Method for designing and manufacturing a diffraction element

Abstract

This method for designing a diffractive element uses a computer to design a diffractive element that performs phase modulation so that emitted light emitted in a first electric field distribution from an emission surface of a diffractive element (10) is condensed in a range between a first distance and a second distance from the diffractive element (10) on a straight line orthogonal to the emission surface, said method comprising: a step for determining an electric field distribution on the emission surface with respect to a spherical wave condensed at a prescribed point in a range on the straight line; a step for calculating a first electric field distribution on the emission surface of the diffractive element (10) by summing the electric field distribution on the emission surface with respect to the spherical wave in said range while taking into account variation in the phase of light in the light propagation direction; and a step for determining the depth of unevenness in the surface of the diffractive element (10) on the basis of the first electric field distribution.　The present invention can thereby provide a method for designing a diffractive element whereby machining, rust removal, and the like can be performed with high precision using emitted light, even for an object that has depth.

Description

[Technical field]

[0001] The present invention relates to a method for designing and manufacturing a diffraction element used for laser processing, rust removal, and the like. [Background technology]

[0002] Laser processing devices are used in a wide range of applications, such as cutting, welding, and printing metals and resins, and removing rust from metals. In these laser processing devices, the part that performs scanning of the emitted light, the so-called head unit, is an issue to be addressed in terms of size and weight reduction. In response to this, attempts have been made to use a diffractive optical element (DOE, hereinafter referred to as "diffractive element" or "DOE") in the head unit of the laser processing device.

[0003] In particular, a kinoform is a diffraction element that only modulates the optical phase and does not change the optical intensity, and here, an example having a concave-convex structure on the surface of a substrate will be described.

[0004] 8 shows a schematic diagram of an optical system in which an image is formed using a conventional diffraction element 40. Light incident on the diffraction element 40 (arrow 1 in the figure indicates the incident direction) exits from the exit surface P0 of the diffraction element 40, and the exiting light from the diffraction element 40 (arrow 2 in the figure indicates the exit direction) is focused (imaged) on the imaging surface P1.

[0005] Here, P0 and P1 are planes, and P0 and P1 are parallel to each other. The x-axis, y-axis, and z-axis in the figure are the axes of a Cartesian coordinate system, and the origin of the coordinates is on P0. The z-axis is the optical axis, and roughly coincides with the direction in which the light emitted from the DOE 40 travels. The x-axis and y-axis are perpendicular to the z-axis, and the xy plane is parallel to the P0 and P1 planes. In other words, the z-axis is perpendicular to the P0 and P1 planes. u0 and u1 in the figure represent the electric field distributions on P0 and P1, respectively.

[0006] If the z coordinate on P0 is z0=0 and the z coordinate on P1 is z1, the relationship between u0 and u1 is expressed by equation (1) from Kirchhoff's diffraction integral equation (see, for example, Non-Patent Document 1).

[0007]

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[0008] where (x0, y0, z0) and (x1, y1, z1) are the coordinates of points on P0 and P1, j is the imaginary unit, λ is the wavelength of light, and g(·) is the propagation function of light emitted from a point, and is expressed by equations (2) to (4).

[0009]

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[0010]

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[0011]

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[0012] Here, j is the imaginary unit and k is the wave number of light. Here, (1+cosθ) / 2 is the inclination factor, which indicates the output angle dependency of the electric field intensity at each point on the image plane from the DOE output surface to each point.

[0013] Since the right-hand side of equation (1) is the convolution integral of u0 and g, when both sides of equation (1) are Fourier transformed, it is expressed as equation (5).

[0014]

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[0015] Here, U1, U0, and G are the Fourier transforms of u1, u0, and g, respectively, and u and v represent spatial frequencies in the x-axis and y-axis directions, respectively.

[0016] From equation (5), U0 is expressed by equation (6).

[0017]

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[0018] By performing an inverse Fourier transform on both sides of equation (6), u0 can be derived as shown in equation (7).

[0019]

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[0020] However, F[·] and F -1 [·] represent the Fourier transform and inverse Fourier transform, respectively.

[0021] In this way, by specifying the electric field distribution u1 on the imaging plane P1, it is possible to calculate the electric field distribution u0 on the DOE exit plane P0.

[0022] Next, a method for designing the unevenness to be formed on the surface of the DOE 40 using the electric field distribution u0 on the DOE emission surface P0 will be described.

[0023] Here, the DOE 40 is a transmissive type, and is a rectangular dielectric material having a uniform refractive index distribution. The uneven shape on the DOE 40 is formed on one side of the rectangular dielectric material, and has a shape in which square or rectangular pixels are arranged in a grid pattern.

[0024] Light is incident on the surface on which the irregularities are formed or on the surface opposite thereto, and is emitted from the surface opposite the incident surface. In such a DOE 40, the electric field distribution u0 on the DOE emission surface P0 is formed by the thickness of the dielectric material in each pixel (the optical path length from the entrance surface to the exit surface). Here, a case where the DOE performs only phase modulation without amplitude modulation of the electric field (kinoform) will be described.

[0025] 9 shows the relationship between the thickness of the transmissive DOE 40 and the phase of light at the DOE exit surface 42. The internal refractive index of the DOE is n1, and the external refractive index of the DOE is n0 (1 in air). The step of the unevenness on the surface of the DOE 40 is d, and the DOE 40 in optical path A43 is thinner than the DOE 40 in optical path B44 by the step (thickness) d. Point b is a point on the optical axis of the DOE exit surface 42 of the optical path B44, and point a is the intersection of the plane including the exit surface 42 of the optical path B44 and the optical axis of the optical path A43. The dotted line in the figure indicates an equiphase surface 45 between the optical paths A43 and B44.

[0026] As shown in FIG. 9, when a plane wave is incident (in the direction of arrow 46), the phase difference Δφ at point a when the phase at point b is taken as the reference (=0) is expressed by equation (8).

[0027]

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[0028] Here, k1 and k0 are the wave numbers of the light inside and outside the DOE 40, respectively, λ1 and λ0 are the wavelengths of the light inside and outside the DOE 40, respectively, and λ is the wavelength of the light in a vacuum.

[0029] Solving equation (8) for d gives equation (9).

[0030]

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[0031] If the light incident on DOE entrance surface 41 is a plane wave, the phase at DOE exit surface 42 is determined by the amount of depression (step difference between concave and convex) d from DOE exit surface 42. The phase difference Δφ of u0 can be expressed by the argument arg(u0) of u0, and is therefore expressed by equation (10).

[0032]

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[0033] Here, since u0 varies on the xy plane, the amount of depression (step difference between the projections and recesses) from the DOE emission surface 42 is expressed as d(x, y).

[0034] If the thickness from the DOE entrance surface 41 to the DOE exit surface 42 (the reference thickness of the DOE 40) is L0, the thickness L(x, y) of the DOE 40 is expressed by equation (11).

[0035]

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[0036] Here, arg(u0) is usually in the range 0~2π or -π~+π, so d is 0~λ / (n1-n0) or -λ / [2(n1-n0)]~+λ / [2(n1-n0)], respectively.

[0037] Since -jλ included in u0 expressed by equation (7) is a constant, u0' shown in equation (12) may be used instead of u0 expressed by equation (7).

[0038]

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[0039] [Non-Patent Document 1] Joseph W. Goodman, "Introduction to Fourier Optics Second Edition", McGROW-HILL Companiews Inc., 1996, pp. 32-53. Summary of the Invention [Problem to be solved by the invention]

[0040] However, in the above-mentioned method of designing the unevenness to be formed on the surface of the DOE, the only imaging surface for which the electric field generated by the DOE can be designed is P1, and the emission range of the light on the DOE exit surface P0 that forms the bright spot on the image surface P1 is the entire DOE exit surface, so it is not possible to design the diameter of the bright spot on image surface P1 to maintain the desired length in the optical axis direction.

[0041] Therefore, when a diffraction element designed by the above-mentioned method is used for laser processing, rust removal, etc., the beam diameter cannot be maintained when the focus of the beam shifts in the optical axis direction, which causes a problem in that the accuracy of the laser processing, rust removal, etc. decreases. [Means for solving the problem]

[0042] In order to solve the above-mentioned problems, the design method of a diffraction element of the present invention is a method for designing, using a computer, a diffraction element that performs phase modulation so that exit light emitted from the exit surface of the diffraction element with a first electric field distribution is focused in a range between a first distance and a second distance from the diffraction element on a line perpendicular to the exit surface, and includes a step of determining an electric field distribution on the exit surface for a spherical wave that is focused at a predetermined point in the range on the line, a step of calculating the first electric field distribution on the exit surface of the diffraction element by adding up the electric field distributions on the exit surface for the spherical wave in the range, taking into account that the phase of light changes in the propagation direction of light, and a step of determining a depth of unevenness on the surface of the diffraction element based on the first electric field distribution.

[0043] Furthermore, a design method for a diffraction element according to the present invention is a method for designing a diffraction element using a computer, which performs phase modulation so that output light emitted from an output surface of the diffraction element with a first' electric field distribution is imaged with a second light intensity distribution on an imaging surface that is perpendicular to a line orthogonal to the output surface and is located in a range between a first distance and a second distance from the diffraction element, and includes the steps of: calculating a second electric field distribution having an intensity that is the positive square root of the second light intensity distribution; determining an electric field distribution on the output surface for a spherical wave that is focused at a predetermined point in the range on the line; calculating a first electric field distribution on the output surface of the diffraction element by adding up the electric field distributions on the output surface for the spherical wave in the range, taking into account that the phase of light changes in the propagation direction of light; calculating a first electric field distribution on the output surface of the diffraction element by convolving the second electric field distribution and the first electric field distribution; and determining a depth of unevenness on the surface of the diffraction element based on the first electric field distribution. Effect of the Invention

[0044] According to the present invention, it is possible to provide a method for designing and manufacturing a diffraction element that can maintain the diameter and power of the emitted light at a predetermined length in the propagation direction of the light, and can perform processing, rust removal, etc. with high precision using the emitted light on an object with depth. [Brief description of the drawings]

[0045] [Figure 1] FIG. 1 is a diagram for explaining a method of designing a diffraction element according to a first embodiment of the present invention. [Diagram 2] FIG. 2 is a flow chart for explaining a method of designing a diffraction element according to the first embodiment of the present invention. [Diagram 3] FIG. 3 is a diagram for explaining a method of designing a diffraction element according to the second embodiment of the present invention. [Figure 4A] FIG. 4A is a diagram for explaining the effect of the method for designing a diffraction element according to the second embodiment of the present invention. [Figure 4B]FIG. 4B is a diagram for explaining the effect of the method for designing a diffraction element according to the second embodiment of the present invention. [Diagram 5] FIG. 5 is a flow chart for explaining a method of designing a diffraction element according to the third embodiment of the present invention. [Figure 6A] FIG. 6A is a diagram for explaining the effect of the method for designing a diffraction element according to the third embodiment of the present invention. [Figure 6B] FIG. 6B is a diagram for explaining the effect of the method for designing a diffraction element according to the third embodiment of the present invention. [Figure 7] FIG. 7 is a diagram for explaining the effect of the method for designing a diffraction element according to the fourth embodiment of the present invention. [Figure 8] FIG. 8 is a diagram for explaining a conventional method for designing a diffraction element. [Figure 9] FIG. 9 is a diagram for explaining a conventional method for designing a diffraction element. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0046] <First embodiment> A method for designing and manufacturing a diffraction element according to a first embodiment of the present invention will be described with reference to FIGS.

[0047] The diffraction element 10 in this embodiment is a so-called kinoform, which does not perform amplitude modulation of the electric field but only phase modulation.

[0048] In the design method of the diffraction element 10 according to the present embodiment, two points on the z axis (z α and z β ), an electric field distribution u0 (first electric field distribution) on the exit surface P0 of the DOE that focuses (images) light between the exit surface P0 and the DOE is determined, and the surface structure (concave-convex structure) of the diffraction element 10 is designed. Here, the z axis of the xyz coordinate system is perpendicular to the DOE exit surface P0.

[0049] 1 shows a schematic diagram of an optical system in which an image is formed using a diffraction element 10 in this embodiment. Light incident on the diffraction element 10 (arrow 1 in the figure indicates the incident direction) is emitted from an exit surface P0 of the diffraction element 10, and the exiting light from the diffraction element 10 (arrow 2 in the figure indicates the exit direction) is incident on two points on the z axis (z α and z β ) and is focused as an emission line 3_1. Here, the light emitted from the DOE has a first electric field distribution u0.

[0050] Here, the x, y, and z axes represent the respective axes of a Cartesian coordinate system, and the DOE output surface P0 is parallel to the xy plane.

[0051] By the way, if the coordinates of a point on the image plane parallel to the DOE exit surface P0 are (x1, y1, z1), and the coordinates of a point on the DOE exit surface are (x0, y0, z0), and the electric field distribution u1 on the image plane is a δ function δ(x-x1, y-y1), that is, if we assume that there is a bright spot at coordinates (x1, y1, z1), then according to formula (1), the electric field distribution u0 on the DOE exit surface for the point with coordinates (x0, y0, z0) is proportional to -jλ·1 / g(x1-x0, y1-y0, z1-z0)·Exp[±j2π(x1x0+y1y0) / {λ(z1-z0)}]. Here, Exp[ξ]=e ξ Since -jλ is a constant, it can be more simply said that u0 is proportional to 1 / g(x1-x0, y1-y0, z1-z0)·Exp[±j2π(x1x0+y1y0) / {λ(z1-z0)}]. The reason u0 is this way is that if you replace u0 on the right-hand side of equation (1) with the above equation, the right-hand side of equation (1) becomes the Fourier transform of a function where all values ​​on the plane are 1. The result of such a Fourier transform is a δ function.

[0052] From this, when there is a bright spot at a certain point (0, 0, z1) on the z-axis shown in FIG. 1, the electric field on the exit surface of the DOE is proportional to 1 / g(-x0, -y0, z1-z0).

[0053] Regarding g(·), since the origin of the x, y, and z axes is on the exit surface of the DOE, z0 = 0, and according to equation (3), only the absolute value of the argument of g is valid, regardless of whether it is positive or negative, g(-x0, -y0, z1-z0) can be written as g(x0, y0, z1).

[0054] Therefore, the electric field distribution u on the DOE exit surface that forms a bright spot centered on a point (0, 0, z1) on the z axis 0、z1 (x0, y0) is expressed by equation (13).

[0055]

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[0056] Here, r and cos θ are expressed by equations (14) and (15).

[0057]

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[0058]

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[0059] From equation (13), z on the z axis α From z β The electric field u0(x0, y0) on the exit surface of the DOE when a set of bright spots (bright line) 3_1 is focused between them is approximated by equation (16).

[0060]

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[0061] In equation (16), u 0、z e multiplied by (x0, y0) -jkz represents the change in phase of the bright spot on the z axis as light propagates along the z axis. That is, e -jkz represents the phase of the bright spot on the z-axis.

[0062] As shown in equation (16), u0 is z on the z axis. α From z β The electric field is the sum of all the electric field distributions on the DOE exit surface of the entire spherical wave that is focused between the two. Here, the spherical wave is from the origin (0,0,0) of the xyz coordinate system to (0,0,z α ) direction. (1+cosθ) / 2 is the inclination factor, which indicates the output angle dependency from the DOE output surface to each point in the electric field intensity at each point on the image plane.

[0063] Thus, in the design method for the diffraction element 10 according to this embodiment, as shown in FIG. 2, first, the electric field distribution on the exit surface for a bright spot in a spherical wave focused at a predetermined distance (range) from the exit surface of the diffraction element 10 is calculated (step S11).

[0064] Next, within a given range (z α ~z β ), the electric field distribution on the emission surface for each bright point of the spherical wave is integrated (added up) taking into account that the phase of the light changes in the light propagation direction to calculate a first electric field distribution u0(x0, y0) (step S12).

[0065] In the case where θ≈0 can be considered in equation (16), cosθ=1 may be set, and u0(x0, y0) may be calculated as shown in equation (17).

[0066]

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[0067] Here, √(x0 2 +y0 2 ) << z, then rz ~ (x0 2 +y0 2 ) / (2z), so u0(x0, y0) may be calculated as shown in equation (18).

[0068]

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[0069] Furthermore, r ~ In the case of z, it is expressed by equation (19).

[0070]

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[0071] The integrand function on the right-hand side of equations (17) to (19) (the equation in the integral) has the phase of a spherical wave. Therefore, by focusing only on the phase, u0(x0, y0) may be calculated as follows:

[0072]

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[0073]

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[0074] By the way, if we continue the integration calculation of the right side of equation (19), we get equation (20).

[0075]

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[0076] Here, Ci(t) is the integral cosine function, and Si(t) is the integral sine function, which are expressed by equations (21) and (22).

[0077]

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[0078]

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[0079] Here, γ (=0.57721...) is Euler's constant and "!" is the symbol for factorial. The expression in Σ on the right-hand side of equations (21) and (22) has a denominator expressed as a factorial and a numerator expressed as a power, so as p increases, the value of the expression in Σ decreases. Therefore, Ci'(t) and Si'(t) shown in equations (23) and (24) may be substituted for Ci(t) and Si(t) in equation (20).

[0080]

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[0081]

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[0082] Here, p Ci_max andp Si_max is an integer of 2 or more and is determined appropriately by the user. Ci_max andp Si_max For example, a predetermined magnitude ε Ci and ε Si Determine p that satisfies equations (25) and (26). Ci_max andp Si_max It may also be

[0083]

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[0084]

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[0085] Using the electric field distribution u0(x0, y0) on the DOE exit surface obtained in this manner, the thickness L(x, y) of the DOE 10 is calculated for each coordinate (x0, y0) on the DOE exit surface from equations (27) and (28) (which are the same as equations (10) and (11), respectively), and the surface structure (convex and concave shape) of the DOE (diffraction element) 10 is designed (step S13).

[0086]

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[0087]

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[0088] In this embodiment, two points (z α and z β ), the electric field distribution at the exit surface of the diffraction element is derived based on the integral value of the electric field distribution of the image formed between the diffraction element and the surface structure (concave-convex structure) of the diffraction element is designed, so that the diameter and power of the emission line can be kept approximately equivalent over a predetermined length (range) in the light propagation direction (z direction). Here, "approximately equivalent" includes equivalent, and may be within a range that can realize the precision required for laser processing, rust removal, etc., using a beam. For example, as described below, it is sufficient that the beam diameter is in the range of about 0.1 mm to about 0.4 mm, or the normalized beam power density is within 10 6 About 10 8 m -2 It is sufficient if the normalized beam power is within the range of about 100W. With this normalized beam power, for example, when the total power of the light emitted from the DOE emission surface is about 100W, which is the normally used rust removal laser power, rust removal is possible. Note that the "normalized beam power density" is the beam power density when the total power of the DOE emission light is 1W.

[0089] Although proportional symbols are used in equations (13) to (20), anything can be multiplied to the right hand side of each equation as long as it does not affect the relative intensity or phase within the electric field distribution u0 on the exit surface of the DOE.

[0090] <Method of manufacturing the diffraction element> Based on the surface structure of the DOE designed as described above, the diffraction element 10 is manufactured. The diffraction element 10 is composed of a plate member made of a transparent material such as ZnS or quartz. The designed surface structure of the diffraction element 10 is formed on the surface of the plate member by known microfabrication. In this way, the diffraction element 10 according to the present embodiment is manufactured.

[0091] The diffractive optical element manufactured in this embodiment can maintain the diameter and power of the emitted light within a desired range in the direction of light propagation (z direction), so that objects with depth can be processed and rust removed with high precision using the emitted light (laser light).

[0092] In addition, because the light is diffused outside the range, even if there are people or objects outside the range, the power density of the light is low and injury or damage is unlikely to occur, so safety can be maintained. This has the advantage that light-shielding walls installed around areas where processing, rust removal, etc. are being carried out to improve safety can be made inexpensive, or the installation of light-shielding walls itself becomes unnecessary.

[0093] Furthermore, the diffractive optical element manufactured in this embodiment is small and lightweight (approximately several tens of grams), allowing the head portion of the laser processing device to be made smaller and lighter than conventional mechanisms.

[0094] <Second embodiment> A method for designing and manufacturing a diffraction element according to a second embodiment of the present invention will be described with reference to Fig. 3 to Fig. 4B. Similarly to the first embodiment, the method for designing a diffraction element according to this embodiment will be described with reference to the flow chart shown in Fig. 2.

[0095] In the first embodiment, in order to calculate the electric field distribution u0 on the exit surface of the DOE, integration is used as shown in equations (16) to (20).

[0096] In this embodiment, in order to simplify the calculation of the electric field distribution u0 by a computer, the bright line on the optical axis (z axis) is treated as a plurality of discrete bright points, and the electric field distribution u obtained from each bright point is 0、Zn A method for calculating the electric field distribution u0 (first electric field distribution) on the exit surface of the DOE by summing the above will be described.

[0097] 3 shows a schematic diagram of an optical system in which an image is formed using a diffraction element 10 in this embodiment. Light incident on the diffraction element 10 (arrow 1 in the figure indicates the incident direction) exits from an exit surface P0 of the diffraction element 10, and the exit light from the diffraction element 10 (arrow 2 in the figure indicates the exit direction) is condensed as multiple (N) bright spots 3_2, 1 to 3_2, N on the z axis. Here, the exit light has a first electric field distribution u0.

[0098] Each of the bright points 3_2, 1 to 3_2, N corresponds to N image planes P n (where n = 1 to N, hereinafter, N is an integer of 2 or more.) P n (where n=1 to N) are each a plane, and are parallel to the DOE exit surface (plane) P0. Here, the image plane P n is within a given range (z1 to z N ) will be distributed.

[0099] P n The center coordinates of the bright point on the top are (0, 0, z n ) (where n = 1 to N), then, as in the first embodiment, a point on the z-axis (0, 0, z n The electric field distribution u on the DOE exit surface that forms a bright spot centered on 0、zn (x0, y0) is expressed by equation (29).

[0100]

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[0101] where r n and cosθ n is expressed by equations (30) and (31).

[0102]

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[0103]

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[0104] Using equation (29), the image plane P n The electric field u0(x0, y0) on the exit surface of the DOE where the bright spots on (n=1 to N) are focused is approximated by equation (32).

[0105]

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[0106] As in the first embodiment, in equation (32), u 0、zn e multiplied by (x0, y0) -jkzn represents the change in phase of the bright spot on the z axis as light propagates along the z axis. That is, e -jkzn represents the phase of the bright spot on the z-axis.

[0107] Thus, in the design method for the diffraction element 10 according to this embodiment, as shown in FIG. 2, first, the electric field distribution on the exit surface for bright spots in the spherical wave focused at each of the predetermined distances (N image planes arranged in a predetermined range) from the exit surface of the diffraction element 10 is calculated (step S11).

[0108] Next, the electric field distributions on the exit surface for the bright points of the spherical wave on each of N image planes arranged in a specified range are added up, taking into account that the phase of the light changes in the light propagation direction, to calculate a first electric field distribution u0(x0, y0) (step S12).

[0109] In equation (32), θ n If it can be considered that cosθ is ≒0, similarly to the first embodiment, n = 1, and u0(x0, y0) may be calculated as shown in equation (33).

[0110]

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[0111] √(x0 2 +y0 2 )≪z n In the case of rn -z n ~ (x0 2 +y0 2 ) / (2z n ), so u0(x0, y0) may be calculated as shown in equation (34).

[0112]

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[0113] The expression in Σ on the right-hand side of equations (33) and (34) has the phase of a spherical wave. Therefore, by focusing only on the phase, u0(x0, y0) may be calculated as follows:

[0114]

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[0115]

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[0116] Using the electric field distribution u0(x0, y0) on the DOE exit surface obtained in this manner, the thickness L(x, y) of the DOE 10 is calculated for each coordinate (x0, y0) on the DOE exit surface from equations (27) and (28) in the same manner as in the first embodiment, and the surface structure (convex and concave shape) of the DOE (diffraction element) 10 is designed (step S13).

[0117] Based on the surface structure of the diffraction element 10 designed in this manner, the diffraction element 10 is manufactured in the same manner as in the first embodiment.

[0118] <Effects> The effects of the method for designing and manufacturing a diffraction element according to the present embodiment of the present invention will be described.

[0119] FIG. 4A shows the simulation results of the beam diameter and peak power density (maximum power density) of the light beam light intensity distribution (the square of the electric field intensity).

[0120] In the simulation of the light beam intensity distribution, the range of the bright line was determined, and the electric field distribution u0 on the DOE exit surface was calculated using equation (33'). Using this electric field distribution u0, the light beam intensity distribution at the image formation was calculated based on equation (1).

[0121] Here, the emission line was located on the z-axis at 500 mm±200 mm (z=300 mm to 700 mm) from the exit surface of the DOE.

[0122] The adjacent image plane P used when calculating the electric field distribution u0 on the DOE exit surface n and P n+1 The intervals between the (n=1 to 79,999) were 5 μm. The uneven shape on the DOE 10 was formed on one side of a rectangular dielectric body, and had a shape in which 2048 square pixels of 5 μm each were arranged in a grid pattern.

[0123] In addition, in the simulation of generating a reconstructed image on the imaging plane, there were 13 imaging planes generating the reconstructed image, their z positions were within the range of 200mm to 800mm, and the interval between adjacent imaging planes was 50mm. In other words, the z positions of the imaging planes generating the reconstructed images were 200mm, 250mm, 300mm, 350mm, 400mm, 450mm, 500mm, 550mm, 600mm, 650mm, 700mm, 750mm, and 800mm (brightness line range + / - 100mm).

[0124] For comparison, Figure 4B shows the full width at half maximum and peak power density (maximum power density) of a Gaussian beam when a lens with a focal length of 500 mm is used as the conventional method. The horizontal axis z in the figure indicates the distance from the principal point on the exit side of the lens.

[0125] The incident beam to the diffraction element (DOE) 10 and the lens used in the simulation had a diameter of 5.1 mm (power density was 1 / e of the peak power density). 2 The diameter of the Gaussian beam is

[0126] In the figure, the horizontal axis "distance z" is the distance from the DOE emission surface, and the vertical axis "normalized peak power density" is the peak power density when the total power of the DOE emission light is 1W.

[0127] Also, the "beam diameter" on the vertical axis is usually 1 / e 2 However, since the light beam intensity distribution determined by the electric field distribution u0 on the DOE exit surface in this embodiment is not Gaussian, the full width at half maximum (FWHM) is used.

[0128] In an optical system using conventional lenses, as shown in FIG. 4B, a beam with a diameter of 414 μm or less is maintained only over a length of 136 mm between 432 mm and 568 mm.

[0129] On the other hand, in this embodiment, a beam having a diameter of 414 μm or less is held at a length of 450 mm between 300 mm and 750 mm.

[0130] In this way, according to the design method of this embodiment, it is possible to design a diffraction element 10 that can maintain the beam diameter at a distance approximately three times longer than in an optical system using a conventional lens.

[0131] Regarding the peak power density of the light beam, which is important in rust removal and processing, in an optical system using conventional lenses, the range in which the fluctuation in the maximum power density of the light beam is within two orders of magnitude is the length of 300 mm, from z = 350 mm to 650 mm.

[0132] On the other hand, in this embodiment, the range in which the fluctuation in the maximum power density of the light beam falls within two digits is a length of 500 mm between z=300 mm and 800 mm.

[0133] In this way, according to the design method of this embodiment, it is possible to design a diffraction element 10 that can suppress fluctuations in the maximum power density of the light beam and maintain the maximum power density of the light beam at about 1.7 times that of an optical system using a conventional lens.

[0134] As described above, in this embodiment, the electric field distribution at the exit surface of the diffraction element is derived based on the sum of the electric field distributions on the exit surface of the diffraction element that produce each image on multiple (N) imaging planes arranged in a predetermined range, and the surface structure (convexoconcave structure) of the diffraction element is designed, so that the diameter and maximum power density of the light beam emitted from the diffraction element can be kept approximately equal over a predetermined length (range) in the light propagation direction (z direction).

[0135] Therefore, the diffractive optical element manufactured in this embodiment can maintain the diameter and maximum power density of the emitted light at a desired length in the light propagation direction (z direction), so that objects with depth can be processed and rusted with high precision using the emitted light (laser light), achieving the same effects as the first embodiment.

[0136] In addition, because the light is diffused outside the range, even if there are people or objects outside the range, the power density of the light is low, making it difficult for them to be injured or damaged, and therefore safety can be maintained. This has the advantage that light-shielding walls installed around areas where processing, rust removal, etc. are being carried out to improve safety can be made inexpensively, and the installation of light-shielding walls themselves is no longer necessary.

[0137] <Third embodiment> A method for designing and manufacturing a diffraction element according to the third embodiment of the present invention will be described with reference to FIGS.

[0138] In the first and second embodiments, a DOE that forms an image of a bright spot has been described as an example. In the present embodiment, a DOE that forms a desired image will be described as an example.

[0139] In detail, in the first embodiment, z is z α ~z β (z is z α more than z β The electric field distribution on the exit surface of the DOE in which the light intensity distributions on a plane parallel to P0 in the range of (below) are approximately equal is shown.

[0140] Similarly, in the second embodiment, the image plane P n The electric field distribution on the exit surface of the DOE where each of the light intensity distributions (n=1 to N) is approximately equal is shown.

[0141] In this embodiment, a diffractive element (DOE) 10 that forms an image of a two-dimensional shape on an imaging plane will be described. The diffractive element 10 performs phase modulation on light that is emitted from the emission surface with a first' electric field distribution so that the light has an intensity distribution of a second electric field distribution that corresponds to a desired light intensity distribution on the imaging plane.

[0142] FIG. 5 is a flow chart illustrating a method for designing the diffraction element 10 according to the present embodiment.

[0143] First, the image plane P n The light intensity distribution to be imaged on the (n=1 to N) plane is q(x, y) (i.e., all the image planes P n The light intensity distribution to be imaged on the plane of the y-axis (n=1 to N) is the same q(x, y). The electric field intensity at this time is √q(x, y), and the electric field distribution with this electric field intensity (second electric field distribution) is called u c (x, y) (step S21). c For example, the real part of the electric field is √q(x, y) and the imaginary part is 0, so u c We can also write (x, y) = √q(x, y) + j 0, where j represents the imaginary unit.

[0144] Here, u c The shape represented by (x, y) can also be a bright spot, as shown in the first and second embodiments.

[0145] Next, the electric field distribution on the exit surface of the diffraction element 10 is calculated for a spherical wave that is focused on the z-axis at a predetermined distance from the exit surface (step S22).

[0146] Next, within a given range (e.g., z α ~z β), the electric field distributions on the emission surface for each spherical wave calculated in step S22 are added up, taking into consideration that the phase of the light changes in the light propagation direction, to calculate a first electric field distribution u0(x0, y0) (step S23). Here, "adding up electric field distributions" includes the integration of the electric field distributions in a predetermined range, and refers to calculating the sum of each electric field distribution in the predetermined range.

[0147] Note that steps S22 and S23 are the same as the methods for calculating the electric field distribution u0 on the DOE exit surface in the first and second embodiments, and are calculated using equations (16) to (26), (17'), (18'), (32), (33), (34), (33'), and (34').

[0148] Next, the electric field distribution on the DOE output surface u 0、l (The first' electric field distribution) is expressed as the above first electric field distribution u0(x0, y0) and the second electric field distribution u c The first electric field distribution u0(x0, y0) is calculated by performing a convolution integral with (x, y) (step S24). Here, the first electric field distribution u0(x0, y0) is the electric field distribution on the exit surface of the DOE for a spherical wave focused in a predetermined range on the optical axis.

[0149]

number

[0150] Here, S represents the integration range, which may be the range on the DOE emission surface or the range including the DOE emission surface.

[0151] The electric field distribution u on the exit surface of the DOE obtained in this way 0、l Using (x0, y0), the depth d(x, y) of the irregularities on the surface of the diffraction element 10 is calculated according to equation (36).

[0152]

number

[0153] Here, n1 is the refractive index inside the diffractive element 10, n0 is the refractive index outside the diffractive element 10, λ is the wavelength of the propagating light, arg(u 0、l (x, y) is the electric field distribution u 0、l This is the deviation angle of (x, y).

[0154] Using d(x, y), the thickness L(x, y) of DOE 10 is calculated for each coordinate (x0, y0) on the DOE exit surface according to equation (28), and the surface structure (convex and concave shape) of DOE (diffraction element) 10 is designed (step S25).

[0155] Based on the surface structure of the diffraction element 10 designed in this manner, the diffraction element 10 is manufactured in the same manner as in the first embodiment.

[0156] <Example 1> In this embodiment, a DOE that forms a filled circular image as a desired image will be described as an example.

[0157] In Fig. 6A and B, the electric field distribution u c The simulation results of the beam diameter (FWHM) and peak power density of the light beam intensity distribution at (x, y) are shown. The incident light to the DOE10 is 5.1 mm in diameter (power density is 1 / e of the peak power density). 2 The electric field distribution u0 that generates the bright line was calculated by equation (33'). The range of this bright line is z 300 mm to 700 mm. The light beam light intensity distribution was simulated as described above (Figures 4A and 4B).

[0158] Electric field distribution u c The light intensity distribution q(x, y) of (x, y) was set to 19 circles with diameters between 10 μm and 1600 μm (diameters of 10 μm, 20 μm, 50 μm, and between 100 μm and 1600 μm in increments of 100 μm).

[0159] As shown in FIG. 6A, if the diameter of q(x, y) is 300 μm to 500 μm (300 μm, 400 μm, 500 μm), the beam diameter can be set to 415 μm or less when z is between 250 mm and 750 mm and has a length of 500 mm.

[0160] Moreover, as shown in FIG. 6B, the fluctuation in peak power density can be suppressed to a maximum of about three times.

[0161] In this way, in this embodiment, the electric field distribution u c When (x, y) is circular, the effect of maintaining the beam diameter and peak power density in the optical axis direction is produced.

[0162] <Example 2> In this embodiment, a DOE that forms a line segment image as a desired image will be described as an example.

[0163] FIG. 7 shows the simulation results of the beam diameter and peak power density when a line segment image is formed.

[0164] u c (x, y) is a line segment extending only in the y direction, and is a line segment of ±5 mm from the origin (a line segment of 10 mm length). The incident light to the DOE 10 is a 5.1 mm diameter (power density is 1 / e of the peak power density). 2 The electric field distribution u0 that generates the bright line was calculated using equation (33'). The range of this bright line is z 300mm to 700mm. The simulation was performed with the distance z in the range of 200mm to 800mm.

[0165] As shown in FIG. 7, the beam width (FWHM) is approximately constant in the y-axis direction, being approximately 3 mm in the range of z=600 mm (200 mm to 800 mm). c The reason why the width of the light intensity distribution of the line segment imaged with the length of the line segment represented by (x, y) being 10 mm is as short as 3 mm is because the intensity distribution of the Gaussian beam that is the incident light to the DOE 10 is maintained. (The power density is 1 / e 2For a Gaussian beam with a diameter of 5.1 mm, its FWHM is 3 mm (= 5.1 mm × √(log e 2 / 2))

[0166] In addition, in the x-axis direction, z is maintained at 350 μm or less within a range of 400 mm (300 mm to 700 mm).

[0167] Moreover, the fluctuation of the peak power density is suppressed to a maximum of 5.3 times within a 400 mm length range of z from 300 mm to 700 mm.

[0168] In this way, according to this embodiment, the beam width can be narrowed to suppress fluctuations in peak power density, and a line segment image can be formed.

[0169] According to this embodiment, a line image can be formed, so that when removing rust using a laser, the line image can be scanned perpendicular to the line while irradiating the object to be removed with laser light, thereby effectively removing rust as a surface.

[0170] In the present embodiment, the image has a circular shape and a line segment shape as an example, but is not limited thereto. The image may have another shape.

[0171] As described above, in this embodiment, the electric field distribution at the exit surface of the diffraction element is derived based on the convolution integral of the sum of the electric field distributions on the diffraction element that respectively image each bright point of the bright line within a predetermined range of the straight line passing through the diffraction element (the electric field distribution on the exit surface of the diffraction element that generates the bright line) and electric field distributions of various shapes, and the surface structure (convexoconcave structure) of the diffraction element is designed, so that the diameter and power of the light beam emitted from the diffraction element can be kept approximately equal over a predetermined length (range) in the propagation direction of the light (z direction).

[0172] Therefore, the diffractive optical element manufactured in this embodiment can maintain the diameter and power density of the emitted light at a desired length in the light propagation direction (z direction), so that objects with depth can be processed and rusted with high precision into a variety of shapes using the emitted light (laser light), achieving the same effects as the first embodiment.

[0173] In the embodiment of the present invention, an example has been shown in which the emitted light from the diffraction element is focused in a direction parallel to the optical axis, but the present invention is not limited to this, and the emitted light may be focused on an axis that is not parallel to the optical axis, but is approximately parallel to the optical axis. The term "approximately the same axis" may be used as long as it is within a range that can achieve the accuracy required for laser processing, rust removal, etc., using a beam.

[0174] In an embodiment of the present invention, the diffractive elements are designed using a computer.

[0175] In the embodiment of the present invention, the structure, dimensions, materials, etc. of each component in the configuration and manufacturing method of the diffraction element are shown as examples, but the present invention is not limited to these. Anything that can exhibit the function and effect of the diffraction element can be used. [Industrial Applicability]

[0176] The present invention relates to a design method and a manufacturing method of a diffraction element for a laser processing device, and can be applied to processing and rust removal using laser light. [Explanation of symbols]

[0177] 10 Diffraction element

Claims

1. A method for designing, using a computer, a diffraction element that performs phase modulation so that light emitted from an exit surface of the diffraction element with a first electric field distribution is focused in a range between a first distance and a second distance from the diffraction element on a line perpendicular to the exit surface, the method comprising: determining an electric field distribution on the exit surface for a spherical wave focused at a predetermined point in the range on the straight line; calculating the first electric field distribution on the exit surface of the diffraction element by adding up the electric field distribution on the exit surface for the spherical wave in the range, taking into consideration that the phase of light changes in the propagation direction of the light; determining a depth of the irregularities on the surface of the diffraction element based on the first electric field distribution; A method for designing a diffraction element comprising:

2. A method for designing, using a computer, a diffraction element that performs phase modulation so that light emitted from an exit surface of the diffraction element with a first' electric field distribution is imaged with a second light intensity distribution on a surface that is perpendicular to a line orthogonal to the exit surface and is located in a range between a first distance and a second distance from the diffraction element, the method comprising: calculating a second electric field distribution having an intensity equal to the positive square root of the second light intensity distribution; determining an electric field distribution on the exit surface for a spherical wave focused at a predetermined point in the range on the straight line; calculating a first electric field distribution on the exit surface of the diffraction element by adding up the electric field distribution on the exit surface for the spherical wave in the range, taking into consideration that the phase of light changes in the propagation direction of the light; calculating a first' electric field distribution on the exit surface of the diffraction element by convoluting the second electric field distribution and the first electric field distribution; determining a depth of the irregularities on the surface of the diffraction element based on the first' electric field distribution; A method for designing a diffraction element comprising:

3. The first electric field distribution u ０ (x ０ , y ０ ) is represented by formula (A) 3. The method for designing a diffraction element according to claim 1 or 2. [0010] Here, z α and z β are the two ends of the predetermined range, (1+cosθ) / 2 is the tilt factor, cosθ=z / r, j is the imaginary unit, k is the wave number of light, and r=√(x ０ ２ +y ０ ２ +z ２ ).

4. N imaging surfaces are arranged in the predetermined range, The first electric field distribution u ０ (x ０ , y ０ ) is represented by formula (B) 3. The method for designing a diffraction element according to claim 1 or 2. [0025] Here, z ｎ is the distance within the predetermined range, (1+cosθ) / 2 is the tilt factor, cosθ=z / r, j is the imaginary unit, k is the wave number of light, r ｎ =√(x ０ ２ +y ０ ２ +z ｎ ２ ).

5. N imaging surfaces are arranged in the predetermined range, The first electric field distribution u ０ (x ０ , y ０ ) is represented by formula (C) 3. The method for designing a diffraction element according to claim 1 or 2. [0030] Here, z ｎ is the distance within the predetermined range, j is the imaginary unit, k is the wave number of light, r ｎ =√(x ０ ２ +y ０ ２ +z ｎ ２ ).

6. N imaging surfaces are arranged in the predetermined range, The first electric field distribution u ０ (x ０ , y ０ ) is represented by formula (D) 3. The method for designing a diffraction element according to claim 1 or 2. [0045] Here, z ｎ is the distance within the predetermined range, j is the imaginary unit, k is the wave number of light, r ｎ =√(x ０ ２ +y ０ ２ +z ｎ ２ ).

7. N imaging surfaces are arranged in the predetermined range, The first electric field distribution u ０ (x ０ , y ０ ) is represented by formula (E) 3. The method for designing a diffraction element according to claim 1 or 2. [0050] Here, z ｎ is the distance within the predetermined range, j is the imaginary unit, k is the wave number of light, r ｎ =√(x ０ ２ +y ０ ２ +z ｎ ２ ).

8. N imaging surfaces are arranged in the predetermined range, The first electric field distribution u ０ (x ０ , y ０ ) is represented by formula (F) 3. The method for designing a diffraction element according to claim 1 or 2. [006] Here, z ｎ is the distance within the predetermined range, j is the imaginary unit, and k is the wave number of light.

9. The depth d(x, y) of the irregularities on the surface of the diffraction element is expressed by the formula (G).

9. A method for designing a diffraction element according to claim 1 or any one of claims 3 to 8. [0070] Here, n １ is the internal refractive index of the diffraction element, n ０ is the external refractive index of the diffractive element, λ is the wavelength of the propagating light, arg(u ０ (x, y) is the first electric field distribution u ０ is the deviation angle of (x, y).

10. The depth d(x, y) of the irregularities on the surface of the diffraction element is expressed by the formula (G').

3. The method for designing a diffraction element according to claim 2. [0080] Here, n １ is the internal refractive index of the diffraction element, n ０ is the external refractive index of the diffractive element, λ is the wavelength of the propagating light, arg(u ０、ｌ (x, y) is the first' electric field distribution u ０、ｌ is the deviation angle of (x, y).

11. The method for designing a diffraction element according to any one of claims 1 to 10 is provided. A method for manufacturing a diffraction element comprising the steps of:

Images