Reflecting type optical system Number:6,785,060 from the United States Patent and Trademark Office (PTO) owispatent A reflecting-type optical system according to the invention includes an optical element composed of a transparent body having an entrance surface, an exit surface and at least three curved reflecting surfaces of internal reflection. A light beam coming from an object and entering at the entrance surface is reflected from at least one of the reflecting surfaces to form a primary image within the optical element and is, then, made to exit from the exit surface through the remaining reflecting surfaces to form an object image on a predetermined plane. In the optical system, 70% or more of the length of a reference axis in the optical element lies in one plane.<H Reflecting, optical, Reflecting, type, 6785060.html, Patent, pto, 6785060

Title: Reflecting type optical system

Abstract: A reflecting-type optical system according to the invention includes an optical element composed of a transparent body having an entrance surface, an exit surface and at least three curved reflecting surfaces of internal reflection. A light beam coming from an object and entering at the entrance surface is reflected from at least one of the reflecting surfaces to form a primary image within the optical element and is, then, made to exit from the exit surface through the remaining reflecting surfaces to form an object image on a predetermined plane. In the optical system, 70% or more of the length of a reference axis in the optical element lies in one plane.

Patent Number: 6,785,060 Issued on 08/31/2004 to Kimura, et al.

Inventors: Kimura; Kenichi (Kanagawa-ken, JP), Tanaka; Tsunefumi (Kanagawa-ken, JP), Kurihashi; Toshiya (Tokyo, JP), Ogura; Shigeo (Tokyo, JP), Araki; Keisuke (Kanagawa-ken, JP), Sekita; Makoto (Kanagawa-ken, JP), Takeda; Nobuhiro (Kanagawa-ken, JP), Uchino; Yoshihiro (Fukuoka-ken, JP), Yanai; Toshikazu (Kanagawa-ken, JP), Nanba; Norihiro (Kanagawa-ken, JP), Saruwatari; Hiroshi (Kanagawa-ken, JP), Akiyama; Takeshi (Kanagawa-ken, JP)
Assignee: Canon Kabushiki Kaisha (Tokyo, JP)

Appl. No.: 10/043,305

Filed: January 14, 2002

Related U.S. Patent Documents


Application Number	Filing Date	Patent Number	Issue Date
612290	Jul., 2000
606824	Feb., 1996	6166866

Foreign Application Priority Data


Feb 28, 1995 [JP]			7-065109
Apr 24, 1995 [JP]			7-123238

Current U.S. Class: 359/729 ; 359/720; 359/726

Field of Search: 359/729,726,720,676,683,731

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Primary Examiner: Sugarman; Scott J.
Attorney, Agent or Firm: Fitzpatrick, Cella, Harper & Scinto

Parent Case Text

This application is a division of application Ser. No. 09/612,290 filed Jul. 7, 2000, which is a division of application Ser. No. 08/606,824 filed Feb. 26, 1996 now U.S. Pat. No. 6,166,866.

Claims

What is claimed is:

1. An optical system forming an image of an object, comprising: at least three curved reflecting surfaces, at least one curved reflecting surface of said at least three curved reflecting surfaces having a shape of rotational asymmetry, wherein an object ray reflected from at least one curved reflecting surface of said at least three curved reflecting surfaces temporarily forms a real image of the object in an optical path of said optical system, and a pupil ray reflected from at least one curved reflecting surface of said at least three curved reflecting surfaces forms a real image of a pupil in an optical path of said optical system.

2. An optical system according to claim 1, further comprising an optical unit including said at least three curved reflecting surfaces, wherein the object ray forms a real image of the object in said optical unit, and the pupil ray forms a real image of the pupil in said optical unit.

3. An optical system according to claim 2, wherein said optical unit is one optical element composed of a transparent medium, and said at least three curved reflecting surfaces are internal reflection surfaces provided in the optical element.

4. An optical system according to claim 1, wherein said at least three curved reflecting surfaces have a shape of rotational asymmetry.

5. An optical system according to claim 4, wherein said at least three curved reflecting surfaces have a shape of symmetry with respect to only one symmetry plane.

6. An optical system according to claim 1, wherein an entrance pupil of said optical system is disposed nearer to the light entrance side than a reflecting surface, which is disposed nearest to the light entrance side among the curved reflecting surfaces included in said optical system.

7. An image pickup apparatus, comprising an optical system forming an image of an object, said optical system comprising: at least three curved reflecting surfaces, at least one curved reflecting surface of said at least three curved reflecting surfaces having a shape of rotational asymmetry, wherein an object ray reflected from at least one curved reflecting surface of said at least three curved reflecting surfaces temporarily forms a real image of the object in an optical path of said optical system, and a pupil ray reflected from at least one curved reflecting surface of said at least three curved reflecting surfaces forms a real image of a pupil in an optical path of said optical system; and an image pickup medium in which an image sensing surface is arranged at a position where an image of an object is formed by said optical system.

Description

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to optical systems of reflecting type and image pickup apparatuses using the same and, more particularly, to such optical systems which, using an optical element of many reflecting surfaces, form an object image on a predetermined plane. Still more particularly, this invention relates to improvements of the compact form of the entirety of the optical system suited to video cameras, still cameras or copying machines.

2. Description of the Related Art

There have been many previous proposals for utilizing the reflecting surfaces of convex and concave mirrors in the optical system for an image pickup apparatus. FIG. 24 schematically shows a so-called mirror optical system composed of one concave mirror and one convex mirror.

In the so-called mirror optical system of FIG. 24, an axial beam 104 coming from an object is reflected from the concave mirror 101. While being converged, it goes toward the object side and is then reflected by the convex mirror 102 to form an image on an image plane 103.

This mirror optical system is based on the configuration of the so-called Cassegrainian reflecting telescope. The aim of adopting it is to shorten the total length of the entire system as the equivalent telephoto system which is constructed with refracting surfaces or lenses alone has a long total length. To this purpose, the optical path is folded twice by using two reflecting surfaces arranged in confronting relation.

Even for the objective lens systems of telescopes, besides the Cassegrainian type, there are known, from a similar reason, a large number of forms with the use of a plurality of reflecting mirrors in shortening the total length of the optical system.

Like this, in a case where a photographic lens would take a long total length, it has been the common practice to employ reflecting mirrors instead of some of the lens members. By folding the optical path to good efficiency, a compact mirror optical system is obtained.

However, the Cassegrainian reflecting telescopes and like mirror optical systems generally suffer a problem due to the vignetting effect by the convex mirror 102, as the object light beam is partly mutilated. This problem will exist so long as the convex mirror 102 is laid at the central passage of the object beam 104.

To solve this problem, the reflecting mirror may be decentered, thus avoiding obstruction of the passage of the object beam 104 by the unintegrated part of the optical system. In other words, the principal ray 106 of the light beam is dislocated away from an optical axis 105. Such an optical system, too, has previously been proposed.

FIG. 25 is a schematic diagram of a mirror optical system disclosed in U.S. Pat. No. 3,674,334, wherein the problem of mutilation described above is solved in such a way that the reflecting mirrors to be used are rotationally symmetric with respect to the optical axis and partly cut off.

The mirror optical system of FIG. 25 comprises, in order of passage of the light beam, a concave mirror 111, a convex mirror 113 and a concave mirror 112, which, when in the prototype design, are, as shown by the double dot-and-dash lines, the complete reflecting surfaces of rotational symmetry with respect to the optical axis 114 of these, the concave mirror 111 is used only in the upper half on the paper of the drawing with respect to the optical axis 114, the convex mirror 113 only in the lower half and the concave mirror 112 only in a lower marginal portion, thereby bringing the principal ray 116 of the object beam 115 into dislocation away from the optical axis 114. The optical system is thus made free from the mutilation of the object beam 115.

FIG. 26 shows another mirror optical system which is disclosed in U.S. Pat. No. 5,063,586. The reflecting mirrors have their central axes made themselves to decenter from the optical axis. As a result, the principal ray of the object beam is dislocated from the optical axis, thus solving the above-described problem.

Referring to FIG. 26, assume that the perpendicular line 127 to the object plane 121 is an optical axis. With a convex mirror 122, a concave mirror 123, a convex mirror 124 and a concave mirror 125 in order of passage of the light beam, it is then proven that the centers of their reflecting areas do not fall on the optical axis 127 and that their central axes (the lines connecting those centers with the respective centers of curvature of the reflecting surfaces) 122a, 123a, 124a and 125a are decentered from the optical axis 127. In connection with this figure, the decentering amount and the radius of curvatures of every one surface are appropriately determined to prevent the object beam 128 from being mutilated by the other mirrors. Thus, an object image is formed on a focal plane 126 with high efficiency.

Besides these, U.S. Pat. Nos. 4,737,021 and 4,265,510 even disclose similar systems freed from the vignetting effect either by using certain portions of the reflecting mirrors of revolution symmetry about the optical axis or by decentering the central axes themselves of the reflecting mirrors from the optical axis.

These reflecting type photographic optical systems, because they have a great number of constituent parts, require highly precise assembly of the individual optical parts to insure satisfactory optical performance. In particular, because the tolerance for the relative positions of the reflecting mirrors is severe, later adjustment of the position and angle of orientation of each reflecting mirror is indispensable.

To solve this problem, one of the proposed methods is to construct the mirror system in the form of, for example, a block, thus avoiding the error which would otherwise result from the stepwise incorporation of the optical parts when in assembling.

It has been known to provide one block with a large number of reflecting surfaces. For example, the viewfinder systems employ optical prisms such as pentagonal roof prisms or Porro prisms.

These prisms are made by molding techniques to unify the plurality of reflecting surfaces. Therefore, all the reflecting surfaces take their relative positions in so much good accuracy as to obviate the necessity of adjusting the positions of the reflecting surfaces relative to one another. However, the main function of these prisms is to change the direction of travel of light for the purpose of inverting the image. Every reflecting surface is, therefore, made to be a flat surface.

For the counterpart to this, there is also known an optical system by giving curvature to the reflecting surface of the prism.

FIG. 27 is a schematic diagram of the main parts of an observing optical system disclosed in U.S. Pat. No. 4,775,217. This optical system is used for observing the external field or landscape and, at the same time, presenting an information display of data and icons in overlapping relation on the landscape.

The rays of light 145 radiating from the information display device 141 are reflected from a surface 142, going to the object side until they arrive at a half-mirror 143 of concave curvature. The reflected ones of the light rays 145 from the half-mirror 143 are nearly collimated by the refractive power of the concave surface 143, and refract in crossing the surface 142, reaching the eye 144 of the observer. The observer views an enlarged virtual image of the displayed data or icons.

Meanwhile, a light beam 146 from an object enters at a surface 147 which is nearly parallel with the reflecting surface 142, and is refracted by it and arrives at the concave surface 143. Since this surface 143 is coated with a half-permeable layer by the vacuum evaporation technique, part of the light beam 146 penetrates the concave surface 143 and refracts in crossing the surface 142, entering the pupil 144 of the observer. So, the observer views the display image in overlapping relation on the external field or landscape.

FIG. 28 is a schematic diagram of the main parts of another observing optical system disclosed in Japanese Laid-Open Patent Application No. Hei 2-297516. This optical system, too, is used for viewing the external field or landscape and, at the same time, noticing the information on the display device in overlapping relation.

In this system, a light beam 154 from an information display 150 enters a prism Pa at a flat surface 157 and is incident on a paraboloidal reflecting surface 151. Being reflected from this surface 151, the display light beam 154 becomes a converging beam. Before the display light beam 154 forms an image on a focal plane 156, three total reflections occur as the beam 154 travels between two parallel flat surfaces 157 and 158 of the prism Pa. A thinning of the entirety of the optical system is thus achieved.

From the focal plane 156, the display light beam 154 exits as a diverging beam and, while repeating total reflection from the flat surfaces 157 and 158, goes on until it is incident on a paraboloidal surface 152. Since this surface 152 is a half-mirror, the beam 154 is reflected and, at the same time, undergoes its refractive power, forming an enlarged virtual image of the display and becoming a nearly parallel beam. After having penetrated the surface 157, the beam 154 enters the pupil 153 of the observer. Thus, the observer looks at the display image on the background of the external field or landscape.

Meanwhile, an object light beam 155 from the external field passes through a flat surface 158b constituting a prism Pb, then penetrates the paraboloidal half-mirror 152 and then exits from the surface 157, reaching the eye 153 of the observer. So, the observer views the external field or landscape with the display image overlapping thereon.

Further, an optical element can be used in the reflecting surface of the prism. This is exemplified as disclosed in, for example, Japanese Laid-Open Patent Applications Nos. Hei 5-12704 and Hei 6-139612 as applied to the optical head for photo-pickup. Such a head receives the light from a semiconductor laser, then reflects it from the Fresnel surface or hologram surface to form an image on a disk, and then conducts the reflected light from the disk to a detector.

The mirror optical systems of the U.S. Pat. Nos. 3,674,334, 5,063,586 and 4,265,510 mentioned before have a common feature that all the reflecting mirrors are made decentered by respective different amounts to one another. Hence, the mounting mechanism for the reflecting mirrors becomes very complicated in structure. It is also very difficult to secure the acceptable mount tolerance.

It should be also noted that the known reflecting-type photographic optical systems are adapted for application to the so-called telephoto type of lens systems as this type has a long total length and a small field angle. To attain a photographic optical system handling field angles from the standard lens to the wide-angle lens, which require an increasing number of reflecting surfaces for correcting aberrations, the parts must be manufactured even more precisely and assembled with even severer a tolerance. Therefore, production costs rise. Otherwise, the size of the entire system tends to increase largely.

Also, the observing optical systems of the U.S. Pat. No. 4,775,217 and the Japanese Laid-Open Patent Application No. Hei 2-297516 mentioned before each have an aim chiefly to produce the pupil image forming function such that, as the information display is positioned remotely of the observer's eye, the light is conducted with high efficiency to the pupil of the observer. Another chief aim is to change the direction of travel of the light. Concerning the positive use of the curvature-imparted reflecting surface in correcting aberrations, therefore, no technical ideas are directly disclosed.

Also, the optical systems for photo-pickup of the Japanese Laid-Open Patent Applications Nos. Hei 5-12704 and Hei 6-139612 mentioned before each limit its use in the detecting purpose. Therefore, these systems are unable to satisfy the imaging performance for photographic optical systems and particularly image pickup apparatus using CCD or like area type image sensor.

SUMMARY OF THE INVENTION

A plurality of reflecting surfaces of curved and flat shapes are formed in unison to produce an optical element. By using a plurality of such optical elements, a mirror optical system is constructed to minimize its size. At the same time, the position and orientation tolerances (assembling tolerances) for the reflecting mirrors are made looser than was heretofore usually necessary mirror optical systems. It is, therefore, a first object of the invention to provide a highly accurate optical system of reflecting type and an image pickup apparatus using the same.

A stop is located at a position nearest the object side in the optical system, and an object image is formed at least once within the optical system. With this, even in a reflecting-type wide angle optical system, the effective diameter of the optical system is shortened. Moreover, a plurality of reflecting surfaces constituting the optical element are given appropriate refractive powers and the reflecting surfaces constituting every optical system are arranged in decentering relation to thereby zigzag the optical path in the optical system to a desired conformation, thus shortening the total length of the optical system in a certain direction. It is, therefore, a second object of the invention to provide a compact optical system of reflecting type and an image pickup apparatus using the same.

To attain the above objects, a reflecting-type optical system according to the invention comprises an optical element composed of a transparent body having an entrance surface, an exit surface and at least three curved reflecting surfaces of internal reflection, wherein a light beam coming from an object and entering at the entrance surface is reflected from at least one of the reflecting surfaces to form a primary image within the optical element and is, then, made to exit from the exit surface through the remaining reflecting surfaces to form an object image on a predetermined plane, and wherein 70% or more of the length of a reference axis in the optical element lies in one plane.

In particular, the characteristic features of the invention are as follows: A stop is located adjacent to the entrance surface of the optical element; The first curved reflecting surface of the optical element, when counted from the object side, has a converging action; The first curved reflecting surface is formed to an ellipsoid of revolution; The shape of the first curved reflecting surface is expressed by using a local coordinate system (x,y,z) for the first curved reflecting surface and letting coefficients representing the shape of a base zone of the first curved reflecting surface be denoted by a, b and t, wherein, putting

A = (a + b) (y.sup.2 cos.sup.2 t + x.sup.2) B = 2ab cost[1 + {(b - a) y sint/(2ab)} + {1 + {(b - a) y sint/(ab)} - {y.sup.2 /(ab)} - {4ab cos.sup.2 t + (a + b).sup.2 sin.sup.2 t} x.sup.2 /(4a.sup.2 b.sup.2 cos.sup.2 t)}.sup.1/2 ] and defining

z=A/B+C.sub.02 y.sup.2 +C.sub.20 x.sup.2 +C.sub.03 y.sup.3 +C.sub.21 x.sup.2 y+C.sub.04 y.sup.4 +C.sub.22 x.sup.2 y.sup.2 +C.sub.40 x.sup.4 the following conditions are satisfied:

Another reflecting type optical system according to the invention comprises an optical element having at least three curved reflecting surfaces of surface reflection whose reference axis lies on one plane and which are formed in unison so as to be opposed to each other, wherein a light beam coming from an object is reflected from at least one of the three curved reflecting surfaces to form an object image and the object image is then re-formed in a contracted fashion on a predetermined plane by the remaining reflecting surfaces.

In particular, the characteristic features of the invention are as follows: A stop is located on an object side of the optical element; The first curved reflecting surface, when counted from the object side, of the optical element has a converging action; The first curved reflecting surface is formed to an ellipsoid of revolution; The shape of the first curved reflecting surface is expressed by using a local coordinate system (x,y,z) for the first curved reflecting surface and letting coefficients representing the shape of a base zone of the first curved reflecting surface be denoted by a, b and t, wherein, putting

A = (a + b) (y.sup.2 cos.sup.2 t + x.sup.2) B = 2ab cost[1 + {(b - a) y sint/(2ab)} + {1 + {(b - a) y sint/(ab)} - {y.sup.2 /(ab)} - {4ab cos.sup.2 t + (a + b).sup.2 sin.sup.2 t} x.sup.2 /(4a.sup.2 b.sup.2 cos.sup.2 t)}.sup.1/2 ] and defining

A further optical system of reflecting type according to the invention comprises an optical element having formed therein in unison at least three curved reflecting surfaces composed of surface-reflecting mirrors and a reflecting surface whose normal line at a point of intersection with a reference axis is inclined with respect to a plane in which the reference axis among the plurality of reflecting surfaces lie, wherein, as a light beam coming from an object repeats reflection from the plurality of reflecting surfaces and then exits to form an image of the object, the object beam coming from the object is once focused to form an object image in one of spaces among the plurality of reflecting surfaces and is then focused to re-form the object image.

In particular, the characteristic features of the invention are as follows: A stop is located on an object side of the optical element; The first curved reflecting surface, when counted from the object side, of the optical element has a converging action; The first curved reflecting surface is formed to an ellipsoid of revolution; The shape of the first curved reflecting surface is expressed by using a local coordinate system (x,y,z) for the first curved reflecting surface and letting coefficients representing the shape of a base zone of the first curved reflecting surface be denoted by a, b and t, wherein, putting

A = (a + b) (y.sup.2 cos.sup.2 t + x.sup.2) B = 2ab cost[1 + {(b - a) y sint/(2ab)} + {1 + {(b - a) y sint/(ab)} - {y.sup.2 /(ab)} - {4ab cos.sup.2 t + (a + b).sup.2 sin.sup.2 t} x.sup.2 /(4a.sup.2 b.sup.2 cos.sup.2 t)}.sup.1/2 ] and defining

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of geometry to explain a coordinate system in embodiments of the invention.

FIG. 2 is a sectional view in the YZ plane of an embodiment 1 of the optical system according to the invention.

FIG. 3 is similar to FIG. 2 except that the path of the pupil light rays is shown.

FIGS. 4A-4F are graphs of lateral aberrations of the embodiment 1.

FIG. 5 is a sectional view in the YZ plane of an embodiment 2 of the optical system according to the invention.

FIGS. 6A-6F are graphs of lateral aberrations of the embodiment 2.

FIG. 7 is a sectional view in the YZ plane of an embodiment 3 of the optical system according to the invention.

FIGS. 8A-8F are graphs of lateral aberrations of the embodiment 3.

FIG. 9 is a sectional view in the YZ plane of an embodiment 4 of the optical system according to the invention.

FIGS. 10A-10F are graphs of lateral aberrations of the embodiment 1.

FIGS. 11A and 11B are a sectional views in the YZ plane and a side elevation view of an embodiment 5 of the optical system according to the invention.

FIG. 12 is a perspective view of the embodiment 5.

FIGS. 13A-13F are graphs of lateral aberrations of the embodiment 5.

FIG. 14 is a sectional view in the YZ plane of an embodiment 6 of the optical system according to the invention.

FIGS. 15A-15F are graphs of lateral aberrations of the embodiment 6.

FIG. 16 is a sectional view in the YZ plane of an embodiment 7 of the optical system according to the invention.

FIGS. 17A-17F are graphs of lateral aberrations of the embodiment 7.

FIG. 18 is a sectional view in the YZ plane of an embodiment 8 of the optical system according to the invention.

FIGS. 19A-19F are graphs of lateral aberrations of the embodiment 8.

FIG. 20 is a sectional view in the YZ plane of an embodiment 9 of the optical system according to the invention.

FIGS. 21A-21F are graphs of lateral aberrations of the embodiment 9.

FIG. 22 is a sectional view in the YZ plane of an embodiment 10 of the optical system according to the invention.

FIGS. 23A-23F are graphs of lateral aberrations of the embodiment 10.

FIG. 24 is a diagram of the fundamental configuration of the Cassegrainian reflecting telescope.

FIG. 25 is a diagram to explain a first method of avoiding the vignetting by putting the principal ray away from the optical axis in the mirror optical system.

FIG. 26 is a diagram to explain a second method of avoiding the vignetting by putting the principal ray away from the optical axis in the mirror optical system.

FIG. 27 is a diagram of an observing optical system using a prism having a curved reflecting surface.

FIG. 28 is a diagram of another observing optical system using a prism having curved reflecting surfaces.

In the drawings, reference character Ri denotes the surface except R1 represents the stop, reference character Di is the separation between adjacent two of the surfaces along the reference axis, and reference characters Ndi and vdi are respectively the refractive index and Abbe number.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Prior to the description of the embodiments, the expression of the various constitutional dimensions and the common features of all the embodiments are described below.

FIG. 1 is a diagram taken to explain a coordinate system by which to define the design parameters for the optical system of the invention. In the embodiments of the invention, as one ray of light (shown by dot-and-dash lines and referred to as the "reference axis" ray) travels from the object side to an image plane, the surfaces are numbered consecutively along this ray and represented by Ri for the i-th surface.

In FIG. 1, the first surface R1 is a stop, the second surface R2 is a refracting surface coaxial to the first surface, the third surface R3 is a reflecting surface tilted relative to the second surface R2, the fourth surface R4 and the fifth surface R5 each are a reflecting surface shifted and tilted relatively to the respective preceding surface, and the sixth surface R6 is a refracting surface shifted and tilted relatively to the fifth surface R5. All of the second to sixth surfaces R2 to R6 are formed on a substrate of glass, plastic or like medium to form a single optical element indicated by reference numeral 10.

In the construction and arrangement of FIG. 1, therefore, the medium from an object plane (not shown) to the second surface R2 is air, the space from the second to sixth surface R2 to R6 is a certain common medium, and the medium from the sixth surface R6 to a seventh surface R7 (not shown) is air.

Since the optical system of the invention is the decentering one, all the surfaces constituting the optical system have no common optical axis. Accordingly, for the embodiments of the invention, an absolute coordinate system is established with the original point at the center of a ray effective diameter of the first surface.

Then, in the embodiments of the invention, the central point of a ray effective diameter of the first surface is assumed to be the original point, and the path of a ray of light passing the original point and the center of the last image forming plane (reference axis ray) is assumed to be a reference axis. Further, the reference axis has an orientation (direction). This orientation points to the direction in which the reference axis ray advances in forming an image.

Though, in the embodiments of the invention, the reference axis on which the design of the optical system is based has been determined as described above, it is to be noted that choice of an axis for the reference of the optical system may otherwise be made as is favorable for the design of optics, good compromise of aberrations, or the expression of the shapes of all the surfaces constituting the optical system. In the general case, however, as the reference axis, use is made of the optical path that intersects an image plane at the center thereof and one of the stop, the entrance pupil, the exit pupil and the first and last surfaces of the optical system at the center thereof.

With this regard, in the embodiments of the invention, determination of the reference axis is made in the steps of selecting a ray which crosses the first surface, that is, the stop plane, at the central point of the ray effective diameter thereof and is to arrive at the center of the last image forming plane (or the reference axis ray), tracing it across each refracting surface and by each reflecting surface, and adopting the found path as the reference axis. The numbering of each surface is determined in the order of succession of the refractions and reflections the reference axis ray undergoes.

Therefore, each time the found surface number increases by one, the reference axis changes its orientation depending on the law of refraction or reflection, finally reaching the center of the image plane.

In each embodiment of the invention, of the surfaces constituting the optical system, the tilted ones are fundamentally all obtained as the result of tilting in one and the same plane. Accordingly, the axes of the absolute coordinate system are defined as follows:

Z axis: the reference axis passing the original point and advancing to the second surface R2;

Y axis: a line passing the original point and making an angle of 90.degree. with respect to the Z axis as obtained by turning counterclockwise in the tilt plane (in the paper of the drawing of FIG. 1); and

X axis: a line passing the original point and perpendicular to each of the Z and Y axes (the line normal to the paper of the drawing of FIG. 1).

To express the shape of the i-th surface constituting part of the optical system, the absolute coordinate system is not as suitable for the purpose of better understanding as using a local coordinate system whose original point is taken at the point of intersection of the reference axis with the i-th surface. In the specific embodiments of the invention, therefore, the numerical data of the design parameters for the i-th surface are given by using the local coordinate system.

As the i-th surface tilts in the YZ plane, the counterclockwise direction from the Z axis of the absolute coordinate system is taken as positive when the tilted angle .theta.i is measured (in units of degree (.degree.).) In the embodiments of the invention, therefore, the original point of the local coordinate system for each surface lies on the YZ plane in FIG. 1. It should be also noted that there is no decentering in the XZ and XY planes. Further, in view of the absolute coordinate system (X,Y,Z), the local coordinate system (x,y,z) for the i-th surface have its y and z axes inclined by .theta.i in the YZ plane. Accordingly, the axes of the local coordinate system are defined as follows:

z axis: a line passing the original point of the local coordinates and making an angle .theta.i with respect to the Z direction of the absolute coordinate system as obtained by turning counterclockwise in the YZ plane;

y axis: a line passing the original point of the local coordinates and making an angle of 90.degree. with respect to the z axis as obtained by turning counterclockwise in the YZ plane; and

x axis: a line passing the original point of the local coordinates and perpendicular to the YZ plane.

Di is the scalar space between the original points of the local coordinates for the i-th and (i+1)st surfaces, and Ndi and vdi are respectively the refractive index and Abbe number of the medium between the i-th and (i+1)st surfaces.

Also, the embodiments of the optical systems of the invention are illustrated in the diagrams and given the numerical data.

The optical system of each of the embodiments of the invention has a spheric surface and an aspheric surface which is rotationally asymmetric. Of these, the spheric ones are expressed as the spheres described by the radius of curvature Ri. The radius of curvature Ri is given a minus sign when the center of curvature lies on the first surface side in the reference axis (the dot-and-dash lines in FIG. 1) oriented from the first surface to the image plane, or a plus sign when on the image plane side.

The shape of the sphere is expressed by the following equation: ##EQU1##

Also, as the optical system of the invention employs at least one aspheric surface which is rotationally asymmetric, the shape of this aspheric surface is expressed by the following equation:

where

A = (a + b) (y.sup.2 cos.sup.2 t + x.sup.2) B = 2ab cost[1 + {(b - a) y sint/(2ab)} + {1 + {(b - a) y sint/(ab)} - {y.sup.2 /(ab)} - {4ab cos.sup.2 t + (a + b).sup.2 sin.sup.2 t} x.sup.2 /(4a.sup.2 b.sup.2 cos.sup.2 t)}.sup.1/2 ]

Since the surface equation described above contains only the terms of even number orders in respect to x, the surface defined by such an equation takes the YZ plane as a plane of symmetry so it has the shape of symmetry with respect to a plane. Further, in a case where the following conditions are satisfied, C.sub.03 =C.sub.2,=0, t=0 its shape is symmetrical with respect to the XZ plane. Further, in a case where the following conditions are satisfied,

its shape is symmetrical with respect to the XZ plane. Further, in a case where the following conditions are satisfied,

its shape is of rotational symmetry. In a case where the foregoing conditions are not satisfied, its shape is of rotational asymmetry.

It should be noted that, in all the embodiments of the invention, "C.sub.02 =C.sub.20 =0" is satisfied. So, the shape is obtained by adding the higher order asymmetric asphere to the basic form of the second order sphere.

In each embodiment of the invention, as shown in FIG. 1, the first surface is the stop. Also, the term "horizontal half-angle of view u.sub.y " used herein means the maximum angle of view of the light beam entering the stop R1 in the YZ plane, and the term "vertical half-angle of view u.sub.x " means the maximum angle of view entering the stop in the XZ plane. Also, the diameter of the first surface or the stop is shown as the aperture diameter. This correlates to the speed of the optical system. It should be noted that since the entrance pupil is in the first surface, the aperture diameter described above is equal to the entrance pupil diameter.

Also, the effective image area on the image plane is shown as the image size. The image size is represented by a rectangular area in which the size in the y direction is a horizontal one and the size in the x direction is a vertical one.

Further, the size of the optical system is shown in each of the embodiments. The optical system size is determined by the effective diameter of the light beam.

Also, as far as the embodiment which has the data of the design parameters cited therein is concerned, its lateral aberrations are shown by graphic representations. These graphs are depicted in every such embodiment by tracing the rays of light whose angles of incidence have the values (u.sub.y, u.sub.x), (0, u.sub.x), (-u.sub.y, u.sub.x), (u.sub.y, 0), (0,0) and (-u.sub.y, 0) in the coordinates of the horizontal and vertical angles of incidence on the stop R1. In the graphs of the lateral aberrations, the abscissa represents the height of incidence on the pupil and the ordinate represents the amount of aberration. In each of the embodiments, basically every surface has the form of plane symmetry with the yz plane made to be the plane of symmetry. Therefore, even in the graphs of the lateral aberrations, the plus and minus directions of the vertical angle of view become the same. For the simplicity of representation, the graphs of the lateral aberrations of the minus direction are omitted.

Next, each of the embodiments is described in detail below.

(Embodiment 1)

FIGS. 2 and 3 are sectional views in the YZ plane of a first embodiment of the optical system according to the invention. This embodiment is a photographic optical system whose horizontal angle of view is 52.6 degrees and whose vertical angle of view is 40.6 degrees. The optical path is even shown in FIG. 2. FIG. 3 shows the optical path of the pupil ray (off-axial principal ray). The numerical values of the parameters of the present embodiment are listed below:

Horizontal Half-Angle of View: 26.3.degree.

Vertical Half-Angle of View: 20.3.degree.

Aperture Diameter: 2.0 mm

Image Size: Horizontal 4 mm.times.Vertical 3 mm

Optical System Size: (X.times.Y.times.Z)=10.4.times.27.4.times.21.2

i Yi Zi .theta.i Di Ndi .nu.di Surface 1 0.00 0.00 0.00 3.40 1 Stop 2 0.00 3.40 0.00 7.00 1.51633 64.15 R* 3 0.00 10.40 25.00 10.00 1.51633 64.15 L* 4 -7.66 3.97 10.00 10.00 1.51633 64.15 L 5 -12.66 12.63 10.00 8.50 1.51633 64.15 L 6 -19.17 7.17 25.00 7.00 1.51633 64.15 L 7 -19.17 14.17 0.00 3.00 1 R 8 -19.17 19.17 0.00 2.00 1.51633 64.15 R 9 -19.17 19.17 0.00 2.07 1 R 10 -19.17 21.24 0.00 0.00 1 I.P. *R for refracting surface; L for reflecting surface; I.P. for image plane

Spherical Shape

R1:.infin.

R2:-4.887

R7:-6.524

R8:.infin.

R9:.infin.

R10:.infin.

Aspherical Shape

R 3: a = -1.61839e+01 b = -1.25665e+01 t = 2.59881e+01 C.sub.02 = 0. C.sub.20 = 0. C.sub.03 = -1.38328e-04 C.sub.21 = 4.61307e-04 C.sub.04 = 9.02763e-06 C.sub.22 = 7.64906e-05 C.sub.40 = 1.02169e-05 R 4: a = -2.50732e+00 b = 2.52739e+00 t = -8.04837e+01 C.sub.02 = 0. C.sub.20 = 0. C.sub.03 = 1.15553e-03 C.sub.21 = 4.86323e-03 C.sub.04 = -1.25972e-04 C.sub.22 = -2.57791e-04 C.sub.40 = -6.89833e-04 R 5: a = -9.53779e+01 b = -3.53371e+01 t = 4.35207e+01 C.sub.02 = 0 C.sub.20 = 0. C.sub.03 = 3.53074e-04 C.sub.21 = -1.26967e-03 C.sub.04 = -2.02832e-05 C.sub.22 = -3.46921e-04 C.sub.40 = -8.12941e-05 R 6: a = 5.05342e+00 b = -8.31188e+00 t = -2.24737e+01 C.sub.02 = 0. C.sub.20 = 0. C.sub.03 = -5.59866e-04 C.sub.21 = -1.17474e-03 C.sub.04 = -1.39401e-04 C.sub.22 = -2.09750e-04 C.sub.40 = -1.35370e-04

In FIG. 2, an optical element 10 has a plurality of curved reflecting surfaces and is made from a glass or like transparent body. The external surface of the optical element 10 is constructed, as comprising, in order of passage of the ray from an object, a refracting surface R2 (entrance surface) having a negative refractive power in concave form toward the object side, four reflecting surfaces, namely, a concave mirror R3 for giving convergence to the ray, a reflecting surface R4, a reflecting surface R5 and a concave mirror R6, and a refracting surface R7 (exit surface) having a positive refractive power in convex form toward the image side. A stop R1 (entrance pupil) is located on the object side of the optical element 10. A quartz low-pass filter, infrared cut filter or like optical correction plate 3 is located in front of a last image plane R10 which is coincident with the image sensing surface of a CCD or like image pickup element (or recording medium). A reference axis of the photographic optical system is indicated by reference numeral 5.

It is to be noted that the two refracting surfaces R2 and R7 each are of rotational symmetry, or a sphere, and all the reflecting surfaces R3 to R6 are symmetrical with respect' to the YZ plane only.

Next, the image forming function in this embodiment is described. A light beam 1 coming from the object, after its amount of incidence is restricted by the stop R1, enters the optical element 10 at the entrance surface R2, in which it is reflected from the surfaces R3 and R4 and once forms an image in the neighborhood of the surface R4. The light beam 1 from the image is then reflected from the surfaces R5 and R6 in succession, then exits from the exit surface R7, then passes through the optical correction plate 3 and then forms an image again on the last image plane R10. It is noted that the object light beam forms the intermediate image in the neighborhood of the surface R4 and the pupil rays forms an intermediate image in a space between the surfaces R5 and R6.

In the present embodiment, the direction of the reference axis entering the optical element 10 and the direction of the reference axis exiting therefrom are parallel to each other and are the same direction. Also, the whole of the reference axis including entering and exiting lies in the paper of the drawing (YZ plane).

In such a manner, the optical elemen