KR101628947B1 - Laser processing method with focus finding function - Google Patents

Abstract

The present invention relates to a laser beam source, a laser beam emitted from the laser beam source, a diffraction element for passing the axial beam and diffracting the non-axial beam, a beam for separating the axial beam and the non- A light focusing unit for focusing a transmission beam onto an object to be processed; a light receiving unit for receiving a laser beam reflected from the object and passing through the light focusing unit and the beam splitter, for measuring a change in the profile of the laser beam according to a positional change of the object; A laser processing apparatus including a profiler is provided.

Description

TECHNICAL FIELD [0001] The present invention relates to a laser processing method having a focus measuring function,

The present invention relates to a laser processing apparatus capable of measuring a focus position of an object to be processed and a laser processing method using the same.

Various laser processing methods such as forming grooves on the surface of the object by irradiating the object with laser or forming a denatured layer inside the object or changing the material properties by applying heat to the object are used. However, in most cases, since the laser processing apparatus and the laser apparatus for focus measurement are separately provided, the overall system configuration becomes complicated, and the equipment cost increases.

The present invention relates to a laser processing apparatus capable of measuring a focus position of an object to be processed by using a processing laser without having a separate laser system for focus measurement and adjusting a focus position of the object to be processed in a constant manner during processing, Laser processing method.

According to a first aspect of the present invention, there is provided a laser irradiation apparatus comprising a laser light source, a diffraction element for passing an axial beam among laser beams emitted from the laser light source, diffracting a non-axial beam, A beam splitter for splitting the transmission beam into a reflection beam and a transmission beam, a light focusing unit for focusing the transmission beam onto an object to be processed, and a laser beam reflected by the object and passing through the light focusing unit and the beam splitter, There is provided a laser processing apparatus including a beam profiler for measuring a profile change of a laser beam in accordance with a change in position.

At this time, the light focusing unit may be a focusing lens.

At this time, the light focusing unit may be an optical scanner.

The laser processing apparatus may further include a blocking plate disposed between the diffraction element and the light focusing unit to block a part of the reserved beam.

At this time, two or more of the blocking plates may be disposed between the diffraction element and the beam splitter.

At this time, the blocking plates may be arranged in the up, down, left, and right directions with respect to the diffraction element.

According to a second aspect of the present invention, there is provided a laser processing apparatus comprising: a laser light source for emitting a P-polarized laser beam; a 1/4 wave plate for generating a phase difference to convert a part of the P- A beam splitter for separating the P wave and the S wave emitted from the birefringent element into a reflected beam and a transmitted beam, respectively, a beam splitter for passing the P wave and the S wave, And a beam profiler for receiving a laser beam reflected by the object to be processed and passing through the focusing lens and the beam splitter and for measuring a change in profile of the laser beam according to a change in position of the object, Is provided.

A laser machining method using a laser machining apparatus according to the first aspect of the present invention is characterized by comprising a first step of passing an axial beam among the laser beams and diffracting a non-axial beam in the diffractive element, A second step of measuring a change in diameter of the axial beam and a stock beam image according to a positional change of an object, a step of processing the first object with the axial beam to calculate a change in the processing line width according to a positional change of the first object, A fourth step of selecting, as a focus position, a position of the first object to be processed at which the machining line width is minimized; a fourth step of selecting, as the focus position, And a fifth step of setting a position of the stock beam image as a reference position and a fifth step of positioning a second object to be processed at the focus position, Wherein the laser processing method for processing the second object to be processed while a sixth step of measuring the degree to which the beam axis and the location of the reserved image beam deviates from the reference position is provided.

In this case, the laser processing method may further include a seventh step of moving the light focusing unit to adjust the position of the axial beam and the stock beam image to reach the reference position.

At this time, the reference position may be the center point coordinates of the axial beam and the reserved beam image.

At this time, the reference position may be a gap between the axial beam image and the stock beam image.

According to the embodiments of the present invention, it is possible to accurately measure the focus position of an object to be processed by using a processing laser without having a separate laser apparatus for focus measurement, and at the same time, the object can be adjusted so as to maintain the focus position during processing . As a result, the entire configuration of the laser processing apparatus can be simplified, and the manufacturing cost can be reduced.

1 is a schematic view of a laser machining apparatus according to a first embodiment of the present invention. FIG. 1 (a) shows a process of selecting a focus position, (b) And the focus position is reset by moving the light focusing unit.
Fig. 2 is a process flow chart showing a laser processing method using the laser processing apparatus shown in Fig. 1. Fig.
Fig. 3 is a schematic view showing the shape of the machining groove according to the position of the first object in the second step shown in Fig. 2. Fig.
4 is a graph showing a change in the processing line width according to the positional change of the first object in the second step shown in Fig.
FIG. 5 is a diagram showing a coordinate change of a diffracted beam image displayed on the beam profiler in steps (a) to (c) of FIG.
FIG. 6 is a view showing a change in the interval between the axial beam image and the stock beam image displayed in the beam profiler in the steps (a) to (c) of FIG. 1;
7 is a perspective view showing a diffraction element and a shield plate of a laser processing apparatus according to a first modification of the present invention.
8 is a schematic view of a laser processing apparatus according to a second modification of the present invention.
FIG. 9 is a graph showing a change in the interval between the axial beam and the stock beam image on the beam profiler according to the distance change between the light scanner and the object shown in FIG.
10 is a schematic view of a laser processing apparatus according to a second embodiment of the present invention.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings, which will be readily apparent to those skilled in the art to which the present invention pertains. The present invention may be embodied in many different forms and is not limited to the embodiments described herein. In order to clearly illustrate the present invention, parts not related to the description are omitted, and the same or similar components are denoted by the same reference numerals throughout the specification.

FIG. 1 is a schematic view of a laser machining apparatus according to a first embodiment of the present invention. FIG. 1 (a) shows a process of selecting a focus position, (b) And the focus position is reset by moving the focusing unit.

1, the laser machining apparatus 100 of the first embodiment includes a laser light source 10, a beam splitter 20, a light focusing unit 30, a beam profiler 40, A diffraction element 90 and a blocking plate 62.

The laser light source 10 generates a laser beam. The laser beam is a working laser beam used for actual processing of the object 50. [ The diffraction element 90 is located on the path of the laser beam, and the axial beam (0th order diffracted beam) is passed straight through, while the non-axial beam (± n th order diffracted beam, n is a natural number) is diffracted.

The beam splitter 20 separates the axial beam and the non-axial beam through the diffraction element 90 into a reflection beam and a transmission beam, respectively. The axial beam passed by the diffraction element 90 is shown by a solid line, the diffracted non-axial beam is shown by a dotted line, and the reflected beam of the beam splitter 20 is shown by a one-dot chain line. On the other hand, in the present invention, the pillar beam is shown only up to the + 1st-order diffraction beam (diffracted to the upper portion of the axial beam) and the -1st diffraction beam (diffracted to the lower portion of the axial beam).

The laser beam generated by the laser light source 10 may be in a random polarization state in which the electromagnetic field vector of the output energy does not have a constant direction with time. In this case, the axial beam passing through the diffraction element 90 can have a larger beam diameter than the diffracted non-axial beams. In the present invention, the object 50 is processed using the axial beam.

The light focusing unit (30) is located on the path of the transmission beam and focuses the transmission beam onto the object to be processed (50). The transmission beam irradiated on the object to be processed 50 is reflected from the surface of the object to be processed 50 and is provided to the beam splitter 20 again via the light focusing part 30. And the divided beams from the beam splitter 20 are provided to the beam profiler 40. [

In the first embodiment of the present invention, a focusing lens is used as the light focusing unit 30, but the scope of the present invention is not necessarily limited thereto. The light focusing unit 30 may include various May be an optical focusing means.

The beam profiler 40 is a light receiving sensor incorporating a plurality of charge coupled devices (CCDs), and measures the profile of the provided laser beam. At this time, the object to be processed 50 can be moved so as to change its distance from the light focusing unit 30, and the size of the laser beam reaching the beam profiler 40 is changed in accordance with the change of the position of the object 50. The beam profiler 40 measures changes in the beam profile (diameter) as the position of the object 50 changes.

The blocking plate 62 is disposed between the diffraction element 92 and the light focusing section 30. [ The blocking plate 62 moves in a direction perpendicular to the irradiation direction of the axial beam to block some of the stocking beam. Two or more of the blocking plates 62 may be disposed between the diffraction element 92 and the beam splitter 20 or between the beam splitter 20 and the light focusing section 30. [

Fig. 2 is a process flow chart showing a laser processing method using the laser processing apparatus shown in Fig. 1. Fig.

Referring to FIGS. 1 and 2, a laser machining method includes a first step (S10) of passing an axial beam in a laser beam and diffracting a non-axial beam in a diffraction element 90, A second step S20 of measuring the change in diameter of the axial beam and the stock beam image according to the change of the position of the object 51 and the second step S20 of processing the first object 51 with the axial beam, A third step S30 for measuring a change in the processing line width in accordance with a change in position, a fourth step S40 for selecting a position of the first object to be processed 51 having the minimum processing line width as the focus position L_Focus, A fifth step S50 of setting the position of the axial beam and the stock beam image on the beam profiler 40 as a reference position when the first object to be processed 51 is at the focus position L_Focus, (52) is arranged at the focus position (L_Focus) and the second object (52) is machined by the shaft beam, the axial beam A sixth step (S60) of measuring the degree to which the position of the image deviates from the reference position, and a seventh step (S70) of adjusting the position of the axial beam and the stock beam image to reach the reference position by moving the light focusing unit (30) .

The object to be processed 50 is an actual product to be processed. The object 50 of the present invention may be a structure in which a step or a slope is formed on a surface to be processed before processing. On the other hand, the object to be processed 50 may include the first object 51 and the second object 52. The first object to be processed 51 may be a specimen and the second object 52 may be a product in which actual processing is performed. The focus position L_Focus and the reference position are obtained by using the first object 51 and then the focus position L_Focus or the reference position is obtained again for the plurality of second objects 52, Processing can be performed. The above-described laser processing method can be applied when the magnification of the focusing lens is known.

More specifically, in the first step S10, the first object to be processed 51 is mounted on the laser processing apparatus. Then, a laser beam is emitted from the laser light source 10 toward the diffraction element 90, and the diffraction element 90 causes the axis beam to pass straight through the laser beam, but diffracts the stock beam as shown in FIG.

In the second step S20, the change in diameter of the diffracted beam image is measured in the beam profiler 40 while the position of the first object 51 is changed as shown in Fig. 1 (a). The beam profiler 40 is connected to a data storage unit (not shown) and transmits measurement data to the data storage unit. At this time, the axis beam is a laser beam whose output is reduced, and is reflected from the surface of the first object to be processed 51 without processing the first object to be processed 50.

On the other hand, as the position of the first object to be processed 51 changes, the diameter of the axial beam and the stock beam image reaching the beam profiler 40 changes. The diameter of the axial beam and the stock beam image becomes larger as the first object 51 is positioned ahead of the focus position L_Focus with respect to the focus position L_Focus and as the position is located behind the focus position L_Focus, And the diameter of the stock beam image is reduced. The focus position L_Focus of the first object to be processed 51 can not be known in the first step S10 even when the magnification of the light focusing unit 30 is determined.

The first object to be processed 51 is processed several times by irradiating the first object 51 with an axial beam while changing the position of the first object 51 in the third step S30. Then, a plurality of machining grooves formed by the axial beams are formed in the first object to be machined 51. The width (machining line width) and the sectional shape of the machining grooves vary depending on the position of the first object to be machined 51.

Fig. 3 is a schematic view showing the shape of the machining groove according to the position of the first object in the second step shown in Fig. 2. Fig.

3 (a) shows a case where the first object to be processed 51 is ahead of the focus position, and (b) shows a case where the first object to be processed 51 is in the focus position. (C) shows a case where the first object to be processed 51 is located behind the focus position. As the first object to be processed 51 is closer to the focus position, the machining groove 55 has a small line width and a deep and sharp sectional shape. 3 (b), the minimum machining line width is denoted by d_min.

4 is a graph showing a change in the processing line width according to the positional change of the first object in the second step shown in Fig.

3 and 4, the measured line width has a minimum value when the first object to be processed 51 is at the focus position L_Focus of the light converging unit 30, and the larger the distance from this position . ≪ / RTI >

In the fourth step S40, the position at which the machining line width becomes minimum is selected as the focus position F_Focus using the data of the machining line width measured in the third step S30. The data storage unit stores the focus position L_Focus.

FIG. 5 is a view showing a coordinate change of a diffracted beam image displayed on the beam profiler in the steps (a) to (c) of FIG. 1, FIG. 5 is a diagram showing a change in the interval between the axial beam image and the stock beam image displayed in the profiler. FIG.

In the fifth step S50, the position of the axial beam and the stock beam image on the beam profiler 40 is measured when the first object 51 is in the focus position L_Focus. The beam profiler 40 stores the position information in a data storage unit (not shown). The stored position information is set to the reference position in accordance with the focus position L_Focus of the first object 51. [

At this time, the position information of the axial beam and the stock beam image may be coordinate information as shown in FIG. 5 (a). In FIG. 5A, the reference coordinates can be set to P1 (a, b) which is the center point coordinate of the axial beam image and P2 (c, d) and P3 (e, f) which are the center point coordinates of the stock beam image.

On the other hand, the positional information of the axial beam and the stock beam image may be the spacing information between the axial beam image and the stock beam image as shown in FIG. 6 (a). In FIG. 6 (a), the reference interval can be set to an interval (focus diameter, D_Focus) between the axial beam image and the stock beam image reaching the beam profiler 40.

In the sixth step S60, after the first object to be processed 51 is removed from the laser processing apparatus, the second object to be processed 52 is mounted, and the laser beam is emitted from the laser light source 10.

At this time, the second object to be processed 52 can be directly mounted on the first focus position L_focus, and even if the second object 52 is mounted at an arbitrary position, The beam profile is measured and the position of the second object 52 is adjusted so that the position of the axial beam and the stock beam image is at the reference position so that the second object 52 finally reaches the first focus position L_focus Lt; / RTI >

Thereafter, when the second object to be processed 52 is moved as shown in Fig. 1 (b) while the second object 52 is being processed with the axial beam, the distance between the light focusing part 30 and the second object 52 And the second object to be processed 50 deviates from the focus position L_Focus. At this time, the degree of deviation of the axial beam and the stock beam image on the beam profiler 40 from the reference position is measured by machining the axial beam.

At this time, the blocking plate 62 blocks the + 1st-order diffracted beam in the reserved beam when the second object 52 moves downward with respect to the irradiation direction of the axial beam, The -1st diffracted beam can be blocked. This makes it easier to distinguish the axial beam and the stock beam image displayed on the beam profiler 40.

According to the present invention, as the second object 52 moves upward, the blocking plate 62 blocks the -1st-order diffracted beam so as to be placed on the beam profiler 40 as shown in Figs. 5 (b) and 6 Only the + 1st-order diffracted beam image is displayed in the stock beam image, but this image can be displayed differently by changing the blocking target of the blocking plate 62 in accordance with the moving direction of the second object 52.

 On the other hand, the extent to which the axial beam and the stock beam image on the beam profiler 40 are deviated from the reference position due to the machining of the axial beam is determined on the basis of the coordinates (c ', d') on the beam profiler 40, , Or may be displayed as an interval (D'_Focus) as shown in FIG. 6 (b).

In the seventh step S70, the light focusing unit 30 is moved as shown in Fig. 1 (c) so that the positions of the axial beam and the stock beam image are adjusted to reach the reference position. 1C, the light focusing unit 30 is retracted toward the beam splitter 20 so that the second object to be processed 52 is moved to the focus position L_Focus As shown in Fig.

At this time, the coordinates of the axial beam image on the beam profiler 40 are plotted as P1 (a, b) as shown in FIG. 5 (c) The interval between images is regressed to D_Focus as shown in 6 (c). The diameter of the axial beam and the stock beam image at this time is the same as the diameter of the axial beam and the stock beam image when the second object 52 is in the focus position L_Focus.

5 and 6, the present invention is not limited to the case where a step is formed on the surface to be processed of the second object to be processed 52, It can be applied to any number of cases.

Especially, when the inclination is formed on the surface to be processed of the second object 52, the degree of deviation of the coordinate of the axial beam image from the reference coordinate is mainly measured according to the movement of the second object 52, The same effect as when the step is formed on the surface to be processed of the second object to be processed 52 can be obtained.

As described above, according to the laser machining apparatus 100 and the method of the present embodiment, the laser beam is irradiated onto the object to be processed 50, (L_Focus) can be accurately measured and the object 50 can be adjusted to maintain the focus position L_Focus even during processing. As a result, the entire configuration of the laser processing apparatus 100 can be simplified, and the manufacturing cost can be reduced.

7 is a perspective view showing a diffraction element and a shield plate of a laser processing apparatus according to a first modification of the present invention.

Referring to Fig. 7, the laser machining apparatus 200 of the first modified example is similar to the laser machining apparatus of the first modification except that the shielding plate blocks the remaining stock beams except one of the stock beams radiated by the diffraction element 90 in three dimensions And has the same configuration as that of the first embodiment described above. The same reference numerals are used for the same members as in the first embodiment.

A slit 91 may be formed in the center of the diffractive element 90. The slit 91 is capable of diffracting the axial beam of the laser beam emitted from the laser light source 10 straightly, while allowing the stock beam to radiate in the three-dimensional direction toward the axial direction of the axial beam (x-axis direction in FIG. 7).

Two or more of the blocking plates 62 may be disposed between the diffraction element 90 and the beam splitter. The blocking plate 62 may be disposed apart from the diffraction element 90 and the beam splitter. In the first modified example, the blocking plate 62 is arranged in the direction of the image 62a, 62b, 62c and 62d with respect to the slit 91 when viewed from the x-axis in Fig. And can block the stockpile emitted in each direction.

That is, the upper shielding plate 62a shields the reserved beam emitted above the x-axis on the xz plane, and the lower shielding plate 62b shields the reserved beam irradiated below the x-axis on the xz plane from the left shielding plate 62c Can shield the reserved beam which has been radiated to the left of the x axis on the xy plane and the right blocking plate 62d can block the reserve beam which has been radiated to the right side of the x axis on the xy plane.

In the first modification, for example, when the object to be processed moves in the y-axis direction, the other shield plates except for the right shield plate 62d are used to block the stockpiles respectively and to radiate rightward from the x- It is possible to prevent two or more stock beam images from being displayed on the beam profiler on three dimensions.

However, it should be understood that the movement of the blocking plates is not necessarily limited as shown in FIG. 7, and that the operation of the blocking plates may be varied depending on the moving direction of the object to be processed.

With the first modification, it is possible to easily distinguish the axial beam and the stock beam image even when the object to be processed and the light focusing part of the first embodiment described above are moved three-dimensionally.

That is, in FIG. 1, when the object 50 and the light focusing unit 30 are two-dimensionally moved, the blocking plate 62 is used to distinguish the axial beam and the stock beam image displayed on the beam profiler The laser machining apparatus 200 of the first modification cuts off the pivot beams emitted on three dimensions by using the shield plates on the upper side 62a, the lower side 62b, the left side 62c and the right side 62d There is an advantage in that it is easy to distinguish the axial beam and the stock beam image displayed on the beam profiler even when the object to be processed and the light focusing part move three-dimensionally.

8 is a schematic view of a laser processing apparatus according to a second modification of the present invention.

Referring to Fig. 8, the laser processing apparatus 300 of the second modification uses an optical scanner as the light focusing unit 30 and an object to be processed 54, which is formed with a curved surface inclination on the surface to be processed The same as the first embodiment described above. In FIG. 8, the configuration of the first embodiment is shown as a basic configuration, and the same reference numerals are used for the same members as in the first embodiment.

FIG. 9 is a graph showing a change in the interval between the axial beam and the stock beam image on the beam profiler according to the distance change between the light scanner and the object shown in FIG.

The laser machining apparatus 300 of the second modification irradiates an axial beam and a stock beam to the object to be processed 54 through the optical scanner of the light focusing unit 30, On the beam profiler 40, the change in the spacing between the axial beam and the stock beam is proportional to each other as shown in FIG.

As described above, in the second modification, the scale parameter, which is a slope of the graph of FIG. 9, is calculated by the data calculator (not shown) and can be additionally stored in the data storage unit (not shown) The focus position L_Focus that has been reset in accordance with the positional change of the laser processing device 54 can be sampled, and the focus measuring and machining precision of the laser processing device 300 can be enhanced.

10 is a schematic view of a laser processing apparatus according to a second embodiment of the present invention.

10, the laser machining apparatus 400 of the second embodiment is configured such that the laser beam polarized by the P wave in the laser light source 10 is oscillated and the quarter wave plate (quarter) is used in place of the diffraction element 90 of the first embodiment. wave plate 80 has the same configuration as that of the first embodiment except that a birefringence element 60 is added between the quarter wave plate 80 and the beam splitter 20 . In FIG. 10, the configuration of the first embodiment is shown as a basic configuration, and the same reference numerals are used for the same members as those of the first embodiment.

The 1/4 wave plate 80 generates a phase difference (90-degree phase delay) with the P-polarized laser beam to change a part of the P-polarized laser beam to S-wave.

The P-wave and the S-wave emitted from the 1/4 wave plate 80 are incident on the birefringent element 60 as shown in FIG. The birefringent element 60 uses the phase difference between laser beams to pass a P wave and refract S wave as shown in FIG. At this time, in the second embodiment, the passed P wave can be used as the working axial beam and the refracted S wave can be used as the measuring stock pile beam.

The birefringence element 60 of the second embodiment may be formed in a trapezoidal shape as shown in FIG. 10, and the degree of refraction of the S wave may vary depending on the acute angle? Of the birefringent element 60 and the length d of the base line It can be different. That is, the second embodiment can control the interval between the P wave and the S wave emitted from the birefringent element 60 by adjusting the acute angle? Of the birefringent element 60 and the length d of the base.

The P wave and the S wave emitted from the birefringent element 60 are irradiated to the object 50 through the beam splitter 20 and the light focusing section 30 as in the first embodiment and then reflected from the object 50 And is displayed on the beam profiler 40 through the beam splitter 20.

On the beam profiler 40, a P wave is displayed at the position of the axial beam image and an S wave is displayed at the position of the stock beam image, respectively, as shown in Fig. 5 (a). In the second embodiment, the output of the P wave and the S wave can be adjusted by diffracting the quarter wave plate 80 and adjusting the incident angle of the laser beam. The output of the S wave can be adjusted to an appropriate level according to the reflectivity of the beam splitter 20 or the object 50. [

As described above, the laser machining apparatus 400 of the second embodiment can increase the intensity of the laser beam reaching the beam profiler 40 compared with the above-described embodiments, It is possible to measure the diameter of the image of the phase laser beam (P wave and S wave) more accurately.

While the present invention has been shown and described with reference to certain preferred embodiments thereof, it will be understood by those of ordinary skill in the art that various changes and modifications may be made without departing from the spirit and scope of the following claims. Those skilled in the art will readily understand.

100, 200, 300, 400: laser processing device
10: Laser light source
20: Beam splitter
30: light focusing part
40: beam profiler
50, 51, 52, 54: object to be processed
55: machining groove
60: birefringent element
62 (62a, 62b, 62c, 62d): a shield plate
80: 1/4 wavelength plate
90: diffraction element
91: slit

Claims (11)

delete delete delete delete delete delete delete A laser beam source, a diffraction element for passing the machining axis beam among the laser beams emitted from the laser beam source, for diffracting the focus-use non-axis beam, the axis beam and the reserve beam emitted from the diffraction element as a reflection beam and a transmission beam, respectively A shielding plate disposed between the diffraction element and the light focusing unit for shielding a part of the stocking beam, and a shield plate for reflecting the light beam reflected by the object to be processed, And a beam profiler for receiving a laser beam passed through the focusing section and the beam splitter and measuring a change in the profile of the laser beam in accordance with a change in the position of the object,
Passing the axial beam among the laser beams in the diffractive element and diffracting the non-axial beam;
A second step of measuring a change in diameter of the axial beam and the stock beam image according to a positional change of the first object in the beam profiler;
A third step of processing the first object with the shaft beam and measuring a change in the processing line width in accordance with the positional change of the first object;
A fourth step of selecting, as a focus position, a position of the first object to be processed whose line width is minimum;
Setting a position of the axial beam and the reserved beam image on the beam profiler as a reference position when the first object is in the focus position; And
A sixth step of arranging a second object to be processed at the focus position and measuring the degree of deviation of the position of the axial beam and the stored beam image from the reference position while processing the second object with the axial beam,
. 9. The method of claim 8,
And adjusting the position of the axial beam and the reserved beam image to reach the reference position by moving the light focusing unit
Further comprising the steps of: 9. The method of claim 8,
Wherein the reference position is the center point coordinate of the axial beam and the reserved beam image. 9. The method of claim 8,
Wherein the reference position is an interval between the axial beam image and the stock beam image.

Images