WO2018029748A1

WO2018029748A1 - Wide-angle lens

Info

Publication number: WO2018029748A1
Application number: PCT/JP2016/073281
Authority: WO
Inventors: 征史小川; 俊樹渡邊; 拓哉坂田
Original assignee: 株式会社トヨテック
Priority date: 2016-08-08
Filing date: 2016-08-08
Publication date: 2018-02-15

Abstract

This central projection wide-angle lens (10) comprises, in the order from the object side, a front group (G11) having a negative refractive power, a diaphragm (12), and a rear group (G12) having a positive refractive power. The front group (G11) includes a negative lens (L12) having a negative refractive power and having a concave correction surface (R104) on the surface facing an image. The correction surface (R104) has a local maximum value (MV) of a second derivative acquired by differentiating a sag amount y twice, and thus the correction surface is capable of minimizing barrel and pincushion distortions while appropriately correcting aberrations.

Description

Wide angle lens

The present invention relates to a wide-angle lens, and more particularly to a wide-angle lens capable of suppressing barrel distortion and pincushion distortion while satisfactorily correcting various aberrations.

Conventionally, a wide-angle lens with a wide angle of view while suppressing the number of lenses has been proposed (Patent Document 1). For example, the technique disclosed in Patent Document 1 is a wide-angle lens having four lenses, and is designed so that various aberrations can be corrected satisfactorily.

Japanese Patent No. 4748220

However, the conventional technique has a problem in that the wide-angle side of the image formed by the wide-angle lens is distorted, and the image is distorted into a barrel shape or a pincushion shape.

The present invention has been made to solve the above-described problems, and an object of the present invention is to provide a wide-angle lens capable of suppressing barrel distortion and pincushion distortion while satisfactorily correcting various aberrations.

In order to achieve this object, the wide-angle lens according to claim 1 is a central projection system, and in order from the object side, includes a front group having a negative refractive power, a stop, and a rear group having a positive refractive power. Composed. The front group includes a negative lens having negative refractive power, and the negative lens has a correction surface that is concave on the image side on the image side surface. The correction surface has a sag amount y that is a distance in the optical axis direction from the origin intersecting the optical axis as y, a radial distance from the origin as x, and an effective radius of x = 1. Indicated by function. A second derivative obtained by differentiating the sag amount y twice has a maximum value.

According to the wide-angle lens of claim 1, the image formed by the central projection type wide-angle lens is easily distorted into a barrel shape or a pincushion type. There is an effect that can be suppressed.

(A) is XY sectional drawing of the wide angle lens in 1st Example of this invention. (B) is a ZY sectional view of a wide-angle lens. (A) is explanatory drawing of the sag amount of a correction surface. (B) is explanatory drawing of the sag amount for every cross section of a correction surface. It is a graph which shows the range of the sag amount of a correction surface. It is a graph which shows the 2nd derivative of the function which shows the sag amount of a correction surface. (A) is a spherical aberration diagram. (B) is a field curvature and astigmatism diagram in a vertical section including the origin. (C) is a distortion diagram in a vertical section including the origin. (D) is a field curvature and astigmatism diagram in a horizontal section including the origin. (E) is a distortion diagram in a horizontal section including the origin. It is explanatory drawing of the condensing position with respect to imaginary height. It is XY sectional drawing of the wide angle lens in 2nd Example. It is a graph which shows the 2nd derivative of the function which shows the sag amount of a correction surface. (A) is a spherical aberration diagram. (B) is a field curvature and astigmatism diagram. (C) is a distortion diagram. It is explanatory drawing of the condensing position with respect to imaginary height. It is XY sectional drawing of the wide angle lens in 3rd Example. It is a graph which shows the 2nd derivative of the function which shows the sag amount of a correction surface. (A) is a spherical aberration diagram. (B) is a field curvature and astigmatism diagram. (C) is a distortion diagram. It is explanatory drawing of the condensing position with respect to imaginary height.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings. First, a wide-angle lens according to an embodiment of the present invention will be described with reference to FIGS. 1 (a) and 1 (b). In the description of the present embodiment, the wide-angle lens 10 of the first example is illustrated, and only the parts common to the examples will be described. FIG. 1A is an XY sectional view of the wide-angle lens 10 in the first embodiment of the present invention. FIG. 1B is a ZY sectional view of the wide-angle lens 10. In this specification, the optical axis Ax of the wide-angle lens 10 is the Y axis, and the axes orthogonal to the Y axis and orthogonal to each other are the X axis and the Z axis. 1A and 1B is the object side, and the right side of FIGS. 1A and 1B is the image side (the same applies to FIGS. 7 and 11).

As shown in FIGS. 1A and 1B, the wide-angle lens 10 is a central projection type lens system. The central projection type lens system means that the image height (height from the optical axis Ax on the image plane) is H, the focal length is f, and the half angle of view (the light beam incident on the lens system and the optical axis Ax. This is a lens system designed so that H = f · tan θ where θ is an angle formed.

The wide-angle lens 10 is a lens system having a maximum field angle of 100 ° or more. Each lens constituting the wide-angle lens 10 is configured to be line-symmetric with respect to the optical axis Ax. Therefore, the intersection of each lens surface and the optical axis Ax is the vertex of each lens surface.

On the image side of the wide-angle lens 10, a glass filter 13, a cover glass 14, and an image sensor 15 are arranged in order from the object side. The glass filter 13 has a parallel plate shape, and has functions such as an infrared cut filter, an ultraviolet cut filter, and a polarizing filter. The cover glass 14 has a parallel plate shape that protects the image sensor 15. The glass filter 13 and the cover glass 14 have substantially no refractive power. The glass filter 13 and the cover glass 14 are not essential, and the glass filter 13 and the cover glass 14 can be omitted.

The imaging element 15 is an element that converts an optical image obtained from the wide-angle lens 10 into an electrical signal, and constitutes an image plane. The imaging element 15 is a rectangular element when viewed from the optical axis Ax direction, and the long side direction is the X-axis direction and the short side direction is the Z-axis direction. The imaging element 15 is not limited to a rectangular shape, and a square imaging element 15 can be used.

The wide-angle lens 10 includes, in order from the object side, a front group G11 having a negative refractive power, a diaphragm 12, and a rear group G12 having a positive refractive power. The front group G11 has a specific aspherical surface (hereinafter referred to as “correction surface”) on the image-side surface (surface R104 in the first embodiment) of a specific negative lens having negative refractive power (the second lens L12 in the first embodiment). ") Is formed.

The correction surface is a concave surface on the image side, and the vertex intersects the optical axis Ax. The correction surface is a rotationally asymmetric surface or a rotationally symmetric aspheric surface. The rotationally asymmetric surface is represented by the following conditional expression (1), and the rotationally symmetric aspheric surface is represented by the following conditional expression (2).

However,
y: Sag amount (distance in the Y-axis direction from the apex to the rotationally asymmetric surface or rotationally symmetric aspheric surface)
c: curvature (1 / reference radius of curvature R)
k: conic constant h: optical axis vertical direction distance X _m Z _n : free-form surface coefficient (m = 0, 1, 2, 3...) (n = 0, 1, 2, 3...)
x, z: position on the XZ plane orthogonal to the Y axis A, B, C...: aspheric coefficient

The correction surface is a surface that greatly contributes to correction for suppressing distortion of the barrel type or the pincushion type while satisfactorily correcting various aberrations of the optical image by the wide-angle lens 10. In order to largely correct the optical image on the correction surface, it is necessary to increase the refractive power of the negative lens, and thus the light beam emitted from the negative lens has a large negative aberration.

Therefore, in the front group G11, a positive lens having a positive refractive power (the third lens L13 in the first embodiment) is disposed on the image side of the negative lens. Thereby, the negative aberration produced by the negative lens can be favorably corrected by the positive lens. Further, the negative aberration generated in the front group G11 can be favorably corrected in the rear group G12 having a positive refractive power.

Next, the shape of the correction surface will be described in detail with reference to FIGS. 2 (a), 2 (b), 3 and 4. FIG. FIG. 2A is an explanatory diagram of the sag amount y of the correction surface. FIG. 2B is an explanatory diagram of the sag amount y for each cross section of the correction surface. FIG. 3 is a graph showing the range of the sag amount y of the correction surface. FIG. 4 is a graph showing the second derivative of the function indicating the sag amount y of the correction surface.

As shown in FIG. 2A, an orthogonal coordinate system (x, y) is defined in which the vertex of the correction surface in the cross section including the optical axis Ax (Y axis) is the origin O and the vertical axis is the Y axis. When the correction surface is a rotationally symmetric aspherical surface, the cross-sectional shapes including the Y axis are all the same, so only the orthogonal coordinate system in the XY cross section will be described.

On the other hand, when the correction surface is a rotationally asymmetric surface, the cross-sectional shapes including the Y-axis are different from each other. Therefore, as shown in FIG. An orthogonal coordinate system tilted by 30 ° around the Y-axis is defined as 30, an orthogonal coordinate system tilted at 60 ° around the Y-axis from the ZY cross-section is defined as 60, and an orthogonal coordinate system tilted 90 ° around the Y-axis from the ZY cross-section (XY cross-section) The orthogonal coordinate system in FIG.

As shown in FIG. 3, the sag amount y of the correction surface is preferably in the range of the lower limit A and the upper limit B. The lower limit A is preferably y = 0.88x ^{^2,} and more preferably ^y = ^-0.14x 4 + ^1.02x ^2. Note that the graph of y = 0.88x ^{2 and} the graph of y = −0.14x ⁴ + 1.02x ² almost overlap, and both graphs have a relationship of −0.14x ⁴ + 1.02x ² ≧ 0.88x ² . It is in.

The upper limit B is preferably y = 1.31x ^{^2,} and more preferably ^y = ^-0.01x 4 + ^1.31x ^2. Incidentally, y = a graph 1.31x ^{^2,} almost overlapping the graph of ^y = ^-0.01x 4 + 1.31x ^2, both the graph of -0.01x ⁴ + 1.31x ^² ≦ 1.31x ² relationship It is in.

The sag amount y of the correction surface satisfies the conditional expression y ≧ 0.88x ² or y ≧ −0.14x ⁴ + 1.02x ² of the lower limit A. And distortion of the pincushion type can be suppressed. Further, the sag amount y of the correction surface satisfies y ≦ 1.31x ² or y ≦ −0.01x ⁴ + 1.31x ² which is a conditional expression of the upper limit B in addition to the conditional expression of the lower limit A. While correcting various aberrations satisfactorily, it is possible to further suppress barrel-type and pincushion-type distortion.

Since the correction surface is a rotationally asymmetric surface or a rotationally symmetric aspheric surface, the sag amount y of the correction surface is expressed by conditional expression (1) or conditional expression (2). The second derivative is calculated by differentiating the sag amount y of the correction surface expressed by the conditional expression (1) or (2) twice (see FIG. 4). When the second derivative of the sag amount y has a maximum value MV, the tangential slope of the sag amount y tends to increase as it approaches the maximum value MV. Since the shape of the correction surface is set in this way, the image formed by the central projection type wide-angle lens 10 is easily distorted into a barrel shape or a pincushion shape. The distortion of the pincushion mold can be suppressed. In particular, by adjusting the tangential slope of the sag amount y that continues to increase as x increases, barrel and pincushion distortion can be further suppressed while favorably correcting various aberrations.

In addition, when the angle of view is 120 ° or more, if the maximum value MV of the second derivative of the sag amount y is between 0.34 ≦ x ≦ 1, various aberrations are corrected satisfactorily and barrel or pincushion Mold distortion can be further suppressed. Since the correction surface is line-symmetric with respect to the optical axis Ax, the maximum value MV of the second derivative of the sag amount y is between 0.34 ≦ x ≦ 1, that is, the maximum value MV. Is between −1 ≦ x ≦ −0.34.

In addition, when the value of x that takes the maximum value MV of the second derivative of the sag amount y is smaller than 1 (greater than −1), the tangent slope of the sag amount y increases from x = 0 to the maximum value MV. If the maximum value MV is exceeded, the slope of the tangent line of the sag amount y tends to decrease. Thereby, distortion of a barrel type or a pincushion type can be further suppressed while correcting various aberrations better.

Hereinafter, the present invention will be specifically described with reference to examples, but the present invention is not limited to these examples. The description common to each embodiment will be described only in the first embodiment, and the description in other embodiments will be omitted.

(First embodiment)
As shown in FIGS. 1A and 1B, the wide-angle lens 10 in the first embodiment is a lens system having a five-lens configuration, and is a lens system designed over the visible light range. The front lens group G11 of the wide-angle lens 10 includes, in order from the object side, a first lens L11 that is a meniscus lens having negative refractive power and convex toward the object side, and a meniscus lens having negative refractive power and convex toward the object side. And a biconvex third lens L13 having a positive refractive power. The first lens L11 is made of glass, and the second lens L12 and the third lens L13 are made of synthetic resin.

Since both the first lens L11 and the second lens L12 are meniscus lenses having negative refractive power and convex toward the object side, the angle of the light beam incident on the first lens L11 with the optical axis Ax is gradually increased. The light is adjusted so as to be gentle and emitted from the second lens L12. As a result, the occurrence of aberration can be suppressed, and the angle of view can be widened while reducing the diameter of the first lens L11.

The rear group G12 includes, in order from the object side, a biconvex fourth lens L14 having a positive refractive power and a fifth lens L15 that is a meniscus lens having a negative refractive power and convex to the image side. . The fourth lens L14 and the fifth lens L15 are cemented to form a cemented lens L145. The fourth lens L14 and the fifth lens L15 are made of synthetic resin.

In the wide-angle lens 10, the lens surfaces of the lenses L11 to L13 are in order from the object side to the surfaces R101 to R106, the diaphragm 12 is the surface R107, the cemented lens L145 is the object side surface R108, the fourth lens L14 and the fifth lens L15. Is the surface R109, and the image side surface of the cemented lens L145 is R110. Further, the surfaces of the glass filter 13 and the cover glass 14 are surfaces R111 to R114 in order from the object side. The object side surface of the image sensor 15 is a surface R115, which is an image surface, and an optical image by the wide-angle lens 10 is formed on the surface R115.

In this embodiment, the surfaces R103, R104, and R110 are rotationally asymmetric surfaces, and the surfaces R105, R106, R108, and R109 are rotationally symmetric aspheric surfaces. The surface R104 is a correction surface, the second lens L12 is the negative lens described above, and the third lens L13 is the positive lens described above.

The wide-angle lens 10 has rotationally asymmetric surfaces R103, R104, and R110 having different shapes in the X-axis direction and the Z-axis direction. In this embodiment, the X-axis direction of the wide-angle lens 10 will be described as a horizontal direction, the Z-axis direction as a vertical direction, an XY section as a horizontal section, and a ZY section as a vertical section. The optical values of this example are shown in Table 1.

The image sensor 15 has a rectangular shape with different vertical and horizontal sizes, whereas the image circle formed by the wide-angle lens 10 is circular. Since the wide-angle lens 10 has rotationally asymmetric surfaces R103, R104, and R110, the image height (height from the optical axis Ax) of the optical image can be set separately in the vertical direction and the horizontal direction. That is, by using the rotationally asymmetric surfaces R103, R104, and R110, the image height of the optical image can be set in accordance with the size of the image sensor 15, so that the barrel-type and pincushion-type distortions can be efficiently prevented while securing the peripheral light amount. Can be corrected.

Table 2 shows lens data of this example. The surface number * symbol indicates a rotationally symmetric aspheric surface, and the surface number ** symbol indicates a rotationally asymmetric surface. The fourth lens L14 and the fifth lens L15 constituting the cemented lens L145 are compared with each other. The fourth lens L14 has a low refractive index and a high Abbe number, the fifth lens L15 has a high refractive index, and , Low Abbe number. As a result, the wide-angle lens 10 can satisfactorily correct chromatic aberration generated in the front group G11.

Table 3 shows the aspheric coefficient data of the surfaces R105, R106, R108, and R109 of this example. In the present specification, a power of 10 is expressed by using E (for example, 1.6 × 10 ⁻⁴ is 1.6E-4). A blank in Table 3 indicates that the coefficient is 0.

Table 4 shows the free-form surface coefficient data of the surface R103 of this embodiment, Table 5 shows the free-form surface coefficient data of the surface R104, and Table 6 shows the free-form surface coefficient data of the surface R110. The conic constants of the surface R103, the surface R104, and the surface R110 are 0, and the blanks in Tables 4 to 6 indicate that the coefficient is 0.

The sag amount y of the correction surface R104 of the 0-series, 30-series, 60-series, and 90-series is expressed by y ≧ 0.88x ² and y ≧ −0.14x ⁴ + 1.02x ² which are the conditional expressions of the lower limit A in FIG. 3 is satisfied, and y ≦ 1.31x ² and y ≦ −0.01x ⁴ + 1.31x ² are satisfied. Therefore, it is possible to further suppress barrel distortion and pincushion distortion while correcting various aberrations favorably.

FIG. 4 shows a second derivative obtained by differentiating the sag amount y of the correction surface R104 indicated by the conditional expression (1) of this embodiment twice. In FIG. 4, the second derivative of the 0 system is indicated by a solid line, the second derivative of the 30 system is indicated by a broken line, the second derivative of the 60 system is indicated by a one-dot chain line, and the second derivative of the 90 system is indicated by a two-dot chain line. All the second derivatives define the effective radius of the correction surface R104 as x = 1.

As shown in FIG. 4, the second derivative of the 60 series and the second derivative of the 90 series have a maximum value MV. The value of x taking the maximum value MV of the second derivative of the 60 series is ± 0.346, and the value of x taking the maximum value MV of the second derivative of the 90 series is ± 0.366.

The slope of the tangent of the sag amount y tends to increase from x = 0 to the maximum value MV, and the slope of the tangent of the sag amount y tends to decrease when the value exceeds the maximum value MV. Since the way of bending of the light beam passing through the correction surface R104 can be locally changed, it is possible to suppress barrel distortion and pincushion distortion while favorably correcting various aberrations. In particular, since the maximum value MV of the second derivative of the sag amount y is in the range of 0.34 ≦ x ≦ 1, it is possible to further suppress various barrel aberrations and pincushion type distortions.

Also, the angle of view is 93.6 ° in the case of 0 system, and the angle of view is 120 ° in the case of 90 system. Since the image sensor 15 is rectangular, when the angle of view is calculated using a trigonometric function, it can be seen that the angle of view of the 30 system is 99.98 ° and the angle of view of the 60 system is 124.64 °. The 0-system and 30-system correction surfaces R104 do not have the maximum value MV, and the 60-system and 90-system correction surfaces R104 have the maximum value MV. Even if there is no maximum value MV, it is possible to suppress barrel-type or pincushion-type distortion. In other words, when the angle of view is larger than 100 °, and probably when the angle of view is larger than 110 °, it is assumed that the distortion of the barrel shape or the pincushion type can be suppressed by providing the maximum value MV on the correction surface R104. The

The aberration diagrams obtained from this example are shown in FIGS. 5 (a) to 5 (e). 5A is a spherical aberration diagram, FIG. 5B is a field curvature and astigmatism diagram in the 0 system (vertical section), and FIG. 5C is a distortion in the 0 system (vertical section). FIG. 5D is a diagram of field curvature and astigmatism in 90 system (horizontal section), and FIG. 5E is a distortion aberration diagram in 90 system (horizontal section). In FIG. 5A, the aberration at the wavelength of 486 nm is indicated by a solid line, the aberration at the wavelength of 588 nm is indicated by a one-dot chain line, and the aberration at a wavelength of 656 nm is indicated by a two-dot chain line. e) shows aberrations at a wavelength of 588 nm.

In FIG. 5A, the horizontal axis is the amount of deviation (mm) in the optical axis Ax direction from the image plane near the optical axis Ax, and the vertical axis is the entrance pupil coordinates (the incident height to the pupil is its maximum height). Standardized value). In FIG. 5B and FIG. 5D, the horizontal axis is the shift amount (mm) in the optical axis Ax direction from the image plane near the optical axis Ax, and the vertical axis is the angle of view (deg) with respect to the optical axis Ax. The aberration S on the sagittal surface is indicated by a solid line, and the aberration T on the tangential surface is indicated by a broken line. In FIG. 5C and FIG. 5E, the horizontal axis represents distortion (%), and the vertical axis represents the angle of view (deg) with respect to the optical axis Ax.

FIG. 6 shows the condensing position with respect to the ideal image height on the surface R115 in the present embodiment. In FIG. 6, the intersection of the surface R115 and the optical axis Ax is the origin O, the horizontal axis is the height (mm) of the optical image in the X-axis (horizontal) direction, and the vertical axis is the optical image in the Z-axis (vertical) direction. The distortion aberration is shown as the height (mm). Each intersection of the grating indicates the height of the ideal image (ideal image height), and each circle indicates the height (condensing position) of the optical image of this embodiment. It is determined that the distortion is corrected more favorably as each circle is closer to each intersection of the lattice. Note that the grating and the optical image are symmetric with respect to the origin O.

In the grid of FIG. 6, the outermost line is set according to the size of the image sensor 15, and the part surrounded by the outermost line is set by dividing it into eight equal parts in the horizontal direction and the vertical direction. Table 7 shows the coordinates (x (mm), z (mm)) of the condensing position in FIG. 6 with respect to the position of the lattice in FIG. The optical image shows a case where the wavelength is 588 nm.

As shown in FIG. 6, the condensing position is located substantially parallel to the lattice of the ideal image height. Thereby, according to the wide-angle lens 10 of the present embodiment, the barrel-shaped distortion in which the optical image is bent inward with respect to the ideal image at the wide-angle end side, or the optical image is bent outward with respect to the ideal image at the wide-angle end side. It is judged that the distortion of the pincushion mold can be suppressed.

(Second embodiment)
As shown in FIG. 7, the wide-angle lens 20 in the second embodiment is a five-lens lens system, which is a lens system designed over the visible light range. The front lens group G21 of the wide-angle lens 20 includes, in order from the object side, a first lens L21 that is a meniscus lens having negative refractive power and convex toward the object side, and a meniscus lens having negative refractive power and convex toward the object side. The second lens L22 is a biconvex third lens L23 having positive refractive power. The first lens L21 is made of glass, and the second lens L22 and the third lens L23 are made of synthetic resin.

Since each of the first lens L21 and the second lens L22 is a meniscus lens having negative refractive power and convex toward the object side, the light beam incident on the first lens L21 has an angle formed with the optical axis Ax gradually. The light is adjusted so as to be gentle and emitted from the second lens L22. As a result, the occurrence of aberration can be suppressed and the angle of view can be widened while reducing the diameter of the first lens L21.

The rear group G22 includes, in order from the object side, a biconvex fourth lens L24 having positive refractive power and a fifth lens L25 that is a meniscus lens having negative refractive power and convex to the image side. . The fourth lens L24 and the fifth lens L25 are cemented to form a cemented lens L245. The fourth lens L24 and the fifth lens L25 are made of synthetic resin.

In the wide-angle lens 20, the lens surfaces of the lenses L21 to L23 are in order from the object side to the surfaces R201 to R206, the diaphragm 12 is the surface R207, the cemented lens L245 is the object side surface R208, the fourth lens L24 and the fifth lens L25. The cemented surface is a surface R209, and the cemented lens L245 has an image side surface R210. The surfaces of the glass filter 13 and the cover glass 14 are surfaces R211 to R214 in order from the object side. The object-side surface of the image sensor 15 is a surface R215, which is an image surface, and an optical image by the wide-angle lens 20 is formed on the surface R215.

In this embodiment, the surfaces R203, R204, R205, R206, R208, R209, and R210 are rotationally symmetric aspheric surfaces. The surface R204 is a correction surface, the second lens L22 is the negative lens described above, and the third lens L23 is the positive lens described above.

Although the X-axis direction of the wide-angle lens 20 will be described as a horizontal direction and the Z-axis direction as a vertical direction, the wide-angle lens 20 does not have a rotationally asymmetric surface, so that the cross-sectional shapes including the optical axis Ax are all equal. Table 8 shows the optical values of this example.

Table 9 shows lens data of this example. The fourth lens L24 and the fifth lens L25 constituting the cemented lens L245 are compared with each other. The fourth lens L24 has a low refractive index and a high Abbe number, the fifth lens L25 has a high refractive index, and , Low Abbe number. As a result, it is possible to satisfactorily correct chromatic aberration generated in the front group G21.

Table 10 shows the aspheric coefficient data of the surfaces R203, R204, R205, R206, R208, R209, and R210 of this example.

The sag amount y of the correction surface R204 satisfies the lower limit A conditional expressions y ≧ 0.88x ² and y ≧ −0.14x ⁴ + 1.02x ² in FIG. 3, and the upper limit B conditional expression in FIG. Certain y ≦ 1.31x ² and y ≦ −0.01x ⁴ + 1.31x ² are satisfied. Therefore, it is possible to further suppress barrel distortion and pincushion distortion while correcting various aberrations favorably.

In this embodiment, a second derivative obtained by differentiating the sag amount y of the correction surface R204 represented by the conditional expression (2) twice is shown in FIG. In this embodiment, since the cross-sectional shapes including the optical axis Ax are all equal, the sag amount y is differentiated twice with h in the conditional expression (2) replaced by x, and the sag amount y of the correction surface R204 is calculated. A second derivative is calculated. The second derivative defines the effective radius of the correction surface R204 as x = 1.

As shown in FIG. 8, the sag amount y of the correction surface R204 has a maximum value MV. The value of x taking the maximum value MV of the second derivative of the sag amount y of the correction surface R204 is ± 0.533. From x = 0 to the maximum value MV, the slope of the tangent of the sag amount y tends to increase, and when the value exceeds the maximum value MV, the slope of the tangent line of the sag amount y tends to decrease. As a result, it is possible to suppress barrel distortion and pincushion distortion while satisfactorily correcting various aberrations. In particular, since the maximum value MV of the second derivative of the sag amount y is in the range of 0.34 ≦ x ≦ 1, it is possible to further suppress various barrel aberrations and pincushion type distortions.

FIG. 9 (a) to FIG. 9 (c) show various aberration diagrams obtained from this example. 9A is a spherical aberration diagram, FIG. 9B is a field curvature and astigmatism diagram, and FIG. 9C is a distortion diagram.

FIG. 10 shows the condensing position with respect to the ideal image height on the surface R215 in the present embodiment. Further, Table 11 shows the coordinates (x (mm), z (mm)) of the condensing position in FIG. 10 with respect to the position of the lattice in FIG. The optical image shows a case where the wavelength is 588 nm.

As shown in FIG. 10, the condensing position is located substantially parallel to the lattice of the ideal image height. Thus, according to the wide-angle lens 20 of the present embodiment, the barrel-shaped distortion in which the optical image is bent inward with respect to the ideal image at the wide-angle end side, or the optical image is bent outward with respect to the ideal image at the wide-angle end side. It is judged that the distortion of the pincushion mold can be suppressed. Furthermore, according to the wide-angle lens 20 of the present embodiment, since there is almost no deviation between each intersection of the grating and the condensing position, it is determined that the distortion aberration can be corrected satisfactorily.

(Third embodiment)
As shown in FIG. 11, the wide-angle lens 30 in the third embodiment is a three-lens lens system, which is a lens system designed near 870 nm in the near-infrared light region. The front lens group G31 of the wide-angle lens 30 includes, in order from the object side, a first lens L31 that is a meniscus lens having negative refractive power and convex toward the object side, and a meniscus lens having positive refractive power and convex toward the image side. And the second lens L32. The first lens L31 is made of glass, and the second lens L32 is made of synthetic resin. The rear group G32 includes a biconvex third lens L33 having a positive refractive power. The third lens L33 is made of synthetic resin.

In the wide-angle lens 30, the lens surfaces of the lenses L 31 and L 32 are surfaces R 301 to R 304 in order from the object side, the diaphragm 12 is a surface R 305, the object side surface of the third lens L 33 is the surface R 306, and the image side of the third lens L 33. The surface is a surface R307. Further, the surfaces of the glass filter 13 and the cover glass 14 are surfaces R308 to R311 in order from the object side. The object-side surface of the image sensor 15 is a surface R312 that is an image surface, and an optical image by the wide-angle lens 30 is formed on the surface R312.

In this embodiment, the surfaces R302, R303, R304, R306, and R307 are rotationally symmetric aspheric surfaces. The surface R302 is a correction surface, the first lens L31 is the negative lens described above, and the second lens L32 is the positive lens described above.

The wide-angle lens 30 will be described with the X-axis direction as the horizontal direction and the Z-axis direction as the vertical direction. However, since the wide-angle lens 30 does not have a rotationally asymmetric surface, the cross-sectional shapes including the optical axis Ax are all equal. Table 12 shows the optical values of this example, and Table 13 shows the lens data of this example.

Table 14 shows the aspheric coefficient data of the surfaces R302, R303, R304, R306, and R307 of this example.

The sag amount y of the correction surface R302 satisfies the conditional expressions y ≧ 0.88x ² and y ≧ −0.14x ⁴ + 1.02x ² of the lower limit A in FIG. 3, and the conditional expression of the upper limit B in FIG. Certain y ≦ 1.31x ² and y ≦ −0.01x ⁴ + 1.31x ² are satisfied. Therefore, it is possible to further suppress barrel distortion and pincushion distortion while correcting various aberrations favorably.

In this embodiment, a second derivative obtained by differentiating the sag amount y of the correction surface R302 indicated by the conditional expression (2) twice is shown in FIG. In this embodiment, since the cross-sectional shapes including the optical axis Ax are all equal, the sag amount y is differentiated twice with h in the conditional expression (2) replaced by x, and the sag amount y of the correction surface R302 is calculated. A second derivative is calculated. The second derivative defines the effective radius of the correction surface R302 as x = 1.

As shown in FIG. 12, the sag amount y of the correction surface R302 has a maximum value MV. The value of x that takes the maximum value MV of the second derivative of the sag amount y of the correction surface R302 is ± 1. Since the tangential slope of the sag amount y tends to increase as it approaches the maximum value MV, barrel-type and pincushion-type distortions can be suppressed while favorably correcting various aberrations. In particular, since the maximum value MV of the second derivative of the sag amount y is in the range of 0.34 ≦ x ≦ 1, it is possible to further suppress various barrel aberrations and pincushion type distortions.

FIG. 13A to FIG. 13C show various aberration diagrams obtained from this example. 13A is a spherical aberration diagram, FIG. 13B is a field curvature and astigmatism diagram, and FIG. 13C is a distortion diagram. FIGS. 13A to 13C show the aberrations when the wavelength is 870 nm.

FIG. 14 shows the condensing position with respect to the ideal image height on the surface R312 in this embodiment. Further, Table 15 shows the coordinates (x (mm), z (mm)) of the condensing position in FIG. 14 with respect to the position of the lattice in FIG. The optical image shows a case where the wavelength is 870 nm.

As shown in FIG. 14, the condensing position is located substantially parallel to the lattice of the ideal image height. Thereby, the wide-angle lens 30 of the present embodiment is a barrel-shaped distortion in which the optical image is bent inward with respect to the ideal image at the wide-angle end side, or a pincushion type in which the optical image is bent outward with respect to the ideal image at the wide-angle end side. It is judged that the distortion of can be suppressed.

The present invention has been described above based on the embodiments and examples. However, the present invention is not limited to the above embodiments and examples, and various improvements can be made without departing from the spirit of the present invention. It can be easily inferred that deformation is possible. For example, in the first and second embodiments, the case where the wide-

angle lenses

10 and 20 have a five-lens configuration has been described, and in the third embodiment, the case where the wide-angle lens 30 has a three-lens configuration has been described. The number of lenses can be set as appropriate.

In the first and second embodiments, the case where the surfaces R104 and R204 of the second lenses L12 and L22 are correction surfaces has been described. However, the present invention is not limited to this, and the surfaces R102 and R102 of the first lenses L11 and L21 are not necessarily limited thereto. Of course, it is possible to use R202 as the correction surface.

In the first embodiment, the case where the surfaces R103, R104, and R110 are rotationally asymmetric surfaces has been described. However, the present invention is not necessarily limited to this. In the front group, it is preferable that at least two surfaces of the meniscus lens having negative refractive power and convex on the object side, the object side surface and the image side surface, are formed as rotationally asymmetric surfaces. It is also possible to provide two or more rotationally asymmetric surfaces in the front group. As the rotationally asymmetric surface increases, the optical image of the wide-angle lens can be set in accordance with the size of the image sensor 15, so that barrel-type and pincushion-type distortion can be corrected efficiently. Moreover, it is preferable that one or more surfaces of the rear group are formed as rotationally asymmetric surfaces. As a result, the aberration generated on the rotationally asymmetric surface of the front group can be corrected satisfactorily.

In the first and second embodiments, the case where the fourth lenses L14 and L24 and the fifth lenses L15 and L25 are cemented to form the cemented lenses L145 and L245 is described. However, the present invention is not necessarily limited thereto. The fourth lenses L14 and L24 and the fifth lenses L15 and L25 can each be an independent lens.

In the first and second embodiments, the fourth lenses L14 and L24 are biconvex lenses having positive refractive power, and the fifth lenses L15 and L25 are meniscus lenses having negative refractive power and convex to the image side. Although the case has been described, the present invention is not necessarily limited thereto, and it is sufficient that the total refractive power of the fourth lenses L14 and L24 and the fifth lenses L15 and L25 is positive. For example, the fourth lens can be a biconcave lens having negative refractive power, and the fifth lens can be a biconvex lens having positive refractive power.

In each of the above embodiments, the sag amount y of the correction surfaces R104, R204, R302 satisfies the lower limit conditional expressions y ≧ 0.88x ² and y ≧ −0.14x ⁴ + 1.02x ² , and the upper limit condition Although the case where the expressions y ≦ 1.31x ² and y ≦ −0.01x ⁴ + 1.31x ² are satisfied has been described, the present invention is not necessarily limited thereto. The correction surface should satisfy at least y ≧ 0.88 × ² . Also in this case, it is possible to suppress barrel distortion and pincushion distortion while correcting various aberrations satisfactorily.

In each of the above embodiments, the case where the first lenses L11, L21, and L31 are made of glass and the other lenses are made of a synthetic resin has been described. It can be changed.

10, 20, 30 Wide-angle lens 12 Aperture G11, G21, G31 Front group G12, G22, G32 Rear group L12, L22 Second lens (negative lens)
L13, L23 Third lens (positive lens)
L31 1st lens (negative lens)
L32 Second lens (positive lens)
R104, R204, R302 Correction surface MV Maximum value

Claims

A central projection method,
In order from the object side, it is composed of a front group having negative refractive power, a diaphragm, and a rear group having positive refractive power,
The front group includes a negative lens having a negative refractive power in which a correction surface concave on the image side is formed on the image side surface;
The correction surface has a sag amount y when the sag amount that is the distance in the optical axis direction from the origin intersecting the optical axis is y, the radial distance from the origin is x, and the effective radius is x = 1. A wide-angle lens characterized in that a second derivative obtained by differentiating a sag amount y twice as a function of x has a maximum value other than the origin.
The wide angle lens according to claim 1, wherein the sag amount y continues to increase as x increases.
The wide-angle lens according to claim 1, wherein the correction surface satisfies y ≧ 0.88 × 2 .
4. The wide angle lens according to claim 3, wherein the correction surface satisfies y ≧ −0.14x 4 + 1.02x 2 .
The wide-angle lens according to claim 3, wherein the correction surface satisfies y ≦ 1.31 × 2 .
The wide-angle lens according to claim 5, wherein the correction surface satisfies y ≦ −0.01x 4 + 1.31x 2 .
The wide-angle lens according to any one of claims 1 to 6, wherein the correction surface has a maximum value of a second derivative of the sag amount y in a range of 0.34≤x≤1.
The wide-angle lens according to claim 1, wherein the front group includes a positive lens disposed on the image side of the negative lens and having a positive refractive power.