JP2008145463A - Elliptic beam shaping optical system and uniformity improving method thereof - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To shape a Gaussian distribution laser beam into an elliptic cross-section beam having homogeneous power. <P>SOLUTION: The elliptic beam shaping optical system comprises: a cylindrical lens Z1 configured to shape the Gaussian beam having a diameter D into the homogeneous beam having an elliptic cross-section (aspect ratio a); an intensity conversion lens Z2 having a focal length L2, disposed at a distance (d) from the lens Z1, configured to shape the Gaussian beam to the homogeneous beam; and an image surface I disposed at a distance (b) from the lens Z2; wherein the minor diameter of the beam at the surface of the lens Z2 made by the cylindrical lens Z1 is D', the composite focal length of the lenses Z1 and Z2 is L, the focal length L2 of the intensity conversion lens Z2 is calculated so as to establish Db=LD', and the elliptic shape formed on the image surface by the lenses having the focal lengths L1 and L2 is obtained, when the aspect ratio does not reach the desired one, L2 is increased within the extent of 2(Db(L1-d))/(D'L1-Db)≥L2≥(Db(L1-d))/(D'L1-Db), the L2 is repeatedly increased until the aspect ratio (a) on the image surface reaches the desired value. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an elliptical beam generating optical system that generates a laser beam having a uniform power density in an elliptical cross section from a laser beam having a Gaussian distribution. Laser processing refers to drilling, heat treatment, cutting, welding, etc. in an object with a laser beam having a strong power density.

  Laser processing uses pulsed light or continuous light such as a carbon dioxide laser or YAG laser depending on the object and purpose. The laser beam has a high power density at the center and a low non-uniform power distribution at the periphery. Actually, there are various distributions, but ideally a Gaussian distribution is used, so the beam from the laser is simply called a Gaussian beam.

  The laser beam may be used as it is (Gaussian beam) for processing, but it may be desired that the power density is uniform within a certain range. If you want to drill a round hole in an object, convert the Gaussian beam to a beam (top hat) with a uniform power density in a circular area that is a lens or diffractive optical component, and then squeeze it with the lens. Irradiate.

  Although it is not very frequent, there are cases where it is desired to drill an elliptical hole in an object. In that case, an elliptical beam with a Gaussian distribution may be sufficient, but depending on the purpose, a laser beam with an elliptical distribution with a uniform power distribution may be required. There is still no means to create a beam with an elliptical cross section with uniform power distribution. There are already several methods for generating laser light with a circular cross section with uniform power distribution. Thus, a method of transforming a beam having a uniform power circular cross section into an elliptical beam by using a mask having an elliptical aperture can be considered, but this is not desirable because a part of the beam power is lost. It would be desirable to convert a circular cross-section Gaussian beam into an elliptically uniform power beam without power loss.

  In order to convert light having a circular cross section into an elliptical cross section, a cylindrical lens may be used. A cylindrical lens is a uniaxial lens. Has the same convex cross section in the axial direction. There is no light collecting property in the axial direction, and there is light collecting property only in the direction perpendicular to the axis. Therefore, a beam having a circular cross section can be converted into an elliptical cross section. However, it is not possible to make an elliptical cross section beam with uniform power distribution.

  There are also lens optical systems and diffractive optical component (DOE) optical systems that convert a Gaussian beam with a circular cross section into a uniform power density (top hat) with a circular cross section. Combining a cylindrical lens and a lens system that converts to a uniform power distribution circular section beam should produce a beam with a uniform elliptical section. But it still has problems.

  A lens optical system that converts a Gaussian beam having a circular section into a uniform power density (top hat) having a circular section has been proposed by various people. For example, there exists a thing like patent document 1. FIG. This is a combination of two aspheric lenses Zh and Zq. FIG. 1 shows a lens system proposed in Patent Document 1 that changes a Gaussian beam into a circular cross-section uniform power distribution. The beam propagation direction is the z direction, and the lens surface is the xy plane.

  Zh is a Gaussian-distributed beam that has a certain intensity within a certain radius Rm, and zero intensity outside that area (it is called a top hat because the intensity distribution resembles a bowler hat). This is called a conversion lens. The intensity conversion lens Zh has a flat front surface, a rear surface having a recess 60 at the center, convex portions 62 and 63 in the middle, and a thickness decreasing surface in the periphery. That is, it has a convex and concave shape. Since it is a lens, it has rotational symmetry with the same shape around the axis. Therefore, the convex portions 62 and 63 are continuous. On the contrary, the rear surface may be flat and the front surface may be convex and concave. Concavities and convexities may be distributed on the front and rear surfaces. This is because the beam is expanded in the central part and the beam is contracted in the peripheral part. Since it is difficult to manufacture with a spherical lens, an aspherical lens is used. Even if it is called an aspherical surface, it has rotational symmetry, and the surface is cut with a blade while rotating the material to create a curved surface.

  With the intensity conversion lens Zh, the incident beam W has a uniform power distribution within a certain radius U, but the phase is distorted. Therefore, it is necessary to align the beam phase and change the beam direction to the axial direction. For this purpose, another lens is provided. That is the phase correction lens Zq. This is a lens having a convex surface 66 near the front central portion, concave portions 64 and 65 at the middle portion, and a flat plate at the peripheral portion. It is cylindrically symmetric and the recesses 64 and 65 are one. This is also difficult to make with a spherical surface, and is an aspherical lens. Let g be the distance between the intensity conversion lens and the phase correction lens. g is called a uniform distance. Zh and Zq are lenses that make a Gaussian-distributed beam with a radius W a uniform power with a radius U. Therefore, the incident Gaussian beam radius W may be referred to as a uniformizable radius W. This is the radius before equalization. On the other hand, the radius after homogenization is referred to as the homogenization radius U. The uniformizable radius W, uniformizing radius U, and uniformizing distance g are important parameters of the intensity conversion lens Zh and the phase correction lens Zq. The radius W of the Gaussian beam is defined as the distance from the center to the place where the intensity is reduced to exp (−2), where the intensity at the center is 1.

  The homogenizer lens in FIG. 1 is an example of W = U. However, W is not necessarily equal to U. Here, the intensity conversion lens Zh converts the Gaussian beam with the radius W into a uniform beam with the radius U, and the phase correction lens Zq changes the uniform beam with the radius U into a phase-in-parallel beam with the radius U. As shown in FIG. 1, the distance g from the intensity conversion lens Zh to the phase correction lens Zq is clearly determined. Even if it is closer or farther than that value, it cannot be converted into a phase-parallel beam by the phase correction lens Zq.

  Light rays included in the Gaussian beam from the laser are indicated by 70 to 82. Since the light rays 70, 71 and 82 incident on the end of the intensity conversion lens Zh are outside the inclination of the convex surfaces 62 and 63, they bend inward at Zh. It reaches the outside of the recesses 64 and 65 of the phase correction lens Zq, and becomes a beam parallel to the axis. The weak power at the periphery is collected to increase the strength. Light rays 73 to 80 having a high power density at the center are spread by the concave surface 60 of the intensity conversion lens Zh. When reaching the phase correction lens Zq, it is considerably dispersed. It becomes a light beam that is parallel and in phase by Zq. The light beam that has just passed through the convex portion 62 travels substantially straight and reaches the concave portion 64 of the phase correction lens Zq to obtain parallelism. As described above, the light beam at the center of the Gaussian beam is expanded and the light beam at the peripheral part is contracted, and a top hat beam having a uniform intensity distribution is obtained immediately after the phase correction lens Zq. Such a lens is sometimes called a homogenizer. A Gaussian beam having a circular cross section is used as a top hat having a circular cross section.

  In addition to Patent Document 1, many lens systems for homogenization have been proposed. In some cases, the radius W of the Gaussian beam is different from the radius U of the homogenized beam. However, it is only necessary to add a convex surface or a concave surface that gives a condensing action or a diverging action to the lens. Is.

However, there is still no optical system that makes uniform with an elliptical cross section beam. In order to transform the circular cross-section beam into an elliptical cross-section, a cylindrical lens will rise to the first candidate. Combining the cylindrical lens with the homogenizer lens of FIG. 1 will appear to yield a uniformly distributed elliptical beam.

  2 and 3 show an example of a beam shaping optical system in which a cylindrical lens and a homogenizer lens for converting into a circular uniform beam are combined. This is an experimental optical system and is not actually used for the generation of elliptical cross-section beams. FIG. 2 shows a zy cross section. FIG. 3 shows a zx cross section. As described above, the cylindrical lenses Zs and Zt reduce the beam only in the y direction.

  This optical system is composed of three lenses: a cylindrical convex lens Zs, a cylindrical concave lens Zt, and an aspheric type intensity conversion lens Zh. The phase correction lens Zq is omitted. Instead, the image plane I is placed at the position of the phase correction lens.

  The cylindrical convex lens Zs and the cylindrical concave lens Zt are lenses that reduce the beam only in the y direction and maintain the same dimensions in the x direction. The lens has a finite curvature only in the y direction and has a curvature of 0 in the x direction. Zs is convex only in the y direction, and Zt is concave only in the y direction. It is necessary to combine two lenses to make a parallel beam with an elliptical cross section. It is called a reducer lens including Zs and Zt. The distance between Zs and Zt is d ', the distance between Zt and Zh is e, and the distance between Zh and image J is g.

  The Gaussian beam 5 having a circular cross section is turned into an anisotropic convergent beam 6 by the reducer lenses Zs and Zt. After Zt, the beam becomes an elliptical cross section beam 7 parallel to the axis. It has a Gaussian power distribution in both the x and y directions.

  This is converted into a power uniform beam 8 by the intensity conversion lens Zh.

  An image plane I is provided at a position where the phase correction lens Zq should be. An image J having an elliptical cross section is formed on the image plane I. In the uniform optical system as shown in FIG. 1, when the distance between Zh and Zq is g, the distance between Zh and the image plane I is set equal to g. In the image J, the power distribution in at least the x direction should be nearly uniform.

US Pat. No. 3,476,463

  When the Gaussian beam is shaped by the optical system of Zs + Zt + Zh in FIGS. 2 and 3, the distribution is as shown in FIGS. In FIG. 4, the horizontal axis represents the distance in the radial direction from the center on the long diameter side (long axis) of the beam cross section of the image J on the image plane I. In FIG. 5, the horizontal axis is the distance in the radial direction from the center on the short diameter side (short axis) of the beam cross section of the image J on the image plane I. The vertical axis represents the beam intensity. As shown in FIG. 4, the beam intensity has a uniform distribution on the longer diameter side. However, the intensity distribution on the minor axis side is not uniform as shown in FIG. FIG. 8A shows the power distribution in the elliptical cross section with contour lines.

  Assuming that the beam diameter incident on the cylindrical lens is a specification value for making the beam uniform by the beam shaping lens, the intensity distribution on the major axis side becomes uniform. However, the short diameter side is not uniform because the beam diameter incident on the beam shaping lens is smaller than the specification value by the cylindrical reducer. This is due to the characteristics peculiar to the beam shaping lens (intensity conversion lens) Zh that the steepness and uniformity are impaired when the incident beam diameter becomes smaller than the design specification.

  Then, the intensity conversion lens Zh is not rotationally symmetric, but has anisotropy in the xy direction, and remains in the x direction (major axis direction) and has a convex and concave shape in the y axis (minor axis) direction. Should be reduced. If the size of the convex and concave portions is reduced to be equal to the reduction ratio in the y direction by the cylindrical lens, there should be no problem. Then, an elliptical cross section beam uniform in the xy direction can be obtained.

  However, it is difficult to make a lens without rotational symmetry. Even an aspherical lens is used to cut the uneven surface with a blade while rotating the material around its axis. So you can only make lenses with rotational symmetry. In order to generate a uniform power with an elliptical cross section, the height distribution of the surface of the lens with an uneven surface having an elliptical distribution can be calculated any number of times. However, the fact that it can be calculated is different from that it can be produced. It is not possible to make a non-rotationally symmetric lens by making the material while rotating it. A plastic lens made of a mold can be used, but a non-rotationally symmetric lens made of quartz or optical glass cannot be easily manufactured. It can be done with time and effort, but it is expensive and impractical.

  It is an object of the present invention to provide an optical system that produces an elliptical cross-section beam having a uniform distribution while using a cylindrically symmetric beam shaping lens (intensity conversion lens) Zh without using a non-rotationally symmetric lens. It is a problem.

  Ra and Rb are the radii of desired elliptical cross sections. Using only the cylindrical convex lens Z1 and the beam shaping lens (intensity conversion lens) Z2 having a uniform possible radius W of W ≦ Rb <Ra, the cylindrical convex lens Z1 and the beam shaping lens Z2 have desired elliptical cross sections (Ra, Rb). Move closer to the distance you want. In addition, the distance b between the image plane I and the beam shaping lens Z2 is made shorter than the uniform distance g of the beam shaping lens.

  When a beam having an elliptical cross section is formed by a cylindrical lens and passed through an intensity conversion (beam shaping lens) lens having rotational symmetry, the uniformity of the beam intensity on the short axis side is improved. The strength uniformity on the short axis side and the strength uniformity on the long axis side are complementary. It cannot be made compatible. When importance is attached to the uniformity on the short axis side, a beam shaping lens having a uniform possible radius W close to Rb is used. When importance is attached to the uniformity on the long axis side, a lens having a uniformizable radius W close to Ra is used. The uniformity on both the short axis side and the long axis side cannot be improved at the same time. However, depending on how W and b are selected, the uniformity on the short axis side and the long axis side can be improved at a desired ratio.

  It is necessary to define the essence of the present invention in more detail. What is the uniformity radius U and the appropriate distance g between the two lenses in the homogenizer lens system composed of the intensity conversion lens Zh and the phase correction lens Zq? It is necessary to discuss in correspondence with the formula of the curved surface and the effective focal length. The radius W of the incident Gaussian beam is defined as the distance to the point at which the center intensity is attenuated to exp (−2). What is the relationship between this and the homogenizer radius U? It must be made clearer.

  FIG. 9 is an explanatory diagram showing the intensity conversion lens Zh and the phase correction lens Zq. This is a rotationally symmetric lens with respect to the optical axis lm. In order to simplify the calculation, it is assumed that the incident side of the intensity conversion lens Zh is a flat surface and the emission side of the phase correction lens Zq is a flat surface. As shown in FIG. 1, both the intensity conversion lens Zh and the phase correction lens Zq have a complicated shape that is partially convex and partially concave. If only the central part is seen, the intensity conversion lens Zh is a concave lens, and the phase correction lens Zq is a convex lens. Of course, the intensity conversion lens Zh can be biconcave and the phase correction lens Zq can be biconvex. By looking only at the central portion, a specific relationship between the effective focal length F, the uniformizing distance g, the uniformizing radius U, and the Gaussian beam radius (uniformizing radius) W will be obtained. This is a fairly complex relationship. It is necessary to understand correctly in lens design.

  A Gaussian beam parallel to the optical axis lm enters the intensity conversion lens Zh from the point E and exits at the point K. Let n be the refractive index of the lens. Since Zh is concave at the K point, it is refracted in the spreading direction. Let α be the angle of inclination of the surface at point K. Since this is a parallel beam, this is the angle between the normal and the beam. Snell's law holds here.

  The refraction angle is θ = α + φ. The beam is refracted upward by φ. It propagates through free space by q and reaches the front M point of the phase correction lens Zq. Refracted at point M to become MN. MN is parallel to the optical axis lm. Snell's law holds at point M, but the same formula as point K. The incident angle at point M should be θ = α + φ and the refraction angle should be α. Therefore, the Zh tangent at the K point and the Zq tangent at the M point are parallel. Snell's law at points K and M can be written as follows:

          nsin α = sin θ = sin (α + φ) (1)

It is assumed that the incident beam of the laser is a Gaussian beam. When the laser beam radius is W and the radius coordinate is s, the power density of the incident Gaussian beam can be expressed as Bexp (−2s ² / W ² ). Since the radius of the Gaussian beam is defined as the distance from the center of the position attenuated to e- ² , W is the beam radius in the above formula.

  The circumferential portion of the width ds at the radius s of the intensity conversion lens Zh has a power obtained by multiplying the power density by 2πsds. Let r be the radius coordinate of the phase correction lens Zq. Let U be the uniform radius of the phase correction lens Zq. The uniform radius U is a radius such that a uniform power density is present therein and a power 0 is present outside the uniform power density. The uniformizing radius U may be the same as or different from the radius W of a Gaussian beam (referred to as a uniformizable radius). The inter-lens distance g is called a uniform distance. This is also an important parameter.

  Therefore, what characterizes the homogenizer is the three parameters of the incident Gaussian beam radius W, the uniformizing radius U, and the uniformizing distance g. W is also called a uniform radius. It should not be confused with the uniformizing radius U. W is the cause and U is the result. However, the relationship between these important parameters W, U, g and the effective focal length F is not clear.

  Since the present invention is defined using the effective focal length F, it is necessary to obtain the relationship. Since Zh and Zq are neither simple concave lenses nor convex lenses, there is no exact focal length. However, focusing only on the central portion, the intensity conversion lens is a concave lens Zh, and the phase correction lens Zq is a convex lens. Therefore, the focal length of only the central portion can be defined.

  Let E be the homogenization density of the homogenized beam. The total power on the circumference of the radius r on the rear surface of the phase correction lens Zq is given by 2πEdrr. The result of integrating this with r is the total power, but since r> U and 0, the integration is only for r ≦ U. The total power of the Gaussian beam is the density integrated from 0 to infinity by s.

(Gaussian beam total power)
^{2π∫sBexp (-2s 2 / W 2)} ds = [- (πBW 2/2) exp (-2s 2 / W 2)] = πBW 2/2 (2)

It is. On the other hand, the total power of the uniformized beam is 2πE integrated from 0 to U by r.

(Total power of uniform beam)
2π∫Edrr = πU ² E (3)

These powers are equal. So

^{πBW 2/2 = πU 2 E} (4)

So

E = BW ² / 2U ² (5)
It becomes.

  Uniformity means that the power of the annular zone having the radius s and the width ds of the intensity conversion lens Zh is equal to the power of the ring body having the radius r and the width dr of the phase correction lens Zq.

2πsBexp (−2s ² / W ² ) ds = 2πEdrdr (6)
This is the uniform condition. Fortunately this can be integrated.

C ₀ − (π / 2) BW2exp (−2s ² / W ² ) = πEr ² (7)

It is. C ₀ is an integral constant. Since s = 0 (light ray along the optical axis lm), r = 0, and (5) holds, so

1-exp (-2s ² / W ² ) = r ² / U ² (8)

This gives the relationship between s and r when the beam at the radius s of the intensity conversion lens Zh reaches the radius r of the phase correction lens Zq. This is the basic formula of the homogenizer.

  The lens curved surface is obtained by considering geometric optics. The curved surface of the intensity conversion lens Zh is given by K (s). This is positive to the right. The curved surface of the phase correction lens Zq is given by H (r). This is also positive to the right. K (s) and H (r) are also positive functions, but K (s) defines a concave lens and H (r) defines a convex lens.

  The slope at the point s of the curved surface K (s) and the slope at the point r of the curved surface H (r) are both tan α.

dK (s) / ds = tan α (9)
dH (r) / dr = tanα (10)

α must be found. By Snell's formula (1)

    nsinα = sinαcosφ + sinφcosα (11)

But divide both sides by cosα,

    tan α = sin φ / (n−cos φ) (12)

It turns out that. This relates the bend angle φ to the curved surface of the lens. There is another condition. That is what relates r and s. The effective optical path length is given by the sum of the product of the refractive index and the optical path. In free space, the optical path itself, and in the lens, the optical path is multiplied by the refractive index.

  The phase correction lens Zq has the effect of returning the beam to parallel and simultaneously aligning the phases. So it is a phase correction lens. The optical path length of EKMN is equal to the optical path length along the optical axis. Let g be the distance from the rear surface of the intensity conversion lens Zh to the front surface of the phase correction lens Zq. Let p be the distance from the front surface of the intensity conversion lens Zh to the rear surface of the phase correction lens Zq. The optical path length along the optical axis is n (p−g) + g. The front is the optical path length in the lens, and the rear is the optical path length in free space. If KM = q, the optical path length of EKMN is the sum of the lens component n (p-q cos φ) and the free space component q. Because it is equal to the optical path length of the optical axis,

    n (p−g) + g = n (p−qcos φ) + q (13)

That's what it means. This is the same phase condition.

      q (ncosφ-1) = (n-1) g (14)

It becomes. From FIG. 9, r is larger than s by qsinφ.

            qsinφ = rs−15 (15)

Delete q from (14) and (15).

  (Ncosφ-1) / sinφ = (n-1) g / (rs) (16)

Φ is deleted from (12) and (16), and tan α is expressed by (rs).

1 / tan ² α = (n−cos φ) ² / sin ² φ = (n ² −2 ncos φ + cos ² φ) / sin ² φ = (n ² sin ² φ + n ² cos ² φ− ² ncos φ + 1−sin ² φ) / sin ² φ = (n ² cos ² φ− ² ncos φ + 1) / sin ² φ + (n ² sin ² φ−sin ² φ) / sin ² φ = (n cos φ−1) ² / sin ² φ + (n ² −1) = {( n-1) g / (rs)} ^1/2 + (n ² -1)
(17)

It becomes. As a result, tan α is obtained.

tan α = [{(n−1) g / (rs−)) ^1/2 + (n ² −1)] ^1/2 (18)

It is. This is equal to dG / ds and dH / dr. The relationship between r and s is determined by the initial uniformization condition (8). When calculating dG / ds, the independent variable is set to s, and when integrating dH / dr, the independent variable is set to r.

dG / ds = [{(n−1) g / (rs−))} ^1/2 + (n ² −1)] ^−1/2 (19)
dH / dr = [{(n−1) g / (rs−))} ^1/2 + (n ² −1)] ^−1/2 (20)

It is. So far, it is an exact formula. No approximation is used. It is a precise formula. Calculations may be made by adding the relationship determined by (8) to r. However, numerical calculations can be performed with complex functions, but analytical calculations cannot be performed. When it is desired to obtain accurate G (s) and H (r), numerical calculation may be performed by a computer.

  However, here I would like to know roughly by approximate calculation. The right side of (19) and (20) includes a variable g / (rs) in the square root of the denominator. g is a distance between lenses, and rs is a difference in radial coordinates. g / (rs) is a value considerably larger than 1. Therefore, let us approximate by dropping the second expression of the denominator square root of (17).

From here it is an approximation.

Approximate expression G (s) = {1 / (n−1) g} ∫ (rs) ds
(21)

Similarly for H (r)

Approximate expression H (r) = {1 / (n−1) g} ∫ (rs−dr) dr
(22)

From (8)

^{-Log (1-r 2 / U} 2) = 2s 2 / W 2 (23)

So,

s = W {-(1/2) log (1-r ² / U ² )} ^1/2 (24)

By substituting this into (22) and integrating by s, H (r) can be obtained. It turns out that it is exact when numerically calculated by a computer. However, since it is only necessary to understand roughly here, (24) is further approximated. Expand to a series and take only one term.

s = Wr / 2 ^1/2 U (25)

Based on this relationship, (22) is integrated.

H (r) = {1−W / 2 ^1/2 U} r ² / {2 (n−1) g}
(26)
Solve (25) in reverse

r = 2 ^1/2 sU / W (27)

By substituting this into (21) and integrating, an approximate expression of G (s) is obtained.

G (s) = {2 ^1/2 U / W−1} s ² / {2 (n−1) g}
(28)

The upper G (s) gives the shape of the central portion of the intensity conversion lens Zh, and H (r) gives the shape of the central portion of the phase correction lens. In order to obtain the entire shape as shown in FIG. The combination of Zh and Zq does not mean that a Gaussian beam of any size can be made uniform. Only those whose incident Gaussian beam radius is W. Therefore, it can be said that the homogenizer is unique to the incident beam radius W. One homogenizer is determined for each incident beam radius W. Therefore, the incident beam radius W that can be made uniform is also referred to as “uniformity radius”. From the perspective of the lens, it is easier to say “uniform radius W”.

  Here, only the focal lengths Fh and Fq in the vicinity of the centers of the intensity conversion lens Zh and the phase correction lens Zq are desired. The reciprocal of the focal length of the lens is obtained by multiplying the sum of the curvatures of the front and rear surfaces by (n-1). The expression indicating the height of the lens surface is a value obtained by multiplying the square of the radius coordinate r by the curvature and dividing by 2. Therefore, the reciprocal of the effective focal length F1 of the intensity conversion lens Zh is

1 / F1 = − {(2 ^1/2 U / W) −1} / g (29)

The reason for the minus is that Zh is a concave lens near the center (when U / W is about 1). If {(2 ^1/2 U / W) −1} is negative, this becomes a convex lens near the center.

  Similarly, the reciprocal of the effective focal length F2 of the phase correction lens Zq is

1 / F2 = {1- (W / 2 ^1/2 U)} / g (30)

It becomes. 1 / F1 + 1 / F2 is always negative. What is said in the above equation is that the effective focal lengths F1 and F2 of Zh and Zq are the radius (uniform radius) W of the incident Gaussian beam, the radius U of the uniformized beam, and the uniformization. It is determined by the distance g. Note that the refractive index n of the lens is not included. In this way, the curved surfaces of the intensity conversion lens Zh and the phase correction lens Zq can be determined. Given the diameter 2W of the incident laser beam, the diameter 2U of the uniformizing beam, and the inter-lens distance g, the lens curved surface can be determined accurately. The present invention uses only an intensity conversion lens without using a phase correction lens. The curved surface of the intensity conversion lens Zh can be determined as described above.

In the present invention, a cylindrical convex lens Z1 having a curvature only in the y direction is used to create a beam having an elliptical cross section, and the intensity distribution is made uniform in the elliptical section by the intensity conversion lens Z2, and a uniform ellipse having a desired eccentricity and shape is obtained. A beam is generated on the image plane. An elliptical uniform beam is made with two lenses of Z1 + Z2. The distance between Z1 and Z2 is d (first distance), and the distance between Z2 and image plane I is b (second distance). Do not use a phase correction lens. The image plane I is brought directly to the position of the phase correction lens. How to make a uniform elliptical beam with such a simple structure? This is a problem. The major axis of the target ellipse is 2Ra, which is equal to the incident beam diameter D (D = 2Ra). The minor axis of the ellipse is 2Rb. This is given in advance.
That is, the eccentricity e = (Ra ² −Rb ² ) ^1/2 / Ra is determined. In particular, the relationship among the cylindrical lens Z1, the intensity conversion lens Z2, and the distances d and b is appropriately determined with emphasis on equalization in the minor axis direction. The uniformity on the long diameter side may be somewhat sacrificed.
The short side diameter is reduced by the cylindrical lens Z1. The short diameter side diameter in Z1 is D, and the short diameter diameter in the Z2 plane is D ′. D ′ / D is a reduction ratio by the cylindrical lens. Let L be the combined focal length of the lenses Z1 and Z2. In this case, the ratio between L and the second distance b and the ratio between D and D ′ are equal.
L: b = D: D ′ (31)
This is the basic formula that determines the relationship of parameters. If b, d, and Z1 are determined, this is an expression for determining the composite focal length L. This means that the focal length L2 of the intensity conversion lens Z2 is determined through the combined focal length. L: b = D: D ′ is the most important formula for determining the parameter relationship of the present invention. This is not a matter of course and is a unique condition of the present invention. (31) can also be written as bD = LD ′. Actually, it is often the case that the desired Ra and Rb images are not obtained only by this, so that a value that is 1 to 2 times the focal length L2 of the intensity conversion lens Z2 obtained from the above formula by trial and error is obtained. And

  The expression of the curved surface Z1 (y) of the cylindrical lens that condenses the rotationally symmetric beam only in the y direction is

Z1 (y) = const−y ² / 2L1 (n−1)
(32)

Is represented by L1 is the focal length in the y direction of the cylindrical lens Z1 (the focal length in the x direction is infinite). Since the parallel Gaussian beam is incident, the beam converges in the y direction at the point of the distance L1. Let the radius of the desired elliptical beam be Ra × Rb.
The short / long diameter ratio Rb / Ra is referred to as an elliptical aspect ratio a. This is a positive number less than one. a ² + e ² = 1. Since the focal length in the y direction of the cylindrical lens Z1 is L1, and the distance between the lens Z1 and the image plane I is d + b, the aspect ratio is a = (L1-db) / L1. If m is a constant of 1-2,
mD ≧ D ′ ≧ aD (m = 1 to 2) (33)
There are such limitations.

  As shown in FIGS. 6 and 7, there is an intensity conversion lens (beam shaping lens) Z2 at a position on the downstream side d of the cylindrical lens Z1. This intensity conversion lens Z2 is a cylindrically symmetric lens and corresponds to the Zh lens shown in FIGS. The approximate focal length has already been described. As shown in FIG. 12, because of the first cylindrical lens Z1, the minor axis side linearly reduces to point C at the focal length L1. Since the distance between Z1C is L1 and the distance between Z2C is (L1-d), the minor axis diameter D 'at Z2 is

            D '= D (L1-d) / L1 (34)

And so on. Here, a case of a convex cylindrical lens will be described. However, a relationship expressed by the same equation holds true for a concave cylindrical lens. In FIG. 12, since the distance between the ICs is (L1-db), the minor diameter on the image plane is D (L1-db) / L1 = aD. Here, in order to make the beam density uniform, the intensity conversion lens Z2 is placed at the position d. The focal length of the intensity conversion lens Z2 is L2. This is the unknown to be determined. Let L be the combined focal length of Z1 and Z2.

L is determined so that L: b = D: D 'as in (31). When the value of L is determined, the focal length L2 of Z2 is determined and the shape of Z2 is determined.

The combined focal length L of the lenses with focal lengths L1 and L2 separated by the distance d is L = L1L2 / (L1 + L2-d) (35)
Given by. Substituting into (31), a preferable L is determined from D, D ′, and b.

L2 is determined from (35). As a result, the focal length L2 of the intensity conversion lens Z2 is known, so that the shape of the intensity conversion lens Z2 can be determined.

  An elliptical shape Ra × Rb on the image plane is given from the beginning. The first and second distances d and b can be freely determined. The focal length L1 of the cylindrical lens Z1 is also freely determined. As described above, one relationship is determined between these variables by the aspect ratio a. Rb / Ra = a = (L1-b-d) / L1.

  Further, one constraint condition is given from the formula (35) of the composite focal length. There is a relationship of D′ L1 = D (L1−d) between the minor axes D and D ′ of the beams on Z1 and Z2. Furthermore, another condition is determined from the fundamental condition bD = LD 'of the present invention. D and a are given from the beginning, and L1, L2, b, and d are parameters that can be freely determined. Since there are four constraint conditions, these values are determined. Write side by side

a = (L1-bd) / L1 (36)
L = L1L2 / (L1 + L2-d) (35)
D ′ = D (L1-d) / L1 (34)

bD = LD '
(31 ')

And so on. There can be various cases. If b, D, D ', and L1 are known and d and L2 are unknown, from (34),

d = L1- (D′ L1 / D)
(37)
And d is obtained. If L is deleted from (35) and (31 ′),

L2 = (L1-d) Db / (D′ L1-bD) (38)
Or L2 = D′ L1b / (D′ L1-bD) (39)
And so on.

When a, b, D, and L1 are known, L2 = b + b ² / aL1 (39) ′
d = (1-a) L1-b (40)
D ′ = D (aL1 + b) / L1 (41)
L = bL1 / (aL1 + b) (42)
And so on.

  If d, b, D, a are known,

L1 = (b + d) / (1-a) (43)
D ′ = D (b + ad) / (b + d) (44)
L = b (b + d) / (b + ad) (45)
L2 = b (b + ad) / a (b + d) (46)
It is.

  In practice, this often does not yield an optimal solution. In that case, L2 is increased little by little and an asymptotic solution is obtained. The power distribution of the ellipse image created on the image plane by the optical system determined by the parameters in the above equation is calculated.

  If the desired aspect ratio a is not reached, the focal length L2 of Z2 is slightly increased to determine parameters, and an ellipse formed on the image plane by the optical system having the parameters is obtained. L2 is increased until the power distribution on the image plane has a desired aspect ratio a. Such repeated operation is performed.

Actually there is a constant m of 1-2,
L2 = m (L1-d) Db / (D′ L1-bD) (47)
Then, a uniform ellipse having a desired aspect ratio a (minor axis direction) is formed.
So the condition for L2 is

2 (L1-d) Db / (D′ L1-bD)> L2 ≧ (L1-d) Db / (D′ L1-bD)> b (48)
That's what it means.

  This determines Z2 by determining the focal length L2 for the Z2 lens. However, Z2 is an intensity conversion lens and there is no uniform focal length L2. However, the approximate focal length at the center can still be determined. Furthermore, since it is the peripheral part that determines the shape of the elliptical beam here, the focal length of only the peripheral part in a certain range of the intensity conversion lens Z2 can be determined.

  Alternatively, the Z2 parameter may be determined first, and the curvature 1 / L1 of the cylindrical lens Z1 may be determined. Which parameters are known in advance and which parameters are unknown can be determined in consideration of the purpose and ease of lens manufacture.

  As shown in FIGS. 6 and 7, a cylindrical convex lens Z1 and a beam shaping lens (intensity conversion lens) Z2 are provided at a distance d, and an image plane I is provided at a distance b from Z2. The cylindrical lens Z1 has a curvature only in the y-axis direction and has a focal length L1. The beam shaping lens Z2 is a rotationally symmetric lens that equalizes a Gaussian-distributed beam in a certain range and has a focal length L2. The diameter of the beam is D, and the minor axis of the beam shaping lens Z2 is D 'by the cylindrical lens Z1. Assuming that the combined focal length is L, bD = LD ′ or b / L = D ′ / D. A Gaussian beam having a diameter D was made incident on the cylindrical convex lens Z1. The cylindrical convex lens Z1 provides a beam having an elliptical cross section (D × D ′) on the surface of the beam shaping lens (intensity conversion lens) Z2. The beam shaping lens Z2 projects an elliptical beam made uniform in the minor axis direction onto the image plane.

The specific wavelength of the laser beam, lens material, distances b and d, and the aspect ratio of the elliptical beam on the image plane in the optical system of Example 1 are shown below.
Laser light wavelength 10.6μm
Lens material ZnSe
Incident beam diameter D 10 mm
Z1Z2 spacing d 30mm
Z2I spacing b 70mm
Aspect ratio (major axis / minor axis) 3

The dimensional specifications of the cylindrical lens Z1 are as follows.
y-direction focal length L1
150mm
Center thickness 5mm

The dimensional specification of the homogenizer lens Z2 is as follows.
Center focal length L2 155mm
Beam minor axis D 'on the surface
8mm
Center thickness 5mm

Aspheric coefficient
a ₁ = + 1.4484123017196962 × 10 ⁻³
a ₂ = −5.85840507058886955 × 10 ⁻⁵
a ₃ = + 1.04364038444764425 × 10 ⁻⁶
a ₄ = −2.035555442429464749 × 10 ⁻⁸
a ₅ = + 6.99874079461343713 × 10 ⁻¹⁰
a ₆ = −2.333758616316805 × 10 ⁻¹¹
a ₇ = + 4.95727690555067414 × 10 ⁻¹³
a ₈ = −6.16256988541364172 × 10 ⁻¹⁵
a ₉ = + 4.11982955579632210 × 10 ⁻¹⁷
a ₁₀ = −1.141466075482261 × 10 ⁻¹⁹

The composite focal length L is from 1/150 + 1 / 155-30 / 150 · 155 = 1 / 84.5 to L = 84.5 mm. b / L = 70 / 84.5 = 0.82. D '/ D = 8/10 = 0.8. B / L = D '/ D.

  FIG. 10 shows the distribution of the beam intensity on the image plane in the major axis direction. FIG. 11 shows the beam intensity distribution in the minor axis direction. The vertical axis represents the beam intensity (arbitrary scale), and the horizontal axis represents the distance (mm) from the center of the image. FIG. 8B shows the intensity distribution in the elliptical cross section with contour lines. According to this, the beam intensity uniformity in the minor axis direction is improved.

  Instead, the beam intensity on the long diameter side is slightly non-uniform. This is unavoidable. It is not possible to make the power density uniform on both the long diameter side and the short diameter side. This is complementary. If the power density on the major axis side is made uniform, the power uniformity on the minor axis side becomes worse. Depending on the purpose, the distances d and b of Z1, Z2 and I are adjusted depending on which of the longer diameter side and the shorter diameter side is more important. FIG. 14 is a photograph of the beam formed on the image plane. The end of the major axis is blurred and the boundary is not clear. However, the end in the short axis direction is sharply cut, and it is well understood that the power uniformity in the short axis direction is excellent.

  In Example 2, as shown in FIGS. 6 and 7, a cylindrical convex lens Z1 and a beam shaping lens (intensity conversion lens) Z2 are provided at a distance d, and an image surface I is provided at a distance b from Z2. The cylindrical lens Z1 has a curvature only in the y-axis direction and has a focal length L1. Up to that point, it is the same as in the first embodiment, but the laser beam and Z1, Z2 lenses are different.

The specific wavelength of the laser beam, lens material, distances b and d, and the aspect ratio of the elliptical beam on the image plane in the optical system of Example 2 are shown below.
Laser light wavelength 10.6μm
Lens material ZnSe
Incident beam diameter D 5 mm
Z1Z2 spacing d 40mm
Z2I spacing b 160mm
Aspect ratio (major axis / minor axis) 2

The dimensional specifications of the cylindrical lens Z1 are as follows.
y-direction focal length L1
400mm
Center thickness 5mm
The dimensional specifications of the homogenizer lens Z2 are as follows.
Center focal length L2 290mm
Beam minor axis D '4.5mm on the surface
Center thickness 5mm

Aspheric coefficient
a ₁ = + 7.7321327906606139 × 10 ⁻⁴
a ₂ = −9.89612177701964627 × 10 ⁻⁵
a ₃ = + 5.591137916782349 × 10 ⁻⁶
a ₄ = −3.42572519777897809 × 10 ⁻⁷
a ₅ = + 3.77092063160010601 × 10 ⁻⁸
a ₆ = −3.9137007140595922 × 10 ⁻⁹
a ₇ = + 2.6266152164999901 × 10 ⁻¹⁰
a ₈ = −1.031414635050615032 × 10 ⁻¹¹
a ₉ = + 2.177778106444905250 × 10 ⁻¹³
a ₁₀ = -1.9051277873103865 × 10 ⁻¹⁵

The combined focal length L is from 1/400 + 1 / 290-40 / 400 · 290 = 1/178 to L = 178 mm. b / L = 160/178 = 0.898. D ′ / D = 4.5 / 5 = 0.9. B / L = D ′ / D.

  FIG. 15 shows the distribution of the beam intensity in the major axis direction on the image plane. FIG. 16 shows the beam intensity distribution in the minor axis direction. The vertical axis represents the beam intensity (arbitrary scale), and the horizontal axis represents the distance (mm) from the center of the image. According to this, the beam intensity uniformity in the minor axis direction is good.

  Instead, the beam intensity on the long diameter side is slightly non-uniform. However, fine fluctuations are reduced as compared with the first embodiment. The same can be said as in the first embodiment, and the power density cannot be made equal on both the long diameter side and the short diameter side. This is complementary. If the power density on the major axis side is made uniform, the power uniformity on the minor axis side becomes worse. Depending on the purpose, the distances d and b of Z1, Z2 and I are adjusted depending on which of the longer diameter side and the shorter diameter side is more important. FIG. 17 is a photograph of the beam formed on the image plane. The short end in the short axis direction is poor and the blur in the end in the long axis direction is reduced. It can be seen that the power uniformity in the minor axis direction is excellent.

  As shown in FIGS. 18 and 19, a cylindrical lens Z1 having a concave surface and a beam shaping lens (intensity conversion lens) Z2 are provided at a distance d, and an image plane I is provided at a distance b from Z2. The concave cylindrical lens Z1 has a curvature only in the y-axis direction and has a focal length L1 (L1 is negative). The beam shaping lens Z2 is a cylindrically symmetric lens that uniformizes a Gaussian-distributed beam in a certain range and has a focal length L2. The diameter of the beam is D, and the major axis of the beam shaping lens Z2 is D ′ (D ′> D) by the cylindrical lens Z1. Assume that the combined focal length is L (positive), and bD = LD ′. A Gaussian beam having a diameter D was made incident on the cylindrical concave lens Z1. The cylindrical concave lens Z1 provides a beam having an elliptical cross section (D × D ′) on the surface of the beam shaping lens (intensity conversion lens) Z2. The beam shaping lens Z2 projects an elliptical beam made uniform in the minor axis direction onto the image plane.

The specific wavelength of the laser beam, lens material, distances b and d, and the aspect ratio of the elliptical beam on the image plane in the optical system of Example 3 are shown below.
Laser light wavelength 10.6μm
Lens material ZnSe
Incident beam diameter D 5 mm
Z1Z2 spacing d
40mm
Z2I spacing b 160mm
Aspect ratio (major axis / minor axis) 2

The dimensional specifications of the cylindrical lens Z1 (concave surface) are as follows.
y-direction focal length L1
-200mm
Center thickness 5mm
The dimensional specification of the homogenizer lens Z2 is as follows.
Center focal length L2 120mm
Beam major axis D '4.5mm on the surface
Center thickness 5mm

Aspheric coefficient
a ₁ = + 1.8708757563220730 × 10 ⁻³
a ₂ = −1.3453033065410883 × 10 ⁻⁴
a ₃ = + 4.26033296791059667 × 10 ⁻⁶
a ₄ = −1.477705124103335926 × 10 ⁻⁷
a ₅ = + 9.0127707272223198 × 10 ⁻⁹
a ₆ = −5.3351447245294607 × 10 ⁻¹⁰
a ₇ = + 2.0207928860732162 × 10 ⁻¹¹
a ₈ = −4.46588810805343239 × 10 ⁻¹³
a ₉ = + 5.304485536769941 × 10 ⁻¹⁵
a ₁₀ = −2.61411358233018697 × 10 ⁻¹⁷

The combined focal length L is from -1 / 200 + 1/120 + 40/200 · 120 = 1/200 to L = 200 mm. b / L = 160/200 = 0.8. D '/ D = 4.5 / 5 = 0.9. B / L = D '/ D.

  FIG. 20 shows the distribution of the beam intensity on the image plane in the major axis direction. FIG. 21 shows the beam intensity distribution in the minor axis direction. The vertical axis represents the beam intensity (arbitrary scale), and the horizontal axis represents the distance (mm) from the center of the image. The long side is spread by a cylindrical lens. The aspect ratio is 2, but the diameter is 10 mm on the longer diameter side. The beam intensity uniformity in the minor axis direction is also good.

  The present invention is applicable even if the first cylindrical is concave. FIG. 22 is a photograph of the beam formed on the image plane. The beam is slightly blurred at the end in the long axis direction. It can be seen that the end in the minor axis direction is sharply cut and the power uniformity in the minor axis direction is excellent.

The figure of the homogenizer lens system which consists of an intensity | strength conversion lens Zh and the phase correction lens Zq, and converts a Gaussian beam into a uniform beam (top hat).

an optical system comprising a cylindrical convex lens Zs having an axis in the x-axis direction, a cylindrical concave lens Zt, and an intensity conversion lens Zh, the beam is reduced in the y-axis direction by Zs, and the beam is made parallel in the y-axis direction by Zt; Yz sectional drawing which shows that the uniformization beam J is projected on the image surface I with the intensity | strength conversion lens Zh.

an optical system comprising a cylindrical convex lens Zs having an axis in the x-axis direction, a cylindrical concave lens Zt, and an intensity conversion lens Zh, the beam is reduced in the y-axis direction by Zs, and the beam is made parallel in the y-axis direction by Zt; FIG. 4 is a zx cross-sectional view showing that a uniform beam J is projected onto an image plane I by an intensity conversion lens Zh while maintaining a beam diameter in the x direction.

FIG. 4 is a beam intensity distribution diagram along a major axis (x direction) of a beam image J formed on the image plane I by the optical system of FIGS.

FIG. 4 is a beam intensity distribution diagram along a minor axis (y direction) of a beam image J formed on the image plane I by the optical system of FIGS.

Using only a cylindrical convex lens Z1 and an intensity conversion lens (beam shaping lens) Z2 that form an elliptical cross section beam, the distance d between Z1 and Z2 is shortened, and an elliptical cross section beam image J uniformly distributed on the short axis side on the image plane. FIG. 2 is a yz cross-sectional view of the optical system of the present invention in which a slab is formed.

Using only a cylindrical convex lens Z1 and an intensity conversion lens (beam shaping lens) Z2 that form an elliptical cross section beam, the distance h between Z1 and Z2 is shortened, and an elliptical cross section beam image J uniformly distributed on the short axis side on the image plane. FIG. 3 is a zx cross-sectional view of the optical system of the present invention in which a slab is formed.

The intensity distribution diagram (1) of the elliptical cross section beam combining the cylindrical convex lens, the cylindrical concave lens Z1 and the intensity conversion lens Z2, and the beam intensity distribution map of the elliptic cross section according to the present invention combining the cylindrical convex lens and the intensity conversion lens.

Explanatory drawing for calculating | requiring the relationship between the lens curved surface of Zh and Zq, and the propagation of a light ray for converting a Gaussian beam into a uniform beam by the intensity | strength conversion lens Zh and the phase correction lens Zq which comprise a homogenizer lens.

FIG. 4 is an intensity distribution diagram along the major axis side of the elliptical beam obtained in Example 1, in which a Gaussian beam is converted into an elliptical cross-section beam by a cylindrical lens and a homogenizer, and the power density is made uniform.

FIG. 4 is an intensity distribution diagram along the minor axis side of the elliptical beam obtained in Example 1, in which a Gaussian beam is converted into a beam having an elliptical cross section by a cylindrical lens and a homogenizer, and the power density is made uniform.

In the optical system of the present invention in which the cylindrical lens Z1 and the intensity conversion lens Z2 are provided at a distance d and the image plane I is provided at a distance b, the incident beam diameter D and the short diameter side diameter D in the intensity conversion lens are provided. The figure for demonstrating the relationship between 'and the focal distance L1 of the cylindrical lens Z1.

In the optical system of the present invention in which the cylindrical lens Z1 and the intensity conversion lens Z2 are provided at a distance d and the image plane I is provided at a distance b, the incident beam diameter D and the short diameter side diameter D in the intensity conversion lens are provided. The concept of the present invention, in which the focal length L2 of the intensity conversion lens Z2 is calculated, is assumed to be equal to the ratio of the combined focal length L and the distance b between Z2I (D '/ D = b / L). Figure to do.

FIG. 3 is a diagram of an elliptic beam image projected on the image plane in the first embodiment.

FIG. 4 is an intensity distribution diagram along the major axis side of an elliptical beam obtained by Example 2 in which a Gaussian beam is converted into an elliptical cross-section beam by a cylindrical lens and a homogenizer, and the power density is made uniform.

FIG. 6 is an intensity distribution diagram along the minor axis side of an elliptical beam obtained by Example 2 in which a Gaussian beam is converted into an elliptical cross-section beam by a cylindrical lens and a homogenizer, and the power density is made uniform.

FIG. 10 is a diagram of an elliptic beam image projected on the image plane in the second embodiment.

A book in which a cylindrical concave lens Z1 and a homogenizer lens for forming an elliptical cross section beam are used, and an image enlarged in the y direction is projected onto the image plane to form an elliptical cross section beam image J that is uniformly distributed on the minor axis side by the homogenizer. Yz sectional drawing of the optical system of invention.

FIG. 3 is a zx sectional view of the optical system of the present invention in which an image having the same size is formed on the image plane in the x direction using a cylindrical convex lens Z1 and a homogenizer lens that form an elliptical cross section beam.

FIG. 7 is an intensity distribution diagram along the major axis side of an elliptical beam obtained by Example 3, in which a Gaussian beam is converted into an elliptical cross-section beam by a cylindrical lens and a homogenizer, and the power density is made uniform.

FIG. 4 is an intensity distribution diagram along the minor axis side of an elliptical beam obtained in Example 3, in which a Gaussian beam is converted into an elliptical cross-section beam by a cylindrical lens and a homogenizer, and the power density is made uniform.

FIG. 10 is a diagram of an elliptic beam image projected on the image plane in the third embodiment.

Explanation of symbols

5 Gaussian beam
6 uniaxial reduced beam
7 Uniaxial parallel beam
8 homogenized beam
70-80, 82 Gaussian beam

Claims (3)

A cylindrical lens Z1 having a finite focal length L1 only in the y direction in order to make a Gaussian beam having a diameter D a uniform beam having an elliptical cross section (long radius Ra, short radius Rb, aspect ratio a = Rb / Ra); An intensity conversion lens Z2 having a focal length L2 made from a Gaussian beam placed at a distance d from Z1 and a focal length L2 and an image plane I placed at a distance b from the intensity conversion lens Z2 are converted by the cylindrical lens Z1. Let D ′ be the minor axis of the elliptical beam formed on the lens Z2 surface,
D> D ′ ≧ aD,
2 (Db (L1-d)) / (D′ L1-Db) ≧ L2 ≧ (Db (L1-d)) / (D′ L1-Db) ≧ b
An elliptical beam shaping optical system characterized by Ra / Rb is 1-10, The elliptical beam shaping optical system of Claim 1 characterized by the above-mentioned. A cylindrical lens Z1 having a finite focal length L1 only in the y direction in order to make a Gaussian beam having a diameter D a uniform beam having an elliptical cross section (long radius Ra, short radius Rb, aspect ratio a = Rb / Ra); An intensity conversion lens Z2 having a focal length L2 made from a Gaussian beam placed at a distance d from Z1 and a focal length L2 and an image plane I placed at a distance b from the intensity conversion lens Z2 are converted by the cylindrical lens Z1. The minor axis of the lens Z2 is set to D ′, the relationship of D> D ′ ≧ aD is satisfied, and the combined focal length of the cylindrical lens Z1 and the intensity conversion lens Z2 is set to L so that Db = LD ′ is established. The focal length L2 of the intensity conversion lens Z2 is calculated, and L2 = (Db (L1-d)) / (D′ L1-Db), and such a focal length L1. The shape of an ellipse formed on the image plane by the lens of L2 is obtained. If the desired aspect ratio is not reached, L2 is set to 2 (Db (L1-d)) / (D′ L1-Db) ≧ L2 ≧ (Db (L1− d)) A method for improving the uniformity of an elliptical beam shaping optical system, which is repeated until the aspect ratio a on the image plane reaches a desired value by increasing in the range of (D′ L1-Db).

Images