Abstract

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.

© 1976 Optical Society of America

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References

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  1. J. U. White, J. Opt. Soc. Am. 32, 285 (1942).
    [CrossRef]
  2. D. Horn and G. C. Pimentel, Appl. Opt. 10, 1892 (1971).
    [CrossRef] [PubMed]
  3. E. O. Schulz-DuBois, Appl. Opt. 12, 1391 (1973).
    [CrossRef] [PubMed]
  4. P. L. Hanst, Advances in Environmental Science and Technology, Vol. II, edited by J. N. Pitts and R. L. Metcalf, (Wiley, New York, 1971), p. 91.
  5. D. R. Herriott and H. J. Schulte, Appl. Opt. 4, 883 (1965).
    [CrossRef]
  6. P. L. Hanst, A. S. Lefohn, and B. W. Gay, Appl. Spectrosc. 27, 188 (1973).
    [CrossRef]

1973 (2)

1971 (1)

1965 (1)

1942 (1)

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Figures (8)

FIG. 1
FIG. 1

Arrangement of the mirrors. With the centers of curvature of the mirrors located at the correspondingly lettered solid circles, the light follows the indicated path through images on the D and E mirrors. After 15 passes, the diagonal mirrors return it along ray 16 to a different part of mirror B. It then retraces its route through all the same images on D and E but each time from a different direction. The new axial reflection points are marked by dots on mirrors A, B, and C. With this adjustment, ray 30 emerges under the B mirror. Rays 17 to 30 are emitted for clarity. The diagonal mirrors together have a combined focal length equal to that of each of the other mirrors.

FIG. 2
FIG. 2

Spots of laser light on the single mirror end of the cell arranged for 48 passes. The initial and final spots are on the diagonal mirrors. In between, the light passes sequentially through the spots in the middle two rows, then through the spots in the next higher and lower rows, etc. The marks A, B, and C indicate the centers of curvature of the three mirrors at the other end of the cell.

FIG. 3
FIG. 3

“Double-mirror” end of the cell aligned for passes of light from three different directions through every image in the array at the other end of the cell. Light enters through the irregular hole in the black background over the middle mirror, goes sequentially through the top spot on the middle mirror, the bottom spots on the outside mirrors, the middle spots on all three, the bottom spot on the middle mirror, and the top spots on the end ones. The exit beam hits the dark target directly under the middle mirror.

FIG. 4
FIG. 4

Two views of the optical system arranged for 12 passes showing the concave mirrors A, B, and C with the two added pairs of diagonal mirrors. Circles locate the centers of curvature of the indicated mirrors. The light path is marked by the solid line until it is offset horizontally in diagonal mirrors F and G, thereafter by the dashed line. Diagonals D and E give appropriate vertical offsets to both the solid and the dashed lines.

FIG. 5
FIG. 5

Effect of horizontal misalignment on the spot diagram with four rows of images. The numbered solid dots show the sequential image locations when the centers of curvature of the A and B mirrors are accurately aligned on the large circles, When B is moved slightly to the dashed circle, the images move from the dots to the adjoining small circles. Their deviations increase to a maximum at 8 halfway through the system, then go back to zero at the exit point 15.

FIG. 6
FIG. 6

Spot diagram on the mirrors using both pairs of diagonals. Solid points are those formed prior to the F and G diagonal mirrors, hollow points are formed after them. Corresponding solid and hollow points are always at the same height, showing that the exit spot is always at the same height regardless of the heights of the intermediate spots.

FIG. 7
FIG. 7

Pattern of images at the single mirror end. Light enters through the irregular hole in the black background at the top-left part of the picture. The A and B mirrors are accurately aligned to form first a rectangular array of 12 spots in three vertical columns and four rows, then after a horizontal offset, 12 more weaker spots that alternate from one side to the other side of the first spots.

FIG. 8
FIG. 8

Effect of misalignment on the pattern shown in Fig. 7. The A and B mirrors are slightly out of alignment in both directions. Even though the columns of images are not straight and the rows are not evenly spaced, the horizontal positions of the exit spots and of the spots on the middle diagonal mirrors are unchanged. The vertical position of the middle spots is displaced, but the final emerging spot is still in the same place.

Equations (1)

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N = ( D / d ) 3 / 2 - 2 D / d + 2.