Optical visual apparatus

The invention provides an optical visual apparatus which eliminates ghost light and is small in size and light in weight so that observation for a long time does not tire the eyes of a user and the user does not suffer from displacement of the apparatus on the head. A half mirror for reflecting image light from a two-dimensional display element is formed in a wedge-shaped profile having a varying thickness such that an opposing surface opposing to a half-coated surface is inclined with respect to the half-coated surface. The inclination angle of the opposing inclined surface and the Abbe's number of the half mirror are so set that ghost light and regular light are overlapped with each other at the position of an eye-ball of the user or the ghost light is reflected to the outside of the field of view of the user so that the ghost light may not be observed by the user.

BACKGROUND OF THE INVENTION 
This invention relates to an optical visual apparatus, and more 
particularly to a half mirror for use with a small size light-weighted 
optical visual apparatus which can be mounted on the head of a user. 
Head-mounted display units for virtual reality, for medical care, for 
military use, for a computer or for individual enjoyment with a large 
screen are known as optical visual apparatus. 
Further, in recent years, a head-mounted display unit with which an image 
from a two-dimensional display element formed form a CRT, an LCD or a like 
element is magnified as a virtual image to be observed draws attention and 
is developed. 
In the head-mounted display unit just described, the system for magnifying 
an image form the two-dimensional display element as a virtual image to be 
observed is such as shown in FIG. 24. Referring to FIG. 24, the system 
includes a two-dimensional display element 10 for displaying an image, and 
a half mirror 20 in the form of a parallel plate of a predetermined 
thickness for branching an optical path. The half mirror 20 has a 
half-coated surface 21 on the side thereof into which light is introduced. 
The system further includes a concave mirror 22 for magnifying the image 
as a virtual image to be observed. 
When a user of the two-dimensional display element having the construction 
described above tries to observe an image from the two-dimensional display 
element as a magnified virtual image, light 23 from the half mirror 20 
illuminated with a light source unit not shown is branched by the half 
mirror 20. Light 24 reflected thereupon from the half-coated surface 21 
toward the concave mirror 22 side is subsequently reflected by the concave 
mirror 22 and forms an optical path of regular light 26 which enters an 
eye-ball 25. 
On the other hand, light 27 coming into the half mirror 20 refractively 
through the half-coated surface 21 is branched into light 28 which goes 
out through the opposite surface of the half mirror 20 and light 29 which 
is reflected by the opposite surface of the half mirror 20 and then goes 
out refractively through the half-coated surface 21 toward the concave 
mirror 22. The latter light 29 forms an optical path of ghost light 30 
which is reflected from the concave mirror 22 and enters the eyeball 25. 
In this manner, the half mirror 20 formed from a parallel plate of a 
predetermined thickness never fails to have an optical path of the light 
29 which comes into and goes out from the half mirror 20, that is, the 
ghost light 30, unless it can totally reflect the incoming light the 
half-coated surface 21 thereof. 
However, the optical visual apparatus which includes the two-dimensional 
display element 10 for displaying an image, the half mirror 20 for 
branching an optical path and the concave mirror 22 for magnifying the 
image as a virtual image to be observed has several problems to be solved. 
In particular, in the optical visual apparatus, when light from the 
two-dimensional display element 10 illuminated with the light source unit 
is branched by the half mirror 20, light 24 reflected from the half-coated 
surface 21 is magnified by the concave mirror 22 and observed as regular 
light 26. Simultaneously, however, light having passed through the 
half-coated surface 21 comes to the opposite surface of the half mirror 
20, and most light 28 of it passes through the opposite surface, but part 
of the light is reflected from the opposite surface. The reflected light 
29 passes refractively through the half-coated surface 21 and is then 
reflected by the concave mirror 22 to make ghost light 30 which enters the 
eye-ball 25 and is observed as a magnified virtual image. 
When an image formed from the regular light 26 and another image formed 
from the ghost light 30 are observed simultaneously, the image composed of 
the two images becomes a double image as seen in FIG. 26 and the original 
image may not sometimes be recognized because such a double image is 
indistinct. Further, observation of such a double image for a long time 
tires the eyes. 
On the other hand, if a beam splitter or a prism is used in order to 
eliminate the ghost light 30, then this gives rise to such problems that 
the apparatus is degraded in balance or in mounting feeling to the user 
or, when the apparatus is used for a long time, the apparatus is displaced 
on the head and the user cannot observe the image well. 
Further, where external light is to be observed as see-through light, if a 
beam splitter or a prism is used, then the light is spectrally diffracted 
due to an angle characteristic of a coating on the beam splitter or by the 
prism. Consequently, the external image is colored and is so hard to 
observe that the original image cannot be observed regularly. Further, 
observation of such an image for a long time tires the eyes. 
SUMMARY OF THE INVENTION 
It is an object of the present invention to provide an optical visual 
apparatus which eliminates ghost light so that observation for a long time 
does not tire the eyes of a user. 
It is another object of the present invention to provide an optical visual 
apparatus which is small in size and light in weight so that observation 
for a long time does not tire the eyes of a user and the user does not 
suffer from displacement of the apparatus on the head. 
In order to attain the objects described above, according to the present 
invention, there is provided an optical visual apparatus, comprising a 
two-dimensional display element for displaying an image, a half mirror for 
branching an optical path from the two-dimensional display element, and a 
concave mirror for magnifying the image based on the optical path from the 
half mirror as a virtual image to be observed, the half mirror having a 
half-coated surface half-coated so as to reflect part of light of the 
image from the two-dimensional display element and pass the remaining part 
of the light therethrough while an opposing surface of the half mirror 
opposing to the half-coated surface is inclined with respect to the 
half-coated surface. 
In the optical visual apparatus, since the half mirror is constructed such 
that the opposing surface thereof opposing to the half-coated surface is 
inclined with respect to the half-coated surface so that the half mirror 
may have a wedge-shaped profile having a varying thickness, it is possible 
to make ghost light overlapped with regular light reflected by the half 
mirror. Particularly where the ghost light and the regular light are 
overlapped with each other at the position of an eye-ball of the user, the 
user can observe only the regular light of a higher intensity but does not 
observe the ghost light. In other words, the ghost light can be eliminated 
only by the improvement in the half mirror. Consequently, the entire 
optical visual apparatus can be constructed in a comparatively small size 
with a comparatively low weight, and observation of the optical visual 
apparatus for a long time does not tire the eyes of the user nor cause 
displacement of the optical visual apparatus. 
Or, since the half mirror in the optical visual apparatus is constructed in 
such a manner as described above, the optical visual apparatus may be 
constructed so that the optical path of the ghost light may be directed to 
the outside of the field of view of the user so as to prevent the ghost 
light from being observed by the user by suitably adjusting the 
inclination angle of the opposing inclined surface opposing to the 
half-coated surface of the half mirror, the thickness of the half mirror 
on the optical axis, the refractive index of the half mirror or some other 
parameter of the half mirror. 
The above and other objects, features and advantages of the present 
invention will become apparent from the following description and the 
appended claims, taken in conjunction with the accompanying drawings in 
which like parts or elements are denoted by like reference characters.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
An optical visual apparatus according to the present invention which 
employs a half mirror having a half-coated surface and an opposing phase 
which is inclined with respect to the half-coated surface so that the 
half-mirror has a wedge-shaped profile with a varying thickness is 
described below with reference to the drawings. 
Referring first to FIG. 1, an optical visual apparatus 50 to which the 
present invention is applied includes a head mounted member 51, a display 
unit 58 supported on the head mounted member 51 at a location in front of 
and in an opposing relationship to the eyes of a user on which the optical 
visual apparatus 50 is mounted for forming an image in the eyes, and a 
connection member 60 for interconnecting the head mounted member 51 and 
the display unit 58 to support the display unit 58 at the location in 
front of the eyes. 
The head mounted member 51 includes a head supported member 53 having a 
curved profile substantially conforming to the head of the user and 
connected to an end portion of the connection member 60. The head 
supported member 53 supports a base end portion of a forehead pad 52 for 
contacting with the forehead of the user. The head mounted member 51 
further includes a pair of side cabinets 55 connected to the opposite ends 
of the head supported member 53 by a pair of hinges 54, a head 
circumference adjustment belt 56 connected for adjustment to the other 
ends of the side cabinets 55, and a hair band 57 connected to and located 
above the side cabinets 55 such that it extends along and adjustably holds 
a top portion of the head of the user. 
The display unit 58 has a display body 59 formed from a housing having a 
shape substantially like goggles and covering the front of the display 
unit 58. 
Referring to FIG. 2, the display body 59 includes a two-dimensional display 
element 61 for displaying an image in the inside of a housing, a light 
source unit 62 for supplying light to the two-dimensional display element 
61, a half mirror 63 for changing an optical path of or passing an image 
from the two-dimensional display element 61, and a concave mirror 64 for 
magnifying the ray of light whose optical path has been changed by the 
half mirror 63 as a virtual image to be observed. 
The half mirror 63 is a flat plate having a substantially wedge-shaped 
profile with a varying thickness as seen in FIG. 3. A major surface of the 
half mirror 63 is formed as a half-coated surface 65 which reflects part 
of light of an image and transmits the remaining part of the light 
therethrough, and an opposing surface 66 of the half mirror 63 is inclined 
with respect to the half-coated surface 65. 
Different forms of the display body having such a construction as described 
above will be described below. 
Referring first to FIG. 4, there is shown a first form of the display body. 
The display body of the first form is generally denoted at 59A and is 
constructed such that a wedge-shaped half mirror 63 formed as a flat plate 
having a varying thickness is disposed obliquely such that the thickness 
thereof gradually decreases upwardly. 
In particular, the display body 59A is mounted on the head of the user such 
that the half mirror 63 is inclined at an inclination angle of 
approximately 45 degrees with the half-coated surface 65 thereof directed 
toward the two-dimensional display element 61 while a thicker portion 
thereof is positioned on the lower side. 
The concave mirror 64 is positioned in an opposing relationship to an 
eye-ball 67 with the half mirror 63 interposed between the concave mirror 
64 and the two-dimensional display element 61 positioned perpendicularly 
to the concave mirror 64. 
In the display body 59A having such a construction as described above, 
light 68 of an image from the two-dimensional display element 61 
illuminated with the light source unit not shown is branched by the half 
mirror 63 into regular light 69 which is reflected by the half-coated 
surface 65 and advances toward the concave mirror 64 and another light 70 
which passes refractively through the half-coated surface 65. The light 70 
passes through the inside of the half mirror 63 and comes to the opposing 
surface 66. 
While most of the light 70 passes through and emerges outwardly from the 
opposing surface 66, part of the light 70 is reflected by the opposing 
surface 66 and makes ghost light 71. The ghost light 71 passes through the 
inside of the half mirror 63 again and comes to the half-coated surface 
65. Then, the ghost light 71 is refracted at the boundary between the 
half-coated surface 65 and the air and then advances toward the concave 
mirror 64. Thereafter, the ghost light 71 is reflected by the concave 
mirror 64 and then passes through the half mirror 63 again so that it is 
observed as a magnified virtual image by the user of the optical visual 
apparatus 50. 
Since this ghost light 71 is produced because an optical path difference or 
an angle difference from regular light is produced by the thickness and 
the refractive index of the half mirror 63 as seen from FIGS. 4 and 5, if 
the inclination angle of the opposing surface 66 opposing to the 
half-coated surface 65, the thickness of the half mirror 63 on the optic 
axis, the material of the half mirror 63 and so forth are varied so that 
the optical path of the ghost light 71 reflected by the concave mirror 64 
and the optical path of the regular light 69 reflected by the concave 
mirror 64 may coincide with each other at the position of the eye-ball 67, 
then the regular light 69 and the ghost light 71 overlap with each other 
and only the regular light 69 having a higher intensity is observed by the 
user while the ghost light 71 is not observed. It is to be noted that, 
while it is shown in FIG. 4 that the regular light 69 and the ghost light 
71 are not fully coincident with each other, there is merely for 
convenience of illustration, and actually, they coincide fully with each 
other and the ghost light 71 is not observed separately from the regular 
light 69. 
Or, also if the inclination angle and the thickness on the optical axis of 
the half mirror 63 are adjusted so that the ghost light 71 is reflected to 
a position outside the field of view in which the user looks at a screen 
produced by the two-dimensional display element 61, it is possible to 
prevent the ghost light 71 from being observed by the user while only the 
regular light 69 is observed. 
By using the wedge-shaped half mirror 63 having a varying thickness in this 
manner, an image free from ghost light can be realized. Thus, since ghost 
light can be eliminated only by the structure of the half mirror 63 
without the necessity for any other structural element, improvement in 
performance and reduction in size and weight can be anticipated. 
Referring now to FIG. 6, there is shown a second form of the display body. 
The display body of the second form is generally denoted at 59B and is a 
modification to but different from the display body 59A of the first form 
described with reference to FIG. 4 above in the mounting structure of the 
half mirror 63. In particular, the display body 59B is constructed such 
that the wedge-shaped half mirror 63 having a varying thickness is 
disposed obliquely such that it is inclined with an inclination angle of 
approximately 45 degrees with the half-coated surface 65 thereof directed 
toward the eye-ball 67 and a thicker portion thereof is positioned on the 
upper side while the concave mirror 64 is located adjacent the half-coated 
surface 65. 
In the display body 59B having such a construction as described above, 
light 68 of an image from the two-dimensional display element 61 comes 
into the half mirror 63 and then advances straightforwardly until it is 
reflected by the concave mirror 64. The reflected light 70 from the 
concave mirror 64 is reflected toward the eye-ball 67 by the half-coated 
surface 65 of the half mirror 63 so that it makes regular light 69 which 
enters the eye-ball 67. 
On the other hand, part of the light 70 reflected from the concave mirror 
64 passes through the half-coated surface 65 and refractively comes into 
the half mirror 63. Then, the light 70 is branched by the opposing surface 
66 opposing to the half-coated surface 65 into light which goes out into 
the air from the opposing surface 66 and ghost light 71 which is reflected 
by the opposing surface 66 opposing to the half-coated surface 65 and goes 
out refractively through the half-coated surface 65 so that it is 
introduced into the eye-ball 67. 
Similarly as with the display body 59A of the first form described 
hereinabove with reference to FIG. 4, if the inclination angle of the 
opposing surface 66 opposing to the half-coated surface 65 of the half 
mirror 63, the thickness of the half mirror 63 on the optical axis, the 
material of the half mirror 63 and so forth are varied so that the optical 
path of the ghost light 71 reflected by the concave mirror 64 and the 
optical path of the regular light 69 reflected by the concave mirror 64 
may coincide with each other at the position of the eye-ball 67, then the 
regular light 69 and the ghost light 71 overlap with each other, and 
consequently, only the regular light 69 having a higher intensity is 
observed by the user while the ghost light 71 is not observed. 
Or, also if the inclination angle or the thickness on the optical axis of 
the half mirror 63, the material of the half mirror 63 or the like is 
varied so that the ghost light 71 is reflected to a position outside the 
field of view in which the user looks at a screen produced by the 
two-dimensional display element 61, it is possible to prevent the ghost 
light 71 from being observed by the user while only the regular light 69 
is observed. 
Referring now to FIG. 7, there is shown a third form of the display body. 
The display body of the third form is generally denoted at 59C and is a 
modification to but different from the display body 59B of the second form 
described with reference to FIG. 6 above in that it additionally includes 
a liquid crystal shutter 72 provided on the outer side of the concave 
mirror 64 and serving as means for adjusting the amount of light to be 
provided to the concave mirror 64. 
In the display body 59C having the construction just described, production 
of regular light 69 and ghost light 71 and optical paths of them are 
similar to those in the display body 59B of FIG. 6, and overlapping 
description thereof is omitted here. 
Since the display body 59C additionally includes the liquid crystal shutter 
72, it becomes easier for the user to observe a condition of the external 
world, and a ray of light which may otherwise come to a location in front 
of the eye-ball 67 can be intercepted. Consequently, a clearer image can 
be observed. 
Referring now to FIG. 8, there is shown a fourth form of the display body. 
The display body of the fourth form generally denoted at 59D is a 
modification to but different from the display body 59C of the third form 
described with reference to FIG. 7 above in that the liquid crystal 
shutter 72 serving as means for adjusting the amount of light is located 
in an opposing relationship to the eye-ball 67 on the outer side of the 
half mirror 63. 
Also in the display body 59D having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59B of FIG. 6, and 
overlapping description thereof is omitted here. Since the liquid crystal 
shutter 72 is located in an opposing relationship to the eye-ball 67, it 
becomes easier for the user to observe a condition of the external world, 
and a ray of light which may otherwise come to a location in front of the 
eye-ball 67 can be intercepted. Consequently, a clearer image can be 
observed. 
Referring now to FIG. 9, there is shown a fifth form of the display body. 
The display body of the fifth form generally denoted at 59E is a 
modification to but different from the display body 59A of the first form 
described with reference to FIG. 4 above in that a lens 73 is interposed 
between the half mirror 63 and the eye-ball 67. 
Also in the display body 59E having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59A of FIG. 4, and 
overlapping description thereof is omitted here. Since the lens 73 is 
located in front of the eye-ball 67, the focus of an image of light 
introduced into the eye-ball 67 can be adjusted to the position of the 
eye-ball 67. Consequently, a clearer image can be observed. 
Referring now to FIG. 10, there is shown a sixth form of the display body. 
The display body of the sixth form generally denoted at 59F is a 
modification to but different from the display body 59B of the second form 
described with reference to FIG. 6 above in that a lens 73 is interposed 
between the half mirror 63 and the eye-ball 67. 
Also in the display body 59F having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59B of FIG. 6, and 
overlapping description thereof is omitted here. 
Since the lens 73 is located in front of the eyeball 67, similarly as in 
the display body 59E described hereinabove with reference to FIG. 9, the 
focus of an image of light introduced into the eye-ball 67 can be adjusted 
to the position of the eye-ball 67. Consequently, a clearer image can be 
observed. 
Referring now to FIG. 11, there is shown a seventh form of the display 
body. The display body of the seventh form generally denoted at 59G is a 
modification to but different from the display body 59A of the first form 
described with reference to FIG. 4 above in that a lens 74 is interposed 
between the half mirror 63 and the two-dimensional display element 61. 
Also in the display body 59G having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59A of FIG. 4, and 
overlapping description thereof is omitted here. Since the lens 74 is 
located in front of the two-dimensional display element 61, the focus of 
the light 68 from the two-dimensional display element 61 can be adjusted 
to the position of the eye-ball 67. Consequently, a clearer image can be 
observed. 
Referring now to FIG. 12, there is shown an eighth form of the display 
body. The display body of the eighth form generally denoted at 59H is a 
modification to but different from the display body 59B of the second form 
described with reference to FIG. 6 above in that a lens 74 is interposed 
between the half mirror 63 and the two-dimensional display element 61. 
Also in the display body 59H having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59B of FIG. 6, and 
overlapping description thereof is omitted here. Since the lens 74 is 
located in front of the two-dimensional display element 61, the focus of 
the light 68 from the two-dimensional display element 61 can be adjusted 
to the position of the eye-ball 67. Consequently, a clearer image can be 
observed. 
Referring now to FIG. 13, there is shown a ninth form of the display body. 
The display body of the ninth form generally denoted at 59J is a 
modification to but different from the display body 59A of the first form 
described with reference to FIG. 4 above in that the concave mirror 64 is 
located in an opposing relationship to the eye-ball 67 and is half-coated 
on a reflection surface thereof adjacent the eye-ball 67 while a 
transmission surface 75 through which light from the external world can 
pass is provided on the outer side of the concave mirror 64. 
Also in the display body 59J having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59A of FIG. 4, and 
overlapping description thereof is omitted here. Since the concave mirror 
64 is half-coated on the reflection surface thereof, the user can observe 
an image from the two-dimensional display element 61 while observing the 
external world. 
Referring now to FIG. 14, there is shown a tenth form of the display body. 
The display body of the tenth form generally denoted at 59K is a 
modification to but different from the display body 59J of the ninth form 
described with reference to FIG. 13 above in that a liquid crystal shutter 
76 serving as means for adjusting the amount of light is provided on the 
external world side of the concave mirror 64 which is half-coated on the 
semispherical reflection surface thereof and has the transmission surface 
75 provided on the outer side thereof. 
Also in the display body 59K having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59A of FIG. 4, and 
overlapping description thereof is omitted here. Since the transmission 
surface 75 which passes light of the external world therethrough is 
provided on the outer side of the concave mirror 64 serving as a lens 
member and the liquid crystal shutter 76 is provided on the external world 
side of the concave mirror 64, the user can observe an image from the 
two-dimensional display element 61 while observing the external world. 
Further, when the user wants to observe only the image from the 
two-dimensional display element 61, the user may operate so as to close 
the liquid crystal shutter 76, but when the user wants to observe the 
external world, the user may operate so as to open the liquid crystal 
shutter 76. 
Referring now to FIG. 15, there is shown an eleventh form of the display 
body. The display body of the eleventh form generally denoted at 59L is a 
modification to but different from the display body 59G of the seventh 
form described with reference to FIG. 11 above in that the concave mirror 
64 is located in an opposing relationship to the eye-ball 67 and is 
half-coated on a reflection surface thereof adjacent the eye-ball 67 while 
a transmission surface 75 through which external light can pass is 
provided on the outer side of the concave mirror 64. 
Also in the display body 59K having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59A of FIG. 4, and 
overlapping description thereof is omitted here. Since the lens 74 is 
located in front of the two-dimensional display element 61, the focus of 
the light 68 from the two-dimensional display element 61 can be adjusted 
to the position of the eye-ball 67. Consequently, a clearer image can be 
observed. Further, since the concave mirror 64 is half-coated on the 
reflection surface thereof and the transmission surface 75 is provided on 
the outer side of the concave mirror 64, a ray of light from the external 
world can be inputted to the display body 59L, and the user can observe an 
image from the two-dimensional display element 61 while observing the 
external world. 
Referring now to FIG. 16, there is shown a twelfth form of the display 
body. The display body of the twelfth form generally denoted at 59M is a 
modification to but different from the display body 59L of the eleventh 
form described with reference to FIG. 15 above in that the concave mirror 
64 is half-coated on the reflection surface thereof adjacent the eye-ball 
67 and has the transmission surface 75 provided on the outer side thereof 
and a liquid crystal shutter 76 serving as means for adjusting the amount 
of light is provided on the external world side of the concave mirror 64. 
Also in the display body 59M having the construction just described, 
production of regular light 69 and ghost light 71 and optical paths of 
them are similar to those in the display body 59A of FIG. 4, and 
overlapping description thereof is omitted here. Since the lens 74 is 
located in front of the two-dimensional display element 61, the focus of 
the light 68 from the two-dimensional display element 61 can be adjusted 
to the position of the eye-ball 67. Consequently, the user can observe a 
clearer image while observing the external world, and when the user wants 
to observe only the image from the two-dimensional display element 61, the 
user may operate so as to close the liquid crystal shutter 76, but when 
the user wants to observe the external world, the user may operate so as 
to open the liquid crystal shutter 76. 
FIGS. 18 to 21 show different examples used in simulation conducted varying 
the construction of the basic optical system and the positional 
relationship of the lenses 73 and 74 ignoring the thickness of the half 
mirror 63. In the simulation, the radius of curvature r, the surface 
separation d, the refractive index nd, the Abbe's number .nu.d and the 
aspherical surface coefficients K, A, B, C and D in the optical path to 
the eye-ball 67 including the lens 73 or lens 74 and the concave mirror 64 
are calculated. Meanwhile, FIG. 17 shows the aspherical surface profile in 
regard to the distance between the same and the optical axis. For the 
aspherical surface profile, in FIG. 17, the direction of the optical axis 
is taken as the Z axis and a direction perpendicular to the optical axis 
(Z axis) is taken as the Y axis, and the advancing direction of light is 
represented in the positive. Then, using the paraxial radius of curvature 
r and the aspherical surface coefficients K, A, B, C and D, the distance 
.DELTA.Z in the Z-axis direction (direction of the optical axis) is 
calculated based on the following expression (1): 
##EQU1## 
In the first example, as seen from FIG. 18 and Tables 1 and 2 given below, 
a concave mirror 64 having a focal length f=27.0 mm is disposed on the 
same straight line as an eye-ball 67 while a two-dimensional display 
element (LCD) 61 is disposed on a line perpendicular to the straight line 
and a lens 74 is located adjacent the two-dimensional display element 
(LCD) 61. Accordingly, the present example has a similar construction to 
that of the display body 59G of the seventh form described hereinabove 
with reference to FIG. 11. 
As surfaces to be observed, the position of the eye-ball 67 is determined 
as a first surface S1, the location of a viewing window 77 as a second 
surface S2, the reflection surface of the concave mirror 64 as a third 
surface S3, the light emergence surface of the lens 74 as a fourth surface 
S4, the light incidence surface of the lens 74 as a fifth surface S5, and 
a surface on which an image from the two-dimensional display element 61 is 
displayed is determined as a sixth surface S6. Then, the surface 
separation is calculated based on the expression (1) given above. The 
aspherical surface coefficient or coefficients to be substituted into the 
expression (1) in this instance are the third surface S3 and the fourth 
surface S4 as seen from Table 2 given below. Here, "d" of the refractive 
index nd appearing in the tables given below represents light of a d ray 
(wavelength: 587.56 mm). 
TABLE 1 
__________________________________________________________________________ 
EXAMPLE 1! 
FOCAL LENGTH 1 f = 27.00 mm 
SURFACE REFRACTIVE 
ABBE'S 
SURFACE 
RADIUS OF SEATION 
INDEX NUMBER 
NUMBER 
CURVATURE (mm) (nd) (.nu.d) 
__________________________________________________________________________ 
S0 r.sub.0 = .infin. 
d.sub.0 = -2000.0 
(VIRTUAL IMAGE) 
S1 r.sub.1 = .infin. 
d.sub.1 = 20.0 
(PUPIL POSITION) 
S2 r.sub.2 = .infin. 
d.sub.2 = 27.0 
S3 r.sub.3 = -61.237 
d.sub.3 = -25.6 
(CONCAVE MIRROR) 
S4 r.sub.4 = -18.406 
d.sub.4 = -4.55 
nd.sub.4 = 1.49154 
.nu.d.sub.4 = 58.0 
(LENS) 
S5 r.sub.5 = .infin. 
d.sub.5 = -1.0 
S6 r.sub.6 = .infin. 
__________________________________________________________________________ 
TABLE 2 
______________________________________ 
ASPHERICAL SURFACE ASPHERICAL SURFACE 
COEFFICIENT OF COEFFICIENT OF 
THIRD SURFACE FOURTH SURFACE 
______________________________________ 
K.sub.3 = 0.14431E + 01 
K.sub.4 = 0.12758E + 01 
A.sub.3 = 0.50200E - 06 
A.sub.4 = -0.25025E - 03 
B.sub.3 = 0.18931E - 08 
B.sub.4 = 0.78300E - 05 
C.sub.3 = -0.61974E - 11 
C.sub.4 = -0.10653E - 06 
D.sub.3 = 0.76573E - 14 
D.sub.4 = 0.52602E - 09 
______________________________________ 
In the second example, as seen from FIG. 19 and Tables 3 and 4 given below, 
a concave mirror 64 having a focal length f=29.88 mm is disposed on the 
same straight line as an eye-ball 67 while a lens 73 is disposed adjacent 
the eye-ball 67 on the strait line and a two-dimensional display element 
(LCD) 61 is disposed on a line perpendicular to the straight line. 
Accordingly, the present example has a similar construction to that of the 
display body 59E of the fifth form described hereinabove with reference to 
FIG. 9. 
As surfaces to be observed, the position of the eye-ball 67 is determined 
as a first surface S1, the light emergence surface of the lens 73 as a 
second surface S2, the light incidence surface of the lens 73 as a third 
surface S3, the reflection surface of the concave mirror 64 as a fourth 
surface S4, and the surface on which an image from the two-dimensional 
display element (LCD) 61 is displayed is determined as a fifth surface S5. 
Then, the surface separation is calculated based on the expression (1) 
given above. The aspherical surface coefficient or coefficients to be 
substituted into the expression (1) in this instance are the second 
surface S2, the third surface S3 and the surface S4 as seen from Table 4 
given below. 
TABLE 3 
__________________________________________________________________________ 
EXAMPLE 2! 
FOCAL LENGTH f = 29.88 mm 
SURFACE REFRACTIVE 
ABBE'S 
SURFACE 
RADIUS OF SEATION 
INDEX NUMBER 
NUMBER 
CURVATURE (mm) (nd) (.nu.d) 
__________________________________________________________________________ 
S0 r.sub.0 = .infin. 
d.sub.0 = -2000.0 
(VIRTUAL IMAGE) 
S1 r.sub.1 = .infin. 
d.sub.1 = 25.0 
(PUPIL POSITION) 
S2 r.sub.2 = -66.832 
d.sub.2 = 5.4 
nd.sub.2 = 1.49154 
.nu.d.sub.2 = 58.0 
(LENS) 
S3 r.sub.3 = -34.019 
d.sub.3 = 21.5 
S4 r.sub.4 = -66.618 
d.sub.4 = -25.42 
(CONCAVE MIRROR) 
S5 r.sub.5 = .infin. 
(LCD) 
__________________________________________________________________________ 
TABLE 4 
______________________________________ 
ASPHERICAL ASPHERICAL ASPHERICAL 
SURFACE SURFACE SURFACE 
COEFFICIENT OF 
COEFFICIENT OF COEFFICIENT OF 
SECOND SURFACE 
THIRD SURFACE FOURTH SURFACE 
(S2) (S3) (S4) 
______________________________________ 
K.sub.2 = -100.0 
K.sub.3 = -0.64617E + 01 
K.sub.4 = 0.72422E + 01 
A.sub.2 = -0.16325E - 03 
A.sub.3 = -0.13760E - 03 
A.sub.4 = 0.67310E - 05 
B.sub.2 = 0.155225E - 06 
B.sub.3 = 0.114620 - E06 
B.sub.4 = -0.83918E - 08 
C.sub.2 = -0.24778E - 08 
C.sub.3 = -0.709600 - E09 
C.sub.4 = -0.16650E - 10 
D.sub.2 = 0.38320E - 11 
D.sub.3 = -0.159270 - E11 
D.sub.4 = 0.41881E - 13 
______________________________________ 
In the third example, as seen from FIG. 20 and Tables 5 and 6 given below, 
a concave mirror 64 having a focal length f=27.00 mm is disposed on the 
same straight line as an eye-ball 67 while a two-dimensional display 
element (LCD) 61 is disposed on a line perpendicular to the straight line. 
Accordingly, the present example has a similar construction to that of the 
display body 59A of the first form described hereinabove with reference to 
FIG. 4. 
As surfaces to be observed, the position of the eye-ball 67 is determined 
as a first surface S1, the reflection surface of the concave mirror 64 as 
a second surface S2, and the surface on which an image from the 
two-dimensional display element (LCD) 61 is displayed is determined as a 
third surface S3. Then, the surface separation is calculated based on the 
expression (1) given above. The aspherical surface coefficient or 
coefficients to be substituted into the expression (1) in this instance 
are the second surface S2 as seen from Table 6 given below. 
TABLE 5 
______________________________________ 
EXAMPLE 3! 
FOCAL LENGTH f = 27.00 mm 
SURFACE 
SURFACE RADIUS OF SEATION 
NUMBER CURVATURE (mm) 
______________________________________ 
S0 r.sub.0 = .infin. 
d.sub.0 = -2000.0 
(VIRTUAL IMAGE) 
S1 r.sub.1 = .infin. 
d.sub.1 = 46.50 
(PUPIL POSITION) 
S2 r.sub.2 = -60.000 
d.sub.2 = -29.55 
(CONCAVE MIRROR) 
S3 r.sub.3 = .infin. 
(LCD) 
______________________________________ 
TABLE 6 
______________________________________ 
ASPHERICAL SURFACE COEFFICIENT 
OF SECOND SURFACE (S2) 
______________________________________ 
K.sub.2 = -0.79543E + 01 
A.sub.2 = -0.48736E - 05 
B.sub.2 = 0.48657E - 08 
C.sub.2 = -0.12418E - 10 
D.sub.2 = 0.15767E - 13 
______________________________________ 
In the fourth example, as seen from FIG. 21 and Tables 7 and 8 given below, 
a concave mirror 64 having a focal length f=26.0 mm is disposed on the 
same straight line as an eye-ball 67 while a two-dimensional display 
element (LCD) 61 is disposed on a line perpendicular to the straight line 
and a lens 74 is located adjacent the two-dimensional display element 
(LCD) 61. Accordingly, the present example has a similar construction to 
that of the display body 59G of the seventh form described hereinabove 
with reference to FIG. 11. 
As surfaces to be observed, the position of the eye-ball 67 is determined 
as a first surface S1, the reflection surface of the concave mirror 64 as 
a second surface S2, the light emergence surface of the lens 74 as a third 
surface S3, the light incidence surface of the lens 74 as a fourth surface 
S4, and the surface on which an image from the two-dimensional display 
element (LCD) 61 is displayed is determined as a fifth surface S5. Then, 
the surface separation is calculated based on the expression (1) given 
above. The aspherical surface coefficient or coefficients to be 
substituted into the expression (1) in this instance are the second 
surface S3, the third surface S3 and the fourth surface S4 as seen from 
Table 8 given below. 
TABLE 7 
__________________________________________________________________________ 
EXAMPLE 4! 
FOCAL LENGTH f = 26.00 mm 
SURFACE REFRACTIVE 
ABBE'S 
SURFACE 
RADIUS OF SEATION 
INDEX NUMBER 
NUMBER 
CURVATURE (mm) (ud) (.nu.d) 
__________________________________________________________________________ 
S0 r.sub.0 = .infin. 
d.sub.0 = -2000.0 
(VIRTUAL IMAGE) 
S1 r.sub.1 = .infin. 
d.sub.1 = 46.50 
(PUPIL POSITION) 
S2 r.sub.2 = -62.822 
d.sub.2 = -23.50 
(CONCAVE MIRROR) 
S3 r.sub.3 = 168.47 
d.sub.3 = -4.45 
nd.sub.3 = 1.49154 
.nu.d.sub.3 = 58.0 
(LENS) 
S4 r.sub.4 = 10.624 
d.sub.4 = -3.79 
S5 r.sub.5 = .infin. 
__________________________________________________________________________ 
TABLE 8 
______________________________________ 
ASPHERICAL ASPHERICAL ASPHERICAL 
SURFACE SURFACE SURFACE 
COEFFICIENT OF 
COEFFICIENT OF COEFFICIENT OF 
SECOND SURFACE 
THIRD SURFACE FOURTH SURFACE 
______________________________________ 
K.sub.2 = -0.12636E + 01 
K.sub.3 = 0.86326E + 02 
K.sub.4 = -0.55900E + 00 
A.sub.2 = 0.31847E - 06 
A.sub.3 = -0.33159E - 03 
A.sub.4 = -0.10200E - 02 
B.sub.2 = -0.56388E - 08 
B.sub.3 = 0.17386E - 05 
B.sub.4 = 0.98432E - 05 
C.sub.2 = 0.15590E - 10 
C.sub.3 = 0.63414E - 08 
C.sub.4 = -0.41761E - 07 
D.sub.2 = -0.15520E - 13 
D.sub.3 = 0.62092E - 10 
D.sub.4 = 0.33410E - 10 
______________________________________ 
Subsequently, different forms of the half mirror 63 which can be applied to 
the first to fourth examples which employs the basic optical system 
described above will be described with reference to FIGS. 22A and 22B and 
Tables 9 and 10. 
In the half mirror 63 of a wedge-shaped profile having a varying thickness, 
as the Abbe's number .nu.d decreases, the angular difference between 
colors by the wavelength increases, and the external world looks with some 
color. Further, as the inclination angle .theta.m of the opposing surface 
66 increases, the prism action increases, and the external world looks 
with some color. 
In particular, referring to FIG. 22A, as the Abbe's number .nu.d decreases 
or the inclination angle .theta.m of the inclined angle increases, white 
light from the external world which enters from the opposing surface 66 
side of the half mirror 63 is refracted by the prism action so that it 
enters the eye-ball with an angular difference between a C ray of red 
light (wavelength: 656.27 mm) and a g ray of blue light (wavelength: 
435.83 mm). The angular difference between the colors by the wavelength is 
represented as an angular difference of refracted rays of light of Tables 
9 and 10 and relates to the Abbe's number .nu.d and the thickness of a 
normal line on the optical axis shown in FIG. 22B (that is, the 
inclination angle .theta.m). Here, "d" of the Abbe's number .nu.d 
represents light of 587.56 mm. 
A fifth example relates to a result of simulation of the relationship 
between the g ray 71 of blue light and the C ray 71 of red light making 
use of such a half mirror 63 of a wedge-shaped profile having a varying 
thickness as shown in FIG. 22A. In the simulation, the refractive index 
nd, the Abbe's number .nu.d and the angular difference of refracted rays 
of the C and g rays are calculated from the inclination angle .theta.m of 
the opposing surface 66 opposing to the half-coated surface 65 and the 
thickness on the optical axis of the half mirror 63 of a wedge-shaped 
profile having a varying thickness. In Table 9 given below, the 
inclination angle .theta.m of the opposing surface 66, the thickness d on 
the optical axis, the refractive index nd, the Abbe's number .nu.d and the 
angular difference between refracted rays of the C and g rays are listed. 
From Table 9, it can be recognized readily that, in order to restrict the 
angular difference between the red light C ray 69 and the blue light g ray 
71 within an allowable range using the half mirror 63 of a wedge-shaped 
profile having a varying thickness, the condition given by the following 
expression: 
EQU Abbe's number .nu.d&gt;45 should be satisfied. 
TABLE 9 
__________________________________________________________________________ 
EXAMPLE 5! 
INCLINATION ANGLE 
THICKNESS ON 
REFRACTIVE 
ABBE'S 
ANGULAR DIFFERENCE 
OF INCLINED FACE 
OPTICAL AXIS 
INDEX NUMBER 
BETWEEN RAYS OF 
(.crclbar.m.degree.) 
(mm) (nd) (.nu.d) 
C & g RAYS 
__________________________________________________________________________ 
1 1.1746 1.0 1.492 58.0 0.00040 
2 1.6972 1.5 1.492 58.0 0.00057 
3 2.1773 2.0 1.492 58.0 0.00071 
4 0.9845 1.0 1.600 45.0 0.00053 
5 1.4243 1.5 1.600 45.0 0.00075 
6 1.8300 2.0 1.600 45.0 0.00095 
7 1.1191 1.0 1.520 64.0 0.00036 
8 1.6176 1.5 1.520 64.0 0.00051 
9 2.0759 2.0 1.520 64.0 0.00065 
__________________________________________________________________________ 
If the fifth example and any of the results of simulation of the basic 
optical system of the first to fourth examples described above are 
combined, then the ghost light 71 can be overlapped with the regular light 
69 using the half mirror 63 of a wedge-shaped profile having a varying 
thickness. 
A sixth example relates to a result of simulation conducted to reflect the 
blue light g ray 69 to a location outside the field of view of the user 
making use of the inclination angle .theta.m of the opposing surface 66 of 
the half mirror 63 of a wedge-shaped profile having a varying thickness 
(refer to FIG. 22A). In the simulation, similarly as in the fifth example 
described above, the refractive index nd, the Abbe's number .nu.d and the 
angular difference of refracted rays of the C and g rays are calculated 
from the inclination angle .theta.m of the opposing surface 66 opposing to 
the half-coated surface 65 and the thickness d on the optical axis of the 
half mirror 63 of a wedge-shaped profile having a varying thickness. In 
Table 10 given below, the inclination angle .theta.m of the opposing 
surface 66, the thickness d on the optical axis, the refractive index nd, 
the Abbe's number .nu.d and the angular difference between refracted rays 
of the C and g rays are listed. From Table 10, it can be recognized 
readily that, in order to restrict the angular difference between the red 
light C ray 71 and the blue light g ray 69 within an allowable range to 
reflect ghost light to the outside of the field of view using the half 
mirror 63 of a wedge-shaped profile having a varying thickness, the 
condition given by the following expression: 
EQU .vertline..theta.m.vertline.&lt;3.7 
degrees should be satisfied. 
TABLE 9 
__________________________________________________________________________ 
EXAMPLE 6! 
INCLINATION ANGLE 
THICKNESS ON 
REFRACTIVE 
ABBE'S 
ANGULAR DIFFERENCE 
OF INCLINED FACE 
OPTICAL AXIS 
INDEX NUMBER 
BETWEEN RAYS OF 
(.crclbar.m.degree.) 
(mm) (nd) (.nu.d) 
C & g RAYS 
__________________________________________________________________________ 
1 3.6584 1.5 1.492 58.0 0.00113 
2 3.6943 2.0 1.492 58.0 0.00114 
3 3.7383 3.0 1.492 58.0 0 00115 
4 3.2555 1.5 1.600 45.0 0.00160 
5 3.2867 2.0 1.600 45.0 0.00161 
6 3.3276 3.0 1.600 45.0 0.00163 
7 3.5416 1.5 1.520 64.0 0.00104 
8 3.5761 2.0 1.520 64.0 0.00105 
9 3.6193 3.0 1.520 64.0 0.00106 
__________________________________________________________________________ 
If the sixth example and any of the results of simulation of the basic 
optical system of the first to fourth examples described above are 
combined, then the regular light 69 can be reflected to the outside of the 
field of view of the user using the half mirror 63 of a wedge-shaped 
profile having a varying thickness. 
In this manner, since the half mirror 63 of a wedge-shaped profile having a 
varying thickness spectrally diffracts light, it is necessary to reduce 
the dispersion of a material by the wavelength and reduce the inclination 
angle, and the material of the half mirror 63 suitable for this should 
have an Abbe's number .nu.d&gt;45, and the inclination angle .theta.m of the 
opposing surface 66 opposing to the half-coated surface 65 should be 
selected so as to be .vertline..theta.m.vertline.&lt;7.3 degrees. 
Having now fully described the invention, it will be apparent to one of 
ordinary skill in the art that many changes and modifications can be made 
thereto without departing from the spirit and scope of the invention as 
set forth herein.