Technical field The present invention relates both to a method and an apparatus for assessing/measuring grammage variation in sheet material.

Many types of sheet material with variations in grammage can be assessed/measured in accordance with the invention within a wide interval of grammages, expressed for instance in gram per square meter (g/m2). Examples of sheet material are paper, paperboard, fibre cloth (non-woven), laminates, plastic film, textiles and veneers.

A central feature of the present invention is the use of a basic element which decays to emit electrons. This phenomenon is termed beta decay and beta radiation.

Furthermore, variations in the grammage of sheet material are caused by local collections of material, often termed formation by those skilled in the art. To distinguish the assessing/measuring method in accordance with the invention from other methods of measuring formations, e. g. optical and visual methods, it is suitable to call the measuring principle in accordance with the invention"beta-formation measuring".

Background art The mass distribution has always been of interest in the manufacture of, for example, paper and paperboard. Even in the manufacture of a simple paper, i. e. a paper produced substantially exclusively of pulp fibres, if a sheet of the paper is held up to daylight or an artificial source of light, the structure will be seen to be more or less patchy.

This structure in the paper is usually termed the formation of the paper. A paper manufacturer can thus perform an ocular inspection of the paper and get some idea of its

formation. Measuring methods based on light transmission have also been developed.

These measuring methods are relatively usual but all of them are unreliable since the optical properties of the paper vary and affect the measurements.

The manufacture of both paper and paperboard has developed in time, resulting in increasingly sophisticated products. The sole paper web can be provided with various types of filler, for instance. As this word indicates, these fillers are in the paper or paperboard itself, i. e. in the body of the paper or paperboard. There are also a large number of surface treatment methods such as sizing and coating, for instance. The principal chemical as regards quantity in these contexts, especially for coating, is called pigment.

Filler and pigment are sometimes the same thing chemically. The existence of all these chemicals in paper and paperboard contributes to variations in the optical properties of these materials, regardless of the grammage of the material.

In the light of this, measuring methods have been developed to determine variations in the grammage or formation of the sheet material, which are based on electron radiation (beta radiation) of the sheet material. A considerable advantage with this type of measuring method is that beta radiation is not affected by varying optical properties of the sheet material, but has direct bearing on the weight or mass of the sheet material in its various parts, i. e. the grammage distribution.

A known method of measuring the grammage distribution of paper, for instance, and which has a high resolution (which is positive) is known as beta radiogram.

In this method an electron source is used in the form of a plastic plate in which some ordinary carbon atoms are replaced by beta radiating carbon 14-atoms. The electron output is uniform across the surface of the plate. The analysis commences by this plate being brought together with the sheet material, e. g. paper, to be analyzed and on the opposite side of the sheet connecting a film sensitive to electron beams, which may be termed photo film. The surface of the sheet material is less than the two surfaces of equal size of the carbon 14 plate and the photo film. The remaining area is taken up by a number of plastic film pieces having known grammages, constituting references. A parcel is thus formed constructed as described. This parcel remains intact for one hour, for instance, before it is separated and the object that at that moment, i. e. at the separation, is of the greatest interest is naturally the photo film. From this it is also understood that the exposure time is one hour. After this the photo film is developed in conventional manner and an image of the

grammage variations in the paper appears in the form of portions of differing light and dark areas on the film. This is generally described as different blackening of the film. The references are also reproduced on the film. The surface of the photo film is read with a scanner, with its varying degrees of blackening, and the readings are entered into a computer. The blackening is converted to grammage in the computer with the aid of the references. A map of the grammage variations in the paper can thus be created. This map or its numerical values can be further refined using various mathematical methods.

As mentioned above, an advantage of this measuring method is that the resolution is high. However, the method has many drawbacks and shortcomings. It is extremely time-consuming, for instance, and requires access to a dark room and developing equipment. Furthermore, it is impossible to study grammage variations in sheet material, e. g. paper, that has a grammage exceeding 120 gram per square meter (g/m2).

The method described above has been developed and improved in recent years. The difference is that the photo film has been replaced by an image plate sensitive to electron beams. With this method also a parcel is created as described earlier. This image plate is much more sensitive to electron radiation than the photo film and the exposure time can therefore be decreased from about one hour to an interval of 15 to 30 minutes. A new type of reader, i. e. scanner, has also been developed. When the image plate has been read by said scanner the readings are dealt with in the manner described above. The scanning is quick and takes only about three minutes and a grammage variation image is created in the computer as in the first-mentioned method. This latter method has been developed for use in, inter alia, the bio-medical field, and the image plate and scanner described are available from several companies, i. e. Fuji Film Ltd.

Although this second method is less time-consuming and simpler to perform than the first mentioned method, it has the same serious drawback as regards the type of sheet material that can be analyzed, i. e. it is not possible to successfully analyze sheet material, e. g. paper, having a grammage exceeding 120 g/m2. The reason for this is that the electron source used is relatively weak, namely a plastic plate containing carbon 14-atoms.

To enable the study of grammage variations in sheet material, e. g. paper, having a grammage exceeding 120 g/m2 a measuring method has been developed using promethium 147 as electron source. It is difficult, and very expensive, to produce a plate containing promethium 147-atoms so instead a certain quantity of this element is used, i. e.

a lump of suitable size, which is inserted into the cavity in a holder such as a cylindrical holder. The electron beam is then allowed to emerge in the form of a cone from one side of the holder. A receiving device, i. e. a body with a small, central hole is applied a certain distance from and below the electron source. These two objects can be supported by a yoke where the electron source is secured on the upper yoke arm and the receiving device on the lower, opposite yoke arm. Said opening run through the receiving device and an electronic detector is applied at the end of the opening. During measuring, which occurs pointwise over the sheet material, the electron beams are allowed to encounter the sheet material, the electron beams are allowed to encounter the sheet material and some of the electrons in the beam will penetrate through it whereas a number of those electrons will penetrate in, down into the cavity and on down into the electronic detector where an imprint is created. A new measurement can be performed by moving either said yoke or the sheet material. A grammage image can be built up by performing many such separate measurements over the surface of the sheet material.

This third measuring method admittedly has the advantage described above, i. e. that even sheet material having a grammage exceeding 120 g/m2 can be studied and analyzed. However, it also has a number of drawbacks. One drawback is that a large part of the electron radiation is not used for measuring but is lost to the surrounds of said cavity. The smaller the diameter of the hole and the cavity the fewer electrons will pass through the cavity and into the detector. Since the diameter of the hole determines the resolution, an extremely long exposure time is necessary if resolutions better than 1 mm are to be obtained. This means that in practice the resolution for this measuring method is poorer than 1 mm. Another drawback is that the measurements are performed pointwise and it is therefore impossible to measure along the sheet material and thus cover a coherent surface section or its entire surface. A third drawback is that promethium 147 has a half- life of 4.5 years. This relatively short half-life means that the quantity of electrons leaving the element per time unit gradually decreases. Since this measuring method does not permit simultaneous measuring of sheet material and references, the entire measuring method must be calibrated at regular intervals. This is performed manually and is extremely time-consuming.

Disclosure of the invention Technical problem As is evident from the above a method and an apparatus are needed for assessing/measuring grammage variations in sheet material ranging from low to high grammages, that are relatively quick, correct, twodimensional and have high resolution.

The solution This need is satisfied by the present invention, both as regards method and apparatus. The first category of invention relates to a method for assessing/measuring grammage variations in sheet material, comprising electrons from an electron source, having an energy exceeding 150 keV, being caused to encounter an elongate section of the surface of the sheet material resting in a certain position against a detector support surface sensitive to electron beams, said surface comprising a multitude of sensor elements and the sheet material and surface being pressed together before the electron beam having a specific width are caused to traverse at constant speed across the elongate surface section of the sheet material, resulting in some of the electrons being absorbed by the sheet material and the remaining electrons penetrating through the sheet material (transmission) and making an imprint in each sensor element in a congruent surface of the support surface, characterised in that between each electron radiation the sheet material and support surface are moved in relation to both the electron source and to each other in a controlled and predetermined manner, the first-mentioned displacement resulting in that, at each traverse, there being at least two traverses, the electron beam encounters an unexposed surface of both the sheet material and the support surface and the last mentioned displacement is effected so that the support surface is displaced further laterally from the electron source than is the case for the sheet material, that the imprint in each sensor element of the support surface is read along the elongate surface section and entered into a computer in which the elongate surface sections, these being at least two in number, are moved towards each other so that a coherent larger measuring surface is formed, and that each reading in the computer is reproduced with a numerical value, which numerical value forms a detailed map of the electron transmission through the measured surface of the sheet material and thus also forms a detailed map of variations in grammage.

Examples of suitable electron sources, i. e. those having an energy exceeding 150 keV, are promethium 147 and krypton 85. The energy of the first element is maximally 200 keV and of the second is maximally 700 keV. Promethium 147 is in solid form and a description has been given earlier of how this element is handled as an electron source. Krypton 85 is a gas and can be enclosed in a pipe, one end of which is made of thin, transparent material. This end is directed towards the sheet material to be analyzed.

As is revealed earlier, the method in accordance with the invention results in a detailed map of grammage variations in the measured surface of the sheet material. The numerical values relating to the electron transmission through the measured surface of the sheet material can be printed out from the computer onto a sheet of paper in graphic form.

The numerical values are transferred to very small areas with colour from white to black, most of the areas thus being in various shades of grey. Such an image can serve as basis for study, i. e. an ocular assessment of grammage variations in paper and paperboard, for instance. By means of ocular assessment and comparison of various images, an experienced paper manufacturer can assess the grammage variation in the paper or paperboard being produced on a scale from good to poor. This describes an application of the method in accordance in the invention in its simplest and widest form.

According to a more sophisticated embodiment of the method in accordance with the invention comparison material with various, known grammages is placed on the support surface as well as the sheet material to be analyzed. The electron beam are also caused to traverse the sections of comparison material, resulting in an imprint in each sensor element in an elongate surface section of the support surface, which imprints are read and entered into the computer and serve therein as standards for the imprints read in each sensor element in the support surface corresponding to the elongate exposed surface sections of the sheet material being analyzed.

If the dimension of the known grammage is stated as gram per m2, then the grammage of the sheet material being analyzed is stated in the same manner.

The electron beam emitted from the electron source are restricted to a specific width by means of screening, the screening also causing the intensity of the imprints in the sensor elements in the support surface in the transverse direction of the elongate surface section to vary, two edge portions having low intensity which increases gently to start with from the edge inwards and thereafter increases strongly, and a centrally

placed portion with maximum intensity. The elongate surface sections that are brought towards each other in the computer lack said two edge portions.

It is possible to use several different types of detector surface, such as an image plate, or a photo film or an electronic detector built up of CCD sensors, CCD being an abbreviation of"Charge Coupled Device". An image plate, available in various shapes, is preferred. Such an image plate is built up of three layers and consists from the bottom up of a carrying, somewhat elastic material, a layer of crystals in the form of (BaF (Br, I): Eu2+ covered by a thin, inert, protective layer. These image plates can be used in measurement after measurement. After such an image plate has been used for one measurement it is regenerated by being exposed to strong light. This takes a few minutes and special apparatus is available for the procedure. If photo film is used, one film is required for each measurement, which is not financially burdensome.

As regards reading the imprints in the detector surface, this is suited to the type of detector surface used. In the case of image plates, including the type of image plate described above, a laser beam can be caused to sweep over the plate so that light is released from the imprints via photo-stimulated luminescence, which light is collected via a light conductor to a photo multiplier where the light is converted to an electric signal that is written in the computer as a numerical value.

The grammage variations measured in the sheet material can be presented and reproduced in many different ways, such as in the form of a histogram describing the grammage distribution or by means of a frequency analysis presented in histogram form.

This presentation and reproduction are described in more detail in the following.

Although the method in accordance with the invention for assessing/measuring grammage variations in sheet material can be used for a large number of different types of sheet material, it has been found to be particularly suitable for paper and paperboard.

The invention also relates to apparatus for assessing/measuring grammage variations in sheet material, comprising a) an electron source, having an energy exceeding 150 keV that is secured in a carriage, movable at constant speed along a device provided with guides or the like, which device, together with the carriage, is vertically movable and is provided on its lower side with a longitudinal gap of a certain width, which determines the width of an electron

beam leaving the electron source and being directed towards sheet material lying immediately beneath it, b) a frame to anchor the sheet material, which frame is resiliently connected to a support means, c) a holder with support means applied below said frame, to which holder a detector surface sensitive to electron beam, and comprising a multitude of sensor elements, is secured, d) an imprint reader, such as a scanner, and e) a computer.

The apparatus is characterised in that the objects b) and c) are adjustably laterally displaceable in relation to the electron source, stationary in this direction, and in that these are also adjustably displaceable in relation to each other.

Each of the objects b) and c) is individually connected to or constitutes a part of a step table. The latter includes an electric motor that moves the table to a predetermined position. A drive means other than an electrically driven motor may be used provided the desired position can be reached.

The carriage carrying the electron source may be rectangular or quadratic and provided with a wheel at each of the four lower corners. To ensure controlled and identical traversing of the carriage time after time, two parallel, elongate tracks can be recessed in the device underneath. The number of wheels need not necessarily be four. Neither is it imperative to provide the carriage with wheels. Instead the carriage may be constructed of a material having low friction or it may be provided with a number of bosses of a material having low friction, enabling the carriage to glide along the surface underneath. This is facilitated if the surface or surfaces along which the carriage slides also consist of a material with low friction.

The device underneath or carriage is connected to a means that presses the device and the carriage down against the objects b) and c) so that the sheet material lies tightly against the detector surface when the carriage with the electron source traverses across the sheet material and the detector surface. If the sheet material is not in close contact with the detector surface air pockets may be formed between these layers of

material and it has been found that such air pockets disturb the electron beam and absorption of the electrons into respectively penetration through the sheet material.

Several means may be used for the purpose described and a suitable means is a compressed-air cylinder. Any drive means can be used as long as it is able to drive the carriage in the direction of movement at constant speed. An example of such a means is a step table.

Advantages A considerable advantage with the invention is that grammage variations in sheet material having a basis weight of up to 1200 g/m2 can be measured. Using a promethium 147 source of electrons enables grammage variations to be measured with great accuracy in sheet material having grammages of up to 300 g/m2. With a krypton 85 electron source sheet material can be analyzed within the grammage range 300-1200 g/m2.

In accordance with the invention it is also possible to perform two- dimensional measurement in even relatively thick sheet material, i. e. at least one surface section of the sheet material can be studied. The resolution is also excellent and better than 1 mm As regards accuracy, comparative experiments have been performed with one of the known measuring methods described earlier on paper having a grammage just under 100 g/m2) (this is because the comparative method cannot perform measurements on sheet material having a grammage exceeding 120 g/m2) and the experiments show that the measuring results are substantially identical.

The measuring method in accordance with the invention is fast and efficient, particularly when an image plate is used as detector surface. Parts of the measuring method can be automated and controlled via a computer. If photo film is used as detector surface the measuring procedure is delayed somewhat by the complicated developing process.

Description of the drawings Figure 1 shows a schematic representation of the carriage in which the electron source is applied, as well as the supporting means and underlying layer of material,

Figure 2 shows a schematic representation of said carriage in direction of traverse and also the devices in which both the sheet material and the image plate are anchored.

Figure 3 shows an intensity image of the imprints in the image plate made by transmitted electrons, Figure 4 shows a profile of the intensity in transverse direction of the elongate surface section in which imprints appeared, Figure 5 shows an intensity image over said elongate surface sections joined together, Figure 6 shows this intensity image inverted and calibrated, Figure 7a, 7b and 7c show the result of comparison measurements, Figure 8a and 8b show alternative ways of presenting the measuring results.

Best embodiment The invention is described in more detail in the following with reference to the accompanying drawings, and the section finishes with two embodiments by way of example.

Figure 1 shows a carriage 1 in cross section, in which the electron source 2 is applied. The carriage is provided with four wheels located at the four lower corners of the parallel-epipedic carriage. Two identical tracks 4 are cut in the device 5 below. A longitudinally running gap 6 of a certain width is to be found in the device 5. The width of this gap can be chosen relatively freely-10 mm by way of example. A lid 7 is also shown in the figure. This lid may be necessary from the measuring point of view but is there primarily to cover the electron beams 8 when the measuring apparatus is not in use. This is to prevent electrons flowing out into the apparatus and possibly to the immediate surroundings of the apparatus when it is not being used for measuring. This displacement of the lid has no influence on how long the electron source can be used for measuring but is merely a precautionary measure from the environmental aspect.

As can be seen from Figure 1 the electrons flow in the form of a beam 8 towards the sheet material 9 to be analyzed. The sheet material 9 rests tightly against the detector surface 10 which is in turn supported by a holder 11.

Figure 2 also shows in cross section how the carriage 1 with its electron source facing downwards, traverses along the device 5 provided with tracks. This figure shows in more detail how the frame for anchoring the object being measured, i. e. the sheet material, and the holder 11 beneath for the detector surface may be designed. The sheet material 9 is secured in some way to the frame 12. The width and length of the frame are optional. Since many types of paper are both converted to and sold in A4 size, it is suitable for the size of the frame to fit A4 measurements. Whether the sheet material is to be exposed to the electron beam 8 lengthways or widthways is also optional. Anchoring the sheet material 9 to the frame 12 can be achieved by some form of clamping device in such a simple manner that a number of strips of tape are attached to the edges of the sheet material and to the frame 12. As can be seen in Figure 2 the frame 12 is connected to a support means 14 by spring means 13.

Below the sheet material 9 is the detector surface 10, this in turn resting on the holder 11 with the support means 15. The detector surface 10 must be secured in some way to the holder 11 and this can be achieved in several ways. The holder 11 may be designed, for instance, so that a detector surface 10 in the form of an image plate fits exactly into a shallow recess in the holder 11. As for the image plates, their lower carrier layer is made of a somewhat resilient material which also has a high friction coefficient and if the holder 11, or at least its outer layer, consists of a material with high friction coefficient, the anchoring will be sufficient even if the holder 11 does not have a recess.

Neither Figure 1 nor Figure 2 shows the means, which may be a compressed air cylinder, which presses the means 5 and carriage 1 down against the sheet material 9 and detector surface 10. This means may be connected to the means 5 as such or to the carriage 1. The result will be the same in both cases. Figure 2, however, shows the spring means 13 that enable the compression causing the sheet material to be in close contact with the detector surface.

The actual measuring procedure can be as follows.

First it must be ensured both the sheet material 9 and the detector surface 10 are firmly secured in relation to each other and to the electron beam 8. Next the objects are

pressed together as described earlier. It is important that the compression is performed identically every time, which means that the lowering of the means 5 is controlled so that it is strictly vertical. The next stage is when the carriage 1 with its electron source 2 and electron beam 8 traverses at constant, predetermined speed across the sheet material 9. The means 5 and its carriage 1 are then raised to their initial position allowing the sheet material 9 and detector surface 10 to be displaced laterally in relation to the electron source 2 which is stationary in this direction. The two objects are moved laterally different distances. The sheet material 9 may be moved laterally, say, 8 mm whereas the detector surface 10 is moved 16 mm.

At this stage there are two possibilities: Either the lid 7 for the electron beam 8 can be closed and the carriage 1 allowed to return to its starting position before the compression is released and the device 5 with its carriage 1 is lifted vertically so that the carriage 1 always commences its traverse from the same side of the apparatus, or the compression can be released on the opposite side of the apparatus and the carriage 1 be allowed to traverse in the opposite direction during emission of the electron beam, in which case a new surface section of the sheet material will be penetrated.

As stated earlier, the number of traverses must be at least two, i. e. at least two different surface sections of the sheet material shall be irradiated. The number of traverses more than two is optional and may be as many as ten. Between each traverse the sheet material 9 and detector surface 10 are displaced both in relation to the electron source 2 and in relation to each other, as described earlier.

As stated above, this results in some electrons penetrating through the sheet material 9 on the exposed surface, forming imprints in the large number of sensor elements in the detector surface 10. After scanning those imprints as described above, a large number of numerical values are obtained in the computer, corresponding to the intensity of the imprints.

Figure 3 shows the result of ten traverses in the form of imprint intensity. It is the areas between the black fields that are of interest and the first traverse refers to surface section 16 furthest to the right, whereas the second traverse refers to the surface section 17 located second to the right, and so on.

These surface sections show patches ranging in colour from light to dark or, if preferred, from white to black and it is these shadings that reproduce the result of the measurement.

On studying the intensity of the imprints across said surface sections it will be found that, as shown in Figure 4, the intensity is extremely low furthest out at the edges of the surface section, and increases gradually further in and then sharply to maximum value at the centre of the surface section. The number zero on the y-axis in Figure 4 corresponds to the middle laterally of one of the surface sections in Figure 3. The thick line 18 in Figure 4 represents the intensity along the central portion of the surface section seen in transverse direction.

The central parts of the ten elongate surface sections are combined in the computer so that a coherent surface or image 19 of the intensity is formed, as shown in Figure 5. Light colour in the picture corresponds to high intensity, indicating that the transmission of electrons is high and the absorption of electrons is high and the absorption of electrons in the sheet material 9 is low, and thus that the grammage is low. The colour scale 20 to the right of the area 19 is without units, the numerical value 1 corresponding to maximum intensity from the imprints in the image plate 10 whereas the numerical value 0 corresponding to minimum intensity from the imprints in the image plate 10.

Figure 6 shows an image 21 calibrated from the image 19. The scale 22 to the right of the image 21 correlates to the dimension gram per m2. In this image the dark parts indicate low basis weight, while the light parts indicate high basis weight.

Example 1 Grammage weight variations were measured on a paper for photo-copying having a basis weight of 80 g/m2 first in accordance with the invention using promethium 147 as electron source, and with an image plate as detector surface, along ten elongate surface sections of the sheet material, and then in accordance with the measuring method described under"Background art"in this specification and termed a second method.

The reason that this comparison was performed with a paper having such relatively low grammage as 80 g/m2 was that said second method is eminently suitable for that type of paper but cannot be used for grammages that are much higher or, to be more specific, for basis weight of at most up to 120 g/m2.

The photo-copying paper consists to 67 % of pulp fibres (a mixture of <BR> <BR> bleached birch sulphate pulp (70 %) and bleached pine sulphate pulp (30 %) ), 22 % filler (precipitated calcium carbonate), 6 % other paper chemicals including starch, retention agent and fluorescent whitening agent. The remaining 5 % consisted of water.

Figure 7 shows the result of the measurements performed, in the form of the number of calibrated intensity points by the thousand within certain relatively narrow grammage intervals. The histogram shown in Figure 7a refers to the comparative method and that in Figure 7b refers to the measuring method in accordance with the invention. A comparison of these two histograms shows that the measuring results are almost identical.

This is confirmed by Figure 7c where the mean number of intensity points for each basis weight interval has been drawn in graph form (0 = the comparative method, + = the method in accordance with the invention). As can be seen, the two curves coincide with each other.

This proves that the measuring accuracy of the measuring method in accordance with the invention is high.

Example 2 In this case grammage variations were measured in accordance with the invention using promethium 147 as electron source and with an image plate as detector surface along ten elongate surface sections of the sheet material, on a totally different type of paper with considerably higher grammage than was the case in Example 1, namely cable paper having a grammage of 140 g/m2.

By cable paper is meant paper that is strong, has high electric insulating capacity and is used, inter alia, in transformers. This paper consisted exclusively of pulp fibres. The pulp was unbleached pine sulphate pulp that had been very frequently washed during manufacture. The paper was thus substantially free from conducting substances.

The paper should also be free from pin holes.

Figure 7b described above shows the measuring result from the measuring method in accordance with the invention in the form of a grammage distribution histogram.

The results of the measuring method in accordance with the invention can be reproduced in several other ways which will be explained and defined below, and illustrated in Figures 8a and 8b.

As point out earlier, paper is in no way homogenous, i. e. exactly the same at every point. Pulp fibres collect to a greater extent on certain surfaces than on other adjacent surfaces, for instance. These collections of material are generally termed flocks. In this context the concept of wave length = k is used. A rule of thumb states that the wave length X corresponds to double flock size. The concept of total formation is also used, which is characterised by the formation number F, defined as the variation coefficient for local grammage variations (w), i. e. the standard deviation divided by the mean grammage (M}).

This is represented in the following equation: F = 6 (W)/M} The standard deviation 6 is obtained, for instance by integrating the area below the effect spectrum of grammage signals for all frequencies, see Figure 8a, and extracting the square root therefrom. In this context frequency means 1, more specifically 1 length unit [mm] The Nordic research institutes in the field of pulp and paper (KCL, PFI and STFI) have, together with a number of paper manufacturers, arrived at the following recommendation for presenting the results of formation measurements.

The term formation refers to the local distribution of grammage over the surface of the sheet. The formation number F (Aa Ab) is defined as the variation coefficient for local grammage variations within the wave length interval ka till Xb mm, i. e. where 6 ( b) is the standard deviation within the wave length interval Xa to Xb mm and w is the mean grammage of the sheet.

A normalized formation number Fn (ka, Xb) can be calculated using the following equation: normalized to the grammage n.

A special case of the normalization is obtained by setting n = g/m2 which gives specific formation Fspec in accordance with the equation: Fspec (ia n Ab) w - Vt

It will be understood from the above that the formation numbers are dimensionless.

As explained above, the formation number F (-a' ) can be obtained by integrating the area below the effect spectrum of the signal for corresponding frequencies.

F3-30, for instance, signifies the formation number for the wave length interval 3-30 mm. It is formation numbers like this that are reproduced in Figure 8b.

If it is imagined that grammage variations are measured in accordance with the invention on a paper that is completely uniform and smooth (such paper does not exist in practice), all the formation numbers reproduced in Figure 8a would have a numerical value of 0. It will therefore be understood that the lower the numerical values in Figure 8b, the better and more uniform the paper being measured. The formation numbers reproduced in such a figure can also be arranged in tabular form where the wave length interval is stated in mm in one column, and the equivalent formation number = F in a column next to it. If the values presented in Figure 8b are converted to a table, the following is obtained: X (mm) F 0,4-30 1,94 0,4-3 0,978 3-30 1,67 0,4-0, 5 0,336 0,5-1 0,559 1-2 0,57 2-4 0,635 4-8 0,842 8-16 1,04 16-32 0,941 It is easily understood that different types of paper have differing uniformity as regards the grammage variation. It is therefore in the first place of value to study and compare the formation numbers in one and the same type of paper, such as, for example, photo-copying paper or cable paper. In this case measurements of paper from the same

paper machine are of great value, but during different shifts and/or different days, and even measurements of how paper produced in one factory is in comparison with that produced in competitors'factories.

Finally, we would like to mention that as far as we know no other measuring method exists for determining grammage variations in relatively thick sheet material such as material having a grammage exceeding 120 g/m2, that enables reproduction of measuring results as shown in Figures 8a and 8b of this patent application.