. It is called AMS-Amplitude Modulation Screening. For more than one hundred years, AM has experienced the development of glass screens, contact screens, and dot-net generators. It has formed rational grids, irrational grids, and composite grids, etc. [6]. From the 90s to the 1990s, the amplitude-modulated screening technology was basically mature. Due to the regular distribution of dots, it is determined that the amplitude modulation screen is easy to generate interference fringes when the amplitude modulation screening is used for multicolor printing. The screen angle of the color separation must be strictly controlled, and the midtone tone shift occurs due to the corners of the dots. When the number of screen lines is low, Loss of image detail, these drawbacks restrict the development of color reproduction technology.
FM screening is a brand-new technology that began research in the early 1980s and was introduced into the market in the 1990s [6,8,9]. It is characterized by the fact that in the unit area (mesh) that corresponds to the amplitude modulation dot, Names are not uniform, in this article are called point elements) the size is the same, the location is randomly distributed, the degree of density of its distribution, that is, the frequency of spatial distribution is a function of image tone information, so it is called frequency modulation screening (FMS-FrequencyModulationScreening). ). In the image of FM screening, there are only a certain number of randomly distributed point elements in the unit mesh. As a whole, there is no visible “net point†in the traditional grid. The distribution of point elements is irregular, so there is no problem with the angle of the screen. Basically eliminates the interference fringes, there is no intermediate level jump phenomenon, and the level reproduction is even and beautiful. Since the dot element is small, the resolution and sharpness of the image are greatly improved, and the fine resolution of the high-resolution amplitude modulation net can be obtained with a low resolution, and the overlay of the high-resolution point elements is small, so that the print quality can be increased. Because there is no concept of screen angle, the overprint accuracy of printing equipment is not high, which provides the possibility for ordinary printing houses to print high-quality color printing products with mid-range laser imagesetters and printers [7]. Because of its prominent advantages, FM screening technology has received people's attention as soon as it appears. The rapid development over the past few years, AGFA, Linotype-Hell, UGRA/KOHAN, Japan Screen, and other companies have launched their own FM screening technology, in the offset printing, flexographic printing, news printing and other fields have excellent development prospects. However, due to the small number of ink-jet screens for FM screens, the requirements for paper, ink, and equipment are high, and there are problems in promotion and application. It is an urgent task for the printing industry in China to research and develop FM screening theory and technology suitable for general printing conditions and to promote it in production.
1 point element random distribution principle Figure 1 is a gray value of 24 when the amplitude modulation network and FM network structure comparison diagram (matrix number to take 8 × 8, the number of gray level 64 + 1). When using the laser electronic screening system to realize amplitude modulation and screening, the gray value of the pixel of the input image is compared with the screening threshold value in the dot model memory (SPM). If the former is greater than or equal to the latter, the laser beam is exposed and generated. Make ink, otherwise it will not be exposed. The screening threshold is regularly arranged in the cell grid. From the center of the grid to the edge of the grid, the screening threshold is gradually increased from small to large, so as to ensure that the dots formed by the pixel's gray value are small to large. The center of the grid expands around until it fills the entire grid [1]. It can be seen that to make the ink dots randomly distributed in the grid, the key is to break the threshold distribution rule in the dot pattern memory so that a certain number of ink dots determined by the gray value of the input image pixels are in the unit network. The grid randomly and uniformly spreads out, ie, a random number sequence of distribution point elements is established within the unit grid. The right side of FIG. 1 shows the distribution order of the FM screening point elements implemented by some algorithm. However, in order to avoid the similar distribution of the dot positions of the same gray value, the fixed dot pattern memory is generally not used in FM screening. Even if the pixel gray value is the same, the number of point elements is the same, but the order of the distribution may be different, thereby realizing Random screening.
Generating a real random number generally requires the use of physical methods, such as the use of radioactive material, or the inherent noise of an electronic computer. However, such a sequence of random numbers cannot be duplicated and cannot be recalculated by the program, and verification is difficult. Furthermore, it is expensive to add additional equipment such as random number generators and circuit links [2]. Therefore, it is practically all to use the mathematical recurrence formula to generate, for a given initial value ξ1, determine ξn+1 (n=1, 2,...). This method is semi-empirical in nature and can only be approximated by random numbers, so it is called pseudo-random number. The use of pseudo-random numbers has two major problems: First, after the recursive formula and the initial value are determined, the entire random number sequence is also uniquely determined, ie, the requirements for independent random numbers cannot be satisfied; second, the resulting random numbers exist. Cyclical cycling. Therefore, when using the pseudo-random method to implement stochastic screening, we must appropriately choose the recursive formula that generates pseudo-random numbers, strive to improve the independence of the pseudo-random number, and distribute evenly over the grid, and we must ensure the period of the pseudo-random number. Greater than the total number of points in the grid.
2 Multiplicative 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, detailed comparisons of the recursive formulas are left for later. Therefore, in the mathematical method of generating pseudo-random numbers, the author prefers the method of multiplicative congruence with better statistical properties, convenient and rapid generation of random numbers, and wider use. The recurrence formula is Xi+1=AXi(modM)(2). That is, the next random number is obtained by multiplying the previous random number by the A-to-M remainder, and is called the multiplicative congruential method. In the multiplicative congruence method, how to use the three parameters X0, A, and M is the key to determining whether it can quickly generate a random number sequence that meets the requirements. According to the literature [2][3][4], it is usually M=2l A=8q±3 X0=2t+1(3) where l, q, and t all take positive integers, and require M and X0 to be prime, X0 is coprime with A [2]. Literature [3] pointed out that M in equation (3) is actually a period of random numbers that can be generated. The required number of random numbers is smaller than the number of random numbers that can be generated. Generally, the number of required random numbers is M/. 4, and the coefficient A generally takes the closest value to A 2l/2 while satisfying the formula A=8q±3. For random screening, the dot matrix structure usually takes 16×16, and the random number is between 1 and 256. Therefore, we take M=256×4=1024, that is, l=10. And 2l/2=210/2=32, take A=35,29,43,37,27,21 (ie, q is 4, 5, 3 respectively), take X0=1, and calculate the result as shown in Table 1. Show. If you use 256 more than 256 random numbers, each random number appears 4 times. X0 takes the same result as the other odd numbers, and when the even number is taken, the period T becomes smaller. This shows that the parameters cannot be selected as such. Document [4] pointed out that taking M = 2l, where l is the length of a digit tail on a digital computer, the maximum possible period for generating a random number is T = 2l-2. Theoretical analysis and statistical tests show that when the value of A is too small or its binary form is arranged in a regular manner, no statistically ideal random number sequence can be generated. Especially for multiplicative congruential method: A=52s+1(4)
From Table 2, we can see that although the maximum number of cycles is as described in [3], T=2l-2, the number of random numbers between 1 and 256 is 64, and the remainder cannot be used directly, even if 256 is used again. It is also the case that multiple codes appear, so the parameters cannot be used this way.
After repeated experiments, the author found that when M takes about 2 l prime numbers, such as M = 1021, 1019, 1033, A takes a proper positive integer (even number, odd number can be), the maximum period of random numbers generated is T = M- 1, a random positive integer less than 256 is exactly 256 (proof of mathematics proof about the maximal period of the pseudo-random number generated by an arbitrary prime M, equal to M-1, as discussed elsewhere).
3 Random screening experiments and results using multiplicative congruent pseudo-random screening experimental process shown in Figure 2. Raster image processor (abbreviated as RIP) is the core of a color desktop publishing system. Its main function 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 the dot matrix information on paper or film. RIP is divided into hardware RIP and software RIP, which are generally amplitude-modulated and networked. The original image is scanned and acquired by a scanner. The image processing software (photoshop) first performs color correction, gradation adjustment, color separation, and the like, and then uses a congruence congruence pseudo-random method to perform FM screening. The screened image is composed of PageMaker to form the required layout. After proper processing, it is sent to the RIP and the imagesetter's output is controlled. The purpose of using the existing RIP to complete the FM screening can be achieved. The results of the study confirm that this is feasible, which opens the way for FM screening using hardware and software of off-the-shelf DTP systems. The novaRIP (a kind of software RIP) is used in the study. The advantage is that it can predict the screening results and discover that the problem can be repeatedly modified.
Figure 2 Multiplicative Congruence Pseudo-random Screening Process Flow Diagram For the sake of brevity, we first try to randomize grayscale images. Figure 3 shows a sample output on a laser printer with an output resolution of 600 dpi. In color printing, large areas of the same color, the same level of spot color are difficult to copy. We tried this at the Air Force Xi'an Printing Factory and achieved satisfactory experimental results. 
Figure 3 Grayscale image random grid output
Literature [4] pointed out that when random screening occurs, texture will appear when the gray value is high. We believe that the main reason for this phenomenon is that when there are a large number of pixels of the same gray value in the image, due to the same pseudo-random number sequence distribution, resulting in the same mutual distribution rules, thus forming a texture, as shown in Figure 4a Show. In this regard, as long as measures are taken to enable pixels of the same grayscale value to be used in the same random number sequence to use different sequence start points, or to use different random number sequences, the distribution rules between them can be different, thereby avoiding textures. The phenomenon is shown in Figure 4b. 
4 Conclusion Using a pseudo-random function to randomly screen the image, use the amplitude modulation screening RIP to convert the text information of the graphic, control and drive the laser imagesetter, and achieve the FM output of the image in the ordinary DTP system, play out CMY The color-coded spot-color proofs open the way for FM screening using hardware and software of off-the-shelf DTP systems.
Experiments show that using the multiplicative congruential method to generate a pseudo-random number sequence is convenient and fast, and it has been used successfully for FM screening. For stochastic screening, appropriate parameters X0, A, and M must be selected to ensure that the random number sequence with a value less than or equal to the dot matrix number and the number of dots equal to the dot matrix number is generated in the shortest period, thereby accelerating the screening process. process.
When there are large areas with the same pixel gray value in the image, just add the same
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