Abstract

Interference methods are reviewed—particularly those developed at the German Academy of Sciences in Berlin—with which the deviations of an optically flat surface from the ideal plane can be measured with a high degree of exactness. One aid to achieve this is the relative methods which measure the differences in planeness between two surfaces. These are then used in the absolute methods which determine the absolute planeness of a surface. This absolute determination can be effected in connection with a liquid surface, or (as done by the authors) only by suitable evaluation of relative measurements between unknown plates in various positional combinations. Experimentally, one uses two- or multiple-beam interference fringes of equal thickness1 or of equal inclination. The fringes are observed visually, scanned, or photographed, and in part several wavelengths or curves of equal density (Äquidensiten) are employed. The survey also brings the following new methods: a relative method, where, with the aid of fringes of superposition, the fringe separation is subdivided equidistantly thus achieving an increase of measuring precision, and an absolute method which determines the deviations of a surface from ideal planeness along arbitrary central sections, without a liquid surface, from four relative interference photographs.

© 1967 Optical Society of America

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References

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  1. M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1964).
  2. C. Dufour, Ann. Phys. (Paris)6, Thèse (1951).
  3. J. Schwider, Opt. Acta 12, 65 (1965).
    [CrossRef]
  4. W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961); Contributions to Interference Microscopy, translated by J. H. Dickson (Hilger & Watts, London, 1964).
  5. E. Lau, W. Krug, Die Äquidensitometrie (Akademie-Verlag, Berlin, 1957).
  6. O. Lummer, Handbuch der Physikalischen Optik, E. Gehrcke, Ed. (J. A. Barth, Leipzig, 1927), Vol. I, p. 416.
  7. H. Koch, Optik und Spektroskopie aller Wellenldngen Jena 1960 (Akademie-Verlag, Berlin, 1962), p. 139.
  8. T. Sakurai, K. Shishido, Sci. Rept. Res. Inst. Tohoku Univ. AI, No. 1 (1949).
  9. J. B. Saunders, J. Res. Natl. Bur. Std. 47, 148 (1951).
    [CrossRef]
  10. D. R. Herriott, J. Opt. Soc. Am. 51, 1142 (1961).
    [CrossRef]
  11. J. Schwider, “Absolute Ebenheitsprüfung aus Relativmessungen zwischen drei Planflächen”, dissertation at the Humboldt-University, Berlin (1966).
  12. C. Fabry, A. Perot, Ann. Chim. Phys. 12, 455 (1897).
  13. S. Tolansky, Multiple-Beam Interferometry (Clarendon Press, Oxford, 1948).
  14. G. Koppelmann, K. Krebs, Optik 18, 349, 358 (1961).
  15. O. Schbnrock, Z. Instrumentenk. 25, 148 (1905); Z. Instrumentenk. 28, 180 (1908).
  16. F. L. Roesler, J. Opt. Soc. Am. 52, 471 (1962).
  17. Rayleigh, Nature 48, 212 (1893).
  18. E. Einsporn, Feingerätetechnik 4, 539 (1955);Feingerätetechnik 10, 67 (1961).
  19. R. Bünnagel, Z. Angew. Phys. 8, 342 (1956); Opt. Acta 3, 81 (1956); Z. Instrumentenk. 73, 214 (1965).
  20. H. Barrell, R. Marriner, Brit. Sci. News 2, 130 (1949).
  21. E. Emerson, J. Res. Natl. Bur. Std. 49, 336 (1952).
    [CrossRef]
  22. O. Schönrock, Z. Instrumentenk. 59, 31 (1939).
  23. J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966).
    [CrossRef]
  24. G. Schulz, Opt. Acta14, in press (1967).
    [CrossRef]
  25. E. Ingelstam, Arkiv Fysik 7, 309 (1953).
  26. H. Wolter, Handbuch der Physik, S. Flügge, Ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 577.
  27. B. S. Thornton, Opt. Acta 4, 41 (1957).
    [CrossRef]
  28. E. Menzel, Naturwiss. 46, 105 (1959).
    [CrossRef]
  29. G. Koppelmann, Habilitationsschrift TU Berlin1965, D 83, S. 194.; Opt. Acta 13, 211 (1966).
  30. G. Schulz, Naturwiss. 48, 565 (1961). U.-C. Minor, G. Schulz, Wiss. Z. Hochsch. Elektrotech. 8, 475 (1962).
    [CrossRef]

1966

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966).
[CrossRef]

1965

J. Schwider, Opt. Acta 12, 65 (1965).
[CrossRef]

1962

1961

G. Koppelmann, K. Krebs, Optik 18, 349, 358 (1961).

D. R. Herriott, J. Opt. Soc. Am. 51, 1142 (1961).
[CrossRef]

G. Schulz, Naturwiss. 48, 565 (1961). U.-C. Minor, G. Schulz, Wiss. Z. Hochsch. Elektrotech. 8, 475 (1962).
[CrossRef]

1959

E. Menzel, Naturwiss. 46, 105 (1959).
[CrossRef]

1957

B. S. Thornton, Opt. Acta 4, 41 (1957).
[CrossRef]

1956

R. Bünnagel, Z. Angew. Phys. 8, 342 (1956); Opt. Acta 3, 81 (1956); Z. Instrumentenk. 73, 214 (1965).

1955

E. Einsporn, Feingerätetechnik 4, 539 (1955);Feingerätetechnik 10, 67 (1961).

1953

E. Ingelstam, Arkiv Fysik 7, 309 (1953).

1952

E. Emerson, J. Res. Natl. Bur. Std. 49, 336 (1952).
[CrossRef]

1951

J. B. Saunders, J. Res. Natl. Bur. Std. 47, 148 (1951).
[CrossRef]

1949

H. Barrell, R. Marriner, Brit. Sci. News 2, 130 (1949).

T. Sakurai, K. Shishido, Sci. Rept. Res. Inst. Tohoku Univ. AI, No. 1 (1949).

1939

O. Schönrock, Z. Instrumentenk. 59, 31 (1939).

1905

O. Schbnrock, Z. Instrumentenk. 25, 148 (1905); Z. Instrumentenk. 28, 180 (1908).

1897

C. Fabry, A. Perot, Ann. Chim. Phys. 12, 455 (1897).

1893

Rayleigh, Nature 48, 212 (1893).

Barrell, H.

H. Barrell, R. Marriner, Brit. Sci. News 2, 130 (1949).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1964).

Bünnagel, R.

R. Bünnagel, Z. Angew. Phys. 8, 342 (1956); Opt. Acta 3, 81 (1956); Z. Instrumentenk. 73, 214 (1965).

Dufour, C.

C. Dufour, Ann. Phys. (Paris)6, Thèse (1951).

Einsporn, E.

E. Einsporn, Feingerätetechnik 4, 539 (1955);Feingerätetechnik 10, 67 (1961).

Emerson, E.

E. Emerson, J. Res. Natl. Bur. Std. 49, 336 (1952).
[CrossRef]

Fabry, C.

C. Fabry, A. Perot, Ann. Chim. Phys. 12, 455 (1897).

Herriott, D. R.

Ingelstam, E.

E. Ingelstam, Arkiv Fysik 7, 309 (1953).

Koch, H.

H. Koch, Optik und Spektroskopie aller Wellenldngen Jena 1960 (Akademie-Verlag, Berlin, 1962), p. 139.

Koppelmann, G.

G. Koppelmann, K. Krebs, Optik 18, 349, 358 (1961).

G. Koppelmann, Habilitationsschrift TU Berlin1965, D 83, S. 194.; Opt. Acta 13, 211 (1966).

Krebs, K.

G. Koppelmann, K. Krebs, Optik 18, 349, 358 (1961).

Krug, W.

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961); Contributions to Interference Microscopy, translated by J. H. Dickson (Hilger & Watts, London, 1964).

E. Lau, W. Krug, Die Äquidensitometrie (Akademie-Verlag, Berlin, 1957).

Lau, E.

E. Lau, W. Krug, Die Äquidensitometrie (Akademie-Verlag, Berlin, 1957).

Lummer, O.

O. Lummer, Handbuch der Physikalischen Optik, E. Gehrcke, Ed. (J. A. Barth, Leipzig, 1927), Vol. I, p. 416.

Marriner, R.

H. Barrell, R. Marriner, Brit. Sci. News 2, 130 (1949).

Menzel, E.

E. Menzel, Naturwiss. 46, 105 (1959).
[CrossRef]

Minkwitz, G.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966).
[CrossRef]

Perot, A.

C. Fabry, A. Perot, Ann. Chim. Phys. 12, 455 (1897).

Rayleigh,

Rayleigh, Nature 48, 212 (1893).

Riekher, R.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966).
[CrossRef]

Rienitz, J.

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961); Contributions to Interference Microscopy, translated by J. H. Dickson (Hilger & Watts, London, 1964).

Roesler, F. L.

Sakurai, T.

T. Sakurai, K. Shishido, Sci. Rept. Res. Inst. Tohoku Univ. AI, No. 1 (1949).

Saunders, J. B.

J. B. Saunders, J. Res. Natl. Bur. Std. 47, 148 (1951).
[CrossRef]

Schbnrock, O.

O. Schbnrock, Z. Instrumentenk. 25, 148 (1905); Z. Instrumentenk. 28, 180 (1908).

Schönrock, O.

O. Schönrock, Z. Instrumentenk. 59, 31 (1939).

Schulz, G.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966).
[CrossRef]

G. Schulz, Naturwiss. 48, 565 (1961). U.-C. Minor, G. Schulz, Wiss. Z. Hochsch. Elektrotech. 8, 475 (1962).
[CrossRef]

G. Schulz, Opt. Acta14, in press (1967).
[CrossRef]

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961); Contributions to Interference Microscopy, translated by J. H. Dickson (Hilger & Watts, London, 1964).

Schwider, J.

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966).
[CrossRef]

J. Schwider, Opt. Acta 12, 65 (1965).
[CrossRef]

J. Schwider, “Absolute Ebenheitsprüfung aus Relativmessungen zwischen drei Planflächen”, dissertation at the Humboldt-University, Berlin (1966).

Shishido, K.

T. Sakurai, K. Shishido, Sci. Rept. Res. Inst. Tohoku Univ. AI, No. 1 (1949).

Thornton, B. S.

B. S. Thornton, Opt. Acta 4, 41 (1957).
[CrossRef]

Tolansky, S.

S. Tolansky, Multiple-Beam Interferometry (Clarendon Press, Oxford, 1948).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1964).

Wolter, H.

H. Wolter, Handbuch der Physik, S. Flügge, Ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 577.

Ann. Chim. Phys.

C. Fabry, A. Perot, Ann. Chim. Phys. 12, 455 (1897).

Arkiv Fysik

E. Ingelstam, Arkiv Fysik 7, 309 (1953).

Brit. Sci. News

H. Barrell, R. Marriner, Brit. Sci. News 2, 130 (1949).

Feingerätetechnik

E. Einsporn, Feingerätetechnik 4, 539 (1955);Feingerätetechnik 10, 67 (1961).

J. Opt. Soc. Am.

J. Res. Natl. Bur. Std.

J. B. Saunders, J. Res. Natl. Bur. Std. 47, 148 (1951).
[CrossRef]

E. Emerson, J. Res. Natl. Bur. Std. 49, 336 (1952).
[CrossRef]

Nature

Rayleigh, Nature 48, 212 (1893).

Naturwiss.

E. Menzel, Naturwiss. 46, 105 (1959).
[CrossRef]

G. Schulz, Naturwiss. 48, 565 (1961). U.-C. Minor, G. Schulz, Wiss. Z. Hochsch. Elektrotech. 8, 475 (1962).
[CrossRef]

Opt. Acta

B. S. Thornton, Opt. Acta 4, 41 (1957).
[CrossRef]

J. Schwider, G. Schulz, R. Riekher, G. Minkwitz, Opt. Acta 13, 103 (1966).
[CrossRef]

J. Schwider, Opt. Acta 12, 65 (1965).
[CrossRef]

Optik

G. Koppelmann, K. Krebs, Optik 18, 349, 358 (1961).

Sci. Rept. Res. Inst. Tohoku Univ.

T. Sakurai, K. Shishido, Sci. Rept. Res. Inst. Tohoku Univ. AI, No. 1 (1949).

Z. Angew. Phys.

R. Bünnagel, Z. Angew. Phys. 8, 342 (1956); Opt. Acta 3, 81 (1956); Z. Instrumentenk. 73, 214 (1965).

Z. Instrumentenk.

O. Schönrock, Z. Instrumentenk. 59, 31 (1939).

O. Schbnrock, Z. Instrumentenk. 25, 148 (1905); Z. Instrumentenk. 28, 180 (1908).

Other

J. Schwider, “Absolute Ebenheitsprüfung aus Relativmessungen zwischen drei Planflächen”, dissertation at the Humboldt-University, Berlin (1966).

S. Tolansky, Multiple-Beam Interferometry (Clarendon Press, Oxford, 1948).

M. Born, E. Wolf, Principles of Optics (Pergamon Press, London, 1964).

C. Dufour, Ann. Phys. (Paris)6, Thèse (1951).

W. Krug, J. Rienitz, G. Schulz, Beiträge zur Interferenzmikroskopie (Akademie-Verlag, Berlin, 1961); Contributions to Interference Microscopy, translated by J. H. Dickson (Hilger & Watts, London, 1964).

E. Lau, W. Krug, Die Äquidensitometrie (Akademie-Verlag, Berlin, 1957).

O. Lummer, Handbuch der Physikalischen Optik, E. Gehrcke, Ed. (J. A. Barth, Leipzig, 1927), Vol. I, p. 416.

H. Koch, Optik und Spektroskopie aller Wellenldngen Jena 1960 (Akademie-Verlag, Berlin, 1962), p. 139.

G. Schulz, Opt. Acta14, in press (1967).
[CrossRef]

H. Wolter, Handbuch der Physik, S. Flügge, Ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 577.

G. Koppelmann, Habilitationsschrift TU Berlin1965, D 83, S. 194.; Opt. Acta 13, 211 (1966).

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Figures (13)

Fig. 1
Fig. 1

Fundamental arrangement for relative measurements in reflected light (on the left) and transmitted light (on the right) with two-beam (heavy) and multiple-beam interference (light).

Fig. 2
Fig. 2

Comparison of the intensity distribution of two-beam and multiple-beam interference.

Fig. 3
Fig. 3

Multiple-beam interference fringes with (a) one and (b) several wavelengths.

Fig. 4
Fig. 4

Arrangement with multiple-beam interference of several wavelengths according to the principle of fringes of superposition. S, white light source; IF, interference filter; W, wedge; A, aperture stop; FP, Fabry-Perot interferometer.

Fig. 5
Fig. 5

Explanation of increase of sensitivity by means of fringes of superposition.

Fig. 6
Fig. 6

Interference microphotograph of a defect dielectric film in scale of 60:1; N = 20. (a) White light fringes. (b) With interference filter of bandwidth 4 nm. (c) With interference filter of bandwidth 12 nm.

Fig. 7
Fig. 7

Measurement of radius at fringes of equal inclination.

Fig. 8
Fig. 8

Intensity-measured thickness distribution along a section by means of multiple-beam interference of equal inclination. S source; PC, pressure chamber; M, multiplier.

Fig. 9
Fig. 9

Model for the derivation of Eq. (1).

Fig. 10
Fig. 10

Special case in order to demonstrate the unsolvability on the whole surface.

Fig. 11
Fig. 11

Positional combinations for three central sections. The points 1, 2, and 3 are the centers of the small circles, where 1 is represented by A, B, and C, respectively.

Fig. 12
Fig. 12

Example of a measurement. (a) Along a section (mean square deviation of a single absolute measurement: long bars; mean square deviation of the mean belonging to: short bars, i.e., < λ/300, λ = 436 nm). (b) Topographical map (contour lines) of a plate.

Fig. 13
Fig. 13

Plates A, B, and C with four positional combinations (from each of these four combinations a photograph must be taken). The plane of reference for each flat surface passes through points 1, 2, and 3 of this surface. r2r3, r1 = r2 (any other value of r1 is also possible, but in this case the method is somewhat modified). In the last combination the plate B has been rotated by an angle Φ compared with the first combination. Φ is arbitrary; in the drawn example Φ = 1/5 (2π). Here five sections of each plate are represented. The three sections containing points 1 coincide in the first, second, and third combination; the other three sections drawn with heavy lines coincide in the second, third, and fourth combinations.

Equations (1)

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x = ( 1 / 2 ) ( a - b + c ) , y = ( 1 / 2 ) ( b - c + a ) , z = ( 1 / 2 ) ( c - a + b ) .

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