Optical system

A curved surface image-conversion optical system is configured to take an image of a hemispherically curved object or project it as a curved surface image, which optical system includes a front unit formed of a transparent medium rotationally symmetric about a center axis and having at least two internal reflecting surfaces and two transmitting surfaces, a rear unit that is rotationally symmetric about the center axis and has positive power, and an aperture located coaxially with the center axis. The front unit includes the first transmitting surface through which a light beam from an object point is incident on the front unit, the first reflecting surface for reflecting the transmitted light beam, the second reflecting surface for reflecting the reflected light beam and the second transmitting surface through which the reflected light leaves the transparent medium.

RELATED APPLICATIONS

This application claims the benefit of Japanese Application No. 2005-153760 filed in Japan on May 26, 2005, the contents of which are incorporated herein by reference in their entirety.

BACKGROUND OF THE INVENTION

The present invention relates generally to an optical system, and more particularly an objective optical system well fit for all sky cameras or the like adapted to form hemispherical object images on a zonal-form flat image plane and a projection optical system suitable for use with panoramic projectors or the like adapted to project zonal images located on an image plane onto a hemispherically curved surface.

In methods heretofore, when projecting images projected onto a domed screen, a plurality of images projected independently through a plurality of projectors have been put together or projected through a wide-angle optical system such as a fisheye lens.

For instance, Japanese Patent Application Publication No. 2001174713 shows an objective optical system for endoscope applications, in which the first reflecting surface that is rotationally symmetric about the center axis and includes an annular convex surface, and the second reflecting surface including a convex surface, are located in front of an image-formation lens to form a hemispherically curved object on a plane. However, there is nothing specific set forth about the optical system whatsoever.

Further, Japanese Patent Application Publication No. 2004287435 shows that a beam splitter, a concave mirror and a ball lens array are combined together to convert a flat image into a curved image.

SUMMARY OF THE INVENTION

In view of the state of the prior art as described above, the present invention has for its object the provision of a curved surface image-conversion optical system well fit for all sky cameras, panoramic projectors or the like, which is capable of taking hemispherically curved object images or projecting them as hemispherically curved images with simplified construction, and which is of small format size and improved resolving power with well-corrected aberrations.

According to the invention, this object is achieved by the provision of an image formation system adapted to form a hemispherical image on an image plane, or a projection system adapted to project a planar image onto a spherical image surface, which includes a front unit formed of a transparent medium rotationally symmetric about a center axis and including at least two internal reflecting surfaces and two transmitting surfaces, a rear unit that is rotationally symmetric about the center axis and has positive power, and an aperture located coaxially with the center axis. In an order of travel of light rays in the case of the image formation system, or in reverse order of travel of light rays in the case of the projection system, said front unit includes a first transmitting surface through which a light beam from an object point is incident on said front unit, a first reflecting surface for reflecting a light beam after transmission through said first transmitting surface, a second reflecting surface for reflecting a light beam after reflection at said first reflecting surface and a second transmitting surface through which a light beam after reflection at said second reflecting surface leaves said transparent medium. A light beam coming from an object travels through said front unit and said rear unit in this order, forming an annular plane image at a position of the image plane off the center axis.

In this case, it is desired that, in a meridional section, two entrance pupils are symmetrically located with the center axis between them.

In one preferable embodiment of the invention, at least one reflecting surface is of rotationally symmetric shape defined by rotation about the center axis of a line segment of any arbitrary shape having no symmetric plane.

In one preferable embodiment of the invention, at least one reflecting surface is of rotationally symmetric shape defined by rotation about the center axis of a line segment of any arbitrary shape including an odd-number degree term.

In one preferable embodiment of the invention, an entrance pupil in the meridional section and an entrance pupil in a sagittal section differ in position.

In a specific embodiment of the invention, an entrance pupil in the meridional section lies near the first transmitting surface in the optical system, and an entrance pupil in the sagittal section lies near the center axis.

In a preferable embodiment of the invention, the number of stop images formed upon projection of said aperture in an opposite direction to a direction of incidence of said light beam is the same, or differs by one, in the meridional section and the sagittal section.

In an embodiment of the invention, it is preferable that, in the meridional section and near an entrance pupil formed by said front unit on an object side, there is a one-way flare stop located for limiting said aperture in said meridional section alone.

In one embodiment of the invention, it is preferable to satisfy the following condition (1) in the meridional section:
−60°<θ1<−20°  (1)
where θ1is the angle of a tangential plane with respect to the center axis at a position of said first transmitting surface, on which the center ray of a center light beam from the center of an angle of view is incident.

In an embodiment of the invention, it is preferable to satisfy the following condition (2):
1.2<H1/H2(2)
where H1is the height of said front unit from the top end to the bottom end perpendicularly to the image plane, and H2is the height from the top end of said front unit to a position of said first transmitting surface, on which the center ray of a center beam from the center of an angle of view is incident.

In an embodiment of the invention, it is preferable to satisfy the following condition (3):
5<|A/B|(3)
where A is an optical path length of a entrance pupil position in a meridional section to a position of said aperture, and B is an optical path length from an entrance pupil position in the meridional section to said first transmitting surface of said front unit.

According to the invention as described above, it is possible to obtain a curved surface-conversion optical system which is capable of taking or projecting hemispherically curved object images with simplified construction, and which is of small format size and improved resolving power with well-corrected aberrations.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The optical system of the invention is now explained with reference to its embodiments.

FIG. 1is a sectional view of the optical system of Example 1 to be described later, as taken along its center axis (rotationally symmetric axis)1, andFIG. 2is a plan view of an optical path through that optical system. With reference toFIGS. 1 and 2, the optical system of the invention is explained. While that optical system will be explained as an image-formation optical system adapted to form an image of a hemispherically curved object, it could be used as a projection optical system adapted to project a hemispherically curved image if the optical path is reversed. InFIG. 2, note that there are an optical path taken by light incident from a direction at an azimuth of 0° and an optical path taken by light incident from a direction at an azimuth of ±14°.

The optical path of the invention includes a front unit10and a rear unit20, each rotationally symmetric about a center axis1. A light beam2coming from a hemispherically curved object100passes through the front unit10and rear unit20in this order, forming an image30A at a position of an image plane30vertical to, and off, the center axis1.

The front unit10includes a resin or other transparent medium that is rotationally symmetric about the center axis1and has a refractive index greater than 1, and has two internal reflecting surfaces12,13and two transmitting (entrance and exit) surfaces11,14. The internal reflecting surfaces12,13and the transmitting surfaces11,14, too, are each of rotationally symmetric shape about the center axis1. The rear unit20includes a coaxial dioptric system such as a lens system, which is rotationally symmetric about the center axis1and has positive power.

The transparent medium of the front unit10is made up of a first transmitting surface11, a first reflecting surface12, a second reflecting surface13and a second transmitting surface14. The first transmitting surface11is located on a side that receives the light beam2from the curved object100with respect to the center axis1. The first reflecting surface12is located in opposition to the first transmitting surface11with the center axis1between them and positioned nearer to the image plane30than to the first transmitting surface11. The second reflecting surface13is located on the same side as the first transmitting surface11with respect to the center axis1and positioned on a side that faces away from the image plane30with respect to the first reflecting surface12. The second transmitting surface14is located on the same side as the first transmitting surface11and positioned on a side that is nearer to the image plane30than to the first reflecting surface12.

The light beam2coming from the curved object100enters the transparent medium via the first transmitting surface11, and arrives at the first reflecting surface12located in opposition to the first transmitting surface11with the center axis1between them, at which it is reflected away from the image plane30. Then, the reflected light travels to the second reflecting surface13located on the same side as the first transmitting surface11with respect to the center axis1, at which it is reflected toward the image plane30side, leaving the transparent medium via the second transmitting surface14. Finally, the light beam passes through a round aperture5that is located coaxially with the center axis1between the front unit10and the rear unit20to form a stop and the rear unit20having positive power, forming an image30A at a radially given position of the image plane30off the center axis1.

The role of the front unit10is to convert the light beam2from the hemispherically curved object100toward the center of the hemisphere into an annular aerial image30A perpendicular to the rotationally symmetric axis1.

It is then required that the surfaces11-14of the front unit10be positioned in such a way as not to interfere with the optical path, and so they be each located with a decentration to obliquely reflect or refract light rays. However, a decentered arrangement generally causes huge decentration aberrations, resulting in poor resolving power or a failure in getting hold of any large angle of view. In the invention, therefore, a rotationally symmetric surface shape formed by rotation about the center axis1of a line segment of any arbitrary shape having an odd-number degree term and having no symmetric surface is used, thereby successfully reducing decentration aberrations to obtain a plane image with high resolving power.

By making the front unit10of the transparent medium, productivity is improved, and by use of the back-surface reflecting surfaces12and13, the aberrations produced can be much better corrected as well.

The role of the rear unit20is to project an annular aerial image30A onto the image plane30. Regarding the annular aerial image30A converted at the front unit10, there is often field curvature with its concave surface lying in the direction of travel of light rays. The rear unit20here has another role of making up for field curvature and astigmatism that remain undercorrected at the front unit10.

Here let the meridional section be defined as a section including the center axis (rotationally symmetric axis)1of the optical system and the center ray (chief ray)20of the center light beam2from the center of an angle of view, and the sagittal section as a section that is orthogonal to that meridional section and includes the center ray (chief ray)20. To obtain an annular plane image, the optical system of the invention is then allowed to have two entrance pupils6Y in that meridional section, with the center axis between them.

An optical system in common use has only one entrance pupil with a stop defined by an aperture located on its rotationally symmetric axis (optical axis). For that reason, with the angle of view growing large, a light beam having a wider angle of view must be incident on the entrance pupil; that is, it is necessary to rely on a lens arrangement such as a so-called fisheye lens arrangement having a concave lens having strong negative power on the object side. However, there is then a problem that the strong negative concave lens incurs image distortion that may otherwise cause surrounding images to become small.

This problem is of much importance for an optical system like the inventive one, for which it is desired that substantially the same resolving power be obtained in every direction of a hemispherical object plane. According to the invention, that problem can be eliminated by forming two separate optical paths on the left and right sides in the meridional section, with the center axis1between them.

Typically, the optical system of the invention is designed such that the entrance pupil6Y on the left side of the center axis1is adapted to seize images on the left hemispherical object plane, and the entrance pupil6Y on the right side is operable to seize images on the right hemispherical object plane. In other words, if, in the meridional section, the entrance pupil6Y is adapted to receive only light beams from objects on one side of the hemisphere, then the entrance pupil6Y on the opposite side with respect to the center axis1can receive light beams from objects on the opposite side of the hemisphere.

Moreover, it is important that the left and right optical paths be located without interference. This is of much importance when, as in the embodiment ofFIG. 1, the optical paths go laterally across the center axis1, because interference of the paths with each surface results in a failure in forming any substantial surface. It is also important that the left and right image planes in the meridional section, too, be located in such positions as not to interfere each other or in such a way that images are formed on positions a bit off the center axis1.

Furthermore, the left and right optical paths are rotationally symmetric with respect to the center axis1, and by rotation of the shape of such meridional section about the center axis1, it is possible to set up a rotationally symmetric optical system in which the image plane in a fan form about the center axis1assumes a generally zonal configuration.

Each entrance pupil6Y, too, provides a zonal one; however, each entrance pupil6Y only appears zonal when viewed from the direction of the center axis1where the lateral angles of view overlap in the meridional section (FIG. 1).

The front unit10may also function to split and project an image of the aperture5located on the center axis1onto two such left and right entrance pupils6Y with the center axis1between them.

For at least one internal reflecting surface, it is desirable to use a rotationally symmetric surface shape defined by rotation about the center axis1of a line segment of any arbitrary shape having an odd-number degree term and having no symmetric plane. The use of that odd-number degree term is preferable for correction of aberrations, because a vertically asymmetric shape can be given to the center of the angle of view.

In the invention, the entrance pupils are optionally formed by back projection of the stop (aperture)5located on the center axis through the front unit10, once the image of the aperture5has been formed. The feature of the invention here is that the entrance pupil positions differ in the meridional and the sagittal section such that in the meridional section, they are positioned near the first transmitting surface11(the entrance pupils6Y in the meridional section), and in the sagittal section, they are positioned on the center axis (rotationally symmetric axis)1(the entrance pupils6X in the sagittal section).

In an optical system including general spherical surfaces, both the entrance pupil in the meridional section and the entrance pupil in the sagittal section are supposed to be formed on the center axis. However, when an optical system like the inventive one is constructed of spherical surfaces, it is impossible to effectively locate a flare stop for cutting off harmful light supposed to enter the transparent medium, because the entrance pupil in the meridional section, too, will lie on the center axis, and so the effective range of the first transmitting surface11will become wide.

With the invention in which at least one internal reflecting surface is defined by rotation of a line segment of any arbitrary shape about the center axis1, it is possible to independently set the curvature of the meridional section and the curvature of the sagittal section, so that only the entrance pupil6Y in the meridional section—formed by back projection of the aperture5, optionally once its image has been formed—can be located on the object side with respect to the center axis1of the front unit10, thereby narrowing the effective range of the first surface (the first transmitting surface)11in the meridional section. This in turn enables unwanted light entering the front unit10to be considerably cut off to reduce flares.

In the sagittal section orthogonal to the center axis1, on the other hand, light beams travel rotationally symmetrically because the optical system is a rotationally symmetric arrangement, and light beams from circumferential object points at the same vertical angle of view are always supposed to pass on the center axis1that is the center of rotation, or leave the front unit10, traveling toward the center axis1. In the sagittal section, therefore, the entrance pupil6X lies on the center axis1.

Such being the arrangement, it is important for the front unit10to include a surface of rotationally symmetric shape that is defined by the rotation about the center axis1of a line segment of any arbitrary shape to enable free control of curvature in the meridional and the sagittal section. At the front unit10here, there are some considerable decentration aberrations arising from reflection or refraction of light at or through the surfaces11-14, each being located with a decentration and having power. For correction of those aberrations, it is important to use, for the internal reflecting surface12,13, in particular, a surface shape obtained by the rotation of a line segment of any arbitrary shape using an odd-number degree term, and having no symmetric surface.

According to such an arrangement with the center axis1as the Y-axis and a section including the center axis1(FIG. 1) as the Y-Z plane, a flare stop slit in the Y-direction can be positioned near the entrance pupils6Y in the meridional section, so that unwanted light can be cut off by that flare stop.

For the flare stop, not just a mechanically slit stop but also a casing designed for eye protection and a transparent pipe (coaxial with the center axis1) with an opaque portion painted black could be used. Alternatively, a reflection coating portion of the reflecting surface13or an optically unavailable area of the front unit10treated with sand or painted with a black paint could be used.

For the formation of the entrance pupils here, it is preferable that the number of images of the stop5formed in the sagittal section be the same as, or at least one more or one less than, that in the meridional section.

In Example 1 given later, the first transmitting surface11and the first reflecting surface12are located across the center axis1, and the second reflecting surface13is located across the center axis1from the first reflecting surface12and on the same side as the first transmitting surface11. In the sagittal section, therefore, a light beam will enter the stop5after transmitting twice through the center axis1, as depicted inFIG. 2. This means that an aperture image, upon back projection of the aperture5, will be formed on the optical axis1between the first transmitting surface11and the first reflecting surface12and on the center axis1between the first reflecting surface12and the second reflecting surface13as well.

In the sagittal section of Example 1, it follows that there is a double image formation, where the once formed aperture image is subject to an additional image formation. For better correction of aberrations, it is more preferable to make the powers in the sagittal section of the surfaces11-14in general, and the surfaces12and13in particular, approximately equal to those in the meridional section, and in the meridional section, it is also preferable, for correction of aberrations, to form the image of the stop5twice. In the invention, therefore, there are two images formed in the meridional section, too, i.e., an image6Y formed near the first transmitting surface11and an image6Y′ formed between the first reflecting surface12and the second reflecting surface13, as depicted inFIG. 1.

Further, if the position of back projection of the aperture5in the meridional section is set on the center axis1, it will go against the purport of the invention, because of an increase in the effective diameter of the entrance surface11, with the result that flares grow large. Furthermore, as the effective diameters of the surfaces11-14become large, it causes them to interfere with one another, rendering it impossible to ensure a wide angle of view in the vertical direction (the Y-direction).

In the invention, therefore, the aperture image6Y of the images of the aperture5subjected to back projection, positioned nearest to the object side, is located near the first transmitting surface11.

In Example 2 (FIG. 4) given later, the first transmitting surface11is located in opposition to the first reflecting surface12, the second reflecting surface13and the second transmitting surface14with respect to the center axis1, and so an image of the aperture5in the sagittal section is subjected to only a single back projection between the first transmitting surface11and the first reflecting surface12. With this, that image is back projected only once onto near the first transmitting surface11in the meridional section, too.

In Example 3 (FIG. 7) described later, the first transmitting surface11, the first reflecting surface12, the second reflecting surface13and the second transmitting surface14are all found on the object side with respect to the center axis1; that is, in the sagittal section, the aperture5is not back projected, because the light beam does not pass through the center axis1in the sagittal section. However, in an arrangement in which the aperture5is not back projected in the meridional section, too, there is one back projection allowed, because it goes against the purport of the invention.

It follows that for correction of aberrations, the number of image formations by the stop5in the sagittal section should preferably be equal to, or one more or one less than, the number of image formations by the stop5in the meridional section.

For an optical system designed to seize a light beam2from a hemispherical object100as contemplated herein, it is desired that an entrance pupil be positioned at the center of the hemisphere. In the optical system of the invention, however, the entrance pupil cannot be located at the center of the hemisphere, because the center axis1lies there. Therefore, the first transmitting surface11is located near the center axis1with such a tilt that the transmitted light beam is refracted toward the image plane side. This prevents the light beam upon transmission of the first transmitting surface11from interfering with the first reflecting surface12on which the light beam is incident via the opposite entrance pupil6Y positioned with the center axis1between them. Further, if a proper tilt is given to the first transmitting surface11, it is then possible to avoid interference between the first reflecting surface11and the second transmitting surface14.

Further in Example 3, the optical path for the front unit10is found on only one side with respect to the center axis1, and so no care is taken of interference of the surfaces with a light beam from the entrance pupil6Y located oppositely with respect to the center axis1. Conversely, however, the first transmitting surface11cannot be located near the center of the hemisphere; the first transmitting surface11comes closer to the hemispherical object100, resulting in a very large observation angle of view. In other words, unless the first transmitting surface11is located with a tilt of about 45° to seize light rays at a wide angle of view in the front unit10, the light beam will be incapable of entering the front unit10.

To allow a hemispherically wide angle of view to be seized in the front unit10, the angle of the first transmitting surface11thus grows important. In other words, it is important to satisfy the following condition (1).
−60°<θ1<−20°  (1)
Here θ1is the angle with respect to the center axis1of a tangential plane at a position of the first transmitting surface11on which the center ray (chief ray)20of the center light beam2from the center of the angle of view is incident.

As the lower limit of −60° to this condition is not reached, it renders it impossible to get hold of a downward angle of view at a hemispherical screen, and with the upper limit of −20° exceeded, it is impossible to get hold of any zenithal angle of view at the hemispherical screen.

The position of the first transmitting surface11with respect to the whole front unit10also grows important to avoid interference between the optical path and the surface. On the basis of the height of the front unit10perpendicularly to the image plane30, let H1stand for the height of the front unit10from the top to the bottom end, and H2represent the height of the front unit10from the top end to the position of the first transmitting surface11on which the center ray20is incident. It is then preferable to satisfy the following condition (2).
1.2<H1/H2(2)

As the lower limit of 1.2 to this condition is not reached, it causes the transmitting surface11to be positioned too low, and so the front unit10per se becomes an obstacle to the field of view, resulting in a failure in getting hold of a wide angle of view on observation.

The feature of the optical system of the invention is that, as described above, the entrance pupils6Y in the meridional section are projected onto near the first transmitting surface11, so that the flare stop for prevention of ghosts or the like can be effectively located. This offers another advantage of downsizing the effective area of the entrance surface11of the optical system in the meridional section and, hence, effectively preventing unwanted light from entering the front unit10, thereby achieving eradication of flares. To this end, it is of much importance to satisfy the following condition (3).

Here, let A be indicative of an optical path length from the position of the entrance pupils6Y in the meridional section to the position of the stop5, and B be indicative of an optical path length from the position of the entrance pupils6Y to the first transmitting surface11of the front unit10. To what degree the entrance pupils6Y are located near the entrance surface11of the front unit10is given by |A/B|. Then, |A/B| should preferably satisfy condition (3).
5<|A/B|(3)

As the lower limit of 5 to condition (3) is not reached, it causes the entrance pupils6Y to be away from the first surface11of the optical system. In other words, the effective diameter of the first surface11grows too large to cut off harmful flare light incident on the front unit10. The larger that value, the more effectively the flare-preventive flare stop can work.

Set out below are the values of A, B, |A/B|, H1,H2and H1/H2in Examples 1, 2 and 3 given later.

Examples 1, 2 and 3 of the optical system according to the invention are now explained in further details; however, their constructional parameters will be given later. The constructional parameters of Example 1 (and Example 7 given later) have been determined as a result of normal ray tracing from an object plane to the image plane30via the front unit10and the rear unit20, as typically illustrated inFIG. 1.

Referring to a coordinate system on normal ray tracing, the origin of a decentered optical surface in a decentered optical system is defined by the center of curvature of the hemispherical object100, the Y-axis positive direction is defined by a direction of the rotationally symmetric axis (center axis)1away from the image plane30, and, the Y-Z plane is defined by the paper ofFIG. 1. as shown typically inFIG. 1. And then, the Z-axis positive direction is defined by a direction opposite to the side of the entrance pupils6Y now considered, and the X-axis positive direction is defined by an axis that forms with the Y- and Z-axes a right-handed orthogonal coordinate system.

The amount of decentration from the center of the origin of the aforesaid optical system on a coordinate system on which that surface is defined (X, Y and Z are indicative of the X-axis direction, the Y-axis direction, and the Z-axis direction, respectively), and the angles of tilt (α, β, γ (°)) of the coordinate systems for defining the surfaces with the centers on the X-, Y- and Z-axes, respectively, are necessary for describing a decentered surface. In that case, the positive signs for α and β mean counterclockwise rotation with respect to the positive directions of the respective axes, and the positive sign for γ means clockwise rotation with respect to the positive direction of the Z-axis. Referring here to how to perform α-, β- and γ-rotations of the center axis of the surface, the coordinate system that defines each surface is first α-rotated counterclockwise about the X-axis of the coordinate system that is defined at the origin of the optical system. Then, the coordinate system is β-rotated counterclockwise about the Y-axis of the rotated new coordinate system. Finally, the coordinate system is γ-rotated clockwise about the Z-axis of the rotated new another coordinate system.

In the case of optical surfaces forming the optical system of each example, when a specific surface and the subsequent surface form together a coaxial optical system, a surface spacing may be determined. In addition, the radius of curvature of each surface and the refractive index and Abbe number of the medium may be determined according to common practices.

It is noted that the term regarding aspheric surfaces, on which no data are mentioned in the later-given constructional parameters, is zero. Refractive indices and Abbe numbers are given on a d-line (587.56 nm wavelength) basis, with length expressed in mm. The decentration of each surface is given in terms of the amount of decentration from the center of curvature of the hemispherical object100.

In this regard, an aspheric surface is a rotationally symmetric aspheric surface given by the following defining formula:
Z=(Y2/R)/[1+{1−(1+k)Y2/R2}1/2]+aY4+bY6+cY8+dY10+ . . .   (a)
Here, Z is an axis, Y is a direction vertical to that axis, R is a paraxial radius of curvature, k is a conical coefficient, and a, b, c, d are the fourth-, sixth-, eighth-, tenth-order aspheric coefficients, respectively. The Z-axis in this defining formula becomes the axis of the rotationally symmetric aspheric surface.

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

Then, there is given a curve F(Y) where the curve (b) is rotated by an angle θ (°) with left rotation defined as positive relative to the X-axis positive direction. This curve F(Y), too, passes on the Y-Z coordinate plane through the origin.

That curve F(Y) is parallelly translated by a distance R in the Z-positive direction (in the Z-negative direction in the case of a negative sign), and the parallel translated curve is then rotated about the Y-axis. The thus obtained rotationally symmetric surface gives an extended rotation free-form surface.

As a consequence, the extended rotation, free-form surface provides a free-form surface (smooth curve) in the Y-Z plane, and a circle with a radius |R| in the X-Z plane.

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

Here, RY is the radius of curvature of a spherical term in the Y-Z section, C1is a conical constant, and C2, C3, C4, C5, . . . are the first-, second-, third- and fourth-order aspheric coefficients, respectively.

In the optical system of the invention, at least one reflecting surface of the front unit10should preferably be such an extended rotation free-form surface that, when expressed by a polynomial in the Y-Z section, takes on a rotationally symmetric shape formed by rotation about the center axis1of a line segment of any arbitrary shape having at least an odd-number degree term yet having no symmetric surface. If such a surface shape is imparted to at least one reflecting surface, it is possible to provide an optical system whose resolving power is improved by correction of decentration aberrations unavoidable with a catoptric system, and diminish the size of that optical system.

FIG. 1is illustrative in section of the optical system of Example 1, as taken along its center axis (rotationally symmetric axis)1, andFIG. 2is a plan view illustrative of an optical path through that optical system. InFIG. 2, an optical path incident from the direction of an azimuth 0° and optical paths incident from the directions of azimuths ±14° are shown.

The optical system of this example is made up of a front unit10that is rotationally symmetric about the center axis1, a rear unit20that is rotationally symmetric about the center axis1and an aperture5located coaxially with the center axis1between the front unit10and the rear unit20, and a light beam2coming from a hemispherically curved object100with the origin as the center of curvature travels through the front unit10and the rear unit20in this order, forming an image30A at a position of an image plane30vertical to, and off, the center axis1. With the center axis1set perpendicularly (vertically), there is an annular image30A formed on the image plane30, which has a full 360°-direction (full-panoramic) angle of view along the circular edge of the hemispherically curved object100with the center of the hemispherically curved object100lying in the center direction of the image and the edge line of the hemispherically curved object becoming an outer circle.

The front unit10includes a resin or other transparent medium that is rotationally symmetric about the center axis1and has a refractive index greater than 1, and includes two internal reflecting surfaces12,13and two transmitting (entrance and exit) surfaces11,14. The internal reflecting surfaces12,13and the transmitting surfaces11,14are each of rotationally symmetric shape about the center axis1. Specifically, the rear unit20is built up of a lens system composed of two lenses L1and L2, each rotationally symmetric about the center axis1, and having positive power.

The transparent medium of the front unit10is made up of a first transmitting surface11, a first reflecting surface12, a second reflecting surface13and a second transmitting surface14. The first transmitting surface11is located on a side on which the light beam2from the curved object100is incident with respect to the center axis1. The first reflecting surface12is located in opposition to the first transmitting surface11, with the center axis1between them and nearer to the image plane30side than to the first transmitting surface11. The second reflecting surface13is located on the same side as the first transmitting surface11with respect to the center axis1and in opposition to the image plane30with respect to the first reflecting surface12. The second transmitting surface14is located on the same side as the first transmitting surface11and nearer to the image plane30side than to the first reflecting surface12.

And then, the light beam2coming from the curved object100enters the transparent medium via the first transmitting surface11, and arrives at the first reflecting surface12located in opposition to the first transmitting surface11with the center axis1between them, at which it is reflected away from the image plane30. Then, the reflected light beam arrives at the second reflecting surface13located on the same side as the first transmitting surface11with respect to the center axis1, at which it is reflected toward the image plane30side, leaving the transparent medium via the second transmitting surface14. The transmitted light enters the rear unit20via the stop-forming round aperture5located coaxially with the center axis1between the front unit10and the rear unit20, forming an image at a radially given position of the image plane30off the center axis1. The first transmitting surface11, the first reflecting surface12, the second reflecting surface13and the second transmitting surface14are all made up of extended rotation free-form surfaces; however, their conical coefficients are zero.

The lens system that forms the rear unit20is composed of, in order from the front unit10side, a positive meniscus lens L1concave on its front unit10side and a double-convex positive lens L2.

With the center axis1passing through the center of the hemispherically curved object100, the center light beam2coming from a position of the curved object100in a direction having an elevation angle of 45° as viewed from the center of curvature of the curved object100is refracted through the first transmitting surface11that is the entrance surface, entering the transparent medium of the front unit10. The transmitted light beam is reflected at the first reflecting surface12and the second reflecting surface13in this order, and then refracted through the second transmitting surface14, leaving the transparent medium of the front unit10. Finally, the transmitted light beam is incident on the rear unit20via the aperture5, forming an image30A at a radially given position of the image plane30off the center axis1.

In the optical system of this example, the aperture (stop)5located between the front unit10and the rear unit20is once projected onto the object side to form an image6Y′ in the meridional section, and that image is again back projected to form an entrance pupil6Y in the meridional section, which lies near the first transmitting surface11of the front unit10. In the sagittal section, on the other hand, two images6X′ and6X are formed on the center axis1(rotationally symmetric axis)1while an entrance pupil6X is formed on the center axis1.

In addition, in the optical system of this example, light beams2,3U and3L coming from the hemispherically curved object100via the entrance pupil6Y (3U is a light beam coming from the center of the hemispherically curved object100and3L is a light beam coming from the circular edge of the hemispherically curved object100) form an image once at a position4Y1near the first reflecting surface12in a section including the center axis1(the meridional section:FIG. 1), and form an image again at a position4Y2between the second reflecting surface13and the second transmitting surface14. In a plane that is orthogonal to the plane including the center axis1and includes the center ray20of that light beam2(the sagittal section:FIG. 2), on the other hand, they form images, once at a position4X1between the first transmitting surface11and the first reflecting surface12and again a position4X2between the second reflecting surface13and the second transmitting surface14.

The specifications of Example 1 are:

Horizontal Angle of View: 360°

Vertical Angle of View (relative to the center of curvature of the hemispherically curved object):

FIG. 3is a transverse aberration diagram for the optical system of this example. Throughout such transverse aberration diagrams in the present disclosure, the angle mentioned at the center is indicative of an angle of view in the perpendicular direction as viewed from the center of curvature of the hemispherical object100(the origin), and each diagram is illustrative of transverse aberrations at that angle of view in the Y (meridional)-direction and the X (sagittal)-direction with the center and edge directions of the hemispherical object100as 0° and 90°, respectively.

Further with respect to the optical system of the invention, in which the radius of curvature of the hemispherical object100is set at 1 m as an example, good images can be obtained if the distance of the image plane30from the rear surface of the double-convex positive lens L2is changed from 2.07 mm (the difference in the Y-direction between the position of decentration (10) and the position of decentration (11) in the constructional parameters given later) to 2.00 mm.

FIG. 4is illustrative in section of the optical system of Example 2 as taken along its center axis (rotationally symmetric axis)1, andFIG. 5is a plan view illustrative, as inFIG. 2, of an optical path through that optical system.

The optical system of this example is made up of a front unit10that is rotationally symmetric about the center axis1, a rear unit20that is rotationally symmetric about the center axis1and an aperture5located coaxially with the center axis1between the front unit10and the rear unit20. A light beam2coming from a hemispherically curved object100with the origin as the center of curvature travels through the front unit10and the rear unit20in this order, forming an image30A at a position of an image plane30vertical to, and off, the center axis1. With the center axis1set perpendicularly (vertically), there is an annular image30A formed on the image plane30, which has a full 360°-direction (full-panoramic) angle of view along the circular edge of the hemispherically curved object100with the center of the hemispherically curved object100lying in the center direction of the image and the edge line of the hemispherically curved object becoming an outer circle.

The front unit10includes a resin or other transparent medium that is rotationally symmetric about the center axis1and has a refractive index greater than 1, and includes two internal reflecting surfaces12,13and two transmitting (entrance and exit) surfaces11,14. The internal reflecting surfaces12,13and the transmitting surfaces11,14are each of rotationally symmetric shape about the center axis1. Specifically, the rear unit20is built up of a lens system composed of two lenses L1and L2, each rotationally symmetric about the center axis1, and having positive power.

The transparent medium of the front unit10is made up of a first transmitting surface11, a first reflecting surface12, a second reflecting surface13and a second transmitting surface14. The first transmitting surface11is located on a side on which the light beam2from the curved object100is incident with respect to the center axis1. The first reflecting surface12is located in opposition to the first transmitting surface11with the center axis1between them and nearer to the image plane30than the first transmitting surface11. The second reflecting surface13is located opposite to the first transmitting surface11with respect to the center axis1and in opposition to the image plane30with respect to the first reflecting surface12. The second transmitting surface14is located opposite to the first transmitting surface11and nearer to the image plane30side than the first reflecting surface12.

The light beam2coming from the curved object100enters the transparent medium via the first transmitting surface11, and arrives at the first reflecting surface12located in opposition to the first transmitting surface11with the center axis1between them, at which it is reflected away from the image plane30. Then, the reflected light beam arrives at the second reflecting surface13located opposite to the first transmitting surface11with respect to the center axis1, at which it is reflected toward the image plane30side, leaving the transparent medium via the second transmitting surface14. The transmitted light enters the rear unit20via the stop-forming round aperture5located coaxially with the center axis1between the front unit10and the rear unit20, forming an image30A at a radially given position of the image plane30off the center axis1. The first transmitting surface11, the first reflecting surface12, the second reflecting surface13and the second transmitting surface14are all made up of extended rotation free-form surfaces; however, their conical coefficients are zero.

The lens system that forms the rear unit20is composed of, in order from the front unit10side, a positive meniscus lens L1concave on its front unit10side and a double-convex positive lens L2.

With the center axis1passing through the center of the hemispherically curved object100, the center light beam2coming from a position of the curved object100in a direction having an elevation angle of 45° as viewed from the center of curvature of the curved object100is refracted through the first transmitting surface11that is the entrance surface, entering the transparent medium of the front unit10. The transmitted light beam is reflected at the first reflecting surface12and the second reflecting surface13in this order, and then refracted through the second transmitting surface14, leaving the transparent medium of the front unit10. Finally, the transmitted light beam is incident on the rear unit20via the aperture5, forming an image30A at a radially given position of the image plane30off the center axis1.

In the optical system of this example, the aperture (stop)5located between the front unit10and the rear unit20is once projected onto the object side to form an image6Y′ in the meridional section, and that image is again back projected to form an entrance pupil6Y in the meridional section, which lies near the first transmitting surface11of the front unit10. In the sagittal section, on the other hand, two images6X′ and6X are formed on the center axis1(rotationally symmetric axis)1while an entrance pupil6X is formed on the center axis1.

And, in the optical system of this example, light beams2,3U and3L coming from the hemispherically curved object100via the entrance pupil6Y (3U is a light beam coming from the center of the hemispherically curved object100and3L is a light beam coming from the circular edge of the hemispherically curved object100) form an image4Y once between the first reflecting surface12and the second reflecting surface13in a section including the center axis1(the meridional section:FIG. 4), and form an image once at a position4X between the first transmitting surface11and the first reflecting surface12in a plane that is orthogonal to the plane including the center axis1and includes the center ray20of that light beam2(the sagittal section:FIG. 5).

The specifications of Example 2 are:

Horizontal Angle of View: 360°

Vertical Angle of View (relative to the center of curvature of the hemispherically curved object):

FIG. 6is a transverse aberration diagram, as inFIG. 3, for the optical system of this example.

FIG. 7is illustrative, in section, of the optical system of Example 3 as taken along its center axis (rotationally symmetric axis)1, andFIG. 8is a plan view illustrative, as inFIG. 2, of an optical path through that optical system.

The optical system of this example is made up of a front unit10that is rotationally symmetric about the center axis1, a rear unit20that is rotationally symmetric about the center axis1and an aperture5located coaxially with the center axis1between the front unit10and the rear unit20. A light beam2coming from a hemispherically curved object100with the origin as the center of curvature travels through the front unit10and the rear unit20in this order, forming an image30A at a position of an image plane30vertical to, and off, the center axis1. With the center axis1set perpendicularly (vertically), there is an annular image30A formed on the image plane30, which has a full 360°-direction (full-panoramic) angle of view along the circular edge of the hemispherically curved object100with the center of the hemispherically curved object100becoming an outer circle and the edge line of the hemispherically curved object100lying in the center direction.

The front unit10includes a resin or other transparent medium that is rotationally symmetric about the center axis1and has a refractive index greater than 1, and includes two internal reflecting surfaces12,13and two transmitting (entrance and exit) surfaces11,14. The internal reflecting surfaces12,13and the transmitting surfaces11,14are each of rotationally symmetric shape about the center axis1. Specifically, the rear unit20is built up of a lens system composed of two lenses L1and L2, each rotationally symmetric about the center axis1, and having positive power.

The transparent medium of the front unit10is made up of a first transmitting surface11, a first reflecting surface12, a second reflecting surface13and a second transmitting surface14. The first transmitting surface11is located on a side on which the light beam2from the curved object100is incident with respect to the center axis1. The first reflecting surface12is located on the same side of the center axis1as the first transmitting surface11and nearer to the image plane30than the first transmitting surface11. The second reflecting surface13is located on the same side as the first transmitting surface11and the first reflecting surface12with respect to the center axis1, and in opposition to the image plane30with respect to the first reflecting surface12. The second transmitting surface14is located coaxially with the center axis1and nearer to the image plane30side than the first reflecting surface12.

The light beam2coming from the curved object100enters the transparent medium via the first transmitting surface11, and arrives at the first reflecting surface12located on the same side as the first transmitting surface11with respect to the center axis1, at which it is reflected away from the image plane30. Then, the reflected light beam arrives at the second reflecting surface13located on the same side as the first transmitting surface11and the first reflecting surface12with respect to the center axis1, at which it is reflected toward the image plane30side, leaving the transparent medium via the second transmitting surface14. The transmitted light enters the rear unit20via the stop-forming round aperture5located coaxially with the center axis1between the front unit10and the rear unit20, forming an image30A at a radially given position of the image plane30off the center axis1. The first transmitting surface11, the first reflecting surface12and the second reflecting surface13of the front unit10are all made up of extended rotation free-form surfaces; however, their conical coefficients are zero. On the other hand, the second transmitting surface14is made up of a rotationally asymmetric aspheric surface with the vertex lying on the center axis1.

The lens system that forms the rear unit20is composed of, in order from the front unit10side, a positive meniscus lens L1concave on its front unit10side and a double-convex positive lens L2.

With the center axis1passing through the center of the hemispherically curved object100, the center light beam2, which comes from a position of the curved object100in a direction having an elevation angle of 45° as viewed from the center of curvature of the curved object100, is refracted through the first transmitting surface11that is the entrance surface, entering the transparent medium of the front unit10. The transmitted light beam is reflected at the first reflecting surface12and the second reflecting surface13in this order, and then refracted through the second transmitting surface14, leaving the transparent medium of the front unit10. Finally, the transmitted light beam is incident on the rear unit20via the aperture5, forming an image30A at a radially given position of the image plane30off the center axis1.

In the optical system of this example, the aperture (stop)5located between the front unit10and the rear unit20is projected onto the object side to form an entrance pupil6Y in the meridional section, which lies near the first transmitting surface11of the front unit10. In the sagittal section, on the other hand, an entrance pupil6X is formed by the aperture (stop)5per se.

And, in the optical system of this example, light beams2,3U and3L coming from the hemispherically curved object100via the entrance pupil6Y (3U is a light beam coming from the center of the hemispherically curved object100and3L is a light beam coming from the circular edge of the hemispherically curved object100) form an image4Y once between the first reflecting surface12and the second reflecting surface13in a section including the center axis1(the meridional section:FIG. 7), but does not form any image in a plane that is orthogonal to the plane including the center axis1and includes the center ray20of that light beam2(the sagittal section:FIG. 8).

The specifications of Example 3 are:

Horizontal Angle of View: 360°

Vertical Angle of View (relative to the center of curvature of the hemispherically curved object):

FIG. 9is a transverse aberration diagram, as inFIG. 3, for the optical system of this example.

FIG. 10is representative of distortions for Examples 1, 2 and 3 in the vertical direction. More specifically, curves for Examples 1, 2 and 3 are obtained by plotting image heights (radial image heights from the center axis1) at the image plane30with respect to the vertical incident angles of view of the optical systems according to Examples 1, 2 and 3. Note here that each angle of view is a vertical incident angle of view, as viewed from the center of curvature (origin) of the hemispherically curved object100with its center direction at 0° and its edge direction at 90°, and that is different from the angles of rays incident actually on the optical system. A curve shown by F*θ is indicative of the case in which the image height is proportional to the incident angle of view (IH∝f·θ where IH is an image height, f is a focal length and θ is an angle of view).

Enumerated below are the constructional parameters of Examples 1, 2 and 3 given above. In what follows, the acronyms “ASS”, “ERFS” and “RE” stand for an aspheric surface, an extended rotation free-form surface and a reflecting surface, respectively.

Further examples of the invention are illustrated inFIGS. 11 and 12. However, no constructional parameters of these further examples are given.

FIG. 11is illustrative, in section, of the optical system of Example 4, as taken along its center axis (rotationally symmetric axis)1. This example is a modification to Example 1, in which the first transmitting surface11is located in opposition to a light beam2coming from a curved object100with the center axis1between them.

The optical system of this example is made up of a front unit10that is rotationally symmetric about the center axis1, a rear unit20that is rotationally symmetric about the center axis1and an aperture5located coaxially with the center axis1between the front unit10and the rear unit20. A light beam2coming from the hemispherically curved object100with the origin as the center of curvature travels through the front unit10and the rear unit20in this order, forming an image30A at a position of an image plane30vertical to, and off, the center axis1. With the center axis1set perpendicularly (vertically), there is an annular image30A formed on the image plane30, which has a full 360°-direction (full-panoramic) angle of view along the circular edge of the hemispherically curved object100, with the center of the hemispherically curved object100lying in the center direction of the image and the edge line of the hemispherically curved object becoming an outer circle.

The front unit10includes a resin or other transparent medium that is rotationally symmetric about the center axis1and has a refractive index greater than 1, and includes two internal reflecting surfaces12,13and two transmitting (entrance and exit) surfaces11,14. The internal reflecting surfaces12,13and the transmitting surfaces11,14are each of rotationally symmetric shape about the center axis1. The rear unit20is specifically built up of a lens system composed of two lenses L1and L2, each rotationally symmetric about the center axis1, and having positive power.

The transparent medium of the front unit10is made up of a first transmitting surface11, a first reflecting surface12, a second reflecting surface13and a second transmitting surface14. The first transmitting surface11is located on a side on which the light beam2from the curved object100is incident with the center axis1between them. The first reflecting surface12is located on the same side as the first transmitting surface11with respect to the center axis1and nearer to the image plane30than the first transmitting surface11. The second reflecting surface13is located in opposition to the first transmitting surface11with the center axis1between them, and in opposition to the image plane30with respect to the first reflecting surface12. The second transmitting surface14is located in opposition to the first transmitting surface11and nearer to the image plane30side than to the second reflecting surface13.

The light beam2coming from the curved object100enters the transparent medium via the first transmitting surface11, and arrives at the first reflecting surface12located on the same side as the first transmitting surface11with respect to the center axis1, at which it is reflected away from the image plane30. Then, the reflected light beam arrives at the second reflecting surface13located in opposition to the first transmitting surface11with respect to the center axis1, at which it is reflected toward the image plane30side, leaving the transparent medium via the second transmitting surface14. The transmitted light enters the rear unit20via the stop-forming round aperture5located coaxially with the center axis1between the front unit10and the rear unit20having positive power, forming an image30A at a radially given position of the image plane30off the center axis1. In this case, at least one of the first transmitting surface11, the first reflecting surface12, the second reflecting surface13and the second transmitting surface14is made up of an extended rotation free-form surface, but at least one of the at least one extended rotation free-form surface is a reflecting surface.

With the center axis1passing through the center of the hemispherically curved object100, the center light beam2coming from a position of the curved object100in a direction having an elevation angle of 45° as viewed from the center of curvature of the curved object100is refracted through the first transmitting surface11that is the entrance surface, entering the transparent medium of the front unit10. The transmitted light beam is reflected at the first reflecting surface12and the second reflecting surface13in this order, and then refracted through the second transmitting surface14, leaving the transparent medium of the front unit10. Finally, the transmitted light beam is incident on the rear unit20via the aperture5, forming an image30A at a radially given position of the image plane30off the center axis1.

In the optical system of this example, the aperture (stop)5located between the front unit10and the rear unit20is once projected onto the object side to form an image6Y′ in the meridional section, and that image is again back projected to form an entrance pupil6Y in the meridional section, which lies near the first transmitting surface11of the front unit10. In the sagittal section, on the other hand, two images are formed on the center axis1(rotationally symmetric axis)1while an entrance pupil is formed on that center axis1.

In addition, in the optical system of this example, light beams2,3U and3L coming from the hemispherically curved object100via the entrance pupil6Y (3U is a light beam coming from the center of the hemispherically curved object100and3L is a light beam coming from the circular edge of the hemispherically curved object100) form an image once at a position4Y1near the first reflecting surface12in a section including the center axis1(the meridional section:FIG. 11), and form an image again at a position4Y2on the stop5side of the second transmitting surface14.

FIG. 12is illustrative, in section, of the optical system of Example 5, as taken along its center axis (rotationally symmetric axis)1. This example is a modification to Example 2, in which the first transmitting surface11is located in opposition to a light beam2coming from a curved object100with the center axis1between them.

The optical system of this example is made up of a front unit10that is rotationally symmetric about the center axis1, a rear unit20that is rotationally symmetric about the center axis1and an aperture5located coaxially with the center axis1between the front unit10and the rear unit20. A light beam2coming from the hemispherically curved object100with the origin as the center of curvature travels through the front unit10and the rear unit20in this order, forming an image30A at a position of an image plane30vertical to, and off, the center axis1. With the center axis1set perpendicularly (vertically), there is an annular image30A formed on the image plane30, which has a full 360°-direction (full-panoramic) angle of view along the circular edge of the hemispherically curved object100with the center of the hemispherically curved object100lying in the center direction of the image30A and the edge line of the hemispherically curved object becoming an outer circle.

The front unit10includes a resin or other transparent medium that is rotationally symmetric about the center axis1and has a refractive index greater than 1, and includes two internal reflecting surfaces12,13and two transmitting (entrance and exit) surfaces11,14. The internal reflecting surfaces12,13and the transmitting surfaces11,14are each of rotationally symmetric shape about the center axis1. The rear unit20is specifically built up of a lens system composed of two lenses L1and L2, each rotationally symmetric about the center axis1, and having positive power.

The transparent medium of the front unit10is made up of the first transmitting surface11, the first reflecting surface12, the second reflecting surface13and the second transmitting surface14. The first transmitting surface11is located in opposition to a side on which the light beam2from the curved object100is incident with the center axis1between them. The first reflecting surface12is located on the same side as the first transmitting surface11with respect to the center axis1and nearer to the image plane30than the first transmitting surface11. The second reflecting surface13is located on the same side as the first reflecting surface12with respect to the center axis1, and in opposition to the image plane30with respect to the first reflecting surface12. The second transmitting surface14is located on the same side as the first transmitting surface11, the first reflecting surface12and the second reflecting surface13and nearer to the image plane30than the second reflecting surface13.

The light beam2coming from the curved object100enters the transparent medium via the first transmitting surface11, and arrives at the first reflecting surface12located on the same side as the first transmitting surface11with respect to the center axis1, at which it is reflected away from the image plane30. Then, the reflected light beam arrives at the second reflecting surface13located on the same side as the first reflecting surface12with respect to the center axis1, at which it is reflected toward the image plane30side, leaving the transparent medium via the second transmitting surface14. The transmitted light enters the rear unit20via the stop-forming round aperture5located coaxially with the center axis1between the front unit10and the rear unit20having positive power, forming an image30A at a radially given position of the image plane30off the center axis1. In this case, at least one of the first transmitting surface11, the first reflecting surface12, the second reflecting surface13and the second transmitting surface14is made up of an extended rotation free-form surface, but at least one of the at least one extended rotation free-form surface is a reflecting surface.

With the center axis1passing through the center of the hemispherically curved object100, the center light beam2coming from a position of the curved object100in a direction having an elevation angle of 45°, as viewed from the center of curvature of the curved object100, is refracted through the first transmitting surface11that is the entrance surface, entering the transparent medium of the front unit10. The transmitted light beam is reflected at the first reflecting surface12and the second reflecting surface13in this order, and then refracted through the second transmitting surface14, leaving the transparent medium of the front unit10. Finally, the transmitted light beam is incident on the rear unit20via the aperture5, forming an image30A at a radially given position of the image plane30off the center axis1.

In the optical system of this example, the aperture (stop)5located between the front unit10and the rear unit20is projected onto the object side to form an entrance pupil6Y in the meridional section, which lies near the first transmitting surface11of the front unit10. In the sagittal section, on the other hand, a single image is formed on the center axis (rotationally symmetric axis)1to form an entrance pupil on the center axis1.

In addition, in the optical system of this example, light beams2,3U and3L coming from the hemispherically curved object100via the entrance pupil6Y (3U is a light beam coming from the center of the hemispherically curved object100and3L is a light beam coming from the circular edge of the hemispherically curved object100) form an image4Y once in a section including the center axis1(the meridional section:FIG. 12), which lies near the first reflecting surface12.

In Examples 1, 2, 3 and 4 described above, each of the reflecting and refracting surfaces of the front unit10is defined by an extended rotation free-form surface that is formed by rotation about the rotationally symmetric axis1of a line segment of any arbitrary shape and has no vertex on the rotationally symmetric axis1; however, that surface could easily be replaced by any desired curved surface.

It is also understood that if the transparent medium that forms the front unit10according to the invention and is rotationally symmetric about the center axis1is used as such, it is then possible to take or project images having a full 360°-direction angle of view; however, if that transparent medium is bisected, trisected, ⅔-sected or the like on a section including the center axis1, it is then possible to take or project images having angles of view of 180°, 120°, 240° or the like about the center axis1.

In the numerical examples given above, the image height is set at 1 m; however, any desired image height could be set by multiplication with a certain factor. If the radius of the hemispherically curved object100is arbitrarily changed, focusing could be implemented by shifting the image plane30in the direction of the center axis1or moving a part of the rear unit20.

Specific examples of the optical system of the invention applied in the form of a panoramic taking optical system31or panoramic projection optical system32are now explained.FIG. 13is generally illustrative of an example of the panoramic taking optical system31of the invention used as a taking optical system attached to the endmost portion of an endoscope. More specifically,FIG. 13(a) is illustrative of the panoramic taking optical system31of the invention that is attached to the endmost portion31of a hard endoscope41to take and view a full 360°-direction image, andFIG. 13(b) is illustrative, in schematic, of that endmost portion. Around the entrance surface11of the front unit10in the panoramic taking optical system31, there is located a flare stop17including a casing having a slit aperture16that extends in a circumferential direction thereby preventing incidence of flare light.FIG. 13(c) is illustrative of an embodiment in which the inventive panoramic taking optical system31is likewise attached to the endmost portion of a soft electronic endoscope42, so that a taken image is shown on a display device43with distortions subjected to image processing for correction.

FIG. 14is illustrative of an example of the panoramic taking optical system31of the invention used as a taking optical system a capsule endoscope44. A full 360°-direction panoramic image of the intestinal wall or the like in close contact with a hemispherical window45at the endmost portion of the capsule endoscope44is taken for observation with the panoramic taking optical system31.

FIG. 15is illustrative of an example of a projector46in which the panoramic projection optical system32of the invention is used as its projection optical system. A panoramic image is displayed on a display device located on the image plane of the system32, so that a full 360°-direction image is projected and displayed on a full 360°-direction screen47through the panoramic optical system32.