JPH09329747A - Image forming optical system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a compact image forming optical system which is constituted so that a wide image pickup area is obtained, the aberration of a light beam is excellently corrected and image distortion is eliminate and whose number of optical parts is reduced, by folding back the optical path. SOLUTION: This image forming optical system is a pentagonal prism body 5 consistuted of a first surface 1, a second surface 2, a third surface 3 and a fourth surface 4. The first and the fourth surfaces 1 and 4 are the refraction surfaces, and the second and the third surfaces 2 and 3 are the reflection surfaces. Besides, the first surface 1 is constituted of the spherical surface and the second, the third and the fourth surfaces 2, 3 and 4 are constituted of the free curved surfaces. The light beam emitted from an object surface O arranged on the back surface of a cover glass 6 is made incident from the first surface 1 of the prism body 5 through the glass 6 and reflected on the second and the third surfaces 2 and 3 in turn. Besides, the reflected light is crossed to the light beam arriving at the second surface 2 from the first surface 1 and emitted outside the prism body 5 from the forth surface 4. Then, it arrives at an image surface I. The free curved surfaces 2-4 are the plane symmetric free curved surfaces which are provided with a rotation symmetric axis neither within the surface nor outside the surface thereof but are provided with only one symmetry plane.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image forming optical system, and more particularly to a small reflective decentered image forming optical system.

[0002]

2. Description of the Related Art Conventionally, as a well-known compact decentering optical system, Japanese Patent Application Laid-Open No. Sho 59-84201 discloses a one-dimensional light receiving lens having a cylindrical reflecting surface.
Two-dimensional imaging is not possible. Also, Japanese Patent Application Laid-Open No. Sho 62-1441
No. 27 uses the same cylindrical surface for twice reflection in order to reduce the spherical aberration of the above invention.

Japanese Patent Application Laid-Open No. Sho 62-205547 discloses that an aspherical reflection is used as the shape of the reflecting surface, but does not mention the shape of the reflecting surface. Further, U.S. Pat. No. 3,810,221 and U.S. Pat.
No. 6,931 each show an example in which a finder optical system of a reflex camera uses a lens system having a rotationally symmetric aspherical mirror and a surface having only one plane of symmetry. However, a plane having only one plane of symmetry is used for correcting the inclination of the observed virtual image.

[0004] Japanese Patent Application Laid-Open No. 1-257834 (US Pat. No. 5,274,406) discloses a rear projection television in which a plane having only one plane of symmetry is used to correct image distortion. Although an example in which the present invention is used for a reflecting mirror is shown, a projection lens system is used for projection onto a screen, and a plane having only one plane of symmetry is used for correcting image distortion.

Japanese Patent Application Laid-Open No. 7-333551 discloses an example of a back-mirror type decentered optical system using an anamorphic surface and a toric surface as an observation optical system.
However, it cannot be used for an imaging optical system because the correction of aberration including image distortion is insufficient.

[0006] None of the above-mentioned prior arts uses a surface having only one symmetrical surface, and does not use a backside mirror in the folded optical path.

[0007]

In the conventional imaging optical system, in order to construct an image distortion-free optical system in which a wide angle of view and aberration are favorably corrected, a rotationally symmetric optical system requires a number of lenses. It became large, large and expensive.

The present invention has been made in view of the above problems of the prior art, and an object thereof is to obtain an image in which a wide image pickup area can be taken and a ray aberration is favorably corrected by folding an optical path. An object of the present invention is to provide an imaging optical system which is compact without distortion and has a small number of optical components.

[0009]

An image forming optical system of the present invention which achieves the above object has at least a decentering optical system and is an image forming optical system for forming an image of light from an object on a surface of an image pickup device. The imaging optical system includes at least one reflecting surface having a reflecting action, and the surface shape of at least one of the reflecting surfaces does not have a rotational symmetry axis both in-plane and out-of-plane, and the symmetric surface It is characterized by comprising a plane-symmetric free-form surface having only one.

This reflecting surface is defined by a straight line from the object side through the pupil center to the axial principal ray reaching the image forming position center of the image pickup device and intersecting the first surface of the image forming optical system. The optical axis is the Z axis, the axis that is orthogonal to the Z axis and that is within the decentered plane of each surface that constitutes the imaging optical system is the Y axis,
When the axis orthogonal to the Z axis and the Y axis is defined as the X axis, it is desirable that at least one of the following conditions (A-1) and (B-1) is satisfied. | RX | <0.5 (1 / mm) (A-1) | RY | <0.5 (1 / mm) (B-1) where RX and RY are the reflection surfaces, respectively. Are the curvatures in the X and Y directions of the portion where the axial chief ray hits.

The reason why the above-mentioned configuration is adopted and the operation thereof will be described below. The use of a plane having only one plane of symmetry (hereinafter referred to as a TFC plane) in the present invention will be described in detail below.

First, the coordinate system used in the following description will be described. An optical axis defined by a straight line until a principal ray of the image center reaching the center of the imaging position from the object side through the pupil center and reaching the center of the imaging position is defined as a Z axis, and is orthogonal to the Z axis. And, the axis in the eccentric plane of each surface constituting the eccentric optical system is defined as the Y axis, orthogonal to the optical axis,
An axis orthogonal to the Y axis is defined as an X axis. The ray tracing direction will be described in the order of tracing from the pupil position to the imaging position.

An overview of the aberration correction up to now is as follows. (1) Generally, in order to favorably correct aberrations with a small number of surfaces, an aspherical surface is generally used in a rotationally symmetric optical system. Similarly, in a reflective optical system, spherical aberration generated by a spherical reflecting mirror is prevented from being generated by using a rotationally symmetric aspheric surface such as a paraboloid. That is, it is a well-known fact that a rotationally symmetric aspherical surface is used in a rotationally symmetric optical system.

(2) In addition, the Mangin mirror (A. Mang
In, 1876), it is a well-known fact that the occurrence of spherical aberration can be reduced by using a back-surface reflecting mirror.

This is because the focal length f of the rear surface mirror is represented by f = -r / 2n from the radius of curvature r of the rear surface mirror and the refractive index n of the medium, and when the same focal length f is obtained, This is because, for example, when the rear surface mirror is made of glass having a refractive index of 1.5, the radius of curvature r is 1.5 times larger than that of the front surface mirror, so that the occurrence of aberration is small.

(3) On the other hand, the concave mirror arranged eccentrically has the above-mentioned Y at the portion where the light beam strikes the reflecting mirror due to the eccentricity.
The focal positions of the light beam in the axial direction and the light beam in the X-axis direction are shifted, and astigmatism also occurs on the axis.

In order to eliminate the occurrence of this astigmatism on the axis, Japanese Patent Application No. 6-211067 or Japanese Patent Application No. 6-211067 of the present applicant.
As described in -256676, an anamorphic surface or a toric surface having a different curvature depending on the direction is used.

(4) Next, the image plane distortion will be described.
The fact that the arrangement of the concave mirror and the convex mirror exerts a good effect on the field curvature aberration is described in detail in Japanese Patent Application No. 5-264828 of the applicant of the present invention. No. 6-127453. In Japanese Patent Application No. 6-256676, a concave mirror is also used.
By using a single sheet, the field curvature can be successfully corrected.

(5) Regarding image distortion, see Japanese Patent Laid-Open No.
As described in US Pat.
A good result can be obtained by constructing a surface having different curvatures depending on the sign in the Y-axis direction. Although the application is different, a rear projection television uses a Fresnel reflection surface similar to the TFC surface used in the present invention in JP-A-1-257834, but the purpose is to correct trapezoidal image distortion. To do
When the real image is projected on the screen by the projection optical system, it is reflected by the reflecting surface, and at this time, it is used in a configuration that corrects only the trapezoidal image distortion. Japanese Patent Application Laid-Open No. 5-30305 discloses a trapezoidal or bow-shaped image distortion caused by an inclined concave mirror.
No. 6.

The elements lacking in each of the above inventions are an attempt to correct aberrations with a combination of the above-mentioned configurations, using an optical system of a folding optical path, with sufficient aberration performance as an image pickup optical system or an image forming optical system. This is something that has not been done.

Regarding the aberration caused by the rotationally symmetric optical system, the behavior of the light beam incident on the lens changes only by the height from the optical axis which is the rotation axis, and this causes the aberration.
How to correct this. However, in the decentered optical system, both the height and the position at which the light beam strikes the surface greatly differ between the upper and lower surfaces in the decentering direction. In other words, although there is no rotational symmetry at all, it becomes impossible to correct aberrations for cylindrical, toric, and anamorphic surfaces based on a rotationally symmetric spherical surface in response to the complex behavior of light rays. .

Here, the free-form surface used in the present invention is defined by the following equation. _{Z = C 2 + C 3 y} + C 4 x + C 5 y 2 + C 6 yx + C 7 x 2 + C 8 y 3 + C 9 y 2 x + C 10 yx 2 + C 11 x 3 + C 12 y 4 + C 13 y 3 x + C 14 y 2 x 2 + C ^{_{15 yx 3 + C 16 x 4}} + C 17 y 5 + C 18 y 4 x + C 19 y 3 x 2 + C 20 y 2 x 3 + C 21 yx 4 + C 22 x 5 + C 23 y 6 + C 24 y 5 x + C 25 y 4 x 2 + C ^{_{26 y 3 x 3 + C 27}} y 2 x 4 + C 28 yx 5 + C 29 x 6 + C 30 y 7 + C 31 y 6 x + C 32 y 5 x 2 + C 33 y 4 x 3 + C 34 y 3 x 4 + C 35 y 2 x in ^{_{5 + C 36 yx 6 + C}} 37 x 7 ····· ···· (a) the above equation, when the eccentric direction and Y-direction, the odd order terms of X are all zero.

With this defining equation, it becomes possible to satisfactorily correct the respective aberrations described below, and the refracting power that can be used as an image-forming optical system by the reflecting mirror that is inclined as in the present invention. It became possible to add (power).

First, since the reference surface is based on the paraboloid of the squared term, spherical aberration is unlikely to occur. Next, since there are odd-order terms of Y and odd-order terms of X, inclination in the Y-axis direction can be given at an arbitrary position on the X-axis.

Since each of Y and X is multiplied by an odd number and an even number, it is possible to give a free curvature to the positive and negative of each axis.

As described above, when used as a reflecting surface that has various degrees of freedom and is eccentrically arranged, it is only by using this defining equation that aberration can be sufficiently corrected even if power is given. It has become possible.

How important this degree of freedom is for aberration correction will be described. In the case of a reflecting mirror that is tilted and has power, rotationally asymmetric field curvature occurs. This curvature of field is such that rays that pass through the pupil and have a spread in the X-axis direction are:
The light is reflected by an eccentrically arranged reflecting mirror and is reflected. The distance from the light beam to the image plane after the light beam strikes the curvature r of the portion hit by the light beam according to the formula f = −r / 2n of the focal length of the back mirror. Refractive index n to r
/ 2n. That is, it is inclined with respect to the optical axis in a direction parallel to the inclined reflecting mirror with respect to the traveling direction of the light beam reflected by the concave mirror disposed eccentrically, and the curvature r of the reflecting mirror is r / r.
A 2n curved image plane is formed.

As described above, the free-form surface has an odd-order term of Y whose curvature can be arbitrarily changed depending on whether the Y-axis is positive or negative. Therefore, the rotationally asymmetric image plane generated by the eccentrically arranged concave mirror is formed. It works effectively for correcting the curvature, especially the inclination of the image plane.

Next, rotationally symmetric field curvature will be described. The reflecting mirror generally causes a curvature of field along the reflecting surface. In the case of the present invention, as described above, a configuration in which the curvature of field can be corrected by a convex mirror paired with a concave mirror is also possible, and the curvature of field generated by each of the two concave surfaces is reduced. It is devised to do. However, the conventional surface shape is not completely corrected because the number of surfaces is small.
In order to correct the field curvature that cannot be completely corrected, a free-form surface that can provide an arbitrary curvature at an arbitrary position is preferable for aberration correction. This is made possible by combining the curvature of the odd-order term of Y and the square of X or more according to the sign of the Y-axis.

Further, in order to reduce the occurrence of astigmatism at an arbitrary place, it becomes possible to correct it by arbitrarily changing the difference between the curvature in the X-axis direction and the curvature in the Y-axis direction. This is made possible by the fact that the square of X and the square of Y independently exist.

More preferably, in consideration of manufacturability of optical parts, it is desirable that the free-form surface is minimized.
Therefore, by making one of the at least three surfaces a free-form surface and the other surface a flat surface, a spherical surface, or an eccentric rotationally symmetric surface, manufacturability can be improved.

More preferably, by satisfying the following conditions, it is possible to provide an imaging optical system having a wide field angle, a large pupil diameter, and excellent aberration correction.

According to the above definition, when the X-axis, the Y-axis, and the Z-axis are set, the ray of the maximum angle of view of the ray that exits the pupil position center and enters the image forming optical system that forms an image intersects each surface. The area to be defined is defined as the effective area, and the rays ~ shown in Table 1 below are traced.

[0034]

That is, an axial chief ray in the optical axis direction at the center of the screen is taken as an upper central view angle ray, an upper right view angle ray, a right central view angle ray, and a lower right view angle ray. Let the ray at the lower center angle of view be. An expression describing the surface shape of the portion where these light rays hit each surface of the optical system (an expression expressing the Z axis as the axis of the surface, or assuming that the surface has no eccentricity, the form of Z = f (X, Y)) The values of the first derivative and the curvature of the equation (2) are obtained. In other words, the first derivative represents the inclination of the portion where the light beam strikes with respect to the definition coordinates of the surface, and the curvature represents the partial curvature of the portion where the light beam strikes. This is because, when each surface of the optical system is arranged eccentrically, the coordinates defining the surface shape can be defined at any position, and even if the curvature or the like at the coordinate center is described, the light ray This is because they may not pass through, and the surface shape is not limited.

First, the partial curvature in the X direction at the position where the axial principal ray of the TFC surface strikes will be described.
In the present invention, the meaning of defining the partial curvature of the surface means that even if the aberration of the TFC surface is sufficiently corrected, if the power of the surface is too large, the occurrence of the aberration will be too large, and This is because the correction becomes impossible.
Assuming that the curvature of the portion where the principal ray in the X direction falls is RX, it is important that the following condition is satisfied: | RX | <0.5 (1 / mm) (A-1) If the curvature of the eccentrically arranged reflecting surface does not exceed the upper limit of 0.5, the reflecting surface is formed by a surface having only one symmetric surface, thereby forming an optical system with less aberration. It becomes possible. On the reflecting surface exceeding this upper limit 0.5,
The occurrence of various aberrations due to the eccentricity becomes extremely large, and it becomes difficult to correct the aberration on other surfaces.

More preferably, when the condition of | RX | <0.1 (1 / mm) (A-2) is satisfied, the reflecting surface is constituted by a surface having only one plane of symmetry. That is important in order not to generate aberration due to decentering.

More preferably, when the condition of | RX | <0.05 (1 / mm) (A-3) is satisfied, the reflecting surface is constituted by a surface having only one plane of symmetry. That is important in order not to generate aberration due to decentering.

Next, the partial curvature in the Y direction at the position where the axial principal ray of the TFC surface strikes will be described. In the present invention, the meaning of defining the partial curvature of the surface means that even if the aberration of the TFC surface is sufficiently corrected, if the power of the surface is too large, the occurrence of the aberration will be too large, and This is because the correction becomes impossible. Assuming that the curvature of the portion hit by the principal ray in the Y direction is RY, it is important to satisfy the following condition: | RY | <0.5 (1 / mm) (B-1) When the curvature of the eccentrically arranged reflecting surface does not exceed the upper limit of 0.5, the reflecting surface is formed by a surface having only one symmetric surface, thereby forming an optical system with less aberration. It is possible to do. On the reflecting surface exceeding the upper limit of 0.5, the occurrence of various aberrations due to eccentricity becomes extremely large, and it becomes difficult to correct the other surfaces.

More preferably, when the condition of | RY | <0.1 (1 / mm) ... (B-2) is satisfied, the reflecting surface is constituted by a surface having only one plane of symmetry. That is important in order not to generate aberration due to decentering.

More preferably, when the condition of | RY | <0.05 (1 / mm) ... (B-3) is satisfied, the reflecting surface is constituted by a surface having only one plane of symmetry. That is important in order not to generate aberration due to decentering.

Next, on the reflecting surface, the value DX of the first derivative in the X-axis direction is D with respect to the inclination DX _axis and the curvature RX at the position where the principal ray passing through the pupil center and reaching the image plane center strikes.
When X _max1 = MAX ((DX−DX _axis ) / RX), it is important to satisfy the following conditions.

| DX _max1 | <100.0 (mm) (1-1) This condition represents the inclination of the reflecting surface in the X direction. When the upper limit of 100.0 in the above conditional expression is exceeded, The inclination of the reflecting surface becomes too large with respect to the principal ray of the image height, and aberrations due to decentering become too large, so that it becomes impossible to correct it on other surfaces.

More preferably, it is important to satisfy the conditional expression | DX _max1 | <10.0 (mm) (1-2).

More preferably, it is important to satisfy the conditional expression | DX _max1 | <6.0 (mm) ... (1-3).

All of the above conditional expressions (1-1) to (1-3) are necessary for obtaining a good observation image at a wide angle of view. Particularly, conditional expression (1-2) is important at a half angle of view of 10 degrees or more, and it is preferable that conditional expression (1-3) be satisfied at a half angle of view of 15 degrees or more.

Next, in the reflecting surface, the inclination in the eccentric direction of the surface, that is, the value DY of the one-time differential in the Y-axis direction passes through the pupil center and the inclination D of the position where the chief ray reaches the image plane center hits.
For the Y _axis and the curvature RY, DY _max2 = MAX ((DY
-DY _axis ) / RY), it is important to satisfy the following conditions.

| DY _max2 | <100.0 (mm) (2-1) This condition represents the tilt of the reflecting surface in the Y direction. When the upper limit of 100.0 in the above conditional expression is exceeded, The inclination of the reflecting surface becomes too large with respect to the principal ray of the image height, and aberrations due to decentering become too large, so that it becomes impossible to correct it on other surfaces.

More preferably, it is important to satisfy the conditional expression: | DY _max2 | <10.0 (mm) (2-2).

More preferably, it is important to satisfy the conditional expression: | DY _max2 | <6.0 (mm) ... (2-3).

All of the above conditional expressions (2-1) to (2-3) are necessary for obtaining a good observation image at a wide angle of view. Particularly, conditional expression (2-2) becomes important at a half angle of view of 10 degrees or more, and it is preferable that conditional expression (2-3) be satisfied at a half angle of view of 15 degrees or more.

Next, the inclination in the X direction at the position where the principal ray having the maximum angle of view in the X direction strikes the reflecting surface that is eccentrically arranged, and the principal ray at the zero angle of view in the X direction strikes the reflecting surface. Of the difference in the X direction from (DX4-
DX1) and (DX6-DX3), and the difference is DX ₃ =
When (DX4-DX1)-(DX6-DX3), it is preferable that the following condition is satisfied: | DX ₃ | <0.4 (3-1)

The conditional expression (3-1) represents the distortion in the X direction of the peripheral image in the X direction. If the upper limit of 0.4 of this conditional expression is exceeded, the left and right ends of the observation image change in the X-axis direction, and the image distortion of the trapezoid becomes large, making it impossible to correct the distortion on other surfaces. Become.

More preferably, it is preferable that the conditional expression | DX ₃ | <0.2 (3-2) is satisfied. This is especially 1
This is important when observing an observation image with little image distortion when trying to secure a half angle of view of 0 degree or more.

It is more preferable that the conditional expression | DX ₃ | <0.1 (3-3) is satisfied. This is especially 1
This is important when observing an observation image with little image distortion when trying to secure a half angle of view of 5 degrees or more.

More preferably, | DX ₃ | <0.05 (3-4) This is because when an attempt is made to secure a half field angle of 20 degrees or more, an observed image with almost no image distortion is obtained. It becomes important when observing.

Next, at the position where the principal ray with the maximum angle of view in the X direction hits the reflecting surface arranged decentered, and the principal ray with the X direction angle of view of zero hits the reflecting surface. Of the difference in the Y direction from (DY4-
DY1) and (DY6-DY3), and the difference is DY ₄ =
(DY4-DY1) - When a (DY6-DY3), | DY 4 | < may satisfy 0.4 · (4-1) The condition.

The conditional expression (4-1) represents the distortion in the Y direction of the peripheral image in the X direction. If the upper limit of 0.4 of this conditional expression is exceeded, the left and right ends of the observed image change in the Y-axis direction, the image distortion that causes the peripheral image to be bowed becomes large, and it becomes impossible to correct on other surfaces. , Resulting in a distorted observation image.

More preferably, it is preferable that the conditional expression | DY ₄ | <0.2 (4-2) is satisfied. This is especially 1
This is important when observing an observation image with little image distortion when trying to secure a half angle of view of 0 degree or more.

More preferably, it is preferable that the conditional expression | DY ₄ | <0.1 (4-3) is satisfied. This is especially 1
This is important when observing an observation image with little image distortion when trying to secure a half angle of view of 5 degrees or more.

More preferably, | DY ₄ | <0.05 (4-4) This is because an observed image with almost no image distortion is obtained especially when trying to secure a half angle of view of 20 degrees or more. It becomes important when observing.

Next, the one-time differential value DX in the X direction at the center of the screen
The difference (DX5−DX _axis ) between the first derivative value DX5 in the X direction at the right end of the maximum angle of view in the X direction on the X _axis and the X axis is DX _max5
In this case, it is important that the value of DX _max5 of the reflecting surface satisfies the following conditional expression: | DX _max5 | <0.5 (5-1)

This is a straight line in the left-right direction passing through the center of the screen,
For example, a horizontal line or the like is curved in a bow shape, resulting in image distortion observed. If this numerical value exceeds the upper limit of 0.5, bow-shaped image distortion will be protruded largely downward, and it will be impossible to correct it on other surfaces.

More preferably, it is important that the conditional expression | DX _max5 | <0.1 (5-2) is satisfied. Especially, in the case of a half angle of view exceeding 10 degrees, this condition is satisfied. Is important to satisfy. Note that the upper limit is determined by the conditional expression (5-
Same as 1).

More preferably, it is important to satisfy the conditional expression | DX _max5 | <0.05 (5-3). Especially, in the case of a half angle of view exceeding 15 degrees, this condition is satisfied. Is important to satisfy. Note that the upper limit is determined by the conditional expression (5-
Same as 1).

More preferably, it is important that the conditional expression | DX _max5 | <0.02 (5-4) is satisfied. Especially, in the case of a half angle of view exceeding 20 degrees, this condition is satisfied. It is important to be satisfied. Note that the upper limit is the same as the conditional expression (5-1).

Next, the one-time differential value DY in the Y direction of the screen center
The difference between the first derivative _DY5 in the Y direction at the right end of the maximum angle of view in the X direction on the X _axis and the X axis ( _DY5 -DY _axis ) is _expressed as DY _max6
In this case, it is important that the value of DY _max6 of the reflecting surface satisfies the following conditional expression: | DY _max6 | <0.5 (6-1) This is image distortion in which a straight line in the horizontal direction passing through the center of the screen, for example, a horizontal line or the like is bowed and curved and observed. This value is the upper limit of 0.
If it exceeds 5, bow-shaped image distortion will be generated convexly downward, and it will be impossible to correct it on other surfaces.

More preferably, it is important that the conditional expression | DY _max6 | <0.1 (6-2) is satisfied. Especially, in the case of a half angle of view exceeding 10 degrees, this condition is satisfied. Is important to satisfy. The upper limit is determined by the conditional expression (6-
Same as 1).

More preferably, it is important that the conditional expression | DY _max6 | <0.05 (6-3) is satisfied. Especially, in the case of a half angle of view exceeding 15 degrees, this condition is satisfied. Is important to satisfy. The upper limit is determined by the conditional expression (6-
Same as 1).

More preferably, it is important to satisfy the conditional expression | DY _max6 | <0.02 (6-4). Especially, in the case of a half angle of view exceeding 20 degrees, this condition should be satisfied. It is important to be satisfied. Note that the upper limit is the same as the conditional expression (6-1).

Next, when the difference between the maximum value and the minimum value within the effective region of the partial curvature of the TFC surface in the X direction is DDX _max7 , it is important to satisfy the following conditional expression.

DDX _max7 <0.5 (1 / mm) (7-1) Under this condition, curvature of field is difficult to change in the X-axis direction. Show that it is important to reduce. If the difference in the curvature in the X direction of the eccentrically arranged reflecting surface exceeds the upper limit of 0.5, the curvature of field increases, and it becomes difficult to obtain a flat image surface.

More preferably, if the condition of DDX _max7 <0.1 (1 / mm) (7-2) is satisfied, it is possible to obtain an image in which the periphery is well corrected.

More preferably, if the condition of DDX _max7 <0.05 (1 / mm) ... (7-3) is satisfied, it is possible to obtain an image that is corrected even better to the periphery.

Next, when the difference between the maximum value and the minimum value within the effective area of the partial curvature in the Y direction of the TFC surface is DDY _max8 , it is important to satisfy the following conditional expression.

DDY _max8 <0.5 (1 / mm) (8-1) Under these conditions, it is difficult to change the curvature in the Y-axis direction. Show that it is important to reduce. If the difference in curvature in the Y direction between the eccentrically arranged reflecting surfaces exceeds the upper limit of 0.5, the curvature of field increases, and it becomes difficult to obtain a flat image surface.

More preferably, if the _condition of DDY _max8 <0.1 (1 / mm) (8-2) is satisfied, it is possible to obtain an image in which the periphery is well corrected.

More preferably, if the _conditions of DDY _max8 <0.05 (1 / mm) ... (8-3) are both satisfied, it is possible to obtain an image with even better correction up to the periphery.

Next, the curvature in the X direction / the curvature in the Y direction at the position where each ray in the effective surface strikes the surface | = | DDXn | /
| DDYn | (where n is 1 to corresponding to the number of the principal ray)
When 6) is DD _xy9 , D is the same in the entire effective area of the reflection surface.
It is important that D _xy9 satisfies the following conditional expression: 0.01 <DD _xy9 <40 (9-1).

This is the image formation position in the X direction of the effective area and Y.
This is a condition for astigmatism being corrected satisfactorily, which corresponds to the ratio of the imaging positions in the directions. If the lower limit of 0.01 is exceeded, the light beam in the X direction forms an image closer to the optical system than the light beam in the Y direction, and astigmatism is more likely to occur.
Conversely, if the value exceeds the upper limit of 40, light rays in the X direction are imaged farther than the optical system with respect to light rays in the Y direction, and astigmatism is greatly generated. Correction becomes impossible. However, in the case of a surface having symmetry with respect to both the Y axis and the X axis, such as a toric surface, this condition is satisfied, but the occurrence of coma aberration and image distortion increases.

More preferably, it is important that the conditional expression 0.1 <DD _xy9 <20 (9-2) is satisfied, and particularly in the case of a half angle of view exceeding 20 degrees, this condition is satisfied. Is important to satisfy.

More preferably, it is important that the conditional expression of 0.3 <DD _xy9 <10 (9-3) is satisfied. Especially, in the case of a half angle of view exceeding 25 degrees, this condition is satisfied. Is important to satisfy.

More preferably, it is important to satisfy the conditional expression of 0.5 <DD _xy9 <6 (9-4). Especially, in the case of a half angle of view exceeding 30 degrees, this condition is satisfied. Is important to satisfy.

[0084]

Embodiments 1 to 6 of the image forming optical system of the present invention will be described below. Cross-sectional views of Examples 1 to 6 are shown in FIGS. 1 to 6, respectively. In the numerical data described later, the surface number is shown as the number of the surface that constitutes the optical system in the order of the order tracking from the object plane to the image plane. The numbers are also optically equivalent. The surface interval is the length measured along the axial principal ray between the previous surface and the next surface (however, the sign is inverted after reflection), and the eccentricity is the distance of the surface relative to the incident axial principal ray. Indicates the tilt angle (°) of the definition axis (positive in the counterclockwise direction).
The refractive index of Examples 1 to 3 is a value for a wavelength of 660 nm,
Examples 4 to 6 show values for the d line. The unit of the length is mm.

In the numerical data described later, the shape of the surface of the free-form surface is defined by the above equation (a), the Y axis and the Z axis of which are in the plane of the drawing, and the YZ plane is symmetrical. It is a symmetrical surface of a free-form surface that has only one surface. In addition,
The term relating to the order for which no data is described is zero.

In each of Examples 1 to 6, two to three of the four optical surfaces forming the prism body made of a pentagonal prism-shaped medium made of a medium having a refractive index larger than 1 including two reflecting surfaces are included. By forming the optical surface by a free-form surface having only one symmetrical surface and the remaining two surfaces or one surface by a spherical surface, the prism body is provided with image forming performance.

In other words, the first and second embodiments are pentagonal prism-shaped having the first surface 1, the second surface 2, the third surface 3 and the fourth surface 4, as shown in the cross sections of FIGS. 1 and 2, respectively. It is a prism body 5, the first surface 1 and the fourth surface 4 are refracting surfaces, the second surface 2 and the third surface 3 are reflecting surfaces, the first surface 1 is a spherical surface, the second surface 2 and the third surface 3 The fourth surface 4 is a free-form surface. Cover glass 6
The light beam from the object surface O provided on the back surface of the prism body 5 is incident on the first surface 1 of the prism body 5 through the cover glass 6 and is reflected by the second surface 2 and the third surface 3 in order. The prism body 5 intersects with the light beam reaching the second surface 2 from the surface 1
To the image plane I. In these examples, the horizontal angle of view (the angle of view in the direction vertical to the paper surface) is 50 degrees, the vertical angle of view (the angle of view within the paper surface) is 37 degrees, and the focal length is 6 m when converted to the coaxial system.
m is an imaging optical system with a pupil diameter of 1.7857 mm.

The third embodiment is a pentagonal prism-shaped prism body 5 having a first surface 1, a second surface 2, a third surface 3 and a fourth surface 4, as shown in the cross section of FIG. The surfaces 1 and 4 are refracting surfaces, the second surface 2 and the third surface 3 are reflecting surfaces, the first surface 1 and the fourth surface are spherical surfaces, and the second surface 3 and the third surface 3 are free-form surfaces. Become. The light rays from the object plane O are reflected on the first surface 1 of the prism body 5.
From the second surface 2 and the third surface 3, and the reflected light intersects with the light beam from the first surface 1 to the second surface 2 and exits from the fourth surface 4 to the outside of the prism body 5. Then, the image reaches the image plane I provided on the back surface through the cover glass 6. This example is
An imaging optical system having a horizontal angle of view (angle of view in the direction perpendicular to the paper) of 50 degrees, a vertical angle of view (angle of view in the plane of the paper) of 37 degrees, a focal length of 6 mm in terms of a coaxial system, and a pupil diameter of 1.7857 mm. It is.

Example 4 is a pentagonal prism-shaped prism body 5 having a first surface 1, a second surface 2, a third surface 3 and a fourth surface 4, as shown in the cross section of FIG. The first surface 1 and the fourth surface 4 are refracting surfaces, and the second surface 2 and the third surface 3 are reflecting surfaces.
Is a spherical surface, the second surface 2, the third surface 3, and the fourth surface 4 are free-form surfaces. This optical system is a projection optical system, and object light from infinity enters from a first surface 1 of a prism body 5 and a second surface 2
And the third surface 3 in order, and the reflected light is reflected from the first surface 1
The light intersects with the light beam reaching the surface 2, exits from the fourth surface 4 to the outside of the prism body 5, passes through the cover glass 6, and reaches the image plane I provided on the back surface thereof. In this embodiment, the object height is 1.447 mm in the X-axis direction (perpendicular to the paper surface), 1.0915 mm in the Y-axis direction (direction in the paper surface), and the object-side NA (numerical aperture) is 0.03 mm.
57 is a projection optical system.

The fifth embodiment is a pentagonal prism-shaped prism body 5 having a first surface 1, a second surface 2, a third surface 3 and a fourth surface 4, as shown in the cross section of FIG. The surfaces 1 and 4 are refracting surfaces, the second surface 2 and the third surface 3 are reflecting surfaces, the first surface 1, the second surface 2 and the third surface 3 are free-form surfaces, and the fourth surface 4 is a spherical surface. Consists of. This optical system is a projection optical system, and object light from infinity enters from a first surface 1 of a prism body 5 and is reflected by a second surface 2 and a third surface 3 in order. From the fourth surface 4 to the prism body 5
And reaches the image plane I provided on the back surface through the cover glass 6. In this embodiment, the object height is 1.447 mm in the X-axis direction (perpendicular to the paper surface), 1.0915 mm in the Y-axis direction (direction in the paper surface), and the object-side NA (numerical aperture) is 0.03 mm.
57 is a projection optical system.

The sixth embodiment is a pentagonal prism-shaped prism body 5 having a first surface 1, a second surface 2, a third surface 3 and a fourth surface 4, as shown in the cross section of FIG. The first surface 1 and the fourth surface 4 are refracting surfaces, and the second surface 2 and the third surface 3 are reflecting surfaces.
Is a spherical surface, and the second surface 2, the third surface 3, and the fourth surface 4 are free-form spherical surfaces. This optical system is a projection optical system, and object light from infinity passes through a separate stop, enters from the first surface 1 of the prism body 5, is reflected by the second surface 2 and the third surface 3 in order, The reflected light intersects with the light beam from the first surface 1 to the second surface 2 and
The light is emitted from the surface 4 to the outside of the prism body 5, reaches the image plane I provided on the back surface of the prism body 5 via the cover glass 6. In this embodiment, the object height is 4.02 mm in the X-axis direction (perpendicular to the paper),
3.03 mm in Y-axis direction (direction in the plane of the paper), NA on the object side
(Numerical aperture) 0.0129.

The constituent parameters of Examples 1 to 6 are shown below. Example 1 Surface No. Curvature Radius Interval Eccentricity Refractive Index Object Surface ∞ 2 1.51374 1 ∞ 0.1 2 5.14554 5 1.52246 3 (Reflective Surface) Free Curved Surface (Aperture) -4 22.5 ° 1.52246 4 (Reflective Surface) Free Curved Surface 5 22.5 ° 1.52246 5 Free-form surface 10 Image surface ∞ 10.85 ° Free-form surface C ₅ -1.7259 × 10 ^-2 C ₇ -2.7401 × 10 ^-2 C ₈ 1.1803 × 10 ^-3 C ₁₀ 1.4324 × 10 ^-3 C ₁₂ 5.2923 × 10 ^-4 Free-form surface C ^{_{5 2.4038 × 10 -2 C 7 2.0287}} × 10 -2 C 8 1.8232 × 10 -3 C 10 2.3734 × 10 -3 C 12 -4.2358 × 10 -5 C 14 -1.4306 × 10 -3 C 16 -2.1648 × 10 - ⁴ C ₁₇ -1.5709 × 10 ^-5 C ₁₉ 2.5253 × 10 ^-4 C ₂₁ -9.0495 × 10 ^-5 Free-form surface C ₅ 2.0 512 × 10 ^-2 C ₇ -6.8638 × 10 ^-3 C ₈ 1.4451 × 10 ^-2 C ₁₀ 1.1589 × 10 ^-2 C ₁₂ 2.9399 × 10 ^-3 C ₁₄ -7.5491 × 10 ^-4 C ₁₆ 6.6724 × 10 ^-4 C ₁₇ 1.4057 × 10 ^-4 C ₁₉ -6.7043 × 10 ^-5 C ₂₁ -1.4187 × 10 ^-4 .

Example 2 Surface number Curvature radius Spacing Decentering Refractive index Object surface ∞ 2 1.51374 1 ∞ 3.2357 2 4.138 (Aperture) 8.0000 1.52246 3 (Reflecting surface) Free curved surface -6.0000 22.5 ° 1.52246 4 Free reflecting surface 7.0000 22.5 ° 1.52246 5 free curved 9.7955 plane ∞ 6.57 ° free curved surface ^{_{C 5 -1.3741 × 10 -2 C 7}} -1.5219 × 10 -2 C 8 4.1326 × 10 -4 C 10 -1.1718 × 10 -4 C 12 2.7049 × 10 - ⁴ C ₁₄ 4.1434 × 10 ^-4 C ₁₆ 2.7833 × 10 ^-4 C ₁₇ -7.9413 × 10 ^-6 C ₁₉ -3.9758 × 10 ^-6 C ₂₁ -9.7917 × 10 ^-6 Free-form surface C ₅ 8.8 248 × 10 ^-3 C ₇ 1.2101 × 10 ^-2 C ₈ 9.7701 × 10 ^-4 C ₁₀ 3.062 1 × 10 ^-4 C ₁₂ 1.1704 × 10 ^-4 C ₁₄ 5.0194 × 10 ^-5 C ₁₆ 4.4158 × 10 ^-5 C ₁₇ -2.2647 × 10 ^-5 C _{19 ^{-2.2923 × 10 -5 C 21 -9.9488 ×}} 10 -6 free curved surface ^{_{C 5 4.8179 × 10 -2 C 7}} 5.8589 × 10 -2 C 8 6.3509 × 10 -3 C 10 2.1715 × 10 -3 C 12 1.0285 × 10 - ³ .

Example 3 Surface number Curvature radius Spacing Decentering Refractive index Object surface ∞ 22.1708 1 4.390 4.0000 1.52246 2 (Reflecting surface) Free curved surface (Aperture) -3.0000 1.52246 3 (Reflecting surface) Free curved surface 4.0000 22.5 ° 1.52246 4 -42.808 1.0000 22.5 ° 5 ∞ 2.0000 1.51374 image plane ∞ -0.21 ° free curved surface ^{_{C 5 -4.4927 × 10 -3 C 7}} -5.0638 × 10 -3 C 8 1.1087 × 10 -4 C 10 6.7113 × 10 -5 C 19 7.2815 × 10 - ³ Free-form surface C ₅ 5.9327 × 10 ^-3 C ₇ 7.3558 × 10 ^-3 C ₈ 2.4745 × 10 ^-4 C ₁₀ 2.6009 × 10 ^-4 C ₁₂ -1.0058 × 10 ^-3 C ₁₄ -1.0969 × 10 ^-3 C _16- 1.3196 × 10 ^-3 C ₁₇ 8.6909 × 10 ^-5 C ₁₉ 2.2790 × 10 ^-4 C ₂₁ 7.8089 × 10 ^-5 C ₂₃ 1.0124 × 10 ^-3 C ₂₅ -1.4448 × 10 ^-3 C ₂₇ 8.5070 × 10 ^-4 C ₂₉ 6.4542 × 10 ^-4 .

Example 4 Surface number Curvature radius Spacing Decentering Refractive index Object surface ∞ ∞ 1 -15.445 10.0000 1.5254 2 (Reflecting surface) Free curved surface (Aperture) -8.0000 1.5254 3 (Reflecting surface) Free curved surface 10.0000 22.5 ° 1.5254 4 Free curved surface 2.0000 22.5 ° 5 ∞ 2.0000 1.51633 Image plane ∞ Free-form surface C ₅ -2.1823 × 10 ^-3 C ₇ -7.2575 × 10 ^-3 C ₈ 5.3928 × 10 ^-5 C ₁₀ -2.2392 × 10 ^-4 Free-form surface C ₅ 1.3258 × 10 ^-2 C ₇ 8.2532 × 10 ^-3 C ₈ 1.1914 × 10 ^-4 C ₁₀ 1.9741 × 10 ^-4 C ₁₂ -5.4958 × 10 ^-5 C ₁₄ -6.2520 × 10 ^-5 C ₁₆ 2.9156 × 10 ^-5 C ₁₇ 3.0366 × 10 ^-5 C ₁₉ 7.1622 × 10 ^-5 C ₂₁ -1.7677 × 10 ^-5 C ₂₃ -2.2836 × 10 ^-6 C ₂₅ -1.0994 × 10 ^-5 C ₂₇ 8.0997 × 10 ^-6 C ₂₉ -2.6965 × 10 ^-5 C ₃₀ -2.0544 x 10 ^-6 C ₃₂ 6.4715 x 10 ^-6 C ₃₄ -1.1 104 x 10 ^-5 C ₃₆ 3.6881 x 10 ^-6 free-form surface C ₅ -1.3951 x 10 ^-1 C ₇ -1.8229 x 10 ^-1 C ₈ 5.8170 × 10 ^-4 C ₁₀ 3.6935 × 10 ^-3 C ₁₂ 2.8695 × 10 ^-3 C ₁₄ 6.2821 × 10 ^-3 C ₁₆ 3.6956 × 10 ^-3 C ₁₇ 4.3385 × 10 ^-4 C ₁₉ 1.0779 × 10 ^-4 C ₂₁ -2.6 104 × 10 ^-4 C ₂₃ -7.1825 × 10 ^-5 C ₂₅ -1.2960 × 10 ^-4 C ₂₇ -1.6079 × 10 ^-4 C ₂₉ -7.7523 × 10 ^-5 C ₃₀ -2.7657 × 10 ^-5 C ₃₂ 1.5948 × 10 ^-5 C ₃₄ -1.3703 x 10 ^-5 C ₃₆ 7.5755 x 10 ^-6 .

Example 5 Surface number Curvature radius Spacing Decentering Refractive index Object plane ∞ ∞ 1 Free curved surface 12.0000 1.5254 2 (Reflective surface) Free curved surface (Aperture) -8.0000 1.5254 3 (Reflective surface) Free curved surface 12.0000 22.5 ° 1.5254 4 -9.002 2.0000 22.5 ° 5 ∞ 2.0000 1.51633 Image plane ∞ -4.49 ° Free-form surface C ₅ 1.5730 × 10 ^-2 C ₇ -7.8390 × 10 ^-2 C ₈ 4.5149 × 10 ^-4 C ₁₀ 2.9787 × 10 ^-4 C ₁₂ -5.5892 × 10 ^-5 C ₁₄ 4.5865 × 10 ^-4 C ₁₆ 3.1477 × 10 ^-4 C ₁₇ 6.4385 × 10 ^-6 C ₁₉ -8.3 800 × 10 ^-5 C ₂₁ -1.0065 × 10 ^-6 Free-form surface C ₅ 3.2524 × 10 ^-2 C ₇ -1.0185 x 10 ^-2 C ₈ -1.7137 x 10 ^-3 C ₁₀ -6.8 674 x 10 ^-4 C ₁₂ -3.9 125 x 10 ^-4 C ₁₄ -5.1878 x 10 ^-4 C ₁₆ 2.060 1 x 10 ^-5 free-form surface C ₅ 2.7073 × 10 ^-2 C ₇ 1.3793 × 10 ^-2 C ₈ -3.6082 × 10 ^-4 C ₁₀ -3.8227 × 10 ^-5 C ₁₂ 1.0380 × 10 ^-5 C ₁₄ -1.4753 × 10 ^-4 C ₁₆ -5.0446 × 10 ^-5 C ₁₇ -2.2375 x 10 ^-6 C ₁₉ -1.2995 x 10 ^-5 C ₂₁ 3.1799 x 10 ^-7 .

Example 6 Surface number Curvature radius Spacing Decentering Refractive index Object plane ∞ ∞ 1 ∞ (Aperture) 1.0000 2 -4.932 12.0000 1.5254 3 (Reflecting surface) Free-form surface -8.0000 1.5254 4 (Reflecting surface) Free-form surface 10.0000 22.5 ° 1.5254 5 Free-form surface 2.0000 22.5 ° 6 ∞ 2.0000 1.51633 Image plane ∞ Free-form surface C ₅ -7.2939 × 10 ^-3 C ₇ -1.4353 × 10 ^-2 C ₈ -3.5114 × 10 ^-4 C ₁₀ -3.3815 × 10 ^-4 C ₁₂ 3.1703 × 10 ^-5 C ₁₄ -2.6397 × 10 ^-5 C ₁₆ 3.2783 × 10 ^-5 C ₁₇ 2.1756 × 10 ^-6 C ₁₉ 5.8039 × 10 ^-6 C ₂₁ -5.2429 × 10 ^-6 Free-form surface C ₅ 1.7055 × 10 ^{-2 _{C 7 1.2235 × 10 -2 C 8}} -2.9021 × 10 -5 C 10 -1.8169 × 10 -4 C 12 3.4015 × 10 -5 C 14 1.4158 × 10 -5 C 16 3.8495 × 10 -5 C 17 1.1846 × 10 - ⁶ C ₁₉ 5.3599 × 10 ^-6 C ₂₁ -4.2 183 × 10 ^-6 Free-form surface C ₅ 1.4365 × 10 ^-2 C ₇ -5.2713 × 10 ^-2 C ₈ -6.0365 × 10 ^-4 C ₁₀ -2.1749 × 10 ^-3 C ₁₂ 1.0886 × 10 ^-3 C ₁₄ 2.407 2 × 10 ^-3 C ₁₆ 1.1789 × 10 ^-3 C ₁₇ 2.5576 × 10 ^-4 C ₁₉ 1.4731 × 10 ^-4 C ₂₁ -2.1692 × 10 ^-4 .

Next, FIGS. 7 and 8 are lateral aberration diagrams of the second embodiment. In these lateral aberration diagrams, the numbers shown in parentheses represent (horizontal angle of view (angle of view in the direction perpendicular to the paper surface), vertical angle of view (angle of view in the paper surface)). Show. Similar lateral aberration diagrams of the sixth embodiment are shown in FIGS.

The conditional expressions (A-1), (B-1), (1-1) to (9-1) in each example of the present invention will be described below.
The values of the parameters regarding (the conditional expression (9-1), the upper part shows the values for the first reflecting surface 2 and the lower part shows the values for the second reflecting surface 3, and regarding the conditional expression (9-1), , The upper row shows the minimum value of each reflective surface, and the lower row shows the maximum value.)

[0100] .

In the above embodiments, the free-form surface of the above-mentioned definition formula (a) is used, but it goes without saying that a curved surface of any definition can be used. However, no matter what definition formula is used, aberrations can be corrected very well by satisfying the conditional expressions shown in the present invention alone or in combination, or by satisfying some of them. Needless to say, the obtained imaging optical system can be obtained. Note that the conditional expressions used in the conventional non-eccentric system such as the curvature of the surface defined by the center of the coordinate system that defines the surface ignoring the eccentricity and the focal length of the surface are large for each surface as in the present invention. If it is eccentric, it has no meaning.

The above-described image forming optical system of the present invention can be constructed, for example, as follows. [1] In an image forming optical system having at least a decentering optical system and forming an image of light from an object on a surface of an image sensor, the image forming optical system includes at least one reflecting surface having a reflecting action, An image forming optical system, characterized in that at least one of the reflecting surfaces has a surface symmetry free-form surface having no rotational symmetry axis both inside and outside the surface and having only one symmetry surface. .

[2] The reflecting surface is defined by a straight line from the object side through the pupil center to the axial chief ray reaching the image forming position center of the image pickup device and intersecting the first surface of the image forming optical system. The defined optical axis is the Z-axis, the axis orthogonal to the Z-axis and in the decentered plane of each of the surfaces forming the imaging optical system is Y.
When the axis is defined as an axis and the axis orthogonal to the Z axis and the Y axis is defined as the X axis, the following condition (A-1) is satisfied: . | RX | <0.5 (1 / mm) (A-1) where RX is the curvature in the X direction of the portion where the axial principal ray hits the reflection surface.

[3] The reflecting surface is defined by a straight line from the object side through the pupil center to the axial principal ray reaching the image forming position center of the image pickup device and intersecting the first surface of the image forming optical system. The defined optical axis is the Z-axis, the axis orthogonal to the Z-axis and in the decentered plane of each of the surfaces forming the imaging optical system is Y.
When the axis is defined as an axis and an axis orthogonal to the Z axis and the Y axis is defined as an X axis, the following condition (B-1) is satisfied, and the imaging optical system according to the above [1]. . | RY | <0.5 (1 / mm) (B-1) where RY is the curvature in the Y direction of the portion where the axial principal ray hits the reflection surface.

[4] The reflecting surface is defined by a straight line from the object side through the pupil center to the axial principal ray reaching the image forming position center of the image pickup device and intersecting the first surface of the image forming optical system. The defined optical axis is the Z-axis, the axis orthogonal to the Z-axis and in the decentered plane of each of the surfaces forming the imaging optical system is Y.
The following conditions (A-1) and (B-1) are satisfied when the axis is defined as the X axis and the axis orthogonal to the Z axis and the Y axis is defined as the X axis [1]. The imaging optical system described. | RX | <0.5 (1 / mm) (A-1) | RY | <0.5 (1 / mm) (B-1) where RX and RY are the reflection surfaces, respectively. Are the curvatures in the X and Y directions of the portion where the axial chief ray hits.

[5] The reflective surface has the following condition (A-
The imaging optical system according to the above [2] or [4], which satisfies 2). | RX | <0.1 ... (A-2).

[6] The reflective surface has the following condition (A-
The imaging optical system according to the above [2] or [4], which satisfies 3). | RX | <0.05 (1 / mm) (A-3).

[7] The reflecting surface has the following condition (B-
The imaging optical system according to the above [3] or [4], which satisfies 2). | RY | <0.1 (1 / mm) (B-2).

[8] The reflecting surface has the following condition (B-
The imaging optical system according to the above [3] or [4], which satisfies 3). | RY | <0.05 (1 / mm) (B-3).

[0110]

[9] The plane of symmetry of the plane-symmetric free-form surface is
An optical axis defined by a straight line until an axial chief ray reaching the image forming position center of the image sensor from the object side through the pupil center intersects the first surface of the image forming optical system is defined as a Z axis, and When the axis orthogonal to the Z axis and within the decentered plane of each surface forming the imaging optical system is defined as the Y axis, and the axis orthogonal to the Z axis and the Y axis is defined as the X axis, The imaging optical system according to any one of the above [1] to [8], which is present on a YZ plane or a plane parallel thereto.

[10] Catadioptric power in the YZ plane of the area where the axial chief ray is reflected in the reflecting surface, and Y
From the above [2], characterized in that at least one of the catadioptric powers in the plane perpendicular to the -Z plane is positive.

The imaging optical system according to any one of [9].

[11] Catadioptric power in the YZ plane of the area where the axial chief ray is reflected in the reflecting surface, and Y
From the above [2], the catadioptric powers in the plane perpendicular to the -Z plane are both positive

The imaging optical system according to any one of [9].

[12] An optical axis defined by a straight line from the object side through the pupil center to the axial principal ray reaching the imaging position center of the image pickup device and intersecting the first surface of the imaging optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The imaging optical system according to any one of [1] to [11] above, wherein the reflecting surface satisfies the following condition. | DX _max1 | <100.0 (mm) (1-1) where DX _max1 = MAX ((DX-DX _axis ) / R
X), with the Y-axis direction as the vertical direction, the axial chief ray at the center of the imaging screen, the chief ray at the upper central angle of view, the chief ray at the upper right angle of view, the chief ray at the right central angle of view, and the lower right angle of view. Is defined as the effective area, and the area where the principal ray of the lower central angle of view intersects the target surface is defined as the effective area. About the X-axis that is perpendicular to the eccentric direction of the surface of the portion where these six chief rays meet the target surface The values that are obtained by differentiating once the formulas that define the surface shape are DX _axis and DX, respectively.
1, DX4, DX5, DX6, DX3, DX
Is the value of DX1, DX4, DX5, DX6, DX3, RX
Is the curvature in the X direction of the portion where the axial principal ray hits the reflecting surface.

[13] Optical axis defined by a straight line from the object side through the center of the pupil to the axial principal ray reaching the center of the imaging position of the image sensor and crossing the first surface of the imaging optical system Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The image forming optical system according to any one of [1] to [12] above, wherein the reflecting surface satisfies the following condition. | DY _max2 | <100.0 (mm) (2-1) where DY _max2 = MAX ((DY−DY _axis ) / R
Y), where the Y-axis direction is the vertical direction, the axial principal ray at the center of the imaging screen, the principal ray at the upper center angle of view, the principal ray at the upper right angle of view, the principal ray at the right central angle of view, and the lower right angle of view. The area where the principal ray of the lower central angle of view intersects with the target surface is defined as an effective area, and the shape of the surface with respect to the Y-axis, which is the eccentric direction of the surface where the six principal rays meet the target surface, is defined. Expression to define 1
DY _axis , DY1, DY4, D
When Y5, DY6, and DY3 are used, DY is DY1, DY
4, the values of DY5, DY6, and DY3, and RY are the curvature in the Y direction of the portion where the axial principal ray hits the reflection surface.

[14] An optical axis defined by a straight line until an axial chief ray that passes from the object side through the pupil center and reaches the imaging position center of the image sensor intersects the first surface of the imaging optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The imaging optical system according to any one of [1] to [13] above, wherein the reflecting surface satisfies the following condition. | DX ₃ | <0.4 (3-1) where DX ₃ = (DX4-DX1)-(DX6-DX
3), with the Y-axis direction as the vertical direction, the axial principal ray at the center of the imaging screen, the principal ray at the upper center angle of view, the principal ray at the upper right angle of view, the principal ray at the right central angle of view, and the lower right angle of view. The area where the principal ray of the lower central angle of view intersects with the target plane is defined as an effective area, and the X-axis, which is the direction in which these six principal rays are orthogonal to the eccentric direction of the surface of the portion corresponding to the target plane, is defined. DX _axis and DX are the values obtained by differentiating the equation defining the shape of the surface once.
1, DX4, DX5, DX6, and DX3.

[15] An optical axis defined by a straight line until an axial chief ray that passes through the center of the pupil from the object side and reaches the center of the image forming position of the image sensor intersects the first surface of the image forming optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The imaging optical system according to any one of [1] to [14] above, wherein the reflecting surface satisfies the following condition. | DY ₄ | <0.4 (4-1) where DY ₄ = (DY4-DY1) − (DY6-DY
3) With the Y-axis direction as the vertical direction, the axial principal ray at the center of the imaging screen, the principal ray at the upper center angle of view, the principal ray at the upper right angle of view, the principal ray at the right central angle of view, and the lower right angle of view The area where the principal ray of the lower central angle of view intersects with the target surface is defined as an effective area, and the shape of the surface with respect to the Y-axis which is the eccentric direction of the surface where the six principal rays meet the target surface is defined. Expression to define 1
DY _axis , DY1, DY4, D
Y5, DY6, and DY3.

[16] An optical axis defined by a straight line from the object side through the pupil center to the axial principal ray reaching the imaging position center of the image pickup device and intersecting the first surface of the imaging optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The imaging optical system according to any one of [1] to [15] above, wherein the reflecting surface satisfies the following condition. | DX _max5 | <0.5 (5-1) where DX _max5 = (DX5−DX _axis ), where the Y-axis direction is the vertical direction, and the axial chief ray at the center of the imaging screen, the upper center The area where the principal ray at the angle of view, the principal ray at the upper right angle of view, the principal ray at the right central angle of view, the principal ray at the lower right angle of view, and the principal ray at the lower central angle of view intersects the target plane is defined as the effective area. DX _axis , DX 1, DX 4, and DX 4 respectively denote the values obtained by differentiating once the equation defining the shape of the surface with respect to the X axis, which is a direction orthogonal to the eccentric direction of the surface of the portion where the six principal rays are the target surface.
5, DX6 and DX3.

[17] An optical axis defined by a straight line until an axial chief ray that passes through the center of the pupil from the object side and reaches the center of the image forming position of the image sensor intersects the first surface of the image forming optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The imaging optical system according to any one of [1] to [16] above, wherein the reflecting surface satisfies the following condition. | DY _max6 | <0.5 (6-1) where DY _max6 = ( _DY5 −DY _axis ), where the Y-axis direction is the up-down direction and the axial chief ray at the center of the imaging screen, the upper center The area where the principal ray at the angle of view, the principal ray at the upper right angle of view, the principal ray at the right central angle of view, the principal ray at the lower right angle of view, and the principal ray at the lower central angle of view intersects the target plane is defined as the effective area. , Which are the eccentric directions of the surface of the portion where these six chief rays hit the target surface.
DY _axis , DY 1, DY 4, DY 5, DY 6, D
Y3.

[18] An optical axis defined by a straight line from the object side through the pupil center to the axial principal ray reaching the imaging position center of the image pickup device and intersecting the first surface of the imaging optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The image forming optical system according to any one of [1] to [17] above, wherein the reflecting surface satisfies the following condition. DDX _max7 <0.5 (1 / mm) (7-1) where the Y-axis direction is the vertical direction, the axial principal ray at the center of the imaging screen, the principal ray at the upper center angle of view, and the upper right angle of view. Chief ray,
The area in which the chief ray at the right central angle of view, the chief ray at the lower right angle of view, and the chief ray at the lower central angle of view intersect with the target surface is defined as the effective area.
The difference between the maximum value and the minimum value of the curvature in the X direction within this effective area is defined as DDX _max7 .

[19] An optical axis defined by a straight line until an axial chief ray that passes through the center of the pupil from the object side and reaches the center of the image forming position of the image sensor intersects the first surface of the image forming optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The imaging optical system according to any one of [1] to [18] above, wherein the reflecting surface satisfies the following condition. DDY _max8 <0.5 (1 / mm) (8-1) where the Y-axis direction is the vertical direction, the axial principal ray at the center of the imaging screen, the principal ray at the upper center angle of view, and the upper right angle of view. Chief ray,
The area in which the chief ray at the right central angle of view, the chief ray at the lower right angle of view, and the chief ray at the lower central angle of view intersect with the target surface is defined as the effective area.
The difference between the maximum value and the minimum value of the curvature in the Y direction within this effective area is defined as DDY _max8 .

[20] An optical axis defined by a straight line from the object side through the pupil center to the axial principal ray reaching the imaging position center of the image pickup device and intersecting the first surface of the imaging optical system. Is the Z-axis, the axis that is orthogonal to the Z-axis and that is within the eccentric plane of each surface that constitutes the imaging optical system is the Y-axis, and the axis that is orthogonal to the Z-axis and the Y-axis is the X-axis. The imaging optical system according to any one of [1] to [19] above, wherein the reflecting surface satisfies the following condition. 0.01 <DD _xy9 <40 (9-1) where the Y-axis direction is the vertical direction, the axial principal ray at the center of the imaging screen, the principal ray at the upper center angle of view, and the principal ray at the upper right angle of view. ,
The area in which the chief ray at the right central angle of view, the chief ray at the lower right angle of view, and the chief ray at the lower central angle of view intersect with the target surface is defined as the effective area.
The curvatures of the equations that define the shape of the surface about the X axis orthogonal to the eccentric direction of the surface where the six principal rays hit the target surface are DDX2, DDX1, DDX4, and DDX, respectively.
5, DDX6 and DDX3, and the curvature of the equation defining the shape of the surface with respect to the Y axis corresponding to the eccentric direction of the surface is DD.
Y2, DDY1, DDY4, DDY5, DDY6, DD
Y3, and DD _xy9 = | DDXn | / | DDYn | (n
Is 1 to 6).

[21] The refractive index (n) of the reflecting surface is 1
[1] to [20], characterized in that it is composed of a rear surface reflecting mirror having a medium larger than (n> 1)
The imaging optical system according to any one of 1.

[0123]

As is apparent from the above description, according to the present invention, a wide imaging area can be obtained by using a reflecting surface formed of a plane-symmetric free-form surface having only one symmetry surface.
Moreover, by folding the optical path, it is possible to obtain a compact image-forming optical system in which ray aberration is well corrected and which has no image distortion and a small number of optical components.

[Brief description of drawings]

FIG. 1 is a sectional view of a first embodiment of an image forming optical system according to the present invention.

FIG. 2 is a sectional view of a second embodiment of the image forming optical system according to the present invention.

FIG. 3 is a sectional view of Example 3 of the imaging optical system of the present invention.

FIG. 4 is a sectional view of Embodiment 4 of the imaging optical system of the present invention.

FIG. 5 is a sectional view of Example 5 of the imaging optical system of the present invention.

FIG. 6 is a sectional view of a sixth embodiment of the image forming optical system of the present invention.

FIG. 7 is a diagram showing a part of a lateral aberration diagram according to a second embodiment of the present invention.

FIG. 8 is a diagram showing the rest of the lateral aberration diagram of Example 2 of the present invention.

FIG. 9 is a diagram showing a part of a lateral aberration diagram according to Example 6 of the present invention.

FIG. 10 is a diagram showing the rest of the lateral aberration diagrams for Example 6 of the present invention.

[Explanation of symbols]

 1 ... 1st surface 1 2 ... 1st surface 2 3 ... 1st surface 3 4 ... 1st surface 4 5 ... Prism body (imaging optical system) 6 ... Cover glass O ... Object surface I ... Image surface

Claims (3)

[Claims] 1. An imaging optical system having at least a decentered optical system for forming an image of light from an object on a surface of an image pickup device, wherein the imaging optical system includes at least one reflecting surface having a reflecting action. An image forming method, characterized in that at least one of the reflecting surfaces has a surface shape which does not have an axis of rotational symmetry in-plane and out-of-plane and which is a plane-symmetric free-form surface having only one symmetry surface. Optical system. 2. The reflection surface is defined by a straight line until an axial chief ray that passes through the pupil center from the object side and reaches the imaging position center of the image sensor intersects the first surface of the imaging optical system. The optical axis that is defined as the Z axis is orthogonal to the Z axis, and the axis within the eccentric plane of each surface that constitutes the imaging optical system is the Y axis, and is orthogonal to the Z axis and the Y axis. The imaging optical system according to claim 1, wherein the following condition (A-1) is satisfied when the axis is defined as the X axis. | RX | <0.5 (1 / mm) (A-1) where RX is the curvature in the X direction of the portion where the axial principal ray hits the reflection surface. 3. The reflection surface is defined by a straight line until an axial chief ray reaching from the object side through the pupil center to the image forming position center of the image sensor intersects the first surface of the image forming optical system. The optical axis that is defined as the Z axis is orthogonal to the Z axis, and the axis within the eccentric plane of each surface that constitutes the imaging optical system is the Y axis, and is orthogonal to the Z axis and the Y axis. The image forming optical system according to claim 1, wherein the following condition (B-1) is satisfied when the axis is defined as the X axis. | RY | <0.5 (1 / mm) (B-1) where RY is the curvature in the Y direction of the portion where the axial principal ray hits the reflection surface.