858 BELL SYSTEM TECHNICAL JOURNAL 



Such, however, is not the case. It was stated earlier that the ingoing rays 

 appear to be directed toward the images of the intermediate reflecting 

 points. This requires that the images of the intermediate reflecting points 

 fall inside of the efi"ective area. In Fig. 5, the images of the notch fall inside 

 of what would otherwise be the effective area. Since the notch is incapable 

 of serving as an intermediate reflector, the more lightly shaded areas are 

 excluded from the effective area. In the absence of the notch, a ray entering 

 at 1 would be reflected at 2 and emerge at 3. In the presence of the notch, 

 however, it passes through plane AOC and escapes in the direction of 4. 



Therefore, in order to determine the effective area of a corner reflector of 

 arbitrary shape and aspect, one must take account of three loci of points 

 defined by the aperture as follows: 



1) The aperture itself 



2) The locus of points determined by taking the direct mirror image of 

 each point of the aperture wath lespect to each of the two surfaces of the 

 trihedral not containing the point. For example, pomt D of Fig. 5 will have 

 the images D' and D" with reference to planes AOB and BOC, respectively. 

 The complete locus of points determined in this way is represented by the 

 dot-dash line of Fig. 5. 



3) Locus of points on aperture after each has been assumed to have been 

 projected through the vertex. This image is pictured by the dotted lines of 

 Fig. 5. 



These three images of the aperture can, for simplicity, be referred 

 to as the first, second, and third images, respectively. The effective area 

 is the area common to the projections of the first, second, and third images 

 of the aperture upon a plane passing through the apex of the reflector and 

 perpendicular to the incident rays. For a given aperture and aspect, a cor- 

 ner reflector can theoretically be replaced by a flat plate located at the apex. 

 The size and shape of the flat plate will vary with the aspect as well as with 

 the configuration of the aperture. The above procedure has been of consid- 

 erable aid in studying reflectors having apertures of arbitrary shape. 



Although the graphical analysis just given is sufficient to enable one to 

 compute the effective area of a reflector for any aspect angle, it is frequently 

 more conveneint to determine the complete response pattern of a reflector 

 experimentally. Most of the experimental results reported in this paper 

 were obtained with a 1.25 centimeter radar arranged as shown in Fig. 6. 

 Echo levels were measured on the screen of a type-A indicator using a cali- 

 brated intermediate frequency attenuator to restore the signal to an arbi- 

 trary reference level. It is believed that the levels measured in this way are 

 accurate to within ± \ decibel. The coordinate system used in recording 

 and presenting the data is given in Fig. 7. The reflector was mounted On a 

 lurntablc which could be rotated al^out horizontal and vertical axes. 



