Why is it "hardly possible to tell on which surface of the cabinet the various parts are painted"? Is it only due to the removal of stereoscopic cues to the disposition of the internal walls of the box? We should also consider the possibility that it is due to the peephole itself.

To understand peepholes, we must first deal with certain properties of lenses, which also apply to the lens of the eye. Consider a lens and a film (Figure 4.6). Consider also a field of object points (the gray region in panel A of Figure 4.6), the images of which are formed on the film by the lens. Even the best of lenses introduces some blur; in other words, the image of a point on an object is a circular region called the circle of confusion. The object points for which the circle of confusion is minimal are said to be in the focus plane. Object points that are less in focus than those in the focus plane, but are not objectionably blurred, are said to be in focus (panels B and C of Figure 4.6). The distance between the nearest object point that is in focus and the farthest object point that is in focus is called the depth of field of that lens.

Just as the distance of the focal plane of most camera lenses can be varied from infinity to a few feet, the visual system can change the shape of the eye's lens (a process called accommodation and thereby vary the distance of the focal plane of the eye (over a greater range than most camera lenses, in young people). If an object is fairly close to the eye (say, less than 10 ft. away), the accommodation of the eye can be a source of information regarding the distance of the object; that is, the accommodation of the eye can serve as a range finder. In detail, the depth is probably derived from the convergence induced by the accommodation convergence reflex, rather than acting as an independent depth cue. I don't think this is worth a footnote, however.

		Fig. 4.6 Focus and depth of field.

Cameras have diaphragms that make it possible to mask off part of the lens, to change the aperture size; similarly, the iris can change the size of the pupil. The smaller the aperture or pupil size, the less light hits the film or the retina. Changing the aperture size also affects depth of field. The smaller it is, the greater the depth of field (see Figure 4.6, panels D and E). Now if a peephole is so small that it effectively reduces the size of the pupil, it is called an artificial pupil. An artificial pupil can enhance pictorial depth by increasing depth of field and thus minimizing the value of information about distance derived from accommodation. For instance, when one looks into a relatively small perspective cabinet (as most are), the eye must focus on the painted surfaces inside the box; because the range is small, one might expect accommodation to disclose the distance of the painted surfaces and thereby diminish the illusion. This would be so, but if the peephole is very small, we should expect the viewer's depth of field to be increased. In such a case, the painting would be nicely in focus even if the eye accommodated so that its focus plane would be at the distance one might expect the walls of a real room to be.

In addition to affecting the depth of field, a peephole can also reduce information about the flatness of a painting just by truncating the visual field - by removing from sight the immediate foreground, surrounding objects, the picture's margin, and the unfocused (but possibly important) sight of one's nose (see Schlosberg, 1941, and Hagen and Jones, 1978).

So Brunelleschi's use of a peephole in his first demonstration was instrumental in producing a compelling experience of depth for two reasons: First, it increased the effectiveness of the illusion by forcing the viewer to place his or her eye at the center of projection of the perspective (thus making the picture a projective surrogate for the scene); second, it reduced the viewer's information regarding the flatness of the picture plane.

There is another aspect of Brunelleschi's technique that merits discussion. Although Brunelleschi's peepshow was similar to seventeenth-century perspective cabinets, it appears to have anticipated certain techniques for the enhancement of depth in monocularly viewed pictures that were not discovered until the first two decades of this century. Here is Harold Schlosberg's (1941) summary of these discoveries:

Box 4.2 Viewing from the center of projection vs. the removal of flatness information : The relative importance of these two factors is not known. For instance, we do not know the extent to which the apparent three-dimensionality of a display is diminished by the presence of stereoscopic cues to flatness. This question could be resolved by comparing the apparent three-dimensionality of a perspective painting seen monocularly through one peephole at the center of projection to the apparent three-dimensionality of the same painting seen binocularly through two peepholes on either side of the center of projection. An experiment by Adams (1972) compares these two conditions and includes a third: viewing through an artificial pupil. Although his data show no effect of the three modes of viewing, I do not consider the experiment definitive on this issue because of the method Adams used in determining perceived depth: He presented a picture representing a floor consisting of rectangular tiles, and a wall parallel to the picture plane that is the far wall of the room into which the spectator is gazing. This wall was also divided into a row of tiles. The observers were asked to vary the height of the tiles on the far wall until they matched the depth of the floor tiles. Subjects systematically underestimated the depth of these foreshortened floor tiles by matching them to wall tiles that were always shorter in height than in breadth, whereas geometric considerations would predict the floor tiles to appear elongated in depth under certain conditions, square under other conditions, and elongated in width under a third set of conditions. This result could be accounted for by the subjects having performed a task that was a compromise between the task they were expected to perform, which required a judgment of depth (but may be difficult), and a comparison of the two-dimensional forms of the foreshortened tiles on the floor and the frontal tiles on the wall (which is likely to be easy). If the task that the subjects performed did not involve the judgment of depth to the extent anticipated, one cannot infer much about the different modes of viewing from the negative results reported.

		Fig. 4.7 Experimental apparatus for Smith and Smith's experiment.

In the period around 1910, when interest in stereoscopy was high, it was widely known that the "plastic" effect could be obtained almost as well by viewing a single picture through a lens as by the use of disparate pictures in the binocular stereoscope... . The plastic depth that can be obtained monocularly is very striking, and must be seen to be appreciated. For optimal results the viewing lens should have the same focal length as the camera lens with which the picture was taken, but any ordinary reading glass works fairly well on pictures from 1-3 in. in size. In a typical snapshot of a person against a mixed background, the person stands out clearly, and plastic space can be seen between him and the background. In a good picture the person takes on solidity and roundness, with the slope of the lapel and the angle of the arms clearly in three dimensions. (p. 601)

For our purposes, it is most important to note that a similar effect can be achieved by "looking at a picture monocularly in a mirror. The mirror seems to break up the surface cues and may well have less obvious effects, such as destroying orientation[of the picture's background.]" (Schlosberg, 1941, p. 603). This is exactly what Brunelleschi did.

In addition to all this non-experimental evidence regarding the impact of Brunelleschi's peepshow, it has been shown in experiments that a proper central projection can be mistaken for a real scene if viewed monocularly from the center of projection. For instance, Smith and Smith (1961) asked subjects to throw a ball at a target in a room that they could view through a peephole (see Figure 4.7). Two groups of subjects threw the ball at a target in a real room. The subjects in one group were actually able to see the room through the peephole, whereas the subjects in the other group thought they were looking at the room but actually were looking at a photograph of the room. When subjects looked through the peephole at the real room, their throws were on the average quite accurate; when subjects looked through the peephole at a photograph of the room, the average throw was not systematically longer or shorter, but it was considerably more variable.⁶ But what is more important than the similar accuracies of the throws was the absence of any awareness on the part of subjects that they had been seeing photographs in the viewing apparatus. In other words, neither in their performance of the ball-throwing task nor in their interpretation of the situation did the participants show any sign that the picture looked different from an actual room. And this implies that the Brunelleschi peephole can give rise to an illusion so strong that it could properly be called a delusion. We will return to this point in Chapter 6.

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⁶ The authors speculate that direct view of the targets permitted some monocular parallax and thus reduced the variability of the throws.