Three-Dimensional Viewing of Distant Objects
with the 'Naked' Eye
Kouichi TOYOSHIMA
Faculty of Liberal Arts, University of Saga, Saga, 840, Japan
phone/fax: +81 952 0366e-mail: toyo@cc.saga-u.ac.jp

abstract
Simple apparatus which enhances three-dimensional recognitionof object is contructed and examined. It is composed of only 4plane 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.

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We obtain three-dimensional recognition of objects mainly by the parallaxbetween 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, moredistant objects will be recognized perspectively. This might be compared to the sightof fictitious giant monsters like "King Kong" or "Godzilla", which may see a landscapewith 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" areplaced 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 alandscape 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 asshown in fig. 1. This will results in the larger parallax between the two eyes andeventually 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-typestereoscope to view a pair of large stereographs. It is true, but did anyone notice thata 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 for2

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 nakedeyes. 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 theother 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 stepladderof 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 themost important parameter is 1.3m, 20 times as large as the separation of human'seyes. 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 andalmost 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-dimensionalrecognition. 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,3

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 theKingdom 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 keepa 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 theuse of large mirrors, one can combine a lens system of unitary magnification, but thenatural feeling of vision may more or less be lost.) Such a large-scale version of thisapparatus 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 astarry sky?

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Figureseye mirrors
objective mirror(right)objective mirror(left)

observervirtual positionof the left eye

virtual positionof the right eye

fig.1

fig.1
Illustration of the optical principle of the apparatus.

5eyemirrorsleft
objective
mirrorright
objective
mirrorfig. 2
Construction of the apparatus employing a stepladder as a frame, seen from theobserving side. The lowest step bars are removed and two stems are attached at bothends to fix the objective mirrors with hinges.

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Table 1. Dimensional parameters of the prototype.
________________________________________________
objective mirrors' size

450mm x 300mm

eye mirror's size

40mm x 40mm

frame width (expanded)

1770mmframe height450mm

effective baseline
1300mm________________________________________________

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