METHOD FOR ALIGNING A PLURALITY OF LASER LINES

Abstract

A method includes aligning a plurality i of juxtaposable laser lines in order to form a continuous overall laser line suitable for heat treating a planar substrate capable of being made to move rectilinearly in a first direction, each laser line being formed by a module that emits a laser line onto the surface S of the planar substrate, on which surface a heat treatment is capable of being carried out.

Claims

1. A method for aligning a plurality i of juxtaposable laser lines in order to form a continuous overall laser line suitable for heat treating a planar substrate capable of being made to move rectilinearly in a first direction, each laser line being formed by a module that emits a laser line onto the surface S of the planar substrate, on which surface a heat treatment is capable of being carried out, said method comprising the following steps: a. acquiring, for each laser line: the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first direction, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles made by the laser line to the axes X, Y, Z, respectively; b. computing, with a computer, the intensity profile I.sub.i for each laser line depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i using an intensity function defined beforehand; c. computing, with a computer, the linear-power-density profile P.sub.G corresponding to the sum of the intensities I.sub.i integrated along the axis X for every point along the axis Y; d. computing, with a computer, the width profile E corresponding to the width of the sum of the intensity profiles I.sub.i along the axis X for every point along the axis Y; e. comparing, with a computer, the values of the linear-power-density profile P.sub.G and of the width profile E to two target values defined beforehand, .sub.P and .sub.E, respectively; f. iterating steps b to e with a new set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i defined so that in each iteration the values of the intensity profile P.sub.G and of the width profile E converge toward the target values .sub.P and .sub.E, respectively; g. adjusting each of the i modules depending on the set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i thus obtained.

2. The aligning method as claimed in claim 1, wherein the intensity function for the computation of the intensity profile I.sub.i, for each laser line, is a function of Gaussian profile.

3. The aligning method as claimed in claim 1, wherein the intensity function for the computation of the intensity profile I.sub.i, for each laser line, is a function of flat-top profile.

4. The aligning method as claimed in claim 3, wherein the function of flat-top profile comprises, as parameters, a minimum beam width comprised between 10 m and 500 m, a flat-top length comprised between 1 cm and 300 cm and an edge steepness comprised between 1 mm and 10 mm.

5. The aligning method as claimed in claim 1, wherein the width of each of the intensity profiles I.sub.i along the axis X is the full width at half maximum.

6. The aligning method as claimed in claim 1, that wherein the intensity function comprises a shape function modeling the geometric shape of the laser line.

7. The aligning method as claimed in claim 6, wherein the shape function is a polynomial Bezier curve defined by at least four control points, two of the four of which points correspond to the two ends of the laser line.

8. The aligning method as claimed in claim 7, wherein the polynomial Bezier curve comprises four control points, two control points of which are randomly chosen to lie at a distance from each end respectively comprised between 10% and 20% of the total length, and at an angle with respect to the axis of the line comprised between 0.1 and +0.1.

9. The aligning method as claimed in claim 1, wherein the values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i of step f are defined using the least-squares method.

10. A computer program containing instructions for executing the steps of a method as claimed in claim 1.

11. A non-transitory computer-readable storage medium on which a computer program containing instructions for executing the steps of a method as claimed in claim 1 is stored.

12. A device for aligning a plurality i of juxtaposable laser lines in order to form a continuous overall laser line suitable for heat treating a planar substrate capable of being made to move rectilinearly in a first direction, each laser line being formed by a module that emits a laser line onto the surface S of a planar substrate, on which surface a heat treatment is capable of being carried out, said device comprising the following modules: a. a module for acquiring, for each laser line: values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first direction, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles of rotation of the laser line about the axes X, Y, Z, respectively; b. a module for computing the intensity profile I.sub.i for each laser line depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, Wt using an intensity function defined beforehand; c. a module for computing the linear-power-density profile P.sub.G corresponding to the sum of the intensities I.sub.i integrated along the axis X for every point along the axis Y; d. a module for computing the width profile E corresponding to the width of each of the intensity profiles I.sub.i along the axis X for every point along the axis Y; e. a module for comparing the values of the linear-power-density profile P.sub.G and of the width profile E to two target values defined beforehand, .sub.P and .sub.E, respectively; f. a module for adjusting each of the i modules depending on the set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i thus obtained.

13. The aligning device as claimed in claim 12, further comprising an observing device that is movable along the axis Y being arranged in the place of the planar substrate so that a focal plane of the observing device corresponds to the plane that would be defined by the surface S of said planar substrate if it was present.

14. The aligning device as claimed in claim 13, further comprising a module for graphically displaying the power and width profiles P.sub.G and E.

15. A process for manufacturing a planar substrate comprising a coating heat treated with juxtaposable laser lines forming a continuous overall laser line, said process comprising: i) a step in which a planar substrate comprising a coating capable of being heat treated is provided; ii) a step of aligning the juxtaposable laser lines using a method as claimed in claim 1; and iii) a step of heat treating the coating using the continuous overall line formed by the laser lines thus aligned.

16. A method for simulating alignment of a plurality i of juxtaposable laser lines in order to form a continuous overall laser line, the method comprising: a. a step of simulating a plurality i of modules each emitting a laser line onto the surface S of a planar substrate capable of being made to move rectilinearly in a first direction; b. a step of generating, for each laser line, the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles of rotation of the laser line about the axes X, Y, Z, respectively; each of the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i being generated randomly in an interval of values defined beforehand; c. a step of aligning the juxtaposable laser lines using a method as claimed in claim 1; d. a step of graphically representing the continuous overall laser line thus simulated.

17. A device for simulating alignment of a plurality i of juxtaposable laser lines in order to form a continuous overall laser line, comprising: a. a module for simulating a plurality i of modules each emitting a laser line onto the surface S of a planar substrate capable of being made to move rectilinearly in a first direction; b. a module for generating, for each laser line, the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first direction, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles of rotation of the laser line about the axes X, Y, Z, respectively; each of the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i being generated randomly in an interval of values defined beforehand; c. a device for aligning the juxtaposable laser lines using a method as claimed in claim 1; d. a module for graphically representing the continuous overall laser line thus simulated.

Description

[0099] The features and advantages of the invention are illustrated by the figures and examples described below.

[0100] FIG. 1 is a schematic representation of an illustrative example of a process for heat treating a planar substrate capable of being made to move rectilinearly, using four juxtaposable laser lines, each laser line being formed by a module that emits a laser line onto the surface S of the planar substrate, on which surface a heat treatment is capable of being carried out.

[0101] FIG. 2 is a graphical representation, taking the form of a chart, of the aligning method of the invention.

[0102] FIG. 3 is a graphical representation of four juxtaposable and non-aligned laser lines formed on a planar substrate.

[0103] FIG. 4 is a graphical representation of the linear-power-density profile P.sub.G along the axis X for every point along the axis Y for the four laser lines of FIG. 3.

[0104] FIG. 5 is a graphical representation of the width profile E corresponding to the full width at half maximum of each of the intensity profiles I.sub.i along the axis X for every point along the axis Y, for all of the four laser lines of FIG. 3.

[0105] FIG. 6 is a graphical representation, taking the form of a chart, of one embodiment of the aligning method of the invention.

[0106] FIG. 7 is a schematic representation of a first embodiment of an aligning device of the invention.

[0107] FIG. 8 is a schematic representation of a second embodiment of an aligning device of the invention.

[0108] FIG. 9 is a graphical representation, taking the form of a chart, of a process for manufacturing a planar substrate comprising a coating heat treated by juxtaposable laser lines forming a continuous overall laser line.

[0109] FIG. 10 is a graphical representation, taking the form of a chart, of the simulating method of the invention.

[0110] FIG. 11 is a graphical representation of the four laser lines of FIG. 3 and of the power and width profiles P.sub.G and E along the axis X for every point along the axis Y after an alignment using the aligning method of the invention.

[0111] FIG. 1 schematically shows an illustrative example of a process 100 for heat treating a planar substrate 101 capable of being made to move rectilinearly, using four juxtaposable laser lines 105a-d, each laser line 105a-d being formed by a module 103 that emits a laser line 105a-d onto the surface S 102 of the planar substrate 101, on which surface a heat treatment is capable of being carried out. In this example, for the sake of simplification, a single laser module 103 has been shown. There are generally as many laser lines as there are laser modules.

[0112] The aligning method of the invention is graphically represented, in the form of a chart, in FIG. 2. The method for aligning a plurality i of juxtaposable laser lines in order to form a continuous overall laser line suitable for heat treating a planar substrate capable of being made to move rectilinearly in a first direction, each laser line being formed by a module that emits a laser line onto the surface S of the planar substrate, on which surface a heat treatment is capable of being carried out, comprises the following steps: [0113] a. acquiring E200, for each laser line: [0114] the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; [0115] the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles made by the laser line to the axes X, Y, Z, respectively; [0116] b. computing E201, with a computer, the intensity profile I=f(X().sub.i, Y().sub.i, Z().sub.i, U().sub.i, V().sub.i, W().sub.i) for each laser line depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i using an intensity function defined beforehand; [0117] c. computing E202, with a computer, the linear-power-density profile P.sub.G corresponding to the sum P.sub.G=.sub.iI.sub.i of the intensities I.sub.i integrated along the axis X for every point along the axis Y; [0118] d. computing E203, with a computer, the width profile E=L(I.sub.i) corresponding to the width of the each of the intensity profiles I.sub.i along the axis X for every point along the axis Y; [0119] e. comparing E204, with a computer, the values of the linear-power-density profile P.sub.G and of the width profile E to two target values defined beforehand, .sub.P and .sub.E, respectively; [0120] f. iterating I206 steps b to e with a new set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V, W.sub.i E205 defined so that in each iteration the values of the linear-power-density profile P.sub.G and of the width profile E converge toward the target values .sub.P and .sub.E, respectively; [0121] g. adjusting E206 each of the i modules depending on the set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i thus obtained.

[0122] In step E203, the function L(I) computes the width of each of the intensity profiles I.sub.i along the axis X for every point along the axis Y.

[0123] FIG. 3 graphically shows four juxtaposable and non-aligned laser lines 150a-d formed on a planar substrate 102. Each of the lines differs from the other lines in its intensity profile I.sub.i, its shape and its coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i.

[0124] FIG. 4 is a graphical representation of the linear-power-density profile 400, P.sub.G .sub.i I.sub.i, i.e of the sum of the intensities I.sub.i along the axis X for every point along the axis Y for the four laser lines of FIG. 3. The horizontal lines 401a and 401b represent the thresholds at 5% about the target value up. The target value is here set to 1 because the intensities I.sub.i have been normalized.

[0125] FIG. 6 shows the width profile E 500 corresponding to the full width at half maximum of each of the intensity profiles I.sub.i along the axis X for every point along the axis Y, for the four laser lines of FIG. 3. The horizontal lines 501a and 501b represent thresholds at 10% about the target value .sub.E.

[0126] One embodiment of the method of the invention is shown in FIG. 6. The method comprises the following steps: [0127] a. the acquisition E200, for each laser line, comprises the following substeps: [0128] i. observing E200a the laser lines; [0129] ii. measuring E200b: [0130] the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; [0131] the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles made by the laser line to the axes X, Y, Z, respectively; [0132] b. computing E201, with a computer, the intensity profile I.sub.i for each laser line depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i using an intensity function of flat-top profile defined beforehand; step E201 comprises the following substeps: [0133] i. computing E201a the coordinates x, y, z using the formula

[00006]$\left(\begin{array}{c}{x}^{}\\ y^{}\\ z^{}\end{array}\right)=R_X\left({U.Math.{(}^{})}_i\right).Math.R_Y\left({V.Math.{(}^{})}_i\right).Math.R_Z\left({W.Math.{(}^{})}_i\right).Math.\left(\begin{array}{c}x\\ y\\ z\end{array}\right)+\left(\begin{array}{c}{X.Math.{(}^{})}_i\\ {Y.Math.{(}^{})}_i\\ {Z.Math.{(}^{})}_i\end{array}\right)$ [0134] where R.sub.X, R.sub.Y et R.sub.Z are the rotation matrices about the axes of the coordinate system X, Y, Z for the Euler angles U().sub.i, V().sub.i, W().sub.i, respectively; [0135] ii. computing E201b the intensities I.sub.i using the formula:

[00007]$I_i\left(x^{},y^{},z^{}\right)=\frac{\sqrt{}}{\sqrt{2}.Math.w_0.Math.\sqrt{1+{\left(\frac{z.Math..Math.}{Z_R}\right)}^2}}.Math.\frac{1}{1+e^{\left(\left|y.Math..Math.\right|-l\right)/a}}.Math.e^{-\frac{2.Math.{\left(x.Math..Math.-F_0\left(y.Math..Math.\right)\right)}^2}{w_0^2\left(1+{\left(\frac{z.Math..Math.}{Z_R}\right)}^2\right)}}$ [0136] c. computing E202, with a computer, the linear-power-density profile P.sub.G=.sub.iI.sub.i integrated along the axis X for every point along the axis Y; [0137] d. computing E203, with a computer, the width profile E corresponding to the full width at half maximum E=LMH(I.sub.i) of the each of the intensity profiles I.sub.i along the axis X for every point along the axis Y; [0138] e. comparing E204, with a computer, the values of the linear-power-density profile P.sub.G and of the width profile E to two target values defined beforehand, .sub.P and .sub.E, respectively; [0139] f. iterating I206 steps b to e with a new set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i E205 defined so that in each iteration the values of the linear-power-density profile P.sub.G and of the width profile L converge toward the target values .sub.P and .sub.E, respectively; [0140] g. adjusting E206 each of the i modules depending on the set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i thus obtained.

[0141] A first embodiment of a device of the invention is schematically shown in FIG. 7. The device for aligning a plurality i of juxtaposable laser lines in order to form a continuous overall laser line suitable for heat treating a planar substrate capable of being made to move rectilinearly in a first direction, each laser line being formed by a module that emits a laser line onto the surface S of the planar substrate, on which surface a heat treatment is capable of being carried out, comprises the following modules: [0142] a. a module 700 for acquiring, for each laser line: [0143] the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; [0144] the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles of rotation of the laser line about the axes X, Y, Z, respectively; [0145] b. a module 701 for computing the intensity profile I.sub.i for each laser line depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i using an intensity function defined beforehand; [0146] c. a module 702 for computing the linear-power-density profile P.sub.G corresponding to the sum of the intensities I.sub.i integrated along the axis X for every point along the axis Y; [0147] d. a module 703 for computing the width profile E corresponding to the width of each of the intensity profiles I.sub.i along the axis X for every point along the axis Y; [0148] e. a module 704 for comparing the values of the linear-power-density profile P.sub.G and of the width profile E to two target values defined beforehand, .sub.P and .sub.E, respectively; [0149] f. a module 706 for adjusting each of the i modules depending on the set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i thus obtained.

[0150] The acquiring module 700 comprises a device 700b for observing the laser lines. This observing device, which is movable along the axis Y, is arranged in the place of the planar substrate so that its focal plane corresponds to the plane that would be defined by the surface S of said planar substrate if it was present. In the figure, for the sake of simplicity, the observing device 700b has been placed beside the substrate.

[0151] The observing device 700b transmits images coded in binary form to a processing sub-module 700a using a telecommunication means 700c. The sub-module 700a processes the transmitted images so as to acquire the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i of each of the laser lines. The coordinates are then transmitted to the module 701 by any suitable telecommunication means 705. Advantageously, the telecommunication means 705 may be a single means used to transmit binary digital information between all the modules.

[0152] The computing modules 701 to 703 and the comparing module 704 are computers comprising one or more central processing units. The adjusting module 706 comprises a processing unit 706a, for example a computer, allowing instructions to be communicated to the holders of the laser modules 103 so as to adjust them depending on the computed sets of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i. The spatial coordinates of the laser modules are computed depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i using a operation for changing coordinate system.

[0153] The instructions are communicated using a suitable telecommunication means 706b. Advantageously, the adjusting module may comprise a display device 707 allowing information to be communicated to an operator in a human-readable format. Examples of information are the power and width profiles P.sub.G and E and information relating to the number and to the length of the laser lines.

[0154] FIG. 8 is a schematic representation of a second embodiment of a device of the invention. In this embodiment, the modules 701 to 704 and the sub-modules 700a and 706a are virtual modules instantiated in the form of objects by a computer program or a software package on the basis of classes in the random-access memory, optionally assisted by a virtual memory, of a computer 802. The computer may comprise a plurality of central processing units, storage media and input-output interfaces. It advantageously comprises telecommunication means 801 and 803 for communicating with the acquiring and adjusting modules. A display device 804 equipped with a graphical interface and in communication with the computer 802 may be advantageous for displaying information to an operator.

[0155] FIG. 9 shows in the form of a chart a process for manufacturing a planar substrate comprising a coating heat treated by juxtaposable laser lines forming a continuous overall laser line.

[0156] The process for manufacturing a planar substrate comprising a coating heat treated by a plurality i of juxtaposable laser lines in order to form a continuous overall laser line suitable for heat treating the planar substrate capable of being made to move rectilinearly in a first direction, each laser line being formed by a module that emits a laser line onto the surface S of the planar substrate, on which surface the heat treatment is carried out, comprises: [0157] a. a step E900 in which a planar substrate comprising a coating capable of being heat treated is provided; [0158] b. a step E200 of acquiring, for each laser line: [0159] the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; [0160] the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles made by the laser line to the axes X, Y, Z, respectively; [0161] c. a step E201 of computing, with a computer, the intensity profile I.sub.i=f(X().sub.i, Y().sub.i, Z().sub.i, U().sub.i, V().sub.i, W().sub.i) in two dimensions X, Y projected into the plane Z=0 for each laser line depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i using an intensity function defined beforehand; [0162] d. a step E202 of computing, with a computer, the linear-power-density profile P.sub.G corresponding to the sum of the intensities I.sub.i integrated along the axis X for every point along the axis Y; [0163] e. a step E203 of computing, with a computer, the width profile E corresponding to the full width at half maximum E=LMH(I.sub.i) of each of the intensity profiles I.sub.i along the axis X for every point along the axis Y; [0164] f. a step E204 of comparing, with a computer, the values of the linear-power-density profile P.sub.G and of the width profile E to two target values defined beforehand, .sub.P and .sub.E, respectively; [0165] g. iterating I206 steps b to e with a new set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i E205 defined so that in each iteration the values of the linear-power-density profile P.sub.G and of the width profile E converge toward the target values .sub.P and .sub.E, respectively; [0166] h. a step E206 of adjusting each of the i modules depending on the set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i thus obtained; [0167] i. a step E901 of heat treating the coating using the continuous overall line formed by the laser lines thus aligned.

[0168] FIG. 10 is a graphical representation, in the form of a chart, of the simulating method of the invention. The method for simulating the alignment of a plurality i of juxtaposable laser lines in order to form a continuous overall laser line comprises: [0169] a. a step E11000 of simulating a plurality i of modules each emitting a laser line onto the surface S of a planar substrate capable of being made to move rectilinearly in a first direction; [0170] b. a step E1001 of generating, for each laser line, [0171] the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i of the centre of the laser line, the axes X and Y being located in the plane of the surface S, the axis X corresponding to said first direction, the axis Y corresponding to a second direction perpendicular to the first, and the axis Z corresponding to a third direction perpendicular to the plane of the surface S; [0172] the values of the coordinates U.sub.i, V.sub.i, W.sub.i, corresponding to the angles of rotation of the laser line about the axes X, Y, Z, respectively; [0173] each of the values of the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i being generated randomly in an interval of values defined beforehand; [0174] c. a step E201 of computing, with a computer, the intensity profile I=f(X().sub.i, Y().sub.i, Z().sub.i, U().sub.i, V().sub.i, W().sub.i) in two dimensions X, Y projected into the plane Z=0 for each laser line depending on the coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i using an intensity function defined beforehand; [0175] d. a step E202 of computing, with a computer, the linear-power-density profile P.sub.G corresponding to the sum of the intensities I.sub.i integrated along the axis X for every point along the axis Y; [0176] e. a step E203 of computing, with a computer, the width profile E corresponding to the full width at half maximum E=LMH(I.sub.i) of each of the intensity profiles I.sub.i along the axis X for every point along the axis Y; [0177] f. a step E204 of comparing, with a computer, the values of the linear-power-density profile P.sub.G and of the width profile E to two target values defined beforehand, .sub.P and .sub.E, respectively; [0178] g. iterating I206 steps b to e with a new set of values X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i E205 defined so that in each iteration the values of the linear-power-density profile P.sub.G and of the width profile E converge toward the target values .sub.P and .sub.E, respectively; [0179] h. a step E1002 of graphically representing the continuous overall laser line thus simulated.

[0180] FIG. 11 is a graphical representation of the four laser lines of FIG. 3 and of the power and width profiles P.sub.G and E for every point along the axis Y after an alignment using the aligning method of the invention. The four juxtaposable laser lines 150a-d are aligned on the planar substrate 102. The linear-power-density profile P.sub.G.sub.iI.sub.i 400 of the intensities I.sub.i along the axis X for every point along the axis Y is located in the middle of the horizontal lines 401a and 401b representing the thresholds at 5% around the target value .sub.P, which is set to 1. The width profile E 500 along the axis X for every point along the axis Y is located in the middle of the horizontal lines 501a and 501b representing the thresholds at 10% about the target value .sub.E.

Example

[0181] Four juxtaposable laser lines were aligned according to the aligning method of the invention. The length of each laser line was 400 mm. FIG. 3 shows these four unaligned lines on a planar substrate.

[0182] The surface of the substrate represents the plane XY of the coordinate system X, Y, Z. The origin of the axes X and Y is indicated in FIG. 3. The origin of the axis Z is on the surface of the substrate. The coordinates X.sub.i, Y.sub.i, Z.sub.i, U.sub.i, V.sub.i, W.sub.i of each of the laser lines 105a-105d before alignment are given in table 1 below. The choice of the origin of the coordinate system is a question of convention and depends on the configuration of the installation in which the aligning method is implemented. In the present example, the origin is arbitrarily defined.

[0183] FIGS. 4 and 7 respectively show the power and width profiles P.sub.G and E for all of the four laser lines and every point along the axis Y. The intensity profile I.sub.i of each of the laser lines is calculated using the flat-top function:

[00008]$I\left(x,y,z\right)=\frac{\sqrt{}}{\sqrt{2}.Math.w_0.Math.\sqrt{1+{\left(\frac{z}{Z_R}\right)}^2}}.Math.\frac{1}{1+e^{\left(\left|y\right|-l\right)/a}}.Math.e^{-\frac{2.Math.{\left(x-F_0\left(y\right)\right)}^2}{w_0^2\left(1+{\left(\frac{z}{Z_R}\right)}^2\right)}}$

[0184] The length of the peak, l, is set to 400 mm, the steepness of the edges, a, is 5.5 and the minimum width of the beam w.sub.0 is 60 m. The quantity Z.sub.R is the Rayleigh length. It is computed using the relationship

[00009]$Z_R=\frac{.Math.w_0^2}{.Math.M^2}$

where is the wavelength of the laser beam, and M.sup.2 is a factor characterizing the divergence of the beam. The factor M.sup.2 is characteristic of the laser line. The values of A and M.sup.2 are 1.00 m and 2.5, respectively.

[0185] The shape function F.sub.0 is a polynomial Bezier curve defined by four control points. Two control points correspond to the two ends of the laser line, and the two other control points are randomly chosen to lie at a distance from each end respectively comprised between 10% and 20% of the total length, and at an angle with respect to the axis of the line comprised between 0.1 and +0.1.

[0186] For each laser line, the intensity profile I.sub.i is simply obtained by calculating the function I(x, y, z) where x, y, z are the spatial coordinates obtained after transformation according to the formula:

[00010]$\left(\begin{array}{c}{x}^{}\\ y^{}\\ z^{}\end{array}\right)=R\left(\begin{array}{c}x\\ y\\ z\end{array}\right)+T$

[0187] Where T is the translation matrix defined by

[00011]$T=\left(\begin{array}{c}{X}_i\\ Y_i\\ Z_i\end{array}\right)$

and R is the translation matrix R=R.sub.X(U.sub.i)R.sub.Y(V.sub.i)R.sub.Z(W.sub.i) in which R.sub.X, R.sub.Y and R.sub.Z are the rotation matrices about the axes of the coordinate system X, Y, Z for the Euler angles U.sub.i, V.sub.i, W.sub.i, respectively.

[0188] Each intensity profile I.sub.i was normalized to 1 in order to simplify the computation of the power profiles P.sub.G.

[0189] The target values .sub.P and .sub.L for the linear-power-density profile P.sub.G and the width profile L are set to 1.0 and 60 m, respectively. The tolerance thresholds are 5% and 10% respectively.

[0190] The coordinates after alignment are indicated in table 1. The continuous overall laser line, the power profile P.sub.G along the axis X for every point along the axis Y and the width profile L along the axis X for any point along the axis Y are graphically shown in FIG. 12.

[0191] This example clearly shows that the aligning method of the invention allows a set of juxtaposable laser lines to be aligned so as to form a continuous overall line with a linear-power-density profile P.sub.G and width profile E that are constant for every point along the axis Y according to the target values .sub.P and .sub.E defined beforehand in the interval of the tolerance thresholds.

TABLE-US-00001 TABLE 1 105a 105b 105c 105d Before alignment X(mm) 0.1 0.03 0.06 0.01 Y(mm) 204.7 600.37 1000.42 1396.83 Z(mm) 7.85 5.96 7.73 6.74 U() 0.04 0.07 0.18 0.05 V() 0 0 0 0 W() 0.03 0.04 0.03 0.01 After alignment X(mm) 0.11 0.17 0.11 0.13 Y(mm) 204.7 604.87 1004.58 1404.33 Z(mm) 0.05 0.06 0.03 0.04 U() 0 0.01 0.02 0.01 V() 0 0 0 0 W() 0 0 0 0