Three-Dimensional Viewing of Distant Objects with the 'Naked' Eye
Kouichi TOYOSHIMA
e-mail: toyo@cc.saga-u.ac.jp
paper styled docs available. paper-1 paper-2
abstract
Simple apparatus which enhances three-dimensional recognition of object
is contructed and examined. It is composed of only 4 plane mirrors and used
to see objects directly. Landscape seen through it is very exotic, which
might be compared to a Gulliver's view in Lilliput.
We obtain three-dimensional recognition of objects mainly by the parallax
between our two eyes. However, the range of this recognition is limited
by the space between the two eyes of about 6.5cm. If we can expand this
space somehow, more distant objects will be recognized perspectively. This
might be compared to the sight of fictitious giant monsters like "King
Kong" or "Godzilla", which may see a landscape with a feeling
just like we see a miniaturized copy of it because of large separations
between their eyes.
We can expand the space between the two eyes optically by using four plane
mirrors. As shown in fig. 1, two pairs of plane mirrors (large and small
ones) are combined parallel with some spaces, like periscopes. Then these
"periscopes" are placed horizontally and are directed to a common
visual field, with a separation between small mirrors fitting to the space
between the two eyes. If one looks at a landscape with this mirror system
as we use a binocular telescope, the virtual positions (images by these
two pairs of mirrors) of right and left eyes are widely separated as shown
in fig. 1. This will results in the larger parallax between the two eyes
and eventually brings about an enhanced perspective feeling to an observer
even for distant objects. This apparatus might be named "macroscope"
or "godzillascope".
One may say that this apparatus is merely a scaled-up version of a mirror-type
stereoscope to view a pair of large stereographs. It is true, but did anyone
notice that a real and single landscape itself can be an object of such
a stereoscope?
Let k be the ratio of the effective baseline length to the human eyes' spacing.
By the geometrical proportionality, same parallax as that with naked eyes
is obtained for k-times distant object through this appartus. Assuming the
proportionality between the parallax and the perspective-sensing range,
the observer will be able to recognize the perspective for k times more
distant objects with this apparatus than by naked eyes. Besides, or as a
result of the enhancement of the perspective, the observer will feel the
landscape itself to be reduced to 1/k in the radial direction. The latter
effect, which is of phycological nature, is the origin of the name "macroscope".
On the other hand, the view angle of objects are not affected (no magnification
or reduction) becaue this apparatus is copmosed of only plane mirrors.
The author have constructed a portable version of this apparatus to examine
views of various landscapes through it. This was facilitated by employing
a stepladder of expandable type as a frame. Its construction is illustrated
in fig.2 and several dimensional parameters are listed in table 1. The virtual
baseline length which is the most important parameter is 1.3m, 20 times
as large as the separation of human's eyes. The eye mirrors are of surface-reflecting
type to avoid double image.
This apparatus was examined by the author as well as tens of people around
him in office and at home. Actually they could get an obvious three-dimensional
feeling for objects at more than 1km distance by this apparatus. The author
and almost all other observers have experienced the feeling of "landscape
miniaturizing", mentioned above, as well.
A binocular telescope, which has somewhat large distance between objective
lenses, also expands the viewing baseline and enhances the three-dimensional
recognition. But, as it's main performance, it simultaneously magnifies
the object and the view through it is far from the feeling of the naked
eye vision. In contrast, through the "macroscope" one can view
a landscape with very natural feeling as if he/she is looking with naked
eyes, except the feeling that the landscape is remarkably shrunk towards
the observer. This is really an exotic and new experience of vision, far
more attractive than the stereoscope which does not bring about a "live"
view. Try to fabricate it by yourself and enjoy an experience of a Gulliver's
view in the Kingdom of Lilliput!
In order to enjoy 3-dimensional views of vast geographical features extending
to tens of kilometers, for example the Grand Canyon, greater space (several
meters) between the two objective mirrors is required, as well as larger
sizes of them to keep a large field of vision. It will simultaneously require
a better flatness of the objective mirrors due to the use at long distances
from an observer. (Alternatively, to avoid the use of large mirrors, one
can combine a lens system of unitary magnification, but the natural feeling
of vision may more or less be lost.) Such a large-scale version of this
apparatus is envisioned as a built-in system installed in a building.
How large baseline and mirrors will be needed to get a perspective view
of a starry sky?
Figures
fig.1
Illustration of the optical principle of the apparatus.
fig. 2
Construction of the apparatus employing a stepladder as a frame, seen from
the observing side. The lowest step bars are removed and two stems are attached
at both ends to fix the objective mirrors with hinges.
Table 1. Dimensional parameters of the prototype. ________________________________________________ objective mirrors' size 450mm x 300mm eye mirror's size 40mm x 40mm frame width (expanded) 1770mm frame height 450mm effective baseline 1300mm ________________________________________________
