Two different multiple traversal optical systems are described; one gives the longest paths, the other the best compensation for vibration and misalignment problems. In the first, seven mirrors in a near confocal arrangement permit a large aperture beam of light to pass through a restricted volume for a discrete and very large number of times. A rectangular array of images corresponding to different numbers of passes appears on four mirrors at one end of the system. At the other end, three mirrors form the array and illuminate each image in it from one or more different directions. The possible numbers of passes are (4mn − 2)k + 2, where m and n are any integers representing, respectively, the number of columns and half the number of rows in the array. k is the number of different directions from which the array is illuminated. Geometrically, the beam may be isolated after thousands of passes; practically, the number is limited by reflection losses. In the second system the addition of four diagonal mirrors to a White cell converts the two lines of images on the single mirror to a rectangular array of images, almost squaring the maximum possible number of passes. With multiples of four rows of images in the array, the position of the output image is invariant to small errors in alignment of the mirrors.
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