JP2589898B2 - Cylindrical lens - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a cylindrical lens, and more particularly to a lens which can obtain a suitable result when used in a scanning optical system.

[0002]

2. Description of the Related Art FIG. 13 is a perspective view of a conventional cylindrical lens. In the figure, O is the origin. For convenience of the following description, a y-axis extending parallel to the symmetry axis of the cylindrical lens 1 through the origin O and an optical axis O
A description will be given using a three-dimensional space including a z-axis that matches A and an x-axis that is orthogonal to the y-axis and the z-axis.

When a parallel light beam L is incident on the cylindrical lens 1 having a focal length f along the optical axis OA, the light goes straight on the yz plane, but is condensed at a predetermined position on the xz plane. As a result, a focal line FL is formed on a Gaussian image plane separated by a distance f in the z direction from a rear principal point (not shown) of the cylindrical lens 1.

Conventionally, surface tilt correction of a scanning optical system has been generally performed by utilizing such optical characteristics of the cylindrical lens 1. This is because, for example, a scanning optical system deflects a light beam from a light source with a polygon mirror and scans the surface to be scanned with the light beam via a scanning lens. Needs to be corrected. Therefore, using a cylindrical lens, the reflection surface of the polygon mirror and the surface to be scanned (image surface) are conjugated to each other at a surface orthogonal to the scanning surface (the xz plane in FIG. 13).

[0005]

As shown in FIG. 13, when a parallel light beam L 'at an angle θ with respect to the z-axis is incident on the cylindrical lens 1 while being on the yz plane, the cylindrical surface of the cylindrical lens 1 Is apparently small, and the focal line FL 'is formed on the light source side (left hand side in the figure) with respect to the Gaussian image plane. For this reason, there is a problem that the image plane is curved. In the following description, the angle θ (θ
The light incident at (0 °) is referred to as “oblique incident light”.

As a solution to this problem, for example,
-7082 and JP-A-62-265615. In the former, the curvature of field is corrected by bending a cylindrical lens. In the latter, the radius of curvature in the plane tilt direction is made larger off-axis than on the optical axis.

However, processing the cylindrical lens as described above is not easy in terms of manufacturing technology.

The present invention has been made to solve the above problems, and provides a cylindrical lens which can be easily manufactured and has a focal line position almost coincident with a Gaussian image plane even for obliquely incident light. The purpose is to do.

[0009]

According to the first aspect of the present invention, there is provided a cylindrical lens for achieving the above object.
A plurality of straight bands extending in a first direction are arranged at irregular intervals in a second direction substantially orthogonal to the first direction;
It consists of a linear zone plate functioning as a diffractive element with a focal length fH, and a concave cylindrical surface with a focal length fG having a symmetry axis parallel to the first direction, and satisfies the following inequality: fH> 0 fG <0 I do.

According to a second aspect of the present invention, in order to achieve the above object, a plurality of straight bands extending in a first direction are formed in a second direction substantially orthogonal to the first direction. At unequal intervals, the focal length f
A linear zone plate functioning as an H diffraction element,
A first optical element consisting of a first plane parallel to a plane including the first and second directions, a concave cylindrical surface having a focal length fG having a symmetry axis parallel to the first direction, A second plane parallel to the first plane.
And further satisfies the following inequality: fH> 0 fG <0.

[0011]

In the cylindrical lens according to the present invention,
The focal length fH of the linear zone plate is a positive value, while the focal length fG of the concave cylindrical surface is a negative value. Therefore, the characteristics of the linear zone plate with respect to the obliquely incident light are completely opposite to those of the concave cylindrical surface. As a result, the respective characteristics are cancelled, and the focal line position for obliquely incident light substantially matches the Gaussian image plane.

[0012]

FIG. 1 is a perspective view showing an embodiment of a cylindrical lens according to the present invention. As shown in the figure, the cylindrical lens 10 is provided on the light source side (the left-hand side in the figure), and functions as a diffraction element with a linear zone plate (hereinafter referred to as “LZP”) 11 and an image side (in FIG. The concave cylindrical surface 12 provided on the right hand side)
It is composed of The x, y, and z axes in the figure are the same as those in the conventional example described above (FIG. 13).

FIG. 2 is a front view of the LZP 11, and FIG. 3 is a side view thereof. As shown in FIG. 2, a plurality of unequally-spaced linear bands LB extending in the y-axis direction are formed in the LZP 11. There are the following three types of these straight bands LB.

(1) A linear groove b1 formed in a step shape as shown in FIG. 3 (a) (2) Blazed as shown in FIG. 3 (b) b2 (3) FIG. In general, the first two of these three types are called phase type, and the remaining ones are called amplitude type. The diffraction efficiency of the type (2) is the best and that of the type (3) is the worst. On the other hand, as shown in FIG. 1, the concave cylindrical surface 12 is finished so as to have a symmetry axis parallel to the straight band LB.

Next, the concave cylindrical surface 12 and the LZP
After considering the characteristics of No. 11, the operation of the cylindrical lens 10 configured as described above will be described. If the radius of curvature of the concave cylindrical surface 12 is R, the refractive index on the light source side relative to the concave cylindrical surface 12 is n1, and the refractive index on the image side is n2, the focal length fG of the concave cylindrical surface 12 is
Is

[0016]

(Equation 1)

## EQU1 ## Here, from the computer simulation, when obliquely incident light of θ = 30 ° is incident on the plano-convex cylindrical lens 1 (FIG. 13) having a focal length fG and made of a medium having a refractive index of 1.51, the focal line becomes a Gaussian image. It was found that the light source side was formed at a distance (0.23 fG) from the surface. If the refractive index of the medium is increased, the amount of shift of the focal line from the Gaussian image plane is slightly reduced, but the refractive index is 1.8.
Even when the medium No. 4 is used, the reduction is about 10%.

Next, the characteristics of the LZP 11 will be considered. Here, as shown in FIG. 4, a plane wave is incident from the left hand side of FIG.
Consider a case where the first-order diffracted wave is converted into a cylindrical wave. If the optical path difference between the light beam that exits the k-th band LB from the optical axis OA (z-axis) and the light beam that passes through the optical axis is an integral multiple of the wavelength, the two lights reinforce each other. That is, the x coordinate Xk of the k-th straight band is

[0019]

(Equation 2)

Is given by Where fH is the LZP
11 is the focal length, and λ is the wavelength of light. Therefore, by forming unequally-spaced linear bands LB in parallel with the y-axis so that the band density increases as the absolute value of the x-coordinate increases from the origin O, it is possible to have a function equivalent to that of the convex cylindrical lens. it can.

More generally, the position of the linear band can be expressed as an equiphase straight line in which the phase difference defined by the following equation is an integral multiple of 2π.

[0022]

(Equation 3)

Here, A and B are constants.

If k = 1 in Equation 2, then

[0025]

(Equation 4)

The coordinates X1 of the first band are obtained. Since fH >> λ, Equation 4 is

[0027]

(Equation 5)

As shown in FIG.

By the way, the position of the first band is when the right side of Equation 3 becomes 2π, and since the value of x is small, the fourth order term is ignored.

[0030]

(Equation 6)

Is obtained. Then, by substituting Equation 5 into Equation 6,

[0032]

(Equation 7)

Is obtained, and this equation 7 is further transformed to

[0034]

(Equation 8)

Is obtained.

Although the term of the coefficient B has been neglected in the above description, this term is a term that gives an additional aberration, and various aberrations are generated in the diffracted light from the LZP 11 by appropriately selecting the value of the coefficient B. can do. Therefore, the coefficient B
By adjusting (1), the aberration generated on the concave cylindrical surface 12 can be corrected, and the aberration of the entire cylindrical lens 10 can be controlled.

Next, from a computer simulation, when obliquely incident light at θ = 30 ° is incident on the LZP 11 having the focal length fH, the focal line is shifted from the Gaussian image plane by a distance (0.13 fH).
It was found that only the light source side was formed. This value does not depend on the wavelength used or the order. The reason can be considered as follows. Since the band pitch of the LZP 11 does not change apparently with respect to obliquely incident light, the light is always focused at a distance fH from the incident point regardless of the incident angle θ when measured along the principal ray. Therefore, the Gaussian image plane of LZP11 and the focal line FL
Is represented by fH * (1−COS θ).

FIG. 5 is a graph showing the relationship between the incident angle θ and the distance from the Gaussian image plane to the focal line. The solid line is a cylindrical lens 1 having a refractive index of 1.51, and the dotted line is a cylindrical lens 1 having a refractive index of 1.84. The cylindrical lens 1 and the chain line are LZ
The characteristics for P11 are shown. As can be seen from the figure, the amount by which the focal line position comes to the light source side with respect to the obliquely incident light is 1.5 times greater for the cylindrical lens 1 than for the LZP11.
Times to 1.7 times larger.

Therefore, in the cylindrical lens 10 of FIG. 1, the focal length fG of the concave cylindrical surface 12 can be set to a negative value, while the focal length fH of the LZP 11 can be set to a positive value, and the ratio of the focal lengths can be appropriately selected. If this is the case, the characteristics of the two with respect to oblique incident light can be offset. As a result, even for obliquely incident light, there is a combination in which the focal line is not located on the light source side, that is, the focal line FL substantially matches the Gaussian image plane. In particular, if the distance between the LZP 11 and the concave cylindrical surface 12 is zero, the value of fH / fG may be set to about -0.6.

Next, the first and second embodiments will be described in more detail, and their optical characteristics will be evaluated.

<First Embodiment> The cylindrical lens according to the first embodiment is constructed as shown in FIG. 1 and constructed according to data shown in Table 1.

[0042]

[Table 1]

Although not shown in the table, the cylindrical lens 10 is finished in a so-called plano-concave cylindrical shape having no curvature in the y direction. Also,
The first surface is LZP11, and the coefficients A and B in Equation 3 are A = 189.05 B = −1.0423. The wavelength used is λ = 633 nm, and first-order diffracted light is used. The diameter of the light beam incident on the cylindrical lens 10 is 2 mm.

Therefore, the focal length of the LZP 11 is fH = 4.2 mm from the equation (8), and the focal length of the concave cylindrical surface 12 is fG = -5.5 mm from the equation (1). Therefore, fH / fG = -0.76.

For example, the pitch of the straight band LB at 1 mm in the x direction from the optical axis OA is 2.7 μm from the equation (3). Therefore, the LZP 11 can be easily formed by a known machine engraving method or photolithography method. Therefore, the manufacture of the cylindrical lens 10 of FIG. 1 is relatively simple.

The focal length f of the cylindrical lens 10 is the combined focal length of the LZP 11 and the concave cylindrical surface 12, and the focal length f is determined by the following equation.

[0047]

(Equation 9)

Therefore, the focal length f of the cylindrical lens 10 according to the first embodiment is 11.8 mm,
The number will be 5.9. The back focus is 1
0 mm.

FIG. 6 is a graph showing the lateral aberration in the x direction of the cylindrical lens according to the first embodiment.
And (c) indicate that the parallel light flux having a diameter of 2 mm is θ = 0.
It shows the lateral aberration when the light is incident at °, θ = 15 °, and θ = 20 °. As can be seen from FIG. 6, according to the first embodiment, a flat image plane can be obtained even for obliquely incident light. In addition, the spherical aberration generated on the cylindrical surface 12 can be corrected by the operation of the coefficient B in Equation 3, and the lateral aberration is within ± 1 μm.

<Second Embodiment> FIG. 7 is a plan view showing an example in which a cylindrical lens according to the present invention is used in a laser beam scanning device. FIG. 8 is a partial side view thereof. The optical system of this laser beam scanning device includes a light source 2 for emitting a parallel laser beam L.
1, a cylindrical lens 22 having a generatrix perpendicular to the scanning plane (yz plane), a doublet lens 23 including two lenses 23a and 23b, a polygon mirror 24,
Fθ lens 25 comprising a plurality of lenses 25a to 25e;
It comprises a cylindrical lens 26 having the same configuration as that of FIG. The optical system is configured according to the data shown in Table 2.

[0051]

[Table 2]

The cylindrical lens 22 composed of the surfaces S1 and S2 and the doublet lens 23 composed of the surfaces S3 to S5 are spaced apart by the sum of their respective focal lengths. The laser beam L from the light source 21 passes through the cylindrical lens 22 and the doublet lens 23, and
It becomes parallel light with a diameter of 21 mm in the z plane and convergent light in the xz plane. The reflection surface 24a of the polygon mirror 24 is located at a position converged in the xz plane.

The fθ lens 25 composed of the surfaces S7 to S16 is
This is described in JP-A-55-53308, and its focal length is 500 mm. Angle of view is 67.2
° and the scan length is 586 mm. The F number is 23.8, and a spot of 25 μm is obtained on the scanning surface 27.

The element constituted by the surfaces S17 and S18 is the cylindrical lens 26 according to the present invention. As shown in FIG. 8, by disposing the cylindrical lens 26 between the fθ lens 25 and the scanned surface 27, the polygon mirror surface 24a and the scanned surface 27 are conjugated in the xz plane,
Thereby, the tilt of the polygon mirror 24 is corrected.

The surface S17 is LZP11, and the coefficients A and B in the equation 3 are A = 23.73 B = 0. In addition, from Equation 8, the focal length fH of the LZP 11 becomes fH = 33.3 mm. In the second embodiment, the beam diameter on the surface S17 is 4.2 mm, and the band pitch at 2.1 mm from the optical axis of the LZP 11 is 10 μm from Equation 4.

The surface S18 is a concave cylindrical surface 12,
From the radius of curvature and the refractive index, fG = −33.38 mm. Therefore, fH / fG = -1.0. From Equation 9, the focal length f of the cylindrical lens 26 is f = 1111.3 mm. The distance from the cylindrical lens 26 to the surface to be scanned 27 is 100 mm, which means that a small amount of convergent light is incident on the cylindrical lens 26 even in the xz plane.

FIGS. 9, 10 and 11 show image heights of this laser beam scanning apparatus of 0 mm and 205 m, respectively.
m and 293 mm. As can be seen from these figures, there is almost no sagittal field curvature, and the cylindrical lens 26 according to the present invention has good light-collecting characteristics.

In the above embodiment, the description has been given of the cylindrical lens composed of the LZP 11 and the cylindrical surface 12, but as shown in FIG.
1 is provided and the other side is a plane 1 parallel to the xy plane.
3 and a concave cylindrical surface 12 on one side and xy on the other side.
The same effect as described above can be obtained also in the cylindrical lens 30 in which the second optical element 32 provided with the plane 14 parallel to the surface is combined.

In the above embodiment, the LZP1
1 and the case where the concave cylindrical surface 12 is arranged on the image surface side, the concave cylindrical surface 12 is arranged on the light source side and the LZP 11 is arranged on the image surface side in the first embodiment. LZP1 in the second embodiment
1, concave cylindrical surface 12 and parallel planes 13, 14
May be arranged in any order.

The cross section of the cylindrical surface is not limited to a circular shape, but may be a parabolic surface, an elliptical surface, or any other higher-order non-required surface.

[0061]

As described above, according to the cylindrical lens of the present invention, while the focal length fH of the linear zone plate is a positive value, the focal length fG of the concave cylindrical surface is a negative value. Since the characteristics of the linear zone plate with respect to oblique incident light are made to be completely opposite to those of the concave cylindrical surface, the focal line position with respect to oblique incident light can be made substantially coincident with the Gaussian image plane. In addition, since the cylindrical lens has a general shape, the cylindrical lens can be easily manufactured.

[Brief description of the drawings]

FIG. 1 is a perspective view showing one embodiment of a cylindrical lens according to the present invention.

FIG. 2 is a front view of the LZP.

FIG. 3 is a side view of the LZP.

FIG. 4 is a perspective view for explaining characteristics of LZP.

FIG. 5 is a graph showing a relationship between an incident angle θ and a distance from a Gaussian image plane to a focal line.

FIG. 6 shows x of the cylindrical lens according to the first example.
It is a graph which shows the transverse aberration of a direction.

FIG. 7 is a plan view showing an example in which a cylindrical lens according to the present invention is used in a laser beam scanning device.

FIG. 8 is a partial side view thereof.

FIG. 9 shows an image height of 0 mm of a laser beam scanning device.
FIG. 4 is a diagram showing lateral aberrations of FIG.

FIG. 10: Image height of laser beam scanning device 20
It is a figure which shows the lateral aberration of 5 mm.

FIG. 11 shows an image height of 29 of a laser beam scanning device.
It is a figure which shows the transverse aberration of 3 mm.

FIG. 12 is a perspective view showing another embodiment of the cylindrical lens according to the present invention.

FIG. 13 is a perspective view of a conventional cylindrical lens.

[Explanation of symbols]

 11 LZP 12 Concave cylindrical surface 13, 14 Plane 31 First optical element 32 Second optical element LB Linear band

Claims (2)

(57) [Claims] 1. A plurality of linear bands extending in a first direction are arranged at irregular intervals in a second direction substantially orthogonal to the first direction, and function as a diffraction element having a focal length fH. A cylindrical lens comprising: a linear zone plate; and a concave cylindrical surface having a focal length fG having an axis of symmetry parallel to the first direction, and satisfying the following inequality: fH> 0 fG <0. 2. A plurality of linear bands extending in a first direction are arranged at unequal intervals in a second direction substantially orthogonal to the first direction, and function as a diffraction element having a focal length fH. A first optical element composed of a linear zone plate and a first plane parallel to a plane including the first and second directions; and a focal length fG having an axis of symmetry parallel to the first direction. A second optical element comprising a concave cylindrical surface and a second plane parallel to the first plane is combined, and the following inequality expression is satisfied: fH> 0 fG <0. Cylindrical lens.