Seeing in depth is such a natural and automatic part of human experience that its basis has remained largely unconscious, taken for granted. Indeed, it took some of the most inventive minds of the Italian Renaissance to overcome the automatic tendency of seeing objects in depth and at their true size. Only after an intense effort did they realize that to paint depth required something much different than painting what was seen, requiring instead an entirely new type of geometry, the geometry of perspective. So it seems that the geometrical study of depth perception has had a very long and interesting history, becoming a highly developed discipline long before the rise of modern science.

This paper will be based on a Friday Evening Discourse which I presented to the Royal Institution in London, in January 1973. It is an attempt to relate how we see the world in three dimensions with how science infers the richness of physical reality from readings from instruments. We shall try to explain same phenomena of perception - including some perceptual errors or illusions - by comparing perception with haw science describes the world in terms of hypotheses. Perceptions will themselves be regarded as predictive hypotheses, set up by brain mechanisms. Like any other hypotheses, perceptions may be dramatically incorrect, and are perhaps seldom if ever completely adequate.

In the last decade computers made possible the generation of static random-dot stereograms without monocular depth and familiarity cues but with controlled binocular disparities. In the '70s advances in computer technology led to the development of on-line generated dynamic random-dot stereograms. These novel methods brought a better understanding of binocular depth perception and its deficiencies. They led to improved quality inspection of LSI components by (a): the proper alignment of stereomicroscopes and (b): the proper screening of stereodeficient inspectors (about 15% of the population). Thus computers led to some new stimuli that gave unexpected insights into the classical field of binocular vision, which in turn led to an improved quality inspection methodology that helped build cheaper computers.

For the design of three-dimensional displays of information obtained in image processing systems it is important to know the spatial resolution of human stereoscopic vision. This knowledge allows presentation of the 3-D information in the format optimal for image visibility, without wasting processing bandwidth on unusable information. (In just such a way, the poor spatial resolution of human color vision was exploited to save transmission bandwidth for color television.) The series of studies reported here establish that the spatial resolution of stereoscopic vision is far poorer than monocular pattern resolution.

The human visual system generates many dimensions of orthogonality and utilizes the output of eight orthogonal systems to generate hypersensitivity, color and depth. Each system can be regarded as a sense in itself and the outputs of all or any can be placed in apposition to give a multiply populated class of conjoint information. Each system has two kinds of independence: (1) each acts alone in the acquisition, utilization and rendition of that array of information for which its own mechanisms are suigeneris; (2) each has an independence manifested only as a consequence of having its informational output placed in apposition to the output of one or many of the other systems.

The real time Computer Graphic system is a powerful tool to enhance visualization of three-dimensional information. This paper introduces the basic concepts of how digital models are created and how a digital image generator processes the model data base to produce an interactive, real time display of the model. Examples of applications are described and photographs of actual computer generated imagery are included to show the realism obtainable from state-of-the-art systems.

A true three-dimensional display based upon the sequential excitation of fluorescence at predetermined controlled locations within a display volume is described. The system equation is developed and used to show that, with the use of appropriate pulsed lasers for excitation sources, a variety of useful displays can be built -Itilizing IC1 or possibly mercury vapor as the display medium.

A hologram generates a continuum of unique rays by means of wavefront reconstruction; but the eye is insensitive to phase, as such. Therefore, a holographic visual effect can be obtained by direct reconstruction of ray directions. This is the principle used in the Parallactiscope, a device which presents real-time CRT images having the holographic properties of autostereopsis and wide-angle (±45°) movement parallax. Viewer aids are not required, and multiple viewers are simultaneously accommodated; each viewer receiving a different pair of retinal images corresponding to his position. A working model of the Parallactiscope having a three-inch display has been built and demonstrated. A 14-inch model is now under construction.

A technique has been designed, developed, and implemented on a semi-routine basis, whereby the major hindrance of Lippmann's elegant concept of integral photography is circumvented without trade-offs, owing chiefly to a novel method of conversion from pseudo-scopic negative to orthoscopic positive, involving a single integral network, without recourse to additional conventional or holographic optics. The Integram* system retains the originally intended full parallax, with very wide acceptance and viewing solid angles; only ordinary incoherent natural or artificial light is used at all stages. The three-dimensional, autostereoscopic, orthoscopic and orthostereoscopic summation image is generated at a 1/1 scale, in full natural colors, and is viewed by transmitted or ambient illumination; it may also be enlarged or reduced without distortions. Angles of over 80° have been achieved in the current 11 x 14 inch samples, where the refractive index of the polyester resin spherilenticulated viewing screens is 1.56. The background, the optics, the technology, proposed refinements, variations and applications of the Integram system are discussed.

Three studies were conducted to evaluate operator performance with conventional and stereo display systems. The first two studies involved perceptual judgment tasks (a modified Howard-Dolman depth discrimination test and a test of stereopsis, using random dot Julesz patterns), while the third employed a perceptual-motor task requiring end-effector positioning and closure. This third task was designed to approximate the major components of undersea object recovery missions. In studies one and two, two methods of displaying stereo information (Fresnel, Field Sequential) were compared. The results of study one indicate that both of these display systems provide adequate information to enhance performance over that given with a conventional monocular display. Study two indicates that thresholds of stereo viewing are comparable using the Fresnel system and the Field Sequential system. The data indicate no difference in thresholds over that obtained directly without viewer aids. In study three a conventional display was compared with the Field Sequential system used in studies one and two. The results indicate that the use of stereo cues reduces both response latency and errors significantly. An analysis of performance changes over repeated testing sessions indicates significant improvement on both variables. These effects, however, are non-differential across display systems, and are probably related to the acquisition of manipulator-specific motorskill learning.

An interactive computerized video stereophotogrammetry system has been developed to quantify the topography recorded by the Mars Viking 1975 lander cameras. The system has supported all surface sample acquisitions and enabled the mapping of the two landing sites out to the remote limits of ranging capability. Returned imaging data is loaded into a time-shared computer system, driven to a pair of high resolution video monitors, and viewed through a scanning stereoscope. A three-space mark, characterized by a pair of coupled dot cursors on the video monitors is moved under trackball control via the computer. The mark may be landed on features of interest and the three-space coordinates established. The mark may be constrained in any desired manner, e.g., to a vertical or horizontal plane in the lander/Martian three-space. The photogrammetrist moves the mark along his perception of the intersection of the surface of constraint with the Martian relief. As the mark is moved, its track may be recorded on the video displays. The three space path is stored in the computer. Data products include vertical profile plots, contour maps, stereo map representations, and photoproducts of the scene with overlayed profiles and contours. The monitors are slaved for parallel viewing. The system is fast, accurate, and versatile.

Projection-type holography is an interesting three-dimensional imaging technique because in this method an autostereoscopic, wide-visual-field/wide-viewing-zone 3-D spatial image can be reconstructed from a tiny piece of hologram. In the former half of this review paper, various versions of the projection-type holography are described in chronological order. In the latter half, synthesis of an intermediate-viewing-angle image from binocular ones is discussed; such a technique is necessary for producing a satisfactory auto-stereoscopic projection-type image form a few element pictures of the object taken from different viewing directions.

Optical depth information, or longitudinal resolution, can be obtained either by using the transversal resolution of two spatially separated observation systems or by using one single system that is sensitive to the traveling time of a signal. Optical transversal information is obtained by comparing the traveling time of signals arriving at two spatially separated points of observation. Thus every optical method to obtain optical three-dimensional information is based on the comparison of time delays caused by the pathlengths that the information carrying signals have to travel. The holodiagram is a bi-polar diagram made to simplify the comparison of distances. It can therefore be used as one unifying method that assists in explaining the possibilities of every method to obtain three-dimensional information.

Several recording and wave reconstructio aspects are discussed through the presentation of different experiments of large scale holographic display. In the described works, the size of objects and of reconstructed images varies around 1 or 2 meters and the holographic plates themselves attained 1 x 1.50 meter. These off-axis holograms are both transmission and/or projection types. Images were generally displayed with laserlight in order to give the best possible viewing conditions. Theroetical and experimental require ments are discussed for the recording as well as for the reconstruction case. Technical compromises involved in the different experiments are mentioned. The presentation of different results shows the impact that 3-D holographic display reaches in different domains, including advertising and artistic 3-D objects copying.

Experiences from investigations in factory environments using holographic interferometry, where special methods must be used to be able to record a hologram of e.g. a big machine-tool. These methods can be considered when making large-scale reflection and transmission holograms for display purposes. It is shown how from a master transmission hologram, either a reflection or a transmission hologram copy can be made and reconstructed using white light. No large-size lenses are used, needed is only long distance illumination from a laser with just one spatial filter. The setup is as simple as possible and arranged directly on a concrete basement floor.

This paper is abstracted from a much longer paper read at the Seminar on 3D Film and Television, at Concordia University, Montreal, Canada, 1-2 April 1977. The complete version, which will be published in those Proceedings next year, includes a description of the "Stereo-70" system and a thorough mathematical analysis of the optical properties of high-efficiency holograms, showing that they are indeed useful for 3D projections. The final sections, included here, describe the underlying concepts and optical principles of the holographic cinematography system. They have been slightly edited for clarity. The editor is indebted to Prof. J.D. Tierney, of Concordia University, for assistance in compiling the manuscript. (S.A. Benton, editor).

Techniques for producing and receiving holograms in light of reduced coherence are described. Both coherent and incoherent methods are considered.

Holographic stereography is a technique for synthesizing a holographic three-dimensional display from a set of specially prepared two-dimensional pictures. Applications for this technique is that already have been investigated include medical and industrial diagnosis (in conjunction with X-ray and ultrasound imagery), 3-D computer display and fabrication of educational aids. With such demanding fields, a good understanding of the imaging properties of holographic stereograms is a prerequisite. We present an analysis of holographic stereogram imagery, show that the synthesis process may cause both degradation in image resolution and two types of distortions. These distortions are analyzed in detail, including experimental examples. Also methods for minimizing image degradations are suggested.

The suitability of holography as a method for recording and reproducing visual displays of terrain is examined in a tutorial, non-mathematical manner. The paper is based chiefly on a literature search combined with some original work by the author. Consideration of requirements for 3-D displays in general and the particular problem of making holograms of terrain is followed by a detailed discussion of the different types of hologram and how they may be used to make terrain displays with different characteristics. Emphasis is on the 2-photograph stereoscopic hologram which is called a "holographic stereomodel". Techniques to enhance certain characteristics of holographic displays such as color rendition and efficient use of illumination are examined and possible uses of holography in tasks related to map making are suggested. A discussion of the advantages and disadvantages of selected types of holograms for terrain display is included.

In biostereometrics, which is a modern approach to the study of biological form and function based on three- and, often, four-dimensional measurement of living organisms and their constituent parts, three-dimensional displays already serve many useful functions. These can be classified into two main categories, where the three-dimensional display is used: (1) as a substitute for the object itself or (2) to highlight spatial or spatio-temporal features of particular interest. In the former category, the ability to "freeze" the form of a living organism and to analyze the resulting photo-optical analog ad infinitum without fear of object movement is a major advantage over conventional direct measurement methods. Applications which fall into the second category are particularly valuable for conceptual and educational purposes. Such applications are expected to grow as clinicians, biomedical scientists, biologists and others become more familiar with the potentials of biostereometrics and suitable graphic display capabilities become more widely available.

A simple device for producing an autostereoscopic visual computer display is described. A true three-dimensional image is generated which may be viewed from a wide variety of observer positions. The device consists of a rotating mirror which reflects the face of a CRT display into a volume of space.

From sections of real or hypothetical objects recorded on a film strip, the Synthalyzer instrument generates, on the periodically and uniformly rising surface of a rotating drum, a dynamic three-dimensional synthesis akin to a solid roentgenogram and viewable through 360° azimuth and 80° elevation. In spite of the transparent character of this reconstruction, the internal morphology of dense complex specimens is, understandably, obscured by peripheral detail. To obviate such inherent but hardly acceltable limitation, optical and electronic controls have been incorporated; they provide means for redissecting the synthesis in any planes normal to the spatially frozen projections of the original sections; for removing a portion of the synthesis on one side of the plane of interest; and for dimming the portion on the other side to enhance the plane under investigation, also to serve as an orientation reference. Thus all of the structural details and relations existing within the synthesis can be analyzed. A working prototype has been successfully built and is discussed together with an ancillary device for large audience dissemination of results of the synthalysis.

TOMAX® is a new type of autostereoscopic display device that has been developed to provide a true 3-D image which does not require special glasses. The system can accept any form of tomographic data that has a sequential format, and provides a series of 2-D pictures in their true spacial relationship. The net effect is a real 3-D image, in that each plane is inherently transparent. By changing the viewers position vis a vis the display, one can observe a parallax containing image. The display system includes a micro-computer, solid state memory, video-digitizer, floppy disk and a varifocal mirror. Various clinical studies have been performed and it appears that autostereoscopic viewing can facilitate image diagnosis.

Quantitative determination of red blood cell surface and volume is desired for cell classification and experimental verification of theoretical models of the membrane properties of normal human erythrocytes. A direct technique has been developed for measuring profiles at appropriate places on the cell. The method makes use of the electron beam of a scanning electron microscope to mark the cell surface with reference lines which can then be viewed at arbitrary angles to provide unequivocal measurements of the height of the sample. The method also provides a reference to test the linear system properties of optical microscopes.

The role of eye-movements in stereoscopic perception of space, other than that of bi-foveal fixation of the object of regard, is discussed. First, it is shown that global fusion and bi-foveal fixation are demonstrably different responses; in pursuit of global fusion, the angle of convergence may be so changing as to shift the intersection of the two visual axes towards a point in space where no object is to be found. Second, a highly accurate change of vergence in tracking an object moving in depth does not, in itself, produce perception of object motion; a certain critical change in vergence must be required, to initiate perceived motion. This "program newness", expressed in terms of a fast retinal image displacement producing a step in retinal disparity, equals, at least, 2 min arc per 0.1 sec of vergence reaction time. A hypothesis is advanced, in the general framework of prediction-oriented theories of perception, to interpret vergence eye-movements as also a means of neutralization of the input "unwanted" by the visual system.

A very high resolution three-dimensional television system has been designed and fabricated for use in the remote manipulation of radioactive materials. The system includes a Stereo TV Camera and a Stereoscopic Display/Control Console, which provides a "live" display, or the picture can be video-taped for viewing at a later time. The Console is for individual viewing, group viewing is by means of projection. The Stereo TV Camera housing contains: a Stereo-Captor (beam splitter), zoom lens, TV camera head, built-in lights, and a pan and tilt. The Display/Control Console consists of: a TV monitor, Stereo-Hood (viewer), controls for camera, stereo, zoom lens, pan and tilt, illumination, audio, and a switcher. The stereo controls adjust convergence and permit a change from 2-D to 3-D. An audio system is included. The television system operates at 1023 TV scan lines, 32 MHz, thus providing a photographic quality stereoscopic image, which can be zoomed in 3-D. A very high resolution Stereoscopic Projection Display is available for group viewing. This consists of a cabinet containing: a very high resolution television monitor, polarized stereo optics, a non-depolarizing back projection screen; and 3-D polarized glasses for each viewer.