Note: Descriptions are shown in the official language in which they were submitted.
HEAD-MOUNTED DISPLAY APPARATUS
EMPLOYING ONE OR MORE FRESNEL LENSES
10
FIELD
This disclosure relates to head-mounted display apparatus employing one
or more Fresnel lenses. In certain embodiments, the apparatus also employs one
or more reflective optical surfaces, e.g., one or more free space, ultra-wide
angle,
reflective optical surfaces (hereinafter abbreviated as "FS/UWA/RO surfaces").
In certain embodiments, the overall optical system is a non-pupil forming
system, i.e., the controlling aperture (aperture stop) of the entire system is
the
pupil of the user's eye.
The one or more Fresnel lenses and, when used, the one or more
reflective surfaces (e.g., the one or more FS/UWA/RO surfaces) are employed to
display imagery from a light-emitting display system held in close proximity
to a
user's eye.
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BACKGROUND
A head-mounted display such as a helmet-mounted display or eyeglass-
mounted display (abbreviated herein as a "HMD") is a display device worn on
the head of an individual that has one or more small display devices located
near
one eye or, more commonly, both eyes of the user.
Some HMDs display only simulated (computer-generated) images, as
opposed to real-world images, and accordingly are often referred to as
"virtual
reality" or immersive HMDs. Other HMDs superimpose (combine) a simulated
image upon a non-simulated, real-world image. The combination of non-
simulated and simulated images allows the HMD user to view the world
through, for example, a visor or eyepiece on which additional data relevant to
the
task to be performed is superimposed onto the forward field of view (FOY) of
the user. This superposition is sometimes referred to as "augmented reality"
or
"mixed reality."
Combining a non-simulated, real-world view with a simulated image can
be achieved using a partially-reflective/partially-transmissive optical
surface (a
"beam splitter") where the surface's reflectivity is used to display the
simulated
image as a virtual image (in the optical sense) and the surface's
transmissivity is
used to allow the user to view the real world directly (referred to as an
"optical
see-through system"). Combining a real-world view with a simulated image can
also be done electronically by accepting video of a real world view from a
camera and mixing it electronically with a simulated image using a combiner
(referred to as a "video see-through system"). The combined image can then be
presented to the user as a virtual image (in the optical sense) by means of a
reflective optical surface, which in this case need not have transmissive
properties.
From the foregoing, it can be seen that reflective optical surfaces can be
used in HMDs which provide the user with: (i) a combination of a simulated
image and a non-simulated, real world image, (ii) a combination of a simulated
image and a video image of the real world, or (iii) purely simulated images.
(The last case is often referred to as an "immersive" system.) In each of
these
cases, the reflective optical surface produces a virtual image (in the optical
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sense) that is viewed by the user. Historically, such reflective optical
surfaces
have been part of optical systems whose exit pupils have substantially limited
not only the dynamic field of view available to the user, but also the static
field
of view. Specifically, to see the image produced by the optical system, the
user
needed to align his/her eye with the optical system's exit pupil and keep it
so
aligned, and even then, the image visible to the user would not cover the
user's
entire full static field of view, i.e., the prior optical systems used in HMDs
that
have employed reflective optical surfaces have been part of pupil-forming
systems and thus have been exit-pupil-limited.
The reason the systems have been so limited is the fundamental fact that
the human field of view is remarkably large. Thus, the static field of view of
a
human eye, including both the eye's foveal and peripheral vision, is on the
order
of ¨150 in the horizontal direction and on the order of ¨130 in the vertical
direction. (For the purposes of this disclosure, 150 degrees will be used as
the
straight ahead static field of view of a nominal human eye.) Well-corrected
optical systems having exit pupils capable of accommodating such a large
static
field of view are few and far between, and when they exist, they are expensive
and bulky.
Moreover, the operational field of view of the human eye (dynamic field
of view) is even larger since the eye can rotate about its center of rotation,
i.e.,
the human brain can aim the human eye's foveal+peripheral field of view in
different directions by changing the eye's direction of gaze. For a nominal
eye,
the vertical range of motion is on the order of ¨40 up and ¨60 down and the
horizontal range of motion is on the order of +¨SO from straight ahead. For
an
exit pupil of the size produced by the types of optical systems previously
used in
HMDs, even a small rotation of the eye would substantially reduce what overlap
there was between the eye's static field of view and the exit pupil and larger
rotations would make the image disappear completely. Although theoretically
possible, an exit pupil that would move in synchrony with the user's eye is
impractical and would be prohibitively expensive.
In view of these properties of the human eye, there are three fields of
view which are relevant in terms of providing an optical system which allows a
user to view an image generated by an image display system in the same manner
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as he/she would view the natural world. The smallest of the three fields of
view
is that defined by the user's ability to rotate his/her eye and thus scan
his/her
fovea over the outside world. The maximum rotation is on the order of 50
from straight ahead, so this field of view (the foveal dynamic field of view)
is
approximately 100 . The middle of the three fields of view is the straight
ahead
static field of view and includes both the user's foveal and peripheral
vision. As
discussed above, this field of view (the foveal+peripheral static field of
view) is
on the order of 150 . The largest of the three fields of view is that defined
by the
user's ability to rotate his/her eye and thus scan his/her foveal plus his/her
peripheral vision over the outside world. Based on a maximum rotation on the
order of 50 and a foveal+peripheral static field of view on the order of 150
,
this largest field of view (the foveal+peripheral dynamic field of view) is on
the
order of 200 . This increasing scale of fields of view from at least 100
degrees
to at least 150 degrees and then to at least 200 degrees provides
corresponding
benefits to the user in terms of his/her ability to view images generated by
an
image display system in an intuitive and natural manner.
In order for the human eye to focus easily on a display that is within 10
inches of the eye, a form of collimation needs to be applied to the light rays
emanating from the display. The collimation serves to make the light rays
appear as if they originate from a distance greater than the actual distance
between the eye and the display. The greater apparent distance, in turn,
allows
the eye to readily focus on an image of the display. Some head-mounted
displays use multiple mirrors or prisms in an attempt to collimate light from
the
display. The use of multiple mirrors or prisms adds bulk and weight, making
such head-mounted displays more cumbersome and heavier than desired.
There thus exists a need for head-mounted displays that are compatible
with the focusing ability as well as with at least the foveal dynamic field of
view
of the human eye. The present disclosure is directed to these needs and
provides
head-mounted displays that produce collimated (or substantially collimated)
light over a wide field of view.
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DEFINITIONS
In the remainder of this disclosure and in the claims, the phrase "virtual
image" is used in its optical sense, i.e., a virtual image is an image that is
perceived to be coming from a particular place where in fact the light being
perceived does not originate at that place.
Throughout this disclosure, the following phrases/terms shall have the
following meanings/scope:
(1) The phrase "a reflective optical surface" (also referred to herein
as a "reflective surface") shall include surfaces that are only
reflective as well as surfaces that are both reflective and
transmissive. In either case, the reflectivity can be only partial,
i.e., part of the incident light can be transmitted through the
surface. Likewise, when the surface is both reflective and
transmissive, the reflectivity and/or the transmissivity can be
partial. As discussed below, a single reflective optical surface
can be used for both eyes or each eye can have its own individual
reflective optical surface. Other variations include using multiple
reflective optical surfaces for either both eyes or individually for
each eye. Mix and match combinations can also be used, e.g., a
single reflective optical surface can be used for one eye and
multiple reflective optical surfaces for the other eye. As a further
alternative, one or multiple reflective optical surfaces can be
provided for only one of the user's eyes. The claims set forth
below are intended to cover these and other applications of the
reflective optical surfaces disclosed herein. In particular, each
claim that calls for a reflective optical surface is intended to cover
head-mounted display apparatus that includes one or more
reflective optical surfaces of the type specified.
(2) The phrase "an image display system having at least one light-
emitting surface" is used generally to include any display system
having a surface which emits light whether by transmission of
light through the surface, generation of light at the surface (e.g.,
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by an array of LEDs), reflection off of the surface of light from
another source, or the like. The image display system can employ
one or multiple image display devices, e.g., one or multiple LED
and/or LCD arrays. As with reflective optical surfaces, a given
head-mounted display apparatus can incorporate one or more
image display systems for one or both of the user's eyes. Again,
each of the claims set forth below that calls for an image display
system is intended to cover head-mounted display apparatus that
includes one or more image display systems of the type specified.
(3) The phrase "binocular viewer" means an apparatus that includes
at least one separate optical element (e.g., one display device
and/or one reflective optical surface) for each eye.
(4) The phrase "field of view" and its abbreviation FOV refer to
the
"apparent" field of view in image (eye) space as opposed to the
"real" field of view in object (i.e., display) space.
SUMMARY
In accordance with a first aspect, a head-mounted display apparatus (100)
is disclosed which includes:
(I) a frame (107) adapted to be mounted on a user's head (105);
(II) an image display system (110) supported by the frame (107) (e.g.,
the frame supports the image system device at a fixed location which, during
use
of the HMD, is outside of the user's field of view);
(III) a reflective optical surface (120) supported by the frame (107),
the reflective optical surface (120) being a continuous surface that is not
rotationally symmetric about any coordinate axis of a three-dimensional
Cartesian coordinate system (e.g., the reflective optical surface can be a
free-
space, ultra-wide angle, reflective optical surface (120) which is not
rotationally
symmetric (is not a surface of revolution) about the x, y, or z axes of a
three-
dimensional Cartesian coordinate system having an arbitrary origin); and
(IV) a Fresnel lens system (115) supported by the frame (107), the
Fresnel lens system (115) being located between the image display system (110)
and the reflective optical surface (120);
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wherein:
(a) the image display system (110) includes at least one light-
emitting surface (81);
(b) during use, the reflective optical surface (120) and the Fresnel
lens system (115) produce spatially-separated virtual images of spatially-
separated portions of the at least one light-emitting surface (81), at least
one of
the spatially-separated virtual images being angularly separated from at least
one
other of the spatially-separated virtual images by at least 100 degrees (in
some
embodiments, at least 150 degrees and, in other embodiments, at least 200
degrees), the angular separation being measured from a center of rotation (72)
of
a nominal user's eye (71); and
(c) during use, at least one point of the reflective optical surface
(120) is angularly separated from at least one other point of the reflective
optical
surface (120) by at least 100 degrees (in some embodiments, at least 150
degrees
and, in other embodiments, at least 200 degrees), the angular separation being
measured from the center of rotation of a nominal user's eye.
For this aspect, during use, the at least one of the spatially-separated
virtual images can be located along a direction of gaze which passes through
the
at least one point of the reflective optical surface and the at least one
other of the
spatially-separated virtual images is located along a direction of gaze which
passes through the at least one other point of the reflective optical surface.
In accordance with a second aspect, a head-mounted display apparatus
(100) is disclosed which includes:
(I) a frame (107) adapted to be mounted on a user's head (105);
(11) an image display system (110) supported by the frame (107) (e.g.,
the frame supports the image display system at a fixed location which, during
use of the HMD, is outside of the user's field of view);
(III) a free-space, ultra-wide angle, reflective optical surface
(120)
supported by the frame (107); and
(IV) a Fresnel lens system (115) supported by the frame (107), the
Fresnel lens system (115) being located between the image display system (110)
and the free-space, ultra-wide angle, reflective optical surface (120);
wherein:
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(a) the image display system (110) includes at least one light-
emitting surface (81);
(b) during use, the free-space, ultra-wide angle, reflective optical
surface (120) and the Fresnel lens system (115) produce spatially-separated
virtual images of spatially-separated portions of the at least one light-
emitting
surface (81), at least one of the spatially-separated virtual images being
angularly separated from at least one other of the spatially-separated virtual
images by at least 100 degrees (in some embodiments, at least 150 degrees and,
in other embodiments, at least 200 degrees), the angular separation being
measured from a center of rotation (72) of a nominal user's eye (71).
In accordance with a third aspect, a head-mounted display apparatus
(100) is disclosed that includes:
(I) a frame (107) adapted to be mounted on a user's head (105);
(II) an image display system (110) supported by the frame (107);
(III) a reflective surface (120) supported by the frame (107); and
(IV) a Fresnel lens system (115) supported by the frame (107), the
Fresnel lens system (115) being located between the image display system (110)
and the reflective optical surface (120);
wherein the Fresnel lens system (115) includes at least one Fresnel lens
element that is curved.
In accordance with a fourth aspect, a head-mounted display apparatus
(100) is disclosed that includes:
(I) a frame (107) adapted to be mounted on a user's head (105);
(II) an image display system (110) supported by the frame (107); and
(111) a Fresnel lens system (115) supported by the frame (107);
wherein:
during use, the Fresnel lens system (115) is located between the image
display system (110) and a nominal user's eye; and
the Fresnel lens system (115) includes at least one Fresnel lens element
(30) having a plurality of facets (31) that are separated from another by
edges
(32) wherein during use of the head-mounted display apparatus, at least some
of
the edges (32) lie along radial lines that (i) pass through a center of
rotation (34)
of a nominal user's eye (35), or (ii) pass through the center of a nominal
user's
8
natural lens (i.e., the nominal user's crystalline lens), or (iii) are normal
to the
surface of a nominal user's cornea.
In certain embodiments of the above aspects of the disclosure, a separate
Fresnel lens system, a separate image display system, and/or a separate
reflective
surface (when used) is employed for each of the user's eyes. In other
embodiments, the reflective optical surface (when used) contributes to the
collimation (or substantial collimation) of the light from the image display
system provided by the Fresnel lens system, such contribution to the
collimation
(or substantial collimation) being achieved through the surface's local radii
of
curvature.
In various embodiments, the HMD apparatus may be a binocular non-
pupil-forming system in which the eye is free to move about its rolling center
throughout its normally obtainable angular extents without being constrained
to
look through an external pupil. Prior HMD devices have alleged that they have
or can provide a wide field of view, but these devices have included an
external
pupil that the eye must look through. Although there is a wide amount of
information provided to the eye, if the eye turns the information is gone.
This is
the fundamental problem with pupil-forming systems which is avoided in
embodiments of the present disclosure which employ reflective surfaces and, in
particular, FS/UWA/RO surfaces.
The reference numbers used in the above summaries of the aspects of the
invention (which reference numbers are representative and not all-inclusive or
exhaustive) are only for the convenience of the reader and are not intended to
and should not be interpreted as limiting the scope of the invention. More
generally, it is to be understood that both the foregoing general description
and
the following detailed description are merely exemplary of the invention and
are
intended to provide an overview or framework for understanding the nature and
character of the invention.
Additional features and advantages of the invention are set forth in the
detailed description which follows, and in part will be readily apparent to
those
skilled in the art from that description or recognized by practicing the
invention
as exemplified by the description herein. The accompanying drawings are
included to provide a further understanding of the invention.
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It is to be understood that the various features of the invention disclosed in
this
specification and in the drawings can be used in any and all combinations.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a side view representation of a head-mounted display apparatus
according to an example embodiment.
FIG. 2 is a front view representation of the head-mounted display
apparatus of FIG. 1.
FIG. 3 is a schematic cross-sectional view of a Fresnel lens element
having facets whose edges pass through the center of rotation of a user's eye
according to an example embodiment.
FIG. 4 illustrates an optical system for a head-mounted display apparatus
that includes a Fresnel lens system and a curved reflective optical surface
according to an example embodiment.
FIG. 5 is a top view of a head-mounted display apparatus illustrating the
use of two curved reflective optical surfaces corresponding to the two eyes of
a
user according to an example embodiment.
FIG. 6 is a schematic diagram illustrating a static field of view of a
nominal human eye for a straight ahead direction of gaze.
FIG. 7 is a schematic diagram illustrating the interaction between the
static field of view of FIG. 6 with a FS/UWA/RO surface according to an
example embodiment. The arrows in FIG. 7 illustrate directions of light
propagation.
FIG. 8 is a ray diagram illustrating a light path from a given pixel on a
display as it is reflected toward an eye according to an example embodiment.
FIG. 9 is a ray diagram illustrating light paths from two pixels on a
display as they are reflected toward an eye according to an example
embodiment.
FIG. 10 is a diagram illustrating variables used in selecting the direction
of the local normal of a reflector according to an example embodiment.
FIG. 11 is a representation of a curved reflector along with light paths
according to an example embodiment.
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FIG. 12 is a block diagram of a side view of an augmented-reality head-
mounted display apparatus having a Fresnel lens system according to an example
embodiment.
FIG. 13 is a ray diagram illustrating light rays in an augmented-reality
head-mounted display apparatus of the type shown in FIG. 12.
FIG. 14 is a ray diagram illustrating display and external light rays in the
augmented-reality head-mounted display apparatus of FIG. 13.
FIG. 15 is a block diagram of a side view of an immersive head-mounted
display apparatus having a Fresnel lens system according to an example
embodiment.
FIG. 16 is a block diagram of a top view of an immersive head-mounted
display apparatus having a Fresnel lens system according to an example
embodiment.
FIG. 17 is a ray diagram illustrating light rays in an immersive head-
mounted display apparatus of type shown in FIGS. 15 and 16.
FIG. 18 is ray diagram illustrating light rays entering an eye of a user
according to an example embodiment.
FIG. 19 is a schematic diagram illustrating geometry for calculating a
local normal to a reflective surface according to an example embodiment.
DETAILED DESCRIPTION
I. Introduction
As discussed above, the present disclosure relates to HMDs which
provide a user with a collimated (or substantially collimated) image through
the
use of a Fresnel lens system, which may be a curved Fresnel lens system (see
below). The Fresnel lens system may be the sole source of collimation in the
optical system or, in embodiments that employ curved reflective optical
surface,
e.g., a FS/UWA/R0 surface, the Fresnel lens system's collimation may be
combined with collimation contributed by the curved reflective optical
surface.
The following discussion begins with a description of embodiments that
employ a FS/UWA/120 surface (Section II) and then proceeds to a discussion of
Fresnel lens systems for use with those embodiments as well as other
embodiments disclosed herein (Section III). Section III also includes a
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discussion of the design process for a FS/UWA/R0 surface that is used in an
optical system that includes a Fresnel lens system. Following Section (III),
embodiments that employ a reflective optical surface that is not a FS/UWA/RO
surface and a curved Fresnel lens systems are discussed (Section IV), followed
by embodiments in which an image display system is viewed directly through a
curved Fresnel lens system without the use of a reflective surface (Section
V).
Finally, a general discussion applicable to the various embodiments disclosed
herein is presented (Section VI).
It should be understood that the discussions of the various components of
HMDs that appear in particular sections of the presentation are not limited to
the
embodiments of that section, but are generally applicable to all of the
embodiments disclosed herein. As one example, the description of the types of
image display systems that may be used in a HMD is applicable to the Section I
embodiments (where the description appears), as well as to the Sections IV and
V embodiments.
IL HMDs That Employ FS/UWA/RO Surfaces
FIGS. 1 and 2 are, respectively, a side view and a front view of a head-
mounted display apparatus 100 shown being worn by a user 105. The head-
mounted display apparatus employs a FS/UWA/RO surface 120.
In one embodiment, the head-mounted display apparatus 100 can be, for
example, an optical see-through, augmented reality, binocular viewer. Because
an optical see-through, augmented reality, binocular viewer is typically the
most
complex form of a HMD, the present disclosure will primarily discuss
embodiments of this type, it being understood that the principles discussed
herein are equally applicable to optical see-through, augmented reality,
monocular viewers, video see-through, augmented reality, binocular and
monocular viewers, and binocular and monocular "virtual reality" systems.
As shown in FIGS. 1 and 2, the head-mounted display apparatus 100
includes a frame 107 adapted to be worn by the user and supported by the
user's
nose and ears in a manner similar to that in which eyeglasses are worn. In the
embodiment of FIGS. 1-2, as well as in the other embodiments disclosed herein,
the head-mounted display apparatus may have a variety of configurations and
can, for example, resemble conventional goggles, glasses, helmets, and the
like.
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In some embodiments, a strap may be used to hold the HMD's frame in a fixed
position with respect to the eyes of the user. In general terms, the outside
surface of the HMD package can assume any form that holds the optical system
in the required orientation with respect to the HMD's display(s) and the
user's
eyes.
The head-mounted display apparatus 100 includes at least one image
display system 110 and, as shown in FIGS. 1 and 2, a free space, ultra-wide
angle, reflective optical surface 120, i.e., a FS/UWA/R0 surface 120, which by
necessity is curved. Surface 120 can be purely reflective or can have both
reflective and transmissive properties, in which case, it can be thought of as
a
type of "beam splitter."
Surface 120 is referred to herein as a "free space" surface because its
local spatial positions, local surface curvatures, and local surface
orientations are
not tied to a particular substrate, such as the x-y plane, but rather, during
the
surface's design, are determined using fundamental optical principles (e.g.,
the
Fermat and Hero least time principle) applied in three dimensional space.
Surface 120 is referred to as an "ultra-wide angle" surface because, during
use, at
a minimum, it does not limit the dynamic foveal field of view of a nominal
user's
eye. As such, depending on the optical properties of the Fresnel lens system
with which the FS/UWA/RO surface is used, the overall optical system of the
HMD can be non-pupil forming, i.e., unlike conventional optical systems that
have an exit pupil which limits the user's field of view, the operative pupil
for
various embodiments of the optical systems disclosed herein will be the
entrance
pupil of the user's eye as opposed to one associated with the external optical
system. Concomitantly, for these embodiments, the field of view provided to
the
user will be much greater than conventional optical systems where even a small
misalignment of the user's eye with the exit pupil of the external optical
system
can substantially reduce the information content available to the user and a
larger
misalignment can cause the entire image to disappear.
FS/UWA/RO surface 120 may completely surround one or both eyes, as
well as the at least one image display system 110. In particular, the surface
can
curve around the sides of the eyes and toward the sides of the face so as to
expand the available horizontal field of view. In one embodiment, the
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FS/UWA/RO surface 120 may extend up to 1800 or more (e.g., more than 200 ),
as best seen in FIG. 5 discussed below. As illustrated in FIG. 2, the HMD may
include two separate FS/UWA/RO surfaces 120R and 120L for the user's two
eyes which are separately supported by the frame and/or a nasal ridge piece
210
(see below). Alternately, the HMD may employ a single FS/UWA/RO surface
that serves both eyes with a single structure, some portions of which are
viewed
by both eyes and other portions of which are viewed by only one eye.
As noted immediately above and as illustrated in FIG. 2, the head-
mounted display apparatus 100 can include a nasal ridge piece 210. The nasal
ridge piece can be a vertical bar or wall which provides a separation between
two FS/UWA/RO surfaces, one for each of the user's eye. The nasal ridge piece
210 can also provide a separation between the fields of view of the user's two
eyes. In this way, the user's right eye can be shown a first representation of
three
dimensional physical reality in the environment by displaying a first image to
the
right eye via a first image display device and a first FS/UWA/RO surface,
while
the user's left eye is shown a second representation of three dimensional
physical
reality in the environment by displaying a second image to the left eye via a
second image display device and a second FS/UWA/RO surface. A separate
display device/reflective surface combination thus services each eye of the
user,
with each eye seeing the correct image for its location relative to the three
dimensional physical reality in the environment. By separating the user's two
eyes, the ridge piece 210 allows the image applied to each eye to be optimized
independently of the other eye. In one embodiment, the nasal ridge piece's
vertical wall may include two reflectors, one on each side, to allow the user
to
see imagery as he/she turns his/her eyes nasally, either to the left or to the
right.
The at least one image display system 110 can be mounted inside the
FS/UWA/RO surface 120 and may be horizontally disposed or at a slight angle
with respect to the horizon. Alternatively, the at least one image display
system
can be located just outside of the FS/UWA/RO surface. The tilt or angle of the
at least one image display system 110 or, more particularly, its at least one
light-
emitting surface, will in general be a function of the location of the pixels,
images, and/or pieces of display information that are to be reflected from the
surface 120.
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In certain embodiments, the head-mounded display apparatus 100 is
configured to create an interior cavity, with the FS/UWA/RO surface being
reflective inward into the cavity. For a FS/UWA/RO surface having
transmissive properties, the image or display information from the at least
one
image display system is reflected into the cavity and to the user's eye from
the
surface while, simultaneously, light also enters the cavity and the user's eye
from
the external world by passing through the reflective surface.
The head-mounted display apparatus can include an electronics package
140 to control the images that are displayed by the at least one image display
system 110. In one embodiment, the electronics package 140 includes
accelerometers and gyroscopes that provide location, orientation and position
information needed to synchronize images from the at least one image display
system 110 with user activities. Power and video to and from the head-mounted
display apparatus 100 can be provided through a transmission cable 150 coupled
to the electronics package 140 or through a wireless medium.
A set of cameras 170 may be situated on opposite sides of the head-
mounted display apparatus 100 to provide input to the electronics package to
help control the computer generation of, for example, "augmented reality"
scenes. The set of cameras 170 may be coupled to the electronics package 140
to receive power and control signals and to provide video input to the
electronics
package's software.
The image display system used in the head-mounted display apparatus
can take many forms, now known or subsequently developed. For example, the
system can employ small high resolution liquid crystal displays (LCDs), light
emitting diode (LED) displays, and/or organic light emitting diode (OLED)
displays, including flexible OLED screens. In particular, the image display
system can employ a high-definition small-form-factor display device with high
pixel density, examples of which may be found in the cell phone industry. A
fiber-optic bundle can also be used in the image display system. In various
embodiments, the image display system can be thought of as functioning as a
small screen television. If the image display system produces polarized light
(e.g., in the case where the image display system employs a liquid crystal
display
where all colors are linearly polarized in the same direction), and if the
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FS/UWA/RO surface is polarized orthogonally to the light emitted by the
display, then light will not leak out of the FS/UWA/RO surface. The
information displayed and the light source itself will accordingly not be
visible
outside of the HMD.
Overall operation of an exemplary embodiment of an optical system
constructed in accordance with the present disclosure, specifically, an
optical
system for an "augmented reality" HMD, is illustrated by the ray-tracings of
FIG. 1, specifically, light rays 180, 185, and 190. In this embodiment,
FS/UWA/RO surface 120 has both reflective and transmissive properties.
Using surface 120's transmissive properties, light ray 190 enters from the
environment through the surface and proceeds towards the user's eye. From the
same region of surface 120, light ray 180 is reflected by the surface (using
the
surface's reflective properties) and joins light ray 190 to create combined
light
ray 185 that enters the user's eye when the user looks in the direction of
point
195, i.e., when the user's direction of gaze is in the direction of point 195.
While
so looking, the user's peripheral vision capabilities allow the user to see
light
from other points in the environment which pass through surface 120, again
using the surface's transmissive properties.
III. Fresnel Lens Systems
In accordance with the present disclosure, the images and/or pieces of
display information provided by the at least one image display system are
adjusted for near viewing prior to entering the user's eye(s). For example, in
the
exemplary embodiment of FIGS. 1 and 2, the adjustment is performed by lens
system 115 which includes one or more Fresnel lens elements and serves to
modify the diopter characteristics of the light beam emanating from the
display
surface thus making it easier for the user to focus on the virtual image of
the
display produced by the overall optical system. FIGS. 12-14 and 15-18 show
other embodiments employing Fresnel lens elements to modify the diopter
characteristics of light emanating from a display. In addition to this
function, the
Fresnel lens elements also serve to magnify the image provided to the user. In
some embodiments, a magnification of between three to six or more may be
obtained with multiple Fresnel lens elements arranged in a stacked
configuration.
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As discussed in more detail below, in certain embodiments, the Fresnel
lens system contains one or more curved Fresnel lens elements, i.e., Fresnel
lenses constructed on curved, rather than flat, substrates. For ease of
reference,
Fresnel lens systems that include a curved Fresnel lens element will be
referred
to herein as "curved Fresnel lens systems," it being understood that not all
of the
Fresnel lens elements used in a curved Fresnel lens system need be curved. The
phrase "Fresnel lens system" will be used to describe the general case of a
lens
system that includes at least one Fresnel lens element (whether curved or
flat)
which performs the function of modifying the diopter characteristics of the
light
beam emanating from an image display system to facilitate near-to-the-eye
viewing of an image of the display. As discussed in more detail below, in
embodiments that employ a FS/UWA/RO surface, if desired, the FS/UWA/RO
surface can also have optical properties that contribute to in-focus, near-to-
the-
eye viewing of images formed on the at least one light-emitting surface of the
image display system.
In general terms, the Fresnel lens systems disclosed herein can comprise
various combinations of flat and/or curved Fresnel lenses selected to adjust
the
diopter of the light emanating from the image display system so as to allow
the
eye to be able to focus on the display and, in the case of "augmented reality"
HMDs, also focus on objects in the external environment. The presence of at
least one curved Fresnel lens in a curved Fresnel lens system provides at
least
one additional parameter (i.e., the curvature of the lens) for controlling
aberrations in the image provided to the user. For example, one or more
Fresnel
lenses having curved configurations can provide substantial reductions in
chromatic aberrations. Furthermore, Fresnel surfaces manufactured on curved
substrates can provide reduced off-axis aberrations.
More generally, the optical properties of the Fresnel lens system and the
one or more Fresnel lenses included therein can be selected empirically or
through analytic ray-tracing. Ray-tracing can, for example, allow optimization
of the apparatus parameters for a particular implementation, such as military
training, flight simulation, gaming and other commercial applications. The
parameters that are available for optimization include, for example, the
curvature
of the display, the dimensions of the display, the curvature of the Fresnel
lenses,
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aspheric parameters in cases where the Fresnel lens system or other parts of
the
optical system include one or more aspheric surfaces, and the Fresnel lens
power
versus the distances from (i) the front of the display screen and (ii) the
user's eye.
In some embodiments, the Fresnel lens elements produce no field
curvature, so a wide field of view can be provided using a small number of
thin
optical components. In other embodiments, the Fresnel lens system can include
one or more aspheric surfaces to aid in the correction of image aberrations.
The
aspheric surface can be applied on either surface of any of the optical
components of the Fresnel lens system. Nominally, the first and second
surfaces
of the Fresnel lens elements will have the same base radius of curvature
(i.e.,
their thickness will be constant over their clear aperture). Additional
aberration
correction or functionality may be achievable by allowing one or more of the
Fresnel lens elements to have different radii on their first and second
surfaces.
In various embodiments, through the use of Fresnel lens elements,
including aspheric Fresnel lens elements, an optical system can be realized as
a
compact and lightweight system, having a large viewable field of view, an
image
quality commensurate with typical human visual resolution, and an overall
structure that can be manufactured in large quantities at low cost. If
desired, the
Fresnel lens system can include one or more diffractive surfaces (diffractive
components) to reduce chromatic aberrations, particularly, lateral chromatic
aberration. For example, lens elements 810, 1330, and 1135 may include one or
more diffractive surfaces. In this way, a corrected image of an image display
device, including a flat image display device, can be achieved either using
the
Fresnel lens system alone or in combination with a FS/UWA/RO surface. In
certain embodiments, the one or more Fresnel lenses will provide most of the
optical power in the system and will be designed to minimize monochromatic
aberrations.
The Fresnel lens elements, which in one embodiment are assembled with
a gap between adjacent lenses, may be made much thinner than typical lenses,
so
the space and weight of the optical system is significantly reduced compared
to
conventional thick lenses. The weight may be further reduced by making all
lenses from plastic. However, glass could also be used. The plastic lenses can
be produced by either diamond machining or molding.
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In certain embodiments, one or more (or all) of the curved Fresnel lens
elements can have facets whose edges lie along radial lines that pass through
the
center of rotation of a nominal user's eye. FIG. 3 illustrates such an
embodiment
where 30 is the Fresnel lens, 31 is a facet of the Fresnel lens, 32 is an edge
of a
facet of the Fresnel lens, and 33 is a radial line which passes through the
center
of rotation 34 of a nominal user's eye 35. FIG. 3 also shows the internal lens
36
(natural lens 36) of the nominal user's eye. Alternatively, one or more (or
all) of
the curved Fresnel lens elements can have facets whose edges lie along radial
lines that pass through the center of a nominal user's natural lens or are
normal to
the surface of a nominal user's cornea.
As noted above, Fresnel lenses are particularly well-suited for use in
HMDs because of their light weight. The lenses can, however, create image
aberrations due to the angle of incidence of the light waves leaving the
display
on the lens surface. In particular, the light waves can pass through
unintended
sections of the Fresnel lens grooves. In accordance with the embodiment
illustrated in FIG. 3, such aberrations can be reduced by providing the
Fresnel
lens with a domed shape, specifically, a spherical shape, centered on the
center
of rotation of a nominal user's eye, such that the edges of the Fresnel facets
are
normal to the surface of the dome everywhere around the lens' surface.
Alternatively, the domed shape (spherical shape) can be centered on the center
of
a nominal user's natural lens or can be concentric with a nominal user's
cornea.
In these ways, light beams pass through the lens parallel to the edges of the
facets and optical aberrations due to these discontinuities are avoided,
improving, among other things, the color response of the lens. It should be
noted that convergent facet edges will reduce optical distortion in a viewed
image even if all of the edges do not exactly satisfy one of the above
conditions,
e.g., if all of the edges do not exactly pass through the center of rotation
of a
nominal user's eye. Accordingly, rather than having a pure spherical shape,
the
Fresnel lens can be substantially spherical (e.g., the Fresnel lens can have
an
aspheric surface) and can still benefit from having at least some convergent
facet
edges.
Although Fresnel lens elements having square, rectangular, or other clear
aperture shapes can be used if desired, in general, the Fresnel lenses will
have
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circular clear apertures. In most applications, the size of the smallest clear
aperture of the lenses making up the Fresnel lens system will determine
whether
or not the overall optical system is a pupil forming or a non-pupil forming
system. In particular, for an overall optical system composed of a Fresnel
lens
system and a FS/UWA/RO surface, the exit pupil of the system will typically be
the image of the smallest clear aperture of the Fresnel lens system produced
by
the optical elements downstream of that aperture (i.e., towards the user's
eye).
That is, the system's overall aperture stop will typically be in the Fresnel
lens
system because in terms of apertures, FS/UWA/RO surfaces behave as if they
have very large clear apertures. Depending on the size and location of the
image
of the smallest clear aperture of the Fresnel lens system produced by the
FS/UWA/RO surface (as well as by any elements of the Fresnel lens system on
the downstream side of the element with the smallest clear aperture), the
overall
system may provide the user with a full foveal dynamic field of view, a full
foveal+peripheral static field of view, or a full foveal+peripheral dynamic
field
of view.
FIG. 4 shows an embodiment of a HMD optical system which employs a
FS/UWA/RO surface and a Fresnel lens system 115 having a flat Fresnel lens
810 and two curved Fresnel lenses 815 and 820, which, as shown in FIG. 4, are
adjacent to one another. Light rays 830, 835, and 840 are shown in this figure
with light 840 entering from the environment and becoming combined with light
830 to create combined light 835 that enters the user's eye when the user
looks
in the direction of point 850. The user's peripheral vision capabilities also
allow
the user to see light from points other than point 850.
More particularly, a diverging wavefront of light 860 emanating from the
at least one image display system 110 is converged in a positive-diopter
Fresnel
lens system having Fresnel lenses 810, 815, and 820 to provide light 830 that
is
between zero diopter and the initial diopter. The initial diopter of the light
emanating from the at least one image display system 110 can, for example, be
approximately D = 1/(0.03 [m]) = 33 dpt. After leaving the Fresnel lens
system,
the light reflects from FS/UWA/RO surface 120 where, if desired, additional
diopter divergence can be removed using the surface curvature techniques
discussed below.
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The total diopter change can, for example, be 33 dpt, and this may be
split between the FS/UWA/RO surface and the Fresnel lenses in various
embodiments. In particular, the amount of diopter change supplied by the
FS/UWA/RO surface can be reduced which in various embodiments may be
advantageous in designing and manufacturing the FS/UWA/RO surface.
Because diopters are additive, however much vergence is supplied by one of the
optical components does not have to be supplied by the other. (This additive
property of diopter values can be used in combining the collimating effects of
the Fresnel lens system and the FS/UWA/RO surface, as well as in combining
the effects of the individual lens elements making up the Fresnel lens system.
It
can also be used to take account of the collimating effects of any other
optical
components that may be part of the overall system.) In the exemplary
embodiment of FIG. 4, a diopter change of 33 dpt will result in a final beam
that
is collimated (0 dpt) or substantially collimated (-0 dpt). This is equivalent
to
light coming from a point essentially infinitely distant, and the light
wavefront
will be flat, resulting in parallel surface normals to the wavefront, shown as
rays
835, across the entrance to the eye. Collimated reflected light can, for
example,
be desirable when the external world includes items that are effectively at
infinity relative to the user. As noted above, the FS/UWA/RO surface 120
admits light ray 840 from the external environment, thus allowing the internal
images to overlay the external images and, in particular, external images
which
are effectively at infinity relative to the user's eye.
As discussed above, prior optical systems used in HMDs that have
employed reflective optical surfaces have been pupil forming and thus have had
limited viewing areas, a typical field of view being ¨60 degrees or less. This
has
greatly limited the value and capability of prior head-mounted display
apparatuses. In various embodiments, the head-mounted displays disclosed
herein have much wider fields of view (FOV), thus allowing much more optical
information to be provided to the user compared to HMDs having smaller fields
of view. The wide field of view can be greater than 1000, greater than 1500,
or
greater than 200 . In addition to providing more information, the wide field
of
view allows the additional information may be processed by the user in a more
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natural manner, enabling better immersive and augmented reality experiences
through a better match of the displayed images to physical reality.
Specifically, in the exemplary embodiment illustrated in FIG. 5, for a
straight ahead direction of gaze, the eye is able to take in a whole viewing
area
represented in FIG. 5 by curved FS/UWA/RO surfaces 201 and 202,
corresponding to at least 150 degrees of horizontal field of view (FOV) for
each
eye (e.g., ¨168 degrees of horizontal FOV). This field of view is composed of
the eye's fovcal field of view and its peripheral field of view. In addition,
the
eye is allowed to move freely about its center of rotation to aim the combined
foveal+peripheral field of view in different directions of gaze, as the eye
naturally does when viewing the physical world. The optical systems disclosed
herein thus allow the eye to obtain information throughout a range of motion
in
the same manner as the eye does when viewing the natural world.
Examining FIG. 5 in more detail, this figure is a simplified line
representation of the front of a user's head 200 as seen from the top. It
shows
FS/UWA/RO surfaces 201 and 202 placed in front of the user's eyes 203 and
204. As discussed above, the FS/UWA/RO surfaces 201 and 202 may rest upon
the user's nose 205 where they come together at the center front 214 of the
user's head 200. As discussed in detail below, the local normals and local
spatial locations of surfaces 201 and 202 are adjusted so that images produced
by
the at least one image display system (not shown in FIG. 5) cover at least
1000
,
e.g., in certain embodiments, at least 1500 and, in other embodiments, at
least
200 , of horizontal FOV for each eye. (Optionally, as also discussed below,
the
local radii of curvature are also adjusted to provide, when combined with a
Fresnel lens system, distant virtual images.) For example, the local normals
and
local spatial locations can be adjusted to cover the user's complete ¨168
degree,
straight ahead, horizontal, static field of view for each eye, with the 168
degrees
extending from edge-to-edge of the FS/UWA/RO surfaces 201 or 202, as shown
by sight lines 210,211 and 212,213. The sight lines thus correspond to the
wide
static field of view (foveal+peripheral) that is provided to the user. In
addition,
the user is free to move his/her eyes around rolling centers 215 and 216 while
continuing to see computer-generated imagery.
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In FIG. 5, as well as in FIG. 11, the FS/UWA/RO surfaces are shown as
parts of spheres for ease of presentation. In practice, the surfaces are not
spheres, but have more complex configurations so that their local normals and
local spatial locations (and, optionally, local radii of curvature) will
provide the
desired static and dynamic fields of view (and, optionally, desired distances
to
the virtual images). Also, in FIG. 5, the right side of the head-mounted
display
apparatus operates identically to left side, it being understood that the two
sides
can differ if desired for particular applications. Also for ease of
presentation,
FIGS. 5-11 do not show an optical system which includes at least one Fresnel
lens between the at least one image display system and the reflective optical
surface, it being understood that in accordance with the present disclosure,
such
an optical system is used in the embodiments disclosed herein.
FIGS. 6 and 7 further illustrate the static and dynamic fields of view
provided by the FS/UWA/RO surfaces disclosed herein. FIG. 6 shows a user's
nominal right eye 71 having a straight ahead direction of gaze 73. The eye's
foveal+peripheral field of view is shown by arc 75, which has an angular
extent
of ¨168 . Note that for ease of presentation, in FIGS. 6-8, the field of view
is
shown relative to the center of rotation of the user's eye as opposed to the
center
or edges of the user's pupil. In fact, the large field of view (e.g., ¨168 )
achieved
by a human eye is a result of the large angular extent of the retina which
allows
highly oblique rays to enter the user's pupil and reach the retina.
FIG. 7 schematically shows the interaction of the field of view of FIG. 6
with a HMD having: (a) an image display system whose at least one light-
emitting surface 81 has a first light-emitting region 82 (illustrated as a
square)
and a second light-emitting region 83 (illustrated as a triangle) and (b) a
FS/UWA/RO surface having a first reflective region 84 which has a first local
normal 85 and a second reflective region 86 which has a second local normal
87.
As indicated above, the FS/UWA/RO surface is both a "free space"
surface and an "ultra-wide angle" surface. In addition, as noted above and
discussed in more detail below, the surface can participate in collimation (or
partial collimation) of the light that enters the user's eye. Such collimation
causes the virtual image produced by the FS/UWA/RO surface and the Fresnel
lens system to appear to be located a long distance from the user, e.g., 30
meters
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or more, which permits the user to easily focus on the virtual image with a
relaxed eye.
The "free space" and "ultra-wide angle" aspects of the FS/UWA/RO
surface can be achieved by adjusting the local normals of the surface so that
the
user's eye sees light-emitting regions of the at least one image display
system as
coming from predetermined regions of the FS/UWA/RO surface (predetermined
locations on the surface).
For example, in FIG. 7, the designer of the HMD might decide that it
would be advantageous for a virtual image 88 of the square to be viewed by the
center portion of the user's retina when the user's direction of gaze is
straight
ahead and for a virtual image 89 of the triangle to be viewed by the center
portion of the user's retina when the direction of gaze is, for example, ¨50
to the
left of straight ahead. The designer would then configure the at least one
image
display system, the FS/UWA/RO surface, the Fresnel lens system and any other
optical components of the system so that the virtual image of the square would
be straight ahead and the virtual image of the triangle would be 50 to the
left of
straight ahead during use of the HMD.
In this way, when the user's direction of gaze (line of sight) intersected
the FS/UWA/RO surface straight on, the virtual image of the square would be
visible at the center of the user's eye as desired, and when the user's
direction of
gaze (line of sight) intersected the FS/UWA/RO surface at 50 degrees to the
left
of straight ahead, the virtual image of the triangle would be visible at the
center
of the user's eye, as also desired. Although not illustrated in FIGS. 6 and 7,
the
same approaches are used for the vertical field of view, as well as for off-
axis
fields of view. More generally, in designing the HMD and each of its optical
components, the designer "maps" the at least one light-emitting surface of the
display to the reflective surface so that desired portions of the display are
visible
to the user's eye when the eye's gaze is in particular directions. Thus, as
the eye
scans across the field of view, both horizontally and vertically, the
FS/UWA/RO
surface shines different portions of the at least one light emitting surface
of the
image display system into the user's eye. Although the foregoing discussion
has
been in terms of the center of a nominal user's retina, the design process
can, of
course, use the location of a nominal user's fovea instead, if desired.
24
"
It should be noted that in FIG. 7, any rotation of the user's eye to right
causes the virtual image 89 of the triangle to no longer be visible to the
user.
Thus, in FIG. 7, any direction of gaze that is straight ahead or to the left
of
straight ahead provides the user with virtual images of both the square and
the
triangle, while a direction of gaze to the right of straight ahead provides a
virtual
image of only the square. The acuity of the virtual images will, of course,
depend on whether the virtual images are perceived by the user's foveal vision
or
the user's peripheral vision.
If the designer of the HMD had placed the virtual image of the square far
to the right in FIG. 7 while leaving the virtual image of the triangle far to
the left,
there would be directions of gaze where only the virtual image of the square
was
visible and other directions of gaze where only the virtual image of the
triangle
was visible. Likewise, based on the principles disclosed herein, the designer
could arrange the virtual image of the square and the virtual image of the
triangle
so that the virtual image of the triangle was always visible, with the virtual
image of the square being visible for some directions of gaze, but not for
others.
As a further variation, the designer of the HMD could place the virtual image
of
the square and triangle at locations where for one or more directions of gaze,
neither image was visible to the user, e.g., the designer could place the
virtual
images just outside the user's static field of view for a straight ahead
direction of
gaze. The flexibility provided to the HMD designer by the present disclosure
is
thus readily apparent.
In one embodiment, the "free space" and the "ultra-wide angle" aspects
of the reflective surface are achieved by using the principles of Fermat and
Hero
pursuant to which light travels along the shortest (least time) optical path.
Commonly-assigned U.S. Patent No. 8,781,794, in the names of G. Harrison, D.
Smith, and G. Wiese, entitled "Methods and Systems for Creating Free Space
Reflective Optical Surfaces," describes an embodiment in which the Fermat and
Hero principles are used to design FS/UWA/RO surfaces suitable for use in
HMDs. See also commonly-assigned U.S. Patent No. 8,625,200, in the
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names of G. Harrison, D. Smith, and G. Wiese, entitled "Head-Mounted Display
Apparatus Employing One or More Reflective Optical Surfaces".
By means of the Fermat and Hero least-time principles, any "desired
portion" of the at least one light-emitting surface of an image display system
(e.g., any pixel of an image display system) can be caused to have any desired
point of reflection at the FS/UWA/R0 surface, provided that the optical path
from the desired portion of the at least one light-emitting surface to the
point of
reflection at the FS/UWA/RO surface and then to the center of rotation of the
user's eye is at an extremum.
An extremum in the optical path means that the first derivative of the
optical path length has reached a zero value, signifying a maximum or a
minimum in the optical path length. An extremum can be inserted at any point
in the field of view by creating a local region of the reflective optical
surface
whose normal bisects (a) a vector from the local region to the user's eye
(e.g., a
vector from the center of the local region to the center of the user's eye)
and (b)
a vector from the local region to the "desired portion" of the light-emitting
surface (e.g., a vector from the center of the local region to the center of
the
"desired portion" of the light-emitting surface). FIGS. 8 and 9 illustrate the
process for the case where the "desired portion" of the at least one light-
emitting
surface of the image display system is a pixel.
Specifically, FIG. 8 shows a light-emitting surface 510 of an image
display system composed of a generally rectangular array of pixels that are
emanating light toward the front of a head-mounted display apparatus in the
direction of light beam 515. Light beam 515 bounces off of reflective optical
surface 520, which for ease of presentation is shown as a flat in FIG. 8. Upon
reflection, light beam 515 becomes light beam 525 that enters the user's eye
530.
For the purposes of determining the surface normal of the reflector for
each pixel, it is only necessary to determine the three-dimensional bisector
of
vectors corresponding to light beams 515 and 525. In FIG. 8, this bisector
vector is shown in two-dimensional form as line 535. Bisecting vector 535 is
normal to the reflective optical surface at point of reflection 540, which is
the
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location on surface 520 where pixel 545 of light-emitting surface 510 will be
visible to the user of the HMD.
Specifically, in operation, pixel 545 in the display surface 510 emits light
beam 515 that bounces off reflective optical surface 520 at an angle
established
by the surface normal corresponding to bisecting vector 535 and its
perpendicular plane 550, yielding by the Fermat and Hero principles, a
reflected
pixel at point of reflection 540 that is seen by the eye 530 along light beam
525.
In order to accurately calculate the surface normal at the point of reflection
540,
the beam 525 can pass through approximately the center 555 of the user's eye
530. The results will remain approximately stable even if the user's eye
rotates,
becoming peripheral vision until, as discussed above in connection with FIGS.
6
and 7, the eye turns so much that that region of the display cannot be seen
with
either the user's fovea! or peripheral vision.
To calculate the position of the surface normal, the use of the method of
quaternions may be employed, where
ql = orientation of beam 515
q2 = orientation of beam 525
and
q3 = the orientation of the desired surface normal 535 = (ql + q2)
/2
The surface normal may also be described in vector notation, as
illustrated in FIG. 10. In the following equation and in FIG. 10, point N is
one
unit away from the point M at the center of the region of interest of the
reflective
optical surface and is in the direction of the perpendicular normal to the
tangent
plane of the reflective optical surface at the point M. The tangent plane of
the
reflective optical surface at point M is controlled to satisfy the relation
expressed
in the following equation such that in three-dimensional space, the surface
normal at the point M bisects the line from the point M to the point P at the
center of the pixel of interest and the line from point M to the point C at
the
rolling center of the user's eye (for reference, point C is approximately 13
mm
back from the front of the eye).
The equation describing the point N on the surface normal at point M is:
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(P-M)+(C-M)
N= ____________________________________ +M1(1 M) (C-111)1
where all the points, N, M, P, and C have components [x, y, z] that indicate
their
position in three-dimensional space in an arbitrary Cartesian coordinate
system.
The resulting normal vector N-M has the Euclidean length
A M1=1
where the two vertical bars represents the Euclidean length, calculated as
follows:
iV ¨ =V[x,, ¨ xõ,,)2 + (y, ¨ ym )2 +(z, ¨ZM )2
As a numerical example, consider the following M, P, and C values:
M = [xm, , zõ] = [4, 8, 10]
P = [2, 10,5]
C = [6, 10, 5]
The point along the normal, N, is calculated as follows:
P ¨ M = [(2-4),(10-8),(5-10)H-2,2,-5]
C-M=R6-4),(10-8),(5-10)]=[2, 2. -5]
(P-M)+(C-M) = [0, 4, -10]
and
(P¨M)-F(C¨M)
N= ____________________________________ + M
M)+(C
= 11-2,2,-5H2,2,-511/10.7703296143 + [4,8,10]
= [0, 0.3713806764, -0.928476691] + [4,8,10]
= [4, 8.3713806764, 9.0715233091]
The geometry is shown in FIG. 19, where the bisector is between the two longer
vectors.
The foregoing is, of course, merely a representative calculation serving to
show the use of the Fermat and Hero principles of least time in determining
local
tangent plane angular constraints for a field of points making up a free-space
(free-form) surface manifold of reflecting regions intended to present a
contiguous virtual image to the viewer. The only real constant is the center
of
the user's eye, and the eye's natural field of view. All other components may
be
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iteratively updated until an appropriate solution for a given image display
system
and reflective optical surface orientation is reached. Looked at another way,
the
pixel image reflection locations, Ml, M2, Mn, and their associated normals
and curvatures may be thought of as a matrix that is "warped" (adjusted) so
that
the FS/UWA/R0 surface achieves the desired virtual image processing of
computer-generated images formed by the image display system.
In applying the Fermat and Hero principles, it should be noted that in
some embodiments, it will be desirable to avoid the situation where the
normals
are adjusted such that the user sees the same pixel reflection at more than
one
point. It should also be noted that in some embodiments, the local regions of
the
reflective optical surface can be very small and may even correspond to a
point
on the reflector, with the points morphing into other points to make a smooth
surface.
To facilitate the presentation, the effects of the presence of a Fresnel lens
system has not been explicitly included in the above discussion of the use of
the
Fermat and Hero principles to design a FS/UWA/RO surface. In practice, the
presence of a Fresnel lens system is readily included in the analysis by using
as
the input to the Fermat and Hero calculations, the directions of propagation
of
the light beams after they have passed through the optical elements making up
the Fresnel lens system (or any other optical elements used in the overall
optical
system). Those directions of propagation can, for example, be determined using
Gaussian optics techniques. If desired, the Fermat and Hero calculations can
be
repeated for different initial light vergence settings as controlled by
changing the
Fresnel lensing power of the Fresnel lens system until desired virtual images
are
obtained.
In order to ensure that the user can easily focus on the virtual image of
the "desired portion" of the at least one light-emitting surface (e.g., the
virtual
image of a pixel), in certain embodiments, the radius of curvature of the
region
surrounding the reflection point (reflection area) is controlled so that after
passing through the Fresnel lens system and reflecting from the FS/UWA/RO
surface, a collimated (or near collimated) image reaches the user. As noted
above, a collimated (or near collimated) image has optical rays that are more
parallel, as if the image had originated at a far distance from the user, tens
to
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hundreds of meters for instance. In order to achieve such a surface, depending
on the collimating power of the Fresnel lens system, the radius of curvature
of
the reflection region of the reflective optical surface corresponding to the
"desired portion" of the at least one light-emitting surface (desired light-
emitting
pixel) may be kept to a radius on the order of (but greater than) one-half the
distance from the reflection region to the actual "desired portion" of the
light-
emitting surface (actual pixel) on the display. More particularly, the radius
will
be on the order of one-half the apparent distance from the reflection region
to the
"desired portion" of the light-emitting surface when the "desired portion" is
viewed through the Fresnel lens system from the location of the reflection
region.
Thus, in one embodiment, the inter-reflected-pixel normal vector from
the pixel of concern to the adjacent pixels satisfies a relationship that
allows
them to establish a radius of curvature on the order of approximately one-half
the
length of the vector from the location of the reflected pixel on the
reflective
surface to the apparent location of the display pixel as seen through the
Fresnel
lens system. Adjustments that affect this parameter include the size of the at
least one light emitting surface and whether the at least one light emitting
surface
is curved.
FIG. 9 illustrates this embodiment. In order to control the radius of
curvature of the region surrounding the pixel reflection so that a collimated
(or
near collimated) image reaches the user, two adjacent pixel reflecting
regions,
such as at the point of reflection 540, are considered. More regions may be
considered for better balance but two are sufficient. With reference to FIG.
9,
two pixel reflective points 540 and 610 are shown with respect to two pixels,
545 and 615, respectively on display surface 510. The surface normals at
points
540 and 610 are calculated along with the angle between their directions. The
radius of curvature is calculated knowing these angles and the distance
between
the points 540 and 610. Specifically, the surface configuration and, if
needed,
the surface's spatial location are adjusted until the radius of curvature is
on the
order of approximately one-half of the average of the lengths of beams 515 and
620 when those lengths are adjusted for the effects of the Fresnel lens
system. In
this way, zero or near-zero diopter light can be provided to the user's eye.
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noted above, this is equivalent to light coming from a point essentially
infinitely
distant, and the light wavefront is flat, resulting in parallel surface
normals to the
light's wavefront.
In addition to controlling the local radii of curvature, in certain
embodiments, as a first order point solution to having a collimated (or near
collimated) image enter the eye, the at least one light emitting surface is
nominally located a distance of one focal length away from the FS/UWA/RO
surface, where the focal length is based on the average value of the radii of
curvature of the various reflective regions making up the FS/UWA/RO surface.
The result of applying the Fermat and Hero principles is a set of
reflective regions that may be combined into a smooth reflective surface. This
surface will, in general, not be spherical or symmetric. FIG. 11 is a two
dimensional representation of such a FS/UWAIRO surface 520. As discussed
above, surface 520 may be constructed such that the radii of curvature at
points
710 and 720 are set to values which, when combined with the collimating
effects
of the Fresnel lens system, provide for relaxed viewing of the image from the
at
least one light-emitting surface of the image display system which is being
reflected by the surface. In this way, looking in a certain direction
represented
by line 730 will provide a collimated (or near collimated) virtual image to
the
eye 530, as will looking in a different direction represented by line 740. To
enable a smooth transition of viewing all across the field of view, the
regions of
the FS/UWA/RO surface may be smoothly transitioned from one control point to
another, as may be performed by using Non-Uniform Rational B-Spline
(NURBS) technology for splined surfaces, thus creating a smooth transition
across the reflective surface. In some cases, the FS/UVVA/RO surface may
include a sufficient number of regions so that the surface becomes smooth at a
fine grain level. In some embodiments, different magnifications for each
portion
of the display (e.g., each pixel) may be provided using a gradual gradient to
allow better manufacturability, realization, and image quality.
From the foregoing, it can be seen that the overall head-mounted display
can be designed using the following exemplary steps: determining a desired
field
of view, choosing a display surface size (e.g., width and height dimensions),
choosing an orientation for the display surface relative to a reflective
surface,
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choosing a candidate location for the Fresnel lens system between the display
and the reflective surface, choosing a candidate configuration for a Fresnel
lens
system, cataloging the position of every pixel on the display surface as seen
through the Fresnel lens system, and choosing a location for display of every
pixel from the display surface on the reflective surface. The display surface
and
the Fresnel lens system can be placed above the eye and tilted toward the
reflective surface, allowing the curvature of the reflective surface to
reflect light
to the eye of the wearer. In further embodiments, the display surface and
Fresnel
lens system may be placed in other positions, such as to the side of the eye
or
below the eye, with the reflective position and curvature selected to reflect
the
light from the display surface appropriately, or being tilted to a different
degree.
In certain embodiments, a three-dimensional instantiation or
mathematical representation of the reflective surface can be created, with, as
discussed above, each region of the reflective surface being a local region
having
a normal that bisects the vectors from the center of that region to the center
of
the user's eye and to the center of a pixel in the display surface (center of
the
apparent position of the pixel resulting from the presence of the Fresnel lens
system). As also discussed above, the radii of curvature of regions
surrounding a
pixel reflection can be controlled so that in combination with the collimating
effects of the Fresnel lens system, a collimated (or near collimated) image
reaches the user across the field of view. Through computer-based iterations,
changeable parameters (e.g., local normals, local curvatures, and local
spatial
locations of the reflective surface and the number of elements, the powers of
the
elements, the curvatures of the elements, and the locations of elements for
the
Fresnel lens system) can be adjusted until a combination (set) of parameters
is
identified that provides a desired level of optical performance over the field
of
view, as well as a manufacturable design which is aesthetically acceptable.
During use, a non-symmetrical FS/UWAIRO surface (which, in certain
embodiments, is constructed from a splined surface of multiple local regions
of
focus) in combination with a Fresnel lens system forms a virtual image of the
at
least one light emitting surface of the image display system that is stretched
across a wide field of view. The FS/UWA/RO surface may be thought of as a
progressive mirror or progressive curved beam splitter or a free-form mirror
or
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reflector. As the eye scans across the field of view, both horizontally and
vertically, the curved FS/UWAJR0 surface shines different portions of the at
least one light-emitting surface of the image display system into the user's
eye.
In various embodiments, the overall optical system is manufacturable in large
quantities at low cost while maintaining an image quality commensurate with
typical human visual resolution.
IV. HMDs That Employ Non-FS/UWA/RO Reflective Surfaces
As noted above, FIG. 4 shows an embodiment of a HMD optical system
which uses a curved FS/UWA/RO surface and a curved Fresnel lens system.
HMD optical systems that employ curved reflective surfaces that are not
FS/UWA/RO surfaces, as well as those employing flat reflective surfaces, can
also benefit from the use a curved Fresnel lens system between an image
display
system and the reflective surface. FIGS. 12-14 show an exemplary embodiment
which employs a flat reflective surface and a curved Fresnel lens system.
In FIG. 12, a user 1300 is shown wearing a head-mounted display which
includes an optical see-through, augmented reality binocular viewer 1310.
Viewer 1310 includes at least one image display system 1320, at least one
reflective surface 1380, and at least one curved Fresnel lens system that
provides
near viewing of the display and a wide field of view. Typically, viewer 1310
will include one display system/curved Fresnel lens system/reflective surface
combination for each eye, although one or more of these components can service
both eyes if desired.
As shown in FIG. 12, the curved Fresnel lens system includes Fresnel
lenses 1330 and 1335. Both a flat Fresnel lens 1330 and curved Fresnel lens
1335 may be employed in various embodiments to provide a field of view of 100
degrees or more. As with the other exemplary embodiments discussed herein,
more or fewer lenses than shown in FIG. 12 may be used in the curved Fresnel
lens system. In one embodiment, a single curved Fresnel lens element can be
used. Note that in embodiments that employ a FS/UWA/RO surface, a single
Fresnel lens element, e.g., a single curved Fresnel lens element, can be used.
In
another embodiment, illustrated in FIGS. 13 and 14, three Fresnel lens
elements
1125, 1130, and 1135 are used.
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An electronics package 1340 is provided for controlling the image that is
displayed by the at least one image display system 1320. The electronics
package 1340 may include accelerometers and gyroscopes for locating and
positioning the user. Power and video to and from the binocular viewer can be
provided through a transmission cable 1350 or wireless medium. A set of
cameras 1370 may be situated on opposite sides of the user's head to provide
input to the HMD's software package to help control the computer generation of
augmented reality scenes.
The optical see-through, augmented reality binocular viewer 1310
includes at least one reflective optical surface 1380 that allows at least one
internally-generated image to overlay at least one image entering the viewer
from the external environment. In particular, light 1386 enters the viewer
from
the external environment by passing through reflective optical surface 1380.
This light combines with light 1385 from the image display system and the
curved Fresnel lens system which has been reflected by reflective optical
surface
1380 towards the user's eye. The result is combined light 1387 that enters the
user's eye when the user looks in the direction of point 1390. The user's
peripheral vision capabilities allow the user to see light from other parts of
reflective optical surface 1380, distant from point 1390.
In one embodiment, as shown, the at least one image display system
1320 and the curved Fresnel lens system (e.g., Fresnel lenses 1330 and 1335)
are
supported above the user's eye(s) and extend in a substantially horizontal
plane
projecting away from the eye(s). For this embodiment, the at least one
reflective
optical surface 1380 can be supported by (coupled to) a bottom edge of a
forward front frame section of the HMD and angled to reflect light from the at
least one image projection device 1320 into the user's eye. In one embodiment,
the reflective optical surface 1380 is angled such that its top end is
furthest from
the user's face while its lower end is closest to the user's face. If desired,
the
reflective optical surface can include flat (or curved) portions oriented on
the
side of the face.
A ray tracing analysis of a head-mounted display apparatus of the type
shown in FIG. 12 is provided in FIGS. 13 and 14. The embodiment of FIGS. 13-
14 uses three Fresnel lens elements 1125, 1130, and 1135, rather than the two
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Fresnel elements 1330 and 1335 of FIG. 12. In FIGS. 13 and 14, light rays
1430, 1435, and 1440 are shown such that light ray 1440 enters from the
environment and is combined with light ray 1430 that has been reflected from
reflective optical surface 1380 to create the combined light ray 1435 that
enters
the user's eye when the user looks in the direction of point 1442 The user's
peripheral vision capabilities also allow the user to see light from other
parts of
reflective surface 1380, distant from point 1442.
As best seen in FIG. 14, the diverging wavefront of light 1460 emanating
from the at least one image projection device 1320 is converged by a positive-
diopter Fresnel lens system having Fresnel lenses 1125, 1130, and 1135 to
provide zero diopter light 1430 which impinges on flat reflective optical
surface
1380, where the light is bent into zero diopter light 1435 that enters the
pupil of
the eye. This is equivalent to light coming from a point essentially
infinitely
distant, and the light wavefront is flat, resulting in parallel surface
normals to the
wavefront, shown as rays 1435, across the entrance pupil to the eye. The
reflective optical surface 1380 also admits light 1440 from the external
environment (see FIG. 13), thus allowing the internal images to overlay the
external images, as also shown in FIG. 14, as externally originating light
beams
1510.
V. Direct View HMDs
In addition to the above applications, a curved Fresnel lens system can
also be used for direct viewing of an image display system without an
intervening reflective optical surface. Such a configuration will be
immersive,
but can include external world information through the use of one or more
video
cameras. By using a Fresnel lens system which comprises stacked Fresnel lenses
an optical system with a short focal length and high power which can project
an
image of a display into a wide field of view can be achieved in a compact
space.
FIG. 15 is a side view representation of a user 900 wearing an immersive
binocular viewer 910 in a head-mounted display. Inside the head-mounted
display apparatus is at least one image display system 920 for each eye that
is
adjusted for near viewing with a curved Fresnel lens system 930. An
electronics
package 940 may include accelerometers and/or gyroscopes to control the image
that is displayed and provides location, orientation and position information
to
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synchronize images on the display with user activities. Power and video to and
from the binocular viewer can be provided through a transmission cable 950 or
wireless medium. A top view of the user 900 and viewers 910 is illustrated in
FIG. 16, including eyes 955 and nose 960 in relation to the viewers 910. The
Fresnel lenses of the Fresnel lens system 930 are stacked and curved.
In this embodiment, the at least one image display system 920 is
mounted to the HMD's frame directly in front of the user's eyes and oriented
essentially vertically such that the pixels emanate light directly in the
direction
of the user's eyes for an immersive virtual world experience. The curved
Fresnel lens system 930 is arranged between the display screen of the image
display system 920 and the user's eyes and allows the eye to focus on the
screen
in close proximity.
The operation of the head-mounted display apparatus illustrated in FIGS.
and 16 may be viewed using ray tracing. FIG. 17 illustrates a diverging
15 wavefront of light 1120 emanating from the at least one image display
system
920 that is collimated by a positive-diopter Fresnel lens system with Fresnel
lenses 1125, 1130, and 1135, to provide approximately zero-diopter light 1140
to
a pupil 1145 of a user's eye. Light 1140 is equivalent to light coming from a
point essentially infinitely distant, and the light wavefront is flat,
resulting in
parallel surface normals to the wavefront, shown as rays 1140, across the
entrance pupil 1145 to the eye.
More particularly, in FIG. 17, it is seen that the curved Fresnel lens
system having Fresnel lenses 1125, 1130, and 1135 allows light 1150 passing
through a field point 1155 at the edges of the Fresnel lenses 1125, 1130, and
1135 to enter the eye from a different direction than a light beam 1160 that
originates at point 1165. The curved Fresnel lens system with Fresnel lenses
1125, 1130, and 1135 allows the light to look like it entered the user's field
of
view along a light ray path 1170. This allows an increase in the apparent
field of
view (the apparent angular subtense) of an amount indicated by angle 1175.
FIG. 18 is a ray tracing showing the collimated parallel rays 1140
entering the eye 1205 through the pupil 1145 and being focused on the fovea
1210 where the highest acuity of vision takes place. The surrounding retina
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1215 responds to the wider field of view but with a lower acuity, for instance
at
points 1220 and 1225.
VI. General Considerations
In terms of the overall structure of the HMD, Table 1 sets forth
representative, non-limiting, examples of the parameters which a HMD display
constructed in accordance with the present disclosure will typically meet. In
addition, the HMD displays disclosed herein will typically have an inter-pixel
distance that is small enough to ensure that a cogent image is established in
the
visual plane of the user.
Various features that can be included in the head-mounted displays
disclosed herein include, without limitation, the following, some of which
have
been referenced above:
(1) In some embodiments, the reflective optical surface (when used)
may be semi-transparent, allowing light to come in from the external
environment. The internal display-generated images can then overlay the
external image. The two images may be aligned through the use of localization
equipment, such as gyroscopes, cameras, and software manipulation of the
computer-generated imagery so that the virtual images are at the appropriate
locations in the external environment. In particular, a camera, accelerometer,
and/or gyroscopes can be used to assist the apparatus in registering where it
is in
the physical reality and to superimpose its images on the outside view. In
these
embodiments, the balance between the relative transmittance and reflectance of
the reflective optical surface can be selected to provide the user with
overlaid
images with appropriate brightness characteristics. Also in these embodiments,
the real world image and the computer-generated image can appear to both be at
approximately the same apparent distance, so that the eye can focus on both
images at once.
(2) In some embodiments, the reflective optical surface (when used)
is kept as thin as possible in order minimize effects on the position or focus
of
external light passing through the surface.
(3) In some embodiments, the head-mounted display apparatus
provides a field of view to each eye of at least 100 degrees, at least 150
degrees,
or at least 200 degrees.
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(4) In some embodiments, the field of view provided by the head-
mounted display to each eye does not overlap the user's nose by any large
degree.
(5) In some embodiments, the reflective optical surface (when used)
may employ a progressive transition of its optical prescription across the
field of
view to maintain focus on the available display area.
(6) In some embodiments, ray tracing may be used to customize
apparatus parameters for a particular implementation, such as military
training,
flight simulation, gaming and other commercial applications.
(7) In some embodiments, the reflective optical surface (when used)
and/or the surface of the display, as well as the properties and locations of
the
Fresnel lenses, and the distances between the display and the reflective
optical
surface (when used) and between the reflective optical surface (when used) and
the eye, can be manipulated with respect to a Modulation Transfer Function
(MTF) specification at the retina and/or the fovea.
(8) In some embodiments, the HMDs disclosed herein can be
implemented in applications such as, but not limited to, sniper detection,
commercial training, military training and operations, and CAD manufacturing.
(9) Although shown as flat in the figures, the image display system
may also have a curved light-emitting surface.
Once designed, the reflective optical surfaces disclosed herein (e.g., the
FS/UWA/R0 surfaces) can be produced e.g., manufactured in quantity, using a
variety of techniques and a variety of materials now known or subsequently
developed. For example, the surfaces can be made from plastic materials which
have been metalized to be suitably reflective. Polished plastic or glass
materials
can also be used. For "augmented reality" applications, the reflective optical
surfaces can be constructed from a transmissive material with embedded small
reflectors thus reflecting a portion of an incident wavefront while allowing
transmission of light through the material. With specific regard to the curved
Fresnel lens systems disclosed herein, the one or more curved Fresnel lenses
of
those systems may be obtained already curved or made from curvable material,
such as curvable glass or plastic to allow curving at assembly time.
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For prototype parts, an acrylic plastic (e.g., plexiglas) may be used with
the part being formed by diamond turning. For production parts, either acrylic
or
polycarbonate may, for example, be used with the part being formed by, for
example, injection molding techniques. A minimum thickness of 2 mm at the
edge may be used, requiring commensurately sized Fresnel components. A
typical Fresnel facet width can be about 200 microns. The reflective optical
surface may be described as a detailed Computer Aided Drafting (CAD)
description or as a non-uniform rational B-Spline NURBS surface, which can be
converted into a CAD description. Having a CAD file may allow the device to
be made using 3-D printing, where the CAD description results in a 3D object
directly, without requiring machining.
The mathematical techniques discussed above can be encoded in various
programming environments and/or programming languages, now known or
subsequently developed. A currently preferred programming environment is the
Java language running in the Eclipse Programmer's interface. Other
programming environments such as Microsoft Visual C# can also be used if
desired. Calculations can also be performed using the Mathcad platform
marketed by PTC of Needham, Massachusetts, and/or the Matlab platform from
MathWorks, Inc., of Natick, Massachusetts. The resulting programs can be
stored on a hard drive, memory stick, CD, or similar device. The procedures
can
be performed using typical desktop computing equipment available from a
variety of vendors, e.g., DELL, HP, TOSHIBA, etc. Alternatively, more
powerful computing equipment can be used including "cloud" computing if
desired.
A variety of modifications that do not depart from the scope and spirit of
the invention will be evident to persons of ordinary skill in the art from the
foregoing disclosure. The following claims are intended to cover the specific
embodiments set forth herein as well as modifications, variations, and
equivalents of those embodiments.
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TABLE 1
Name Description Units Minimum Maximum
Distance of reflective mm 10 400
surface from eye
Distance of reflective mm 10 400
surface from display
Display size Horizontal mm 9 100
Vertical mm 9 100
Display resolution Horizontal pixels 640 1920+
Vertical pixels 480 1080+
HMD weight grams 1 1000
HMD size Distance in mm 10 140
front of face
Human pupil size mm 3 to 4 5 to 9
Size of reflective e.g., less than mm 30 78
surface the width of
the head/2
Number of reflective units 1 3+
surfaces
Maximum illumination e.g., bright fc, footcandles 5,000 10,000
to the eye enough to
allow viewing
on bright
sunny day
Battery life hours 3 4
Optical resolution Largest arcminute RMS 1 10
angular blur blur diameter
Estimated 1 5
number of
line pairs of
resolution
Maximum variation in Percent 0 20
apparent brightness of
the image
Maximum image Percent 0 5
distortion
Estimated maximum Percent/degree 0 5
derivative of brightness
