Image observing apparatus

An image observing apparatus has two light sources, a scanning mirror upon which light beams from the two light sources are incident in common, and two optical systems. The two optical systems respectively lead the light beams emitted from the two light sources and scanned by the scanning mirror to the right and left eyes of an observer. The light beams emitted respectively from the two light sources are scanned by the scanning mirror and form two-dimensional images for the right and left eyes on predetermined surfaces. Central field angle principal rays emitted respectively from the two light sources and reflected by the scanning mirror, exist on the same plane. Then, an angle made by the scanning mirror and by a surface vertical to the central field angle principal rays emerging from the two optical systems, is set so as to fall within a predetermined range.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an image observing apparatus suited to a head mounted display (HMD) and the like.

2. Related Background Art

At the present, a display device employed for the HMD is exemplified such as a transparent type liquid crystal element, a reflection type liquid crystal element, or an EL (Electroluminescence) element. These types of elements are, as necessary pixels must be all built up in the elements, easy to have occurrence of a pixel defect and hard to be manufactured.

Further, a display device is proposed in U.S. Pat. No. 5,467,104, wherein an image is displayed and observed by employing a scanning device without using a two-dimensional display device such as the liquid crystal element and the EL element.

U.S. Pat. No. 5,467,104 discloses a scan type image display device that scans light beams assuming respective colors of Red, Green, and Blue in a horizontal direction and in a vertical direction, and directly forms the image on a retina via an optical system. An extremely high speed scan of the light beams is requested for the scan type image display device disclosed in U.S. Pat. No. 5,467,104, and therefore an extremely small-sized device is employed for a scanning element such as a mirror for scanning the light. Accordingly, the light beam to be scanned is quite narrow and therefore has an extremely small diameter (a diameter of an exit pupil) in a position of a pupil of an observer.

Methods for expanding the small diameter of the exit pupil are also proposed (U.S. Pat. Nos. 5,701,132 and 5,757,544).

On the other hand, a comparatively small-sized optical system using an eccentric free-form curved surface optical system is also proposed (Japanese Patent Application Laid-Open No. 2001-004955).

Known further is an image display device (Japanese Patent Application Laid-Open No. H11-095144) in which a scanning means is shared with optical systems corresponding to right and left eyes.

According to configurations disclosed in U.S. Pat. Nos. 5,701,132 and 5,757,544, an intermediate image is temporarily formed to expand the diameter of the exit pupil, and hence the device tends to be scaled up due to an elongated optical path.

Further, according to Japanese Patent Application Laid-Open No. H11-095144, two scanning devices for the horizontal direction and the vertical direction are employed, and consequently the configuration becomes complicated. In the construction disclosed in Japanese Patent Application Laid-Open No. H11-095144, when trying to obtain the HMD having a further wide field angle, the scanning device for the vertical direction becomes extremely elongate in the horizontal direction, resulting in the scale-up of the image observing apparatus.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide a small-sized image observing apparatus of such a type that two-dimensional image is formed by a scanning device.

An image observing apparatus exemplified according to the present invention has two light sources for right and left eyes, a scanning mirror upon which light beams from the two light sources are incident in common, and two optical systems for the right and left eyes. The two optical systems respectively lead the light beams emitted from the two light sources and scanned by the scanning mirror to the right and left eyes of an observer. The light beams emitted respectively from the two light sources are scanned by the scanning mirror and thereby respectively form two-dimensional images for the right and left eyes on predetermined surfaces. Central field angle principal rays emitted respectively from the two light sources and reflected by the scanning mirror, exist on the same plane. Then, an angle made by the scanning mirror and by a surface vertical to the central field angle principal rays emerging from the two optical systems, set so as to fall within a predetermined range.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Embodiments of an image observing apparatus according to the present invention will hereinafter be described with reference toFIGS. 1 and 2.

Referring toFIGS. 1 and 2, the reference numeral1demotes a two-dimensional scanning mirror (scanning mirror),2denotes an optical system for a left eye,3denotes an optical system for a right eye,6denotes a light source,7denotes a collimator lens, and8(8L,8R) represent exit pupils of the optical systems2,3respectively, which are defined as positions where the right and left eyes of an observer should be disposed.

FIG. 1is a sectional view (a top view) showing optical paths from the scanning mirror1to the exit pupils8(8L,8R) for the right and left eyes.FIG. 2is a sectional view (a top view and a side view) of an optical path from the light source6L for the left eye to the exit pupil8L of the optical system2for the left eye.

The light source6is constructed of, though not illustrated, luminescent diodes (Light Emitting Diodes: LEDs) for three colors such as R(red), G (green) and B (blue), wherein the 3-color LEDs are disposed in optically equivalent positions by use of dichroic prisms etc. Further, the light sources6are independently provided for the right and left eyes. InFIG. 2, the light source6L for the left eye is illustrated, while the light source6R for the right eye is not illustrated. The 3-color LEDs configuring the light source6is independently capable of modulating a period of light emitting time and a light intensity, corresponding to image information and can be treated, as viewed from the scanning mirror1, the optical systems2,3, etc, as if being a white point light source capable of changing the color, the intensity and a gradation.

The collimator lenses7are likewise independently provided for the right and left eyes. InFIG. 2, the collimator lens7L for the left eye is illustrated, while the collimator lens7R for the right eye is not illustrated. The collimator lenses7(7L,7R) substantially collimate beams of light from the light sources6(6L,6R), and thus lead the collimated light to the scanning mirror1.

A predetermined surface is two-dimensionally, in horizontal/vertical directions, scanned with the light emitted from the light sources6and modulated based on the image information thereby forming a two-dimensional image thereon. The light deflected by the scanning mirror1gets incident on the optical systems2,3, wherein the light is led via the optical systems2,3to the both eyes (the exit pupils8) of the observer. Through the optical systems2,3, the observer observes the two-dimensional image formed by the scanning as an enlarged virtual image.

The scanning mirror1is disposed in a middle position between the optical systems2,3and is shared with these two optical systems. The light source6L for the left eye and the collimator lens7L are, as shown inFIG. 2, disposed on the right side of the scanning mirror1and above (in a direction perpendicular to a plane H) a local meridional section (the plane H (=XZ plane) formed by a field angle central beam after being reflected by the scanning mirror1) extending from the scanning mirror1to the exit pupil8L. The light source6R for the right eye and the collimator lens7R are disposed in a mirror symmetry with, though not illustrated, the light source6L for the left eye and the collimator lens7L, and also disposed on the left side of the scanning mirror1and above the plane H. With this arrangement, the right and left observing systems can be disposed without any mechanical interference, whereby a compact configuration of the whole optical system can be attained. It is to be noted that the light sources6(6L,6R) and the collimator lenses7(7L.7R) may also be disposed under the plane H.

Further, on the plane H, a mechanical deflection angle of the scanning mirror1is on the order of ±6.25°, and an optical deflection angle thereof is on the order of ±12.5°. At this time, a field angle beam of ±15° (in a laterally horizontal direction) is obtained on the surface of the exit pupil8. As a matter of course, the scanning is simultaneously conducted in a vertical direction, and a field angle beam of ±11.3° (in an up-and-down perpendicular direction) is obtained on the surface of the exit pupil8.

The following is an in-depth description of each of the elements for the left eye. The explanations of the respective elements for the right eye are omitted, however, these elements are symmetric with the elements for the left eye and have the same action.

The optical system2is configured by a prism (a first optical element) P1, a prism (a second optical element) P2and a diffusion reflection plate4. An exit surface P1eof the prism P1and an incidence surface B of the prism P2take substantially the same configuration and are cemented. The exit surface P1eand the incidence surface B may, however, be disposed with a minute air layer therebetween.

The prism P2has three optical surfaces A1, A2and B. The optical surface A1has reflex action (total reflection from an internal surface is effected twice) and transmissive action. Part of the optical surface B is formed with a minute transmissive opening (minute transmissive pinhole)5, and an area peripheral to this pinhole5serves as a reflection surface. The optical surface A2is a surface exhibiting only the reflex action. The optical surface B acts as the incidence surface and the reflection surface as well. The optical surface A1acts as the exit surface (the exit surface toward the diffusion reflection plate4and the exist surface toward to the exit pupil8), the incidence surface (the incidence surface serving for when incident upon the prism P2from the diffusion reflection plate4) and the reflection surface (the internal total reflection is effected twice).

The diffusion reflection plate4takes a parallel-flat plate configuration, wherein the surface on the side of the prism P2has diffusion action, and the surface on the other side serves as a return reflection surface4a.

Reflective coats are formed on the reflection surfaces P1b, P1c, P1dof the prism P1, the optical surface A2of the prism P2and the return reflection surface4aof the diffusion reflection plate4. The reflective coat is also formed on the area excluding the minute transmissive opening5on the optical surface B of the prism P2. Note that a metallic coat is adopted as the reflective coat. The metallic coat has a flat characteristic of spectral reflectance characteristic and has advantages of being inconspicuous in coloring of the reflected light and of having almost no difference in reflectance with respect to the light different in its polarizing direction.

To begin with, the optical path from the scanning mirror1to the exit pupil8L shown inFIG. 1will be explained.

Each field angle beam reflected and scanned by the scanning mirror1is incident on the incidence surface P1aof the prism P1, then reflected by the reflection surfaces P1b, P1c, P1din this sequence and exits the exit surface P1e. At this time, an image of the light source6is formed once as an intermediate image inside the prism P1. Namely, it follows that a two-dimensional image of the first time is formed on this intermediate imaging plane.

The light exiting the exit surface P1eof the prism P1is incident on the minute transmissive opening5formed in the optical surface B of the prism P2, then reflected by the optical surface A1(the internal total reflection) and the optical surface A2in this sequence, again gets incident on the optical surface A1at an angle equal to or smaller than a critical angle, and exits the optical surface A1.

Then, after exiting the prism P2, the intermediate image of the light source6is again formed on the diffusion reflection plate4. Namely, it follows that the two-dimensional image is formed on the diffusion reflection plate4. A light beam that is diffusion-reflected by the diffusion reflection plate4forms a thick light beam (unillustrated) having a small F-number (bright). Further, the diffusion reflection plate4, which is a return reflection surface, reflects the incident light so as to return this light in a direction substantially opposite toward the incident direction. To be specific, the light reflected by the diffusion reflection plate4is again incident upon the optical surface A1of the prism P2, exits the prism2from the optical surface A1after being reflected by the optical surface A2, then totally reflected by within the optical surface A1and reflected by the optical surface B toward the exit pupil8(an eyeball), and reaches the exit pupil8.

The observer places the left eye close to the position of the exit pupil8, thereby enabling visual recognition of an enlarged image of the two-dimensional image formed on the diffusion reflection plate4.

It should be noted that the two-dimensional scanning mirror1, the minute transmissive opening5and the exit pupil8are in a conjugate relationship with each other.

A reciprocating optical path formed by the prism2and the diffusion reflection plate4will be again briefly described.

The light emerging from the exit surface P1eof the prism P1travels in the sequence such as the optical surface B (transmission (1))>the optical surface A1(reflection (1))>the optical surface A2(reflection (2))>the optical surface A1(transmission (2))>the return reflection surface4a(diffusion surface)>the optical surface A1(transmission (3))>the optical surface A2(reflection (3))>the optical surface A1(reflection (4))>the optical surface B (reflection (5))>the optical surface A1(transmission (4)). Thus, it is understood that the light traces the optical path back so far at the boundary of the reflection on the return reflection surface4. A path from the optical surface B (transmission (1)) to the return reflection surface4is an outgoing path, and an optical path from the return reflection surface4to the optical surface B (reflection (5)) is an return path. This reciprocating optical path serves to make the optical system compact even in such a type of optical system that the intermediate image is formed twice, which needs an elongate optical path.

Note thatFIGS. 1 and 2illustrate only the light beams regularly reflected by the diffusion reflection plate4. A diameter of the exit pupil8is on the order of 1.5 mm.

In the present embodiment, the scanning mirror1involves using a scanning mirror of which the maximum effective diameter is as extremely small as 3 mm or smaller. This scanning mirror1performs the horizontal and vertical scanning and leads the light beam based on the image information to the optical systems2and3.

The two-dimensional scanning mirror1having the effective diameter of 2.5 mm and the transmissive opening5having a size (aperture) of which a diameter is 3 mm, are in the conjugate relationship with each other.

Further, the first intermediate imaging plane of the intermediate image of the light reflected by the scanning mirror1, is formed in a position Q1between the reflection surface P1band the reflection surface P1cafter the beam of light has got incident on the prism P1. The second intermediate imaging plane of the intermediate image is formed in a position Q2in the vicinity of the return reflection surface (diffusion reflection plate4). Thus, one intermediate imaging plane is formed outside (on the side of the ear) each of the right and left eyes, and another intermediate imaging plane is formed inside (on the side of the nose) each of the right and left eyes. Moreover, an inclined angle θ of the two-dimensional scanning mirror1with respect to the surface perpendicular to the same plane is 15°.

Next, features of the present embodiment will be explained.

In the present embodiment, as shown inFIG. 3, two central field angle principal rays, after exiting each of the two light sources6L,6R for the right and left eyes and being reflected by the two-dimensional scanning mirror1, exist within the same plane H (XZ plane). Then, the following conditional expression is satisfied:
5°<θ<80°,
where θ represents an angle of the two-dimensional scanning mirror1in a reference state to a surface vertical to the central field angle beams between the right and left in the positions where the beams exit the optical systems2,3for the right and left eyes (a surface V (XY plane) vertical to the plane H). It should be noted that the reference state of the two-dimensional scanning mirror1corresponds to a state where the scanning mirror is not driven and is, if the mechanical deflection angle is, e.g., ±6.25°, a state where the scanning mirror1is at 0°, that is, at its center. Further, the central field angle principal ray is the beam of the center of the field angle and is, specifically, the beam traveling through the center of the two-dimensional image formed by the scanning by means of the scanning mirror1and through the center of the exit pupil8.

If θ is less than a lower limit of the above expression, the optical path led to the optical system2for the left eye from the two-dimensional scanning mirror1is overlapped with the optical path led to the two-dimensional scanning mirror1from the light source6R for the right eye, with the result that a disposition of the right and left light sources6L,6R becomes hard to make. If θ is larger than the upper limit of the above expression, the incident angle of the light upon the two-dimensional scanning mirror increases, and hence a large amount of distortion unpreferably occurs due to a deviation peculiar to the driving of the two-dimensional scanning mirror.

Preferably, the following conditional expression is established:
10°<θ<60°

More preferably, if the numerical range meets the following conditional expression, allowance is given to the layout of the right and left light sources, and there reaches such a level that almost no distortion occurs due to the deviation peculiar to the driving of the two-dimensional scanning mirror:
10°<θ<50°

The reflection surface (the return reflection surface) for the return reflection in the optical system according to the present embodiment may be shared with the reflection surface A1or A2. In this case, the number of the optical surfaces can be reduced, and therefore the optical system can be downsized.

The diameter of the two-dimensional scanning mirror1is very small and therefore scans by reflection-deflecting a narrow beam (from 1 to 2 mm in diameter). The HMD is the observing optical system, and hence, if the narrow beam remains incident upon the eyeball as it is, a sufficient exit pupil diameter is not obtained, resulting in a cause of fatigue.

Such being the case, the diffusion reflection plate4is inserted in the vicinity of the intermediate imaging plane Q2, with the optical system up to the intermediate imaging plane Q2being defined as the beam optical system, the downsizing is facilitated, and the diameter of the exit pupil8is set large. If the reflection type optical system is employed, the light beam is returned, so that the optical members before being incident on the diffusion reflection plate4and the optical members after the reflection can be shared advantageously enough to attain the downsizing.

The light beams from the light sources6travel via the two-dimensional scanning mirror1, and form the intermediate imaging planes Q1and Q2. The two-dimensional scanning mirror1is disposed in the position conjugate with the exit pupils8of the optical systems2,3. The light beams from two-dimensional scanning mirror1form the two-dimensional images on the intermediate imaging planes Q1and Q2.

Some portions (the portions from the light sources6up to the intermediate imaging plane Q1) of the optical systems2and3configure a relay optical system that forms the intermediate images with the light beams emitted from the light sources. The two-dimensional scanning mirror1is disposed in a position corresponding to a stop of this relay optical system, and the stop (a scanning reflection member) of the relay optical system and the exit pupil8of the optical system are set in a conjugate relationship, thereby preventing the light beam from being vignetted when the observer places the eye onto the exit pupil8.

Another, that is, the third conjugate plane exists along the optical paths between the two conjugate planes of the two-dimensional scanning mirror1and the exit pupils8of the optical systems, wherein the minute transmissive opening5is positioned on this third conjugate plane.

In the case of widening the field angle by use of the two-dimensional scanning mirror1shared with the right and left optical systems, it is preferable that two relay optical systems be provided.

Accordingly, the two-dimensional scanning mirror1is disposed in the position of the stop in the first relay optical system, and three optical members such as the stop (the minute transmissive opening5) of the second relay optical system and the exit pupils8of the optical systems2,3are set in the conjugate relationship, thereby preventing the light beam from being vignetted even when widening the field angle.

In the optical system2, the minute area (the minute transmissive opening)5exhibiting the transmissive action exists in the beam effective area on the reflection surface B, and the beam effective area excluding the minute area5exhibiting the transmissive action is set as a surface exhibiting only the reflecting action.

The light emitted from the light source6is transmitted through the minute transmissive opening5on the reflection surface5and forms the intermediate imaging plane in the vicinity of the diffusion reflection surface5, and the light beam therefrom is reflected by the reflection surface B, thereby forming an enlarged image.

It is general that a half-mirror is used as a means for simultaneously actualizing the transmission and the reflection of the light. When the light travels through the half-mirror twice by the transmission and the reflection, a light amount thereof becomes ¼ (25%) in principle, and a light utilizing efficiency declines.

By contrast, according to the present embodiment, a high light utilizing efficiency is actualized by changing a diameter of the light beam depending on a case where the light transmits the reflection surface B and a case where the light is reflected by the reflection surface B. Namely, when the light is made transmitted through the reflection surface B, an area of the portion where the light beam transmits the reflection surface B is made small while the light beam remains as a narrow beam. Then, only this minute area is formed not as the reflection surface but as the opening5and thus transmits the light (the metallic coat is not applied over only this area). On the other hand, in the case of reflecting the light on the reflection surface B, the diameter of the light beam on the reflection surface B is made expanded by the action of the diffusion reflection plate4, whereby the beams from other than the minute area are all reflected. On the occasion of this reflection, the light penetrating the minute area is lost, however, it is possible to actualize the light utilizing efficiency that is by far higher than in the case of employing the half-mirror.

It is preferable that for the case of reflection, a ratio (Db/Da) be equal to or smaller than 10%, where Da represents the effective area and Db represents the area of the minute transmissive portion (the opening5). When this value is 10%, 100%-transmission is attained when transmitted and 90%-reflection is attained when reflected, with the result that the light utilizing efficiency becomes 90% (which does not take account of the surface reflection, absorption by the reflective coat, etc).

Further, if Db/Da is larger than 10%, the light amount in the minute transmissive area5decreases when reflected, and it is unpreferable that a difference in brightness might be observed when observing the enlarged image. Further, if the Db/Da ratio is equal to or lower than 5% (if the light utilizing efficiency is equal to or larger than 90%), almost no decrease in the light amount is observed in the minute transmissive area5. Moreover, although the minute transmissive area5takes preferably a circular or elliptical shape, it may also take a rectangular shape. It is desirable that the minute transmissive areas5be disposed in symmetric positions in a lateral or vertical direction within the reflection effective area. This arrangement facilitates acquisition of positional accuracy when manufacturing the minute transmissive area5.

As described above, the optical systems2and3form the optical path (outgoing path) along which the light beams reflected by the one or more reflection surfaces Ai eccentric with respect to the light beams from the two-dimensional scanning mirror1reach the diffusion reflection plate4, and form the optical path (return path) along which the light beams are, after being reflected in the return backward direction by the diffusion reflection plate4, reflected on one or more eccentric reflection surfaces Ai and the reflection surface B, and exit the optical surface(s) Ai.

The light beams from the light sources6pass through the two-dimensional scanning mirror1, after traveling forward along the outgoing path and traveling backward along the return path via the return diffusion reflection plate4, are then reflected by the reflection surfaces eccentric to the light beams and are led to the eyeballs8while forming an optical path different from the return path.

With this arrangement, the light beams after exiting the reciprocating optical path can be set in the direction different from the direction in which the light beams enter the reciprocating optical path, and the interference with the incident light upon the reciprocating optical path can be avoided.

The intermediate imaging plane and the diffusion surface are set on the return diffusion reflection plate4for the outgoing path and the return path, the narrow beam optical system is established on the outgoing path, while the diffused light optical system capable covering the wide exit pupils is established on the return path, thus attaining the downsizing of the optical system and the expansion of the exit pupils.

The optical systems2and3include the prism members P1and P2each composed of three or more optical surfaces that have the plurality of rotational asymmetric surfaces (which are so-called “free-form curved surfaces”).

The optical system according to the present invention is the eccentric optical system, and therefore an eccentric aberration occurs. The eccentric aberration occurred is reduced by the plurality of rotational asymmetric surfaces.

Further, an aspect ratio, that is, a ratio of the horizontal direction to the vertical direction on the display screen, can be set without any restriction by making the scanning mirror movable. Moreover, the aspect ratio of the display screen, which is set by use of the scanning mirror, can be also changed to a necessary value (3:4 or 9:16) by the plurality of reflection surfaces included in the optical systems2and3.

It is preferable that the rotational asymmetric surface takes a plane-symmetric configuration in which the local meridional section (the plane H) is the only one symmetric surface. This is because the working and manufacturing can be more facilitated than in the case of having none of the symmetric property. Furthermore, if configured as the prism member, the plurality of conventional components (optical surfaces) can be replaced with one prism member, thereby making the assembling adjustment easier.

The optical systems2and3employ the construction of having one or more internal total reflection surfaces, wherein at least two or more total reflections take place.

Herein, the total reflection is a phenomenon, wherein the light beam is reflected theoretically 100% when the light beam enters at a angle equal to or greater than the critical angle to the normal line of the surface when reflected within the prism or within the glass. The total reflection is higher in the light utilizing efficiency than the metallic coat reflection and dielectric film reflection, and can therefore eliminate the loss of the light amount on the surface. In the present embodiment, the internal total reflection surfaces are provided in the reciprocating optical path.

The optical system is configured so that the light beams from the right and left eyeballs8L,8R are reflected outward (on the sides of the ears) on the reverse light beam traces on the local meridional sections to the two-dimensional scanning mirror1and to the light sources6from the eyeballs8, thereafter travel through before the right and left eyeballs and are led to the two-dimensional scanning mirror1inward (on the side of the nose).

For establishing the HMD optical system having the elongate optical paths by use of the single two-dimensional scanning mirror1, it is required that the two-dimensional scanning mirror1be disposed in the middle (in the vicinity of the nose) between the right and left eyes. Then, with this configuration, the optical paths are developed in the right and left directions, and hence the elongate optical paths can be accommodated within the HMD optical system while making the up-and-down breadth compact.

The optical system has the two intermediate imaging planes, wherein on the local meridional section, one intermediate imaging plane is provided outside (on the side of the ear) of each of the right and left eyes8L and8R and another intermediate imaging plane is provided inside (on the side of the nose) of each of the right and left eyes8L and8R.

For enabling the field angle to be widened by use of the single two-dimensional scanning mirror1, the light beams from the light sources6are formed twice as the intermediate images. With this contrivance, the degree of freedom in design is increased.

When the intermediate image is formed twice, however, the optical path length in the optical system becomes extremely elongate, resulting in a scale-up. With the construction described above, the widening of the field angle and the compact configuration by use of the single two-dimensional scanning mirror1can be simultaneously accomplished.

Further, if the return reflection surface is a curved surface, the directions of the light beams of the peripheral image can be individually controlled when reflected, and therefore the optical system can be downsized more readily than in the case where the return reflection surface is the flat surface. If the return reflection surface is the rotational asymmetric surface, the directions of the beams of the peripheral image can be controlled without any restriction, so that the downsizing is more facilitated than in the case of the curved surface. The metallic mirror coating capable of reflecting as much as 100% is applied over this return reflection surface, whereby the loss in the light amount is reduced to the greatest possible degree.

Further, the return reflection surface may be formed on a component separate from the prism or on the prism surface.

Examples of the numerical values will hereinafter be explained. The present embodiment involves using a local-paraxial axis, which will be described. InFIGS. 1 and 2, a surface vertex coordinate system of the first surface (the exit pupil8) is illustrated inFIG. 2. In the present embodiment, each surface is rendered just shift-eccentric in the x-axis direction and tilt-eccentric about the y-axis. It should be noted that only the two-dimensional scanning mirror1is rendered tilt-eccentric (15°) about the x-axis. Further, the general meridional section described above and a sagittal section are each a definition of the general-paraxial axis, while the local meridional section and a local sagittal section are each a definition of a local-paraxial axis that will hereinafter be described. Moreover, as to the local paraxial-axis, definitions of a local radius-of-curvature, a local surface-to-surface interval, a local focal length and local refractive power, which correspond to the eccentric system, will be explained as below.

In the present embodiment, the light beams emitted from the light source6and traveling through the center of the secondary image and the center of the exit pupil8of the optical system, are defined as the central field angle principal rays. Then, the present embodiment employs not a set of the conventional radius-of-curvature, surface-to-surface interval, focal length and refractive power that are based on the reference of the surface vertex of each surface, but a set of the local radius-of-curvature, the local surface-to-surface interval, the local focal length and the local refractive power that are based on the reference of the hit point (the incident point) of the central field angle principal ray on each surface.

Herein, the local radius-of-curvature denotes a local radius-of-curvature (a radius of curvature on the local meridional section, and a radius of curvature on the local sagittal section) at the hit point on the optical surface. Further, the local surface-to-surface interval represents a value (a distance on the central field angle principal ray, a value without air conversion) of a distance between the two hit points on the present surface and the next surface. Moreover, the local focal length represents a value calculated by a conventional focal length calculating method (paraxial axis tracing) from the local radius-of-curvature, the refractive power in front and in rear of the surface and the local surface-to-surface interval. The local refractive power is a value of an inverse number of the local focal length.

Note that the embodiment shows the local radius-of-curvature, a refractive index of the surface, the local surface-to-surface interval and the local focal length together with the conventional radius of curvature, surface-to-surface interval, eccentricity, refractive index and Abbe number. Table 1 shows numerical value data in the present embodiment. In the general-paraxial axis in Table 1, rx represents a radius of curvature in the meridional section, ry denotes a radius of curvature in the sagittal section, d designates a surface-to-surface interval (parallel to the surface vertex coordinate system of the first surface), eccentricity (shift represents parallel eccentricity of the surface vertex of each surface with respect to the surface vertex coordinate system of the first surface, and tilt degree is tilt eccentricity in the meridional section from the exit pupil to the two-dimensional scanning mirror), nd represents a refractive index of d-line, vd designates an Abbe number, and FXY denotes a free curved surface. Further, an element attached with M represents a reflection surface, an element attached with (M(dif) represents a diffusion reflection surface), and the refractive index nd of d-line is given a reverse sign. Note that Table 1 shows the numerical value data of the reverse trace to the two-dimensional scanning mirror from the exit pupil, the tilt degree as the tilt eccentricity is an angle on the xz-section inFIG. 2, and hence tilt eccentricity 15° (yz-section) about the x-axis of the two-dimensional scanning mirror is omitted. A definition formula of FXY (free curved surface) is given as follows. (In the surface vertex coordinate system of each surface:)

z: the sagitta of the surface parallel to the z-axis,

c: the curvature of in each-surface vertex coordinates

k: The conic constant

Cj: the coefficient of xmyn

The symbol Cj represents the coefficient of the free curved surface, however, this coefficient is expressed with xmynin Table 1. In the case of this free curved surface, the free-form curved surface coefficient contains a coefficient concerning the paraxial axis, and hence the values of the meridional section radius-of-curvature rx and the sagittal section radius-of-curvature ry of the general-paraxial axis are not coincident with the actual meridional section radius-of-curvature rx and the actual sagittal section radius-of-curvature ry on the surface vertex. There are also shown the actual meridional section radius-of-curvature rx and the actual sagittal section radius-of-curvature ry at the pint (0, 0), i.e., on the surface vertex. Moreover, in the local-paraxial axis, there are shown local radii-of-curvature local-rx and local-ry, a local surface-to-surface interval local-d (the reflection surface is the reverse symbol), local focal lengths local-fx and local-fy, and a surface refractive index nd (the reflection surface in the reverse symbol). Shown further are a hit point coordinate (the surface vertex is 0, 0) on each surface and angles-of-view 2Wx and 2Wy (a total full field angle of a plus (+) side and a minus (−) side) at the exit pupils.

This application claims priority from Japanese Patent Application No. 2004-351468 filed on Dec. 3, 2004, which is hereby incorporated by reference herein.