Abstract

The shape of any aspherical surface with rotational symmetry can be very easily found with great accuracy using Newton fringes formed against a spherical test plate. To make it possible, a special mathematical procedure is devised for use with a special measuring system here described.

© 1970 Optical Society of America

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References

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  1. A. Offner, Appl. Opt. 2, 153 (1963).
    [CrossRef]
  2. D. Malacara, Appl. Opt. 4, 1371 (1965).
    [CrossRef]
  3. M. V. R. K. Murty, Appl. Opt. 3, 531 (1964).
    [CrossRef]
  4. B. P. Hildebrand, K. A. Haines, R. Larkin, Appl. Opt. 6, 1267 (1967).
    [CrossRef] [PubMed]
  5. J. Strong, Procedures in Experimental Physics (Prentice-Hall, Englewood Cliffs, N.J., 1958), p. 64.
  6. R. M. Scott, in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, Inc., New York, 1965), Vol. 3, p. 90.

1967 (1)

1965 (1)

1964 (1)

1963 (1)

Haines, K. A.

Hildebrand, B. P.

Larkin, R.

Malacara, D.

Murty, M. V. R. K.

Offner, A.

Scott, R. M.

R. M. Scott, in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, Inc., New York, 1965), Vol. 3, p. 90.

Strong, J.

J. Strong, Procedures in Experimental Physics (Prentice-Hall, Englewood Cliffs, N.J., 1958), p. 64.

Appl. Opt. (4)

Other (2)

J. Strong, Procedures in Experimental Physics (Prentice-Hall, Englewood Cliffs, N.J., 1958), p. 64.

R. M. Scott, in Applied Optics and Optical Engineering, R. Kingslake, Ed. (Academic Press, Inc., New York, 1965), Vol. 3, p. 90.

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Figures (5)

Fig. 1
Fig. 1

Observed fringes.

Fig. 2
Fig. 2

Plotting of results.

Fig. 3
Fig. 3

Formation of Newton fringes: (a) fringe above the surfaces; (b) fringe below the surfaces.

Fig. 4
Fig. 4

Measuring of fringe positions.

Fig. 5
Fig. 5

Experimental arrangement to measure fringe positions.

Equations (8)

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N ( x ) / 2 = S ( x ) + A x + B x 2 ,
A = [ N ( x ) N ( x + ) ] / 4 x + ,
S e ( x m ) = S T ( x m ) ,
N ( x m ) / 2 = S e ( x m ) + A x m + B x m 2 ,
B = 1 x m [ S T ( x m ) x m A + N ( x m ) 2 x m ] .
N ( x ) / 2 = S e ( x ) + A x + B x 2 .
O P D = A B ¯ + C B ¯ .
O P D = 2 D E ¯ ,

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