Training of Bioptical Vision

Bioptical Art - Liviu Iliescu

To understand more clearly the results of the experiments largely covered by "Bioptical art", the training of one’s vision is a must.

As is known, binocular vision resulting from the use of both eyes–is the main factor in perceiving depth and distance in a space ranging up to some 300 meters. Moreover, binocular vision allows global perception in an angle of almost 180o (looking straight ahead).

The term bioptical vision, introduced by me, refers to a wider range of visual perceptions, also including normal ones, as will be seen further on. Vision is actually a binocular one, but different stimuli for either eye are added to the normal ones, evoked in stereoscopy, holography or in the virtual reality.

In certain cases, one can skip over theoretical descriptions, which may not seem explicit enough at first. After studying the test cards, theory may be resumed.

Sharp vision at different distances is due to the modification of the curvature of the crystalline lens, hence of the focal distance of the eye, resulting in visual accommodation. On the other hand, the angle between the axes of the eyes, the so-called convergence angle, hence eye convergence should also be modified.

Figure 1 schematically illustrates the modification of conver- gence with the distance at which one gazes (angles V and V'). Figure 1 also shows perspective elements which, as is known, may also be grasped by one eye alone. There is a natural coordination between accommodation and convergence.

Test-cards present pairs of drawings, one for either eye. They should be looked at from a distance of 30-40 cm. Another coordination between accommodation and convergence is required, different from the natural one, which makes necessary a certain training.

This new coordination is spontaneously performed by some persons and not so easily by others. In a small number of cases, coordination cannot be achieved, especially by aged persons who require eyeglasses for reading. Slight training is necessary, the same as in gymnastics, since the muscles which act on the crystalline lens and on the eye ball exert an effort. Training is, of course, beneficial. When looking at bioptical pictures placed at several meters’ distance, the effort is much lower. Difficulties in bioptical vision are similar with those met in stereoscopy, where normal coordination between accommodation and convergence should also be modified.

Actually, the test-cards3 presented are elements used in bioptical compositions. The psychophysical response of different subjects submitted to the tests pointed to the conclusion that some persons are gifted and some are even super-gifted (similarly to people with a so-called "ear for music").

The psychophysical reponse depends to a smaller extent on the cultural level of the subjects, but interpretations do.

To get stereoscopic images from drawings or photographs, one uses stereoscopes or some types of vision.

Bioptical effects are generally associated to arrangement in space. In order to train one’s vision on the pairs of drawings and reproductions existing in this book, I recommend the use of some techniques, considered as more appropriate, and denoted by M.


To separate the image formed in one eye from that formed in the other, a cardboard diaphragm is used. Its size is of about 20 × 30 cm and it should be held with the larger side on the vertical, as in figure 2a. The position of the diaphragm is right, when each eye looks at only one of the rectangular shapes (Fig. 2b) but binocular vision results in a single rectangular shape, where there first appear elements standing out in space.


First, one looks with the naked eye (without any diaphragm) at an object placed at a greater distance (at least several meters). Then, as one of the test-cards is placed at a relatively small distance from the eyes (7-10 cm), three dim rectangular shapes are seen.

The book is removed at a greater distance from the eyes, up to 25-30 cm, and the rectangle in the middle of the image is gazed at all the time. When details are seen clearly, observation is delayed for at least one minute, and then spatial effects and other bioptical effects appear. Figure 3a shows the position of the three rectangles, P being the main image and S the secondary images. If necessary, reading spectacles may be used, even if the object seen seems unclear when gazing at a distance, because it is essential that image P in the book should be the most clear.


As in the case of M2, the test-card is looked at with the naked eye but this time the book is placed at a greater distance from the eyes (50-80 cm).

A pencil is held in hand closer to the eyes (25-30 cm) and its tip is stared at, so that, behind it, the two rectangles of the test-card are seen duplicated5. By getting closer to or farther from the book, the image of three rectangles will be seen, the same as in M2.

Bioptical effects appear in the middle rectangle here as well. The pencil is removed and one looks with the naked eye, maintaining the axes of the eyes crossed. Details that stand out in space are seen in depth in reverse order to those of M2.

M2 is more difficult to use and requires somewhat higher con- centration.


Bioptical effects are perceived when looking with one naked eye, while the other is looking through an optical device, consisting of two mirrors mounted periscope-wise (figure 4). One of the mirrors of this device may be adjusted so that image pairs could be looked at in bioptical correspondence, from small distances (25...50) up to tens of meters.

The periscope should be placed horizontally to look at test-cards (figures and details of reproductions, denoted by DR1, DR2..., etc.). For reproductions R1, R2... where image pairs are placed on the vertical, the periscope should be placed on a vertical. The device may be manufactured by a craftsman or, if it arouses greater interest, it may be produced serially. I arranged pairs on a vertical, when creating bioptical compositions, for psychophysical reasons, in order to get a more accurate fusion. I also had in mind the possible obtainment of perspective effects on a vertical.



M1 and M2 shall be applied first.

M3 should be practised–though it seems more difficult for some subjects .since it provides a reverse order of depths, as compared to M1 and M2.

All test-cards are to be studied, including those denoted byDR1, DR2... Those that do not yield a fused image from the beginning, should be skipped over. They should be studied again later on.6

The whole set of test-cards should be studied several times. Bioptical vision is formed step by step and the following effects are to be observed.

When noticing up-down duplicated images, the book shall be slightly rotated.

Some subjects will not be able to see fused images in all test-cards. Double images on the sides will persist. A solution might be the increasing of the distance of vision, possibly with 5-10 cm.

It is known that one eye has a leading role; bioptical effects shall therefore be noticed with the book rotated by 180o (writing upside down).

Test-cards will be gazed at for some minutes in a normal way, then the techniques described above will be applied, then the normal way again, creating psychophysical cycles.

A gradual increase of depths with time shall be noticed, pointing to a dynamics of the depth of the virtual space.



Fig.5–Ovals are seen in space, recalling the shape of a spring.

Fig.6–A pyramid with apex up is seen using M1 or M2. With M3, the pyramid is seen with apex down.

Fig.7–With M1 or M2, the small horizontal side appears downwards. With M3 the effect is reverted.

Fig.8–A reclining prismatic form.

Fig.9–Form spatially opposed to that of figure 8. It has a vertical position and is structured otherwise.

Fig.10 -With7 M1 or M2, the normal perspective is contra- dicted; with M3, it is confirmed as the smaller horizontal side appears more remote.

Fig.11–The obviously plane form8 acquires a spatial transformation, without using the known perspective effects. The transition from plane to a space devoid of perspective elements is called by us "transition to the hyperspace" or, simply, hyperspace.

Fig.12–Supplementary forms, noticeable both with M1 or M2, and with M3. A circle inscribed in a square appears. The sides of the square are not stable (there occur displacements among the constituent sides, on one hand, and as compared to the circle, on the other hand).

Fig.13–There occur disturbances in the binocular conver- gence; the triangle is displaced as to the circle. Kinetic effects occur in the composition but this possibility should be carefully considered, to avoid the appearance of duplications, of unpleasant disharmonies.

Fig.14–When looking with M1 or M3 (instabilities occur in the case of M2), black is superposed on white, resulting in a silvery hue.9 In order to coordinate eye convergence in the case of vision with M2 or M3, the two small triangles above the figure shall be looked at till they seem to be three.

Fig.15–A succession of triangles in colour perspective (with M1 or M2), namely: the big red triangle in front and the blue one at a distance (as it appears in nature, in colour perspective). With M3, the linear and the colour perspective are reverted, which justifies the term "antispace" (the same as in figures 8, 9 and 10, where M3 results in reverted linear perspective).

Fig.16–Opposite effects as compared to figure 15.

Fig.17 and Fig.18–Effects of colour fusion and of so-called "retinal rivalry".10 It occurs when observing for a longer period, in sequences of some 5 seconds, now a colour, now another one, now a mixture. One can look at the book rotated with 180o, taking into account the fact that one of the eyes has a leading role.

Fig.19–Areas of the mixt bioptical picture (model DR11).

Fig.20–Reproductions from the author’s patent RO 67678. The drawing looked at with M1 or M2 seems a pyramid with apex down; with M3 the apex is up (to the eye).

Fig.21–With M2, one gets either three circles in the upper part, or three in the lower part (reference circles). When looking at the centre, the circles seem to gradually detach in the space: some in front of the plane of the page, the others behind it. Farther circles seem bigger (though they are equal in size), nearer ones look smaller (space illusion which I never found recorded).

With M3 the fusion is more lax; four reference circles may appear instead of three. By training, one succeeds in seeing three circles, then mid circles are gazed at. Circles are seen in reverse position as compared to M2 gazing.

Fig.22–Same procedure as in Fig. 21. There occurs a psycho- physical mixture of the colours (fluctuating, nacreous, phantom-like hues, detached from the background), especially when gazing with M3.


These details are denoted by DR1, DR2, DR3..., corresponding to reproductions R1, R2, R3. In order to train bioptical vision M1, M2 or M3 are used. The same effects are noticed in general, yet this time pictorial forms are complex.

DR1 and DR2. Details show hyperrealistic effects (beside the known ones), as they appear in nature, in three dimensions. These effects can be reproduced only bioptically. Some of the glitters of objects in nature are perceived either by one eye or by the other. It is obvious that the hyperrealists’ desire of surpassing reality cannot be fulfilled by the usual technique of painting which presents the same elements for both eyes. Moreover, bioptical methods give birth to a stronger impression of transparency (DR2), thanks to the spatial disposition of the represented forms. They also rule out flaws that are not common, an effect which I call "retinal cooperation" (as opposed to retinal rivalry).

DR3, DR4, DR5 and DR7. Test-cards have a perspective orientation, when looked at with M1 or M2. Vision with M3 results in antispace effects which can be perceived only after longer training. The psychic accommodation to reverting elements disposition in this new type of space is less easy, especially because of form contradiction, with vanishing lines contrary to the natural one. These test-cards include details from illustrations R3, R4, R5 and R7, photographs of some pictures I made, which represent a kind of translation into abstract modalities of some imaginary landscapes.

–DR6 and DR9. A greater stability of colour fusion may be noticed, due to the presence of yellow, crossing the colour fields in correspondence.

–DR8. The oval shows fluctuating nacreous hues as well as spatially disposed elements, such as the spiral that surrounds the oval.

–DR10a. The test-card should be looked at with M1, M2 or M3, noticing the transition from a flat form of the surface (surface-space) to the hyperspace. Actually, perception is still spatial, but the transition from plane to space with change of form has been called by me–as already mentioned–hyperspace.

–DR10b and DR10c. Test-cards were obtained by cutting out details from illustration R10. These were chosen so as to give rise to the so-called retinal rivalry described by Helmholtz. The term is suggestive, though it is obvious that the effect is psychophysical.

–DR11 represents the model of a mixed bioptical composition, made up of areas represented in figure 19. The main bioptical com- position is painted in area A (for instance that from reproduction R3).

This composition should be looked at with M4.

In the neighbouring areas B, C, D and E, there appear bioptical pairs B-C and D-E, which repeat the forms of A (the case of the model) or further develop the main theme. These pairs may be fused with the naked eye when painting a picture, using M3 (for instance, the base RZ of about 1 meter is looked at at a distance of 4-8 meters, depending on the genetic endowment or on the training of the viewer).

In model DR11, one may notice pairs B-C or D-E, by using M1 or M2. The mixed bioptical composition may be designed so that the elements of the rectangle D be rigorously the same as those of the main composition A, placed in the dotted area D (corresponding to D). Thus, pair D-D, looked at in the model by means of M1 or M2, and on a larger scale by means of M3 (in the case of a painting), evoke sensations of increased colour brightness as well as the impression of looking through a small glass window.


3 Test-cards and compositions have been worked out by me following personal studies. My methods and formulas have been patented (Patent RO no 67678 from 1974).

4 M1, M2 and M3 have been known for long. "Science et Vie", no 927 of December 1994 describes M2 and M3. Useful instructions and explanations about training stereoscopic viewing by M2 are supplied by Marc Grossman and Rachel Cooper in Magic Eye, How to See 3D (Andrews and McMeel, Kansas City, 1995). A.I. Tudorovskii, Teorija opticheskikh priborov, Izd. Akademii Nauk SSSR, Moscow, vol. II, 1952, p. 54. Figure 282 shows a series of four pairs of circular spots in stereoscopic correspondence. Viewed by means of M1…M4, they seem to acquire three dimensions.

5 Image formation is plotted in figure 3b, for people better acquainted with geometric figures. The retina and the crystalline lens stand for the eye. The virtual image of the middle rectangle P is formed close to the tip of the pencil, corresponding to the images on the retinas of the two eyes A'1 and A'2. The pair of the test rectangles A1 and A2 is formed in A ''1 and A''2 and there result the two secondary images S. The modification of distance MN and the focusing of gaze on the tip of the pencil results in a fused image P, by the superposition of images A'1 and A'2.

6 Bioptical vision should be trained on test-cards alone, not necessarily on reproductions R1, R2.

7 Figures 8, 9 and 10, first observed with M1, M2 or M3 and then normally looked at, seem ambiguous, with spatial reversals, as in the case of the well-known optical illusion of the cube corner, which looks now convex, now concave. The ambiguous illusion of the cube corner was known in the Antiquity, as proved by a photograph of a mosaic floor from the 2nd century, in Antioch, published by E.H. Gombrich in "Art and Illusion". V. Vasarely has created several compositions in modern times, using the illusion of the cube corner. Bioptical techniques rule out such ambiguities, which still appear when looking with the naked eye, contributing to the so-called residual impressions.

8 René Berger uses the terms "surface-space" and space-surface (Découverte de la peinture, vol. 2). He takes over some aspects of post-impressionist painting currents from art critiques: space in compositions, relation between linear and colour perspective, vanishing lines and colour dosage. He describes the technique used by cubism to represent shapes in a plane and introduces the notion "surface-space", considering that on the [plane-our note] surface of a picture, depths (perspective effects) are perceived. He then describes the reduction to the [plane-our note] surface of a picture, using even contradictions between representations with tendencies to depths and colour perspectives. This transformation is called by him space [plane-our note] surface. In addition to Berger's findings, I have experimented a third possibility - to create a different space, amplified as compared to the geometrical datum. I call it hyperspace.

9 Effect described by the German physicist Hermann von Helmholtz (1821-1894).

10 Term created by Hermann von Helmholtz.