(3) binoculars. All three systems are Stereoscopic visual displays: Principles, improved by providing a viewing hood to position the O's head in front of the device to reduce extraneous viewing devices, alignment procedures* stimulation. The viewing hood and prisms (or ) usually are GEORGE SPERLINGt attached to one end of a sturdy, Bell Telephone Laboratories, Murray Hill, New Jersey 07974 lightweight frame. The other end of and the frame should be quickly and New York University, New York, New York 10003 conveniently attachable to the display device itself in order to provide rapid The principle of binocular (stereoscopic) depth perception is that the visual changeovers between normal and system interprets the slight differences between the views seen by the two eyes stereoscopic viewing of the visual as depth cues. In computer-generated displays, two slightly different images are display. The binoculars system also produced on the left and right halves of the display surface and viewed by a prism, , or binoculars system that delivers the appropriate image to each eye. The prism system is the simplest, the mirror system gives the best optical quality, and the binoculars system is useful for producing large apparent images from small display surfaces. All three systems can be adapted for group viewing and all require careful alignment (null adjustment of accommodative distance and vergence distance). Objective and subjective methods of alignment are described. (0)

THE PRINCIPLE OF STEREOSCOPIC limitations of image quality and of DEPTH PERCEPTION information content.1 In normal vision, the two eyes receive slightly different views of the VIEWING DEVICES world, and the differences between the I shall be concerned here not with views are interpreted by the visual the psychological problem of how to system as visual depth. The name given compose a stereogram in order to to the depth perception that arises provide the desired illusions of depth,2 from differences between the images but rather with the simple technical viewed by the eyes is stereoscopic problem of how to use a cathode (b) depth perception; the two oscilloscope (CRO) display system corresponding images are called a economically and efficiently to stereo pair (of images) or a stereogram, provide two different views. Basically, L R when they are produced artificially. there are only two methods of The principle of stereoscopic depth producing the two images of the perception is illustrated in Fig. 1. stereogram: (1) to use two different In normal vision there are many CROs, one for each image, and (2) to other important cues to depth, such as use two different subareas of a single those provided by the change in view CRO display surface (e.g., the left and produced by a head movement, the right halves), and to view each subarea interposition of objects, perspective separately with each eye. transformations, sizes of known The method of two CROs is more objects, distance haze, vergence of the expensive and has inherent in it the (c) eyes, etc. Of these, only the depth cue problem of adjusting the two CROs to produced by head movements is not be electronically equivalent. The readily simulated by a visual display two-CRO solution is useful mainly system which presents an appropriate when it is necessary to separate the stereogram to the two eyes. In fact, stereogram members (not readily Fig. 1. The principle of stereoscopic most stereoscopic viewing devices possible on a single display surface depth perception. (a) Top view of an require the head to remain still; even because the two display areas are o viewing two surfaces (8" 8, ). The when they do not, head movements constrained to be adjacent to each two eyes see the nearer surface against are relatively easy to measure. As this other) and when independent different parts of the background, as head-movement information readily hardware control of such parameters indicated. The displacement (between can be incorporated into a as x- and y-axis magnification is the two views) of the foreground stereoscopic display system, the desired. For example, to control relative to the background is the simulation of normal binocular vision independently the stimulus area in a stereoscopic depth cue. (b) The by a computer display system large annular neighborhood of each stereogram, i.e., the views seen by the introduces virtually no limitations that computer-generated display, it is left 'and right eye. The stereo pair of are not already inherent in convenient to separate the stereogram images may, of course, be produced monocularly viewed displays, i.e., the members. In principle, however, the either on a visual display surface or by problems of viewing two CROs are the viewing a natural object. *Originally presented at the North same as those in viewing two subareas (c) Perspective drawing of the illusion Atlantic Treaty Organization, Advanced of one CRO, and the examples will of depth that results from viewing the Studies Institute on: On-Line Computing stereogram in (b). Note that the for Behavioral Science, Department of refer only to the latter case. Psychology. Sheffield. England, July 19. The three main methods of viewing projection of 8, against 8, in (b) 1970. subareas of a display surface separately exaggerates its size; when S, is seen in tRequests for reprints should be sent to: with each eye are illustrated in Fig. 2; stereoscopic depth (c), the apparent G. Sperling, Room 20518. Bell Telephone Laboratories, Murray Hill, New Jersey they are (1) a prism viewing system, size of 8, approximates its actual size 07974. (2) a mirror viewing system, and (a) rather than its projected size (b).

154 Behav, Res. Meth. & Instru., 1971, Vol. 3 (3) "smaller" stereogram than a near viewer, but he perceives differently shaped objects because perceived eRO depth relations do not vary linearly with viewing distance. Whereas the shape of a two-dimensional object remains invariant with changes in viewing distance, the three-dimensional shape of an object defined by a stereogram changes as the viewing distance changes. In producing M stereograms, the absolute retinal size at which they will be viewed must be taken into account, and the viewer must also consider this.

Mirror Method (Wheatstone, 1838) The advantages of the mirror method are: it is virtually free from optical distortion when good quality front-surface mirrors are used; it is extremely easy to adjust by rotating (0) (b) (e) the mirrors slightly; and it allows Fig. 2. Three stereoscopic viewing systems: (a) prisms, (b) mirrors convenient placement of masks to (c) bin~culars. Land R indicate the nominal centers of the left and right images: limit the field of view, thereby giving respectively, of the stereogram: M = mask, eRO =cathode ray oscilloscope (the good control of the overlap area (the visual display surface). Dashed lines indicate lines of sight extended to their shared display area between the two intersection. In (a) and (b) their intersection occurs at the accommodative subareas which serves as a buffer zone distance of the display indicating correct alignment of the systems. In (c), the for each subarea). The disadvantage of accommodative distance is assumed to be infinity, and the lines of sight are the mirror system relative to the prism parallel, again indicating correct alignment. system is that it is more complicated to construct. Like prisms, mirrors can can be made detachable, but as the kinds of glass, combined so as to be worn as spectacles to facilitate binoculars can be located far from the minimize the chromatic aberration group viewing. display, they do not interfere with inherent in the use of an elementary normal viewing and can be left prism.) In a useful variation of the permanently in place. prism method, the single prism (in either or in both eyes) is replaced by a Prism System (Brewster, 1856) pair of equal prisms. The prisms in The advantage of the prism viewing such a pair can be rotated against each system is that it is the easiest to other to produce-in effect-a single H---+--················V implement. A prism is needed only in prism of variable power. This is a one eye, and this may even be held by convenience, but it adds to optical hand. In fact, with practice, Os can distortion. learn to deviate their eyes (either The prism method for group diverged or crossed) so that the prism viewing. With some slight is superfluous. However, unnatural modifications, the prism method can deviation of the eyes is undesirable for be adapted for group viewing. The reasons to be discussed later. prism (or prisms), preferably I The disadvantages of the prism adjustable, is fitted on spectacle , I method are: the prism produces a frames that are worn either alone or I distortion of straight lines ("prism immediately in front of the viewer's \ distortion"); the power of a prism usual spectacles (when these are used). \ varies depending on the eye's direction Because there is now no \ of gaze and on their vergence, and this centerline-separation shield, each eye effect interacts with any the 0 will see both images of the stereogram, H-.J-~LI....u may be using (Fry, 1937; Ogle, 1951); i.e., the entire display. This extraneous the prism reduces the optical quality stimulation may create serious viewing of the image being viewed (particularly problems. The simplest way to restrict by introducing chromatic aberration, the viewing of each eye to its intended which is disturbing against dark member of the stereo pair is by means backgrounds); and the of a corresponding pair of crossed cen terline-separation shield, which Polaroids, one pair of which is fixed to F extends forward from the nose to the the display surface and the other to center of the display, is an awkward the spectacle lenses (Fig. 3); the restriction of the image being viewed. remaining extraneous stimulation is The optical quality of the image can removed by darkening the room. Fig. 3. Prism-plus-Polaroid system be improved by using two low-power The more persons who wish to view for group viewing. Spectacle frame (F) prisms, one in front of each eye, a display, the farther away they must contains Polaroid filters and an instead of one strong prism, and by stand. (The adjustable prism permits adjustable prism (AP). V (vertical) and using achromatic prisms. (Achromatic the 0 to vary his viewing distance.) A H (horizontal) indicate the direction prisms are composed of two different distant viewer not only sees a of polarization of the Polaroid filters.

Behav. Res. Meth. & Instru., 1971, Vol. 3 (3) 155 The mirror system would seem to It is not necessary here to define Matching Accommodative Distance have an advantage over the prism additive scales of accommodation and and Vergence Distance (Alignment) system in enabling each half of a vergence (see Emsley, 1948; Sperling, An important design consideration curved display surface to be viewed 1970). It is sufficient simply to refer in stereoscopic displays is insuring that perpendicularly, thus reducing the to the actual distance from the a to an vergence is appropriate for the foreshortening that results from the object for which accommodation or accommodative distance of the nonperpendicular view in the prism vergence is appropriate. The stimulus display. For example, let the system. In any viewing system, the dimension that is crucial to accommodative distance be 1 m. Then, first-order horizontal foreshortening accommodation is called the when the lines of sight of each eye are error can be compensated by accommodative distance of an object; pointed at the nominal centers of their adjustment of the x-axis the eye's response is the respective visual display, these lines of magnification. However, perpendicular accommodated distance. Similarly, the sight should intersect at 1 m, It is the viewing eliminates the first-order critical stimulus dimension for task of the engineer to insure that the vertical foreshortening error, as well as vergence is the vergence distance of an lateral separation of the left and right the horizontal error. When the display object; the response is the verged stereo images on the display surface surface is a true circular arc, the distance. For example, in normal and the optics of the viewing device second-order errors (due to vision an object at a distance of 1 m are adjusted to accomplish this. noncorresponding screen curvature in from an a causes the lenses of his eyes The alignment procedure may be the two images) also are eliminated by to adjust accommodation until they divided into four steps which are best perpendicular viewing, but these errors accurately light rays emanating carried out in the following sequence: are unlikely, in any case, to be from a distance of 1 m, and it causes (1) determine the accommodative significant in comparison to other his eyes to converge so that the lines distance of the display; (2) alter the image defects. of sight of the two eyes intersect at a accommodative distance if desired; distance of 1 m. (3) measure the vergence distance of Binoculars Method In the world of real objects, the the display; (4) adjust the vergence The usual implementation of mirror stimulus to accommodation and the distance to equal the accommodative and prism systems limits precisely stimulus to vergence are perfectly distance. For many purposes, a simple controlled viewing to one a per CRO. correlated, and the visual system takes subjective method that bypasses the When there are several as, these this into account. For example, when first three steps will suffice, but it is systems require the multiplication of a stimulus only to accommodation and useful also to know objective methods. CROs and the associated viewing not to vergence is presented (i.e., one (1) Measuring accommodative device, one system for each' O. One eye is kept covered), then the eyes distance. The easiest way to determine way to overcome this multiplication is nonetheless verge upon it (i.e., even accommodative distance in the prism to use binoculars to view the displays. the covered eye points at it). Similarly, and mirror systems is to measure the Because they magnify the images, a stimulus to vergence causes the eyes optical path with a ruler. In binoculars binoculars can be placed farther from to accommodate appropriately. systems, a camera with a ground-glass the displays than the direct viewing Fortunately, there is some flexibility viewer probably is the simplest way to devices; consequently, many as can in the visual system so that the eyes determine the accommodative distance view the same display simultaneously. can be accommodated for one distance of the display. The camera is If desired, they can be viewing it at and verged upon a different distance, placed at eye position and focused to different magnifications. but only a limited amount of produce a sharp image. The The disadvantages of the binoculars accommodation-vergence disparity can determination depends, of course, on method are: the viewing stand with be tolerated. When this amount is the previous calibration of the camera binoculars on it must be rigidly fixed exceeded, then either a failure of lens, and it is the more accurate the relative to the display; the system is accommodation occurs (producing a greater the . difficult to adjust (particularly blurred image) or a failure of vergence (2) AI t erin g accommodative centering the images) and difficult to occurs (producing a "double" image), distance. To alter accommodative maintain in adjustment; viewing is or both occur. distance, an ordinary spectacle lens difficult for the a because his head placed before the eye is all that is must be exactly positioned vis a vis the A computer can readily generate required. The power D in diopters of binoculars, and the optical quality is stereograms that define objects at the required lens is given by the likely to be the poorest of the numerous different vergence distances formula methods. On the other hand, it is far (and thereby give complex illusions of cheaper to obtain a large effective stereoscopic depth), but no convenient display area by viewing a small CRO way has yet been discovered to (1) with binoculars than by buying a large concomitantly covary the stimuli to CRO. When very small displays are accommodation. For example, by where AI is the initial accommodative required, they are conveniently varying their vergence distance, distance (in meters) and A 2 is the produced by inverting the binoculars. different objects defined by a desired final distance. Positive values The optical quality of binoculars is stereogram may subjectively appear to of D indicate convex (positive) lenses much less critical when they are used be at different depths, ranging from and negative values indicate concave to minify than when they are used to immediately in front of the nose to (negative) lenses. magnify. infinity, even though accommodative (3) Measuring vergence distance. distance remains fixed (at the distance The best method requires constructing ALIGNMENT from the a to the display). Generally, a device for producing two narrow Accommodation and Vergence the inability to vary independently the collimated beams of light (e.g., two Accommodation is the technical accommodative distance of segments penlights with small apertures at the term for the amount of focusing of the of a computer-generated display is not front). The collimators should be lens of the eye. Vergence refers to the an important limitation. It is sufficient mounted on a board with the front angle between the two eyes that is to vary the overall accommodative ends 6 em apart and the rear ends required to place the image of a single distance, and this is easily done by adjustable. The main requirement is object onto corresponding points of placing spectacle lenses in front of the that the dual beams should produce the two retinas. a's eyes. clearly defined spots at a distance 156 Behav. Res. Meth. & Instru., 1971, Vol. 3 (3) Ap Ap V = m _ Sand S = m - V (2)

1)/2 P-'2 E qua t ion 2 relates the lateral i\ M M : ' separation of any two corresponding points in the stereogram to their vergence distance provided A, p, and A A t;.. P .. m are known. Determination of the accommodative distance, A, was outlined above. The interpupillary CC distance, p, may be taken as .06 m. ~ m-2p "i (The average population value is about + p - 6.2 em.) The dual parallel light beams project on the screen with the lateral separation of m (Fig. 4a). ~ ~ ~ R It may be noted here that perceived stereoscopic depth depends far more (c) (0) (b) on relative values of lateral separation, S, for two different objects in the stereogram than it does on the Fig. 4. Calibration of vergence distance. (a) Two parallel beams of light are absolute value of S. Also, exact produced by the colIimators (Q). The light beams (f) pass through the alignment (and perceived depth) will stereoscopic viewing device (d) to project onto the display surface with a lateral vary slightly between Os because of separation of m em. The apertures of the colIimators are mounted on a board (b) their different interpupillary distances. and are separated by the interpupillary distance (p), nominally 6 em. (4) Adjusting vergence distance. In (b) Diagram to illustrate that when the lateral separation is diminished by p prism and mirror systems, vergence (twice p/2), the vergence distance changes from infinity (parallel lines) to a distance is easily adjusted by varying vergence distance of A (the accommodative distance). (c) The display surface, the power of the prism and the angle showing a stereogram (L, R). The Ms are assumed to be separated bv a lateral of rotation of the mirror. Binoculars separation of m, corresponding to a vergence distance of infinity-e.g., as in (a). systems also require a prism The lateral separation between the As is m - p, corresponding' to a vergence adjustment. The prism is placed on the distance of A (the accommodative distance), e.g., as in (b). The Cs are laterally large side of the binoculars (i.e., away separated by m - 2p, corresponding to a vergence distance of A{2. In a from the eye); because of the larger stereoscopic view, the Cs would appear to be in front of the screen, the As in the distances, very weak prisms will plane of the screen, and the Ms behind it. The stereogram is correctly aligned suffice. Fine adjustments of vergence when vergence distance equals accommodative distance; for prism viewing this distance usually are made by varying occurs when the nominal centers of the Land R subfields have the same lateral the lateral separation, S, of the separation as the As in (c). stereogram directly under program control. The final value of vergence equal to accommodative distance of accommodative distance be m, the distance should normally be set equal the display surface. interpupillary distance be p, and the to the accommodative distance, The dual beams are placed at the unaltered accommodative distance of assuming an interpupillary distance of same vantage point as the eyes and the display be A. Then the vergence 6cm. pointed at the display; there they distance of any object on the screen is Subjective Method of Aligning produce two spots on the display related to the lateral separation of the Vergence Distance (Haploscopic surface (Fig.4a). When the angle two images by Method) between the beams has previously been adjusted to the desired vergence distance (the point at which the beams intersect), the distance between the two spots (lateral separation) will I define this vergence distance on the ( b) ...... -+- -+-+-4 display surface. As a practical matter, it is useful to I set the collimated beams parallel because their projections on the display surface then define the lateral t-+-+- --t-+--f separation of objects at infinite vergence d i stance. This is the maximum lateral separation of "real" objects. When the lateral separation of I two images on the display surface is L R (c) t-t-+- -T-+-l decreased by the interpupillary distance (typically 6 cm) then the I vergence dist ance equals the (0) accommodative distance. The relation between lateral separation on the display surface (S) Fig. 5. Haploscopic method of adjusting vergence. (a) The test patterns. View and vergence distance (V) can be of the display surface showing the left (L) and right (R) members of the expressed in general terms.f Let the stereogram. Each line is centered in its field. (b) Stereoscopic appearance when lateral separation on the display the viewing system is properly adjusted. (c) Stereoscopic appearance of a surface between points at infinite maladjusted system.

Behav. Res. Meth. & Instru., 1971, Vol. 3 (3) 157 In this method, a stereogram such as relation, i.e., appropriate to real FRY, G. A. An experimental analysis of the that illustrated in Fig. 5 is presented. objects. accommodation-convergence relation. American Journal of Optometry, 1937, The engineer adjusts the prisms, the When viewing continuously visible 14,402-414. mirrors, or the stereo pair's lateral stereograms in which the two images OGLE, K. N. Distortion of the image by separation on the display surface until are very similar, there is great prisms. Journal of the Optical Society of America, 1951, 41, 1023-1028. the 0 reports that the vertical line tolerance for alignment error, and SPERLING, G. Binocular vision: A physical (which is seen only by the right eye) successful vergence occurs even with and a neural theory. American Journal of falls in the middle of the horizontal I ar g e accommod ation-vergence Psychology, 1970,83,461-534. disparities. Some experiments, "n"ATI>TUN~, C. Contributions to the line (which is seen only by the left physiology of vision. Part the first. On eye). however, require presentation of some remarkable and hitherto unobserved Haploscopic adjustment is virtually basically different stimuli to each eye. phenomena of binocular vision. incumbent in the binoculars system. It To insure that the eyes are correctly Philosophical Transactions of the Royal is also useful in group viewing, as it verged in such cases, the engineer Society, 1838,8,371-394. NOTES allows Os to make accurate should do two things: (1) He should 1. The divergence of light from an alignments, and it is particularly provide a "visual frame" that is seen object-the stimulus to accommodation helpful in diagnosing failures to by both eyes, within which the diverse (focusing) of the eye-is exceedingly perceive stereoscopic depth. stimulus materials appear; and (2) he awkward to simulate in any kind of display; see section on Accommodation and should adjust the vergence distance Vergence. Other Considerations individually for each 0 (subjective 2. See the section entitled, (3) Measuring In all three systems, the viewer method) under conditions as similar as vergence distance. 3. The treatment is simplified by should be encouraged to wear possible to those of the experiment. assuming small angles, Le., that the spectacles if he normally uses them for REFERENCES unaltered accommodative distance (the objects at the accommodative distance BREWSTER, D. The stereoscope, its "viewing distance") is large relative to the of the display. Only in his normal history, theory and construction. interpupillary distance and relative to the viewing mode will his accommodation London: Murray, 1856. picture width of each member of the EMSLEY, H. H. Visual optics. (4th ed.) stereogram. In practice, angles almost and his vergence be in their normal London: Hatton Press, 1948. always are small.

158 Behav. Res. Meth. & Instru., 1971, Vol. 3 (3)