138 PHOTOGRAMMETRIC ENGINEERING errors in planimetry proved to agree very the accompanying diagrams. well with the practical results. The error propagation formulae were de­ In summary, the results of the tests are rived in accordance with the well known very promising, and it seems desirable laws of the method of least squares and that the method be tested under varying for two different cases of the control point circumstances, also with such simple in­ location. struments as mirror stereoscopes and I n particular, the principles of the nu­ single image comparators (coordinato­ merical corrections and of compensation in graphs etc.) the control points were applied. In a Some examples of the theoretical dis­ similar way the error distribution in a tribution of the standard errors of the final triangulation strip can be derived and x-and y-coordinates are demonstrated in demonstrated. Two Sketching Devices for Oblique Aerial Photographs MIRIAM HERZOG, Engineer in Training, assisted by GIF FORD M. MAST, President, and w. K. GANNETT, Director of Engineering, Mast Development Company, Inc. ABSTRACT: The Mechanical Oblique Sketcher and the Optical Oblique Sketcher are two novel answers to the problem of rectifying aerial photos. The Mechanical Oblique Sketcher is a mechanization of a point by point geometric rectification procedure. The Oblique Photo Sketcher is a pro­ jection device for diapositives which utilizes an intense point source of light focused on a small aperture, simple lens to produce an unusual depth af field, permitting imaging the diapositive on a grossly tilted sur­ face. ERIAL photographs, taken at an ob­ of maps and charts from daily recon­ A lique angle to the earth, provide use­ naissance information. The need for a de­ ful photogrammetric information only if vise was expressed by the Photo Recon­ the normal, vertical view can be repro­ naissance Laboratory, \Vright-Patterson duced. Rectification of aerial photos is a Air Force Base. In answer thereto Mast complicated procedure since it involves Development Company, Inc., Davenport, the translation of a perspective view into Iowa, designed two such instruments­ orthographic projection. Rectification is first the Mechanical Oblique Sketcher and generally accomplished by either special second, the Optical Oblique Sketcher. drafting instruments or by rectifying pro­ THEORY UNDERLYING THE MECHANICAL jection machines. Two characteristics of OBLIQUE SKETCHER (M.O.S.) these devices have been: 1. the rectifying projectors were too The Mechanical Oblique Sketcher is bulky to be conveniently trans­ based on an application of Synthetic ported; Projective Geometry suggested by Prof. 2. the drafting machines required te­ A. C. Bendixen of Ohio State University dious, eye-straining plotting. Research Foundation. His suggestion ap­ In view of these objections, one can see plies a characteristic of homologous quad­ that there existed a need for a simple, rea­ rangles namely, homologous figures are sonably accurate, transportable rectifica­ projections of the same plane figure on tion device. One use for such a device different planes. would be the prompt bringing up-to-date In Figure 1, ABCD and A'B'C'D' are SKETCHING DEVICES FOR OBLIQUE PHOTOS 139 E o c FIG. 1. Geometry of mechanical oblique sketcher. two homologous quadrangles. A'B'C' D' are extended through A' and B'; their form a square in a map; ABCD are the intersection is the rectified position of same four points in an oblique photograph point P. of an essentially plane surface, and are obviously projections of the same points MECHANIZATION OF THE GEOMETRY on a different plane. Extending three of The Mechanical Oblique Sketcher con­ the sides of the square and its diagonals sists of three units, the transmitter, or we can find two lines such as E'G' and "master," the receiver, or "slave," and a H'j('. These lines serve a similar function four-channel amplifier (see Figures 2 and to measuring lines in the measure point 3). The master and slave units are basically perspective drawing system. Similarly, ex­ alike. Each unit consists of two torque tending the sides of the quadrangle A BCD, units, and a base bar, on which the base lines EG and HK are constructed so that points are positioned. One end of each the diagonals of the quadrangles intersect torque unit base slides and pivots on the the lines at their mid-point. base bar. The torque unit bases are pro­ vVithin this geometric configuration any vided with three reticles for aligning the point in the plane of figure ABCD can be three paints on the metrical line. The transferred to the plane of A'B'C'D'. torque unit carriages ride along the bases For example, let P be any point in the on stainless steel rods. Each torque unit plane ABCD. Lines from it may be drawn of the slave is equipped with a servo through the base points A and B and ex­ motor. The scribe arms pivot about a tended until they cross EG and HK at F common point, the scribe. Each arm ex­ and J. Reversing the procedure, point J' tends through a pivot mounting above the is located on line H'K' so that a' and b' base point and then through a similar are in the same proportion as a and b mounting on the torque unit. in Figure ABCD. Point F' is located in the In use, the M.O.S. master unit is placed same manner. From points F' and J' lines over the photo; the M.O.S. slave unit is FIG. 2. Schematic of mechanical oblique sketcher. 140 PHOTOGRAMMETRIC ENGINEERING FIG. 3. Mechanical oblique sketcher. similarly aligned over the map. The OPTICAL PRINCIPLES INVOLVED IN torque unit bases are made to coincide OBLIQUE PROJECTION with the metrical lines, while the base Theoretically, projection of a positive points are located on the base bar. The transparency of an aerial photo on an scribe arms correspond, Figure 1, to the oblique surface is an accurate and simple extensions of the lines through P and the means of rectification. However, in prac­ base points. As the scribe moves, the tice, accuracy must be sacrificed to retain angle between the scribe arm and the simplicity. In Figure 4 the conventional torque unit base changes. To compensate systems of pinhole, point source, and for this change in angle, the torque unit stereoptic projection are compared. The is forced to move, rotating a ball-bearing pinhole method and point source method lead screw. The degree of rotation of the have the advantage that no projection lead screw is measured by 60 cycle coarse distance is defined. This unrestricted pro­ and vernier synchros. The signal of these jection distance is limited by the fact that synchros is amplified, combined, and com­ the circles of confusion which accompany pared with the signal from like synchros pinhole projection, increase as the image on the slave unit. The unbalance of the is magnified. Stereoptic projection, on the synchro signals actuates the servo motors other hand, forms a sharp image at some on the slave unit. The servo motor on the definite distance from the projector. This slave drives a similar lead screw, moving characteristic is objectionable in oblique the scribe arm of the slave. projection for two reasons: first, focus can The amplifier consists of two separate, be maintained on a tilted screen only by twin units, one for the right servo and one tilting the lens to meet the Scheimpflug for the left. condition, i.e. that the plane of lens, film, Although the M.O.S. is simple to manip­ and screen intersect in one line. ulate, its use is restricted. A minimum Second, a condition which a rectification error of about plus or minus 1/32" is the projector must satisfy in order to repro­ greatest accuracy which this instrument duce the actual view, is that proportional­ can achieve. The imperfections in the ity exist between the projector and the M.O.S. stem from the fact that the geo­ photographing camera. That is, the ratio metrical construction upon which it is of the diapositive size to the distance be­ based is not readily adaptable to mechan­ tween the diapositive and the lens, must ization, e.g., in some positions backlash of equal the ratio of the negative size to the the slide bars tends to be critical, and distance between the negative and the great freedom of movement is required to camera lens. avoid binding. The Optical Oblique Sketcher combines The inadequacies of the Mechanical some of the advantages and eliminates Oblique Sketcher led Mast Development some of the disadvantages of conventional Company engineers into a search for a pinhole and point source and stereoptic simpler, more accurate method of rectify­ projection. The ingenuity ofthe instrument ing aerial photos. This search resulted in is in its size relationships. By using an proposing to the Air Force the develop­ intense point source of light focused on a ment of the Optical Oblique Photo Sketcher. very small lens, the effective aperture SKETCHING DEVICES FOR OBLIQUE PHOTOS 141 OBLIQUE PHOTO SKETCHER FIG. 4. Comparison of methods. becomes on the order of f/80. One can see the use of multiple element lense~. The in Figure 4 that the effect produced by circle of the arc itself forms the iris oi the such a system is similar to pinhole pro­ lens. Tilting the lenses, in accordance with jection in that there are no distortion the Scheimpflug condition, was demon­ problems. On the other hand, the fact that strated to give no perceptible improve­ a tiny lens is used provides a sharp image ment in definition. at one distance from the lens, and a circle Patent No.