OA18364A - A method of printing an image on a security document, security document and substrate comprising an image printed by such a process. - Google Patents

Abstract

The invention relates to a method for printing an image from a source image comprising the steps of: defining an order of juxtaposition of the ink dots in cells of the image as well as an orientation of said ink dots in said cells, the cells having identical dimensions so that each cell can comprise a dot of each of the inks used, the different dots being juxtaposed, calculating (102) a number of said printable cells in the image, resizing (103) the source image whose number of pixels corresponds to the number of cells in the final image, performing (104) stochastic screening by thresholding, using the screened image, generating (105) a usable file by drawing, for each individual cell of the usable file, dots of each of the inks used. The invention also relates to a security document and a substrate comprising an image printed by such a method.

Description

Method of printing an image on a document: security, security document and substrate comprising an image printed by such a process

The invention relates to a method of printing a final image from a source image on a security document or on a substrate intended to be attached to a security document. The invention also relates to a security document comprising a final image printed using such a method. The invention also relates to a substrate comprising a final image printed using such a method and intended to be attached to a security document.

The invention relates more particularly, although not exclusively, to the printing of a final image on a banknote or on a substrate subsequently attached to a banknote.

TECHNOLOGICAL BACKGROUND OF THE INVENTION

In the field of banknotes, it is known practice to produce security elements from inks that are substantially invisible to visible light but visible under the action of other wavelengths such as for example under infrared light or else. ultraviolet light. These security elements thus turn out to be more difficult to reproduce by possible counterfeiters since such elements cannot be observed and are therefore not reproducible by common reproduction means such as commercial photocopiers.

It is possible to apply traditional printing techniques, known for conventional inks, to print these security elements from substantially invisible inks. However, this has the drawback that most of the dots of different colored inks are then found superimposed, which considerably degrades the saturation of the colors obtained and therefore the quality of the final image.

To overcome this defect, a method is known which consists in juxtaposing the ink dots on the support to avoid any superposition detrimental to the colorimetric rendering. The size of the ink dots is then further modulated so as to locally change the apparent density of each primary color on the final image and thus to reconstitute the corresponding zone of the source image.

But even according to this second more advantageous method, the final image obtained has several drawbacks.

The first drawback is that of a relatively low resolution preventing the reproduction of fine details, so that checking the authenticity of the note on which the final image is printed is difficult to perform. Indeed, the juxtaposition of the points implies a division of the effective resolution of the final image by as many primary colors used. For example, a screen of 150 lines per inch (or about 60 lines per centimeter, standard screen for printing good quality magazine images) will give an effective screen size of 50 lines per inch if three colors juxtaposed (or about 20 lines per centimeter, inferior ruler even than used for printing on newsprint).

Another drawback is linked to the physical phenomenon known as point fattening. Due to the physical properties of any ink and the scattering of light in the printing substrate, the apparent size of a printed dot is not the same as its theoretical size calculated when screening the image. source. This difference in size is not constant but varies with the perimeter (i.e. size) of the point. Thus, the screen for the implementation of the second method (of which the size of the points varies and of which certain points of the same color are brought to touch each other above a coverage rate of 50%) will undergo significant colorimetric distortions. if the source image is not corrected at the time of dithering. This correction, based on empiricism or a complicated color management process, is made all the more difficult by the fact that the inks used are not visible in daylight and that the measurement and quality control tools standard are not suitable.

OBJECT OF THE INVENTION

An object of the invention is to provide a printing process which makes it possible to print a final image of good resolution and of better controlled color on a security document, or on a substrate then attached to a security document, even then. that said image is printed from inks substantially invisible to daylight. An aim of the invention is also to provide a security document comprising such a final image. An aim of the invention is furthermore to provide a substrate intended to be attached to a security document and comprising such a final image.

BRIEF DESCRIPTION OF THE INVENTION

With a view to achieving this goal, a method of printing a final image on a security document, or on a substrate intended to be attached to a security document, from a source image, is proposed. the final image being printed by juxtaposing dots of ink of identical dimensions without superimposing said dots, at least two inks substantially invisible to visible light being used for printing the final image, the method comprising the steps of:

- define during a first step an order of juxtaposition of the ink dots in cells of the final image as well as an orientation of said ink dots in said cells, the cells having identical dimensions so that each cell can include a point of each of the inks used, the different points being juxtaposed,

- calculate a number of said printable cells in the final image,

- resize the source image accordingly to obtain a resized source image whose number of pixels corresponds to the number of cells in the final image calculated in the previous step,

- perform a stochastic rasterization by thresholding on the resized source image to obtain a rasterized source image, and

- using the raster image, generate a file usable by printing means by drawing, for each individual cell of the usable file, points of each of the inks used, in accordance with their presence or absence of after the rasterized source image, and according to the order of juxtaposition and the orientation defined during the first step.

Thus, even though each cell of the final image is sized to receive a juxtaposition of dots of each ink used by the printing means, the method according to the invention makes it possible to determine, for each of said cells, whether a dot of the first ink is actually printed or not and what is its position within the cell (relative position with respect to the other points and orientation). It is the same for the second ink as well as for any other inks ... The dots of the different inks used are thus of identical sizes but have a frequency which varies from one zone to another of the final image since 'they are not necessarily present in all cells.

The method according to the invention therefore makes it possible to determine the optimal position of the ink dots to be printed (relative position with respect to the other dots and orientation) so that the combination of the radiations of the adjacent dots of the final image reconstitutes a corresponding zone of the source image. It turns out that this makes it possible to obtain a final image having a good resolution because the size of each point can thus be close to the minimum size reproducible by the printing system considered. Thus, FIGS. 1a and 1b represent the same final image respectively printed with a method of the prior art, that is to say a method in which the dots have different dimensions within the same image, and with the method according to the invention. In Figure 1a the dots all have a triangular shape varying in diameter from 20-255 micrometers while in Figure 1b the dots all have a triangular shape with a unique size of 100 micrometers. The two figures la and lb clearly illustrate that the figure lb presents a much sharper image, having in particular more details, than the figure la.

The method according to the invention therefore makes it possible to obtain a final image having a good resolution. This makes it easier to check the authenticity of the security document on which such an image is printed.

Advantageously, the juxtaposition of the ink dots makes it possible to have an additive effect of the light emitted by the various ink dots during their excitation, which makes it possible to have a final image of good light intensity. This further facilitates the verification of the authenticity of the security document.

Furthermore, the final image printed using the method according to the invention proves to be more resistant to production variations and in particular to registration errors between the colors due to the printing means used compared to an image printed according to methods of the invention. prior art. In this way, even with a registration error, the final image printed with the method according to the invention will retain good sharpness. This is advantageous because the control of manual as well as automated registration is made very difficult by the use of substantially invisible inks requiring special viewing conditions. A greater tolerance to registration errors constitutes a gain in terms of productivity and in terms of fault rate.

In addition, the method according to the invention allows greater stability of the colors used than traditional methods since the ink dots all have the same dimensions and since each dot of a given ink is isolated and never touches a neighboring dot. the same color, regardless of the coverage rate considered. The different ink dots of a given color thus all react in the same way to the dot gain phenomenon, which allows a step to compensate for this relatively simple phenomenon to be implemented. The method according to the invention therefore facilitates the printing of the final image.

By visible light, or daylight, is understood of course all the electromagnetic waves which are visible to the human eye (which corresponds substantially to a range of wavelengths ranging from 380 to 800 nanometers).

By substantially invisible is meant any ink which is intended to be invisible to visible light and to be visible under an excitation of another wavelength to limit its detection but which, however discreet it may be, may prove to be slightly visible under daylight, generally due to a slightly different brightness from the rest of the security document. This gloss, however, is an undesirable effect of the ink.

Likewise, by cell or even pixel is meant the geometric entity which fictitiously cuts out an image but which is not printed.

For the present application, the diameter of an ink point is to be understood according to its general mathematical definition, that is to say that this term diameter refers to the greatest distance separating two entities from this ink point. Thus, when it is a question here of a diameter of an ink point, this does not mean that said ink point is necessarily circular.

With a view to achieving this aim, a security document is also proposed comprising an image printed with the method according to the invention as described above.

Still with a view to achieving this aim, a substrate intended to be attached to a security document and comprising an image printed with the method according to the invention as described above is also proposed.

BRIEF DESCRIPTION OF THE DRAWINGS

Figures la and lb have already been described previously.

Furthermore, the invention will be better understood in the light of the following description of a particular non-limiting embodiment of the invention. Reference will be made to the attached figures, among which:

- the . FIG. 2 is a diagram showing the main steps of the method according to the invention,

- Figures 3 and 4 are highly enlarged views of parts of a final image printed by the process symbolized in Figure 2, Figure 3 corresponding to a part of the final image appearing white and Figure 4 corresponding to part of the final image predominantly yellow,

- Figure 5 is a greatly enlarged view of part of a final image printed by the process symbolized in Figure 2, but with a different form of dots than for Figures 3 and 4, Figure 5 corresponding to a part of the final image appearing in white color.

DETAILED DESCRIPTION OF THE INVENTION

With reference to the various figures, the printing method according to the invention aims here at printing a final image on a banknote from a source image, the final image being printed by juxtaposition of dots of ink of dimensions identical. The source image is for example a photograph or any other image in digital form.

Preferably, the final image is printed from three inks that are substantially invisible in daylight. The three inks here are all fluorescent inks; that is, inks which are excited by invisible ultraviolet light and which in return emit visible colored light. For example, the three inks are chosen such that the first ink emits a red color, the second ink emits a green color and the third ink emits a blue color when said inks are subjected to ultraviolet excitation.

Preferably, these three inks are chosen so that the chromaticity, measured on an area of the final image corresponding to a white area in the source image and therefore to a maximum and equivalent coverage of the three inks, is equal to the chromaticity of the white point defined in a standard screen profile such as sRGB (for Standard Red Green Blue in English or the standard space of red green blue color which is defined by standard CIE 61966-2-1, CIE being the acronym for Commission Internationale de 1'Eclairage). It is recalled that in the chromaticity diagram normalized by the CIE, the coordinates of the white point of the sRGB color space are:.

x = 0.3127; y = 0.3291.

This makes it possible to have greater stability of the colors used. In this way, the final image visible under excitation requires at most only tiny corrections to compensate for the dot gain phenomenon and thus to approximate the colors of the source image when it is observed on a calibrated screen. and profiled to sRGB standard.

The method according to the invention comprises an initial step 101.

According to a particular embodiment, during said initial step 101, the shape of the ink dots which will be printed on the banknote is selected. Here we define a shape of an ink point and an arrangement of said points in cells to obtain a complete tiling of the plane.

Preferably, we choose ink dots in the shape of a triangle. Indeed, the triangular shape allows better nesting of the ink dots while maintaining a perfect tiling of the plane. It is thus possible to obtain an image of better resolution. Preferably, the ink dots are in the shape of an equilateral triangle. In this way, the ink dots are optimally nested, an equilateral triangle pointing in one direction being nested between two equilateral triangles pointing in the opposite direction so that said three triangles form a trapezoidal cell.

The ink dots once printed have a diameter of 100 micrometers here and are spaced between them by 10 micrometers.

The shape and size of the dots therefore define the cells of the final image. Indeed, the cells are dimensioned so that each cell can include a point of each of the inks used, the different points being juxtaposed. The cells of the same image therefore have identical dimensions which are fixed and not modifiable. Such a cell 1 is here referenced in FIGS. 3 and 4 and thus comprises two triangular dots, adjacent and pointing upwards, of two different inks and a triangular dot pointing downwards of ink of the third color and framed by the two more ink points. Thanks to their trapezoidal shape, the cells themselves also fit into each other.

During this initial step 101, the order of juxtaposition of the ink dots within the cells of the final image is also determined. This order of juxtaposition is preferably determined so that the arrangement of the inks in the final image limits as much as possible the visual artefacts in said final image. Typically, the dots of the same ink are not arranged in a structure allowing horizontal, vertical or diagonal lines to appear on the final image. In particular, the order of juxtaposition remains the same for cells of the same row of cells but is switched from one row of cells to another. In this way, each of the three inks is assigned periodically on the same line and a change of order of said inks is carried out at each line change. This judicious permutation of the order of juxtaposition of the inks at each new line makes it possible to avoid unwanted visual artifacts such as line structures running through the final image. Preferably, only two orders of juxtaposition of the ink dots within a single cell are selected for the entire final image, each line comprising an order of juxtaposition different from that of the two lines surrounding it. Referring to Figure 3, the first row of cells in the image has a first order of juxtaposition (first ink, second ink, third ink), the second row of cells has a second order of juxtaposition (second ink, third ink, first ink), the third line again includes the first order of juxtaposition, the fourth line again includes the second order of juxtaposition ...

At the same time, during this initial step 101, the orientation of the ink dots within the cells of the final image is also determined. In particular, the orientation of the points is here affected periodically on the same line and a change of this periodicity is effected at each change of line. Referring to Figure 3, the first row of cells in the image has a first order of orientation (triangle pointing upwards then triangle pointing down), the second row has a second order of orientation (triangle pointing down then triangle pointing up), the third line again has the first order of orientation, the fourth line again has the second order of orientation ...

This judicious permutation of the order of orientation of the points with each new line further helps to avoid unwanted visual artifacts. This also makes it possible to obtain a tiling of the plane as complete as possible and even, when the shape of the points allows it, which is the case here with the triangular shape, a total tiling of the plane.

Because of the different orientation of the points from one line to another, the orientation of the cells also varies accordingly from one line to another.

In addition, due to the alternation of the points on the same line, the orientation of two successive cells on the same line is also different.

This judicious permutation of the order of orientation of the cells with each new row and within the same row further helps to avoid unwanted visual artefacts.

Once this initial step 101 has been completed, the number of printable cells in the final image is calculated during a second step 102, knowing that the size of the cells was fixed during the initial step 101 and that we know the desired size of the final image. More precisely, we calculate the number of printable cells both in a first direction of the image and a second direction of the image perpendicular to the first.

In a third step 103, in view of the number of printable cells in the final image in the first direction and in the correspondingly resized image. This one resizes an image implemented source size by a second direction pixel, source to obtain step 103 is resampling the source image to a number of cells according to the first the second direction calculated during corresponding to the direction and according to the second step width

1'image height

At

102. Due to a height ratio out of 1 for the cells considered, resized in this way also presents a different width ratio from that during a fourth step thresholding an image each layer of red color, (since colors different stochastic by dithering resized to get

Specifically, for green, blue i the final image red, blue regardless of the intensity of the source image.

104, one carries out one of the rasterized source image.

of the image will be printed from inks and green) a screening is in order to reduce the many the resized source carried out corresponding color levels, namely 256 only two levels. The two or more levels are of the all color type (meaning an absence of color) and non-zero color intensity (meaning a presence of the or nothing, that is to say zero intensity of color). Thus, each pixel of the rasterized source image is defined by a triplet of binary values:

- a first binary value which is at 0 to signify an absence of red color or at 255 to signify a presence of red color, and

- a second binary value which is at 0 to signify an absence of green color or at 255 to signify a presence of green color,

a third binary value which is at 0 to signify an absence of blue color or at 255 to signify a presence of blue color.

Thus, the rasterized source image is encoded here in a computer file of RGB (Red Green Blue) type having only 8 possible color values:

- (0, 0, 0);

- (255, 255, 255);

- (255, 0, 0);

- (255, 0, 255);

- (255, 255, 0);

- (0, 0, 255);

- (0, 255, 255); and

- (0, 255, 0).

As a variant, the rasterized source image is defined by three separate monochrome computer files (comprising only binary values of 0 or 1) and each describing a separate red, green or blue color layer in place of the aforementioned single file.

The thresholding generating the screening is carried out either with a single threshold value and diffusion of the error to neighboring pixels, or with a matrix of different thresholds governing the thresholding of several pixels (the screening is then said to be ordered). In an even more privileged way, the screening is implemented using the Jarvis-Judice-Ninke algorithm.

During a fifth step 105, a

Γ "

file that can be used by printing means by drawing for each cell of the file that can be used the appropriate shape of the dots of each of the inks used when their presence is dictated by the rasterized source image obtained in step 104. To this end, the different cells of the rasterized source image are scanned one by one. For a binary value of 0 in the cell, no ink dot should be printed on the banknote so that the corresponding information is indicated in the exploitable file. For a binary value of 255 in the cell, an ink dot of the corresponding color, and according to the shape and size defined in the initial step 101, must be printed so that the corresponding information is indicated in the file exploitable.

The exploitable file is for example a vector file or even a bitmap file at the resolution of the printing means considered. The exploitable file is for example composite or even made up of several separate sub-files.

During a sixth step 106, the image is then printed on the banknote using the exploitable file.

In this way, the method according to the invention makes it possible to modify the printing frequency of the ink dots of the different inks available for printing the final image by controlling the actual printing or not of the ink dots in each of the cells, and making sure that no points overlap.

With reference to FIG. 3, a white part of the final image is thus composed of cells comprising all the juxtaposed ink dots, namely a green ink dot, a red ink dot and a blue ink dot. . With reference to FIG. 4, a yellow part of the final image consists mainly of cells comprising only two juxtaposed ink dots, that is to say a green ink dot and a blue ink dot. , and therefore further an unprinted area corresponding to the intended location of the red ink dot.

Of course, the invention is not limited to the embodiment described and it is possible to provide variant embodiments without departing from the scope of the invention as defined by the claims.

In particular, although here the printing method according to the invention has been implemented for printing a final image on a banknote, the method according to the invention can be implemented for the printing of a final image on any other type of security document such as for example a passport, an identity card, an official document, etc. As a variant, the method according to the invention could be implemented for printing of a final image on a substrate which will then be attached (for example by gluing or by transfer) on a security document (such as a banknote, a passport, an identity card, an official title ... ). The substrate is for example an adhesive plastic film or a transferable polymer layer. Although here the final image is printed from three inks, said image could be printed from a different number of inks and even with only two inks, as is for example described in the patent application of Applicant EP 1 985 458. Moreover, instead of the inks described emitting primary colors Red, Green, Blue, inks emitting other colors can be used. It is also possible to use inks other than fluorescent inks such as, for example, anti-Stokes inks, that is to say inks reemitting at a wavelength less than the excitation wavelength (for example, emitting visible light when illuminated by infrared light). In all cases, the inks used will of course be of different colors and substantially invisible in daylight.

Furthermore, the points may have a shape other than triangular. FIG. 5 thus illustrates a particular embodiment in which the ink dots have a hexagonal shape, a cell of the image also being symbolized and referenced 1 in FIG. 5. As a variant, the dots may have a shape. rectangular or any other shape allowing complete tiling of the final image. In the event that the shape of the dots is not configurable by the printing means chosen implementing the method according to the invention, an ink dot may be formed by several drops of the same ink. For example, a rectangular ink point can be obtained by approximation using several substantially circular ink drops. However, this will lead to a lower saturation and intensity of the color obtained due to the incomplete tiling of the plane by the approximate dot shapes (areas of the substrate or of the security document not receiving ink and therefore being "lost" with regard to the potential of luminous intensity). In any event, the ink dots themselves are only juxtaposed in the present application and in no way superimposed. The only tolerance here is the possible superposition of drops of the same ink to form an ink dot of a particular shape.

Likewise, the ink dots may have a different size from what has been described provided that the dots of the same image have the same size. The ink dots will typically have a diameter between 10 and 150 micrometers, limits included. Preferably, the ink dots will have a diameter of between 50 and 110 micrometers, limits included. It will be preferable to have the smallest possible dot diameter while remaining qualitatively printable for the printing means used for implementing the method according to the invention. The dots will therefore preferably be chosen to be close to the minimum size reproducible by the printing process considered.

The initial step may be different from what has been said. For example, the initial step could also include a selection of the dimensions of the ink dots (it being understood that for the same image the dimensions of all the ink dots are identical). The initial step may not include a selection of the shape of the points. The initial step may include a selection of the general orientation of all the cells so that a general direction of highest resolution of the cells coincides with the direction of the source image having the most details. For the examples illustrated by FIGS. 3, 4 and 5, the cells have the overall shape of a rectangle: the direction of highest resolution of these cells coincides in this case with the width of these rectangles. FIG. 1b thus presents an image for which the orientation of the points, and therefore of the cells, is in a vertical direction. The cells may have an overall shape other than rectangular, for example square. However, it will be preferable to have cells in the overall shape of a rectangle in order to preserve a final image of better resolution, even if the latter is different from one direction to another.

Although here the screening step is implemented by a Jarvis-Judice-Ninke algorithm, said step can be implemented by other error diffusion algorithms such as Floyd-Steinberg. As a variant, other types of algorithms could be used such as ordered screening algorithms of the Bayer algorithm type, etc.

Although here the colorimetric coordinates of the white point chosen as target correspond to the coordinates of the white point defined in the sRGB standardized profile, it is possible to choose as a reference during the formulation of the inks, any white point described in a screen profile. or standard RGB color space associated with the source image (for example: the “Adobe RGB” space or the “ProPhoto RGB” space). This will in all cases allow greater stability of the colors used. In this way, the final image visible under excitation will only require tiny corrections at most to compensate for the dot gain phenomenon and thus to approximate the colors of the source image when it is observed on a calibrated screen. and standard profile. In practice, we will most often select as the white point, depending on the chosen profile, one or other of the most common standardized illuminants: D65 (white point defined by the coordinates x = 0.3127, y = 0.3291 in the diagram chromaticity normalized by the CIE used in the sRBG profile) and D50 (white point having as coordinates x = 0.3457, y = 0.3585 in the chromaticity diagram normalized by the CIE used for example in the ProPhoto RGB profile).

Claims (17)

1. Method of printing a final image on a security document, or a substrate intended to be attached to a security document, from a source image, the final image being printed by juxtaposition of dots. inks of identical dimensions without superposition of said dots, at least two inks substantially invisible to daylight being used for printing the final image, the method comprising the steps of: - define during a first step (101) an order of juxtaposition of the ink dots in cells of the final image as well as an orientation of said ink dots in said cells, the cells having identical dimensions of so that each cell can include a point of each of the inks used, the different points being juxtaposed, - calculate (102) a number of said printable cells in the final image, - resize (103) the source image accordingly to obtain a resized source image whose number of pixels corresponds to the number of cells in the final image calculated in the previous step, - perform (104) a stochastic rasterization by thresholding on the resized source image to obtain a rasterized source image, and - Using the raster image, generate (105) a file that can be used by printing means by drawing, for each individual cell of the file that can be used, dots of each of the inks used, in accordance with their presence or their absence according to the rasterized source image, and according to the order of juxtaposition and the orientation defined during the first step (101). 2. Printing method according to claim 1, wherein during the first step (101) a shape of ink dots is also selected for printing the final image. 3. Printing method according to claim 2, wherein the ink dots are chosen in the form of a triangle. 4. Printing method according to one of the preceding claims, wherein during the first step (101) a size of ink dots is also selected for printing the final image. 5. Printing method according to one of the preceding claims, wherein during the first step (101) the order of juxtaposition of the ink dots in the cells is selected so that, of a row of cells to another, the order of juxtaposition of the ink dots inside the cells is swapped. 6. Printing method according to one of the preceding claims, in which during the first step (101) the order of orientation of the ink dots in the cells is selected so that, from one line to the next. another, the order of orientation of the ink dots inside the cells is swapped. 7. Printing method according to one of the preceding claims, wherein during the first step (101) is defined a general orientation of the cells so that a direction of higher resolution of the cells coincides with a direction of l. source image with the most detail. 8. Printing method according to one of the preceding claims, wherein the inks used are fluorescent inks. 9. Printing method according to one of claims 1 to 7, wherein the inks used are anti-Stokes inks. 10. Printing method according to one of the preceding claims, wherein the ink dots have a diameter between 10 and 150 micrometers. 11. Printing method according to one of the preceding claims, wherein the ink dots have a diameter between 50 and 110 micrometers. 12. Printing method according to one of the preceding claims, wherein three inks are used for printing the final image, an ink emitting a green color, an ink emitting a red color and an ink emitting a blue color. when excited by light other than visible light. 13. Printing method according to claim 12, wherein said three inks are chosen so that when they are juxtaposed in equal proportions, said inks have a resulting chromaticity close to the white point defined in a red-green-blue color profile. standard suitable for representing the source image. 14. Printing method according to claim 12, wherein said three inks are chosen so that when they are juxtaposed in equal proportions, said inks have a resulting chromaticity close to the white point defined by the coordinates x = 0.3127, y = 0.3291 in the chromaticity diagram standardized by the International Commission on Illumination. 15. The printing method according to claim 12, wherein said three inks are chosen so that when they are juxtaposed in equal proportions, said inks exhibit a resulting chromaticity close to the white point defined by the coordinates x = 0.3457, y = 0.3585 in the chromaticity diagram standardized by the International Commission on Illumination. 16. Security document comprising an image printed according to the printing method defined according to any one of claims 1 to 15. 17. Substrate intended to be attached to a security document, comprising an image printed according to the printing process defined according to any one of claims 1 to 15.