Abstract

A Fizeau interferometer is described with which to test the flatness of optical surface up to 240-mm diam. A mercury mirror of suitable diameter is used as a flatness standard. A simple 240-mm diam lens is sufficient. For easy testing of the surfaces of wedge-shaped glass plates without adjustment difficulties the illumination and photographic arrangement, mounted in the same frame, can be tipped on an axis, going through the test surface. The influence of the aberration of the simple lens is discussed. Experimental results of the measurement of an optical flat are presented.

© 1968 Optical Society of America

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References

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  1. R. Bünnagel, Opt. Acta 3, 81 (1956).
    [CrossRef]
  2. R. Bünnagel, Z. Instrumentenk 73, 214 (1965).
  3. R. Barrell, S. Marriner, NPL, Brit. Sci. News2, No. 17.
  4. S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Vol. 2, p. 295.
  5. G. D. Dew, J. Sci. Instr. 43, 409 (1966).
    [CrossRef]
  6. E. Brodhun, O. Schönrock, Z. Instrumentenk 22, 357 (1902).
  7. E. Wickers, Chem. Eng. News 39, 1111 (1942).
    [CrossRef]
  8. R. Bünnagel, Z. Angew. Phys. 8, 447 (1956).

1966 (1)

G. D. Dew, J. Sci. Instr. 43, 409 (1966).
[CrossRef]

1965 (1)

R. Bünnagel, Z. Instrumentenk 73, 214 (1965).

1956 (2)

R. Bünnagel, Opt. Acta 3, 81 (1956).
[CrossRef]

R. Bünnagel, Z. Angew. Phys. 8, 447 (1956).

1942 (1)

E. Wickers, Chem. Eng. News 39, 1111 (1942).
[CrossRef]

1902 (1)

E. Brodhun, O. Schönrock, Z. Instrumentenk 22, 357 (1902).

Barrell, R.

R. Barrell, S. Marriner, NPL, Brit. Sci. News2, No. 17.

Brodhun, E.

E. Brodhun, O. Schönrock, Z. Instrumentenk 22, 357 (1902).

Bünnagel, R.

R. Bünnagel, Z. Instrumentenk 73, 214 (1965).

R. Bünnagel, Opt. Acta 3, 81 (1956).
[CrossRef]

R. Bünnagel, Z. Angew. Phys. 8, 447 (1956).

Dew, G. D.

G. D. Dew, J. Sci. Instr. 43, 409 (1966).
[CrossRef]

Marriner, S.

R. Barrell, S. Marriner, NPL, Brit. Sci. News2, No. 17.

Schönrock, O.

E. Brodhun, O. Schönrock, Z. Instrumentenk 22, 357 (1902).

Timoshenko, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Vol. 2, p. 295.

Wickers, E.

E. Wickers, Chem. Eng. News 39, 1111 (1942).
[CrossRef]

Woinowsky-Krieger, S.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Vol. 2, p. 295.

Chem. Eng. News (1)

E. Wickers, Chem. Eng. News 39, 1111 (1942).
[CrossRef]

J. Sci. Instr. (1)

G. D. Dew, J. Sci. Instr. 43, 409 (1966).
[CrossRef]

Opt. Acta (1)

R. Bünnagel, Opt. Acta 3, 81 (1956).
[CrossRef]

Z. Angew. Phys. (1)

R. Bünnagel, Z. Angew. Phys. 8, 447 (1956).

Z. Instrumentenk (2)

E. Brodhun, O. Schönrock, Z. Instrumentenk 22, 357 (1902).

R. Bünnagel, Z. Instrumentenk 73, 214 (1965).

Other (2)

R. Barrell, S. Marriner, NPL, Brit. Sci. News2, No. 17.

S. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill Book Co., Inc., New York, 1959), Vol. 2, p. 295.

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Figures (9)

Fig. 1
Fig. 1

Optical arrangement of the instrument: A—light source, B0, B1—diaphragm, F—monochromatic filter, K—camera, L1—condenser, L2—field lens, L3—large lens, L4—photoobjective, M—focusing screen, P—test flat or glass standard, Q—mercury mirror or test plate, S1—deviation mirror, and S2—deviation mirror (semireflecting), scale in millimeters.

Fig. 2
Fig. 2

Mechanical arrangement of the instrument: 1—base plate, 2—leveling screws, 3—columns for support plate, 4—carriage, 5—tracks for carriage, 6—columns for the bearing, 7—tip axis, 8—tip frame, 9—drawbar for tip frame, 10—bridge for lens L3 with adjustment arrangement, 11—plate for illumination arrangement, 12—cardan joint for plate 11, 13—adjustment support, 14—cardan joint for camera, 15—washer for focusing, 16—adjustment support, 30—support plate, A—light source, B0, B1—diaphragm, F—monochromatic filter, K—camera, L1—condenser, L2—field lens, L3—large lens, L4—photoobjective, M—focusing screen, P—test plate, Q—mercury holder, S1—deviation mirror, and S2—deviation mirror (semireflecting).

Fig. 3
Fig. 3

Mechanical arrangement of test plate, standard plate, and carriage: 1—base plate, 3—columns for support plate, 4—carriage, 5—carriage tracks, 30—support plate for mercury vessel, 31—nipple for glass plate, 32—leveling screws for mercury vessel, 33—columns for upper plate, 34—plate springs, 35—support for upper plate, 36—leveling screws for upper plate, 37—worm gear with flexible spindle, 38—bearing pins, 39—hinged plates for six-point suspension, 42—table plate of the carriage, 44—bearing nipples for plate 30, 45—bearing pans, 46—flexible spindle, Ag—silver plate 1 mm thick, Hg—mercury about 0.2 mm thick, G—lower glass plate, P—test plate, Q—mercury vessel, and R—groove.

Fig. 4
Fig. 4

View of the instrument. A—light source, B0, B1—diaphragm, F—monochromatic filter, K—camera, L1—condenser, L3—large lens, L4—photoobjective, M—focusing screen, Q—mercury vessel, S1—deviation mirror, S2—deviation mirror (semireflecting), 1—base plate, 2—adjustive screws, 3—columns for mercury vessel Q and test plate P, 5—carriage tracks, 7—tip axis, 8—tip frame, 9—drawbar, 10—bridge for collimator lens, 15—washer for focusing, 35—support for upper plate, and 36/37—leveling screws and worm gear with flexible spindle for upper plate.

Fig. 5
Fig. 5

Path of the interfering rays; B0—diaphragm, B0′—image of Bo reflected from P, B ¯ 0 —image of B0 reflected from Q, E—surface element of P, E—surface element of Q, E′, Ē′—images from E, Ē on M, L3—large lens, L4—photoobjective, M—focusing screen, P—test flat, Q—reference flat, S2—deviation mirror, δ —distance of P and Q, ~0.1 mm, and —angle between P and Q, ~5 see of arc.

Fig. 6
Fig. 6

v(s) as a function of distance s from center 0. + P0 and −P0 are in optimal position.

Fig. 7
Fig. 7

Illustration of the distortion: P ¯ —image point without distortion, Δs′—difference caused by distortion.

Fig. 8
Fig. 8

Multiple beam interferogram, 240-mm diam × 30-mm circular flat supported at six points on the periphery above a mercury mirror as a standard of flatness.

Fig. 9
Fig. 9

Topography of a 240-mm diam × 30-mm circular flat support at six points on the periphery (distance of the level contours 20 nm).

Equations (6)

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v ( s ) = v 0 + c s 2 ,
Δ s = v ¯ s - s
s = 0 P v ( s ) d s = 0 P ( v 0 + c s 2 ) d s = v 0 s + c ( s 2 / 3 ) .
v ¯ = ( s 0 / s 0 ) ,
s 0 = 0 P v ( s ) d s = 0 P 0 ( v 0 + c s 2 ) d s - v 0 s 0 + c ( s 0 3 / 3 ) .
v ¯ = v 0 + c ( s 0 2 / 3 ) ,

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