Multiple prism image forming optical system

A high-performance image-forming optical system made compact and thin by folding an optical path using reflecting surfaces arranged to minimize the number of reflections. The image-forming optical system has a first prism placed on the object side and a second prism placed on the image side and does not form an intermediate image. The first and second prisms each have a first surface through which a light beam enters the prism, a second surface reflecting the incident light beam in the prism, a third surface reflecting the reflected light beam in the prism, and a fourth surface through which the light beam exits from the prism. At least one of the second and third surfaces has a rotationally asymmetric curved surface configuration that gives a power to a light beam and corrects aberrations due to decentration. Any optical element that gives a refracting power contributing to the image-forming action of a light beam is not placed between the second prism and an image formed by the image-forming optical system.

BACKGROUND OF THE INVENTION
 1. Field of the Invention
 The present invention relates to image-forming optical systems. More
 particularly, the present invention relates to a decentered optical system
 with a reflecting surface having a power for use in optical apparatuses
 using a small-sized image pickup device, e.g. video cameras, digital still
 cameras, film scanners, and endoscopes.
 2. Description of the Invention
 Recently, with the achievement of small-sized image pickup devices,
 image-forming optical systems have also been demanded to reduce the size,
 weight, and the cost of video cameras, digital still cameras, film
 scanners, endoscopes, etc.
 In the general rotationally symmetric coaxial optical systems, however,
 optical elements are arranged in the direction of the optical axis.
 Therefore, there is a limit to the reduction in thickness of the optical
 systems. At the same time, the number of lens elements unavoidably
 increases because it is necessary to correct chromatic aberration produced
 by a rotationally symmetric refracting lens used in the optical systems.
 Therefore, it is difficult to reduce the cost in the present state of the
 art. Under these circumstances, there have recently been proposed optical
 systems designed to be compact in size by giving a power to a reflecting
 surface, which produces no chromatic aberration, and folding an optical
 path in the optical axis direction.
 Japanese Patent Application Unexamined Publication Number [hereinafter
 referred to as "JP(A)"] 7-333505 proposes to reduce the thickness of an
 optical system by giving a power to a decentered reflecting surface and
 folding an optical path. In an example thereof, however, the number of
 constituent optical members is as large as five, and actual optical
 performance is unclear. No mention is made of the configuration of the
 reflecting surface.
 JP(A) 8-292371, 9-5650 and 9-90229 each disclose an optical system in which
 an optical path is folded by a single prism or a plurality of mirrors
 integrated into a single block, and an image is relayed in the optical
 system to form a final image. In these conventional examples, however, the
 number of reflections increases because the image is relayed. Accordingly,
 surface accuracy errors and decentration accuracy errors are transferred
 while being added up. Consequently, the accuracy required for each surface
 becomes tight, causing the cost to increase unfavorably. The relay of the
 image also causes the overall volumetric capacity of the optical system to
 increase unfavorably.
 JP(A) 9-222563 discloses an example of an optical system that uses a
 plurality of prisms. However, because the optical system is arranged to
 relay an image, the cost increases and the optical system becomes large in
 size unfavorably for the same reasons as stated above.
 JP(A) 9-211331 discloses an example of an optical system in which an
 optical path is folded by using a single prism to achieve a reduction in
 size of the optical system. However, the optical system is not
 satisfactorily corrected for aberrations.
 JP(A) 8-292368, 8-292372, 9-222561, 9-258105 and 9-258106 all disclose
 examples of zoom lens systems. In these examples, however, the number of
 reflections is undesirably large because an image is relayed in a prism.
 Therefore, surface accuracy errors and decentration accuracy errors of
 reflecting surfaces are transferred while being added up, unfavorably. At
 the same time, the overall size of the optical system unavoidably
 increases, unfavorably.
 JP(A) 10-20196 discloses an example of a two-unit zoom lens system having a
 positive front unit and a negative rear unit, in which the positive front
 unit comprises a prism of negative power placed on the object side of a
 stop and a prism of positive power placed on the image side of the stop.
 JP(A) 10-20196 also discloses an example in which the positive front unit,
 which comprises a prism of negative power and a prism of positive power,
 is divided into two to form a three-unit zoom lens system having a
 negative unit, a positive unit and a negative unit. However, the prisms
 used in these examples each have two transmitting surfaces and two
 reflecting surfaces, which are all independent surfaces. Therefore, a
 relatively wide space must be ensured for the prisms. In addition, the
 image plane is large in size to conform to the Leica size film format.
 Accordingly, the prisms themselves become unavoidably large in size.
 Furthermore, because the disclosed zoom lens systems are not telecentric
 on the image side, it is difficult to apply them to image pickup devices
 such as CCDs. In either of the examples of zoom lens systems, zooming is
 performed by moving the prisms. Accordingly, the decentration accuracy
 required for the reflecting surfaces becomes tight in order to maintain
 the required performance over the entire zooming range, resulting in an
 increase in the cost.
 The above-mentioned JP(A) 10-20196 discloses an optical system having, as
 shown in FIG. 17, a first prism 210, a stop 202, a second prism 220
 similar to the first prism 210, a refracting lens 204, and an image plane
 203. The first prism 210 has a first transmitting surface 211, a first
 reflecting surface 212, a second reflecting surface 213, and a second
 transmitting surface 214. The second prism 220 has a first transmitting
 surface 221, a first reflecting surface 222, a second reflecting surface
 223, and a second transmitting surface 224. In this optical system,
 however, a principal ray a entering the first prism 210 and a principal
 ray b exiting from the first prism 210 (principal ray entering the second
 prism 220 ) and further a principal ray c exiting from the second prism
 220 lie approximately parallel to each other, and the principal rays a and
 c extend in an approximately straight line. Moreover, the second prism 220
 is placed right behind the first prism 210 in series, and the lens 204,
 which has a refracting power, is placed between the second prism 220 and
 the image plane 203. Therefore, the degree of design freedom is limited to
 a considerable extent. In addition, it is difficult to make the optical
 system thin in the direction of the thickness.
 When a general refracting optical system is used to obtain a desired
 refracting power, chromatic aberration occurs at an interface surface
 thereof according to chromatic dispersion characteristics of an optical
 element. To correct the chromatic aberration and also correct other ray
 aberrations, the refracting optical system needs a large number of
 constituent elements, causing the cost to increase. In addition, because
 the optical path extends straight along the optical axis, the entire
 optical system undesirably lengthens in the direction of the optical axis,
 resulting in an unfavorably large-sized image pickup apparatus.
 In decentered optical systems such as those described above in regard to
 the prior art, an imaged figure or the like is undesirably distorted and
 the correct shape cannot be reproduced unless the formed image is
 favorably corrected for aberrations, particularly rotationally asymmetric
 distortion.
 Furthermore, in a case where a reflecting surface is used in a decentered
 optical system, the sensitivity to decentration errors of the reflecting
 surface is twice as high as that in the case of a refracting surface, and
 as the number of reflections increases, decentration errors that are
 transferred while being added up increase correspondingly. Consequently,
 manufacturing accuracy and assembly accuracy, e.g. surface accuracy and
 decentration accuracy, required for reflecting surfaces become even more
 strict.
 SUMMARY OF THE INVENTION
 In view of the above-described problems of the prior art, an object of the
 present invention is to provide a high-performance and low-cost
 image-forming optical system having a minimal number of constituent
 optical elements.
 Another object of the present invention is to provide a high-performance
 image-forming optical system that is made compact and thin by folding an
 optical path using reflecting surfaces arranged to minimize the number of
 reflections.
 To attain the above-described objects, the present invention provides an
 image-forming optical system having a positive refracting power as a whole
 for forming an object image. The image-forming optical system has a first
 prism and a second prism, which are each formed from a medium having a
 refractive index (n) larger than 1 (n&gt;1). The second prism is placed on
 the image side of the first prism. The image-forming optical system does
 not form an intermediate image. The first prism has, in order from the
 object side thereof, a first surface through which a light beam enters the
 first prism, and a second surface that reflects the light beam in the
 first prism. The first prism further has a third surface that reflects the
 reflected light beam in the first prism, and a fourth surface through
 which the light beam exits from the first prism. At least one of the
 second and third surfaces of the first prism has a curved surface
 configuration that gives a power to a light beam. The curved surface
 configuration has a rotationally asymmetric surface configuration that
 corrects aberrations due to decentration. The second prism has, in order
 from the object side thereof, a first surface through which a light beam
 enters the second prism, and a second surface that reflects the light beam
 in the second prism. The second prism further has a third surface that
 reflects the reflected light beam in the second prism, and a fourth
 surface through which the light beam exits from the second prism. At least
 one of the second and third surfaces of the second prism has a curved
 surface configuration that gives a power to a light beam. The curved
 surface configuration has a rotationally asymmetric surface configuration
 that corrects aberrations due to decentration. Any optical element that
 gives a refracting power contributing to the image-forming action of a
 light beam is not placed between the second prism and an image formed by
 the image-forming optical system.
 Another image-forming optical system according to the present invention,
 which is provided to attain the above-described objects, is an
 image-forming optical system having a positive refracting power as a whole
 for forming an object image. The image-forming optical system has a first
 prism and a second prism, which are each formed from a medium having a
 refractive index (n) larger than 1 (n&gt;1). The second prism is placed on
 the image side of the first prism. The image-forming optical system does
 not form an intermediate image. The first prism has, in order from the
 object side thereof, a first surface through which a light beam enters the
 first prism, and a second surface that reflects the light beam in the
 first prism. The first prism further has a third surface that reflects the
 reflected light beam in the first prism, and a fourth surface through
 which the light beam exits from the first prism. At least one of the
 second and third surfaces of the first prism has a curved surface
 configuration that gives a power to a light beam. The curved surface
 configuration has a rotationally asymmetric surface configuration that
 corrects aberrations due to decentration. The second prism has, in order
 from the object side thereof, a first surface through which a light beam
 enters the second prism, and a second surface that reflects the light beam
 in the second prism. The second prism further has a third surface that
 reflects the reflected light beam in the second prism, and a fourth
 surface through which the light beam exits from the second prism. At least
 one of the second and third surfaces of the second prism has a curved
 surface configuration that gives a power to a light beam. The curved
 surface configuration has a rotationally asymmetric surface configuration
 that corrects aberrations due to decentration. The second prism is
 arranged such that the axial principal ray that is led from the third
 surface of the second prism to the fourth surface of the second prism is
 closer to the axial principal ray that is led from the third surface of
 the first prism to the fourth surface of the first prism than the axial
 principal ray of the light beam incident on the first prism that is led
 from the first surface of the first prism to the second surface of the
 first prism and the extension of this axial principal ray.
 Still another image-forming optical system according to the present
 invention, which is provided to attain the above-described objects, is an
 image-forming optical system having a positive refracting power as a whole
 for forming an object image. The image-forming optical system has a first
 prism and a second prism, which are each formed from a medium having a
 refractive index (n) larger than 1 (N&gt;1). The second prism is placed on
 the image side of the first prism. The image-forming optical system does
 not form an intermediate image. The first prism has, in order from the
 object side thereof, a first surface through which a light beam enters the
 first prism, and a second surface that reflects the light beam in the
 first prism. The first prism further has a third surface that reflects the
 reflected light beam in the first prism, and a fourth surface through
 which the light beam exits from the first prism. At least one of the
 second and third surfaces of the first prism has a curved surface
 configuration that gives a power to a light beam. The curved surface
 configuration has a rotationally asymmetric surface configuration that
 corrects aberrations due to decentration. The second prism has, in order
 from the object side thereof, a first surface through which a light beam
 enters the second prism, and a second surface that reflects the light beam
 in the second prism. The second prism further has a third surface that
 reflects the reflected light beam in the second prism, and a fourth
 surface through which the light beam exits from the second prism. At least
 one of the second and third surfaces of the second prism has a curved
 surface configuration that gives a power to a light beam. The curved
 surface configuration has a rotationally asymmetric surface configuration
 that corrects aberrations due to decentration. The fourth surface of the
 first prism and the first surface of the second prism face each other. The
 third surface of the second prism does not face the second surface of the
 first prism but lies closer to the fourth surface of the first prism than
 the second surface of the first prism. Consequently, the first and second
 surfaces of the first prism and the third and fourth surfaces of the
 second prism and further the image plane do not lie in parallel on a line
 extending straight from the axial principal ray entering the first prism.
 The third and fourth surfaces of the second prism and the image plane are
 off the line extending straight from the axial principal ray entering the
 first prism.
 The reasons for adopting the above-described arrangements in the present
 invention, together with the functions thereof, will be described below in
 order.
 The first image-forming optical system according to the present invention,
 which is provided to attain the above-described objects, has a first prism
 and a second prism, which are each formed from a medium having a
 refractive index (n) larger than 1 (N&gt;1). The second prism is placed on
 the image side of the first prism. The image-forming optical system does
 not form an intermediate image.
 A refracting optical element such as a lens is provided with a power by
 giving a curvature to an interface surface thereof. Accordingly, when rays
 are refracted at the interface surface of the lens, chromatic aberration
 unavoidably occurs according to chromatic dispersion characteristics of
 the refracting optical element. Consequently, the common practice is to
 add another refracting optical element for the purpose of correcting the
 chromatic aberration.
 Meanwhile, a reflecting optical element such as a mirror or a prism
 produces no chromatic aberration in theory even when a reflecting surface
 thereof is provided with a power, and need not add another optical element
 only for the purpose of correcting chromatic aberration. Accordingly, an
 optical system using a reflecting optical element allows the number of
 constituent optical elements to be reduced from the viewpoint of chromatic
 aberration correction in comparison to an optical system using a
 refracting optical element.
 At the same time, a reflecting optical system using a reflecting optical
 element allows the optical system itself to be compact in size in
 comparison to a refracting optical system because the optical path is
 folded in the reflecting optical system.
 Reflecting surfaces require a high degree of accuracy for assembly and
 adjustment because they have high sensitivity to decentration errors in
 comparison to refracting surfaces. However, among reflecting optical
 elements, prisms, in which the positional relationship between surfaces is
 fixed, only need to control decentration as a single unit of prism and do
 not need high assembly accuracy and a large number of man-hours for
 adjustment as are needed for other reflecting optical elements.
 Furthermore, a prism has an entrance surface and an exit surface, which are
 refracting surfaces, and a reflecting surface. Therefore, the degree of
 freedom for aberration correction is high in comparison to a mirror, which
 has only a reflecting surface. In particular, if the prism reflecting
 surface is assigned the greater part of the desired power to thereby
 reduce the powers of the entrance and exit surfaces, which are refracting
 surfaces, it is possible to reduce chromatic aberration to a very small
 quantity in comparison to refracting optical elements such as lenses while
 maintaining the degree of freedom for aberration correction at a high
 level in comparison to mirrors. Furthermore, the inside of a prism is
 filled with a transparent medium having a refractive index higher than
 that of air. Therefore, it is possible to obtain a longer optical path
 length than in the case of air. Accordingly, the use of a prism makes it
 possible to obtain an optical system that is thinner and more compact than
 those formed from lenses, mirrors and so forth, which are placed in the
 air.
 In addition, an image-forming optical system is required to exhibit
 favorable image-forming performance as far as the peripheral portions of
 the image field, not to mention the performance required for the center of
 the image field. In the case of a general coaxial optical system, the sign
 of the ray height of extra-axial rays is inverted at a stop. Accordingly,
 if optical elements are not in symmetry with respect to the stop, off-axis
 aberrations are aggravated. For this reason, the common practice is to
 place refracting surfaces at respective positions facing each other across
 the stop, thereby obtaining a satisfactory symmetry with respect to the
 stop, and thus correcting off-axis aberrations.
 Accordingly, the present invention adopts an arrangement in which two
 prisms are provided to obtain a satisfactory symmetry with respect to the
 stop, thereby enabling not only axial aberrations but also off-axis
 aberrations to be favorably corrected. If only one prism is provided,
 asymmetry with respect to the stop is enhanced, and off-axis aberrations
 are unavoidably aggravated.
 For the reasons stated above, the present invention adopts a basic
 arrangement in which the image-forming optical system has a first prism
 and a second prism placed on the image side of the first prism and does
 not form an intermediate image. In addition, it is desirable that the
 image-forming optical system should be approximately telecentric on the
 image side.
 Next, the arrangement of an image-forming optical system that is
 approximately telecentric on the image side will be described in detail.
 As has been stated above, reflecting surfaces have a high decentration
 error sensitivity in comparison to refracting surfaces. Therefore, it is
 desirable to provide an arrangement of an optical system that is as
 independent of the high decentration error sensitivity as possible. In the
 case of a general coaxial optical system arranged to be approximately
 telecentric on the image side, because extra-axial principal rays are
 approximately parallel to the optical axis, the positional accuracy of the
 extra-axial rays is satisfactorily maintained on the image plane even if
 defocusing is effected. Therefore, the image-forming optical system
 according to the present invention is arranged to reflect the property of
 the above-described arrangement. In particular, to prevent the performance
 of an optical system using a reflecting surface, which has a relatively
 high decentration error sensitivity, from being deteriorated by focusing,
 it is desirable to adopt an arrangement in which the optical system is
 approximately telecentric on the image side, whereby the positional
 accuracy of extra-axial rays is maintained favorably.
 Such an arrangement enables the present invention to be suitably applied to
 an image pickup optical system using an image pickup device, e.g. a CCD,
 in particular. Adopting the above-described arrangement minimizes the
 influence of the cosine fourth law. Accordingly, it is also possible to
 reduce shading.
 As has been stated above, adopting the basic arrangement of the present
 invention makes it possible to obtain a compact image-forming optical
 system that has a smaller number of constituent optical elements than in
 the case of a refracting optical system and exhibits favorable performance
 throughout the image field, from the center to the periphery thereof.
 In the image-forming optical system according to the present invention, the
 first prism has, in order from the object side thereof, a first surface
 through which a light beam enters the first prism, and a second surface
 that reflects the light beam in the first prism. The first prism further
 has a third surface that reflects the reflected light beam in the first
 prism, and a fourth surface through which the light beam exits from the
 first prism. At least one of the second and third surfaces of the first
 prism has a curved surface configuration that gives a power to a light
 beam. The curved surface configuration has a rotationally asymmetric
 surface configuration that corrects aberrations due to decentration. The
 second prism has, in order from the object side thereof, a first surface
 through which a light beam enters the second prism, and a second surface
 that reflects the light beam in the second prism. The second prism further
 has a third surface that reflects the reflected light beam in the second
 prism, and a fourth surface through which the light beam exits from the
 second prism. At least one of the second and third surfaces of the second
 prism has a curved surface configuration that gives a power to a light
 beam. The curved surface configuration has a rotationally asymmetric
 surface configuration that corrects aberrations due to decentration.
 When a light ray from the object center that passes through the center of
 the stop and reaches the center of the image plane is defined as an axial
 principal ray, it is desirable that at least one reflecting surface in
 each prism should be decentered with respect to the axial principal ray.
 If at least one reflecting surface is not decentered with respect to the
 axial principal ray, the axial principal ray travels along the same
 optical path when incident on and reflected from the reflecting surface,
 and thus the axial principal ray is intercepted in the optical system
 undesirably. As a result, an image is formed from only a light beam whose
 central portion is shaded. Consequently, the center of the image is
 unfavorably dark, or no image is formed in the center of the image field.
 It is also possible to decenter a reflecting surface with a power with
 respect to the axial principal ray.
 When a reflecting surface with a power is decentered with respect to the
 axial principal ray, it is desirable that at least one of surfaces
 constituting a prism used in the present invention should be a
 rotationally asymmetric surface. It is particularly preferable from the
 viewpoint of aberration correction that at least one reflecting surface
 should be a rotationally asymmetric surface.
 The reasons for adopting the above-described arrangements in the present
 invention will be described below in detail.
 First, a coordinate system used in the following description and
 rotationally asymmetric surfaces will be described.
 An optical axis defined by a straight line along which the axial principal
 ray travels until it intersects the first surface of the optical system is
 defined as a Z-axis. An axis perpendicularly intersecting the Z-axis in
 the decentration plane of each surface constituting the image-forming
 optical system is defined as a Y-axis. An axis perpendicularly
 intersecting the optical axis and also perpendicularly intersecting the
 Y-axis is defined as an X-axis. Ray tracing is forward ray tracing in
 which rays are traced from the object toward the image plane.
 In general, a spherical lens system comprising only a spherical lens is
 arranged such that aberrations produced by spherical surfaces, such as
 spherical aberration, coma and curvature of field, are corrected with some
 surfaces by canceling the aberrations with each other, thereby reducing
 aberrations as a whole.
 On the other hand, rotationally symmetric aspherical surfaces and the like
 are used to correct aberrations favorably with a minimal number of
 surfaces. The reason for this is to reduce various aberrations that would
 be produced by spherical surfaces.
 However, in a decentered optical system, rotationally asymmetric
 aberrations due to decentration cannot be corrected by a rotationally
 symmetric optical system. Rotationally asymmetric aberrations due to
 decentration include distortion, curvature of field, and astigmatic and
 comatic aberrations, which occur even on the axis.
 First, rotationally asymmetric curvature of field will be described. For
 example, when rays from an infinitely distant object point are incident on
 a decentered concave mirror, the rays are reflected by the concave mirror
 to form an image. In this case, the back focal length from that portion of
 the concave mirror on which the rays strike to the image surface is a half
 the radius of curvature of the portion on which the rays strike in a case
 where the medium on the image side is air. Consequently, as shown in FIG.
 11, an image surface tilted with respect to the axial principal ray is
 formed. It is impossible to correct such rotationally asymmetric curvature
 of field by a rotationally symmetric optical system.
 To correct the tilted curvature of field by the concave mirror M itself,
 which is the source of the curvature of field, the concave mirror M is
 formed from a rotationally asymmetric surface, and, in this example, the
 concave mirror M is arranged such that the curvature is made strong
 (refracting power is increased) in the positive direction of the Y-axis,
 whereas the curvature is made weak (refracting power is reduced) in the
 negative direction of the Y-axis. By doing so, the tilted curvature of
 field can be corrected. It is also possible to obtain a flat image surface
 with a minimal number of constituent surfaces by placing a rotationally
 asymmetric surface having the same effect as that of the above-described
 arrangement in the optical system separately from the concave mirror M.
 It is preferable that the rotationally asymmetric surface should be a
 rotationally asymmetric surface having no axis of rotational symmetry in
 the surface nor out of the surface. If the rotationally asymmetric surface
 has no axis of rotational symmetry in the surface nor out of the surface,
 the degree of freedom increases, and this is favorable for aberration
 correction.
 Next, rotationally asymmetric astigmatism will be described.
 A decentered concave mirror M produces astigmatism even for axial rays, as
 shown in FIG. 12, as in the case of the above. The astigmatism can be
 corrected by appropriately changing the curvatures in the X- and Y-axis
 directions of the rotationally asymmetric surface as in the case of the
 above.
 Rotationally asymmetric coma will be described below.
 A decentered concave mirror M produces coma even for axial rays, as shown
 in FIG. 13, as in the case of the above. The coma can be corrected by
 changing the tilt of the rotationally asymmetric surface according as the
 distance from the origin of the X-axis increases, and further
 appropriately changing the tilt of the surface according to the sign
 (positive or negative) of the Y-axis.
 The image-forming optical system according to the present invention may
 also be arranged such that the above-described at least one surface having
 a reflecting action is decentered with respect to the axial principal ray
 and has a rotationally asymmetric surface configuration and further has a
 power. By adopting such an arrangement, decentration aberrations produced
 as the result of giving a power to the reflecting surface can be corrected
 by the surface itself. In addition, the power of the refracting surfaces
 of the prism is reduced, and thus chromatic aberration produced in the
 prism can be minimized.
 The rotationally asymmetric surface used in the present invention should
 preferably be a plane-symmetry free-form surface having only one plane of
 symmetry. Free-form surfaces used in the present invention are defined by
 the following equation (a). It should be noted that the Z-axis of the
 defining equation is the axis of a free-form surface.
 ##EQU1##
 In Eq. (a), the first term is a spherical surface term, and the second term
 is a free-form surface term.
 In the spherical surface term:
 c: the curvature at the vertex
 k: a conic constant
 r=(X.sup.2 +Y.sup.2)
 The free-form surface term is given by
 ##EQU2##
 =C.sub.2 X+C.sub.3 Y
 +C.sub.4 X.sup.2 +C.sub.5 XY+C.sub.6 Y.sup.2
 +C.sub.7 X.sup.3 +C.sub.8 X.sup.2 Y+C.sub.9 XY.sup.2 +C.sub.10 Y.sup.3
 +C.sub.11 X.sup.4 +C.sub.12 X.sup.3 Y+C.sub.13 X.sup.2 Y.sup.2 +C.sub.14
 XY.sup.3 +C.sub.15 Y.sup.4
 +C.sub.16 X.sup.5 +C.sub.17 X.sup.4 Y+C.sub.18 X.sup.3 Y.sup.2 +C.sub.19
 X.sup.2 Y.sup.3 +C.sub.20 XY.sup.4 +C.sub.21 Y.sup.5
 +C.sub.22 X.sup.6 +C.sub.23 X.sup.5 Y+C.sub.24 X.sup.4 Y.sup.2 +C.sub.25
 X.sup.3 Y.sup.3 +C.sub.26 X.sup.2 Y.sup.4 +C.sub.27 XY.sup.5 +C.sub.28
 Y.sup.6
 +C.sub.29 X.sup.7 +C.sub.30 X.sup.6 Y+C.sub.31 X.sup.5 Y.sup.2 +C.sub.32
 X.sup.4 Y.sup.3 +C.sub.33 X.sup.3 Y.sup.4
 +C.sub.34 X.sup.2 Y.sup.5 +C.sub.35 XY.sup.6 +C.sub.36 Y.sup.7
 where C.sub.j (j is an integer of 2 or higher) are coefficients.
 In general, the above-described free-form surface does not have planes of
 symmetry in both the XZ- and YZ-planes. In the present invention, however,
 a free-form surface having only one plane of symmetry parallel to the
 YZ-plane is obtained by making all terms with odd-numbered powers of X
 zero. For example, in the above defining equation (a), the coefficients of
 the terms C.sub.2, C.sub.5, C.sub.7, C.sub.9, C.sub.12, C.sub.14,
 C.sub.16, C.sub.18, C.sub.20, C.sub.23, C.sub.25, C.sub.27, C.sub.29,
 C.sub.31, C.sub.33, C.sub.35, . . . are set equal to zero. By doing so, it
 is possible to obtain a free-form surface having only one plane of
 symmetry parallel to the YZ-plane.
 A free-form surface having only one plane of symmetry parallel to the
 XZ-plane is obtained by making all terms with odd-numbered powers of Y
 zero. For example, in the above defining equation (a), the coefficients of
 the terms C.sub.3, C.sub.5, C.sub.8, C.sub.10, C.sub.12, C.sub.14,
 C.sub.17, C.sub.19, C.sub.21, C.sub.23, C.sub.25, C.sub.27, C.sub.30,
 C.sub.32, C.sub.34, C.sub.36, . . . are set equal to zero. By doing so, it
 is possible to obtain a free-form surface having only one plane of
 symmetry parallel to the XZ-plane.
 Furthermore, the direction of decentration is determined in correspondence
 to either of the directions of the above-described planes of symmetry. For
 example, with respect to the plane of symmetry parallel to the YZ-plane,
 the direction of decentration of the optical system is determined to be
 the Y-axis direction. With respect to the plane of symmetry parallel to
 the XZ-plane, the direction of decentration of the optical system is
 determined to be the X-axis direction. By doing so, rotationally
 asymmetric aberrations due to decentration can be corrected effectively,
 and at the same time, the productivity can be improved.
 It should be noted that the above defining equation (a) is shown as merely
 an example, and that the feature of the present invention resides in that
 rotationally asymmetric aberrations due to decentration are corrected and,
 at the same time, the productivity is improved by using a rotationally
 asymmetric surface having only one plane of symmetry. Therefore, the same
 advantageous effect can be obtained for any other defining equation that
 expresses a rotationally asymmetric surface.
 Incidentally, when the first prism is formed from two reflecting surfaces
 and two transmitting surfaces as stated above, the degree of freedom for
 aberration correction increases, and thus the amount of aberration
 produced in the first prism is minimized. In addition, because the
 relative decentration between the two reflecting surfaces is small,
 aberrations produced by the two reflecting surfaces are corrected with
 these reflecting surfaces by canceling the aberrations with each other.
 Therefore, the amount of aberration produced in the first prism is
 favorably small. It is more desirable that the two reflecting surfaces
 should have powers of different signs. By doing so, it is possible to
 enhance the effect of correcting each other's aberrations by the two
 reflecting surfaces and hence possible to obtain high resolution.
 When the second prism is formed from two reflecting surfaces and two
 transmitting surfaces as in the case of the first prism, the degree of
 freedom for aberration correction increases, and thus the amount of
 aberration produced in the second prism is minimized. In addition, because
 the relative decentration between the two reflecting surfaces is small,
 aberrations produced by the two reflecting surfaces are corrected with
 these reflecting surfaces by canceling the aberrations with each other.
 Therefore, the amount of aberration produced in the second prism is
 favorably small. It is more desirable that the two reflecting surfaces
 should have powers of different signs. By doing so, it is possible to
 enhance the effect of correcting each other's aberrations by the two
 reflecting surfaces and hence possible to obtain high resolution.
 It is preferable to minimize the relative decentration between the first
 and second reflecting surfaces at points where the optical axis is
 reflected by the two reflecting surfaces. By doing so, it becomes possible
 to reduce the amount of decentration aberrations produced from the prism,
 and the amount of rotationally asymmetric aberrations produced from the
 prism reduces.
 In the present invention it is important to arrange the image-forming
 optical system so that any optical element that gives a refracting power
 contributing to the image-forming action of a light beam is not placed
 between the second prism and an image formed by the image-forming optical
 system.
 Regarding the reduction in the thickness of an image-forming optical system
 using prisms, when a device that is used to receive an image formed by the
 image-forming optical system is an electronic image pickup device, e.g. a
 CCD, in particular, it is necessary to insert a low-pass filter, an
 infrared cutoff filter, etc. Therefore, if a lens or the like other than
 such filters is interposed between the second prism and the image plane,
 the thickness increases correspondingly. This unfavorably weakens the
 present invention's effect of achieving a compact image-forming optical
 system by folding the optical path through a prism optical system.
 In addition, it is desirable in the present invention to arrange the second
 prism such that the axial principal ray that is led from the third surface
 of the second prism to the fourth surface of the second prism lies closer
 to the axial principal ray that is led from the third surface of the first
 prism to the fourth surface of the first prism than the axial principal
 ray of the light beam incident on the first prism that is led from the
 first surface of the first prism to the second surface of the first prism
 and the extension of this axial principal ray.
 FIG. 16 shows one form of the image-forming optical system according to the
 present invention. As illustrated in the figure, the second prism 20 is
 arranged such that the axial principal ray h that is led from the third
 surface 23 of the second prism 20 to the fourth surface 24 of the second
 prism 20 lies closer to the axial principal ray g that is led from the
 third surface 13 of the first prism 10 to the fourth surface 14 of the
 first prism 10 than the axial principal ray f of the light beam incident
 on the first prism 10 that is led from the first surface 11 of the first
 prism 10 to the second surface 12 of the first prism 10 and the extension
 (dashed line) of the axial principal ray f. With this arrangement, the
 positional relationship between the first prism 10, the second prism 20
 and the image plane 3 can be changed from a straight-line parallel
 relationship such as that shown in FIG. 17 to a positional relationship in
 which, as shown in FIG. 16, the first prism 10 faces the second prism 20
 in a direction oblique to the horizontal direction as viewed in FIG. 16
 (in the case of FIG. 16, the first prism 10 faces the second prism 20 in
 an obliquely right upward direction). Accordingly, it is possible to
 realize a reduction in the thickness of the image-forming optical system
 in comparison to the arrangement in which the constituent elements of the
 image-forming optical system are disposed in parallel in a straight line
 as shown in FIG. 17. In particular, to realize an image-forming optical
 system of wide field angle, it is necessary to increase the size of the
 first prism 10, which is placed on the object side, in order to ensure the
 sufficiently large beam width. That is, it is necessary to increase the
 size of the first surface 11 as an entrance surface, the size of the
 second surface 12 as a reflecting surface for turning back the incident
 light beam, and the surface separation between the first and second
 surfaces 11 and 12. Consequently, the first prism 10 becomes large and
 thick as a whole (this is particularly noticeable at a portion thereof
 closer to the entrance surface). Therefore, if the second prism 20,
 together with the image plane 3, is placed in parallel to the first prism
 10 in a straight line, it is necessary to provide a space for placing the
 second prism 20 in a direction in which the thickness further increases.
 This goes against the demand to achieve a compact image-forming optical
 system. Accordingly, it is desirable from the viewpoint of achieving a
 compact image-forming optical system to place the second prism 20 in an
 oblique positional relation to a structural portion of the first prism 10
 that extends from the first surface 11 to the second surface 12, as stated
 above.
 In addition, it is desirable in the present invention to arrange the first
 and second prisms as follows. The fourth surface of the first prism and
 the first surface of the second prism face each other. The third surface
 of the second prism does not face the second surface of the first prism
 but lies closer to the fourth surface of the first prism than the second
 surface of the first prism. Consequently, the first and second surfaces of
 the first prism and the third and fourth surfaces of the second prism and
 further the image plane do not lie in parallel on a line extending
 straight from the axial principal ray entering the first prism. The third
 and fourth surfaces of the second prism and the image plane are off the
 line extending straight from the axial principal ray entering the first
 prism.
 As shown in FIG. 16, the fourth surface 14 of the first prism 10 and the
 first surface 21 of the second prism 20 face each other. The third surface
 23 of the second prism 20 does not face the second surface 12 of the first
 prism 10 but lies closer to the fourth surface 14 of the first prism 10
 than the second surface 12 of the first prism 10. Consequently, the first
 and second surfaces 11 and 12 of the first prism 10 and the third and
 fourth surfaces 23 and 24 of the second prism 20 and further the image
 plane 3 do not lie in parallel on a line extending straight from the axial
 principal ray a entering the first prism 10. The third and fourth surfaces
 23 and 24 of the second prism 20 and the image plane 3 are off the line
 extending straight from the axial principal ray a entering the first prism
 10. With this arrangement, the positional relationship between the first
 prism 10, the second prism 20 and the image plane 3 can be changed from a
 straight-line parallel relationship such as that shown in FIG. 17 to a
 positional relationship in which, as shown in FIG. 16, the first prism 10
 faces the second prism 20 in a direction oblique to the horizontal
 direction as viewed in FIG. 16 (in the case of FIG. 16, the first prism 10
 faces the second prism 20 in an obliquely right upward direction).
 Accordingly, it is possible to realize a reduction in the thickness of the
 image-forming optical system in comparison to the arrangement in which the
 constituent elements of the image-forming optical system are disposed in
 parallel in a straight line as shown in FIG. 17. In particular, to realize
 an image-forming optical system of wide field angle, it is necessary to
 increase the size of the first prism 10, which is placed on the object
 side, in order to ensure the sufficiently large beam width. That is, it is
 necessary to increase the size of the first surface 11 as an entrance
 surface, the size of the second surface 12 as a reflecting surface for
 turning back the incident light beam, and the surface separation between
 the first and second surfaces 11 and 12. Consequently, the first prism 10
 becomes large and thick as a whole (this is particularly noticeable at a
 portion thereof closer to the entrance surface). Therefore, if the second
 prism 20, together with the image plane 3, is placed in parallel to the
 first prism 10 in a straight line, it is necessary to provide a space for
 placing the second prism 20 in a direction in which the thickness further
 increases. This goes against the demand to achieve a compact image-forming
 optical system. Accordingly, it is desirable from the viewpoint of
 achieving a compact image-forming optical system to place the second prism
 20 in an oblique positional relation to a structural portion of the first
 prism 10 that extends from the first surface 11 to the second surface 12,
 as stated above.
 It is desirable to arrange the first prism such that the first and fourth
 surfaces thereof face each other across the prism medium, and the second
 and third surfaces thereof face each other across the medium, thereby
 forming a Z-shaped optical path, and to arrange the second prism such that
 the first and fourth surfaces thereof face each other across the prism
 medium, and the second and third surfaces thereof face each other across
 the medium, thereby forming a Z-shaped optical path.
 It is desirable from the viewpoint of design and aberration correcting
 performance to arrange the first and second prisms so that the optical
 path in each prism is formed in a Z-shape (including an optical path in
 the form of a mirror image of a Z-shape, a zigzag optical path bent at
 acute angles, and a zigzag optical path bent at obtuse angles), thereby
 preventing any portions of the optical path from intersecting each other.
 By doing so, in the first prism, the incidence and exit directions of the
 axial principal ray as reflected at the second surface are opposite to
 those of the axial principal ray as reflected at the third surface. In the
 second prism also, the incidence and exit directions of the axial
 principal ray as reflected at the second surface are opposite to those of
 the axial principal ray as reflected at the third surface. Therefore, it
 is easy to make aberration correction.
 It is desirable to arrange the first prism such that the first surface,
 which is a transmitting surface through which a light beam enters the
 first prism, and the fourth surface, which is a transmitting surface
 through which the light beam exits from the first prism, are not adjacent
 to each other but in a positional relationship in which a reflecting
 surface lies between the first and fourth surfaces, and to arrange the
 second prism such that the first surface, which is a transmitting surface
 through which a light beam enters the second prism, and the fourth
 surface, which is a transmitting surface through which the light beam
 exits from the second prism, are not adjacent to each other but in a
 positional relationship in which a reflecting surface lies between the
 first and fourth surfaces.
 By arranging the first and second prisms as stated above, the angle of
 reflection in each prism can be made gentle in comparison to a prism of
 the type in which the entrance and exit surfaces are adjacent to each
 other. Accordingly, the aggravation of aberrations is reduced, and the
 degree of design freedom increases. It should be noted that the term "the
 entrance and exit surfaces are adjacent to each other" is concerned with
 the positional relationship between only optical surfaces such as
 transmitting surfaces and reflecting surfaces. The same is the case with
 the above-mentioned "positional relationship in which a reflecting surface
 lies between the first and fourth surfaces". That is, even when there is a
 chamfered portion without an optical action or a ghost or flare preventing
 coating surface between two transmitting surfaces or between a
 transmitting surface and a reflecting surface, these two surfaces are
 regarded as adjacent to each other unless an optical surface having an
 optical action is present therebetween.
 In addition, it is desirable that the optical path length for the axial
 principal ray from the first to fourth surfaces of the first prism should
 be longer than the optical path length for the axial principal ray from
 the first to fourth surfaces of the second prism.
 By adopting the above-described arrangement, the size of the second prism
 can be made smaller than the size of the first prism. Accordingly, even
 when the first prism increases in size as the result of widening the field
 angle, the image-forming optical system can be made compact in size as a
 whole by reducing the size of the second prism.
 In this case, it is desirable for the first and second prisms to satisfy
 the following condition:
EQU 0.10&lt;L2/L1&lt;0.85 (1)
 where L1 is the optical path length for the axial principal ray from the
 first to fourth surfaces of the first prism, and L2 is the optical path
 length for the axial principal ray from the first to fourth surfaces of
 the second prism.
 If L2/L1 is not larger than the lower limit of the condition (1), i.e.
 0.10, the second prism becomes excessively small in size and hence
 difficult to produce. Alternatively, the first prism becomes excessively
 large in size. This goes against the demand to achieve a compact
 image-forming optical system. If L2/L1 is not smaller than the upper
 limit, i.e. 0.85, it becomes difficult to construct a second prism that is
 sufficiently compact relative to the first prism.
 It is more desirable to satisfy the following condition:
EQU 0.10&lt;L2/L1&lt;0.70 (1-1)
 It is even more desirable to satisfy the following condition:
EQU 0.20&lt;L2/L1&lt;0.70 (1-2)
 It is still more desirable to satisfy the following condition:
EQU 0.20&lt;L2/L1&lt;0.60 (1-3)
 It is still more desirable to satisfy the following condition:
EQU 0.20&lt;L2/L1&lt;0.50 (1-4)
 It is still more desirable to satisfy the following condition:
EQU 0.20&lt;L2/L1&lt;0.40 (1-5)
 In addition, by giving a negative refracting power to the first prism, a
 wide field angle for imaging can be obtained. This is because the negative
 power enables rays of wide field angle to be converged and thus it is
 possible to converge the light beam when the rays enter the second unit,
 which is formed from the second prism. This is favorable from the
 viewpoint of aberration correction when an optical system having a
 relatively short focal length is to be constructed.
 It is preferable to place the stop on the image side of the first prism. By
 doing so, in a case where the first reflecting surface has a negative
 power and is approximated by a spherical surface, the center of curvature
 of the first reflecting surface and the stop position are approximately
 coincident with each other. Therefore, it is possible to eliminate comatic
 aberration in theory.
 Regarding the configuration each prism surface, it is desirable that both
 the second and third surfaces of the first prism should be arranged to
 have a rotationally asymmetric surface configuration that gives a power to
 a light beam and corrects aberrations due to decentration.
 It is also desirable that both the second and third surfaces of the second
 prism should be arranged to have a rotationally asymmetric surface
 configuration that gives a power to a light beam and corrects aberrations
 due to decentration.
 It is desirable that the rotationally asymmetric surface configuration of
 at least one of the second and third surfaces of the first prism should be
 arranged in the form of a plane-symmetry free-form surface having only one
 plane of symmetry.
 It is also desirable that the rotationally asymmetric surface configuration
 of at least one of the second and third surfaces of the second prism
 should be arranged in the form of a plane-symmetry free-form surface
 having only one plane of symmetry.
 It is desirable that the rotationally asymmetric surface configurations of
 both the second and third surfaces of the first prism should be arranged
 in the form of a plane-symmetry free-form surface having only one plane of
 symmetry.
 It is also desirable that the rotationally asymmetric surface
 configurations of both the second and third surfaces of the second prism
 should be arranged in the form of a plane-symmetry free-form surface
 having only one plane of symmetry.
 It is desirable that the first prism should be arranged such that the only
 one plane of symmetry of the plane-symmetry free-form surface that forms
 the second surface of the first prism and the only one plane of symmetry
 of the plane-symmetry free-form surface that forms the third surface of
 the first prism are formed in the same plane.
 It is also desirable that the second prism should be arranged such that the
 only one plane of symmetry of the plane-symmetry free-form surface that
 forms the second surface of the second prism and the only one plane of
 symmetry of the plane-symmetry free-form surface that forms the third
 surface of the second prism are formed in the same plane.
 It is desirable to arrange the first and second prisms so that the only one
 plane of symmetry of each of the plane-symmetry free-form surfaces that
 form the second and third surfaces of the first prism and the only one
 plane of symmetry of each of the plane-symmetry free-form surfaces that
 form the second and third surfaces of the second prism are formed in the
 same plane.
 It is desirable to arrange the first prism such that at least one of the
 first and fourth surfaces thereof has a rotationally asymmetric surface
 configuration that gives a power to a light beam and corrects aberrations
 due to decentration. A refracting surface having such a surface
 configuration is effective in correcting aberrations due to decentration.
 It is desirable that the rotationally asymmetric surface configuration of
 at least one of the first and fourth surfaces in the first prism should be
 arranged in the form of a plane-symmetry free-form surface having only one
 plane of symmetry.
 It is desirable to arrange the second prism such that at least one of the
 first and fourth surfaces thereof has a rotationally asymmetric surface
 configuration that gives a power to a light beam and corrects aberrations
 due to decentration. A refracting surface having such a surface
 configuration is effective in correcting aberrations due to decentration.
 It is desirable that the rotationally asymmetric surface configuration of
 at least one of the first and fourth surfaces in the second prism should
 be arranged in the form of a plane-symmetry free-form surface having only
 one plane of symmetry.
 In the present invention, the effective way of enhancing the symmetry
 required for the image-forming optical system and thereby favorably
 correcting aberrations, including off-axis aberrations, is to place a
 pupil between the first and second prisms and to place the second prism
 between the pupil and the image plane.
 In this case, it is desirable to place the stop on the pupil.
 In the present invention, it is desirable for the image-forming optical
 system to have a first prism having a diverging action on the object side
 of the stop and a second prism having a converging action on the image
 side of the stop, and also desirable for the image-forming optical system
 to be approximately telecentric on the image side.
 In an image-forming optical system using a refracting optical element, the
 power distribution varies according to the use application. For example,
 telephoto systems having a narrow field angle generally adopt an
 arrangement in which the entire system is formed as a telephoto type
 having a positive front unit and a negative rear unit, thereby making the
 overall length of the optical system shorter than the focal length.
 Wide-angle systems having a wide field angle generally adopt an
 arrangement in which the entire system is formed as a retrofocus type
 having a negative front unit and a positive rear unit, thereby making the
 back focus longer than the focal length.
 In the case of an image-forming optical system using an image pickup
 device, e.g. a CCD, in particular, it is necessary to place an optical
 low-pass filter or an infrared cutoff filter between the image-forming
 optical system and the image pickup device to remove moire or to eliminate
 the influence of infrared rays. Therefore, with a view to ensuring a space
 for placing these optical members, it is desirable to adopt a retrofocus
 type arrangement for the image-forming optical system.
 It is important for a retrofocus type image-forming optical system to be
 corrected for aberrations, particularly off-axis aberrations. The
 correction of off-axis aberrations depends largely on the position of the
 stop. As has been stated above, in the case of a general coaxial optical
 system, off-axis aberrations are aggravated if optical elements are not in
 symmetry with respect to the stop. For this reason, the common practice is
 to place optical elements of the same sign at respective positions facing
 each other across the stop, thereby obtaining a satisfactory symmetry with
 respect to the stop, and thus correcting off-axis aberrations. In the case
 of a retrofocus type system having a negative front unit and a positive
 rear unit, the power distribution is asymmetric in the first place.
 Therefore, the off-axis aberration-correcting performance varies to a
 considerable extent according to the position of the stop.
 Therefore, the stop is placed between the object-side, first prism having a
 diverging action and the image-side, second prism having a converging
 action, thereby making it possible to minimize the aggravation of off-axis
 aberrations due to the asymmetry of the power distribution. If the stop is
 placed on the object side of the object-side diverging prism or on the
 image side of the image-side converging prism, the asymmetry with respect
 to the stop is enhanced and becomes difficult to correct.
 In this case, the image-forming optical system may consist of the first
 prism of diverging action placed on the object side of the stop and the
 second prism of converging action placed on the image side of the stop.
 That is, the image-forming optical system may be formed from these prisms
 alone.
 In the image-forming optical system according to the present invention,
 there is only one image-formation plane throughout the system. As has been
 stated above, the decentration error sensitivity of a reflecting surface
 is higher than that of a refracting surface. In a reflecting optical
 member arranged in the form of a single block as in the case of a prism,
 surface accuracy errors and decentration errors of each surface are
 transferred while being added up. Therefore, the smaller the number of
 reflecting surfaces, the more the manufacturing accuracy required for each
 surface is eased. Accordingly, it is undesirable to increase the number of
 reflections more than is needed. For example, in an image-forming optical
 system in which an intermediate image is formed and this image is relayed,
 the number of reflections increases more than is needed, and the
 manufacturing accuracy required for each surface becomes tight, causing
 the cost to increase unfavorably.
 It is preferable that the axial principal ray entering the second prism and
 the axial principal ray exiting therefrom should be approximately parallel
 to each other. This is because if the incident and emergent axial
 principal rays are approximately parallel to each other, focusing can be
 performed by moving the second prism linearly along the optical axis.
 Let us define the power of a decentered optical system and that of an
 optical surface. As shown in FIG. 15, when the direction of decentration
 of a decentered optical system S is taken in the Y-axis direction, a light
 ray which is parallel to the axial principal ray of the decentered optical
 system S and which has a small height d in the YZ-plane is made to enter
 the decentered optical system S from the object side thereof. The angle
 that is formed between that ray and the axial principal ray exiting from
 the decentered optical system S as the two rays are projected onto the
 YZ-plane is denoted by .delta.y, and .delta.y/d is defined as the power Py
 in the Y-axis direction of the decentered optical system S. Similarly, a
 light ray which is parallel to the axial principal ray of the decentered
 optical system S and which has a small height d in the X-axis direction,
 which is perpendicular to the YZ-plane, is made to enter the decentered
 optical system S from the object side thereof. The angle that is formed
 between that ray and the axial principal ray exiting from the decentered
 optical system S as the two rays are projected onto a plane
 perpendicularly intersecting the YZ-plane and containing the axial
 principal ray is denoted by .delta.x, and .delta.x/d is defined as the
 power Px in the X-axis direction of the decentered optical system S. The
 power Pyn in the Y-axis direction and power Pxn in the X-axis direction of
 a decentered optical surface n constituting the decentered optical system
 S are defined in the same way as the above.
 Furthermore, the reciprocals of the above-described powers are defined as
 the focal length Fy in the Y-axis direction of the decentered optical
 system S, the focal length Fx in the X-axis direction of the decentered
 optical system S, the focal length Fyn in the Y-axis direction of the
 decentered optical surface n, and the focal length Fxn in the X-axis
 direction of the decentered optical surface n, respectively.
 The relationship between the power of each surface and the power of the
 entire optical system will be described below. The value obtained by
 dividing the power of the second surface of the first prism by the power
 of the entire optical system is denoted by Pxs3/Px for the X-axis
 direction and Pys3/Py for the Y-axis direction. The value obtained by
 dividing the power of the third surface of the first prism by the power of
 the entire optical system is denoted by Pxs4/Px for the X-axis direction
 and Pys4/Py for the Y-axis direction. The value obtained by dividing the
 power of the second surface of the second prism by the power of the entire
 optical system is denoted by Pxs10/Px for the X-axis direction and
 Pys10/Py for the Y-axis direction. It is desirable that both Pxs3/Px and
 Pys3/Py should be negative. By giving a relatively strong negative power
 to the second surface of the first prism, it is possible to converge rays
 of wide field angle in the optical system and hence possible to reduce the
 size of the prism. Of the reflecting surfaces in the first prism, the
 second surface is closest to the object side. In a case where a retrofocus
 type optical system is formed by using negative and positive units,
 aberrations produced in each unit are reduced and aberrations produced in
 the entire optical system are also reduced by increasing the spacing
 between the front unit, which is a negative unit, and the rear unit, which
 is a positive unit. Therefore, it is desirable to increase the negative
 power of the second surface, which is a reflecting surface closest to the
 object side in the first prism. Non-decentered optical systems suffer from
 the problem that the overall length becomes unavoidably long. In an
 optical system that is decentered and has a folded optical path as in the
 present invention, the overall size of the optical system can be reduced
 even when the overall length along the optical axis increases.
 It is more desirable to satisfy at least one of the following conditions:
EQU -2&lt;Pxs3/Px&lt;0 (2)
EQU -2&lt;Pys3/Py&lt;0 (3)
 If Pxs3/Px or Pys3/Py is not larger than the lower limit, i.e. -2, the
 negative power of the second surface of the first prism becomes
 excessively strong. Accordingly, to obtain a predetermined power with the
 entire optical system, the load imposed on another surface having a
 positive power must be increased. Consequently, it becomes impossible for
 the optical system to maintain a favorable aberration correction condition
 as a whole. If Pxs3/Px or Pys3/Py is not smaller than the upper limit,
 i.e. 0, the negative power of the second surface of the first prism
 becomes excessively weak. Consequently, the light beam-converging action
 weakens, and the overall size of the optical system becomes unfavorably
 large.
 It is even more desirable to satisfy at least one of the following
 conditions:
EQU -1&lt;Pxs3/Px&lt;-0.02 (2-1)
EQU -1&lt;Pys3/Py&lt;-0.02 (3-1)
 The meaning of the upper and lower limits of each of the conditions (2-1)
 and (3-1) is the same as the above.
 It is still more desirable to satisfy at least one of the following
 conditions:
EQU -0.7&lt;Pxs3/Px&lt;-0.4 (2-2)
EQU -0.7&lt;Pys3/Py&lt;-0.4 (3-2)
 The meaning of the upper and lower limits of each of the conditions (2-2)
 and (3-2) is the same as the above.
 It is desirable that both Pxs4/Px and Pys4/Py should be positive. When the
 third surface of the first prism is provided with a relatively strong
 positive power, it forms a positive rear unit of a retrofocus type optical
 system. In the first prism of the present invention, the first surface and
 the third surface are not placed at the same position and not provided
 with the same configuration. Therefore, the first surface and third
 surface of the first prism can be arranged as different surfaces, which
 are optically separate from each other. Accordingly, even if the third
 surface of the first prism is formed as a reflecting surface of strong
 positive power, decentration aberrations can be minimized.
 It is even more desirable to satisfy at least one of the following
 conditions:
EQU 0&lt;Pxs4/Px&lt;2 (4)
EQU 0&lt;Pys4/Py&lt;2 (5)
 If Pxs4/Px or Pys4/Py is not larger than the lower limit, i.e. 0, the
 positive power of the third surface of the first prism becomes excessively
 weak. Accordingly, to obtain a predetermined power with the entire optical
 system, the load imposed on another surface having a positive power must
 be increased. Consequently, it becomes impossible for the optical system
 to maintain a favorable aberration correction condition as a whole. If
 Pxs4/Px or Pys4/Py is not smaller than the upper limit, i.e. 2, the
 positive power of the third surface of the first prism becomes excessively
 strong. Consequently, the power assigned to this surface increases
 excessively, and aberrations, including decentration aberrations, produced
 by this surface become excessively large and hence impossible to correct
 by another surface.
 It is still more desirable to satisfy at least one of the following
 conditions:
EQU 0.1&lt;Pxs4/Px&lt;1 (4-1)
EQU 0.1&lt;Pys4/Py&lt;1 (5-1)
 The meaning of the upper and lower limits of each of the conditions (4-1)
 and (5-1) is the same as the above.
 It is still more desirable to satisfy at least one of the following
 conditions:
EQU 0.3&lt;Pxs4/Px&lt;0.8 (4-2)
EQU 0.3&lt;Pys4/Py&lt;0.8 (5-2)
 The meaning of the upper and lower limits of each of the conditions (4-2)
 and (5-2) is the same as the above.
 By increasing the surface separation between the second and third surfaces
 of the first prism, it is possible to reduce aberrations produced in the
 entire optical system when it is arranged in the form of a retrofocus type
 optical system. Assuming that the optical path length for the axial
 principal ray between the second and third surfaces of the first prism
 (the optical path length being obtained by multiplying the distance
 between the surfaces by the refractive index) is S3-S4 and the focal
 length in the X-axis direction of the entire optical system is Fx, it is
 desirable for (S3-S4)/Fx to satisfy the following condition:
EQU 1&lt;(S3-S4)/Fx&lt;20 (6)
 This condition is equivalent to the spacing between the front and rear
 units of the above-described retrofocus type optical system, which has
 negative and positive units. If (S3-S4)/Fx is not larger than the lower
 limit, i.e. 1, the negative and positive powers of the two surfaces become
 excessively strong, and it becomes impossible to correct aberrations in
 the entire optical system, If (S3-S4)/Fx is not smaller than the upper
 limit, i.e. 20, the surface separation between the second and third
 surfaces of the first prism becomes excessively large. Consequently, the
 overall size of the optical system becomes unfavorably large even if the
 optical system has a folded optical path.
 It is even more desirable to satisfy the following condition:
EQU 2&lt;(S3-S4)/Fx&lt;15 (6-1)
 The meaning of the upper and lower limits of the condition (6-1) is the
 same as the above.
 It is still more desirable to satisfy the following condition:
EQU 3&lt;(S3-S4)/Fx&lt;9 (6-2)
 The meaning of the upper and lower limits of the condition (6-2) is the
 same as the above.
 The following is a description of the power of the second surface of the
 second prism. This surface is placed relatively close to the stop and
 therefore aggravates relatively little aberrations in the peripheral
 image. Accordingly, it is possible to give a strong positive power to the
 second surface of the second prism. For this reason, favorable
 image-formation performance can be obtained by giving a relatively strong
 positive power to the second surface of the second prism although this
 surface has a large amount of displacement.
 In addition, it is desirable to satisfy at least one of the following
 conditions:
EQU O&lt;Pxs10/Px&lt;3 (7)
EQU O&lt;Pys10/Py&lt;3 (8)
 If Pxs10/Px or Pys10/Py is not larger than the lower limit, i.e. 0, the
 positive power becomes excessively weak. Accordingly, a positive power
 must be assigned to another surface having a large amount of displacement.
 Consequently, decentration aberrations become large and impossible to
 correct favorably. If Pxs10/Px or Pys10/Py is not smaller than the upper
 limit, i.e. 3, the positive power of the second surface of the second
 prism becomes excessively strong. Consequently, aberrations produced by
 the second surface of the second prism becomes excessively large and hence
 difficult to correct by another surface.
 It is even more desirable to satisfy at least one of the following
 conditions:
EQU 0.1&lt;Pxs10/Px&lt;2 (7-1)
EQU 0.1&lt;Pys10/Py&lt;2 (8-1)
 The meaning of the upper and lower limits of each of the conditions (7-1)
 and (8-1) is the same as the above.
 It is still more desirable to satisfy at least one of the following
 conditions:
EQU 0.2&lt;PXs10/Px&lt;1 (7-2)
EQU 0.2&lt;Pys10/Py&lt;1 (8-2)
 The meaning of the upper and lower limits of each of the conditions (7-2)
 and (8-2) is the same as the above.
 When a ray that is emitted from the object center and passes through the
 center of the stop to reach the center of the image is defined as an axial
 principal ray, it is necessary that the incident angle (shown by .theta.
 in FIG. 16) of the axial principal ray as reflected by the third surface
 of the first prism should satisfy the following condition in order to
 reduce the thickness of the optical system in the direction of the optical
 axis:
EQU 10.degree.&lt;S4.theta.&lt;60.degree. (9)
 where S4.theta. denotes the angle of incidence of the axial principal ray
 on the third surface of the first prism.
 If S4.theta. is not larger than the lower limit of the condition (9), i.e.
 10.degree., the incident angle becomes small, so that the second prism and
 the first prism undesirably overlap each other. Consequently, it becomes
 impossible to construct the first prism itself. If S4.theta. is not
 smaller than the upper limit, i.e. 60.degree., the amount of displacement
 becomes excessively large, and decentration aberrations produced by this
 surface become large and impossible to correct by another surface.
 It is more desirable to satisfy the following condition:
EQU 20.degree.&lt;S4.theta.&lt;50.degree. (9-1)
 The meaning of the upper and lower limits of the condition (9-1) is the
 same as the above.
 It is still more desirable to satisfy the following condition:
EQU 30.degree.&lt;S4.theta.&lt;40.degree. (9-2)
 The meaning of the upper and lower limits of the condition (9-2) is the
 same as the above.
 In the image-forming optical system according to the present invention,
 focusing of the image-forming optical system can be effected by moving all
 the constituent elements or moving only one prism. However, it is also
 possible to effect focusing by moving the image-formation plane in the
 direction of the axial principal ray exiting from the surface closest to
 the image side. By doing so, it is possible to prevent displacement of the
 axial principal ray on the entrance side due to focusing even if the
 direction in which the axial principal ray from the object enters the
 optical system is not coincident with the direction of the axial principal
 ray exiting from the surface closest to the image side owing to the
 decentration of the image-forming optical system. It is also possible to
 effect focusing by moving a plurality of wedge-shaped prisms, which are
 formed by dividing a plane-parallel plate, in a direction perpendicular to
 the Z-axis. In this case also, focusing can be performed independently of
 the decentration of the image-forming optical system.
 In the image-forming optical system according to the present invention, if
 at least one prism is formed by using an organic material such as a
 plastic material, the cost can be reduced. It is desirable to use a
 material of low moisture absorption, such as amorphous polyolefin, because
 such a material has a minimum change in image-forming performance with
 changes in moisture.
 In the present invention, temperature compensation can be made by using a
 diverging prism and a converging prism. By providing the prisms with
 powers of different signs, it is possible to prevent the focal shift due
 to changes in temperature, which is a problem arising when a plastic
 material is used to form a prism.
 In the present invention, it is desirable that each of a plurality of
 prisms should have a positioning portion for setting a relative position,
 which is provided on a surface having no optical action. In a case where a
 plurality of prisms each having a reflecting surface with a power are
 provided as in the present invention in particular, relative displacement
 of each prism causes the performance to be deteriorated. Therefore, in the
 present invention, a positioning portion for setting a relative position
 is provided on each surface of each prism that has no optical action,
 thereby ensuring the required positional accuracy. Thus, the desired
 performance can be ensured. In particular, if a plurality of prisms are
 integrated into one unit by using the positioning portions and coupling
 members, it becomes unnecessary to assemble and adjust a plurality of
 prisms which would otherwise be separate from each other. Accordingly, the
 cost can be further reduced.
 Furthermore, the optical path can be folded in a direction different from
 the decentration direction of the image-forming optical system according
 to the present invention by placing a reflecting optical member, e.g. a
 mirror, on the object side of the entrance surface of the image-forming
 optical system. By doing so, the degree of freedom for layout of the
 image-forming optical system further increases, and the overall size of
 the image-forming optical apparatus can be further reduced.
 In the present invention, the image-forming optical system can be formed
 from prisms alone. By doing so, the number of components is reduced, and
 the cost is lowered. Furthermore, a plurality of prisms may be integrated
 into one prism at each of the front and back sides of the stop. By doing
 so, the cost can be further reduced.
 In the present invention, the image-forming optical system may include
 another lens (positive or negative lens) as a constituent element in
 addition to the first and second prisms at one or each of a plurality of
 positions selected from a position on the object side of the first and
 second prisms, a position between the two prisms, and a position on the
 image side of the two prisms.
 The image-forming optical system according to the present invention may be
 a fast, single focal length lens system. Alternatively, the image-forming
 optical system may be arranged in the form of a zoom lens system
 (variable-magnification image-forming optical system) by combining it with
 a single or plurality of refracting optical systems that may be provided
 between the two prisms or on the object or image side of the two prisms.
 In the present invention, the refracting and reflecting surfaces of the
 image-forming optical system may be formed from spherical surfaces or
 rotationally symmetric aspherical surfaces.
 In a case where the above-described image-forming optical system according
 to the present invention is placed in an image pickup part of an image
 pickup apparatus, or in a case where the image pickup apparatus is a
 photographic apparatus having a camera mechanism, it is possible to adopt
 an arrangement in which a prism member provided in the front unit is
 placed closest to the object side among optical elements having an optical
 action, and the entrance surface of the prism member is decentered with
 respect to the optical axis, and further a cover member is placed on the
 object side of the prism member at right angles to the optical axis. The
 arrangement may also be such that the prism member provided in the front
 unit has on the object side thereof an entrance surface decentered with
 respect to the optical axis, and a cover lens having a power is placed on
 the object side of the entrance surface of the prism member in coaxial
 relation to the optical axis so as to face the entrance surface across an
 air spacing.
 If a prism member is placed closest to the object side and a decentered
 entrance surface is provided on the front side of a photographic apparatus
 as stated above, the obliquely tilted entrance surface is seen from the
 subject, and it gives the illusion that the photographic center of the
 apparatus is deviated from the subject when the entrance surface is seen
 from the subject side. Therefore, a cover member or a cover lens is placed
 at right angles to the optical axis, thereby preventing the subject from
 feeling incongruous when seeing the entrance surface, and allowing the
 subject to be photographed with the same feeling as in the case of general
 photographic apparatus.
 A finder optical system can be formed by using any of the above-described
 image-forming optical systems according to the present invention as a
 finder objective optical system and adding an image-inverting optical
 system for erecting an object image formed by the finder objective optical
 system and an ocular optical system.
 In addition, it is possible to construct a camera apparatus by using the
 finder optical system and an objective optical system for photography
 provided in parallel to the finder optical system.
 In addition, an image pickup optical system can be constructed by using any
 of the foregoing image-forming optical systems according to the present
 invention and an image pickup device placed in an image plane formed by
 the image-forming optical system.
 In addition, a camera apparatus can be constructed by using any of the
 foregoing image-forming optical systems according to the present invention
 as an objective optical system for photography, and a finder optical
 system placed in an optical path separate from an optical path of the
 objective optical system for photography or in an optical path branched
 from the optical path of the objective optical system for photography.
 In addition, an electronic camera apparatus can be constructed by using any
 of the foregoing image-forming optical systems according to the present
 invention, an image pickup device placed in an image plane formed by the
 image-forming optical system, a recording medium for recording image
 information received by the image pickup device, and an image display
 device that receives image information from the recording medium or the
 image pickup device to form an image for observation.
 In addition, an endoscope system can be constructed by using an observation
 system having any of the foregoing image-forming optical systems according
 to the present invention and an image transmitting member for transmitting
 an image formed by the image-forming optical system along a longitudinal
 axis, and an illumination system having an illuminating light source and
 an illuminating light transmitting member for transmitting illuminating
 light from the illuminating light source along the longitudinal axis.
 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.

DESCRIPTION OF THE PREFERRED EMBODIMENTS
 Examples 1 to 3 of the image-forming optical system according to the
 present invention will be described below. It should be noted that
 constituent parameters of each example will be shown later.
 In each example, as shown in FIG. 1, an axial principal ray 1 is defined by
 a ray emanating from the center of an object and passing through the
 center of a stop 2 to reach the center of an image plane 3. A hypothetic
 plane is taken in the plane extending through the intersection between the
 axial principal ray 1 and the entrance surface (first surface) 11 of the
 first prism 10 at right angles to the axial principal ray 1 entering the
 entrance surface 11. Another hypothetic plane is taken in the plane
 extending through the intersection between the axial principal ray 1 and
 the exit surface (fourth surface) 14 of the first prism 10 at right angles
 to the axial principal ray 1 exiting from the exit surface 14. Another
 hypothetic plane is taken in the plane extending through the intersection
 between the axial principal ray 1 and the entrance surface (first surface)
 21 of the second prism 20 at right angles to the axial principal ray 1
 entering the entrance surface 21. Another hypothetic plane is taken in the
 plane extending through the intersection between the axial principal ray 1
 and the exit surface (fourth surface) 24 of the second prism 20 at right
 angles to the axial principal ray 1 exiting from the exit surface 24. The
 intersection of each hypothetic plane and the associated optical surface
 is defined as the origin for this optical surface and decentered optical
 surfaces present between it and the subsequent hypothetic plane (the image
 plane in the case of the final hypothetic plane). A positive direction of
 a Z-axis is taken in the direction of travel of the axial principal ray 1
 (the axial principal ray 1 entering the entrance surface in the case of
 the hypothetic plane determined with respect to the intersection of each
 entrance surface; the axial principal ray 1 exiting from the exit surface
 in the case of the hypothetic plane determined with respect to the
 intersection of each exit surface). A plane containing the Z-axis and the
 center of the image plane is defined as a YZ-plane. An axis extending
 through the origin at right angles to the YZ-plane is defined as an
 X-axis. The direction in which the X-axis extends from the obverse side
 toward the reverse side of the plane of the figure is defined as a
 positive direction of the X-axis. An axis that constitutes a right-handed
 orthogonal coordinate system in combination with the X- and Z-axes is
 defined as a Y-axis. FIG. 1 shows the hypothetic planes and a coordinate
 system concerning the hypothetic plane determined with respect to the
 intersection of the entrance surface 11 of the first prism 10.
 Illustration of the hypothetic planes and the coordinate system is omitted
 in FIGS. 2 and 3.
 In Example 1 to 3, the decentration of each surface is made in the
 YZ-plane, and the one and only plane of symmetry of each rotationally
 asymmetric free-form surface is the YZ-plane.
 Regarding decentered surfaces, each surface is given displacements in the
 X-, Y- and Z-axis directions (X, Y and Z, respectively) of the vertex
 position of the surface from the origin of the associated coordinate
 system, and tilt angles (degrees) of the center axis of the surface [the
 Z-axis of the above equation (a) in regard to free-form surfaces; the
 Z-axis of the following equation (b) in the case of aspherical surfaces]
 with respect to the X-, Y- and Z-axes (.alpha., .beta. and .gamma.,
 respectively) . In this case, positive .alpha. and .beta. mean
 counterclockwise rotation relative to the positive directions of the
 corresponding axes, and positive .gamma. means clockwise rotation relative
 to the positive direction of the Z-axis.
 Among optical surfaces constituting the optical system in each example, a
 specific surface (including a hypothetic plane) and a surface subsequent
 thereto are given a surface separation when these surfaces form a coaxial
 optical system. In addition, the refractive index and Abbel's number of
 each medium are given according to the conventional method.
 The configuration of each free-form surface used in the present invention
 is defined by the above equation (a). The Z-axis of the defining equation
 is the axis of the free-form surface.
 Aspherical surfaces used in the present invention are rotationally
 symmetric aspherical surfaces given by the following equation:
 Z=(y.sup.2 /R)/[1+{1-(1+K)y.sup.2 /R.sup.2 }.sup.1/2 ]+Ay.sup.4 +By.sup.6
 +Cy.sup.8 +Dy.sup.10 + (b)
 In the above equation, Z is an optical axis (axial principal ray) for which
 the direction of travel of light is defined as a positive direction, and y
 is taken in a direction perpendicular to the optical axis. R is a paraxial
 curvature radius, K is a conic constant, and A, B, C, D . . . are 4th-,
 6th-, 8th- and 10th-order aspherical coefficients, respectively. The
 Z-axis of this defining equation is the axis of the rotationally symmetric
 aspherical surface.
 In the constituent parameters (shown later), those terms concerning
 free-form surfaces and aspherical surfaces for which no data is shown are
 zero. The refractive index is expressed by the refractive index for the
 spectral d-line (wavelength: 587.56 nanometers). Lengths are given in
 millimeters.
 Free-form surfaces may also be defined by Zernike polynomials. That is, the
 configuration of a free-form surface may be defined by the following
 equation (c). The Z-axis of the defining equation (c) is the axis of
 Zernike polynomial. A rotationally asymmetric surface is defined by polar
 coordinates of the height of the Z-axis with respect to the XY-plane. In
 the equation (c), A is the distance from the Z-axis in the XY-plane, and R
 is the azimuth angle about the Z-axis, which is expressed by the angle of
 rotation measured from the Z-axis.
 x=R.times.cos (A)
EQU y=R.times.sin (A)
EQU Z=D.sub.2 +D.sub.3 Rcos (A)+D.sub.4 Rsin (A)
EQU +D.sub.5 R.sup.2 cos (2A)+D.sub.6 (R.sup.2 -1)+D.sub.7 R.sup.2 sin (2A)
EQU +D.sub.8 R.sup.3 cos (3A)+D.sub.9 (3R.sup.3 -2R) cos (A)
EQU +D.sub.10 (3R.sup.3 -2R) sin (A)+D.sub.11 R.sup.3 sin (3A)
EQU +D.sub.12 R.sup.4 cos (4A)+D.sub.13 (4R.sup.4 -3R.sup.2) cos (2A)
EQU +D.sub.14 (6R.sup.4 -6R.sup.2 +1)+D.sub.15 (4R.sup.4 -3R.sup.2) sin (2A)
EQU +D.sub.16 R.sup.4 sin (4A)
EQU +D.sub.17 R.sup.5 cos (5A)+D.sub.18 (5R.sup.5 -4R.sup.3) cos (3A)
EQU +D.sub.19 (10R.sup.5 -12R.sup.3 +3R) cos (A)
EQU +D.sub.20 (10R.sup.5 -12R.sup.3 +3R) sin (A)
EQU +D.sub.21 (5R.sup.5 -4R.sup.3) sin (3A)+D.sub.22 R.sup.5 sin (5A)
EQU +D.sub.23 R.sup.6 cos (6A)+D.sub.24 (6R.sup.6 -5R.sup.4) cos (4A)
EQU +D.sub.25 (15R.sup.6 -20R.sup.4 +6R.sup.2) cos (2A)
EQU +D.sub.26 (20R.sup.6 -30R.sup.4 +12R.sup.2 -1)
EQU +D.sub.27 (15R.sup.6 -20R.sup.4 +6R.sup.2) sin (2A)
EQU +D.sub.28 (6R.sup.6 -5R.sup.4) sin (4A)+D.sub.29 R.sup.6 sin (6A) (c)
 In the above equation, to design an optical system symmetric with respect
 to the X-axis direction, D.sub.4, D.sub.5, D.sub.6, D.sub.10, D.sub.11,
 D.sub.12, D.sub.13, D.sub.14, D.sub.20, D.sub.21, D.sub.22. . . should be
 used.
 Other examples of surfaces usable in the present invention are expressed by
 the following defining equation (d):
EQU Z=.SIGMA..SIGMA.C.sub.nm XY
 Assuming that k=7 (polynomial of degree 7), for example, a free-form
 surface is expressed by an expanded form of the above equation as follows:
EQU Z=C.sub.2 +C.sub.3 y+C.sub.4.vertline.x.vertline.
EQU +C.sub.5 y.sup.2 +C.sub.6 y.vertline.x.vertline.+C.sup.7 x.sup.2
EQU +C.sub.8 y.sup.3 +C.sub.9 y.sup.2.vertline.x.vertline.+C.sub.10 yx.sup.2
 +C.sub.11.vertline.x.sup.3.vertline.
EQU +C.sub.12 y.sup.4 +C.sub.13 y.sup.3.vertline.x.vertline.+C.sub.14 y.sup.2
 x.sup.2 +C.sub.15 y.vertline.x.sup.3.vertline.+C.sub.16 x.sup.4
EQU +C.sub.17 y.sup.5 +C.sub.18 y.sup.4.vertline.x.vertline.+C.sub.19 y.sup.3
 x.sup.2 +C.sub.20 y.sup.2.vertline.x.sup.3.vertline.
EQU +C.sub.21 yx.sup.4 +C.sub.22.vertline.x.sup.5.vertline.
EQU +C.sub.23 y.sup.6 +C.sub.24 y.sup.5.vertline.x.vertline.+C.sub.25 y.sup.4
 x.sup.2 +C.sub.26 Y.sup.3.vertline.x.sup.3.vertline.
EQU +C.sub.27 y.sup.2 x.sup.4 +C.sub.28 y.vertline.x.sup.5 +C.sub.29 x.sup.6
EQU +C.sub.30 y.sup.7 +C.sub.31 y.sup.6.vertline.x.vertline.+C.sub.32 y.sup.5
 x.sup.2 +C.sub.33 y.sup.4.vertline.x.sup.3.vertline.
EQU +C.sub.34 y.sup.3 x.sup.4 +C.sub.35
 y.sup.2.vertline.x.sup.5.vertline.+C.sub.36 yx.sup.6
 +C.sub.37.vertline.x.sup.7.vertline. (d)
 Although in the surface configuration is expressed by a free-form surface
 using the above equation (a), it should be noted that the same
 advantageous effect can be obtained by using the above equation (c) or
 (d).
 FIGS. 1 to 3 are sectional views of Examples 1 to 3, respectively, taken
 along the YZ-plane containing the axial principal ray. Constituent
 parameters of these examples will be shown later. In the constituent
 parameters, free-form surfaces are denoted by "FFS", aspherical surfaces
 by "ASS", and hypothetic planes by "HRP" (Hypothetic Reference Plane).
 Examples 1 to 3 each have, in order in which light passes from the object
 side, a first prism 10, a stop 2, a second prism 20, and an image plane
 (image-formation lane) 3. The first prism 10 is formed from a first
 surface 11, a second surface 12, a third surface 13, and a fourth surface
 14. The first surface 11 is a first transmitting surface. The second
 surface 12 is a first reflecting surface. The third surface 13 is a second
 reflecting surface. The fourth surface 14 is a second transmitting
 surface. Rays from the object enter through the first transmitting surface
 11 and are reflected successively by the first reflecting surface 12 and
 the second reflecting surface 13 and then exit from the second
 transmitting surface 14. The second prism 20 is formed from a first
 surface 21, a second surface 22, a third surface 23, and a fourth surface
 24. The first surface 21 is a first transmitting surface. The second
 surface 22 is a first reflecting surface. The third surface 23 is a second
 reflecting surface. The fourth surface 24 is second transmitting surface.
 Rays from the object enter through the first transmitting surface 21 and
 are reflected successively by the first reflecting surface 22 and the
 second reflecting surface 23 and then exit from the second transmitting
 surface 24.
 In the constituent parameters (shown later), the displacements of each of
 the surface Nos. 2 to 6 are expressed by the amounts of displacement from
 the hypothetic plane 1 of surface No. 1. The vertex positions of the
 surface Nos. 7 and 8 are each expressed by only the surface separation
 along the axial principal ray from the hypothetic plane 2 of surface No.
 6. The displacements of each of the surface Nos. 9 to 13 are expressed by
 the amounts of displacement from the hypothetic plane 3 of surface No. 8.
 The image plane is expressed by only the surface separation along the
 axial principal ray from the hypothetic plane 4 of surface No. 13.
 In all Examples 1 to 3, the image height is 1.6.times.1.2 millimeters. The
 focal length Fx in the X-axis direction is determined by conversion from
EQU Ix=Fx.times.tan.theta.x
 where Ix is the image height in the X-axis direction, and .theta.x is the
 field angle in the X-axis direction.
 In Example 1, the horizontal half field angle is 26.3.degree., and the
 vertical half field angle is 20.3.degree.. The entrance pupil diameter is
 1.15 millimeters. Therefore, the F-number is 2.8, and the focal length Fx
 is 3.43 millimeters, which is equivalent to 35 millimeters in terms of the
 focal length of a silver halide camera.
 In Example 2, the horizontal half field angle is 31.7.degree., and the
 vertical half field angle is 24.9.degree.. The entrance pupil diameter is
 1.15 millimeters. Therefore, the F-number is 2.25, and the focal length Fx
 is 2.68 millimeters, which is equivalent to 28 millimeters in terms of the
 focal length of a silver halide camera.
 In Example 3, the horizontal half field angle is 19.1.degree., and the
 vertical half field angle is 14.6.degree.. The entrance pupil diameter is
 1.15 millimeters. Therefore, the F-number is 4.02, and the focal length Fx
 is 4.83 millimeters, which is equivalent to 50 millimeters in terms of the
 focal length of a silver halide camera.
 The image-forming optical system according to the present invention can be
 applied to other sizes, as a matter of course. The present invention
 includes not only an image pickup optical system using the image-forming
 optical system according to the present invention but also an image pickup
 apparatus incorporating the image pickup optical system.
 Constituent parameters in the foregoing Examples 1 to 3 are shown below. In
 the tables below: "FFS" denotes a free-form surface; "ASS" denotes an
 aspherical surface; and "HRP" denotes a hypothetic plane.
 EXAMPLE 1