If the illumination of the image produced by a wide-angle lens covering a field of 120° follows the cosine-fourth-power law, the illumination at the edge of the field will be one-sixteenth that at the center in the absence of vignetting. By introducing negative distortion, the illumination may be expected to be more uniform from the center to the edge of the field. In particular if there is no vignetting and if the diaphragm precedes the lens, there will be uniform illumination, even for a field as great as 180°, if the distortion is such that r′=f sinβ where r′ is the distance from center of the field to a given image point, β is the corresponding angular distance from the axis in the object space, and f is the focal length corresponding to the part of the image in the neighborhood of the axis.
During the war Zeiss developed a mapping lens with a large amount of negative distortion and a second rectifying system by which undistorted copies could be obtained from the distorted negative made with the camera lens. A German mapping lens and rectifying unit have been brought to this country, and detailed results of tests made at the National Bureau of Standards are given in the following paper. The lens, termed the Pleon, covers a field of 130°, and the distortion closely follows the law r′=fβ, the distortion being somewhat less than that of the preceding formula. Measurements of the resolving power, of the effective size of the entrance pupil for different angular distances from the axis, and of the net distortion of the two systems are given. In the final print there is significant residual distortion resulting from the failure of the distortions of the two systems to exactly annul each other.
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