Patent Publication Number: US-2022215213-A1

Title: Digital halftoning with spiral dots

Description:
TECHNICAL FIELD 
     The invention relates to the field of digital halftoning methods used for printing images, in particular by means of lithographic or flexographic printing presses, and by digital printing techniques such as inkjet printing. 
     BACKGROUND ART 
     Printing presses and digital printers cannot vary the amount of ink or toner that is applied to particular image areas except through digital halftoning, also called dithering or screening. Digital halftoning is the process of rendering the illusion of a continuous-tone image with a number of dots, also called halftone dots. The digital image produced by digital halftoning is called a halftone raster image or screen. Both multilevel and binary halftoning methods are known. The halftone dots produced by binary methods consist of pixels which represent image data and pixels which represent non-image data. 
     Binary digital halftoning is a well-known technique, which is explained in detail by Robert Ulichney in his book “Digital Halftoning”, MIT Press, 1987, ISBN 0-262-21009-6, wherein chapter 5 about ‘clustered-dot ordered dither’ is background art for the present invention including the use of threshold tiles for rendering continuous-tone images. 
     Another overview of digital halftoning methods is disclosed in an article “Recent trends in digital halftoning”, Proc. SPIE 2949, Imaging Sciences and Display Technologies, (7 Feb. 1997); doi: 10.1117/12.266335 wherein also multilevel digital halftoning is explained. 
     AM (amplitude modulated) screening is a widely used clustered-dot-ordered dithering technique wherein the size of the halftone dots is modulated in order to represent different densities of an image. When printing an AM image, each halftone dot corresponds to a certain amount of ink, called further a blob, which has to be pressed or jetted onto the substrate to be printed, dried and cured in a (very) short time, which may especially produce problems when printing with multiple inks on top of each other, whether wet-on-wet or wet-on-(semi)dry. The spreading of the ink on the substrate or previous lay down ink layers, which is determined by the thickness of the blob, and the local (de)wetting and/or absorption of the ink on the substrate, renders the printed blob locally uncontrollable, thereby producing noise in the printed image and substrate depended print quality. 
     Such problems can be addressed by other screening technologies such as FM (frequency modulated) screening or techniques involving error diffusion. In both these techniques, the image density of the halftone dots is modulated by the frequency of the dots instead of the dot size. However also these techniques are characterized by other issues like print stability, poor smoothness of flat tones, higher dot gain and higher wear of printing plates in long print runs. 
     Hybrid screening techniques are available which combine AM and FM methods so as to obtain the advantages of both. Said screening techniques however involve the use of multiple threshold tiles for rendering a continuous-tone image, which requires more memory space to store these multiple threshold tiles, for example a threshold tile with FM method in the highlights, a threshold tile with AM method in the midtones and another threshold tile with FM method in the shadows. In addition, the transitions from one threshold tile to another may produce density jumps in the printed image whereby calibration of said screening techniques also takes more service time than AM and FM. 
     US2007/0002384 discloses a method of controlling thickness of an ink blob in an AM halftone region of a printing plate or an intermediate image carrier on a digital press. The method generates a raster image with regularly tiled halftone dots, which comprise one or more ink-receptive rings enclosing a non-receptive portion. In other words, the ink-receptive rings form a closed loop, which completely encloses the portion that does not accept ink; as a result, the extent at which the ink can spread within the dot remains limited because no further spreading of the ink within the dot is possible as soon as the enclosed portion is filled. 
     Application WO2019/081493 A1 (AGFA NV) discloses a halftone raster image comprising a plurality of spiral halftone dots to control spreading of the ink. It is found that the use of said spiral halftone dots may generate annoying local patterns when the spirals are growing, especially in the mid-tones caused by aliasing effects between pixel-grid and shape of the spirals. 
     SUMMARY OF INVENTION 
     So there is still a need for an alternative halftone image which allows a better control of the spreading of the printed ink blob, so that the image quality is less dependent on the nature of the substrate, and the image noise is low especially in highlights and mid-tones. 
     These problems are solved by the halftone raster image, wherein the halftone dots, preferably arranged according to a screen frequency (FREQ) and screen angle (a), comprise: 
     (i) image pixels arranged as a first arc ( 200 ) or as a plurality of arcs which together represent a first spiral ( 100 ); and
 
(ii) non-image pixels arranged as a second arc ( 201 ) or as a plurality of arcs which together represent a second spiral ( 101 ); and
 
wherein neighbour halftone dots from said plurality of halftone dots represent a double spiral or triple spiral. Neighbour halftone dots are halftone dots which are located nearby each other. Said neighbour halftone dots are in the present invention mutually connected whereby they form one or more double spirals or triple spirals. Hereby no local patterns are formed especially in the mid-tones. At the moment that neighbouring halftone dots are touching or connecting each other said local patterns are formed which are annoying and also density jumps may occur at said touching points or connecting points which is also prevented by the presented invention.
 
     The arrangement according a screen frequency (FREQ) and screen angle (a), for said neighbour halftone dots, which are mutually connected and forming a double spiral, said double spiral is preferably oriented in the direction of said screen angle. The axis between feed point from one of said mutually connected neighbour halftone dot and the feed point from the other neighbour halftone dot has as angle said screen angle. 
     The plurality of halftone dots will be referred to herein as “spiral dots” and said neighbour halftone dots will be referred to herein as “mutually-connected spiral dots”. The image pixels are represented by the black areas in the figures. The non-image pixels define non-printing areas and correspond to the empty space that is left in the dot as represented by the white areas in the figures. The two dots at the left hand side of  FIG. 9  have a low dot coverage (low percentage of image pixels) and represent highlights of an image, while the two dots at the right hand side of  FIG. 9  have a high dot coverage and represent shadows of said image. An arrangement according a screen frequency (FREQ) and screen angle (a) results in regularly tiled halftone dots. The halftone raster image is for rendering a continuous-tone image (CT). 
     The first spiral grows in length from a feed point ( 2003 ,  1003 ), also called inner end, spiral-wise to an outer end ( 2005 ,  1005 ). The spiral may overlap with neighbouring halftone dots usually from midtones to shadows Said overlapping may cause local patterning in the halftone raster image which results in a noisy halftone raster image. By the presence of said mutually-connected spiral dots this local patterning is less or absent in the halftone raster image from the present invention. Further said arc growing and spiral growing is also defined by a start angle for its bending or windings. 
     Neighbour halftone dots from said plurality of halftone dots representing a double spiral may be connected to form also a lemniscate (=∞). 
     Preferably in the invention the outer ends ( 2005 ,  1005 ) of the first spirals of a number of neighbouring halftone dots are connected to each other to represent the double spiral ( FIG. 5 ;  FIG. 12 ;  FIG. 13 ;  FIG. 14 ) or triple spiral ( FIG. 16 ) or lemniscate. The number of said halftone dots is more preferably two or three or four. By connecting the outer ends the local patterning is not visible in the halftone image and shall not result in sudden density jumps when said halftone image is printed at the place where neighbouring halftone dots are connecting. 
     The image pixels define areas of the image which is to be printed, typically with ink, e.g. by a printing press or an inkjet printer, or with toner, e.g. in a laser printer. We will mainly refer herein to printing with ink, but the skilled person understands that the same reasoning equally applies to printing with other types of colorant such as toner or sublimation dye or applies to printing with varnish or white ink. 
     In the highlights of the image, the number of image pixels per dot is low so that they cannot form a complete winding of the first spiral but just a section thereof, which is referred to as the “first arc”. The empty space which is partially enclosed by the first arc also may be considered as another arc, which is referred to herein as the “second arc”. In the midtones and shadows of the image, the number of image pixels per dot is higher so that they can form one or more windings of the “first spiral”, thereby also defining a “second spiral” of non-image pixels defined by the empty space between the windings of the first spiral. 
     Without being bound by theory, it can be observed upon magnification of the printed image that the shape and size of the printed ink blob is less affected by uncontrolled spreading of the ink because, when the ink blob is pressed onto the substrate, e.g. by a printing press, the excess ink that is printed by the first arc or first spiral can flow into the empty space that corresponds to the second arc or second spiral. The empty space defines an ink channel that can accept ink, which is printed from the first arc/spiral, thereby providing means for controlling the spreading of the ink. 
     Contrary to the halftone dots disclosed in US2007/0002384, wherein the empty rings are not connected to each other, the empty arcs used in the spiral dots of our invention can be connected to one another (thereby forming the second spiral), so that the ink blob has more room to spread within the dot. As a result, the raster image of the present invention produces well-shaped ink dots on the printed substrate, resulting in an improved quality of the reproduced images and less dot gain, which is especially advantageous when printing on absorbent, uncoated paper stock such as newsprint. 
     Due to said better ink spreading, our invention allows to obtain a good print quality with less ink consumption than conventional techniques because the excess ink that is sitting on top of a printed blob, when printed with a conventional raster image, contributes to the density of the printed image by filling the empty space formed by the second arc or the second spiral. 
     Moreover, the lower extent of local ink accumulation produces thinner ink drops on the printed substrate and therefor enables faster drying of the printed copies. 
     In a preferred embodiment of our invention, which is defined by claim  5 , the second spiral is open-ended, i.e. not terminated by image pixels at the outer edge of the halftone dot, so that it forms an open channel that can guide excess ink out of the dot. The open channel enables a further spreading of the ink and, as a result, more ink saving and still faster drying. 
     Another advantage of the raster image of our invention is that it can be produced by a single threshold tile for the full range of density values per colour, such as cyan, magenta, yellow or black, so that it can be implemented without installing additional memory in current image processors, prepress workflow systems and raster image processors (RIP&#39;s), digital printers and plate setters: thus one single threshold tile per color channel. 
     The rendering of higher image densities in the highlights and mid-tones of the image can be realised simply by growing the length of the first spiral by adding more arcs to it, thereby producing more windings of the first spiral around the centre of the dot (and, as a result, also more windings of the second spiral). Higher image densities can also be obtained by increasing the thickness of the first arc or the first spiral. Both embodiments can be combined in the same image, i.e. the image density of the halftone dot can be increased by growing the length and by increasing the thickness of the first spiral. In the shadows of the image, where the halftone dots touch or even overlap, higher image densities can be obtained by shrinking the length and/or thickness of the second spiral or the second arc. 
     The length and thickness of first and/or second spiral may be determined by printing targets comprising different spiral-shaped halftone dots. For example by the following preferred embodiment: 
     A method for generating a threshold tile for rendering a continuous-tone image on a print medium, the method comprises the following step:
 
generating a target with a plurality of patches; wherein a patch comprises a plurality of halftone dots wherein each halftone dot comprises:
         (i) image pixels arranged as a first arc ( 200 ) or as a plurality of arcs which together represent a first spiral ( 100 ); and   (ii) non-image pixels arranged as a second arc ( 201 ) or as a plurality of arcs which together represent a second spiral ( 101 ); and   (iii) wherein the first arc, the first spiral, the second arc and/or the second spiral have a selected length and/or selected thickness; and
 
printing said target on said print medium; and selecting from said plurality of patches a patch by determining density of the printed non-image pixels in the halftone dots in said patch; and
 
whereby the determined density is greater or equal than a reference density; and
 
whereby threshold entries of said threshold tile are determined for transforming a local density of the continuous-tone image in halftone dots comprising pixels as defined in (i) and (ii); and according the selected length and/or thickness from the first arc, first spiral, the second arc and/or the second spiral from said selected patch.
       

     The halftone raster image of our invention is preferably used in lithographic and flexographic printing systems. The present invention also provides advantages when used in combination with digital printers, in particular inkjet systems. These and other applications and advantages of our invention are further described in the detailed description. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  and  FIG. 6 :  FIG. 1  is an enlargement of a raster image comprising Archimedean spiral dots which have a 50% dot coverage and which are tiled regularly in a square grid. 
         FIG. 6  represents multiple dot coverages produced by the same threshold tile as in  FIG. 1 . 
         FIG. 2 : is an enlargement of a raster image comprising spiral dots which have a 50% dot coverage and a square shape with rounded edges. 
         FIG. 3 : is an enlargement of a raster image comprising (i) Archimedean spiral dots which have a 50% dot coverage and (ii) a clustered dot in between the spiral dots. 
         FIG. 4 : is an enlargement of a raster image comprising Archimedean spiral dots having a 90% dot coverage. 
         FIG. 5 : is an enlargement of a raster image wherein a plurality of neighbouring spiral dots are forming a double spiral. 
         FIG. 7 : shows an example of a threshold tile comprising threshold values from 1 to 256 which can be used to generate a halftone image with spiral halftone dots according to the invention. 
         FIG. 8  shows the spiral dot that is generated by the threshold tile of  FIG. 7  for a halftone dot having a threshold value of 22, which corresponds to a dot coverage of 8.6% (=22/256). 
         FIG. 9 : shows four spiral dots which comprise 
       (i) image pixels arranged as a first arc ( 200 ) or as a plurality of arcs which together represent a first, clockwise rotating spiral ( 100 ), and 
       (ii) non-image pixels arranged as a second arc ( 201 ) or as a plurality of arcs which together represent a second, clockwise rotating spiral ( 101 ). Said first arc and first spiral having a feed point, also called inner end ( 2003 ,  1003 ) and an outer end ( 2005 ,  1005 ). 
         FIG. 10  and  FIG. 11 : show an enlargement of a raster image comprising Archimedean spiral dots and additionally comprising clustered halftone dots having non-image pixels. 
         FIG. 12  and  FIG. 13 : show each a double spiral. 
         FIG. 14  shows two double spirals which are also connected to each other. 
         FIG. 15  and  FIG. 16 : show each a triple spiral. 
     
    
    
     DESCRIPTION OF PREFERRED EMBODIMENTS 
     Definitions 
     A halftone dot is a picture element of a screen, and can be e.g. circular-, elliptical-, diamond- or square-shaped. In the highlights and midtones of the image, the halftone dots are isolated from one another, while above a coverage of approximately 50% the dots connect with each other. 
     A screen, also called halftone raster image, is an area broken down into printing and non-printing picture elements (halftone dots or lines) wherein the size and/or number of dots per area varies according to the tone values (also called density) of the original such as a continuous-tone image (CT). 
     Screening, also called halftoning, is the method whereby a continuous-tone image (CT) is transformed into a halftone raster image or a set of halftone raster images. The transformation may involve the use of one or more threshold tiles. The number of threshold tiles depends normally on the number of colour channels comprised in the continuous-tone image (CT). 
     A continuous-tone (digital) image is defined by various image formats, also called raster graphics format, of which non-limiting examples are Portable Network Graphics (PNG), Tagged Image File Format (TIFF), Adobe Photoshop Document (PSD), Joint Photographic Experts Group (JPEG) and bitmap (BMP). A continuous-tone image (CT) typically has a large colour depth, such as 8-bit grayscale or 48-bit colour. 
     Screen frequency, sometimes called screen definition or screen ruling, is the number of halftone dots and screen lines per unit length in the direction that yields the greatest value. It is measured in lines per cm or lines per inch (LPI). Low-frequency screens give a coarse appearance whereas high-frequency screens give a fine and smooth appearance. 
     RIP is the abbreviation of raster image processor. A RIP converts the information of a page (containing images, text, graphic elements and positional commands) to a halftone raster image, which may be sent to an output device, such as an image setter, plate setter or digital printer. The RIP may also be included in the output device. 
     Resolution, also called addressability, is the number of image elements (dots, pixels) per unit length that can be reproduced by an output device such as a monitor, printing plate or on paper. Normally expressed in units (dots) per cm or inch (dpi). High resolution means good rendering of detail. Output devices with a high resolution allow to use a high screen frequency. 
     Raster Image 
     The raster image of the present invention is suitable for rendering a continuous-tone image (CT), i.e. it creates the illusion of a continuous-tone image (CT) on a printed copy. This requirement implies that the screen frequency is above 40 lines per inch (LPI; 15.7 lines/cm), more preferably above 60 LPI (23.6 lines/cm) and most preferably above 100 LPI (39.4 lines/cm). If the screen frequency is below 40 LPI, the dots become visible at viewing distance, also called reading distance, which is about 20 cm. Such low screen frequencies are typically used in artistic screening, which is used for decorative purposes such as patterned illustrations, wherein it is intended that the individual dots are visible to the naked eye. Raster images wherein the dots are clearly visible at viewing distance are therefore not an embodiment of the present invention. A raster image has also a resolution (DPI), defined in dots per inch. 
     The raster image of the present invention comprises spiral dots which are preferably regularly tiled, e.g. tiled along a triangular, rectangular or hexagonal grid and preferably tiled along a square grid (e.g.  FIG. 1 ). The spiral dots may also be used in (semi)-random arranged halftone dots, such as blue noise or white noise arranged halftone dots. However regularly tiled spiral dots are preferred in order to avoid irregular structures in the printed images. The distance between the centres or feed points of neighbouring dots may range from 50 μm to 400 μm. 
     The raster image may further comprise conventional halftone dots, such as AM dots and/or FM dots, in combination with the spiral dots of the present invention. In a more preferred embodiment, the raster image consists entirely of spiral dots according to the invention. AM and/or FM dots forming image pixels may preferably occur in the highlights and AM and/or FM dots forming non-image pixels may preferably occur in the shadows. The halftone raster image of the present invention and preferred embodiments of it may thus also comprise additional other types of halftone dots, such as a plurality of clustered halftone dots, e.g. AM halftone dots, preferably regularly tiled, and more preferably arranged with the same screen angle 
     (α) or said screen angle (α)+k times 15° wherein k is a non-zero integer if the plurality of halftone dots from the present invention are arranged with said screen angle. Preferably said last arrangement has the same screen frequency (FREQ) or 2 times or 3 times or 4 times or N times said screen frequency (FREQ), whereby N is a non-zero integer or ½ or ⅓ times or ¼ times or 1/N times said screen frequency (FREQ), whereby N is a non-zero integer if the plurality of halftone dots from the present invention is arranged with said screen frequency (FREQ). 
     Said other types of halftone dots or said plurality of clustered halftone dots are preferably comprised in the shadows of said halftone raster image whereby said halftone dots are formed by non-image pixels, which allows a better spreading of ink in the shadows and avoids picking and linting, which are typical offset-related ink-issues related to substrate. Most preferably the halftone raster image in the present invention and in its preferred embodiments have in shadows of the halftone raster image additional one or more clustered halftone dots, preferably a plurality of regularly tiled clustered halftone dots wherein said halftone dots comprise a cluster of non-image pixels. Said cluster of non-image pixels is preferably circular-, elliptical, diamond- or square shaped. 
     If said continuous-tone image (CT) has a section with a tone-value of 100%, the halftone-raster image from the present invention and its preferred embodiments, may have a part in said halftone raster image, corresponding to said section, wherein said part comprises a plurality of halftone dots wherein each halftone dot comprises:
         non-image pixels arranged as a second arc ( 201 ) or as a plurality of arcs which together represent a second spiral ( 101 ); and/or   non-image pixels forming a clustered halftone dot. At print of said halftone raster image said non-image pixels from said part shall be filled with ink. Said plurality of halftone dots may be arranged according the screen frequency (FREQ) or other screen frequency and the screen angle or other screen angle, preferably said screen frequency (FREQ) or said other screen frequency is above 40 lines per inch (15.7 lines/com), more preferably the maximum size of said halftone dots is 3 mm, most preferably 1 mm. The non-image pixels forming said clustered halftone dot may be circular-, elliptical-, diamond- or square-shaped.       

     The screen angle (a) of the raster image according to the present invention is preferably selected from the group consisting of 0°+k×30°, 7.5°+k×30°, 15°+k×30°, 22.5°+k×30° wherein k is a negative or positive integer. The most preferred embodiments have a screen angle (a) selected from the group consisting of 0°, 15°, 75°, 90°, 45°, 67.5°, 22.5°, 7.5°, 82.5° and 37.5°. The screen angles are measured as conventionally defined in the printing industry, i.e. counterclockwise from the horizontal axis to agree with the Cartesian coordinate system. When multiple raster images are combined in multi-colour printing, the screen angle difference between the colour selections is preferably a multiplier of 15° or a multiplier of 30°. 
     Spiral Dots 
     Preferably the spiral dots in the image of the present invention comprise only one “first arc” or one “first spiral”, i.e. all the image pixels together form a single arc or a single spiral which may have a number of windings. However, also raster images with halftone dots wherein the image pixels are arranged into more than one arc or more than one spiral are embodiments of the present invention. In such embodiments, multiple arcs or spirals representing image pixels may be mutually connected at a common centre. Therefore, when we refer herein to the “first arc” or the “first spiral” (singular), it should be clear that halftone dots with multiple first arcs or spirals are also embraced by the present invention ( 304 ). Said multiple first arcs from said halftone dots forms image-clusters preferably around the centre of the halftone dot wherein in between non-image-clusters are formed. An image-cluster is hereby a clustering of image pixels and a non-image-cluster is hereby a cluster of non-image pixels. The image-clusters are then arcs whether or not with protrusions and/or having same or different thickness. The same remark applies to the second arc and the second spiral. 
     A spiral may be regarded as a combination of a plurality of arcs. An arc is a curved line which does not form a closed loop and typically corresponds to a segment of e.g. a circle or an ellipse, but also less conventional shapes are embraced by the term in the context of the present invention, e.g. segments of an optionally rounded rectangle or an optionally rounded triangle. 
     In a preferred embodiment, the centre of the first arc or spiral may be a point (a single image or non-image pixel) but it can also be a clustered halftone dot similar to AM dots of the prior art. The central dot may have any shape, such as a circle or a square. The central dot may be larger in halftone dots which represent high image densities and smaller in halftone dots which represent low image densities. 
     All the arcs which together constitute the first spiral are preferably mutually connected so that the first spiral represents a continuous line. The first spiral may also contain isolated non-image pixels or may comprise disconnected arcs, so that the first spiral is interrupted by empty space at one or more locations. In that embodiment, the empty space which separates adjacent arcs of the first spiral may be regarded as protrusions of the second spiral into the first spiral. Such protrusions of the second spiral may cut the first spiral completely into disconnected arcs, or incompletely whereby the first spiral is not interrupted but reduced locally to a lower thickness. 
     The second spiral represents the non-image pixels of the raster image of our invention, i.e. the empty space between the arcs of the first spiral(s). In one embodiment of the invention, the space between adjacent windings of the first spiral is completely empty, i.e. does not contain any image pixel. In such embodiment, the empty space forms a continuous second spiral. In another embodiment of the invention, the first spiral comprises protrusions of image pixels which extend into the empty space between the windings; such protrusions may connect two adjacent windings of the first spiral, thereby dividing the second spiral into two or more segments which are separated from one another by the mentioned protrusions of the first spiral. Other embodiments of the second arc or the second spiral may comprise isolated image pixels, i.e. image pixels which do not touch the first spiral, in the empty space between adjacent windings of the first spiral. 
     The protrusions of the first arc or the first spiral may align so as to form one or more radial lines in the spiral dot. The thickness of such a radial line may be e.g. from one pixel to five pixels. For high screen frequencies, e.g. above 150 LPI (59 lines/cm), the thickness of said radial line(s) may be one or two pixels. The radial line may connect the centre of the spiral dot to the outer edge of the spiral dot, or may connect just two or more windings of the first spiral without making contact with the centre or the outer edge. The angle of a radial line may depend on the screen angle (a) and/or start angle of the spiral. 
     In a highly preferred embodiment of our invention, the second arc or second spiral is open-ended, i.e. not terminated by image pixels at the outer edge of the halftone dot, so that it forms an open channel that guides excess ink out of the dot in a controlled way. In embodiments without such open channel, the higher ink accumulation may lead to uncontrolled ink splashes outside the outer edge of the dot, thereby producing irregularly shaped ink dots on the printed copies, resulting in a lower image quality. 
     In a preferred embodiment, the thickness of the first and second arc and of the first and second spiral is independently from 1 to 10 pixels, more preferably from 2 to 5 pixels, which preferably corresponds to a thickness from 1 μm to 75 μm. 
     The raster image in the present invention has preferably a resolution (DPI) larger than 600 DPI, more preferably larger than 1200 DPI. For example, for security printing sometimes a halftone raster image, having a resolution of 9600 DPI, is used for rendering a continuous-image. The spiral dots in  FIG. 1-6 ,  FIG. 10-11  for example are arranged according a screen frequency (FREQ) and a screen angle of 45°, which defines theoretical centres of gravity. 
     The selection of the minimum thickness of the arc and spiral may be based on the resolution of the printing technique for which the raster image is intended. The maximum thickness, which enables the controlled ink spreading referred to above, may be determined by the specific type of substrate on which the halftone raster image shall be printed and/or may be determined by the desired screen frequency. These and other selections, such as start angle and phase vector characteristics, are preferably made in an input field of a user interface of a halftone generator. 
     It shall be clear to the skilled person that the same dot coverage can be produced with different spiral dots of the same overall size: a dot consisting of just one winding of a first spiral of a certain thickness produces the same coverage as a dot with more windings of a first spiral of a lower thickness. 
     The thickness of the first arc or first spiral may also vary within the same dot, e.g. smaller at the centre than at the edge of the dot. Such a spiral dot may produce less graininess, especially in the mid-tones of the image. 
     The winding of the arcs and spirals used in the present invention may be clockwise or counterclockwise, and both these embodiments can be combined in the same raster image.  FIGS. 1-6  represent spiral dots with clockwise windings. 
     The start angle of the first arc or first spiral, at the centre of the dot, is preferably the same for all spiral dots in the image. In alternative embodiments of the invention, the start angle of each spiral dot is chosen randomly by a random number generator. This is a less preferred embodiment because the dots may touch each other in an irregular way which may result in noisiness but it may ‘break’ a repeating patterning caused by a moiré interaction between the screen frequency (FREQ), screen angle (α) and resolution of said halftone raster image (DPI). 
     The shape of the first arc or first spiral may be of any type and different types of arcs and spirals can be combined within the same raster image. 
     In a preferred embodiment, the first spiral is Archimedean, as defined by the formula 
     
       
      
       r=a+b×θ 
      
     
     wherein r is the radial distance, θ is the polar angle and a and b are parameters which define the opening of the spiral at its centre and the distance between adjacent windings. The definition can even be more extended by the formula 
     
       
      
       r=a+b×θ 
       (1/n)  
      
     
     wherein n is a constant which determines how tightly the spiral is wrapped. 
     In other embodiments, the first spiral may also be a circle involute, part of an Euler spiral, part of a logarithmic spiral, or a Fermat&#39;s spiral. 
     Other types of spirals may be generated with a Gielis super formula, of which the following are suitable examples: 
     
       
         
           
             ρ 
             = 
             
               
                 ρ 
                 ⁡ 
                 
                   ( 
                   φ 
                   ) 
                 
               
               = 
               
                 
                   R 
                   ⁡ 
                   
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                     φ 
                     ) 
                   
                 
                 · 
                 
                   
                     ( 
                     
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                           ⁡ 
                           
                             ( 
                             
                               
                                 m 
                                 · 
                                 φ 
                               
                               4 
                             
                             ) 
                           
                         
                         a 
                       
                       ⁢ 
                       
                         | 
                         
                           p 
                           2 
                         
                       
                       ⁢ 
                       
                         + 
                         
                           | 
                           
                             
                               sin 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     m 
                                     · 
                                     φ 
                                   
                                   4 
                                 
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                             b 
                           
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                               p 
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                     1 
                     
                       p 
                       1 
                     
                   
                 
               
             
           
         
       
     
     Example 1 
     
         
         
           
             a=b=1 m=10 
             p 2 =p 3 =5 p 1 =8 
             0≤φ≤14·2π 
             R(φ)=φ 2.55    
           
         
       
    
     Example 2 
     
         
         
           
             a=b=1 m=6 
             p 2 =0 p 3 =p 1 =100 
             0≤φ≤14·2π 
             R(φ)=φ 2.4    
           
         
       
    
     The first spiral may also be an elliptical spiral. In such embodiment, the major axis of the ellipse is preferably oriented along the screen angle (α) or perpendicular to the screen angle (α) of the raster image. 
     As already indicated in the Summary of the Invention, the ink channel which is defined by the second arc or second spiral allows controlled spreading of the ink that is printed at areas defined by the first arc or first spiral, thereby enabling to obtain a higher image quality with less ink than in the state of the art. In addition, the controlled spreading of the ink also allows to reduce print mottle. In the prior art, print mottle is reduced by modification of the surface of the substrate, e.g. by applying an ink absorbing coating or by corona treatment or flame treatment before printing. The present invention allows to avoid such modification for some substrates. In addition, it also provides a better water absorption of the paper so that water interference mottle is reduced. It may even reduce shine-through, also called print-through, in absorbent substrates, whereby images become visible at the backside of the substrate. 
     The present invention also allows to reduce moiré, which is known in the prior art to occur when different colours, screen frequencies and screen angle (α)s are printed on top of each other as disclosed in “The Theory of the Moiré Phenomenon” of Isaac Amidror; Kluwer Academic Publishers, (2000; ISBN 0-7923-5950-X), see Chapter 3 “Moiré minimization”. When using a multi-colour press with more than one colour station, it seems that the second spiral in the halftone dots printed by one colour station can also act as an ink channel for the ink which has already been printed by another colour station. As a result, the spreading of the ink laid down on the substrate by the first colour station can be controlled in a better way than with conventional techniques such as AM halftoning, resulting in less moiré. 
     AM screens consist of halftone cells wherein the image pixels are grouped in a single cluster, which is often called an AM dot. In AM screening, a higher relative image density is obtained by growing the size of said single cluster. Such AM dots have no feed point as the halftone dots in the present invention. 
     In order to reduce the moiré effect, such as subject moiré, even further it is also preferred to use spiral dots comprising multiple windings of a thin first spiral rather than dots which produce the same coverage with less but thicker windings. Multiple windings render the moiré effect less visible because such dots give the impression of a higher screen frequency . . . . 
     The present invention is also less subject to a tone jump at the mid-tones, which may occur in conventional AM screens. When the edges of growing halftone dots of the present invention touch, the sudden tone jump, also called density jump, which is known in the prior art, can be reduced because the accumulation of ink induced by the touching dots is drained by the ink channels in the dots. 
     Another big difference between AM halftone dots from conventional AM screens and spiral halftone dots from the present invention when the spiral dots are arranged according a screen frequency (FREQ) and screen angle (α) is that the difference between theoretical gravity, according to said screen frequency (FREQ) and said screen angle (α), and actual gravity of a halftone dot has a larger range with a spiral halftone dot due said represented second spiral. 
     The spreading of the ink further enables faster drying of the printed copies. This allows to align press work with a proof, since they are both dry one doesn&#39;t have to account for dryback. Faster drying also reduces the risk of ink setoff, i.e. the transfer of ink from one printed copy to the back side of another copy lying on top of it, for example in the press delivery tray. The invention is therefore also very well suited for use with a perfecting press, which allows the simultaneous printing on both sides of a substrate in one pass through the press. Faster drying is also beneficial for printing on uncoated foils or plastics, and in newspaper printing. Faster printing speeds can be achieved and printed jobs can be brought faster to a bindery. In offset printing with heatset ink, the temperature of the drying ovens can be lowered, thereby saving energy costs. Likewise, offset printing with curable ink becomes possible with less energy consumption by the curing unit, (UV LEDs, UV bulb or electron beam). The faster drying enabled by the present invention may also provide better trapping so that ink trap mottle is reduced. 
     Inkjet printing also benefits from advantages of the present invention. Especially when the surface tension of the substrate causes dewetting, the raster image of the present invention gives a better print quality, such as uniform solid patches, compared to conventional AM screens, because the ink channel prevents local accumulation of ink on the substrate. The present invention enables inkjet printing at a high screen frequency, e.g. above 200 LPI (78.7 lines/cm), on a variety of substrates such as coated (plastic) film, translucent (plastic) film and newsprint, which was not achievable by state-of-the-art AM halftoning methods. 
     The better uniformity of patches, produced by the raster image of the present invention, makes it is easier to measure colour profiles for colour management systems and easier to match colour images, e.g. with online colour monitoring by measuring the printed copies during the press run. As a result, a print job comes faster in colour and less substrate is wasted. 
     Threshold Tile 
     The raster image of the present invention is preferably generated by one or more threshold tiles, sometimes called threshold arrays, which transform a continuous-tone image (CT) to a halftone raster. Said transformation is also called threshold rendering. The use of threshold tiles is well known in the art. More information about threshold tiles is disclosed in e.g. “Digital Color Halftoning” by Henry R. Kang, chapter 13; published in the SPIE/IEEE Series on Imaging Science and Engineering (11 Nov. 1999; ISBN 0-8194-3318-7); and in “Digital halftoning” by Robert Ulichney, chapter 5 and 6 (publisher MIT Press Cambridge, Mass., USA; 1987; ISBN 0-262-21009-6). A conventional way of generating threshold tiles for AM screens is disclosed in the following patent applications: U.S. Pat. Nos. 5,155,599, 5,903,713 and EP0910206. Neighbouring spiral dots may grow in a different way, similar to conventional screens as disclosed in “Recent trends in digital halftoning”, Proc. SPIE 2949, Imaging Sciences and Display Technologies, (1997); doi: 10.1117/12.266335. 
     When used for binary digital halftoning, one threshold tile is sufficient to generate the raster image of the present invention. As a result, the number of threshold tiles is preferably the same as the number of colour channels in the continuous-tone image (CT). This provides the advantage that the generation of raster images in accordance with the present invention can easily be integrated in current image processors, prepress workflow systems and raster image processors (RIP&#39;s), because there is no need to switch between different threshold tiles as used in hybrid halftoning techniques, which require a larger memory than is necessary for the methods of the present invention. 
     For multilevel digital halftoning, the threshold tile comprises multiple equally sized arrays, one for each level. The shape of such arrays comprising threshold values can be a square or a rectangle but also Utah-shaped arrays or diamond-shaped arrays are suitable. More information about multilevel halftoning can be found in e.g. U.S. Pat. No. 5,903,713. 
     The transformation of a continuous-tone image (CT) to the halftone image of the present invention by means of one or more threshold tiles is similar to the prior art: the halftone dot coverage, which is typically expressed as a percentage and is defined by the number of image pixels in the dot, increases, as defined by the threshold tile, proportional to the corresponding density of the original continuous-tone image (CT). The dot coverage of the spiral dots of the present invention can be increased in various ways: by growing the length of the first arc or first spiral and thereby increasing the dot size, as governed by consecutive values of the threshold tile; by increasing the thickness of the first arc or first spiral without increasing the dot size (thereby shrinking the empty space of the second spiral), either locally e.g. by adding protrusions to the first spiral, by increasing the thickness of one or more segments of the first spiral, and/or by increasing the thickness of the complete first spiral; by inserting image pixels inside the second spiral; or by a combination of any of these methods. 
     In the highlights of the raster image, the dot coverage may be too low for the image pixels to represent a complete winding of the first spiral. The image pixels then represent a segment of the first spiral, i.e. a first arc. The transition from highlights to midtones is preferably made by increasing the thickness of said first arc and/or by growing the length of said first arc until a complete winding of the first spiral is formed. Still higher coverage can be obtained by increasing the thickness and/or the length of said first spiral which then may consist of more than one winding, including partial windings. 
     From a certain threshold coverage, preferably larger than 40%, more preferably larger than 50% and most preferably larger than 55%, the first spiral can no longer grow in length without overlapping with a neighbouring dot. Above said threshold, darker images can be produced by shrinking the length and/or thickness of the second spiral, or by inserting image pixels inside the second spiral. At still higher dot coverages, the second spiral shrinks further and becomes an arc (the second arc). 
     Due to the overlap between neighbouring dots, spiral dots with a high dot coverage no longer have an open-ended second spiral. Nevertheless, the advantages of the invention are still provided by such spiral dots, because the closed second spiral still defines a channel that can accept ink, so that a better print quality is produced with more uniform patches versus the state-of-the-art AM threshold tiles. The known advantages of state-of-the-art AM threshold tiles versus FM threshold tiles are also provided by the present invention, namely smoothness of flat-tones and rendering of mid-tones and better printing stability. Simultaneously, the present invention also provides the advantages of state-of-the-art FM threshold tiles versus AM threshold tiles, namely rendering of fine details and closing in the shadows. Also no irregular “worms”, or spaghetti-like structures are generated by the present invention as in 2 nd  order FM threshold tiles which make the printed images more grainy, especially in vignettes and mid-tones. 
     In a preferred embodiment, a set of threshold tiles is used to generate the a cross-modulated (XM) raster image according to the present invention, comprising small spiral dots of which the frequency is modulated in the highlight and shadow areas of the image, and larger spiral dots of which the amplitude is modulated in the mid-tones. As a result, screen frequencies above 200 LPI (78.7 lines/cm) are possible. The ratio between resolution and screen frequency of the halftone raster image is preferably below 12, more preferably below 10. For example, when the resolution is 2400 DPI (945 dots/cm), the screen frequency is preferably above 240 LPI (94.5 lines/cm). 
     The one or more threshold tiles may be generated by a threshold tile generator, also called a halftone generator, which is comprised in a raster image processor or in a prepress workflow system, in accordance with options selected by the user via an input field of a user interface. Conventional options comprise image resolution, screen frequency, screen angle (α) and screen shape. In accordance with the present invention, the number of options is preferably expanded by an input field for selecting the maximum thickness of the first and the second arc or spiral. An extra input field may be added for selecting the shape of the spiral dot (e.g. circular, elliptical, etc., as described above) and preferably also a parameter which further defines the selected shape such as ellipticity. Another input field may be added for the selection of one or more radial lines through the centre of the spiral dots and optionally also an additional input field for the specification of the thickness of the radial lines. 
     The generator generates the threshold tile from these above-mentioned input fields, preferably by means of a screen function that defines a spiral-shape, such as the Archimedean spiral described above. The spiral shape or radial lines are preferably generated by calculation in polar coordinates contrary to state-of-the-art halftone generators wherein Cartesian coordinates are used. 
     Applications 
     The halftone raster image of the present invention can be used in various printing techniques, most preferably lithographic printing, flexographic printing and digital printing. 
     The raster image can be exposed on a light- or heat-sensitive material such as a lithographic or flexographic printing plate precursor by means of a laser, preferably a violet or an infrared laser. After processing the exposed precursor, which may be hidden to the user in a so-called “development on-press” method, a printing plate carrying the raster image of the present invention is obtained. That plate can then be mounted on a printing press wherein ink is supplied to the plate which is then transferred onto the substrate to be printed. 
     When used for flexographic printing, the raster image of the present invention is represented on the flexographic plate by spiral dots in relief. Compared to conventional flexography, these halftone dots can be impressed more easily onto the substrate so that a better transfer of ink from the flexographic printing plate to the substrate can be achieved, especially by means of the open-ended ink channel. 
     It is known that small halftone dots, e.g. when using FM screens, are difficult to reproduce accurately with lithographic printing plates, due to the limited resolution of the image recording layer. Likewise, small printing dots in the lithographic image wear out easily, reducing the run length of the plate. These problems can be reduced by the present invention, which combines aspects of AM screens with the advantages of FM screens, such as rendering fine details and closing in the shadows. The raster image of our invention is therefore advantageously used in combination with lithographic printing plates, in particular lithoplates comprising a photopolymer as image recording layer, which are often used for newspaper printing. Also thermal, i.e. infrared-sensitive, lithographic plates are advantageously used in combination with the present invention. 
     In a digital printing technique the raster image of the present invention is applied onto the substrate without a plate, e.g. by jetting ink with an inkjet printer. Preferred inkjet inks to be used in the context of this invention are UV-curable inks, (eco-)solvent inks and aqueous inks. All these techniques are well known in the art. 
     Preferred inkjet printing techniques include wet-on-dry printing and wet-on-wet printing, either by jetting directly on a substrate or by jetting on and transferring from a transfer belt or drum onto a substrate. The predefined ink channel formed by the second spiral provides the mentioned advantages especially when jetting on non-absorbing substrates such as PET, polyethylene or the label substrates which are typically used in flexography. Our invention also allows to use high frequency screening in single pass inkjet systems. 
     Alternative printing techniques which may benefit from the present invention are screen printing, serigraphy, gravure printing, etching, pad printing, or transfer printing; and digital printing techniques such as xerography, electrophotography, iconography, magnetography, laser printing, dye-sublimation printing, dot-matrix printing, thermal printing, nanography, or thermal (wax) transfer. 
     The substrate on which the raster image may be printed can be of any kind, e.g. plastic films or foils, release liner, textiles, metal, glass, leather, hide, cotton and of course a variety of paper substrates (lightweight, heavyweight, coated, uncoated, paperboard, cardboard, etc.). The substrate may be a rigid work piece or a flexible sheet, roll or sleeve. Preferred flexible materials include e.g. paper, transparency foils, adhesive PVC sheets, etc., which may have a thickness less than 100 micrometres and preferably less than 50 micrometres. Preferred rigid substrates include e.g. hard board, PVC, carton, wood or ink-receivers, which may have a thickness up to 2 centimetres and more preferably up to 5 centimetres. The substrate may also be a flexible web material (e.g. paper, adhesive vinyl, fabrics, PVC, textile). A receiving layer, for example an ink-receiving layer, may be applied on the substrate for a good adhesion of the reproduced image on the substrate. 
     In another embodiment, the present invention can also be used in  3 D halftoning, such as stereolithography, digital light processing, fused deposition modelling, selective laser sintering, selective laser melting, electronic beam melting and laminated object manufacturing