JP2003344762A - Shaping lens for laser beam and method of designing shaping lens for laser beam - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a shaping lens for laser beam and method of designing the shaping lens in which multiformity does not appear in a rear propagation position in a beam homogenizer in which a beam having a Gaussian type intensi ty distribution such as a CO<SB>2</SB>laser is converted into a substantially homogeneous distribution with an intensity conversion lens and converted into a parallel beam with a phase correction lens. <P>SOLUTION: The power distribution I<SB>2</SB>(s) after the output is shaped with the phase correction lens is not of a top-hat but of a super Gaussian cexpä-(s/ω)<SP>2m</SP>}, (m=5 to 50). <P>COPYRIGHT: (C)2004,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention utilizes a low density beam such as a carbon dioxide gas laser beam in the center and high density in the peripheral portion for precise processing. However, it relates to a combination of lenses for shaping so that the power distribution is hardly disturbed.

[0002]

2. Description of the Related Art Since carbon dioxide laser beams have high energy, they are used for thermal processing, surface processing, fine perforation processing and the like. For example, in the field of thermal processing, it is used for surface hardening treatment of metals and the like (engine cam treatment, etc.). In addition, carbon dioxide gas can be used for making fine holes in printed circuit boards.
Expected to use ZaBeam. Since the carbon dioxide laser emits infrared light, the lens is made of ZnSe which is transparent to infrared light.
A lens is used.

A carbon dioxide laser beam that oscillates in a pulsed manner may be branched into a large number of beams and a special lens may irradiate the printed circuit board to form a large number of holes at once. There are times when you want to make holes.

The problem here is the radial power distribution inside the beam. The beam emitted from the carbon dioxide laser is a divergent beam. It is possible to use a zoom optical system to form a parallel beam, and it is also possible to change the divergence size with a collimator lens.

However, no matter how the size is changed by the lens, when the laser beam is made into a parallel beam, the power distribution is such that the power is high in the center and low in the peripheral portion, that is, inside and outside. There is little disturbance in the angular direction and there is symmetry about the axis.
Often has a power distribution that can be simply approximated by a Gaussian distribution. Since the laser beam is repeatedly reflected and excited by the resonators on both sides, it ideally has a Gaussian distribution. There are many applications where a Gaussian distribution with a high power density at the center and a low power density at the periphery can be fully used.

However, it may be inconvenient to use a laser beam having a high energy for heat processing and hole drilling. For example, when used for drilling, the hole may penetrate properly at the center but may not penetrate at the peripheral part. It may also become a hemispherical depression. In order to cleanly drill a hole having a constant diameter with a laser beam, it is desired that the power density of the beam be constant within a certain radius range (r <a). There have been proposed some optical components for keeping constant power in a certain range.

“Beam splitting method” A kaleidoscope, a segment mirror, and the like. The laser beam is expanded and passed through an optical component that has several minute square gratings, and a parallel square beam is created by the square gratings and superposed on one another at a certain distance. The square lattice is represented by Sij (xi, yj). xi is i
The x coordinate of the column and yj are the y coordinates of the j rows. Since all the lights of these square gratings are superposed on one square, the density Sm is

[0008]       Sm (x, y) = ΣSij (xi, yj) = PM (1)

[0009] P is the average power density and M is the number of square grids. Since the beam powers equally come from the high density portion and the low density portion, the energy density of the square portion becomes M times as high as the average power. This is easy to understand in principle, but the result is not a parallel beam. It only gives a square isopycnic beam at some focal plane. Furthermore, if the beam is carried far away by the optical system, the beam will be disturbed and it is difficult to use. In other words, the phase relationship is completely disordered, and there is a drawback that it can only be used for thermal processing and drilling at the focal plane. Even if the power density is made spatially uniform, if the beams are not parallel beams with the same phase, the beams will be disturbed due to the positional shift between the front and the rear, and they cannot be actually used.

USP 3,476,463 (Justin
L. Kreuzer) has proposed a method in which two aspherical lenses L1 and L2 are combined to generate a laser beam having uniform power and a uniform phase within a circle having a radius R.
The front surface of the first lens L1 is a flat surface, and the rear surface thereof is a concave lens for redrawing the Gaussian distribution into a uniform distribution. The second lens L2 is a lens for collimating the beam and has a convex front surface and a flat rear surface. The radius of each lens is R. At the radius R, the rear surface of L1 is perpendicular to the axis,
The L2 front surface is perpendicular to the axis. The beam passing through the outer periphery r = R of L1 passes through the outer periphery r = R of L2. So the beam through r = R is axis-parallel.

The first lens L1 transforms the Gaussian beam into a uniform distribution. It refracts the central beam to expand it. The peripheral beam is discarded. Since the beam power of the peripheral portion is large and is dispersed and weak, it is difficult to focus the beam. It throws it away. Since the center of the Gaussian beam is expanded, there is a uniform distribution in front of the second lens. The refraction angle of the beam of the first lens for homogenization with the second lens is determined as a function of radius. Once the refraction angle is determined, the curvature of the rear surface of the first lens for realizing the refraction angle can be calculated. The first lens is a concave lens having a single concave because it discards ambient light. Although the inflection point (the second derivative is 0) exists in a ring shape, it is a concave lens and has a simple shape.

In the second lens L2, the tilted beam is converted into a beam parallel to the axis. The tilt angle is known, and the tilt angle of the surface of the lens for converting it into a parallel beam is uniquely determined. Therefore, the curvature of the surface of the second lens can also be calculated. The second lens is a convex lens having one convex portion.

Just to make the derivative coefficient 0 at radius r = R
Since it is selected, an inflection point in the lens surface (the second derivative is 0)
Does not exist. The radius of the rear surface of the first lens is r₁Seki
Z as a number₁(R₁) And the curved surface of the front surface of the second lens
Radial coordinate r_TwoZ as a function of _Two(R_Two). r = R
Since the differential coefficient is 0 at the outer periphery of

With r ₁ = R

[Equation 13] r ₂ = R

[Equation 14]

There is. Moreover, since the output on the rear surface of the second lens is a constant value I,

I ₂ (r ₂ ) = I 0 ≦ r ₂ ≦ R (4)

Therefore, Since the lens radius is R,
There is no part of r ₂ > R.

This does not narrow the beam only by expanding it by the first lens L1. Therefore, only the beam included in the divergence radius R of the lens is used. Therefore, the light amount up to the radius R of the incident beam is made uniform by the lens having the radius R. Assuming that the power distribution of the incident beam is I ₁ (r ₁ ), the average value of the amount of light entering the region of radius R (πR ² ) is obtained as the uniform output I of the second lens.

[0019]

[Equation 15]

The amount of light entering the radius R of the first lens is uniformly distributed over the entire second lens having the radius R. The output I ₂ (r ₂ ) immediately after the second lens is uniform over the entire lens surface. What is good about this lens is that the second lens has a differential coefficient of 0 at r ₂ = R and no further negative differential coefficient is formed. Since only the light incident on the first lens up to r ₁ = R is refracted, the first lens is totally divergent. In other words, it only refracts the light rays outward. Then, the second lens only converts the divergent type into a parallel type beam, so that the second lens has only a convex surface and does not include a concave surface portion at all, and the shape of the second lens is simple and accurate. Therefore, the parallelism of the beam after passing through the second lens is high. A good quality uniform beam can be generated.

On the other hand, however, this can use only the beam incident on the first lens up to r ₁ = R. All light incident on R <r ₁ is wasted. This is a drawback. Since that point is difficult to understand, I will explain it in detail. As in (2) and (3), there is always a portion where both the lens surface differential coefficients become 0 at a radius common to the first lens L1 and the second lens L2. It may be said that r ₁ = r ₂ .

Here, it is defined as "frame ring". Here, r ₁ = R and r ₂ = R are the rings. The inside of the frame is called the forehead (r <R), and the outside is called the outside of the frame (r> R)
Let's decide The light that enters the forehead of the first lens (r ₁ <R) is called the forehead light, and the amount of light is called the forehead light amount Q _e .
The light incident on the outside of the forehead (r ₁ > R) of the first lens is referred to as the forehead light, and the light amount thereof is referred to as the forehead light amount Q _f .

[0023]

[Equation 16]

[0024]

[Equation 17]

In the conventional example, the frame (r = R) is the edge of the lens.
Same as (r = D) and (R = D)
It It facilitates the design of the second lens,
Forehead light Q _fHas the drawback of throwing away all. Outside the forehead
Light has a low density and is scattered over a wide range.
Make the lens surface design difficult. Second throws out extraneous light
It facilitates lens design.

It has been mentioned that it has the disadvantage of wasting extraneous light. Not only that, but since the forehead and the lens edge are the same (R = D), the relationship of (5) is always established, which becomes a constraint condition. (5) means that the average value of the in-frame light is the same as the value of the uniform light after the second lens. Since the laser beam power has a Gaussian distribution, it is strong at the center and weak at the periphery. If more laser light is to be used effectively, R will be increased and the value I of uniform light will decrease. Since the uniform light amount I is the power required for laser processing, the lower limit is limited depending on the type of processing. A weak uniform light intensity I is useless.

If a strong uniform light quantity I is required, the forehead must be narrowed (R must be small). When the forehead is narrowed, all the power outside the forehead is wasted, and the laser power utilization efficiency is significantly reduced. There is such a trade-off relationship.
Only within the forehead (D = R, r <R, Z ₁ (R) '=
It is nothing but a lens system that can utilize only 0, Z ₂ (R) ′ = 0).

Japanese Laid-Open Patent Publication No. 10-153750 “Laser Beam Shaping Optical Component” is a two-lens optical component that is capable of enlarging and reducing and that gives a constant output within a certain radius w and 0 output outside of it. is suggesting. What's more, it is a lens that can be used effectively by collecting not only the power within the frame but also the power outside the frame. Therefore, it is difficult to design the shape of the portion of the second lens larger than R. Therefore, a wave-optical method is used instead of geometrical optics.

The radius coordinate of the first lens L1 is r₁age,
Let the electric field complex amplitude of the light behind L1 be a ₁(R₁) Express
And the radius coordinate of the second lens L2 is r_TwoAs in front of L2
The electric field complex amplitude of the light on the plane_Two(R_Two) And L1 Ren
The height of the rear surface (curved surface) is h ₁(R₁) And L2
The height (curved surface) of the front of the h_Two(R_Two) And then Ren
D is the distance between the edges of the parallel incident laser beam in front of L1.
The intensity distribution (square of the amplitude) is I₁(R₁), On the back of L2
The intensity distribution of the output beam is I_Two(R_Two)age

[0030]

[Equation 18]

[0031]

[Formula 19]

[0032]

[Equation 20]

Calculate by n is the refractive index of the lens. However, since there is a condition that the power within the radius w is made uniform on the rear surface of the second lens, the output I ₂ (r ₂ ) immediately after the second lens is

I ₂ (r ₂ ) = I r ₂ ≦ w (11) I ₂ (r ₂ ) = 0 r ₂ > w (12)

I am trying to do so. Since it resembles a bowler hat, the distribution of such I ₂ (r ₂ ) is a top hat type (TO
P HAT). 2w is the diameter of the top hat.

The amplitude on the front surface of the first lens L1 is {I ₁ (r
₁ )} ^1/2 . (8) is the phase difference kh ₁ (r ₁ ) (n− when passing through the first lens L ₁ from the front surface to the rear surface.
The refraction of lens L1 is accounted for by giving 1). That is, exp {jkh ₁ (r ₁ ) (n−
1)} is a wave-optical expression of Snell's law.

(10) is the amplitude on the front surface of the second lens and the rear
Amplitude in plane {I_Two(R_Two)}^1/2To relate
And after all, it expresses Snell's law. J of (9)₀
(Kr ₁r_Two/ D) is the 0th-order Bessel function.

(9) expresses the change in amplitude when light propagates from L1 through free space, and it can be said that this is the essence of wave optics. It is a modification of the Kirchhoff Huygens formula. However, since it cannot be integrated as it is, many approximations are made.

Two lens surface points (x₁, Y₁), (X
_Two, Y_Two) Distance {(x₁-X_Two) ^Two+ (Y₁-Y_Two)
^Two+ D^Two}^1/2Is approximated by a quadratic function
Yes. The distance in exp () is also a quadratic function approximation.
However, the denominator distance is simply the axial distance d
It is replaced by and becomes a 0th-order approximation. That's it
Calculations cannot be done without such approximation. like that
Even if it is approximated, the calculation is not easy and the amount of calculation is still large.

While including such an approximation,
L1 lens thickness h₁(R₁) And the thickness h of the L2 lens
_Two(R_Two) Can be asked. Such pure wave light
By calculating the geometrical shapes of the curved surfaces of the two lenses
ing. The beam obtained is I _Two(R_Two) Should be half
A top-hat type uniform beam with a uniform value within the diameter w
Become.

Looking at the above equation, Snell's law is expressed as exp {j
Since it is in the form of kh ₂ (r ₂ ) (n−1)},
It cannot be distinguished that the L1 lens diverges light (inside the forehead) and condenses light (outside the forehead). It is designed to capture the power of a beam of any radius. Therefore, it should be possible to design a complicated second lens (including not only a convex surface but also a concave surface) that can utilize an incident beam outside the forehead. There is no clear distinction between in-frame, out-of-frame and out-of-frame as in geometric optics. Since it contains many approximations, it is difficult to trace the causal relationship accurately.

[0042]

According to the method proposed by the present inventor, the inventor has a top hat distribution immediately after the second lens L2 (phase correction lens),

I ₂ (r ₂ ) = C (r ₂ ≦ w), I ₂ (r ₂ ) = 0 (r ₂ > w) (13)

A lens having the following condition was produced. And I tried to use it for drilling with the optical system as shown in FIG. Up to now, the first lens L1 and the second lens L2 have been called, but sometimes the first lens is the intensity conversion lens and the second lens L2.
Is called a phase correction lens. Since it is difficult to understand if the calculation formula has many suffixes, the radius coordinate r ₁ of the first lens L1 (intensity conversion lens) is set to r, and the radius coordinate r ₂ of the second lens L2 (phase correction lens) is set to s.

R ₁ = r, r ₂ = s (14)

It is However, these notations are sometimes mixed after that.

In FIG. 1, the laser beam emitted from the laser device enters the zoom optical system while expanding, and the two beams (intensity conversion lens L1 and phase correction lens L2) form a parallel beam having a uniform power density. Has been converted to. After that, the structure is such that it is expanded through a hole in the mask and condensed by a condenser lens to irradiate the image plane. Actually, the image plane is an object to be processed such as a printed circuit board.
This is called a beam homogenizer. It is called a homogenizer because it is a device that makes the power density uniform.

The beam power after the second lens L2 of the beam homogenizer manufactured by the wave optics method was measured two-dimensionally. The result is shown in FIG. Although there are many minute irregularities, a circle with a radius of 70 mm has a roughly constant power, and the power outside the circle is 0.
Has become. That is the desired power distribution, and the desired distribution is obtained.

However, when the power is measured at a position 100 mm away from the second lens L2, the power is discontinuously large at one end although it is within a circle with a radius of about 70 mm as shown in FIG. 2 (b). Has become. It cannot be said that the distribution is very uniform. In reality, it is impossible to bring the object to be processed immediately after the second lens.
Since the object to be processed is placed far behind the lens, the disturbance of the power distribution in the rear is a serious problem.

Since the second lens L2 (phase correction lens) forms parallel beams, it seems that once the uniform distribution is achieved, the distribution becomes permanently uniform. But it wasn't. It was found that the power distribution in the axial direction changes. The axial power change was unexpected.

There is an error in the calculation of the lens even though it is a parallel beam. Therefore, some are not parallel. Therefore, the power distribution will be different in the axial direction. It may be an error in the lens design, but it seems that not only that but also the phenomenon of beam diffraction. In other words, the error and diffraction may cause the beam collapse (power non-uniform distribution) behind the beam homogenizer.

FIG. 3 shows a beam having a uniform distribution in a certain range, which is expressed by superimposing a large number of Gaussian distribution beams. FIG. 3B shows a strict top hat (step) type (I ₂ (r ₂ ) = C (r ₂ ≦ w), I
₂ (r ₂ ) = 0 (r ₂ > w)) is approximated by Gaussian beam superposition.

In the case of the step type, it is approximated by the sum of an infinite number of Gaussian beams having a narrow spread. If it is not an infinite number, the discontinuity of the shoulder portion r ₂ = w cannot be expressed. The problem with step-type output was that it was approximated by superposition of an infinite number of beams. If a large number of Gaussian beams must be present at such a minute pitch, diffraction will occur significantly between them.
Diffraction occurs more intensely as the grating spacing is narrower and the number of equivalent beams is larger. The present inventor has considered that vigorous diffraction occurs when superposed Gaussian beams having an infinitesimal small grating width, and the power distribution may be disturbed due to the diffraction even though the beams are parallel beams.

However, that is just a hypothesis. Is it possible to achieve one comprehensive beam by approximating it by superposition of minute Gaussian beams? It is still unclear whether the diffraction of the beam that first appears as a minute Gaussian beam really occurs or whether it really works.

The second lens L2 is not surely understood.
The present inventor has thought that such a beam collapse nonuniformity may occur behind the homogenizer because it imposes a stepped (top hat) non-continuous distribution behind.

[0056]

SUMMARY OF THE INVENTION The present inventor believes that the discontinuity of the steep shoulders r ₂ = w of the step-type output causes the beam power disturbance in the axial direction. Therefore, I thought that it would be better to make the shoulder of the step smoother. The reason for this can be approximated by a smaller finite number of Gaussian functions if the shoulder portion is gentle as shown in FIG. A Gaussian beam with a large divergence has a small diffraction and can maintain a Gaussian divergence.
It can be said that a Gaussian beam is an excellent beam shape. If it is a parallel beam, the width is almost the same, but even if it is a diverging or contracting beam, it remains Gaussian. Therefore, if a parallel beam is made by a lens, a wide Gaussian beam can propagate without changing its shape.

Based on such an idea, the present inventor designed the lens so that the shoulder has a gentle slope and a beam distribution without discontinuity is obtained. By doing so, the condition of uniform power immediately after the second lens L2 is not completely satisfied, but the power distribution can be made almost unchanged by the subsequent propagation in the axial direction. Actually, it is impossible to place the object to be processed immediately after the lens L2, and since the object to be processed is placed about 100 mm behind the second lens, this is preferable.

According to the present invention, the power distribution immediately after the second lens is not made into a complete step, but is set to a super Gaussian of m = 5 to 50 so as to prevent power deviation due to diffraction behind the lens. That is, if the power distribution immediately after the lens is I ₂ (r ₂ ),

I ₂ (r ₂ ) = cexp {− (r ₂ / ω) ^2m } m = 5 to 50 (15)

I ₂ (s) = cexp {− (s / ω) ^2m } m = 5 to 50 (16)

That is, (15) and (16) are just different expressions of the same formula. c is a proportional constant. ω
Is a parameter indicating the spread. Ω is used to distinguish it from the radius w of the top hat. Since this is power, the amplitude of light is its square root, and exp {-
(R ₂ / ω) ^m }. (15), (16)
The formula fully expresses the basis of the present invention. The present invention can be said to be in the expressions (15) and (16).

If m = 1, it is a Gaussian function,
It shows the same distribution as the original Gaussian beam. The Gaussian function is an infinitely differentiable function with excellent continuity. It is a smooth distribution function with a peak in the center. The square m = 2 is also infinitely differentiable. The square, m = 4, is also infinitely differentiable. There is no special name for m = 2 or m = 4. A generalized exp {-(r /
ω) ^2m } is not called individually, but is collectively called a super Gaussian function. m is an integer, and is called only when m = 1. This function is still infinitely differentiable if m is a finite integer.

As m increases, the distribution becomes localized within the range of r ≦ ω. Therefore, the rounded function with m = 1 is m
As the number increases, it becomes square. It becomes a square shape and approaches the above steps, but if m is finite, it is continuous and infinitely differentiable. In the limit of infinite m, the above step function (I ₂ (r ₂ ) = I (r ₂ ≦
ω), I ₂ (r ₂ ) = 0 (r ₂ > ω)). It is the above-mentioned (top hat) that made m infinity ∞. Therefore, the present inventor thinks that the influence of diffraction appears strongly due to superposition of infinitely small Gaussian beams, resulting in a non-uniform distribution behind the lens (FIG. 2B).

In the present invention, the power distribution on the rear surface of the second lens L2 (phase correction lens) is set to Super Gaussian instead of Top Hat. The incident beam is a Gaussian beam with a spread b, and the power distribution I on the rear surface of the phase correction lens L2
Let ₂ (r ₂ ) be a super Gaussian, and calculate the shapes of the surface of the first lens (intensity conversion lens) L1 and the surface of the second lens L2 (phase correction lens) that can realize it by a geometrical optics method. Then, at the rear position d, the power uniformity is evaluated to determine the order m. The meaning of the following procedure will be described later.

A. Design of curved surface G (r) of intensity conversion lens L1 Differential equation (π ⁻¹ b ⁻² ) exp (−r ² / b ² ) rdr = cexp {− (s / ω) ^2m } sds (17)

By solving, the relationship between the radius r of the intensity conversion lens L1 and the radius s of the phase correction lens is obtained. There is a relation that the beam emitted from r of the intensity conversion lens reaches the point of the radius s of the phase correction lens. This gives the relationship between r and s.

The shape G (r) of the surface of the intensity conversion lens L1 is

[0068]

[Equation 21]

Calculated and determined by

B. Design the curved surface H (s) of the phase correction lens L2

[0071]

[Equation 22]

It is determined by

C. The decision m of the super Gaussian order m is an extra parameter. The optimum m is determined by using the power uniformity at a constant distance d behind the homogenizer as an evaluation criterion. The optimum m depends on the rear reference distance d. Therefore, there is no common optimum m in advance. After the shape of the lens is determined, the uniformity at the rearward constant distance d is evaluated by a wave optical means.

The amplitude of the rear surface of the phase correction lens is A (x ₁ ,
y ₁ ) and the phase is φ (x ₁ , y ₁ ),

Φ (x ₁ , y ₁ ) = 1 (20)

A (x ₁ , y ₁ ) = cexp {− (s / ω) ^m } (21)

S ² = x ₁ ² + y ₁ ² (22)

The initial condition immediately after the phase correction lens is given by, and the amplitude at the position d behind the phase correction lens is A
(X ₂ , y ₂ ), the phase is φ (x ₂ , y ₂ ) _,

[0079]

[Equation 23]

The super Gaussian order m is set to 5 by evaluating the homogeneity of the amplitude in the backward d.
Decide on a single value between ~ 50.

[0081]

BEST MODE FOR CARRYING OUT THE INVENTION [A. Lens Design Method (By Geometrical Optics)] A lens system design method of the present invention will be described with reference to FIG. Two lenses are shown in FIG. The first lens L1 is an intensity conversion lens. It transforms a Gaussian beam into a super-Gaussian distribution, which is a nearly uniform distribution. Although the above-mentioned conventional example also uses the intensity conversion lens, it has a completely uniform distribution (top hat). This is not the case for the present invention, which is not uniform but is not completely uniform and has a super Gaussian distribution.
The second lens L that bends the beam by the intensity conversion lens L1
A super Gaussian distribution is realized in front of the 2 phase correction lens. The phase correction lens L2 converts a beam having a substantially constant power density into a parallel beam.

Therefore, the design of the intensity conversion lens L1 has an effect of making the Gaussian distribution super Gaussian in front of the phase correction lens L2 which is separated by a certain distance, and its design guideline is clear. Since the beam localized in the central portion is expanded, the intensity conversion lens L1 becomes a concave lens near the center (r <R in the forehead). Up to that point, it is the same as the above-mentioned conventional example. However, in order to utilize as many Gaussian beams as possible, it is necessary to refract light in the peripheral portion (outside the forehead r> R) toward the center.

Therefore, not only the concave lens but also the peripheral portion is further thinned, and the intensity conversion lens L1 has a cross-section close to a letter B. In that respect, it differs from the conventional example. Since the light in the peripheral portion is effectively used, the shape of the surface outside R of the phase correction lens and inside ω is extremely difficult.

Although the power is made substantially uniform by the intensity conversion lens L1, the direction of the beam is various because extra-frame light is also used. It is necessary to correct it to a parallel beam. The phase correction lens in the latter stage corrects the tilted beam to convert it into a parallel beam.

The phase-correcting lens has a substantially uniform beam formed into a parallel beam, and therefore has a concave portion at the peripheral portion and a convex lens portion at the central portion. The cross-sectional shape of the phase correction lens has an inverted B shape and is a shape complementary to the intensity conversion lens.

It is assumed that the incident beam I ₁ (r) coming from the laser is a Gaussian beam. So the distance r from the center
The incident beam can be described as a function of It can be written as the incident beam I ₁ (r). The input surface of the intensity conversion lens L1 is a flat surface. The output surface has irregularities, and the irregularities are written as G (r) as a function of the radius r. The uneven function G
By (r), the central beam is expanded and the peripheral beams are drawn into the central portion.

The super Gaussian distribution I ₂ (s) having a substantially uniform distribution is set on the front surface of the phase correction lens H which is separated by just L. s is a radial coordinate in the phase correction lens. The front of the phase correction lens has unevenness,
The rear surface is flat. H on the front surface of the phase correction lens
(S). After all, the purpose of lens design is to determine G (r) and H (s). Although it is common to the conventional example, it is different in that it also collects and uses extra-forehead light.

[A1. Surface shape G of the intensity conversion lens L1
Calculation of (r)] A laser beam is converted into an appropriately spread parallel beam by a collimator or the like. That is the input distribution I ₁
(R). It is assumed that the beam at the point r at the intensity conversion lens L1 is refracted at the point s on the front surface of the phase correction lens L2 separated by L. The relationship between r and s is such. R by the intensity conversion lens
Beam is refracted to s of the phase correction lens. Since the incident beam up to r in the intensity conversion lens becomes the super Gaussian I ₂ (s) from the center of the phase correction lens to s, it is assumed that I ₁ (r) is integrated from the center of the intensity conversion lens to r. , I from the center of the phase correction lens to s
_The integral of ₂ (s) is always the same.

[0089]

[Equation 24]

This is the law of conservation of beam power. The law of conservation of beam power gives the relationship between the radial position r in the intensity conversion lens and the radial position s in the phase correction lens. Since it is assumed that they have the same distribution in the circumferential direction, they are integrated in the angular direction and have 2π. Although it is written in the integral display, it is also possible to display the derivative by taking the integral symbol.

The incident beam (laser beam or its collimated beam) is a Gaussian beam having a known spread b. It

I ₁ (r) = (b ² π) ⁻¹ exp (−r ² / b ² ) (25)

It becomes The first (b ² π) ⁻¹ is a normalization constant. The square of the amplitude of the Gaussian beam is a Gaussian function, and the amplitude itself has a functional form of exp (-r / b).

The converted super Gaussian has an order m of 5
Although it is set to 50, m is set to a value in the range. ω is the divergence (beam waist), which is set to a desired value in advance.

I ₂ (s) = cexp {− (s / ω) ^2m } (26)

C is a normalization constant, which is a value close to (ω ² π) ⁻¹ but cannot be analytically shown. Such a normalization constant is such that the integral of I ₁ (r) and I ₂ (s) from 0 to infinity is 1, but it is not special 1 but other common constants. It may be. In (24), which requires conservation of beam power, Gaussian on the right side can be integrated. The super Gaussian on the right side cannot be analytically integrated, but can be numerically calculated by a computer.

[0097]

[Equation 25]

This is the equation that determines the relationship between r and s. Because of the refraction of the intensity conversion lens, the beam that has passed through the point of radius r of the intensity conversion lens passes through the point of s of the phase correction lens that is separated by L. If the tilt angle is Φ,

TanΦ = (s−r) / L (28)

It is This is the formula that determines the beam angle between the two lenses.

Since what is a parallel beam on the front surface of the intensity conversion lens becomes a beam with an inward inclination angle Φ at the point of the radius r on the rear surface, FIG. 6 shows the relationship between the refraction angles of the light rays on the intensity conversion lens. Show. The inward gradient ε of the lens surface that gives the inclination of Φ can be easily obtained. From Snell's law

[0102] nsinε = sin (ε + Φ) (29)

The following relationship holds. n is a lens refractive index. An inward gradient ε of the lens surface at a point r from here
(R) can be obtained. The tangent tan ε of the inward gradient ε (r) is equal to the derivative of the surface G (r) of the intensity conversion lens.

G (r) '= tan ε (30)

From (29)

[0106]

[Equation 26]

(27), (28), (29), (31)
From, a differential equation of G (r) with respect to r is obtained, which can be integrated to obtain the equation of the surface of G (r). It can be done accurately by numerical calculation. Try to make an approximate formula to improve the visibility.

[0108]

[Equation 27]

It becomes like this. By integrating this by r, the shape G (r) of the rear surface of the intensity conversion lens
Can be calculated. In (32), (n-1)
L is a constant and the variable is (s−r), but the equations that give s as a function of r are (24) and (27).

[0110]

[Equation 28]

As a result, the surface shape of the intensity conversion lens is determined. Within the forehead (r <D), the intensity conversion lens diverges the beam, so r <s. Forehead ring r = R and s =
r is the radius of the forehead ring R is the radius of the lens D
Is equal to. Therefore, the integral is calculated only in the range of r <s. The lens surface of the forehead is orthogonal to the axis. G '
(R) = 0.

The present invention is not so, and even the amount outside the frame (r> D) is included in the calculation, and then r> s. The incident Gaussian beam spreads out of the forehead and its contribution remains for a long time.

[A2. Surface shape H of the phase correction lens L2
Calculation of (s)] The front surface of the phase correction lens is an inclined surface H (s)
The rear surface is flat. FIG. 7 shows the relationship between the refraction angles of the phase correction lens. Light incident on the front surface at an angle Φ and a radius of s may be refracted into a parallel beam. Since a beam with an inclination of Φ is made into a parallel beam, if the inward and outward inclination angle of the surface is η, from Snell's law

[0114] nsin η = sin (Φ + η) (34)

The following holds. The shape of the front surface of the phase correction lens is H (s). This is the shape of the depression, not the height. G (r) and H (s) can be obtained by finding the shape of the depression.
Is complementary and easy to understand. The negative of the derivative is η
Is equal to the tangent of.

[0116]

[Equation 29]

This is also an accurate expression, and (27), (2
From 8), (29), and (31), r, s, and Φ are obtained as a function of s, and integrated by s, the accurate shape of the phase correction lens is obtained. I will give an approximate expression for this as well.

[0118]

[Equation 30]

By integrating this by s,
The shape of the front surface of the phase correction lens can be determined.
The relationship of r to s is given by (15).

[0120]

[Equation 31]

Thus, the surface shapes G (r) and H (s) of the intensity conversion lens and the phase correction lens are calculated. Since they are not analytic functions, they are represented by the aspherical lens representation. The expression of an aspherical lens expresses a curved surface by the sum of a spherical surface component and even-ordered aspherical surface components A ₂ , A ₄ , ... If the spherical surface component is represented by 0 and it is expressed only by the aspherical surface component, it is simply G (r ) Is an even polynomial of r (G (r) = ΣA
It is only expressed as _m r ^2m ). The lens is even-ordered because the lens is symmetric with respect to the axis and the odd-ordered component is zero. The polynomial order and the approximation order are the same. The greater the number of polynomials, the higher the accuracy, but the longer the calculation time. Therefore, the curved surface is expressed by a polynomial of an appropriate finite degree as an aspherical lens expression.

(33) and (37) are very similar expressions.
The only difference is whether the integration variable is r or s. This means that if the beam at point r of the intensity conversion lens reaches s of the phase correction lens, the gradient on that surface is the same. Therefore, the intensity conversion lens and the phase correction lens have complementary shapes. However, since r = s is not true, the irregularities do not fit perfectly, but the opposing surfaces are very similar.

Also in this case, the above-mentioned conventional example is within the frame (r
Since only <D) is calculated, s <r. Since the forehead ring r = D coincides with the radius of the lens, the calculation is stopped there. On the forehead D, the plane is orthogonal to the axis. H '
(R) = 0. This also includes contributions from outside the frame (r> R). Since the incident Gaussian beam is divergent, the contribution from outside the forehead remains forever, but in the case of the intensity conversion lens, r simply increases as it is, and the error of the curved surface is small and the error is small. However, in the case of the phase correction lens, since the increment of ds is extremely small with respect to the increment of dr, most of the Gaussian beam input hits the small portion and it is difficult to make it parallel.

Therefore, the differential coefficient H (s) 'around R <s ≦ ω of the phase correction lens becomes extremely large, causing a deviation and an error. In fact, the disturbance of the distribution at the 100 mm propagation position is H (s) around R <s ≦ ω of the phase correction lens.
It seems that the error is due to. The shapes of (33) and (37) are similar, but the behavior when s is around ω is completely different. The error of R <s ≦ ω of the phase correction lens is a problem, and the adoption of Super Gaussian reduces the error. The meaning of the present invention is that the accuracy of the phase correction lens around R <s ≦ ω is likely to increase, so that the uniformity of the back distance d of the phase correction lens after propagation is excellent.

[B. Analysis of Diffraction by Wave Optics] When the order m of Super Gaussian is determined, the shapes of the lens surfaces of the intensity conversion lens and the phase correction lens can be completely determined by the geometrical optics method described above. However, the problem here is 50 mm behind the phase correction lens or 10
It is a power distribution at 0 mm. Even if the phase correction lens has a clean step type (top hat) power distribution, it is not desirable as a beam for laser processing if the power distribution is not uniform 100 mm behind it.

The inventor considers that the uneven distribution of the distribution from the uniform distribution (top hat type) may be due to diffraction. I think that the power distribution will change from uniform to non-uniform due to diffraction.

In the conventional geometrical optics consideration, since the ray is traced, the influence of diffraction cannot be discussed. What actually happens to the power distribution behind the lens?
In other words, geometric optics does not know what the amplitude of light will be.

The present inventor thinks that it is not possible to know how the power varies in the optical path direction due to diffraction without using wave optics.

The wave optics is based on the Huygens principle, and if the amplitude is known on a certain plane, the amplitude of light at an arbitrary position behind it is given as a superposition of waves. The principle is simple, but the calculation is not easy. It is also difficult to give boundary conditions. Since the lens is thick, boundary conditions along the lens surface should be given in order to handle the amplitude of light emitted from the lens.

FIG. 10A is a geometrical optics analysis, FIG.
(B) shows an analysis of wave optics. According to the geometrical optics as shown in FIG. 10A, the thickness of the lens can be correctly evaluated. Since the thickness can be evaluated correctly, the phase change can be calculated exactly. However, since it is a ray analysis, the diffraction after the phase correction lens cannot be evaluated.
According to the wave optics as shown in FIG. 10B, it is desirable that the diffraction phenomenon after the phase correction lens can be described more accurately. However, it is difficult to analyze the propagation only by wave optics.

When collimating with a phase correction lens as shown in FIG. 11, the wave optics treats the lens thickness as 0. Therefore, in the broken line portion of FIG. 11, the phase is the same and the intensity is super Gaussian. However, in reality, the lens has a sag (cutting depth), and the influence of the sag is remarkable particularly in the outer peripheral portion of the lens. Therefore, in the wave optics method, the lens has a thickness of 0 and the initial boundary surface is a flat surface. In principle, calculation should be performed by giving a boundary condition along the lens surface, but that is difficult.

There are several causes. The calculation itself is difficult, and it is difficult to give a lens surface having a complicated curvature as a simple boundary condition. For this reason, wave optics must be calculated by considering the lens as a single plane with no thickness, and superimposing changes in the amplitude of light starting from the plane.

Therefore, the equation for determining the lens surface cannot be obtained by the wave optics calculation. The lens surface is determined by the geometrical optics method as described above. To define light in spatial coordinates, it is necessary to determine the amplitude and phase. In the present invention, 100 mm or 5 after the phase correction lens
To evaluate the light at 0 mm, the amplitude is determined by wave optics and the phase is determined by geometric optics.

As described above, the intensity conversion lens and the phase correction lens can be designed by the geometrical optics method. But it still had one parameter m. It is of super Gaussian order m. So geometrically lens G
Even if (r) and H (s) are determined, m still exists as a degree of freedom parameter. Going further, which m is optimal? Must be evaluated. It should be evaluated by an evaluation criterion that the power distribution is not disturbed even after 100 mm or 50 mm (generally, the position at the rear d) due to diffraction.

The evaluation is, of course, valid,
In order to actually measure the power with a photodetector, lenses having super Gaussians of various orders m are actually manufactured, and a laser beam is passed through the phase correction lens to obtain 100
This means measuring the power in mm. Therefore, the lens has to be actually manufactured.

Infrared beam of carbon dioxide laser (10.6 μ
A lens that passes through m) is not so useful in ordinary glass because of its large absorption. ZnSe, which has little absorption in the infrared, will be used as a lens material. Although ZnSe may be polycrystalline, it is a material that is difficult to make and is an expensive lens. It is difficult to measure a laser power distribution by making a lot of it every order m.

100 m behind the phase correction lens by calculation
We want to find the power distribution at m. Such a calculation is performed by a wave-optical method. That is, the present invention intends to adopt a complementary method in which geometrical optics is used for lens design and wave optics is used for lens evaluation.

The design and evaluation of the lens may be consistent if they can be made only by geometrical optics or only wave optics, but wave optics has a drawback that it is difficult to handle a curved lens, and the design of the lens surface is difficult. Can not be used for. Since geometrical optics only traces the beam, it is not suitable for calculating the power distribution behind the lens.

Therefore, the wave optics is used to evaluate the lens. With the wave optics, the power distribution of light at an arbitrary distance behind the phase correction lens can be easily calculated. It is desirable that the top-hat distribution be retained even in the rear, which can be calculated by wave optics. Since the order m of Super Gaussian remains as a parameter, it is possible to obtain what kind of m is optimum by wave optics calculation.

FIG. 9 is an explanatory diagram showing beam propagation in wave optical analysis. The propagation direction of the beam is the z direction.
A plane 1 and a plane 2 orthogonal to the z axis are assumed. Surface 1 and surface 2 are z
In the direction, only d is two planes (xy plane) that are separated from each other. Surface 1
Is A (x ₁ , y ₁ ), and the amplitude on the surface 2 is A (x ₂ ,
y ₂ ), the phase of surface 1 is φ (x ₁ , y ₁ ), and the phase of surface 2 is φ (x ₂ , y ₂ ).

The Kirchhoff-Huygens formula can be approximated by some

[0142]

[Equation 32]

U (x ₁ , y ₁ ) = A (x ₁ , y ₁ ) exp {jφ (x ₁ , y ₁ )} (39)

U (x ₂ , y ₂ ) = A (x ₂ , y ₂ ) exp {jφ (x ₂ , y ₂ )} (40)

The following relationship is given. A (x, y) is the amplitude and φ (x, y) is the phase. With such an expression, 100 mm behind the phase correction lens as an evaluation surface,
The power distribution on the evaluation surface is analyzed by wave optics. The evaluation surface is not limited to 100 mm, and may be 200 mm or 50 mm behind the phase correction lens depending on the purpose. The evaluation surface changes depending on how much distance the object to be processed is actually placed behind the phase correction lens (the distance d between the phase correction lens and the evaluation surface changes).

It is assumed that the rear surface of the phase correction lens is the surface 2 where the phases are aligned and the amplitude has a super Gaussian distribution.

(Rear surface of phase correction lens A (x ₁ , y ₁ )) φ (x ₁ , y ₁ ) = 0 (41) A (x ₁ , y ₁ ) = cexp {− (s / b) ^2m } (42)

(Surface A (x ₂ , y ₂ ; Evaluation Surface) 100 mm Behind the Phase Correction Lens φ (x ₂ , y ₂ ) (43) A (x ₂ , y ₂ ) (44)

There is a relationship of By setting d = 100 mm and substituting (41) and (42) into the equations (38) to (40), the amplitude and phase at A (x ₂ , y ₂ ) can be obtained. The uniformity of the beam power is evaluated from the amplitude and phase. If it is too uneven, it is not suitable as a beam homogenizer. If it is uniform enough to withstand actual use, it is a pass. There are not many lenses actually manufactured, but it is possible to use 10
The uniformity at the 0 mm propagation position was evaluated, and it was found that the power was uniform even at the 100 mm propagation position if the super Gaussian order m was 5 to 50.

When it exceeds 50, the value becomes close to the top hat (a constant value I when r <w, 0 when r> w) and 1 for discontinuity.
The distribution at the 00 mm propagation position becomes non-uniform as shown in FIG. If m is 5 or less, the density of the beam is high in the center and low in the periphery, and the density difference is significant, and laser processing may not be performed well. Therefore, the order m of Super Gaussian is preferably 5 to 50. What to do with the order m? This should be decided depending on how much distance d behind the phase correction lens the object is actually placed.

[C. More detailed design method of phase correction lens and intensity conversion lens by geometrical optics] Even when the target power density is Super Gaussian, an error is likely to occur in the calculation of the curved surface of the phase correction lens around r = ω. This is because the incident Gaussian beam spreads widely outside the forehead (r> R) and they are condensed to try to convert them all into parallel light near the narrow r = ω of the phase correction lens. In that case, it is not good to use (37) which is originally an approximate expression. The whole calculation of the phase correction lens is performed by an accurate formula, or the integral calculation is performed by an accurate formula even only in the vicinity of r = ω of the phase correction lens, so that the problem of nonuniformity at the 100 mm propagation position is further alleviated. Try to lead the exact formula here.

Equation (28), Snell's law (34), (3
5) is an accurate expression. The approximation of (36) with sin Φ is regarded as tan Φ and cos Φ is regarded as 1, which is a fairly rough approximation. The same applies to intensity conversion lenses. A small rs is a good approximation, but rs may be large in some cases. When the gradient of the intensity conversion lens is large even within the forehead,
For example, when r is large outside the frame. If r-s becomes large, the previous term cannot be ignored, and an error will occur in the calculation calculated by ignoring it.

I would like to formulate a more accurate formula by eliminating the approximation.
It is made by the limitation based on the origin of the phase correction lens that the phases are aligned. The optical distance from the front surface of the intensity conversion lens to the rear surface of the phase correction lens should be constant. Let u be the linear distance from the r point of the intensity conversion lens to the s point of the phase correction lens. Because the straight line connecting rs makes an angle of Φ with the axis and the height is (s-r).

[0154] u = (s−r) cosecΦ (45)

It is The distance from the front surface of the intensity conversion lens to the rear surface of the phase correction lens is L + q. The axial distance from the rear surface of the intensity conversion lens to the front surface of the phase correction lens is L. q is the sum of the thicknesses of the intensity conversion lens and the phase correction lens on the axis (r = 0, s = 0). The optical distance on the axis (refractive index × distance) is L + nq. Light that travels at an angle of Φ from the r point of the intensity conversion lens and travels to the s point of the phase correction lens propagates in free space at the distance u between the r point and the s point, and L + q-ucosΦ propagates in the lens. become. The optical distance through the points r and s is u + n (L + q-
ucosΦ). Because they are equal

[0156] u + n (L + q-ucosΦ) = L + nq (46)

This is the true phase correction.

[0158]

[Expression 33]

That is,

[0160]

[Equation 34]

From this and the equation (35), an accurate equation without approximation can be obtained. Square (35),

[0162]

[Equation 35]

A curved surface H (s) of the phase correction lens is obtained by taking the square root and integrating with s.

(A) If s ≦ R (within forehead), the phase correction lens is

[0165]

[Equation 36]

[0166]

(B) If the amount is outside the frame (s> R), the phase correction lens

[0168]

[Equation 37]

It becomes: The exact formula of the phase correction lens is (5
It becomes like 0) and (51). This is an accurate expression with the condition that the phases are aligned. That is, it was approximated as in (37). A large error occurs when s-r is large. Since even a slight error is integrated, it gradually increases. It can be considered that they accumulated and caused a large error.

In the denominator of the integrand of (50) or (51), if r and s are small and s-r is small near the center of the lens, the rear term is large, so the previous n ² -1 can be ignored. However, it is not correct to ignore n ² -1 when the center-of-center s-r becomes a large positive number. Also s,
When r exceeds the ring, s-r becomes a large negative number.
Then, the previous n ² −1 cannot be ignored, and the surface integral H (s) is affected. In the case of visible light such as quartz, n = 1.4, so n ² −1 = 1 is small, but
Since ZnSe for infrared light has a value of about n = 2.4, it becomes a considerably large value at about n ² −1 = 4.7 and cannot be ignored.

Therefore, in the calculation in a region close to the forehead ring (s = R) or outside the frame (s> R), it is not an approximate expression (50), (5
The formula in 1) should be used. The relation between s and r is (2
Given by 7). Although (50) and (51) are slightly difficult to calculate, they can be easily calculated by using a computer. This is an accurate expression obtained by imposing a condition that the phases are aligned and does not include approximation. When designed by this calculation, since the phases are perfectly aligned on the rear surface of the phase correction lens, the beam turbulence at the 100 mm propagation position should be greatly reduced.

In the point that the error due to such an approximate calculation has an influence, a rather serious problem occurs in the intensity conversion lens. This is because the beam angle Φ shifts even with a slight deviation of the surface angle, but it is expanded by the inter-lens distance L, and an error of LΔΦ occurs on the phase correction lens surface. Even in the intensity conversion lens L1, the accurate expression of the curved surface G (r) is similar to that of the phase correction lens,

(C) If r ≦ R (within forehead), the intensity conversion lens is

[0174]

[Equation 38]

If (b) out of the frame (r> R), the intensity conversion lens is

[0176]

[Formula 39]

It becomes: The exact formula of the intensity conversion lens is (5
2) and (53). That is, it was approximated by (33). It is only an approximation, and it can be considered that a small error is included and they are accumulated to generate a large error.

The cause of the non-uniformity in the backward propagation position of the homogenizer of the conventional example may be the influence of diffraction, but rather the main cause is considered to be the accumulation of errors due to approximation calculation. Then, not only the continuity of I ₂ is increased by using the target beam distribution I ₂ as super Gaussian, but also the curved surfaces G (r) and H (s) of the lens are calculated by an accurate integration formula, so that the phases are neatly aligned, It is believed that the power nonuniformity at the propagation position is reduced.

[0179]

Example An aspherical homogenizer was designed by the method described above. As an incident laser, wavelength λ
A carbon dioxide gas laser of = 10.6 μm was used. Beam diameter (1 / e ² ) φ15m of this with a collimator lens system
m Gaussian beam (b = 15 mm). The distance L between the intensity conversion lens L1 and the phase correction lens L2 is 170 mm. One of the purposes is to make the output beam φ15 mm (1 / e
² ) The intensity is to have a uniform distribution on the order of Super Gaussian (ω = 15 mm). Another purpose is 100 mm (d = 1) behind the phase correction lens L2.
This means that the power distribution at 00 mm) does not collapse.

The order of Super Gaussian was set to m = 30. Table 1 shows laser conditions such as beam diameter, beam waist, and radius of curvature.

[0181]

[Table 1]

Super Gaussian is set to m = 30. The curved surface (aspherical lens) L1 of the intensity conversion lens and the curved surface (aspherical lens) L2 of the phase correction lens can be determined by a geometrical optical method. The curved surface of an aspheric lens

[0183]

[Formula 40]

Expressed. r is the radius from the center of the lens to the peripheral portion and is a parameter. c is the curvature. K is a correction coefficient, and if K = 0, the lens has a perfect spherical surface and the radius of curvature is 1 / c. Therefore, the first half is the expression for spherical lenses, and the second half expresses the aspherical coefficient. The lens has central symmetry, and the odd-order coefficient of r is 0 (A <sub>2i
+ 1</sub> = 0). So ^{r 2, r 4,} ... coefficients of even-order and so ^{r 20} _{A 2, A 4,} may be obtained only ... _{A 20.} It is up to you which degree you want to calculate,
Here, the term A ₂₀ of r to the 20th power is calculated.

The units of the aspherical coefficients A ₂ , A ₄ , ... A ₂₀ are mm ^-1 , mm ^-3 , ..., mm ^-19 here.
D is the diameter (mm) of the entire lens, and CA is the diameter (mm) of the curved surface portion. CT is the thickness at the center of the lens. E
T is the thickness of the edge of the lens, and ET 'is the thickness at the outermost part of the curved surface of the lens.

[L1 intensity conversion lens]

[0187]

[Table 2]

Terms above the 20th power are not calculated. The aspherical surface coefficient of the intensity conversion lens is above. It is determined that the beam refracted by the intensity conversion lens has a super Gaussian power distribution of m = 30 by the phase correction lens. Since c = 0, the spherical component is 0 and is defined only by the aspherical coefficient.

Since this is difficult to understand, FIG. 15 shows a curve of the shape G (r) of the rear surface of the intensity conversion lens. The vertical axis represents the height of the rear surface, and the horizontal axis represents the position of radius r. In the portion near the center, it becomes a concave surface that rises with the square of r, and when r = 6 mm, G (r) is about 0.1 mm at maximum. When it is 7 mm or more, the surface starts to recede and becomes a convex surface. G becomes negative at r = 9 mm. When r = 15 mm, the value is −0.
About 1 mm, r = 20 mm, about -0.3 mm, r = 22.5
It is about -0.45 mm in mm.

[0190]

[Table 3]

Although the front surface of the phase correction lens is a curved surface, the backward displacement from the plane is represented here. Therefore, it seems that the tendency of unevenness is similar to that of the intensity conversion lens, but it is actually the opposite. The intensity conversion lens G (r) and the phase correction lens H (s) always have the same gradient (G '= H') under the constraint condition that the beam at the r point goes to the s point, and thus are expressed as a deviation from the front surface. It is easier to understand the correspondence if you do.

Since c = 0 of the phase correction lens, the spherical component is 0. The lens diameter, curved surface diameter, thickness, etc. are made substantially the same. FIG. 16 shows the curved surface of the front surface of the phase correction lens as a function of the radius s.

Although the phase correction lens is complementary to the intensity conversion lens, it is still quite different in shape. R in the center
It becomes a convex surface that rises as the square of (or s). 6.1m
The maximum value for m is 0.012 mm. Outside of that, the surface recedes and H = 0 is cut at s = 7.6 mm for the first time. s = 8
H (s) drops sharply at mm-9mm-0.11mm
become. Here, the phase correction lens is shown only up to s = 9 mm, but since the target spread (1 / e ² ) ω of the super Gaussian beam is 15 mmφ, there is only a spread of 7.5 mm in radius.

Since the front surface of the phase correction lens has such a power distribution, the phase correction lens uses only the area within 9 mm. Therefore, only up to 9 mm is shown here. The outer shape is arbitrary. In actuality, the amount of cutting is reduced so that the outside is hardly cut. Therefore, the phase correction lens has a shape with convex portions at the center and the peripheral portion (FIG. 11), but the convex portion at the peripheral portion is not so meaningful.

Promet for measuring the laser beam intensity
A laser scope UFF100 manufactured by ec was used. The laser scope has a copper needle with a pinhole of 10 to 300 μm processed at the tip of 250 to 1500 RPM.
The intensity distribution is measured by scanning the laser light while rotating with.

M used as a quality indicator of laser light
² is a mode master BMS-6 manufactured by Coherent
It measured using B.

FIG. 12 shows the intensity of laser light immediately after the phase correction lens. The left side shows the laser beam on a white background. φ1
A circular beam with a nearly uniform power of 5 mm (ω = 7.5 m
m). On the right, the beam power change is measured in a certain diameter direction. The horizontal axis is μm, and as designed, up to 7,000 μm, with almost uniform power, 7,000 μm to 80
The power drops sharply at 00 μm.
It corresponds to the distribution of Super Gaussian (ω = 7.5 mm).

FIG. 13 shows the two-dimensional power measurement result. (A) is a two-dimensional power distribution immediately after leaving the phase correction lens. Although the same thing as in FIG. 12 is measured, it can be seen that it is almost uniform within φ15 mm in both the x direction, the y direction and any direction. FIG. 13B shows the measurement result of the power distribution after propagating 100 mm behind the phase correction lens. Although it is slightly distorted compared to immediately after the phase correction lens, it still maintains a uniform circular beam with a diameter of 15 mm.

FIG. 14 shows a comparison between measured and calculated values of the gradient distribution in a certain diameter direction at the 100 mm propagation position. The solid line shows the measurement result, and the broken line shows the calculation (analysis) result.
Compared to FIG. 12, the power drops slightly around φ15 mm, but it can be said that the power is still almost constant at φ15 mm. It can be seen that the analysis results and the actual measurements are in good agreement.

[0200]

The intensity conversion lens L1 which is an aspherical lens
And a phase correction lens L2 are combined to convert a Gaussian beam such as a carbon dioxide gas laser into a super Gaussian beam having a substantially uniform distribution. If the top hat is completely made, the power distribution will be disturbed behind the phase correction lens, but since the desired power distribution is Super Gaussian with a slight skirt around the periphery, even after 100 mm or 200 mm the homogenizer exits, a uniform power distribution is achieved. The distribution is not so disturbed.

By adopting Super Gaussian, the discontinuity of the lens can be reduced and the influence of diffraction can be reduced. When the intensity conversion lens collects light that is weak and spread outside the Gaussian beam width b, if it is a strict top hat, it is necessary to collect those front parts in a very narrow range of the phase correction lens. Therefore, the curvature of the lens of the phase correction lens changes remarkably and the error increases. For this reason, the phases are not aligned immediately after the phase correction lens, and for that reason, power nonuniformity is noticeable 100 mm, 200 mm, or the rear thereof.

According to the present invention, since the power density changes gently at the boundary of ω instead of the top hat, the change in curvature of the phase correction lens can be suppressed and the accuracy becomes higher. Therefore, the turbulence of the beam after the phase correction lens is reduced.

The intensity conversion lens and the phase correction lens are designed by a geometrical optical method, and the power disturbance due to diffraction after the homogenizer is emitted is analyzed by a wave optical method.
Diffraction can be evaluated by a wave-optical method to determine the optimum super Gaussian order m. Since the spread b of the Gaussian beam of the first laser and the target spread ω of the uniform beam are various, the embodiment (b = 15 mm, ω
= 15 mm, d = 100 mm), m = 30 is not always optimum. However, for any combination of b and ω, the power distribution 100 mm after the emission can be calculated by the wave optics method, and the superiority or inferiority of m can be compared. Therefore, the optimum m, the optimum intensity conversion lens, and the optimum phase correction lens can be provided.

The present invention makes it possible to design an optimum lens by eclectically combining both the wave optics and the geometrical optics.

[Brief description of drawings]

FIG. 1 is a laser device, a zoom optical system, an intensity conversion lens,
FIG. 3 is a configuration diagram of a beam homogenizer including a phase correction lens and a laser perforation optical system including a transfer optical system.

FIG. 2 is a top-hat type (r ≦ b
When the intensity conversion lens and the phase correction lens are designed by requesting a power distribution of a constant value I, 0 for r> b, the power distribution immediately after the phase correction lens (a) and the propagation position 100 mm behind the phase correction lens 2D power distribution measurement diagram showing the power distribution (b) in FIG. The distribution is largely disturbed from the uniform distribution at the 100 mm propagation position.

FIG. 3 is a diagram in which a uniform distribution is approximated as a set of many minute Gaussian distributions whose axes are slightly shifted. (A) When the distribution deviates considerably from the uniform distribution and the distribution has a tail at the end, it can be approximated by a few Gaussian beams having a relatively large beam diameter and the influence of diffraction is small. (B)
It shows that the distribution is closer to the uniform distribution and the distribution is well cut off at the edges, and the influence of diffraction becomes large.

FIG. 4 is an aspherical beam homogenizer including an intensity conversion lens that reshapes an incident Gaussian beam into a uniform distribution and a phase correction lens that converts a beam having a uniform distribution but tilted with respect to the axis into a beam parallel to the axis. Optics diagram.

FIG. 5 magnifies the light in the center of the incident Gaussian beam,
The figure which shows the design method of the intensity conversion lens which condenses the light of a peripheral part and converts it into uniform power.

FIG. 6 is an optical system diagram showing a relationship among incident light, emitted light, and a lens inclination angle in the intensity conversion lens.

FIG. 7 is an optical system diagram showing the relationship between the angles of incident light and emitted light and the lens tilt angle in the phase correction lens.

FIG. 8: The incident parallel beam is given a tilt angle Φ by the intensity conversion lens, and the beam exiting the r point of the intensity conversion lens forms the tilt angle Φ with the axis and propagates to the s point of the phase correction lens for phase correction. The figure explaining that it becomes a parallel beam with a lens.

FIG. 9 shows beam propagation in wave optics analysis, first
The amplitude of a plane as _{a 1 (x 1, y 1} ), then diagram the amplitude of the second surface indicates that the _{a 2 (x 2, y 2} ) spaced by distance d.

FIG. 10 is a diagram showing a geometrical optics treatment (a) in which the lens thickness can be accurately taken into consideration and a wave optics treatment (b) in which the lens is treated as having a thickness of 0.

FIG. 11 is a diagram illustrating a problem in a wave optical analysis in which the lens thickness is treated as 0.

FIG. 12 is a photograph (a) showing the beam intensity immediately after the phase correction lens of the homogenizer manufactured in Example.
The graph which shows the beam power intensity measurement result along a certain diameter.

13A is a diagram showing a measurement result of a two-dimensional power distribution immediately after the phase correction lens of the homogenizer according to the example of the present invention, and FIG. 13A is a diagram showing a measurement result of the two-dimensional power distribution after 100 mm propagation from the phase correction lens. Figure (b).

FIG. 14 shows a phase correction lens 1 of the device in the embodiment.
The graph which shows the analysis result (broken line) and the measurement result (solid line) of the power distribution in a 00 mm propagation position.

FIG. 15 is a diagram showing the curvature of the rear surface of the intensity conversion lens in the example.

FIG. 16 is a diagram showing the curvature of the front surface of the phase correction lens in Example.

[Explanation of symbols]

1 intensity interchangeable lens 2 Phase correction lens 3 outside 4 frame Within 5 forehead

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Keiji Fuse             Lives 1-3-3 Shimaya, Konohana-ku, Osaka City, Osaka Prefecture             Tomo Denki Kogyo Co., Ltd. Osaka Works F term (reference) 2H087 KA26 LA26 PA02 PA17 PB02                       QA01 QA05 QA18 QA21 QA33                       QA42 RA03 RA12

Claims (3)

[Claims] 1. A power distribution having a high density in a central portion and a low density in a peripheral portion and (π ⁻¹ b ⁻² ) ex at a point r from the center.
The incident laser beam I ₁ (r) having a Gaussian power distribution of p (−r ² / b ² ) is shaped into a parallel beam having a power distribution that is not completely uniform but almost uniform in a certain radius range s ≦ ω. In a set of lenses, the beam diameter is expanded in the central part and reduced in the peripheral part, and the power distribution I ₂ (s) at a point s from the center, which is a substantially uniform distribution with a width ω
Super Gaussian cexp {-(s / ω) ^2m }
Curved surface G such that (m = 5 to 50) (c is a constant)
An intensity conversion lens L1 having (r), and a phase matching lens L2 having a curved surface H (s) which is placed at a distance L from the lens and refracts the intensity-converted laser beam to form a beam parallel to the axis, The integral of the incident beam power from the center O to the center r of the intensity conversion lens L1 is equal to the integral of the outgoing beam power from the center of the lens of the phase correction lens L2 to s. As a relationship between the radius coordinate r of the intensity conversion lens L1 and the radius coordinate s of the phase correction lens L2,
The surface shape G (r) of 1 is given by The shape H (s) of the surface of the phase correction lens is calculated by A laser beam shaping lens characterized by being determined by. 2. A power having a high density in the central part and a low density in the peripheral part.
Has a distribution, and at the point r from the center (π^-1b^-2) Ex
p (-r^Two/ B^Two) With Gaussian power distribution
Laser beam I₁Complete (r) within a certain radius range s ≤ ω
Parallel beam with power distribution that is not uniform but nearly uniform
It is a set of lenses that are shaped into
Expanded and reduced the beam diameter at the periphery, almost uniform in width ω
The power distribution at the point s from the center
Gaussian cexp {-(s / ω)^2m} (M = 5-5
0) (c is a constant) the strength with a curved surface G (r)
The conversion lens L1 and the intensity that is placed a distance L away from it
A beam parallel to the axis that refracts the converted laser beam
With a phase matching lens L2 having a curved surface H (s)
Center of the intensity conversion lens L1
The integral of incident beam power from O to r is complementary
Output beam power from the center of the positive lens L2 to s
Equal to the integral of [Equation 4] As the radial coordinate r of the intensity conversion lens L1 and the phase correction
The relationship of the radius coordinate s of the lens L2 is determined geometrically and the strength is determined.
The shape G (r) of the surface of the conversion lens L1 is [Equation 5] And calculate the surface shape H (s) of the phase correction lens by [Equation 6] Calculated by the method of geometrical optics
The amplitude of the rear surface of the ₁, Y₁), The phase is φ (x₁，
y₁), And φ (x₁, Y₁) = 1, A (x₁, Y₁)
= Cexp {-(s / ω)^m}, S^Two= X₁ ^Two+ Y₁ ^Two
The initial condition immediately after the phase correction lens is given by
The amplitude at the position d behind the positive lens is A (x_Two，
y_Two), The phase is φ (x_Two, Y_Two)age, [Equation 7] To evaluate the homogeneity of the amplitude in the backward d.
By and the super Gaussian degree m between 5 and 50
Intensity conversion lens with one value and its order m
And that the phase correction lens is manufactured.
Laser beam forming lens design method. 3. A power distribution having a high density in the central portion and a low density in the peripheral portion, and (π ⁻¹ b ⁻² ) ex at a point r from the center.
The incident laser beam I ₁ (r) having a Gaussian power distribution of p (−r ² / b ² ) is shaped into a parallel beam having a power distribution that is not completely uniform but almost uniform in a certain radius range s ≦ ω. In a set of lenses, the beam diameter is expanded in the central part and reduced in the peripheral part, and the power distribution I ₂ (s) at a point s from the center, which is a substantially uniform distribution with a width ω
Super Gaussian cexp {-(s / ω) ^2m }
Curved surface G such that (m = 5 to 50) (c is a constant)
An intensity conversion lens L1 having (r), and a phase matching lens L2 having a curved surface H (s) which is placed at a distance L from the lens and refracts the intensity-converted laser beam to form a beam parallel to the axis, The integral of the incident beam power from the center O of the intensity conversion lens L1 to r is equal to the integral of the outgoing beam power from the center of the lens of the phase correction lens L2 to s. As a result, the relationship between the radial coordinate r of the intensity conversion lens L1 and the radial coordinate s of the phase correction lens L2 is determined, the ring with r = s is a frame (r = s = R), and the surface shape G of the intensity conversion lens L1 is G. If r ≦ R (within the forehead) of (r), then If it is out of the frame (r> R), the intensity conversion lens is And calculate the surface shape H (s) of the phase correction lens as s
If ≦ R (within the amount), then If it is out of the frame (s> R), the phase correction lens is A laser beam shaping lens characterized by being calculated as follows.