Abstract:
A concentric optical system usable as either an imaging optical system or an ocular optical system, which enables a clear image to be obtained at a field angle of up to about 90° and with a pupil diameter of up to about 10 millimeters with substantially no chromatic aberration. The concentric optical system includes a first optical component having a first semitransparent reflecting surface (2), and a second optical component having a second semitransparent reflecting surface (3). The first and second semitransparent reflecting surfaces (2 and 3) have respective centers of curvature disposed at approximately the same position (1). The first and second optical components are different in dispersion from each other. The first and second semitransparent reflecting surfaces (2 and 3) are arranged so that a bundle of light rays passing through the first semitransparent reflecting surface (2) is reflected by the second semitransparent reflecting surface (3), and the bundle of light rays reflected by the second semitransparent reflecting surface (3) is reflected by the first semitransparent reflecting surface (2) and then passes through the second semitransparent reflecting surface (3). The optical system satisfies the condition of 0.2&lt;ν 1  /ν 2  &lt;1.00, where ν 1  is the Abbe&#39;s number of the first optical component, and ν 2  is the Abbe&#39;s number of the second optical component.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a concentric optical system which is usable as either an ocular optical system or an imaging optical system. More particularly, the present invention relates to a concentric optical system which provides a high resolution, a wide field angle and a large pupil diameter with minimal chromatic aberration. 
     2. Background of Related Art 
     A Schmidt system, which is well known as an objective for astronomical telescopes, is generally arranged such that an aspherical lens which is close to a plane-parallel plate is placed at the spherical center of a concave mirror to correct spherical aberration, and a diaphragm is disposed at the spherical center to correct coma and astigmatism. 
     Concentric optical systems, which are represented by the above Schmidt system, are free from coma and astigmatism by virtue of the diaphragm disposed in the vicinity of the center of curvature of the concave mirror. However, since the curvature of field cannot be corrected, a large field curvature occurs. 
     U.S. Reissued Pat. No. 27,356 discloses an ocular optical system which uses a semitransparent concave mirror and a semitransparent plane mirror to project an object surface at a distance, and which adopts an arrangement wherein the field curvature produced by the semitransparent concave mirror is corrected by curving the object surface. In U.S. Reissued Pat. No. 27,356, however, the semitransparent concave mirror and the semitransparent plane mirror are each formed from a single independent constituent element. Therefore, when the field angle is widened, off-axis aberrations such as astigmatism, coma, etc. are likely to occur. In addition, the radius of curvature of the semitransparent concave mirror reduces, which is unfavorable from the manufacturing point of view in actual practice. 
     There has also been a known arrangement in which light rays are reflected by a forward mirror to once turn back the optical axis, and the reflected rays are reflected again by another mirror. The arrangement is known as a reflecting telephoto objective. FIG. 24 is a sectional view showing U.S. Pat. No. 3,700,310 as one example of the reflecting telephoto objective. Referring to the figure, rays successively pass through lenses A, B, C and D and are reflected by a mirror 12. The reflected rays pass through the lenses D and C and are reflected by a mirror 13. Then, the reflected rays successively pass through the lenses C, F, G, H and I to form an image. 
     In the conventional reflecting telephoto objective, however, the mirrors 12 and 13 are totally reflecting mirrors. Therefore, it is necessary in order to prevent a bundle of rays entering through the foremost surface R 1  from being cut by the mirror 12 or 13 to increase the size of the mirrors 12 and 13 or to provide the pupil position in the range of from the foremost surface R 1  to the rearmost surface R 6 . Accordingly, the pupil of the conventional reflecting telephoto objective is provided between the foremost and rearmost surfaces of the entire lens system to prevent the image from darkening without an increase in size of the entire lens system. In the above-described U.S. Pat. No. 3,700,310, the pupil is provided on the surface R 6 . 
     However, since it is necessary to take the turn-back optical paths into consideration when installing the mirrors, the degree of freedom is disadvantageously low, and the aberration correcting capability is also deteriorated. In addition, different lenses are used for each turn-back optical path, such as the lenses A and B and the central lens E, and the lens D and the lenses F to I, which are disposed in the center thereof, in U.S. Pat. No. 3,700,310. Accordingly, the arrangement is complicated, and thus the conventional optical system involves problems such as reduction in productivity, rise in cost, etc. 
     SUMMARY OF THE INVENTION 
     In view of the above-described problems of the related art, an object of the present invention is to provide a concentric optical system usable as either an imaging optical system or an ocular optical system, which enables a clear image to be obtained at a field angle of up to about 90° and with a pupil diameter of up to about 10 millimeters with substantially no chromatic aberration. 
     To attain the above-described object, the present invention provides a concentric optical system which includes at least two, first and second, optical components having at least two semitransparent reflecting surfaces, each having a concave surface directed toward a pupil plane. The semitransparent reflecting surfaces are disposed so that each semitransparent reflecting surface transmits light rays at least once and reflects them at least once. The first and second optical components are different in dispersion from each other. A pupil that is formed by the first and second optical components lies outside the range of from the foremost surface to the rearmost surface of the optical system. 
     With the above-described arrangement of the present invention, the pupil position is provided outside the range of from the foremost surface to the rearmost surface of the optical system, thereby enabling an increase in the degree of freedom of aberration correction. In addition, since the arrangement is simple, the productivity can be effectively improved, and the production cost can also be reduced. 
     In addition, the present invention provides a concentric optical system which includes a first optical component and a second optical component. The first optical component has a first semitransparent reflecting surface which has a center of curvature disposed substantially on an optical axis, and which has a concave surface directed toward the center of curvature. The first optical component is formed from a medium having a refractive index (n) larger than 1 (n&gt;1). The second optical component has a second semitransparent reflecting surface which has a center of curvature disposed at approximately the same position as the center of curvature of the first semitransparent reflecting surface. The second optical component is formed from a medium having a refractive index (n) larger than 1 (n&gt;1). The medium of the first optical component and the medium of the second optical component are different in dispersion from each other. In addition, a pupil that is formed by the first and second optical components lies outside the range of from the foremost surface to the rearmost surface of the optical system. 
     In addition, the present invention provides a concentric optical system which includes a first optical component having a first semitransparent reflecting surface, and a second optical component having a second semitransparent reflecting surface. The first and second semitransparent reflecting surfaces have respective centers of curvature disposed at approximately the same position. The first and second optical components are different in dispersion from each other. The first and second semitransparent reflecting surfaces are arranged so that a bundle of light rays passing through the first semitransparent reflecting surface is reflected by the second semitransparent reflecting surface, and the bundle of light rays reflected by the second semitransparent reflecting surface is reflected by the first semitransparent reflecting surface and then passes through the second semitransparent reflecting surface. In addition, a pupil that is formed by the first and second optical components lies outside the range of from the foremost surface to the rearmost surface of the optical system. 
     In the above-described arrangements, it is preferable that the at least two optical components, which are different in dispersion from each other, lie adjacent to each other. 
     Each semitransparent reflecting surface preferably has a transmittance in the range of from 20% to 80%. 
     It is preferable to dispose a device which is composed of polarizing optical elements so as to cut off light rays passing through the at least two semitransparent reflecting surfaces without being reflected by either of them. 
     The above-described concentric optical systems may be usable as either an ocular optical system or an imaging optical system. 
     Further, it is preferable to satisfy the following condition: 
     
         0.2&lt;ν.sub.1 /ν.sub.2 &lt;1.00                           1 
    
     where ν 1  is the Abbe&#39;s number of the first optical component, and V 2  is the Abbe&#39;s number of the second optical component. 
     When the field angle in each of the vertical and horizontal directions is 40° or more, it is preferable to satisfy the following condition: 
     
         0.5&lt;ν.sub.1 /ν.sub.2 &lt;0.98                           2 
    
     When the field angle in each of the vertical and horizontal directions is 40° or more, and the pupil diameter is 10 millimeters or more, it is preferable to satisfy the following condition: 
     
         0.5&lt;ν.sub.1 /ν.sub.2 &lt;0.95                           3 
    
     The reason for adopting the above-described arrangements in the present invention and the functions thereof will be explained below. 
     The concentric optical system of the present invention will be explained below as an imaging optical system for the sake of convenience. However, it is easy to use the concentric optical system as an ocular optical system by modifying the arrangement such that the image surface in the optical system of the present invention formed as an imaging optical system is replaced by an object point. Thus, it will be clear that the present invention has constituent features required to form an ocular optical system. That is, the concentric optical system of the present invention can also function as an ocular optical system by inverting the arrangement of the imaging optical system described below. 
     In the above-described U.S. Reissued Pat. No. 27,356, the semitransparent concave mirror and the semitransparent plane mirror are each formed from a single independent constituent element. Therefore, when the field angle is widened, off-axis aberrations such as astigmatism, coma, etc. are likely to occur. In addition, the radius of curvature of the semitransparent concave mirror reduces, which is unfavorable from the manufacturing point of view in actual practice. In Japanese Patent Application No. 05-264828, which is a prior application filed by the present applicant, the space between the above-described constituent elements is filled with a glass or other vitreous material, thereby making the optical arrangement even more favorable from the manufacturing point of view. In addition, a semitransparent concave mirror is disposed in place of the semitransparent plane mirror, and the distance between the semitransparent concave mirror and the semitransparent convex mirror is increased, thereby succeeding in correcting field curvature and coma almost completely. 
     In U.S. Reissued Pat. No. 27,356, the optical elements having semitransparent surfaces can be handled as thin lenses, and therefore, chromatic aberration is not a serious problem. However, in the above-described prior application, a thick lens having two semitransparent curved surfaces is used, and therefore, the problem of chromatic aberration cannot be ignored. Accordingly, it is not easy to obtain an optical system which satisfies the demand for a wide field angle and a large pupil diameter. 
     Thus, it is necessary in order to obtain a wide field angle and a large pupil diameter to solve the problem of both axial chromatic aberration and lateral chromatic aberration. The causes of the two chromatic aberrations will be explained below with reference to FIG. 2, which shows a concentric optical system. In FIG. 2, the pupil position of the concentric optical system is denoted by reference numeral 1, a first semitransparent curved surface by 2, a second semitransparent curved surface by 3, and an image surface by 4. As shown in the figure, the first semitransparent curved surface 2 is disposed closer to the pupil plane 1, while the second semitransparent curved surface 3 is disposed away from the pupil plane 1. A point on the first semitransparent curved surface 2 at which an axial upper marginal ray a passes through the surface 2 is denoted by reference symbol a-1, and a point on the second semitransparent curved surface 3 at which the axial upper marginal ray a passes through the surface 3 is denoted by reference symbol a-2. A point on the first semitransparent curved surface 2 at which an extra-axial principal ray b passes through the surface 2 is denoted by reference symbol b-1, and a point on the second semitransparent curved surface 3 at which the extra-axial principal ray b passes through the surface 3 is denoted by reference symbol b-2. 
     First, the causes of lateral chromatic aberration will be explained. Herein, lateral chromatic aberration in which the magnification decreases as the wavelength becomes shorter is defined as positive lateral chromatic aberration, whereas lateral chromatic aberration in which the magnification increases as the wavelength becomes shorter is defined as negative lateral chromatic aberration. In a case where the thick lens having the two semitransparent curved surfaces 2 and 3 is formed from a single vitreous material, at the points b-1 and b-2 the ray is subjected to positive refracting action which increases as the wavelength becomes shorter. Accordingly, the magnification at the image surface 4 reduces, resulting in positive lateral chromatic aberration. 
     Next, the causes of axial chromatic aberration will be explained. Herein, axial chromatic aberration in which the focal length shortens as the wavelength becomes shorter is defined as positive axial chromatic aberration, whereas axial chromatic aberration in which the focal length lengthens as the wavelength becomes shorter is defined as negative axial chromatic aberration. At the point a-1, the first semitransparent curved surface 2 has negative power, and therefore, the ray is subjected to negative refracting action which increases as the wavelength becomes shorter, resulting in negative axial chromatic aberration. At the point a-2, the second semitransparent curved surface 3 has positive power, and therefore, the ray is subjected to positive refracting action which increases as the wavelength becomes shorter, resulting in positive axial chromatic aberration. Since the axial chromatic aberrations produced at the points a-1 and a-2 are opposite in direction to each other, these aberrations can cancel each other. However, the axial chromatic aberrations produced at the points a-1 and a-2 considerably differ in quantity from each other, so that these aberrations cannot be canceled by each other. The reason for this is as follows: The axial marginal ray height at the point a-1 is much greater than the axial marginal ray height at the point a-2. Accordingly, the amount of axial chromatic aberration produced at the point a-1 is much larger than the amount of axial chromatic aberration produced at the point a-2. Consequently, at the image surface 4, the focal length lengthens as the wavelength becomes shorter, resulting in negative axial chromatic aberration. 
     When the rays are reflected at the first and second semitransparent curved surfaces 2 and 3, no chromatic aberration is produced. Therefore, there is no effect on either of the axial and lateral chromatic aberrations, as a matter of course. 
     When the field angle is narrow, the radius of curvature of each semitransparent curved surface is large. Therefore, the axial chromatic aberration is a matter of little concern, and only the lateral chromatic aberration becomes a problem. When the field angle widens, the lateral chromatic aberration becomes further conspicuous. In addition, since the radius of curvature of each semitransparent curved surface reduces, the axial chromatic aberration also becomes conspicuous. That is, in a case where the thick lens having the two semitransparent curved surfaces 2 and 3 is formed from a single vitreous material, both the lateral and axial chromatic aberrations become problems, and it becomes essential, in order to obtain an image which is clear as far as the edges of the visual field, to effectively correct the lateral chromatic aberration in particular. 
     The present invention has succeeded in correcting both the lateral and axial chromatic aberrations with good balance and thereby obtaining an image surface of high resolution even in a case where the concentric optical system is formed by using a thick lens having two semitransparent curved surfaces. 
     The chromatic aberration correcting scheme of the present invention will be explained below with reference to FIG. 1. In order to correct chromatic aberration, the vitreous material that fills the space between the two semitransparent curved surfaces 2 and 3 must be formed from vitreous materials which are different in dispersion (Abbe&#39;s number) from each other. The basic principle of the chromatic aberration correcting scheme will be explained below. Referring to FIG. 1, the cemented surface between the different vitreous materials is denoted by reference numeral 5. A point on the first semitransparent curved surface 2 (which is closer to the pupil plane 1) at which the axial upper marginal ray a passes through the surface 2 is denoted by reference symbol a-1. Points on the cemented surface 5 at which the axial upper marginal ray a passes through the surface 5 for the first, second and third time are denoted by reference symbols a-2, a-3, and a-4, respectively. A point on the second semitransparent curved surface 3 (which is away from the pupil plane 1) at which the axial upper margin ray a passes through the surface 3 is denoted by reference symbol a-5. A point on the first semitransparent curved surface 2 at which an extra-axial principal ray b passes through the surface 2 is denoted by reference symbol b-1. Points on the cemented surface 5 at which the extra-axial principal ray b passes through the surface 5 for the first, second and third time are denoted by reference symbols b-2, b-3, and b-4, respectively. A point on the second semitransparent curved surface 3 at which the extra-axial principal ray b passes through the surface 3 is denoted by reference symbol b-5. 
     First, the method of correcting lateral chromatic aberration will be explained. The extra-axial ray bundle b first passes through the first semitransparent curved surface 2, which is closer to the pupil plane 1, and then passes through the second semitransparent curved surface 3, which is away from the pupil plane 1, after passing through the cemented surface 5 of the optical system three times, which is formed from vitreous materials of different dispersion. Thus, the positive lateral chromatic aberration produced at the points b-1 and b-5 is canceled by negative lateral chromatic aberration produced at the points b-2, b-3 and b-4, thereby enabling the lateral chromatic aberration to be corrected at the image surface 4. More specifically, it is preferable to satisfy the following condition: 
     
         ν.sub.1 /ν.sub.2 
    
     where ν 1  is the Abbe&#39;s number of a lens system that constitutes the semitransparent curved surface 2, which is closer to the pupil plane 1, and ν2 is the Abbe&#39;s number of a lens system that constitutes the semitransparent curved surface 3, which is away from the pupil plane 1. 
     With the above-described arrangement, negative lateral chromatic aberration is produced at the points b-2, b-3 and b-4 so as to cancel the positive lateral chromatic aberration produced at the points b-1 and b-5. 
     However, if the optical system is arranged so as to satisfy the condition of ν 1  &lt;ν 2  to correct the lateral chromatic aberration, it becomes difficult to effectively correct the axial chromatic aberration. The reason for this is as follows: At the points a-2 and a-3, negative axial chromatic aberration is produced, whereas, at the point a-4, positive axial chromatic aberration is produced. Therefore, it is difficult to completely cancel the large amount of negative axial chromatic aberration produced at the point a-1. 
     Next, the method of correcting axial chromatic aberration will be explained. To correct axial chromatic aberration completely, it is necessary to satisfy the following condition: 
     
         ν.sub.1 &gt;ν.sub.2 
    
     If the condition is satisfied, positive axial chromatic aberration is produced at the points a-2 and a-3, whereas, at the point a-4, negative axial chromatic aberration is produced. Accordingly, the negative axial chromatic aberration produced at the point a-1 can be canceled almost completely. 
     However, if the optical system is arranged so as to satisfy the condition of ν 1  &gt;ν 2  to correct the axial chromatic aberration, it becomes difficult to effectively correct the lateral chromatic aberration. The reason for this is that at all the points b-2, b-3 and b-4, positive lateral chromatic aberration is produced, and it becomes impossible to cancel the positive lateral chromatic aberration produced at the points b-1 and b-5. 
     As described above, the lateral chromatic aberration correcting scheme and the axial chromatic aberration correcting scheme run counter to each other. Therefore, it is difficult to correct both the chromatic aberrations simultaneously. To cope with the demand for achievement of a wide field angle, it is important to minimize axial chromatic aberration while effectively correcting lateral chromatic aberration. Accordingly, it is essential to correct lateral chromatic aberration with priority to axial chromatic aberration by setting the Abbe&#39;s numbers of the optical components of the optical system so as to satisfy the condition of ν 1  &lt;ν 2 . 
     When the Abbe&#39;s numbers of the optical components of the optical system are set so as to satisfy the condition ν 1  &lt;ν 2 , if the value of ν 1  /ν 2  is small, sufficiently large negative lateral chromatic aberration can be produced at the points b-2, b-3 and b-4 to cancel the positive lateral chromatic aberration produced at the points b-1 and b-5. In this case, however, the negative axial chromatic aberration produced at the points a-2 and a-3 becomes excessively large, so that the negative axial chromatic aberration produced at the point a-1 is undesirably multiplied. Conversely, if the value of ν 1  /ν 2  is excessively large when the Abbe&#39;s numbers of the optical components of the optical system are set so as to satisfy the condition ν 1  &lt;ν 2 , it is possible to suppress the negative axial chromatic aberration produced at the points a-2 and a-3, and hence possible to reduce the amount of negative axial chromatic aberration produced in the entire optical system. In this case, however, the amount of negative lateral chromatic aberration produced at the points b-2, b-3 and b-4 is insufficient, so that the positive lateral chromatic aberration undesirably remains uncorrected in the optical system. 
     To correct both lateral and axial chromatic aberrations with good balance, it is essential to satisfy the following condition: 
     
         0.2&lt;ν.sub.1 /ν.sub.2 &gt;1.00                           1 
    
     If the relationship between the Abbe&#39;s numbers of the vitreous materials of the lenses constituting the optical system, i.e. ν 1  /ν 2 , is not larger than the lower limit of the above condition, i.e. 0.2, an excessively large amount of axial chromatic aberration is produced, resulting in an increase in the chromatic difference of focus (i.e. the amount of shift of focus according to color). Conversely, if ν 1  /ν 2  is not smaller than the upper limit of the above condition, i.e. 1.00, an excessively large amount of lateral chromatic aberration is produced, resulting in an increase in the chromatic difference of magnification (i.e. the amount of deviation of magnification according to color). Accordingly, ν 1  /ν 2  which falls outside the range of the above condition is unfavorable from the viewpoint of practical use. 
     In a case where an image of higher resolution is required, the axial and lateral chromatic aberrations must be corrected with better balance. Therefore, it is preferable to satisfy the following condition: 
     
         0.4&lt;ν.sub.1 /ν.sub.2 &lt;0.98                           1&#39; 
    
     The upper and lower limits of the above condition have been set for the reasons stated above. 
     When a wide field angle of 40° or more is required, there must be an increase in the angle of incidence of the extra-axial principal ray b on the first semitransparent curved surface 2, which is closer to the pupil plane 1, and also on the second semitransparent curved surface 3, which is away from the pupil plane 1. Accordingly, astigmatism is likely to occur. In addition, a wide field angle of 40° or more causes an increase of the difference between the angles of incidence of extra-axial upper and lower ray bundles on each of the semitransparent curved surfaces 2 and 3. Therefore, occurrence of comatic aberration is unavoidable. When a wide field angle of 40° or more is required, it is necessary, in order to minimize the amount of astigmatism and coma produced in the optical system, to reduce the radii of curvature of the two semitransparent curved surfaces 2 and 3 to thereby reduce the angle of incidence of the extra-axial ray bundle on the two semitransparent curved surfaces 2 and 3. By doing so, however, the axial ray bundle is subjected to larger refracting action by the two semitransparent curved surfaces 2 and 3. Consequently, the dispersion of the axial ray bundle inevitably becomes large, resulting in an increase of the chromatic difference of focus. It is necessary in order to obtain a clear image not only to effectively correct off-axis aberrations such as astigmatism and coma but also to minimize the chromatic difference of focus. To minimize the chromatic difference of focus, it is necessary to reduce the difference between the Abbe&#39;s numbers of the optical components constituting the semitransparent curved surfaces 2 and 3. Therefore, when a wide field angle of 40° or more is required, it is essential to satisfy the following condition: 
     
         0.5&lt;ν.sub.1 /ν.sub.2 &lt;0.98                           2 
    
     The upper and lower limits of the above condition have been set for the reasons stated above. 
     In a case where an image of higher resolution is required, the chromatic difference of focus should preferably be further minimized. Therefore, it is essential to satisfy the following condition: 
     
         0.6&lt;ν.sub.1 /ν.sub.2 &lt;0.98                           2&#39; 
    
     The upper and lower limits of the above condition have been set for the reasons stated above. 
     When a wide field angle of 40° or more is given, the pupil may be frequently rolled to observe the edges of the visual field. In this case, if a sufficiently large pupil diameter is not given, the edges of the visual field look unsharp. Thus, it becomes impossible to clearly observe the edges of the visual field. Therefore, in a case where a wide field angle is provided, and there are many occasions to observe the edges of the visual field, a large pupil diameter is required. 
     Increase of the pupil diameter causes an increase in the difference between the refracting action which the rim portion of the axial ray bundle undergoes and the refracting action which the paraxial portion of the axial ray bundle undergoes at the semitransparent curved surface 2, which is closer to the pupil plane 1, and also at the semitransparent curved surface 3, which is away from the pupil plane 1. Accordingly, spherical aberration is likely to occur. In addition, there is a further increase in the difference between the angle of incidence of the extra-axial upper ray bundle and that of the extra-axial lower ray bundle at the two semitransparent curved surfaces 2 and 3. Therefore, coma is likely to occur. When the field angle is as wide as 40° or more, and the pupil diameter is as large as 10 millimeters or more, the radii of curvature of the two semitransparent curved surfaces 2 and 3 must be increased in order to effectively correct both spherical and comatic aberrations. By doing so, the refracting action which the axial ray bundle undergoes at the two semitransparent curved surfaces 2 and 3 reduces, and the difference between the incidence angles of the extra-axial upper and lower ray bundles also reduces. Accordingly, it becomes possible to minimize the amount of spherical and comatic aberration produced in the optical system. 
     On the other hand, since the angle of incidence of the extra-axial principal ray b on the two semitransparent curved surfaces 2 and 3 increases, the extra-axial principal ray b is considerably refracted at the two semitransparent curved surfaces 2 and 3, resulting in an increase in the dispersion of the extra-axial principal ray b, and thus causing an increase in the chromatic difference of magnification. To minimize the chromatic difference of magnification, it is essential to increase the difference between the Abbe&#39;s numbers of the optical components constituting the two semitransparent curved surfaces 2 and 3. Therefore, when the field angle is 40° or more, and the pupil diameter is 10 millimeters or more, it is essential to satisfy the following condition: 
     
         0.5&lt;ν.sub.1 /ν.sub.2 &lt;0.95                           3 
    
     The upper and lower limits of the above condition have been set for the reasons stated above. 
     In a case where an image of higher resolution is required, the chromatic difference of magnification should preferably be further minimized. Therefore, it is essential to satisfy the following condition: 
     
         0.5&lt;ν.sub.1 /ν.sub.2 &lt;0.90                           3&#39; 
    
     The upper and lower limits of the above condition have been set for the reasons stated above. 
     Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification. 
     The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a view used to explain the basic arrangement of the concentric optical system according to the present invention and the reason why the amount of chromatic aberration produced in the concentric optical system is small. 
     FIG. 2 is a view used to explain the reasons for chromatic aberration produced in a concentric optical system which is formed from a single vitreous material. 
     FIG. 3 is a sectional view of Example 1 of the concentric optical system according to the present invention. 
     FIG. 4 is a sectional view of Example 2 of the present invention. 
     FIG. 5 is a sectional view of Example 3 of the present invention. 
     FIG. 6 is a sectional view of Example 4 of the present invention. 
     FIG. 7 is a sectional view of Example 5 of the present invention. 
     FIG. 8 is a sectional view of Example 6 of the present invention. 
     FIG. 9 is a sectional view of Example 7 of the present invention. 
     FIG. 10 is a sectional view of Example 8 of the present invention. 
     FIG. 11 is a sectional view of Example 9 of the present invention. 
     FIGS. 12(a) to 12(d) (10) graphically show spherical aberration, astigmatism, distortion and lateral aberration in Example 1. 
     FIGS. 13(a) to 13(d) (10) graphically show various aberrations in Example 2 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIGS. 14(a) to 14(d) (10) graphically show various aberrations in Example 3 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIGS. 15(a) to 15(d) (10) graphically show various aberrations in Example 4 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIGS. 16(a) to 16(d) (10) graphically show various aberrations in Example 5 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIGS. 17(a) to 17(d) (10) graphically show various aberrations in Example 6 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIGS. 18(a) to 18(d) (10) graphically show various aberrations in Example 7 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIGS. 19(a) to 19(d) (10) graphically show various aberrations in Example 8 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIGS. 20(a) to 20(d) (10) graphically show various aberrations in Example 9 in the same way as in FIGS. 12(a) to 12(d) (10). 
     FIG. 21 is a perspective view of an example in which the concentric optical system of the present invention is used as an imaging optical system in a finder optical system of a compact camera. 
     FIG. 22 is a sectional view of an example in which the concentric optical system of the present invention is used as a part of an objective. 
     FIGS. 23(a) and 23(b) show an example in which the concentric optical system of the present invention is used as an ocular optical system of a head-mounted display system. 
     FIG. 24 is a sectional view of one example of a conventional reflecting telephoto objective. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Examples 1 to 9 of the concentric optical system according to the present invention will be described below with reference to the accompanying drawings. 
     EXAMPLE 1 
     Example 1 of the present invention will be explained below with reference to FIG. 3. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Examples of numerical values in this example will be shown later. In the following numerical data, nd denotes the refractive index of the lens for the spectral d-line, and νd denotes the Abbe&#39;s number (the same shall apply hereinafter). 
     In this example, the field angle is 20°, the pupil diameter is 15 millimeters, the focal length is 40 millimeters, and F-number is 2.7. The value of the condition ν 1  /ν 2  is 0.448. 
     FIGS. 12(a) (1), 12(b), 12(c) and 12(d) (10) graphically show spherical aberration, astigmatism, distortion and lateral aberration, respectively, in this example. 
     EXAMPLE 2 
     Example 2 of the present invention will be explained below with reference to FIG. 4. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 20°, the pupil diameter is 6 millimeters, the focal length is 40 millimeters, and F-number is 6.7. The value of the condition ν 1  /ν 2  is 0.971. 
     FIGS. 13(a) to 13(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     EXAMPLE 3 
     Example 3 of the present invention will be explained below with reference to FIG. 5. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 40°, the pupil diameter is 3 millimeters, the focal length is 40 millimeters, and F-number is 13.3. The value of the condition ν 1  /ν 2  is 0.931. 
     FIGS. 14(a) to 14(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     EXAMPLE 4 
     Example 4 of the present invention will be explained below with reference to FIG. 6. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 80°, the pupil diameter is 6 millimeters, the focal length is 40 millimeters, and F-number is 6.7. The value of the condition ν 1  /ν 2  is 0.835. 
     FIGS. 15(a) to 15(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     EXAMPLE 5 
     Example 5 of the present invention will be explained below with reference to FIG. 7. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 40°, the pupil diameter is 20 millimeters, the focal length is 40 millimeters, and F-number is 2.0. The value of the condition ν 1  /ν 2  is 0.695. 
     FIGS. 16(a) to 16(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     EXAMPLE 6 
     Example 6 of the present invention will be explained below with reference to FIG. 8. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 80°, the pupil diameter is 10 millimeters, the focal length is 40 millimeters, and F-number is 4.0. The value of the condition ν 1  /ν 2  is 0.798. 
     FIGS. 17(a) to 17(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     EXAMPLE 7 
     Example 7 of the present invention will be explained below with reference to FIG. 9. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Reference symbols P1 and P2 denote polarizing optical elements, for example, polarizing plates, quarter-wave plates, etc. (as one specific example, P1 is a polarizing optical element having a polarizing plate stacked on the pupil side thereof and a quarter-wave plate stacked on the image surface side thereof; and P2 is a quarter-wave plate). In this example, the polarizing optical elements P1 and P2 are disposed to cut off flare light that passes through the first and second semitransparent reflecting surfaces 2 and 3 and reaches the image surface 4 without being reflected by either of the first and second semitransparent reflecting surfaces 2 and 3. Further, in this example, a plano-convex lens L is disposed between the pupil position 1 and the first semitransparent reflecting surface 2. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 90°, the pupil diameter is 10 millimeters, the focal length is 45 millimeters, and F-number is 4.5. The value of the condition ν 1  /ν 2  is 0.552. 
     FIGS. 18(a) to 18(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     EXAMPLE 8 
     Example 8 of the present invention will be explained below with reference to FIG. 10. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. Reference symbols L1 and L2 denote lenses. In this example, the lenses L1 and L2 are cemented to both sides, respectively, of a thick lens having the two semitransparent curved surfaces 2 and 3 in order to correct off-axis aberrations, e.g. coma and astigmatism, even more effectively. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 80°, the pupil diameter is 8 millimeters, the focal length is 20 millimeters, and F-number is 2.5. The value of the condition ν 1  /ν 2  is 0.674. 
     FIGS. 19(a) to 19(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     EXAMPLE 9 
     Example 9 of the present invention will be explained below with reference to FIG. 11. In the figure, reference numeral 1 denotes a pupil position, 2 a first semitransparent reflecting surface, 3 a second semitransparent reflecting surface, 4 an image surface, and 5 a cemented surface. In this example, power is given to the cemented surface 5 between two vitreous materials which are different in dispersion from each other. Examples of numerical values in this example will be shown later. 
     In this example, the field angle is 60°, the pupil diameter is 10 millimeters, the focal length is 45 millimeters, and F-number is 4.0. The value of the condition ν 1  /ν 2  is 0.851. 
     FIGS. 20(a) to 20(d) (10) graphically show various aberrations in this example in the same way as in FIGS. 12(a) to 12(d) (10). 
     Numerical data in the above-described examples will be shown below. 
     
         ______________________________________Surface Curvature      SurfaceNo.     radius         separation nd    νd______________________________________Example 11       pupil position 1                  43.3262       -443.9127      4.000      1.7158                                   29.43       ∞        21.915     1.5382                                   65.54       -104.8939      -21.915    1.5382                                   65.5   (reflecting surface 3)5       ∞        -4.000     1.7158                                   29.46       -443.9127      4.000      1.7158                                   29.4   (reflecting surface 2)7       ∞        21.915     1.5382                                   65.58       -104.8939      6.1119       image surface 4Example 21       pupil position 1                  59.2722       -60.9542       4.000      1.4904                                   68.33       ∞        18.777     1.4870                                   70.44       -62.4049       -18.777    1.4870                                   70.4   (reflecting surface 3)5       ∞        -4.000     1.4904                                   68.36       -60.9542       4.000      1.4904                                   68.3   (reflecting surface 2)7       ∞        18.777     1.4870                                   70.48       -62.4049       2.0009       image surface 4Example 31       pupil position 1                  52.0952       -52.7218       4.000      1.4971                                   65.53       ∞        13.778     1.4870                                   70.44       -54.4350       -13.778    1.4870                                   70.4   (reflecting surface 3)5       ∞        -4.000     1.4971                                   65.56       -52.7218       4.000      1.4971                                   65.5   (reflecting surface 2)7       ∞        13.778     1.4870                                   70.48       -54.4350       9.0049       image surface 4Example 41       pupil position 1                  33.2772       -54.0726       4.000      1.5181                                   55.83       ∞        15.236     1.5227                                   66.84       -56.9032       -15.236    1.5227                                   66.8   (reflecting surface 3)5       ∞        -4.000     1.5181                                   55.86       -54.0726       4.000      1.5181                                   55.8   (reflecting surface 2)7       ∞        15.236     1.5227                                   66.88       -56.9032       7.5909       image surface 4Example 51       pupil position 1                  36.7112       -100.9813      4.000      1.5768                                   41.93       ∞        22.553     1.6200                                   60.34       -79.5946       -22.553    1.6200                                   60.3   (reflecting surface 3)5       ∞        -4.000     1.5768                                   41.96       -100.9813      4.000      1.5768                                   41.9   (reflecting surface 2)7       ∞        22.553     1.6200                                   60.38       -79.5946       2.0009       image surface 4Example 61       pupil position 1                  31.0982       -58.3138       4.000      1.5292                                   52.23       ∞        17.350     1.5399                                   65.44       -60.7829       -17.350    1.5399                                   65.4   (reflecting surface 3)5       ∞        -4.000     1.5292                                   52.26       -58.3138       4.000      1.5292                                   52.2   (reflecting surface 2)7       ∞        17.350     1.5399                                   65.48       -60.7829       5.1509       image surface 4Example 71       pupil position 1                  28.2392       ∞        4.000      1.5163                                   64.13       ∞ (lensL)                  12.000     1.7550                                   27.64       -164.4962      5.0005       -94.5660       2.000      1.6274                                   35.66       ∞        2.000      1.5163                                   64.17       ∞        17.969     1.5517                                   64.58       -79.3677       -17.969    1.5517                                   64.5   (reflecting surface 3)9       ∞        -2.000     1.5163                                   64.110      ∞        -2.000     1.6274                                   35.611      -94.5660       2.000      1.6274                                   35.6   (reflecting surface 2)12      ∞        2.000      1.5163                                   64.113      ∞        17.969     1.5517                                   64.514      -79.3677       8.08515      image surface 4Example 81       pupil position 1                  6.9982       ∞ (lensL 1)                  18.000     1.5163                                   64.13       -39.2062       0.750      1.6209                                   37.34       ∞        10.033     1.6480                                   55.35       -37.5176       -10.033    1.6480                                   55.3   (reflecting surface 3)6       ∞        -0.750     1.6209                                   37.37       -39.2062       0.750      1.6209                                   37.3   (reflecting surface 2)8       ∞        10.033     1.6480                                   55.39       -37.5176 (lensL 2)                  0.750      1.5163                                   64.110      ∞        2.00011      image surface 4Example 91       pupil position 1                  35.0122       -61.8973       4.000      1.5139                                   57.33       181.9043       16.203     1.5172                                   67.34       -63.0690       -16.203    1.5172                                   67.3   (reflecting surface 3)5       181.9043       -4.000     1.5139                                   57.36       -61.8973       4.000      1.5139                                   57.3   (reflecting surface 2)7       181.9043       16.203     1.5172                                   67.38       -63.0690       10.7619       image surface 4______________________________________ 
    
     It should be noted that the concentric optical system of the present invention may be provided as one lens in an ocular optical system or an imaging optical system. Alternatively, the concentric optical system alone may constitute an ocular optical system or an imaging optical system. Examples of such arrangements will be shown below. The concentric optical system of the present invention may be applied to imaging optical systems as follows: As shown, for example, in the perspective view of FIG. 21, the concentric optical system of the present invention may be used in a finder optical system F i  of a compact camera C a  in which a photographic optical system O b  and the finder optical system F i  are provided separately in substantially parallel to each other. Further, as shown in the sectional view of FIG. 22, a concentric optical system ML of the present invention, which is composed of first and second semitransparent reflecting surfaces 2 and 3, may be disposed behind a front lens group GF and an aperture diaphragm D with their centers of curvature made approximately coincident with the point of intersection between the plane of the diaphragm D and the optical axis, thereby constituting an objective lens system L o . An image that is formed by the objective lens system L O  is erected by a Porro prism erecting system, in which there are four reflections, provided at the observer side of the objective lens system L o , thereby enabling an erect image to be observed through an ocular lens O c . 
     Further, when used as an imaging optical system, the concentric optical system of the present invention may be arranged as a front-diaphragm optical system. 
     As an ocular optical system, the concentric optical system of the present invention may be used, as shown for example in the perspective view of FIG. 23(a), for a head-mounted display system HMD designed so that a virtual image is projected in an eyeball of an observer M as a magnified image, thereby enabling the observer M to view a virtual aerial magnified image. In this case, as shown in the sectional view of FIG. 23(b), an ocular optical system is composed of a liquid crystal display device LCD for displaying an image, and a concentric optical system ML of the present invention, which is composed of first and second semitransparent reflecting surfaces 2 and 3. The concentric optical system ML is disposed such that the centers of curvature of the first and second semitransparent reflecting surfaces 2 and 3 lie in the vicinity of an eye point (pupil position) EP on the observer side, in order to project an image displayed on the liquid crystal display device LCD in the observer&#39;s eyeball as a magnified image. 
     As will be clear from the foregoing description, it is possible according to the present invention to obtain a concentric optical system usable as either an imaging optical system or an ocular optical system, which enables a clear image to be obtained at a field angle of up to about 90° and with a pupil diameter of up to about 10 millimeter with substantially no aberration. By using such a concentric optical system, it is possible to provide, for example, a head-mounted display system which enables observation of an image that is clear as far as the edges of the visual field at a wide presentation field angle.