Journal of the Society of Motion Picture Engineers (1930-1949)

tery; but it affords the connection of ideas most necessary to establish between director and stereotechnician. Object Distances and Image Distances Next we must see how the position of the camera in front of the scene is related to the image of that scene in front of the spectator. Denoting by dn the distance from the camera to a given object point, there will be a corresponding image point seen by a spectator in the theater as having a nearness factor, Nn. Specifically, we may refer to an image point at No (infinity) deriving from an object point at do, an image point at NI deriving from a point at d\, and so on. Now if we were to graph the distance of object points do, d\, d% . . . against the actual distance, P, of the corresponding image points from the spectator, it must not be supposed that the result would necessarily be a straight line. This represents an important but entirely special type of stereoscopic transmission; that is to say, one in which the rendering of distance is a linear function. We shall meet this again later on, but it is worth observing here that linear transmission does not of itself produce an orthostereoscopic image, or one which is geometrically congruent with the original scene. There may be a multiplying factor either greater or less than unity by which a given length is stretched or shrunk, though of course uniformly throughout the scene. A New Unit: The Rho We now come to the problem of relating do, di, d-i ... in the scene to -/V0, NI, JV2 ... in the theater. Here another important step forward has been taken in the simplification of stereo calculations by introducing a new unit of distance. It can be shown that if a reciprocal distance unit is employed, equal numbers of depth units in the scene will always correspond with equal changes of nearness factor in the cinema, no matter whether the transmission system is linear or nonlinear. Thus at one stroke a mass of difficult computation is done away with, and depth ranges in the scene can be manipulated by simple arithmetical addition and subtraction. The new distance unit has been named a rho ("reciprocal" denoted by the Greek letter p), and to bring it to a convenient size it is defined as the reciprocal of the distance in inches multiplied by an arbitrary constant, the p constant (K), which has been set at 6,000. Thus we may write distance in p = 6,000* distance in in. (2) This is equivalent to 500 divided by distance in feet, and the units of course decrease with increasing distance, and vice versa, as is shown in Table I. Table I Distance p Distance P 100ft 5 6ft 83 50 10 5 100 33 15 4ft 6 in. 111 25 20 4 2 120 20 25 4 125 10 50 3 4 150 7 71 3 167 Whereas distances in linear units are expressed as do, d\, d2 . . ., the corresponding p distances are designated DO, D\, D% . . . . All measurements on the set and on location are made with a tape graduated in p on one side and in feet and inches on the other, for focusing. (In passing, it is worth noting that if lensfocus scales were engraved in p, they would be calibrated with equal separations for equal p differences, in place of the present unequally divided scales. Furthermore, depth of focus tables would need only one entry under each focal * Because of the superior convenience of a decimal system of linear units, we have recently converted to the metric system. 1 metric p = 10,000 /distance in cm. 254 October 1952 Journal of the SMPTE Vol. 59