JP4611111B2 - Optical system - Google Patents

Description

  The present invention relates to an optical system, and more particularly to an optical system capable of simultaneously capturing a plurality of continuous parallax images whose parallax directions are continuously rotated with respect to an object.

Conventionally, separate right and left eye mirror optical systems or triangular prisms are arranged on the entrance side of a photographic optical system with one common imaging optical system and one imaging surface, and the left and right entrance pupils are divided. It is known in Patent Document 1, Patent Document 2, Patent Document 3, Patent Document 4, and the like that the right and left parallax images are captured in parallel on the same imaging surface.
Japanese Patent Laid-Open No. 7-134345 Japanese Patent Laid-Open No. 8-106067 JP 2003-60947 A Japanese Patent No. 3298905

  However, in an optical system that captures parallel parallax images in parallel, the parallax images that can be captured simultaneously are a pair of parallax images in a specific parallax direction, for example, the horizontal direction, and other vertical directions, diagonal directions, and the like. In order to obtain parallax images in different parallax directions, the right-eye and left-eye mirror optical systems or triangular prisms must be rotated around the optical axis and photographed as separate screens.

  In this case, when the object is fast moving, the relative positions are different, so that it is not possible to simultaneously capture parallax images in a plurality of different parallax directions.

  The present invention has been made in view of such problems of the prior art, and an object of the present invention is to simultaneously capture a plurality of continuous parallax images whose parallax directions are continuously rotated with respect to an object. It is to provide an optical system.

An optical system of the present invention that achieves the above object includes a front group that is rotationally symmetric about a central axis passing through the center of the image plane, a circular aperture that is rotationally symmetric about the central axis and has positive power, and is coaxial with the central axis. And a rear group having
The front group includes one or more optical action surfaces that convert an image of the circular aperture of the rear group into an entrance pupil that is coaxial with the center axis in a cross section including the center axis,
Within the cross section including the central axis, the luminous flux that travels from the object toward the two apertures of the entrance pupil that is symmetric with respect to the central axis and enters the front group passes through the front group and the rear group in order, and enters the image plane. Are imaged separately on the opposite sides with respect to the point through which the central axis passes ,
The front group includes at least one reflecting surface that is rotationally symmetric about a central axis, and at least one of the reflecting surfaces is a double image of a common object within a cross section including the central axis. Of a surface shape that forms an image as a real image or a virtual image of
The front group includes a transparent medium that is rotationally symmetric about a central axis, and the transparent medium has two internal reflection surfaces and two refractive surfaces, and the cross-section including the central axis includes the entrance pupil. The light beam traveling toward the two apertures enters the transparent medium through the refracting surface of the incident surface, is sequentially reflected by the inner reflecting surface, exits from the transparent medium through the refracting surface of the exit surface, and passes through the rear group. After that, the images are separately imaged at opposite positions with respect to the point through which the central axis of the image plane passes.
A light beam that travels from the object toward the two apertures of the entrance pupil and enters the front group forms an intermediate image once in the cross section including the central axis, and is orthogonal to the cross section including the central axis. In the plane containing the central ray of
In the cross section including the central axis, when the optical path length from the entrance pupil position to the circular aperture is A, and the optical path length from the entrance pupil position to the entrance plane in the front group is B,
5 <| A / B | (2)
It satisfies the following conditions .

Further, at least one of the reflection surface or the transmission refracting surface is a rotationally symmetric aspheric surface having a surface apex on the central axis, and the effective diameter of the surface is D and the radius of curvature near the surface apex is R. When
10 <| D / R | (1)
It is desirable to satisfy the following conditions.

Further, when the focal length in the cross section including the central axis of the entire optical system is Fy, the focal length in the plane perpendicular to the cross section and including the central ray is Fx,
−10 <Fy / Fx <0.5 (3)
It is desirable to satisfy the following conditions.

Further, the focal length in the cross section including the central axis of the entire optical system is Fy, the focal length in the plane perpendicular to the cross section including the central ray is Fx, and the cross section including the central axis of the front group is in the cross section. When the focal length is Ffy, orthogonal to the cross section, and the focal length in the plane including the central ray is Ffx,
−1000 <Fx / Ffx <−0.1 (4)
Or
0.1 <Fx / Ffx <1000 (5)
It is desirable to satisfy the following conditions.

Further, the focal length in the cross section including the central axis of the entire optical system is Fy, the focal length in the plane perpendicular to the cross section including the central ray is Fx, and the cross section including the central axis of the front group is in the cross section. When the focal length is Ffy, orthogonal to the cross section, and the focal length in the plane including the central ray is Ffx,
−100 <Fy / Ffy <−0.001 (6)
It is desirable to satisfy the following conditions.

  Further, at least one of the reflection surface or the transmission / refractive surface is a rotationally symmetric shape formed by rotating a line segment having no symmetry surface around a central axis, or an arbitrary number including an odd-order term. It can also be configured to have a rotationally symmetric shape formed by rotating a line segment of the shape around the central axis.

  In the present invention, an optical system capable of simultaneously capturing a plurality of continuous parallax images whose parallax directions are continuously rotated around the central axis in the direction of the object is obtained. It can be used for an optical system of a collision prevention device, an optical system for taking and observing a stereo image, and the like.

Hereinafter, a description will be given of an optical system of the present invention with reference to Examples. Example 4 is a reference example.

  FIG. 1 is a cross-sectional view including a central axis (rotationally symmetric axis) 1 of an optical system 50 of Example 1 to be described later. The optical path takes only an optical path incident on one side with respect to the central axis 1. An optical path symmetrical with respect to 1 also exists at the same time, but is not shown. FIG. 2 is a front view showing the optical path within the entrance pupil 2 of the optical system 50 and the transparent medium 19 of the front group 10. FIG. 3 is a diagram showing an example (a) of an object imaged by the optical system 50 and an image (b) imaged on the image plane 30. The optical system 50 of the present invention will be described with reference to FIGS. Hereinafter, the optical system 50 of the present invention will be described as an imaging system on the image plane 30.

  The optical system 50 of the present invention includes a front group 10 that is rotationally symmetric about the central axis 1 passing through the center of the image plane 30, a rotationally symmetric positive power around the central axis 1, and a circular shape that is coaxial with the central axis 1. A rear group 20 having an aperture (aperture) 21. The front group 10 has an image of the circular aperture 21 of the rear group 20 in the shape of a ring zone coaxial with the central axis 1 and in the vicinity of the entrance surface 11 of the front group. 1 or more optical action surfaces (reflective surfaces, refracting surfaces) 11 to 14 to be converted into the entrance pupil 2 located at the center. Then, in the cross section including the central axis 1, before proceeding toward two openings of the entrance pupil 2 symmetric with respect to the central axis 1 from the object (FIG. 3A) not shown in the left direction in FIG. The light beams incident on the group 10 pass through the front group 10 and the rear group 20 in order, and are formed separately on the opposite sides with respect to the point through which the central axis 1 of the image plane 30 passes. It is.

  Further, in the optical system 50 of the present invention, in the cross section including the central axis 1, the front group 10 shows an image of the circular opening 21 of the rear group 20 in the shape of an annular zone coaxial with the central axis 1 as shown in FIG. 2. Since it is converted into the entrance pupil 2 located in the vicinity of the entrance surface 11 of the front group, the front group 10 has a positive power in the cross section including the central axis 1, and the image of the aperture 21 is obtained by back ray tracing in FIG. In this case, an image is formed in the vicinity of the position 5 in the transparent medium 19 (in the case of FIG. 1, the image of the image at the position 5 by the incident surface 11 becomes the entrance pupil 2). Further, in a plane orthogonal to the plane including the central axis 1, the surfaces 11 to 14 constituting the front group 10 are all concentric with the central axis 1, so that the front group 10 has no power. It becomes an optical system. Therefore, the light beam from the object forms an intermediate image at least once in the cross section including the rotational symmetry axis 1 in FIG. 1 (in the case of FIG. 1, the image is formed once in the vicinity of position 4 in the transparent medium 19). The image is orthogonal to the cross section and does not form an image in a plane including the axial principal ray 3 (FIG. 2).

  1, the front group 10 includes a transparent medium 19 having a rotationally symmetric shape around the central axis 1, and the transparent medium 19 includes at least one inner reflection surface 12, 13 ( In the case of FIG. 1, it has two surfaces) and at least two refracting surfaces 11 and. The transparent medium 19 has a rotationally symmetric shape around the central axis 1, and the refracting surfaces 11 and 14 and the internal reflection surfaces 12 and 13 also have a rotationally symmetric shape around the central axis 1.

  As in the embodiment of FIG. 1, when the front group 10 includes at least one reflecting surface 12, 13 that is rotationally symmetric about the central axis 1, at least one surface 13 of the reflecting surface is centered. In the cross section including the axis 1, it is necessary to take a surface shape that forms an image of a common object as a real or virtual image of a double image.

  Alternatively, when the front group 10 is composed of only a plurality of refractive and transmissive surfaces that are rotationally symmetric about the central axis 1, at least one of the refractive and transmissive surfaces is a common object within the cross section including the central axis 1. It is necessary to take a surface shape that forms a double image as a real image or a virtual image (Example 4).

  When the front group 10 has a reflection surface or a refractive transmission surface that forms such a double image in a cross section including the central axis 1, the image plane passes through two openings of the entrance pupil 2 that is symmetrical with respect to the central axis 1. The images formed separately are images having parallax with each other, which can contribute to imaging of a stereoscopic image, distance measurement, and the like.

  Hereinafter, this point will be described with reference to FIG. FIG. 3 is a diagram showing an example (a) of an object plane imaged by the optical system 50 of FIG. 1 and an image (b) imaged on the image plane 30. When the object plane of FIG. 3A passes through the optical system 50 of the present invention, the center (c) of the object plane is the center O (center of the image plane 30 as shown in FIG. 3B. It is converted into a circle (c) with a constant radius centered on the intersection with the axis 1). Then, the image plane 30 is imaged as an image obtained by deforming the object planes (1) to (12) of FIG. 3A on the outside and inside of the circle (c). (C) in FIG. 3B and positions (1) to (12) inside and outside thereof correspond to positions (1) to (12) on the object plane in FIG. It can be seen that the deformed image of the object plane in (a) is formed on the outside and inside of the circle (c).

  Now, the direction of a straight line d′-d ′ passing through the center (c) of the object plane in FIG. 3A and the direction on the diameter dd passing through the center O of the image plane 30 in FIG. If it is located on the same cross section including the central axis 1, the image of the straight line d'-d 'on the object plane in FIG. 3 (a) has a diameter passing through the center O of the image plane 30 in FIG. 3 (b). A double image is formed as a one-dimensional image on both sides of the center O on the boundary dd ((1)-(9)-(c)-(11 on the straight line d′-d ′ on the object plane) )-(3) is a one-dimensional image of (1)-(9)-(c)-(11)-(3) on the both sides of the center O on the diameter dd of the image plane 30. It is imaged as an image.) A one-dimensional image formed on one side with the center O on the diameter dd on the image plane 30 as a boundary is connected via the entrance pupil 2 on the opposite side on the same cross section including the central axis 1. The one-dimensional image on the other side with respect to the center O is an image formed through the entrance pupil 2 at a position facing the center O, and the two one-dimensional images are the object It is a one-dimensional image having parallax between the openings of the annular entrance pupil 2 in the direction of the straight line d′-d ′ on the surface, that is, the parallax direction d′-d ′. Therefore, in the image plane 30 in FIG. 3B, two one-dimensional images with the center O on all the diameters passing through the center O are images having parallax in the direction of each other, and the diameter d− By searching for coincident points on both sides of the center O on d, the distance to each point on the object plane and the three-dimensional positional relationship can be obtained. Therefore, the optical system 50 of the present invention can be used for a distance measuring optical system, an optical system of a collision prevention device, an optical system for capturing and observing a stereo image, and the like.

  By the way, a rotationally symmetric aspherical surface having a surface apex on the central axis 1 is used as one of the surface shapes that forms an image of a common object in the front group 10 as a real image or a virtual image of a double image. it can. It is also possible to form an arbitrary line shape having no top on the central axis 1 by a rotation free-form surface that can be rotated around the optical axis.

When using a rotationally symmetric aspherical surface having a top on the central axis 1 as a surface shape of a reflective surface or a refractive and transmissive surface that forms an image of a common object as a real or virtual image of a double image, When the effective diameter (diameter centered on the central axis 1) of the surface is D and the radius of curvature near the surface top is R,
10 <| D / R | (1)
It is preferable to satisfy the following conditions.

  If the radius of curvature R is smaller than half of the effective diameter D of the surface, the shape of the area of the surface through which the light beam passing through the entrance pupil 2 passes is determined by higher order terms other than the aspherical spherical term. This makes it easy to form a double image. If the lower limit of 10 is exceeded, the separation angle for separating the light beam into two becomes small, the angle of view for obtaining the separated parallax image is too narrow to be practically used, and the total length of the optical system 50 The diameter of the annular entrance pupil 2 cannot be increased.

More preferably,
100 <| D / R | (1-1)
It is preferable to satisfy the following conditions.

  In the present invention, by arranging the annular entrance pupil 2 in the vicinity of the entrance surface 11 of the front group 10, it becomes possible to reduce the effective diameter of the light beam incident on the optical system 50 through the entrance surface, It is possible to provide an action such as further reflecting the light beam in the remaining space.

  In the optical system 50 of the present invention, in the cross section including the central axis 1, the optical path length from the entrance pupil 2 position to the stop 21 position is A, and the optical path length from the entrance pupil 2 position to the first surface of the front group 10 is Assuming that the value in which the traveling direction of the light beam is positive is B and the ratio thereof is A / B, in Examples 1 to 6 described later, the following is obtained.

Example 1 Example 2 Example 3 Example 4 Example 5 Example 6
A 174.166 82.205 83.367 214.364 176.809 133.536
B 3.136 0.211 0.557 -51.126 0.000 -2.606
｜ A / B ｜ 55.538 389.597 149.588 4.193 2.430 × 10 ¹⁴ 51.248
.

  Here, | A / B | is a value representing the degree to which the entrance pupil 2 is arranged in the vicinity of the entrance surface 11 of the front group 10.

  In the present invention, the iris 21 is projected to the object side only by the cross section including the central axis 1 to form the entrance pupil 2, and the entrance pupil 2 is arranged closer to the entrance surface 11, so that the viewing angle of view is 100. It has succeeded in taking widely over °. Furthermore, by arranging the entrance pupil 2 in the vicinity of the entrance surface 11, it is possible to effectively arrange a flare stop that prevents ghosts and the like.

This makes it possible to reduce the incident surface 11 of the optical system 50 in the cross section including the central axis 1, and to arrange another surface having a reflecting action near the front group 10, particularly in the vicinity of the first surface 11. It is possible to greatly contribute to the development. Furthermore, unnecessary light incident on the first surface 11 can be effectively prevented, and an effect for flare countermeasures is exhibited. Further, since the effective surface is small, the optical system 50 can be configured to be small. here,
5 <| A / B | (2)
It is desirable to satisfy

  If the lower limit of 5 of the condition (1) is exceeded, the entrance pupil 2 is separated from the first surface 11 of the optical system, the effective diameter of the first surface 11 is increased, and a wide angle of view cannot be obtained or harmful flare is caused. Light increases. The larger this value is, the more effectively the flare stop for preventing flare can work.

More preferably,
10 <| A / B | (2-1)
It is preferable to satisfy the following conditions.

  In the optical system 50 of the present invention, it is preferable to arrange a flare stop near the entrance pupil 2. Thereby, the flare light incident on the optical system 50 can be effectively cut.

  Next, when a plane including the rotationally symmetric axis 1 is a YZ plane, orthogonal to the YZ plane, and a plane including the principal ray 3 is an XZ plane, the principal ray 3 in the YZ plane. Dependent rays separated from each other by a minute distance (0.1 mm) are tracked, and the focal point in the cross section including the central axis of the front group 10 is determined from the angle formed by the dependent rays and the principal ray when emitted from the front group 10 or the optical system 50. A distance Ffy, a focal length Ffx in a plane orthogonal to the cross section and including the principal ray 3, and similar focal lengths Fy and Fx of the entire system 50 are set. Regarding Examples 1 to 6 to be described later, values and ratios of these parameters are as follows.

Example 1 Example 2 Example 3 Example 4
Ffx 90.909 74.627 64.516 161.290
Ffy 35.779 3.205 6.592 9.132
Fx -3.333 × 10 ³ -4.545 × 10 ² -384.615 1.000 × 10 ^-4
Fy -1.311 -0.650 -0.804 -4.411
Fy / Fx 3.944 × 10 ^-4 1.447 × 10 ^-3 2.107 × 10 ^-3 -4.412 × 10 ^-4
Fx / Ffx -36.667 -6.091 -5.962 62.000
Fy / Ffy -0.037 -0.203 -0.122 -0.483

Example 5 Example 6
Ffx 119.048 93.458
Ffy 63.271 12.739
Fx -666.667 -102.041
Fy -3.181 -1.184
Fy / Fx 4.774 × 10 ^-3 1.165 × 10 ^-2
Fx / Ffx -5.600 -1.092
Fy / Ffy -0.050 -0.093
.

  The greatest feature of the present invention is that the annular image formed in the cross section including the rotational symmetry axis 1 in the front group 10 is relayed on the image plane 30 in the rear group 20. In order to achieve such a configuration, it is essential to have a focal length of the entire system that is significantly different in each cross-sectional direction. The following conditional expression (3) defines this significantly different focal length.

−10 <Fy / Fx <0.5 (3)
If the lower limit of −10 of the condition (3) is exceeded, the focal length in the Y direction becomes too long compared to the focal length in the X direction, and the angle of view cannot be increased. When the upper limit of 0.5 is exceeded, the focal length in the Y direction becomes too short compared to the focal length in the X direction, and aberration correction in the Y direction, particularly the occurrence of curvature of field and astigmatism increases. At the same time, the difference between the inner diameter and the outer diameter of the annular image becomes small, and the total resolving power cannot be obtained particularly when the resolving power of the image sensor arranged on the image plane 30 is limited.

More preferably,
-2 <Fy / Fx <0.2 (3-1)
It is preferable to satisfy the following conditions.

  Next, the relationship between the focal length of the entire system 50 in the X direction and the Y direction and the focal length of the front group 10 will be defined.

−1000 <Fx / Ffx <−0.1 (4)
Conditional expression (4) represents how much the front group 10 affects the focal length of the entire system 50. If the lower limit of -1000 of the conditional expression (4) is exceeded, it indicates that the focal length of the front group 10 becomes shorter than the focal length of the entire system 50. Then, like the optical system 50 of the present invention, an intermediate image is formed in an optical system that originally does not form an intermediate image in the X direction, and the optical system 50 of the present invention cannot be configured. . If the upper limit of −0.1 of the conditional expression (4) is exceeded, the focal length of the front group 10 becomes too long, and the rear group 20 tries to compensate for that, so the rear group 20 is burdened, and the rear group The aberration generated at 20 increases, and the resolving power of the peripheral image decreases due to curvature of field, astigmatism, lateral chromatic aberration, and the like. As a result, for the entire optical system, the resolution of the outer peripheral portion of the annular image hitting the top or bottom is deteriorated.

Or, instead of the conditional expression (4),
0.1 <Fx / Ffx <1000 (5)
It is preferable to satisfy the following conditional expression: If the lower limit of 0.1 of this conditional expression (5) is exceeded, the focal length of the front group 10 becomes too long and the rear group 20 tries to compensate for that, so the rear group 20 is burdened, and the rear group 20 As a result, the resolving power of peripheral images is reduced due to curvature of field, astigmatism, lateral chromatic aberration, and the like. As a result, for the entire optical system, the resolution of the outer peripheral portion of the annular image hitting the top or bottom is deteriorated. If the upper limit of 1000 of the conditional expression (5) is exceeded, it indicates that the focal length of the front group 10 becomes shorter than the focal length of the entire system 50. Then, like the optical system 50 of the present invention, an intermediate image is formed in an optical system that originally does not form an intermediate image in the X direction, and the optical system 50 of the present invention cannot be configured. .

next,
−100 <Fy / Ffy <−0.001 (6)
It is important to satisfy the following conditional expression. Regarding the Y direction, an image formed in an annular shape in the front group 10 is projected on the image plane 30 in the rear group 20, and therefore has a different sign in principle. If the lower limit of −100 of the conditional expression (6) is exceeded, the focal length of the front group 10 becomes too short, the annular intermediate image formed by the front group 10 becomes smaller, and at the same time, aberrations occurring in the front group 10. It becomes impossible to compensate for this by the rear group 20. If the upper limit of -0.001 of the conditional expression (6) is exceeded, the focal length of the front group 10 becomes too long and the entire apparatus becomes large. In addition, the pupil diameter required for the rear group 20 becomes large, and correction of chromatic aberration, in particular, in the rear group becomes difficult.

  Each of the above conditional expressions is more preferably satisfied simultaneously with conditional expressions (4) and (6) or conditional expressions (5) and (5).

More preferably, regarding conditional expressions (4) to (6),
−100 <Fx / Ffx <−0.5 (4-1)
2 <Fx / Ffx <100 (5-1)
-1 <Fy / Ffy <-0.01 (6-1)
It is preferable to satisfy the following conditions.

  Examples 1 to 6 of the optical system of the present invention will be described below. The configuration parameters of these optical systems will be described later. The configuration parameters of these embodiments are based on the result of tracking the normal ray from the object plane to the image plane 30 through the front group 10 and the rear group 20, as shown in FIG.

  In the forward ray tracing, the coordinate system is the origin of the decentered optical surface of the decentered optical system in the first to fourth embodiments, for example, as shown in FIG. 1, the position where the entrance pupil 2 is projected on the rotational symmetry axis (center axis) 1. The direction along the light traveling direction of the rotationally symmetric axis (center axis) 1 is the Z-axis positive direction, and the inside of FIG. 1 is the YZ plane. Then, the direction opposite to one side of the entrance pupil 2 currently considered in FIG. 1 is the Y axis positive direction, and the Y axis, the Z axis, and the axes constituting the right-handed orthogonal coordinate system are the X axis positive direction. And In Examples 5 to 6, for example, as shown in FIG. 11, the center at which the image plane 30 intersects the rotational symmetry axis (center axis) 1 is the origin, and the traveling direction of light on the rotational symmetry axis (center axis) 1 The direction along the Z-axis positive direction is defined as the YZ plane. Then, the direction opposite to one side of the entrance pupil 2 currently considered in FIG. 11 is the Y axis positive direction, and the Y axis, the Z axis and the axis constituting the right-handed orthogonal coordinate system are the X axis positive direction. And

  For the decentered surface, the amount of decentering from the center of the origin of the optical system in the coordinate system in which the surface is defined (X-axis direction, Y-axis direction, and Z-axis direction are X, Y, and Z, respectively) and the optical system The inclination angles (α, β, γ (°), respectively) of the coordinate system defining each surface centered on the X axis, Y axis, and Z axis of the coordinate system defined at the origin are given. In this case, positive α and β mean counterclockwise rotation with respect to the positive direction of each axis, and positive γ means clockwise rotation with respect to the positive direction of the Z axis. Note that the α, β, and γ rotations of the central axis of the surface are performed by rotating the coordinate system defining each surface counterclockwise around the X axis of the coordinate system defined at the origin of the optical system. Then rotate it around the Y axis of the new rotated coordinate system by β and then rotate it around the Z axis of another rotated new coordinate system by γ. It is.

  Further, among the optical action surfaces constituting the optical system of each embodiment, when a specific surface and a subsequent surface constitute a coaxial optical system, a surface interval is given, in addition, the curvature radius of the surface, The refractive index and Abbe number of the medium are given according to conventional methods.

  It should be noted that a term relating to an aspheric surface for which no data is described in the constituent parameters described later is zero. The refractive index and the Abbe number are shown for the d-line (wavelength 587.56 nm). The unit of length is mm. The eccentricity of each surface is represented by the amount of eccentricity from the position where the entrance pupil 2 is projected onto the rotational symmetry axis (center axis) 1 as described above.

  The aspheric surface is a rotationally symmetric aspheric surface given by the following definition.

^{Z = (Y 2 / R)} / [1+ {1- (1 + k) Y 2 / R 2} 1/2]
+ AY ⁴ + bY ⁶ + cY ⁸ + dY ¹⁰ +...
... (a)
However, Z is an optical axis (axial principal ray) with the light traveling direction being positive, and Y is a direction perpendicular to the optical axis. Here, R is a paraxial radius of curvature, k is a conic constant, a, b, c, d,... Are fourth-order, sixth-order, eighth-order, and tenth-order aspherical coefficients, respectively. The Z axis of this defining formula is the axis of a rotationally symmetric aspherical surface.

  Further, the Y-rotation free-form surface is defined by the following definition formula (b).

R (Y) = C ₁ + C ₂ Y + C ₃ Y ² + C ₄ Y ³ + C ₅ Y ⁴ + C ₆ Y ⁵ + C ₇ Y ⁶
+ ··· + C ₂₁ Y ²⁰ + ··· + C _{n + 1} Y ⁿ + ····
Z = ± R (Y) [1- {X / R (Y)} ² ] ^1/2 (b)
This Y rotation free-form surface is a rotationally symmetric surface formed by rotating the curve R (Y) around the Y axis. As a result, the surface becomes a free-form surface (free-form curve) in the YZ plane and a circle with a radius | C ₁ | in the XZ plane.

  The extended rotation free-form surface is a rotationally symmetric surface given by the following definition.

  First, the following curve (c) passing through the origin on the YZ coordinate plane is determined.

^{Z = (Y 2 / RY)} / [1+ {1- (C 1 +1) Y 2 / RY 2} 1/2]
C ₂ Y + C ₃ Y ² + C ₄ Y ³ + C ₅ Y ⁴ + C ₆ Y ⁵ + C ₇ Y ⁶
+ ··· + C ₂₁ Y ²⁰ + ··· + C _{n + 1} Y ⁿ + ····
... (c)
Next, a curve F (Y) obtained by rotating the curve (c) in the positive direction of the X axis and turning the counterclockwise to the positive angle θ (°) is determined. This curve F (Y) also passes through the origin on the YZ coordinate plane.

  The curve F (Y) is translated in the positive Z direction by a distance R (or negative Z direction if negative), and then the rotationally symmetric surface formed by rotating the translated curve around the Y axis is expanded and rotated. Let it be a free-form surface.

  As a result, the extended rotation free-form surface becomes a free-form surface (free-form curve) in the YZ plane and a circle with a radius | R | in the XZ plane.

  From this definition, the Y-axis becomes the axis of the extended rotation free-form surface (rotation symmetry axis).

Where RY is the radius of curvature of the spherical term in the YZ section, C ₁ is the conic constant, C ₂ , C ₃ , C ₄ , C ₅ . Aspheric coefficient.

  FIG. 1 shows a cross-sectional view including the central axis (rotation symmetry axis) 1 of the optical system 50 of the first embodiment. However, in FIG. 1, only the optical path incident on one side with respect to the central axis 1 is illustrated, and an optical path that is symmetrical with respect to the central axis 1 also exists at the same time, but is not illustrated. A front view showing the optical path in the entrance pupil 2 of the optical system 50 and the transparent medium 19 of the front group 10 is shown in FIG. In addition, the coordinate system taken on the rotational symmetry axis (center axis) 1 is entered in the YZ sectional view of FIG. same as below.

  The optical system 50 of this embodiment converts a one-dimensional object in all directions passing through the center of the common object in front of the front group 10 along the central axis 1 (point (c) in FIG. 3A) to this optical system. As a pair of one-dimensional parallax images in which the diameter of the entrance pupil 2 of the system 50 is the eye width (baseline length), an image is formed at a diagonal position on the diameter in the same direction as the direction of the one-dimensional object on the image plane 30 ( FIG. 3B is an optical system.

  This optical system 50 is rotationally symmetric about the central axis 1 on the incident side of the rear group 20 having a circular aperture (aperture) 21 coaxial with the central axis 1. A front group 10 of a catadioptric optical system made of a transparent medium 19 having a symmetric shape is disposed. The front group 10 has an image of the circular aperture 21 of the rear group 20 in the shape of an annular zone coaxial with the central axis 1. It is configured to convert to the entrance pupil 2 located in the vicinity of the entrance surface 11 of the front group 10.

In this embodiment, the front group 10 is rotationally symmetric about the central axis 1, both of which are an aspherical entrance surface (refractive surface) 11 having an apex on the rotationally symmetric axis (central axis) 1 and an inner surface. The transparent medium 19 includes a reflective surface 12, an internal reflective surface 13, and an exit surface (refractive surface) 14. In this front group 10, at least one surface, preferably a reflecting surface, is composed of an optical surface with D / R> 10, where D is the effective diameter of the optical surface and R is the radius of curvature near the top of the surface. Thus, the entrance pupil 2 which is an image viewed from the front of the front group 10 of the circular aperture stop 21 in the rear group 20 is divided into two left and right entrance pupils in the meridional plane (cross section including the central axis 1). Is possible. In Example 1, the values of D and R of the internal reflection surface 13 are:
D 46.24
R -0.13 × 10 ^-5
｜ D / R ｜ 0.35 × 10 ⁸
In order to form a double image, a light beam incident on both ends in the diagonal direction within the effective diameter of the inner surface reflecting surface 13 by a higher order term other than the aspherical spherical term is separated into two. It can contribute enough.

  The rear group 20 is rotationally symmetric about the central axis 1 and has a positive meniscus lens L1 having a concave surface facing the object side, a circular aperture stop 21, a biconvex positive lens L2, and a biconvex positive lens L3. The positive lens system has a four-group four-lens configuration of a positive meniscus lens L4 having a convex surface facing the object side.

  In the cross section including the central axis 1 in FIG. 1, the light beams from the common object that are not shown in the left direction in the figure are separated toward the two openings of the entrance pupil 2 that is symmetric with respect to the central axis 1. Then, the light enters the transparent medium 19 of the front group 10 from the entrance surface 11 of the front group 10, is reflected twice in turn by the inner surface reflecting surface 12 and the inner surface reflecting surface 13, and passes through the refracting surface 14 of the exit surface. The luminous fluxes separately emitted from 19 are separately imaged on the opposite sides from the point where the central axis 1 of the image plane 30 passes through the rotationally symmetric lens system of the rear group 20.

  In this embodiment, the light beam incident on the entrance pupil 2 forms an intermediate image once at a position 4 between the reflecting surface 12 and the reflecting surface 13 in the sectional view including the rotational symmetry axis 1 in FIG. In the sagittal plane orthogonal to the cross section (FIG. 2), intermediate image formation is not performed until it enters the image plane 30. The image of the stop 21 in the rear group 20 is formed at a position 5 between the refracting surface 11 and the reflecting surface 12 in the front group 10, and the entrance pupil 2 is formed on the refracting surface 11 as a virtual image of the image of the stop 21. ing.

  In this embodiment, the aberration generated in the front group 10 for separating the light beam and the aberration generated in the rear group 20 mainly having an image forming function are mutually corrected, so that the overall condition is good. It is possible to enter an aberration state.

The specification of this Example 1 is
Angle of view 100 °
Entrance pupil diameter 0.41mm x 6.80mm
Diaphragm diameter φ2.00mm
Image size φ1.88 ~ φ6.12mm
It is.

  A view similar to FIG. 1 of the optical system 50 of the second embodiment is shown in FIG. 4, and a view similar to FIG. 2 is shown in FIG. The optical system 50 of this embodiment converts a one-dimensional object in all directions passing through the center of the common object in front of the front group 10 along the central axis 1 (point (c) in FIG. 3A) to this optical system. As a pair of one-dimensional parallax images in which the diameter of the entrance pupil 2 of the system 50 is the eye width (baseline length), an image is formed at a diagonal position on the diameter in the same direction as the direction of the one-dimensional object on the image plane 30 ( FIG. 3B is an optical system.

  This optical system 50 is rotationally symmetric about the central axis 1 on the incident side of the rear group 20 having a circular aperture (aperture) 21 coaxial with the central axis 1. A front group 10 of a catadioptric optical system made of a transparent medium 19 having a symmetric shape is disposed. The front group 10 has an image of the circular aperture 21 of the rear group 20 in the shape of an annular zone coaxial with the central axis 1. It is configured to convert to the entrance pupil 2 located in the vicinity of the entrance surface 11 of the front group 10.

In this embodiment, the front group 10 is rotationally symmetric about the central axis 1, both of which are an aspherical entrance surface (refractive surface) 11 having an apex on the rotationally symmetric axis (central axis) 1 and an inner surface. The transparent medium 19 includes a reflective surface 12, an internal reflective surface 13, and an exit surface (refractive surface) 14. In this front group 10, at least one surface, preferably a reflecting surface, is composed of an optical surface with D / R> 10, where D is the effective diameter of the optical surface and R is the radius of curvature near the top of the surface. Thus, the entrance pupil 2 which is an image viewed from the front of the front group 10 of the circular aperture stop 21 in the rear group 20 is divided into two left and right entrance pupils in the meridional plane (cross section including the central axis 1). Is possible. In Example 2, the values of D and R of the internal reflection surface 13 are:
D 25.76
R -1.12
｜ D / R ｜ 23.00
In order to form a double image, a light beam incident on both ends in the diagonal direction within the effective diameter of the inner surface reflecting surface 13 by a higher order term other than the aspherical spherical term is separated into two. It can contribute enough.

  The rear group 20 includes a circular aperture stop 21 and, in this example, an abstract lens 22 having a rotationally symmetrical lens system and having a positive power.

  Then, in the cross section including the central axis 1 in FIG. 4, the light beams from the common object that are not shown in the left direction in the figure are separated toward the two openings of the entrance pupil 2 that is symmetric with respect to the central axis 1. Then, the light enters the transparent medium 19 of the front group 10 from the entrance surface 11 of the front group 10, is reflected twice in turn by the inner surface reflecting surface 12 and the inner surface reflecting surface 13, and passes through the refracting surface 14 of the exit surface. The luminous fluxes separately emitted from 19 are separately imaged on the opposite side through a point where the central axis 1 of the image plane 30 passes through the rotationally symmetric lens system of the rear group 20.

  In this embodiment, the light beam incident on the entrance pupil 2 forms an intermediate image once at a position 4 between the reflecting surface 12 and the reflecting surface 13 in the cross-sectional view including the rotational symmetry axis 1 in FIG. In the sagittal plane orthogonal to the cross section (FIG. 5), no image is formed until it enters the image plane 30. Then, the image of the diaphragm 21 in the rear group 20 forms an image at a position 5 near the refractive surface 11 in the transparent medium 19 of the front group 10, and the entrance pupil 2 is formed on the refractive surface 11 as a virtual image of the image of the diaphragm 21. ing.

  Even in this embodiment, the aberration generated in the front group 10 for separating the light flux and the aberration generated in the rear group 20 mainly having an image forming function are corrected to each other, so that the overall condition is good. It is possible to enter an aberration state.

The specification of Example 2 is
Angle of view 140 °
Entrance pupil diameter 0.15mm x 4.41mm
Diaphragm diameter 1.20mm
Image size φ1.94 ~ φ5.70mm
It is.

  FIG. 6 shows a diagram similar to FIG. 1 of the optical system 50 of Example 3, and FIG. 7 shows a diagram similar to FIG. The optical system 50 of this embodiment converts a one-dimensional object in all directions passing through the center of the common object in front of the front group 10 along the central axis 1 (point (c) in FIG. 3A) to this optical system. As a pair of one-dimensional parallax images in which the diameter of the entrance pupil 2 of the system 50 is the eye width (baseline length), an image is formed at a diagonal position on the diameter in the same direction as the direction of the one-dimensional object on the image plane 30 ( FIG. 3B is an optical system.

  This optical system 50 is rotationally symmetric about the central axis 1 on the incident side of the rear group 20 having a circular aperture (aperture) 21 coaxial with the central axis 1. A front group 10 of a catadioptric optical system made of a transparent medium 19 having a symmetric shape is disposed. The front group 10 has an image of the circular aperture 21 of the rear group 20 in the shape of an annular zone coaxial with the central axis 1. It is configured to convert to the entrance pupil 2 located in the vicinity of the entrance surface 11 of the front group 10.

  In this embodiment, the front group 10 is rotationally symmetric about the central axis 1, and both the incident surface (refractive surface) 11 made of an aspheric surface having a surface apex on the rotationally symmetric axis (central axis) 1 are rotated. It consists of a transparent medium 19 consisting of an inner reflection surface 12 consisting of a Y-rotation free-form surface having no surface apex on the axis of symmetry (center axis) 1, an inner reflection surface 13, and an exit surface (refractive surface) 14. In this embodiment, these Y-rotation free-form surfaces can sufficiently contribute to the separation of the light beams incident near the opposite ends in the diagonal direction within their effective diameters to form a double image.

  The rear group 20 includes a circular aperture stop 21 and, in this example, an abstract lens 22 having a rotationally symmetrical lens system and having a positive power.

  Then, in the cross section including the central axis 1 in FIG. 6, the light beams from the common object that are not shown in the left direction in the figure are separated toward the two openings of the entrance pupil 2 that is symmetric with respect to the central axis 1. Then, the light enters the transparent medium 19 of the front group 10 from the entrance surface 11 of the front group 10, is reflected twice in turn by the inner surface reflecting surface 12 and the inner surface reflecting surface 13, and passes through the refracting surface 14 of the exit surface. The luminous fluxes separately emitted from 19 are separately imaged on the opposite side through a point where the central axis 1 of the image plane 30 passes through the rotationally symmetric lens system of the rear group 20.

  In this embodiment, the light beam incident on the entrance pupil 2 forms an intermediate image once at a position 4 between the reflecting surface 12 and the reflecting surface 13 in the sectional view including the rotational symmetry axis 1 in FIG. In the sagittal plane orthogonal to the cross section (FIG. 7), no image is formed until it enters the image plane 30. The image of the diaphragm 21 of the rear group 20 is formed at a position 5 near the refractive surface 11 outside the transparent medium 19 of the front group 10, and this position 5 becomes the entrance pupil 2.

  Even in this embodiment, the aberration generated in the front group 10 for separating the light flux and the aberration generated in the rear group 20 mainly having an image forming function are corrected to each other, so that the overall condition is good. It is possible to enter an aberration state.

The specification of this Example 3 is
Angle of view 120 °
Entrance pupil diameter 0.18mm x 4.56mm
Diaphragm diameter 1.20mm
Image size φ2.60 ~ φ5.77mm
It is.

  FIG. 8 shows a cross-sectional view similar to FIG. 1 including the central axis (rotation symmetry axis) 1 of the optical system 50 of the fourth embodiment. FIG. 9 shows an optical path projection diagram on a plane including the central axis (rotation symmetry axis) 1 of the optical system 50 and perpendicular to FIG. FIG. 10 is a front view showing the entrance pupil 2 of the optical system 50 and the optical path in the front group 10.

  The optical system 50 of this embodiment converts a one-dimensional object in all directions passing through the center of the common object in front of the front group 10 along the central axis 1 (point (c) in FIG. 3A) to this optical system. As a pair of one-dimensional parallax images in which the diameter of the entrance pupil 2 of the system 50 is the eye width (baseline length), an image is formed at a diagonal position on the diameter in the same direction as the direction of the one-dimensional object on the image plane 30 ( FIG. 3B is an optical system.

  This optical system 50 is rotationally symmetric about the central axis 1 on the incident side of the rear group 20 having a circular aperture (aperture) 21 coaxial with the central axis 1. A front group 10 of a refractive optical system composed of a plurality of symmetrical aspherical lenses L11 to L16 is arranged, and the front group 10 is coaxial with the central axis 1 for the image of the circular aperture 21 of the rear group 20. It is configured to convert to an entrance pupil 2 that is annular and located in the front group 10.

In this embodiment, the front group 10 is composed of six double-sided aspherical lenses L11 to L16 that are rotationally symmetric about the central axis 1, and all of the aspherical surfaces have a rotationally symmetric non-spherical surface having a top on the central axis 1. It consists of a spherical surface. In this front group 10, when the effective diameter of at least one refractive transmission surface is D and the radius of curvature near the surface top is R, by configuring with an optical surface with D / R> 10, It is possible to divide the entrance pupil 2, which is an image viewed from the front of the front group 10 of the circular aperture stop 21, into two left and right entrance pupils in the meridional plane (cross section including the central axis 1). In Example 4, the values of D and R on the rear surface (surface facing the rear group 20) of the double-sided aspheric lens L16 closest to the rear group 20 are:
D 52.51
R 2.00
｜ D / R ｜ 26.26
The light beam incident near the opposite ends of the aspherical surface within the effective diameter of the aspherical surface by a higher-order term other than the spherical surface of the aspherical surface contributes enough to split into two and form a double image. can do.

  The rear group 20 is rotationally symmetric about the central axis 1 and has a positive meniscus lens L1 having a convex surface facing the object side, a biconvex positive lens L2, a circular aperture stop 21, and a biconvex positive lens L3. The positive lens system has a four-group four-lens configuration of a positive meniscus lens L4 having a convex surface facing the object side.

  Then, in the cross section including the central axis 1 in FIG. 8, the light beams from the common object that are not shown in the left direction in the figure are separated toward the two openings of the entrance pupil 2 that is symmetric with respect to the central axis 1. , And enters the front group 10 through the first lens L11 of the front group 10, is sequentially refracted by the second lens L12 to the sixth lens L16, passes through the rotationally symmetric lens system of the rear group 20, and is centered on the image plane 30. The images are separately formed on the opposite sides with respect to the point through which the axis 1 passes.

  In this embodiment, the light beam incident on the entrance pupil 2 forms an intermediate image once at a position 4 near the rear surface of the fifth lens L5 in the cross-sectional view including the rotational symmetry axis 1 in FIG. In the sagittal plane orthogonal to (FIG. 9), intermediate image formation is not performed until it enters the image plane 30. The image of the diaphragm 21 of the rear group 20 is formed at a position 5 between the second lens L12 and the third lens L13 of the front group 10, and the image of the diaphragm 21 is formed by the first lens L11 and the second lens L12. An entrance pupil 2 is formed as a virtual image.

  In this embodiment, the aberration generated in the front group 10 for separating the light beam and the aberration generated in the rear group 20 mainly having an image forming function are mutually corrected, so that the overall condition is good. It is possible to enter an aberration state.

The specification of this Example 4 is
Angle of view 28 °
Entrance pupil diameter 2.00mm x 18.63mm
Diaphragm diameter φ3.82mm
Image size φ2.14 to φ5.85mm
It is.

  A view similar to FIG. 1 of the optical system 50 of the fifth embodiment is shown in FIG. 11, and a view similar to FIG. 2 is shown in FIG. The optical system 50 of this embodiment converts a one-dimensional object in all directions passing through the center of the common object in front of the front group 10 along the central axis 1 (point (c) in FIG. 3A) to this optical system. As a pair of one-dimensional parallax images in which the diameter of the entrance pupil 2 of the system 50 is the eye width (baseline length), an image is formed at a diagonal position on the diameter in the same direction as the direction of the one-dimensional object on the image plane 30 ( FIG. 3B is an optical system.

  This optical system 50 is rotationally symmetric about the central axis 1 on the incident side of the rear group 20 having a circular aperture (aperture) 21 coaxial with the central axis 1. A front group 10 of a catadioptric optical system made of a transparent medium 19 having a symmetric shape is disposed. The front group 10 has an image of the circular aperture 21 of the rear group 20 in the shape of an annular zone coaxial with the central axis 1. It is configured to convert to the entrance pupil 2 located in the vicinity of the entrance surface 11 of the front group 10.

  In this embodiment, the front group 10 is rotationally symmetric about the central axis 1, all of which are an entrance surface (refractive surface) 11 made of an extended rotation free-form surface, an internal reflection surface 12, an internal reflection surface 13, and an exit surface. It consists of a transparent medium 19 composed of a surface (refractive surface) 14. Note that the conic constant of these extended rotation free-form surfaces is zero. In the front group 10, particularly, the inner reflecting surfaces 12, 13 are incident on the opposite ends in the diagonal direction within the effective diameter of the inner reflecting surfaces 12, 13 due to higher-order terms other than the spherical term of the extended rotation free-form surface. It can contribute enough to separate into two and form a double image.

  The rear group 20 is rotationally symmetric about the central axis 1 and has a positive meniscus lens L1 having a convex surface on the object side, a positive meniscus lens L2 having a convex surface on the object side, a biconcave negative lens L3, and both It consists of a cemented lens of a convex positive lens L4, a circular aperture stop 21 located on the cemented surface of the cemented lens, a biconvex positive lens L5, and a positive lens system of a five-group six-lens configuration including a biconvex positive lens L6. .

  Then, in the cross section including the central axis 1 in FIG. 11, light beams from a common object that is not shown in the left direction of the figure are separated toward two openings of the entrance pupil 2 that is symmetrical with respect to the central axis 1. Then, the light enters the transparent medium 19 of the front group 10 from the entrance surface 11 of the front group 10, is reflected twice in turn by the inner surface reflecting surface 12 and the inner surface reflecting surface 13, and passes through the refracting surface 14 of the exit surface. The luminous fluxes separately emitted from 19 are separately imaged on the opposite side through a point where the central axis 1 of the image plane 30 passes through the rotationally symmetric lens system of the rear group 20.

  In this embodiment, the light beam incident on the entrance pupil 2 forms an intermediate image once at a position 4 between the reflecting surface 12 and the reflecting surface 13 in the sectional view including the rotational symmetry axis 1 in FIG. In the sagittal plane orthogonal to the cross section (FIG. 12), no image is formed until it enters the image plane 30. The image of the stop 21 in the rear group 20 is formed at a position 5 between the refracting surface 11 and the reflecting surface 12 in the transparent medium 19 of the front group 10 and is incident on the refracting surface 11 as a virtual image of the image of the stop 21. A pupil 2 is formed.

  Even in this embodiment, the aberration generated in the front group 10 for separating the light flux and the aberration generated in the rear group 20 mainly having an image forming function are corrected to each other, so that the overall condition is good. It is possible to enter an aberration state.

The specification of this Example 5 is
Angle of view 100 °
Entrance pupil diameter 0.80mm x 9.78mm
Diaphragm diameter 2.93mm
Image size φ1.99 to φ5.99 mm
It is.

  A view similar to FIG. 1 of the optical system 50 of Example 6 is shown in FIG. 13, and a view similar to FIG. 2 is shown in FIG. The optical system 50 of this embodiment converts a one-dimensional object in all directions passing through the center of the common object in front of the front group 10 along the central axis 1 (point (c) in FIG. 3A) to this optical system. As a pair of one-dimensional parallax images in which the diameter of the entrance pupil 2 of the system 50 is the eye width (baseline length), an image is formed at a diagonal position on the diameter in the same direction as the direction of the one-dimensional object on the image plane 30 ( FIG. 3B is an optical system.

  This optical system 50 is rotationally symmetric about the central axis 1 on the incident side of the rear group 20 having a circular aperture (aperture) 21 coaxial with the central axis 1. A front group 10 of a catadioptric optical system made of a transparent medium 19 having a symmetric shape is disposed. The front group 10 has an image of the circular aperture 21 of the rear group 20 in the shape of an annular zone coaxial with the central axis 1. It is configured to convert to the entrance pupil 2 located in the vicinity of the entrance surface 11 of the front group 10.

In this embodiment, the front group 10 is rotationally symmetric about the central axis 1, both of which are an aspherical entrance surface (refractive surface) 11 having an apex on the rotationally symmetric axis (central axis) 1 and an inner surface. The transparent medium 19 includes a reflective surface 12, an internal reflective surface 13, and an exit surface (refractive surface) 14. In this front group 10, at least one surface, preferably a reflecting surface, is composed of an optical surface with D / R> 10, where D is the effective diameter of the optical surface and R is the radius of curvature near the top of the surface. Thus, the entrance pupil 2 which is an image viewed from the front of the front group 10 of the circular aperture stop 21 in the rear group 20 is divided into two left and right entrance pupils in the meridional plane (cross section including the central axis 1). Is possible. In Example 1, the values of D and R of the internal reflection surface 13 are:
D 43.80
R -1.33 × 10 ^-5
｜ D / R ｜ 3.29 × 10 ⁶
In order to form a double image, a light beam incident on both ends in the diagonal direction within the effective diameter of the inner surface reflecting surface 13 by a higher order term other than the aspherical spherical term is separated into two. It can contribute enough.

  The rear group 20 is rotationally symmetric about the central axis 1 and has a positive meniscus lens L1 having a convex surface facing the object side, a negative meniscus lens L2 having a concave surface facing the object side, and a convex surface facing the object side. A positive meniscus lens L3, a circular aperture stop 21, a cemented lens of a negative meniscus lens L4 and a biconvex positive lens L5 having a convex surface facing the object side, a positive meniscus lens L6 having a convex surface facing the object side, and a biconvex lens The positive lens system is composed of a positive lens system composed of 7 elements in 6 groups.

  Then, in the cross section including the central axis 1 in FIG. 13, light beams from a common object that is not shown in the left direction in the figure are separated toward two openings of the entrance pupil 2 that is symmetric with respect to the central axis 1. Then, the light enters the transparent medium 19 of the front group 10 from the entrance surface 11 of the front group 10, is reflected twice in turn by the inner surface reflecting surface 12 and the inner surface reflecting surface 13, and passes through the refracting surface 14 of the exit surface. The luminous fluxes separately emitted from 19 are separately imaged on the opposite side through a point where the central axis 1 of the image plane 30 passes through the rotationally symmetric lens system of the rear group 20.

  In this embodiment, the light beam incident on the entrance pupil 2 forms an intermediate image once at a position 4 between the reflecting surface 12 and the reflecting surface 13 in the sectional view including the rotational symmetry axis 1 in FIG. In the sagittal plane orthogonal to the cross section (FIG. 14), no image is formed until it enters the image plane 30. The image of the stop 21 in the rear group 20 is formed at a position 5 between the refracting surface 11 and the reflecting surface 12 in the transparent medium 19 of the front group 10 and is incident on the refracting surface 11 as a virtual image of the image of the stop 21. A pupil 2 is formed.

  Even in this embodiment, the aberration generated in the front group 10 for separating the light flux and the aberration generated in the rear group 20 mainly having an image forming function are corrected to each other, so that the overall condition is good. It is possible to enter an aberration state.

The specification of Example 6 is
Angle of view 100 °
Entrance pupil diameter 0.80mm x 9.45mm
Diaphragm diameter 2.70mm
Image size φ2.05-φ5.99mm
It is.

  The configuration parameters of Examples 1 to 6 are shown below. In the table below, “ASS” indicates an aspherical surface, “YRFS” indicates a Y rotation free-form surface, and “ERFS” indicates an extended rotation free-form surface. “IDL” indicates an ideal lens. “RE” indicates a reflective surface.

Example 1
Surface number Curvature radius Surface spacing Eccentricity Refractive index Abbe number Object surface ∞ ∞
1 ∞ (entrance pupil) -6.65 Eccentricity (1)
2 ASS [1] 17.52 1.8830 40.7
3 ASS [2] (RE) -10.56 1.8830 40.7
4 ASS [3] (RE) 5.26 1.8830 40.7
5 ASS [4] 16.48
6 -161.04 20.00 1.7620 40.1
7 -33.05 32.48
8 ∞ (Aperture) 0.10
9 12.16 5.62 1.4970 81.5
10 -29.28 0.10
11 9.91 5.01 1.6204 60.3
12 -39.58 0.10
13 8.32 2.15 1.7859 44.2
14 37.54 2.00
Image plane ∞
ASS [1]
R 0.00
k -6.3047 × 10 ⁺²⁷
a 7.7540 × 10 ^-6
b 1.7502 × 10 ^-9
c -1.1235 × 10 ^-11
d 5.6493 × 10 ^-15
ASS [2]
R 0.00
k -2.3809 × 10 ⁺¹
a -8.4686 × 10 ^-6
b 1.7120 × 10 ^-9
c 1.7760 × 10 ^-12
d -9.4138 × 10 ^-16
ASS [3]
R 0.00
k -1.3000 × 10 ⁺¹
a 5.8645 × 10 ^-6
b 2.2749 × 10 ^-9
c -1.3811 × 10 ^-11
d 1.2551 × 10 ^-14
ASS [4]
R 0.00
k -1.0263 × 10 ⁺¹
a 1.2129 × 10 ^-5
b 1.9876 × 10 ^-8
c 4.4798 × 10 ^-11
d -1.6528 × 10 ^-13
Eccentricity (1)
X 0.00 Y -30.00 Z 0.00
α 0.00 β 0.00 γ 0.00.

Example 2
Surface number Curvature radius Surface spacing Eccentricity Refractive index Abbe number Object surface ∞ ∞
1 ∞ (entrance pupil) -0.71 Eccentricity (1)
2 ASS [1] 18.43 1.8830 40.8
3 ASS [2] (RE) -4.11 1.8830 40.8
4 ASS [3] (RE) -1.07 1.8830 40.8
5 ASS [4] 10.87
6 ∞ (Aperture) 3.50
7 IDL 4.47
Image plane ∞
ASS [1]
R 0.68
k -2.4501 × 10 ⁺¹⁹
a 1.6632 × 10 ^-6
b -8.2041 × 10 ^-10
ASS [2]
R -110.41
k 7.8658
a -1.0026 × 10 ^-5
b 1.0431 × 10 ^-8
c -4.1325 × 10 ^-12
ASS [3]
R -1.12
k -2.0004
a 2.0366 × 10 ^-4
b -1.1329 × 10 ^-6
c 2.2020 × 10 ^-9
ASS [4]
R -7.44
k -1.1687
a 2.0636 × 10 ^-3
b -2.3025 × 10 ^-5
c 9.2967 × 10 ^-8
Eccentricity (1)
X 0.00 Y -33.20 Z 0.00
α 0.00 β 0.00 γ 0.00.

Example 3
Surface number Curvature radius Surface spacing Eccentricity Refractive index Abbe number Object surface ∞ ∞
1 ∞ (entrance pupil) Eccentricity (1)
2 ASS [1] Eccentricity (2) 1.8830 40.7
3 YRFS [1] (RE) Eccentricity (3) 1.8830 40.7
4 YRFS [2] (RE) Eccentricity (4) 1.8830 40.7
5 YRFS [3] Eccentricity (5)
6 ∞ (aperture) 3.50 Eccentricity (6)
7 IDL 4.12
Image plane ∞
YRFS [1]
C ₁ 3.5286 × 10 ⁺¹ C ₂ -1.0315 C ₃ -9.6674 × 10 ^-2
C ₄ -2.3210 × 10 ^-3 C ₅ -4.0592 × 10 ^-6
YRFS [2]
C ₁ 1.3506 × 10 ⁺¹ C ₂ -1.6876 C ₃ 4.9906 × 10 ^-2
C ₄ -1.4575 × 10 ^-3 C ₅ -4.2825 × 10 ^-4
YRFS [3]
C ₁ -1.0687 × 10 ⁺¹ C ₂ 2.3460 C ₃ 2.0089 × 10 ^-1
C ₄ 1.6813 × 10 ^-1
ASS [1]
R 66.06
k -1.0364 × 10 ⁺¹
a 9.2919 × 10 ^-6
b -5.9493 × 10 ^-9
Eccentricity (1)
X 0.00 Y -35.23 Z 0.00
α 0.00 β 0.00 γ 0.00
Eccentric (2)
X 0.00 Y 0.00 Z -8.83
α 0.00 β 0.00 γ 0.00
Eccentricity (3)
X 0.00 Y 0.00 Z 4.28
α -90.00 β 0.00 γ 0.00
Eccentricity (4)
X 0.00 Y 0.00 Z 3.27
α -90.00 β 0.00 γ 0.00
Eccentricity (5)
X 0.00 Y 0.00 Z 9.04
α 90.00 β 0.00 γ 0.00
Eccentricity (6)
X 0.00 Y 0.00 Z 28.76
α 0.00 β 0.00 γ 0.00.

Example 4
Surface number Curvature radius Surface spacing Eccentricity Refractive index Abbe number Object surface ∞ ∞
1 ∞ (entrance pupil) -56.27 Eccentricity (1)
2 ASS [1] 6.09 1.8830 40.7
3 ASS [2] -0.33
4 ASS [3] 13.07 1.8830 40.7
5 ASS [4] 63.32
6 ASS [5] 4.68 1.8830 40.7
7 ASS [6] 24.60
8 ASS [7] 6.22 1.8830 40.7
9 ASS [8] 6.04
10 ASS [9] 17.32 1.8830 40.7
11 ASS [10] 15.83
12 ASS [11] 8.15 1.8830 40.7
13 ASS [12] 37.20
14 29.79 1.23 1.7495 35.3
15 6.28 2.36
16 9.39 7.20 1.4970 81.5
17 -10.59 0.10
18 ∞ (Aperture) 0.00
19 13.45 11.39 1.6204 60.3
20 -17.40 0.10
21 6.23 2.00 1.7859 44.2
22 100.92 2.00
Image plane ∞
ASS [1]
R 70.26
k 1.0315
a -2.4623 × 10 ^-6
ASS [2]
R 88.71
k -1.2825 × 10 ¹⁰
a 1.8607 × 10 ^-6
ASS [3]
R 43.04
k 3.6119 × 10 ^-1
a 1.4073 × 10 ^-5
ASS [4]
R 26.22
k -2.3136 × 10 ^-1
a 3.5115 × 10 ^-5
ASS [5]
R -35.59
k 0.0000
a 1.2914 × 10 ^-5
ASS [6]
R 3898.10
k 0.0000
a -3.0244 × 10 ^-6
ASS [7]
R 95.34
k 0.0000
a 1.3144 × 10 ^-5
ASS [8]
R 45.61
k 0.0000
a 1.5361 × 10 ^-5
ASS [9]
R 37.36
k 0.0000
a 6.1272 × 10 ^-6
ASS [10]
R 69.65
k 0.0000
a 2.6211 × 10 ^-5
ASS [11]
R -111.97
k 0.0000
a 3.6489 × 10 ^-5
ASS [12]
R 2.00
k -2.8996 × 10 ⁴
a 1.5060 × 10 ^-5
Eccentricity (1)
X 0.00 Y -30.00 Z 0.00
α 0.00 β 0.00 γ 0.00

Example 5
Surface number Curvature radius Surface spacing Eccentricity Refractive index Abbe number Object surface ∞ ∞
1 ∞ (entrance pupil plane) Eccentricity (1)
3 ERFS [1] Eccentricity (2) 1.8348 42.7
4 ERFS [2] (RE) Eccentricity (3) 1.8348 42.7
5 ERFS [3] (RE) Eccentricity (4) 1.8348 42.7
6 ERFS [4] Eccentricity (5)
8 10.16 Eccentricity (6) 1.6816 44.0
9 17.38 Eccentricity (7)
10 6.49 Eccentricity (8) 1.6796 51.1
11 47.91 Eccentricity (9)
12 -17.21 Eccentricity (10) 1.7528 30.1
13 2.27 (Aperture) Eccentricity (11) 1.6761 47.7
14 -65.08 Eccentric (12)
15 8.85 Eccentricity (13) 1.5423 48.8
16 -161.93 Eccentricity (14)
17 5.61 Eccentricity (15) 1.4920 67.7
18 -10.28 Eccentricity (16)
Image plane ∞
ERFS [1]
RY ∞
θ 8.63
R -30.00
C ₃ 1.4564 × 10 ^-2
C ₄ 5.1891 × 10 ^-4
ERFS [2]
RY ∞
θ -22.63
R -29.08
C ₃ -2.3468 × 10 ^-2
C ₄ 5.0000 × 10 ^-4
C ₅ -2.0000 × 10 ^-5
ERFS [3]
RY ∞
θ -15.80
R -15.47
C ₃ 1.1196 × 10 ^-3
C ₄ -1.8330 × 10 ^-4
C ₅ 1.6660 × 10 ^-5
ERFS [4]
RY ∞
θ 8.01
R -16.59
C ₃ -2.4780 × 10 ^-2
C ₄ -7.1046 × 10 ^-5
Eccentricity (1)
X 0.00 Y -30.00 Z -63.44
α 0.00 β 0.00 γ 0.00
Eccentric (2)
X 0.00 Y 0.00 Z -66.78
α 90.00 β 0.00 γ 0.00
Eccentricity (3)
X 0.00 Y 0.00 Z -53.48
α 90.00 β 0.00 γ 0.00
Eccentricity (4)
X 0.00 Y 0.00 Z -65.23
α 90.00 β 0.00 γ 0.00
Eccentricity (5)
X 0.00 Y 0.00 Z -52.33
α 90.00 β 0.00 γ 0.00
Eccentricity (6)
X 0.00 Y 0.00 Z -15.43
α 0.00 β 0.00 γ 0.00
Eccentricity (7)
X 0.00 Y 0.00 Z -13.41
α 0.00 β 0.00 γ 0.00
Eccentricity (8)
X 0.00 Y 0.00 Z -13.29
α 0.00 β 0.00 γ 0.00
Eccentric (9)
X 0.00 Y 0.00 Z -11.21
α 0.00 β 0.00 γ 0.00
Eccentric (10)
X 0.00 Y 0.00 Z -10.30
α 0.00 β 0.00 γ 0.00
Eccentric (11)
X 0.00 Y 0.00 Z -7.76
α 0.00 β 0.00 γ 0.00
Eccentric (12)
X 0.00 Y 0.00 Z -5.96
α 0.00 β 0.00 γ 0.00
Eccentric (13)
X 0.00 Y 0.00 Z -5.86
α 0.00 β 0.00 γ 0.00
Eccentric (14)
X 0.00 Y 0.00 Z -4.00
α 0.00 β 0.00 γ 0.00
Eccentric (15)
X 0.00 Y 0.00 Z -3.90
α 0.00 β 0.00 γ 0.00
Eccentric (16)
X 0.00 Y 0.00 Z -2.00
α 0.00 β 0.00 γ 0.00.

Example 6
Surface number Curvature radius Surface spacing Eccentricity Refractive index Abbe number Object surface ∞ ∞
1 ∞ (entrance pupil) Eccentricity (1)
2 ASS [1] Eccentricity (2) 1.8348 42.7
3 ASS [2] (RE) Eccentricity (3) 1.8348 42.7
4 ASS [3] (RE) Eccentricity (4) 1.8348 42.7
5 ASS [4] 33.12 Eccentricity (5)
6 6.72 1.36 1.6204 60.3
7 199.30 0.51
8 -9.52 0.55 1.7477 37.0
9 -27.46 0.10
10 6.08 2.37 1.7440 44.8
11 7.60 0.16
12 ∞ (Aperture) 0.00
13 98.44 (Aperture) 0.55 1.7552 27.6
14 2.99 1.09 1.5512 46.7
15 -9.29 0.10
16 6.36 1.66 1.7440 44.8
17 12.29 0.10
18 5.26 1.86 1.4877 70.4
19 -15.05 2.00
Image plane ∞
ASS [1]
R 0.00
k -6.3047 × 10 ²⁷
a 4.5316 × 10 ^-6
b 1.7275 × 10 ^-9
c -8.1518 × 10 ^-12
d 4.1919 × 10 ^-15
ASS [2]
R 0.00
k -2.3809 × 10
a -8.9084 × 10 ^-6
b 9.9615 × 10 ^-10
c 3.0546 × 10 ^-12
d -1.7171 × 10 ^-15
ASS [3]
R -0.00
k -1.3000 × 10 ¹
a 9.1379 × 10 ^-7
b 8.0294 × 10 ^-9
c -2.5281 × 10 ^-11
d 2.1044 × 10 ^-14
ASS [4]
R 0.00
k -1.0263 × 10 ¹
a -3.2922 × 10 ^-5
b 2.0084 × 10 ^-8
c 7.7715 × 10 ^-12
d -1.5578 × 10 ^-14
Eccentricity (1)
X 0.00 Y -30.00 Z 0.00
α 0.00 β 0.00 γ 0.00
Eccentric (2)
X 0.00 Y 0.00 Z -4.66
α 0.00 β 0.00 γ 0.00
Eccentricity (3)
X 0.00 Y 0.00 Z 11.81
α 0.00 β 0.00 γ 0.00
Eccentricity (4)
X 0.00 Y 0.00 Z 2.83
α 0.00 β 0.00 γ 0.00
Eccentricity (5)
X 0.00 Y 0.00 Z 11.64
α 0.00 β 0.00 γ 0.00.

  As described above, the optical system of the present invention is capable of simultaneously imaging a plurality of continuous parallax images whose parallax directions are continuously rotated with respect to the object with the central axis (rotation symmetry axis) directed toward the object. Although described as a system, the present invention is not limited to a photographing optical system and an observation optical system, but can be used as a projection optical system that projects an image with the optical path reversed.

It is sectional drawing containing the central axis of the optical system of Example 1 of this invention. FIG. 6 is a front view showing an entrance pupil of the optical system of Example 1 and an optical path in a front group of transparent media. It is a figure which shows the example (a) of the object imaged with the optical system of Example 1, and the image (b) imaged on an image surface. It is sectional drawing containing the central axis of the optical system of Example 2 of this invention. FIG. 6 is a front view showing an entrance pupil of the optical system of Example 2 and an optical path in a front group of transparent media. It is sectional drawing containing the central axis of the optical system of Example 3 of this invention. FIG. 10 is a front view showing an entrance pupil of an optical system of Example 3 and an optical path in a front group of transparent media. It is sectional drawing similar to FIG. 1 containing the central axis of the optical system of Example 4 of this invention. FIG. 10 is an optical path projection view onto a plane that includes the central axis of the optical system of Example 4 and is perpendicular to FIG. 8. FIG. 10 is a front view showing an entrance pupil of the optical system of Example 4 and an optical path in the front group. It is sectional drawing containing the central axis of the optical system of Example 5 of this invention. FIG. 10 is a front view showing an entrance pupil of an optical system of Example 5 and an optical path in a front group of transparent media. It is sectional drawing containing the central axis of the optical system of Example 6 of this invention. FIG. 10 is a front view showing an entrance pupil of an optical system of Example 6 and an optical path in a front group of transparent media.

Explanation of symbols

1 ... Center axis (axis of rotational symmetry)
2 ... Entrance pupil 3 ... Axial principal ray 4 ... Object intermediate imaging position 5 ... Image position of aperture 10 ... Front group 11 ... Incident surface (refractive surface)
12, 13 ... Internal reflecting surface 14 ... Ejection surface (refractive surface)
19 ... Transparent medium 20 ... Front group 21 ... Circular aperture (aperture)
22 ... Ideal lens 30 ... Image plane 50 ... Optical system (present invention)
L1-L7: Lenses constituting the rear group L11-L16: Aspherical lenses constituting the front group

Claims (7)

A front group that is rotationally symmetric about the central axis passing through the center of the image plane, and a rear group that is rotationally symmetric about the central axis and has a positive power, and has a circular aperture coaxial with the central axis,
The front group includes one or more optical action surfaces that convert an image of the circular aperture of the rear group into an entrance pupil that is coaxial with the center axis in a cross section including the center axis,
Within the cross section including the central axis, the luminous flux that travels from the object toward the two apertures of the entrance pupil that is symmetric with respect to the central axis and enters the front group passes through the front group and the rear group in order, and enters the image plane. Are imaged separately on the opposite sides with respect to the point through which the central axis passes ,
The front group includes at least one reflecting surface that is rotationally symmetric about a central axis, and at least one of the reflecting surfaces is a double image of a common object within a cross section including the central axis. Of a surface shape that forms an image as a real image or a virtual image of
The front group includes a transparent medium that is rotationally symmetric about a central axis, and the transparent medium has two internal reflection surfaces and two refractive surfaces, and the cross-section including the central axis includes the entrance pupil. The light beam traveling toward the two apertures enters the transparent medium through the refracting surface of the incident surface, is sequentially reflected by the inner reflecting surface, exits from the transparent medium through the refracting surface of the exit surface, and passes through the rear group. After that, the images are separately imaged at opposite positions with respect to the point through which the central axis of the image plane passes.
A light beam that travels from the object toward the two apertures of the entrance pupil and enters the front group forms an intermediate image once in the cross section including the central axis, and is orthogonal to the cross section including the central axis. In the plane containing the central ray of
In the cross section including the central axis, when the optical path length from the entrance pupil position to the circular aperture is A, and the optical path length from the entrance pupil position to the entrance plane in the front group is B,
5 <| A / B | (2)
An optical system characterized by satisfying the following conditions . At least one of the reflecting surface or the transmission / refracting surface is a rotationally symmetric aspheric surface having a surface apex on the central axis, and when the effective diameter of the surface is D and the radius of curvature near the surface apex is R,
10 <| D / R | (1)
Optical system according to claim 1, characterized by satisfying the following condition. When the focal length in the cross section including the central axis of the entire optical system is Fy, the focal length in the plane perpendicular to the cross section and including the central ray is Fx,
−10 <Fy / Fx <0.5 (3)
Satisfy the condition according to claim 1 or 2 optical system wherein the. The focal length in the cross section including the central axis of the entire optical system is Fy, the focal length in the plane orthogonal to the cross section and including the central ray is Fx, and the focal length in the cross section including the central axis of the front group Is Ffy, orthogonal to the cross section, and the focal length in the plane including the central ray is Ffx,
−1000 <Fx / Ffx <−0.1 (4)
Or
0.1 <Fx / Ffx <1000 (5)
Optical system of any one of claims 1, wherein the condition is satisfied for 3. The focal length in the cross section including the central axis of the entire optical system is Fy, the focal length in the plane orthogonal to the cross section and including the central ray is Fx, and the focal length in the cross section including the central axis of the front group Is Ffy, orthogonal to the cross section, and the focal length in the plane including the central ray is Ffx,
−100 <Fy / Ffy <−0.001 (6)
Satisfy conditions optics according to any one of claims 1 to 4, wherein the. The at least one surface of the reflection surface or the transmission refracting surface has a rotationally symmetric shape formed by rotating an arbitrary-shaped line segment having no symmetry surface around a central axis. 6. The optical system according to any one of items 1 to 5 . The at least one surface of the reflection surface or the transmission refracting surface has a rotationally symmetric shape formed by rotating an arbitrary-shaped line segment including an odd-order term around a central axis. The optical system according to any one of 6 .

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