Note: Descriptions are shown in the official language in which they were submitted.
2 ~ Q .3
-- 1
SYSTEM FOR PRODUCING STATIONARY OR MOVING
THREE-DIMENSIONAL IMAGES BY PROJECTION
FIELD OF THE INVENTION
The present invention describes a device capable of
reproducing ~tationary or moving three-dimensional images by
pro~ection, using ordinary llght.
10 BACKGROUND OF TH~ INVENTION
"1
The sy~tems of taking and reproducing images with
depth developed up to now can be dlvided $nto two ma~or
groups, namely the most modern ones, developed since 1947,
15 based on the formation of images due to the interference of
beam8 of coherent-l~ght, which are called holographic sys-
tems, and the oldest, whlch do not record by interference of
waves, which-are-known--as non-holographic sy~tems.
Among the latter, stereoscoplc and three-dimension-
20 al systems are dlstlngulshed'from each other. The termstereoscopic is used for systems in which two distinct
images, one for each eye,_are used ln the reproduction. The
term three-dimenslonal is u~ed to dlstlngulsh systems which
use a greater number of taken and reproduced lmages, allow-
25 lng observatlon wlthln a wlde viewlng angle, wlthoutlnconvenlenclng the observers by plaalng optical fllters or
any other contrlvance before them.
The technlque of holography ls bnsed on photography
by reconstructlon of wAvefronts. These systems regulre
30 coherence of the llght sources for lmage-taklng and repro-
ductlon. Both the obJects whlch are to be recorded as well as
the lmage~ whlch are to be reproduced need to be lllumlnated
wlth coherent llght only. This has hlndered the commerclal-
lzlng of systems uslng this process whlch are capable of
35 maklng photographs of dlstant obJects whlch, llke the moon,
cannot be llt up wlth a coherent beam. It 18 found lmposslble
to photo~reph sunsets or reflectlons of the sun or moon on
i.
20~8&Q3
the sea, landscapes etc. Finally, as observatlon through
transparency is necessary, the size of the reproduced image
is limited.
In the stereoscopic systems, the photograph is taken
5 through two obJectlves which are separated from one another
by a dlstance approxlmately equal to the average value of the
dlstance between human eyes.
For thiC stereoscopic photography, ~pecial ~ystems
of lenses have been developed whlch are suitable for attach-
10 ment to conventional cameras, such as the Fazekas camera,whlch i9 descrlbed in U.S. Patent 4,525,045~
There are stereoscopic systems in whlch the brlng-
lng of a different lmage to each eye 1~ obtalned by pro-
ce~ses which are not suitable for pro~ection. They lnclude
15 those which place an optical system, ~uch a~ the Brewster
pri~ms and Wheat~tone flat mirrors, between the observers and
reproduced image tNorllng, J.A., The Stereoscopic Art. ... A.
Reprint. J. Smpk--60,--No-. 3,--286-308 (March 1953)], or the
Kempf concave mlrror (U.S. Patent 4,623,223).
The stereoscoplc systems suitable for pro~ectlon
dlffer gre~tly dependlng on the process used to bring the
lmage taken up by the left lens to the left eye and that
taken up by the rlght lens to the right eye. The best known
and most widely used ln stereoscoplc proJectlons wlth
25 movement are those whlch employ colored, polarlzed fllter~ or
shutterlng.
The main llmltation of the stereoscoplc ~ystem~ used
in pro~ectlon 18 that they necessarily lnconvenlence the
observer by placlng optlcal fllters or a shuttQring mechanlsm
30 ln front of him.
Among the three-dlmenslonal systems of reproductlon
uslng ordlnary llght whlch have been developed up to the
present, there are 80me whlch are capable of showlng the
reproduced image on the rlght or left ~lde when the observer
35 moves to the left or rlght or vlce versa.
Most of the~e three-dlmensional reproductlon devlces
employ a dlffu~lon surface on whlch the various lmages are
- . - . .. .: .,,: , - .
: . . :.: ,. ': ~ '. ' . . ; : . , .
:
,,, . . .. ,, ,. : :.,
: .. .. .: . : ~. :
20~6~3
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prlnted, pro~ected, generated, amplifled or Qimply transmit-
ted. Typical printing system~ aFe oneQ which use the photo-
graphic material ltself as a dlffusion surface with pro-
Jectlon onto ~n opaque or tranYlucent surface in cinema-
5 tography or pro~ected television, typical generatlon sys-
tems are those in whlch the diffusion surface is the cathode
ray tube itself; and typlcal transmlssion systems are tho~e
which employ light conductors or amplifiers.
It is lmportant to emphaslze one essential charac-
10 terlstlc common to any dlffuslon surface whlch greatlyaffects the design of all devices for three-dlmenslonal
reproduction which use thls type of surface.
This essential characterlstic 18 that: ~Any polnt of
the diffuslon surface 18 converted lnto a centar transmlttlng
15 light photons ln all dlrectionsn.
- As a consequence, any observer, whatever hls posl-
tlon, wlll see the whole lmage reproduced on the dlffuslon
surface.
If two or more lmages nre reproduced at the same
20 tlms on the ~a~e polnt of the dlffuslon surface, the photons
comlng from ~he different images appear mlxed together, what-
ever th_lr dlreetion.
For thls reason, dlstlngulshlng the dlfferent lm~ges
reproduced on the dlffuslon surf~ee 18 achleved by reservlng
25 a dlfferent plsGe for eaeh of them, that 18 by me~ns of
sealar image dlfferentlatlon~.
All systems whleh contaln a dlffuslon screen
sueeeed, by dlfferent methods, ln reservlng a dlfferent
portlon on lt for each lmage. Thls posltlon 18 usua~ly a
30 vertleal band of very small wldth.
In the ~ystems for the reproductlon of statlonary
photographle l-ages lt 18 on the photographlG ~aterlal
ltself, whleh aGts a8 dlffuslon 8urfaee, th~t the lmages
appear dlvlded lnto flne vertleal strlpes. The elemept
35 entrusted wlth dlvldlng the lmage~ lnto flne strlpes 18
norm~lly a sheet of eyllndrleal lenses.
Among the systems whleh use thls technlgue mentlon
,
;. . : ~ . - : ~
,... ... . .
20~86Q3
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may be made of the following:
U.S. Patent 1,918,705 to Ives whlch descrlbes a pro-
cess for obtainlng three-dimensional lmages on photographic
materlal.
Glenn'~ U.S. Patent 3,482,913 which describes a
method and the apparatu~ needed to compose three-dlmenQional
photograph~.
Wah-Lo's U.S. Patent 4,086,585 whlch descrlbes a
system and a camera for controlllng the fleld depth in three-
10 -dimenslonal photography.
In the sy~tem~ for the reproduction of movlng images
by proJectlon, the diffusion surface consist~ of an opaque
material if the proJectlon is a front proJectlon or of a
translucent materlal if the proJection 18 a rear pro~ection.
15 In all cases, the images appear on thls surface dlvlded lnto
flne vertic~l strlpes.
Amon~ the sy~tems whlch employ this technlque
mentlon may be made~of~
Patent 1,883,290 to Ives whlch describe~ a method of
20 front proJectlon on an opsque screen ln whlch the element
whlch dlvldes the lmage lnto flne vertlcal strlpe~ ls.the
same sheet of vertlcal cyllndrlcal lense~ throuoh whlch
observ~tlon 18 effected and another method of rear proJectlon
onto a translucent surface ln whlch the element whlch dlvldes
25 the lmages lnto flne vertlcal strlpes 18 also a sheet of ver-
tlcal cyllnders used ln the method of copylng dlfferent fllms
onto a slngle one. In the flrst case, lt wlll be necessary to
ellmlnate the brlghtness generated by the mlrror lmage of the
proJectors on the cyllnder sheet and ln the second an AdJu~t-
30 ment of hlgh preclslon 18 requlred ln order to posltlon thelmage strlpes on each cyllnder.
U.S. Patent 4,078,854 to Yano descrlbes two methods
of three-dlm6ns~0nal reproductlon by rear proJectlon. In the
flrst, correspondlng to ~lgs. 1, 2, 3 and 4 of the patent,
35 the dlffuslon 8creen, whlch 18 m~de of tr~nslucent m~terl~l,
appears between two sheets of cyllndrlcal lense8 has the task
of dlvldlng the lmage lnto flne vertl¢al 8trlpe8 on the dlf-
, -: , . .
.. .. . .
. .. . . .
. . ., . . , :; : - ,
2~86~3
-
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fusion surface. The second method of this patent, which re-
places the diffusion ~urface by a ~heet of horlzontal cylin-
drlcal len~es will be di~cus~ed further below.
U.S. Patent No. 4,737,840 to Mori~hlta de~cribes a
5 method whlch i8 ba~ed on rear proJection through a vertical
opaque grld loeated in front of the diffusion surface. In the
dlffuslon ~urface each image always appears at a dlfferent
place, in a dlfferent vertlcal strlpe.
Other proeesses of reproduelng movlng lmages exl~t
10 ln whlch the dlffuslon surface i~ formed by the ends of llght
conductors, as descrlbed in U.S. Patent No. 4,571,616 to
Hal~ma, in whlch each image also appears withln a different
vertleal ~trlpe. In thls case, the lmages are positioned
after being gulded through llght eonduetor~.
In all the~e eases, the viewing 18 effected through
an optlcal sereen of vertleal eyllndrlcal len~e~ the foeal
lines of whleh are eontalned in a plane in whlch the
diffusion s~rfaea i~ situated. ~ -~-~ ~ -
__ Below there is flrst glven a erltieal examlnatlon of
20 the three-dlmenslonal horlzontal parallax reproduetlon sys-
- tems deserlbed above.
The factors to be taken into aeeount ln th~ compari-
. _ .
son of the dlfferent systems are:
The orthoseopie vlewing angle, the guallty of the
25 lmage reprodueed, and the cost resultlng from the.aomplexltyof manufaeture.
The maxlmum vlewlng angle 19 llmlted by the aper-
ture of the vertlesl eyllnder, the ratlo between the width
thereof and lts foeal length; lf thls nngle is exeeeded,
30 observatlon takes plaee on an l~age llne eorresponding to the
adJaeent eyllnder, produelng the undesirable pseudoseopie
effect, that 18 to say, lnverted depth.
Hals~a, ln hls aforementloned patent, (see page 1-65)
polnts out the l-portanee of this problem.
If the 8et of 8trlpe8 eorr98pondlng to eaeh eyllnder
oeeuples the wldth of the l~tter, the maxlmum vlewing angle
wlthout pseudoseopy 18 expressed by:
.. .. .. ..
.:: .. : :
2 0 '~ 3
.
-- 6 --
wide cyllnder
2 arctan --------------
2 x focal length
5 which, for ordinsry materials, the indice~ of refraction of
whlch vary around 1.5, has an approximate value of S4Q, which
is clearly insufficlent ln many case~.
The prçservatlon of this an~le on the wldth of the
entlre screen requlres preclse correspondence between each
10 cyllnder and lts lmage (group of strlpes). Thls corre-
spondence is difficult to achieve when the lentlcular sheet
charged wlth generatlng the lmage divlded into fine vertical
stripes is not the same as that used ln the observation of
the lma~e. Thls lack of correspondence 18 a problem to be
15 taken into account in the photographic reproduction ~y~tems
and in those other rear pro~ection systems ln which, such as
th~t used by Yves 290, the dlvlsion of the lm~ge lnto fine
vertlcal strlpes 18 effected ln a process dlfferent from that
of proJectlon. Thls dlfflculty 18 foreseen by Yve~ 290
20 hlmself although he does not propose any method of solvlng it
(see page 3, 103-106).
Slnce the orthoscoplc vlewlng angle is a function of
the rstlo between the wldth of ~he image and lts focal
length, in order to increase this angle two procedures may be
25 employed: elther lncrease the wldth of the lmage correspond-
. lng to each cylinder or decrease the focal length of the
cylinder wlth respect to lts wldth, uslng materials of very
high indlces of refraction (close to 2).
Both methods are mentioned ln Ives 290.
The first, increase in the size of the image repro-
duced, can be noted on p~ge 3, 58-65. In thls method, ~ 1088
of quallty upon reproductlon re8ults, due to the fact th~t
the dlstance between the ~xe8 of the cyllnders i8 greater
than the dl~meter thereof, dark vertical llnes therefore
35 appearlng between cylinders; see Ives 290, page 3, 65-75. The
enormou8 complexlty of manufacture of thl~ lentlcular 8heet
18 obvlous.
The second, basea on the relatlve decrease of the
., . . . . . .... .. :
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- . . .,: . ., -, . ,: : .:, .: :
,, . . .: .. .,;, . ...
: - . . , ~ .. .. : . , . :: : :,
2 ~ 3
focal length by lncrea~e of the index of refraction, leeds to
the need of placing opaque sheets between cylinders,
substantially complicating manufacture (~ee Ives, 290, page
4, 45-50).
S In both cases, the complex section of these cylin-
de~s recommends front pro~ection and, as a result, an un-
desirable brightnes~ appears on the lenticular 3heet caused
by the specular vision of the pro~ectors. This new dlfflculty
makes lt necessary to proJect onto a sultably lncllned ver-
lO tlcal sheet facing the proJectors and ob~ervers (see Ives
290, page 4, 60-65).
The quallty of the lmage -ls llmlted by the
transverse dimension of the cylindrlcal lens, whlch, ln lts
turn, 18 llmlted by that of the vertlcal band of the lmage.
It i9 to be taken lnto account that the wldth of
each vertlcal lmage band must be as many tlmes less than the
slze of the cyllnder a8 the number of lmages reproduced. For
this rea~on, the ~lze of the cylinder 18 llmited by the slze
of the lmage, whlch, ln lts turn, is less than that of sald
20 cyllnder.
The condltlon for a strlpe of wldth "d" not belng
perceptlble for a healthy eye 18 that
vlewlng alstance ln meters
d ~ ----------________________
3,500
For example: 0.3 ~ for ~ dlstance of 1 m, and
0.08 ~m for a distance of 0,25 m.
If lO lmages are used, the wldth of each lmage
30 strlpe must be 0.03 and 0.008 ~ respectlvely. These values
are on the order of only 15 times greater than the wavelength
of visibl~ llght. If a number of l~ges greater than 10 were
used the sltuatlon would, loglc~lly, become worse. The dif-
flcultles ln manufacture are obvious and, therefore, the
35 prlce of the co~ ercial product 18 hlgh. In systems ln
whlch, llke Halsna's, the ~ oge 18 posltloned through optl¢al
conductors, this dlfflculty cay be lncap~ble of solutlon.
It 18 lmportant to polnt out that the lnventors of
. . :. :: : :,.. , , ,:
2 ~ Q 3
-- 8 --
systems based on the ~calar dlfferentiation of images, who
have tried to provide their system with a large orthoscopia
viewlng angle, have had to solve the problem of deslgnlng
cyllndrical elements with a large aperture.
This is the reason why, in these systems, the
orthoscopic viewlng angle colncides wlth the aperture angle
of the vertical cyllnders through which the vlewlng 18
effected.
For this reason, the systems bssed on the scalar
}O dlfferentiatlon of images of hlgh value of orthoscoplc
viewlng angle glve rlse to de~lgns of vertical cyllnders
whlch are very expensive or impossible to construct.
Furthermore, a hlgh ortho~copic vlewlng angle, with
the need of continulty and great depth ln the reproduction,
15 reguires a large number of images. As has been pointed out,
a large number of images, in a scal~r dlfferentlatlon sy~tem,
requlres some cyllnders al80 of hlgh transverse slze, slnce
- - each cyllnder must hous~-as m~ny strlpes as lmages, and these
strlpes cannot be made lndeflnitely small. Therefore, the
20 slze of the cyllnders is condit~oned and the quallty of th~
reproductlon may be defflclent.
These reasons exE~aln why the~e systems have not
been successfully marketed, nct even ln clnematography wlth
8mall proJectlon screens.
Secondly, wlthln thls general technlque, there are
lncluded the lntegral reproductlon systems. This 18 the name
glven to systems capable of reproduclng horlzontal and ver-
tical parallax slmultaneously.
The lnventlon 18 that of Llppmann, the famous French
30 optlclan ln 1908 (Llppm~nn, M.G., Epreuves Reverslbles
Donn~nt la Sensatlon du Rellef. J. Phys. 7, 4th Serles, 821-
825 (Nov-1908)).
The b~sls of lntegr~l photography 18 to prepare
fly's eyes lens sheet, of gl~ss or pl~stlc, wlth ~ tremendous
35 nu~ber of spherlc~l pl~no-convex lenses (for ex~mple 10,000).
One ex~mple of lntegr~l reproductlon 18 Ando's Pat-
ent 3,852.524.
.
. , , , , ., : . ~ . I .
- . ~ . :~ . ,.. ,. . . :
: . :,.,. : ::: . .:
. ~ . . . : , : . .-
:: . . :- : -
- 2~6~3
g
Ando, at no time, mentions the number of images
taken nor the wldth of the band required for their
transmisslon; he slmply says that they are multiple and that
a carrler of very hlgh frequency must be u~ed.
In fact, this process of lmage ta~lng and repro-
ductlon requlres the handlln~ of an enormou~ amount of
lnformatlon, because 2-dlmen~ional lmage 18 received behind
every plano-convex lens.
In order to make the system work, the number of
10 plano-convex lenses used, both for the reproducing and the
taklng of lmages, must be on the order of thousands.
Apart from these difficulties and the use of
spherical optlcal screens, the reproductlon 18 always carried
out in all the forms described in his patent through a
15 dlffuslon surface wlth all the drawbacks whlch thls use
entails.
Halsma, ln hls aforementioned Patent No. 4,571,616
-descrlbes an lntegra-~eHef system based on taklng the lmage
wlth conventlonal c~meras formlng a square mosalc. He glves
20 as an example a number of 9 cameras arranged ln 3 columns of
3 cameras each.
The reproductlon 18 contlnued by posltlonlng nlne
dlfferent sections of lmages behlnd each spherlcal lens, at
the rate of one section for each image taken. The adJustment
25 18 achleved by appropriately posltlonlng the optlcal con-
ductors by mech~nical means. While we have previously seen
the comple~lty of manufacture brought about by the posltlon-
lng of lma~e strlpes behlnd each cyllnder, the problem here
18 much more serlous, slnce lt lnvolves posltlonlng n2
30 squares of lmages behlnd each spherlcal mlcrolens.
In additlon, ln the system descrlbed by Haisma a
diffusion surface is used, in thls caRe the ends of optical
conductors.
The abov~ntloned drawbacks of the horlzont~l
35 parall~x reproductlon 8y8tems ~180 appear here not only in
the reproductlon of th~ horizontal parallax but also ln the
roproductlon of tho vortlcal parall~x ~nd they h~vo pro nto~
.` .: "- , ' ...
. .
. .. . . .
.~ . ... .. . . .
2 ~ 3
-- 10 --
the successful marketing of thls system.
Certaln other field~ of appllcation also exist, a~
in robotics, where also, as in the aforementioned Ando pat-
ent, optical screen~ of ~pherlcal len~e~ are u~ed; ~ee for
5 example U.S. Patent No. 4,410,804 to Stauffer. His purpose,
however, i8 to obtaln data on the dl~tance of the ob~ects and
their slze, and never three-dimensional reproduction with
vertical and horlzontal parallaxes of images.
The only system of whlch knowledge 1~ had whlch does
10 not employ diffusor surfaces is that described by Yano.
Yan~, in the second part of his U.S. Patent
4,078,854, replaces the diffusion surface by a sheet of
horlzontal cyllndrlcal lenses, but does not do 80 ln order to
deslgn a new system based on the angular differentlation of
15 images, but rather as a mere variant of what was described in
the flrst part and based on the scalar dlfferentlatlon on a
dlffuslon surface of translucent materlal.
I-n fact, the system 18 referr6d to ln that patent as
a stereoscoplc reproduction system, havlng a very small
20 number of-lmages reproduces (see page 1, 10-13) which at most
can be fl,ve (sQe page S, 30-32) wlth a wlde vlewlng margln,
but, ~8 recognlzed ln that patent (see page 3, 32-36), there
are vlewer~ who wlll see the same lmage wlth both eyes and
for whom lt 18 necessary to provide a sensatlon of depth by
25 other means.
For thls, thls last-mentloned devlce has two
elements, a convergent optlcal Qy~tem whlch condltlons and
makes dlfflcult the proJectlon of lmages of large slze and a
screen composed of two sheets of cyllndrlcal lenses; the
30 aperture of the cyllnder8 has a concrete and fixed value
lndependent of the distance between obJectlves-proJectors and
the proJection dlst~nce; whlch makes lt obvlous that lts
deslgn 18 not based on the angular dlfferentlation of lmages.
Accordlngly, thls last-~entloned system dQscrlbed ln
35 the 8econd part Of Yano'8 Patent 1B a mere variant Of what i8
described ln the flr8t part, which is based on the 8calar
differentlatlon of lmages ~nd llke all the others, wlth
.: ~.-, ,. : .: :
. ,:: ,, -: , .- , . :. ~
11
various drawback~.
Flnally, it should be noted that the above systems
were deslgned ln order to cause an image taken ln lts
entlrety by a slngle camera to reach each eye. There iq
5 concerned th~ achlev1ng of thr~-dimenslon~l vlsion by
ca~slng each eye to see on image taken by a different camera
and therefore located at ~ different place.
This concept 18 described ln greater or lesser
length by the prevlou~ lnventors: see for Qxample~ Ives 290
10 page 4, 10-25, Ives 705 page 1, 95-100 and page 2, 0-2, Glen
page 1, 65-70, Halsma page 1, 24-29, Yano page 1, 14-19 and
page 2, 29-32.
SUMMARY OF THE INVBNTION
The system formlng the obJect of this lnventlon 18
based on the angular dlfferentlatlon of lmages, for whlch lt
18 necessory, ln a~*itlorl to e~lmlnatlng the diffuslon sur~
face, to deslgn the reproductlon of lmages ln ~ manner dlf-
20 ferent than that used ln the prevlous system.
In a system based on the ongular dlfferentlatlon oflmoges, from each polnt of observatlon a ~ectangle 18 seen of
each lmage, whlch rectongle wlll dlffer for each polnt of
observatlon. The group of rectangles correspondlng to one
25 observatlon polnt wlll form a slngle lmage dlfferent from
that correspondlng to any other polnt.
In the angular dlfferentlatlon of lmages no dlf-
fuslon surfaces on whlch the dlfferent lmoges ore focussed 18
employed. An lmoglnary plane exlsts on whlch the lmages are
30 focussed, but thls plane does not exlst physlcally.
For pedagoglcal reasons, sold plane can be thought
of 08 a transparent surface.
In order to follow the some order of esposltlon 08
that used ln the examlnatlon of the prevlous processes, we
35 wlll begln by deflnlng the fund~ental characterlstlc of any
transparent surface:
~Any polnt on the transparent surface 18 transform-
, - ;: ~ .: :-.~,
': :. ' :', ' ,", : ~ . r
o 3
ed lnto a center which emlts photons which retain the same
dlrectlon as the lncldent photon."
Consequently:
- Any viewer, whatever hls positlon, w~ll see a
5 slngle point of the pro~ected lmage. Thls po~nt 18 the lnter-
section with the transparent surface of the line which ioins
the optlcal center of the proJectlon obJectlve to the optlcal
center of the viewer. For each position of observatlon there
wlll correspond a separate lmsge or polnt.
- If two or more lmages are proJected at the same
tlme from dlfferent posltlons ln space onto the transparent
surface, the photons coming from the different proJectlons
wlll retaln thelr direction after passing through it. The
different images can be dlstinguished because the photons of
15 each emerge from thls tr~nsparent surface at a dlfferent
angle: that i8 to say ~An~ular Im~ge Dlfferentl~tlon~ can be
used.
- ln order brlefly to descrlbe the lnventlon wh-lch i'8
the obJect of thls appllcatlon, an optical sheet of vertlcal
20 cyllnders wlll flrst of all ba placed ln front of thi~
transparent surface at a dlstance away equal to the fooal
length of these cyllndrlcal lenses.
The focal length of the cyllndrlcal lenses 18 chosen
ln such a way that the ratlo of the transverse slze of the
25 cyllnder to its focal length 18 at least equal to the ratlo
between the dlstanGe between two contlguous proJection
obJectlves and the proJectlon dlstance, and never greater
than twlce this value.
After positioning the verticsl cylinders wlth the
30 above ~haracterlstlcs, any vlewer, whatever his posltlon,
wlll see as many lmage seg~ents a~ there are proJectlon
obJectlves. These s6g~ents wlll llne up ln a 81ngle llnear
seg~ent. Thls llnear l~age seg~ent wlll be dlfferent for each
polnt of observatlon and wlll be cont~lned ln the llne
35 resultlng fro~ the lnterseGtlon of the plane whlah contalns
the proJectlon obJectlves and the observer wlth the
transparent proJectlon surfaoe.
, . ~. . . . .
2 ~ 3
- 13 -
If the system merely attempts to reproduce the
horizontal parallax, according the former European Patent
0273845 of the same applicant, the proJectlon ob~ectives wlll
be located on a horlzontal llne and a second optlcal screen
5 of horlzontal Gyllnders, the focal llnes of which are ln the
same f~cal plane of the vertlcal cylinders and therefore
coincide wlth the transp~rent screen lmaglned for lnstructlon
purpose~, wlll take care of convertlng the above segment lnto
a rectangle the base of whlch wlll be of the slze of thls
10 same segment and the helght of whlch wlll be that of the
transparent surface. To each polnt of observatlon there wlll
corre~pond a dlfferent lmage rectangle and the group of these
rectangles wlll form a slngle and dlfferent lmage at each
polnt of observatlon.
The focal length of these horlzontal cyllnders must
- be a8 sm~ 8 posslble as compared wlth th~lr wldth (seml-
clrcular cyllnders) ln order that thelr ~perture permlts the
viewlng, f~om a~y ~olnt, of a--rect~ngle whlch 18 as hlgh as
the o~tlc~l system ltself.
' The present lnventlon covers the case ln whlch the
sys~em 18 lntegral, that 18 to say, lt 18 deslred to re-
produce vertlcal parallax ln addltlon to horlzontal parallax,
thenj the above horlzontal cyllnders must be deslgned ln a
manner slmllar to that descrlbed for the vertlc~l ~yllnders.
25 In thls case, the fact must be taken lnto account that the
proJectlon obJectlves whlch prevlously formed a line now form
a rectangle.
Summarlzlng, the optlcal system whlch 18 the obJect
of thls lnvention conslsts of two sheets of cyllndrlcal
30 lenses whlch are perpendlcular to each other and such that
the resultant vertlcal optlcal aperture covers at least two
vertlcal pro~ectlon obJectlves ~nd at most three and the
resultant horizontal optlcal aperture covers at least two
horlzontal proJectlon obJQ¢tlvQs and at mGst three.
The syste~ thus deslgned is for~ed of cyllnders of
vQry small aperture, that is to say, of a very large radlus
a8 co~pared wlth lt8 tran8ver8e slze. Thls 8mall aperture
?
2 Q ~ 3
- 14 -
value is furthermore lndependent of the orthoscopic viewing
angle. In thls way, cyllnders of each and lnexpenslve manu-
facture can produce orthoscoplc vlewing angles which are as
large as desired. The ~lze of the cyllnders, there belng
5 concerned a system based on image an~ular dlfferentlatlon, is
lndependent of the number of lmages reproduced and therefore
the quallty of the reproduction can be vary hlgh. If an
addltional convergent optical system is not used, lmages of
large size can be reproduced wlthout dlfflculty. Front
lO proJection is achieved by merely replacing one of the sheets
of lenses by mlrror~, without the specular lmage of the
pro~ectlon obJectlves belng apparent at any tlme. Rear
proJection does not require special adJustments of preclslon
and each observer sees a dlfferent image with each eye.
Finally, the advantages of thls system as compared
wlth all other systems are: -
A) The orthoscoplc viewlng angle can be made as
large as desl-~ed, lt- dependlng only on the number of
proJectlon obJectlves, the dlstance between them, and the
20 proJectlon dlstance.
B) The slze of wldth of the cyllnders 18 not llmlted
by the number of lmages and can be deslgned as small as de-
slred, 80 that the guallty of the lmage 18 only llmlted by
the condltions of manufacture of these cyllnders.
C) When the vlewer leaves the fleld of vlslon, no
pseudoscopy takes place.
D) It 18 not necessary to create a complex means for
dlvldlng the proJected lmages lnto ordered and lnterlaced
vertlcal strlpes, nor 18 there regulred the collaboratlon of
30 other convergent optlcal syste~s ln addltlon to the len-
tlcular plane, the rear proJectlon requlres no adJustments ln
preclslon and, flnally, the system of the lnventlon 18 easler
to manufacture and simpler to lmplement whatever the slze of
the lmage reproduced.
E) The lmages percelved by ea¢h eye of the vlewer
are dlfferent, regardle8s of hls locatlon.
F) The lntegral reproductlon systems are easy to
2 ~ 3
- 15 -
manufacture.
G) Front proJection 18 achieved very easlly by
replacing one of the sheets of lenses by another sheet of
mlrrors.
It should be polnted out that thls system ls only
valld for proJectlon and cannot be used in photographic
reproductlons on paper. On the other hand, lt is po~slble,
with thls system, to deslgn three-dimenslonal slide vlewers.
10 ~RIEF DESCRIPTION OF THE DRAWING
Flgs. 1, 2 and 3 explaln the ldeas on whlch the new
system 18 based, whlle Flgs. 4, 5 and 6 descrlbe the system
whlch i8 the obJect of ~hls lnventlon.
In thls flgures:
Flg. 1 shows the horizontnl parallax an~le E wlth
whlch an obJect P 18 seen at a dlstance 1 from a vlewer wlth
a dlstance b betweenrhis eyes.
Fig. 2 shows dlagrammatlcally a vlewer 0~ looklng at
20 an obJect P through the window AB.
, Flg. 3 shows dlagrammatlcally-m vlewers l~ 2 . . .
_ looklng at an obJect P through the wlndow AB.
Flg. 4 shows n cameras CCl, CC2...CCn separated from
each other by dlstance Kc, wlth thelr optlcal axes parallel.
Flg. 5 shows the arrangement of the proJectlon
obJectlves PF~, PF~...PF~ and of the optlcal screen of ver-
tlcal cyllnd0rs (1) of focal length f and transverse slze d.
The dlstance between two adJacent proJectlon obJectlves 19 K~
and the proJectlon dlstance 18 B.
Flg. 6 shows the optlcal system whlch 18 the obJect
of thls lnventlon, fro~ whlch there can be noted, ln lts
front part, the optlcal screen of vertlcal cyllnders (1) and
ln lts rear part the optlcal screen of horlzontal cyllnders
(2); ~e~ 18 the thlckness of the system; V 18 the vlewlng
35 angle; S 18 the horlzontal angle at whlch two pro~ectlon
obJectlve8 are 8een; f i8 the focal length Of the vertlcal
cyllnd ru; 8 lo th ~roJ-ctlon dlgtonc-; X~ 18 th- dl8tanc
` . ~
- 16 -
between two ad~acent pro~ectlon obJectlves; and PR" PR2...P~
i i8 the location of the optical centers of the proJe~tlon
obJective~.
S pETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Binocular vision 18 vlslon whlch mak~s lt posQible
to appreciate the dlstance away of obJects. Thls functlon 1-Q
obtalned by means of the angle through which the eyes turn.
10 Let llnes IlAl and DlA2 be the lines of vision to lnflnlty of
the left eye Il and the right eye Dl respectively. See Fig.
1 which diagrammatically ~howQ the blnocular observation of
an obJect P.
If the ~yes turn to look at ~n obJect P sltuated at
15 a dlstance 1 on the stralght llne IlAl, the rlght eye wlll do
so in ~n ongul~r qu~ntlty ~ glven by the equatlon
b
t~n E ~
-~~
ln whlch b 18 the dlstance between the eyes of the observer.
The angle E 18 called the angle of horlzontal
parallax. As the eyes are normally on a horlzontal llne,
systems whlch reproduce thls parallax are sufflclent and
25 satlsfactory. For thls reason, the taklng and reproductlon of
horlzontal parallax constltute the essentlal part of three-
-dlmenslon~l vlewing based on lmage angular dlfferentlatlon,
as wlll be explalned below.
Assume a vlawer ~0," looklng at an ob~ect P through a
30 wlndow of wldth A~ present ln a wall perpendlcular to the
llnes of vlslon to lnflnlty.
Flg. 2 shows the optlcal dlagram of a vlewer 0~ look-
lng at an obJect P through the wlndow AB.
Thls Flg. 2 shows thls vlewer l ln pl~ne vlew, wlth
35 hl~ rlght eye Dl ~nd hls left eys Il. The bundle of llght
ray8 whlch, comlng from the land8cape, pass through I~ ~homo-
centrlc on Il) 18 the one whlch 8erves to form the lmage of
the left eye. Slmllarly, the bundle of llght ray8 whlch p~ss
2Q~8~3
- 17 -
through Dl (homocentrlc on Dl) serves to form the image of
the rlght eye.
The perceptlon of three-dimensions i8 achieved when
the braln synthesizss the images from the left and right eyes
5 formsd by these two bundles of light ray~, whlch pa88 through
the non-colncidlng polnts Il and Dl.
The straiyht llne AB contained ln the trace of the
plane contalning the wlndow is consldered to be broken up
~nto the serles of lnflnitely close polnts Fl, F~... Fl...F~l,
10 Fn~
It is important to note that every ray belonging to
the homocentric beam Il, as well as every ray belonging to
the homocentric beam Dl, is contained ln the group of homo-
centric beams F~, Fz... Fl...Fnl, Fn~ provided that the
15 dlstance F~-F~ for any 1 18 sufficiently small.
If several viewers l, 2--- ~ looklng at the same
ob~ect through the front window AB and situated at dlfferent
- -- polnts are-consldered,~s~nce-it 18 not necessary to conslder
the vertlcal p~rall~x, all the p~lrs of eyes can be repre-
20 sented by thelr proJectlon on a common horlzontal plane. Flg.
3 shows the optlcal dlagram of m observers looking at an
obJect through the wlndow AB.
It 18 clear that, for obvlous topologlcal reasons,
every homocentrlc beam I~ or D~ 18 contalned ln the serles of
25 homocentrlc beams F~, F2... Fl....Fn~, Fn~ provided that the
dlstance Fl-F~l 18 sufflclently small.
Stated dlfferently:
~ The lmage formed, taklng as basls the homocentrlc
beams I~ or D~ whlch correspond to the left and rlght eyes of
30 the vlewer D~, and for any vlewer D~, can be syntheslzed by ";f
sultably selecting and composlng sections of the lmages
formed, taklng a8 b~sls the homocentrlc beams F~, F2...Fl...
Fn~ Fn~ provlded that the distance Fl-F~ 18 sufflclently
small~.
The demonstratlon contlnues to be valld whatever the
curve mny be whlch contalns the homoc~ntrlc be~ms Fl, F~
Fl...Fn~ as long as lt 18 contlnuous and passes through
., ... ~
. . : - .~ . ~ - .
2~8603
- 18 -
points A and B.
The mlnlmum separatlon necessary (or si~e of the
reproductlon elements) ln order not to see that the lmage is
formed of bands, and the necessary separation (or distance
5 between optlcal centers of obJectlves on the taklng of the
lmages) ln order to be able to reproduce the varlation of
parallax ln apparently contlnuous form are very dlfferent.
Experlence shows that the number of reproduction
el~ments requlred for proper reproductlon 18 much greater
10 than that necessary for three-dlmQnslonal taklng of lmages.
The process whlch ls the obJect of the present ln-
ventlon, llke shutterlng ln clnematography, makes lt pos-
slble, wlth a small number of lmages taken, to reproduce wlth
a large number of elements. In clnematography, the same lmage
15 18 repeated for several shutterlngs. In three-dlmenslonal
reproductlon, the s~me lmage wlll be repeated in various
reproductlon elements.
In thls way, fro~r~ac~-puint--of observstlon the same
lmage wlll be seen throu~ah ~ l~rge number of vertlcal re-
20 productlon elements. These reproductlon elements, whlch ~re
adJacent to each other, plll form a rectangle. Thls rectangle
wlll be dlfferent for each polnt of observatlon. The group of
rectangles correspondlng to all the lmages wlll form a slngle
and separate lmage for each positlon of vlewlng.
The proper vlewlng condltlons lmpo-~e practlcal
llmlts on the dlstance between the optlcal centers of the
contlguous obJectlves of the cameras upon photography ~nd the
dlstance between the optlcal centers of the ~dJacent
proJectlon obJectlves upon reproductlon.
The maxlmum dlstance between the optlcal centers of
the obJectlves of the cameras is lmposed, for each depth of
fleld, by the condltlon of contlnulty of the l~age upon the
reproduetlon. Thls condltlon 18 the s~ms for all three-
-dlmenslonal reproductlon systems of the prlor art and th~t
35 of the present lnventlon.
The dl8t~nce between the adJacent optlcal centers of
the proJectlon obJectlve8 when lmage angular dlfferentlatlon
.
. , . .. : - : ; ~ i: ...
20~03
is used is determlned by the ratio between the proJectlon
aperture and the vlewlng aperture.
The pro~ectlon aperture 18 the ratlo between the
dlstance between the optlcal centers of two adJacent pro-
5 Jectlon obJectiveY and the proJectlon dlstance.
The vlewlng aperture 18 the ratlo between the
dl~tance between the eye~ of a vlewer and the viewing
dlstance.
Our experience h~s shown that three-dlmensional
10 vlewing wlth lmage angular dlfferentlatlon 1~ acceptable even
for proJectlon aperture value~ three or four tlmes greater
than the viewlng values.
As has Just been ~hown, the mo~t obvlou~ form of
recordlng the horlzontal parallax 18 to have as many
15 recording obJectlves a~ polnts 1. Nevertheless, experlence
8~0WB that this number of recorded images can be much smaller
than the number of polnts 1.
n other words,-the dlstance between obJ~ctlves upon
the recordlng can be much greater than tne dlstance Fl-F
20 used ln the pr1or descrlptlon.
~ hus, the method of recordlng wlll consist of a
serles of recordlng ob~ectlve~ the optlcal centers of whlch
are located on a horlzontal llne separated from each other by
a dlstance Kc whlch wlll be a functlon of the recordlng depth
25 of fleld.
Flg. 4 shows thls procedure dlagrsmmstlcally. For
slmpllclty ln the dr~wlng lt has been assumed that each
obJectlve belongs to a separate camera and that the optlcal
sxes of these obJectlves are parallel to each other. In
30 general, several or all of the ob~ectlves can belong to a
slngle c~mera and the optlcal axes can be lncllne~.
In Flg. 4, CCl~ CC~, CX~... CC~ are the n chambers
wlth the optlcal centers of the obJectlves separated by
dlstance K¢ and locsted on the horlzontal llne ZZ'.
Upon proJectlon, the same number of proJectlon
obJectlve8 i8 u8ed a8 the number of camera obJeatlve8 whlch
were used upon the taklng of the lmage. Each of them wlll
;, . , -
. . ... ;.
, ~ . . - - .. . . . . ,.. .. :
- : , ~ . . . . ..
,' : . . .. : ! .
- 20 -
proJect an lmage onto a transparent optico-cylindr~cal
3creen.
Flg. 5 shows dlagrammatlcally the arrangement of the
proJection obJectlves PRl, PR2...PF~ separated from each other
5 by the dlstance KR proJectln~ on the optlco-cyllndrlcal
reproduotlon screen.
In this figure, for the sake of simplicity, each
obJectlve has been shown as belonglng to a single pro~ector
and to all the parallel optical axes. Actually, some or all
10 the ob~ectives may belong to a slngle proJector and the
optical axes may be inclined.
It is important to bear in mind that the angle form-
ed by the different films of images upon pro~ection muQt be
the same as that formed by the fllms of images upon the
15 recording. Otherwl~e, the plane surfaces of equal parallax
upon-the recording wlll be reproduced a~ curved surfaces upon
reproductlon, unles~ a compensatory lnclln~tlon 18 lntroduced
- - lnto the process of prlntlng the fll~s.
The dlstance B from the proJectlon obJectives to the
20 screen 18 lmposea by the focal length of the proJectlon
obJectlves snd th~ slze of the optlco-cyllndrlcal screen.
The optlco-cyllndrlcal sGreen (1) 18 formed of
cyllnders of a wldth d, which 18 sufflclently small not to be
perceived, experlence showing that for a healthy eye the
25 width d of the cyllnder must be smaller than the vlewlng
dlstance ln meters divlded by 3,500. The focal length f is
glven by:
d
- B --------
2X~
deduced by2~quatlng the aperture of each cyllnder G - d/f
wlth that, B ~ under-whlch three proJectlon obJectives are
seen. Actual~y, the aperture of the cylinder c~n be lncluded
35 betwe~n thls value, vlslon coverlng three proJection obJec-
tlves, and half thereof, vlslon coverlng two proJectlon
ob~ectlve8. In thi8 way, an lmperceptlble transltlon from one
image band tO the next 18 achleved 8ince the part of the
,
; .. .. , , ::,
., . . . : , . :, , . ... ,:. , . ,.. ~, .
. .. . .,. .- . ,
.. :: . :...... ..
.. . - ..... .. .. ~ . ~ . .
, . ` ; : : : . .:. ~ 1 ~ ,
,. .. ..
21 2 ~ AC 8 ~ Q 3
image from pro~ectlon obJective PRI 18 smoothly mixed wlth
that proJected by its nelghbors PR~ and PRl~l.
If the proJectlon obJectlves are separated from each
other, the parallax reproductlon decrease~ although the
5 three-dimenslonal vlew~ng angle lncreases, and vlce versa.
For a given number of proJectlon obJectlves, to each
variation of distance between them, if the ~ame pro~ection
dlstance is malntalned, there correspond~ a dlfferent cyl~n-
drlc~l screen, since the relationshlp between transverse slze
10 and focal length of the cyllnder must be made equal to the
ratlo between distance between proJectlon obJectives and
proJectlon dlstance.
If one only had avallable the optical screen of
vertical cylinders (1) described above, the vlew of the
15 lmages would be llmited to a llnear segment composed of as
many eub-segments 08 there ~re images or- proJectlon
obJeotlves. Thl8 llne~ segment 18 glven by the lnter-
~ectlon- of the pl~ne whlch passes through the ~roJection
obJectlves and the vlewlng polnt wlth the plane whlch
20 contalns the abovementloned transparent optlcal sheet of
vertlcal eyllnders.
In order for the vertlcal planes to be formed
adequately, another optlcal sheet of horlzontal cyllnders 18
used, of sufflclent aperture 80 that any vlewer, regardless
25 of hls height, 18 able to see the entire vertlcal component
of the lmage. In general, seml-elrcular cyllnders ean be
ehosen, slnee they have the maximum aperture, wlth a
transverse slze whlch, a8 ln the vertlcal case, must be small
~nough to be lmpereeptlble.
Thus, the optleal reproduetlon system wlll remain as
shown ln Flg. 6 and lt wlll be viewed by transpareney. In
thls Flg. 6, there ean be noted the vlewlng angle V, whloh 18
a function of the ratlo ~etween the dlstance of separatlon
between the flrst proJectlon obJective and the la8t pro-
35 Jectlon obJectlve and the proJectlon dlstance ~.
The aperture angle S of the vertlc~l cyllnders ean
be considered in the 8ame manner, lt being ~ function of the
.. . . . .
~. ''.'~ , ,' : . . .
- 22 -
ratio between the separatlon between two ad~acent proJection
obJectlves KR and the proJection distance B, which ratio i~
the same as that obtained between the transverse size of the
vertical cylinder d and its focal length f.
In thl~ flgure, the vlewlng of the vertlcal
component through the optical sheet of horizontal cylinders
can also be noted.
In order that the focal llne~ of the horlzontal and
vertlcal cyllnders colnclde ln the same plane, the thlcknes~
10 of the optlcal ~ystem must have the value:
n
e ~ ---- (r2-rl)
n-l
15 in which r2 and rl are the radii of the vertical and horizon-
tal cyllnders respectlvely and n i~ the index of refraction
of the substance of whlch the optlcal system 1~ made.
As further embodiment, the same bases as have served
to create a three-dlmenslonal rep,roductlon system with varl-
20 atlon of the horlzontal parallax are valld for the deslgn ofan n lnte~ral reproduction svstem" whlch reproduces the hor-
, lzontal and vertlcal parallax slmultaneously.
In thls case the proJection obJectives will be
~arranged on a rectangle.
25For the deslgn of the vertical cylinders (1) the
same developments as set forth above apply.
The horizontal cylinders (2) are desi~ned ln a
manner slmllar to the deslgn of the vertlcal cyllnders. The
ratlo of the transverse slze of the cyllnder to lts focal
30 length 18 at least equal to the ratlo b~tween the dlstance
between three vertlcal proJectlon obJectlves and the proJec-
tlon dlstance.
For the focal length of the horlzontal cyllnders
there ~ust be satlsfled the egyatlon:
dN B
2K,,V
~n which dN ~ the transver8e slze of the horlzontal cyllnder
~ - the proJectlon dlstance
!
. . . -.. ' .. . .. .
.. , . ... - ~ ,
. ~ ~ . . .
'' `~: : ' '. ' '
2~186~3
- 23 -
X~ ~ the dlstance between adJacent vertlcal proJec-
tion obJectlves.
For the thlckness e, the formula given above ln
connectlon wlth the horizontal parallax reproduction system
5 remains valld.
The above mathematlcal restrlctlons only condltion
the transverse dlmenslons and the aperture of the optlcal
elements.
The rest of the optlcal characterlstlcs, such as
10 whether lenses or mlrrors, optically convergent or divergent,
can be selected arbitrarlly.
.
35
. ~
, : ,: , . -
,
:: - :. , . ,, , : , :
