Abstract

The superposition of several periodic or quasiperiodic patterns produces moiré effects. In particular, the combination of three grid structures adds great flexibility to the use of moiré phenomena. Information about the fringe structure, given by vector addition in Fourier space, allows investigation of formations, interpretation, and expectation problems concerning moiré-pattern parameters. Any frequency and orientation of the pattern is possible, using three-line gratings. On the other hand, three quasiperiodic gratings with variations of frequency and/or orientation result in a zone-plate shape of the moiré pattern regardless of grating distortions. Both elliptical and hyperbolic zone plates occur. Several illustrations demonstrate these phenomena and indicate some potential applications.

© 1974 Optical Society of America

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  1. Lord Rayleigh, Philos. Mag. 47, 81 (1874); Philos. Mag. 47, 193 (1874).
  2. A. Righi, Nuovo Cimento 21, 203 (1887); Nuovo Cimento 22, 10 (1888).
  3. A. Schuster, Philos. Mag. 48 (6), 609 (1924).
  4. V. Ronchi, Attualita scientifiche, No. 37 (N. Zanichelli, Bologna, 1925), Ch. 9.
  5. C. V. Raman and S. K. Datta, Trans. Opt. Soc. 27, 51 (1925/26).
  6. S. K. Datta, Trans. Opt. Soc. 28, 214 (1926/27).
  7. P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, Oxford, England, 1969); A. J. Durelli and V. J. Parks, Moiré Analysis of Strain (Prentice-Hall, Englewood Cliffs, N. J., 1970).
  8. R. Lehmann and A. Wiener, Feingerätetechnik 2, 199 (1953).
  9. A. Pirard, Analyse des Contraintes, Mém. GAMAC 5, No. 2, 1 (1960).
  10. G. Oster, M. Wasserman, and C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).
  11. G. L. Rogers, Proc. Phys. Soc. 73, 142 (1959).
  12. A. W. Lohmann, Optik 18, 514 (1961).
  13. C. A. Sciammarella, Exp. Mech. 5, 154 (1965).
  14. A. W. Lohmann and D. P. Paris, Appl. Opt. 6, 1567 (1967).
  15. I. Leifer, J. M. Walls, and H. N. Southworth, Opt. Acta 20, 33 (1973).
  16. J. Moser, S. Bahčevandžijev, M. Janoska, and Lj. Janićijević, God. Zborn. PMF Skopje 15A, 113 (1964).
  17. R. L. Conger, L. T. Long, and J. A. Parks, Appl. Opt. 7, 623 (1968).
  18. L. A. Sayce, Photogr. J. 80, 454 (1940).

1973 (1)

I. Leifer, J. M. Walls, and H. N. Southworth, Opt. Acta 20, 33 (1973).

1968 (1)

R. L. Conger, L. T. Long, and J. A. Parks, Appl. Opt. 7, 623 (1968).

1967 (1)

A. W. Lohmann and D. P. Paris, Appl. Opt. 6, 1567 (1967).

1965 (1)

C. A. Sciammarella, Exp. Mech. 5, 154 (1965).

1964 (2)

J. Moser, S. Bahčevandžijev, M. Janoska, and Lj. Janićijević, God. Zborn. PMF Skopje 15A, 113 (1964).

G. Oster, M. Wasserman, and C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).

1961 (1)

A. W. Lohmann, Optik 18, 514 (1961).

1960 (1)

A. Pirard, Analyse des Contraintes, Mém. GAMAC 5, No. 2, 1 (1960).

1959 (1)

G. L. Rogers, Proc. Phys. Soc. 73, 142 (1959).

1953 (1)

R. Lehmann and A. Wiener, Feingerätetechnik 2, 199 (1953).

1940 (1)

L. A. Sayce, Photogr. J. 80, 454 (1940).

1925 (1)

V. Ronchi, Attualita scientifiche, No. 37 (N. Zanichelli, Bologna, 1925), Ch. 9.

1924 (1)

A. Schuster, Philos. Mag. 48 (6), 609 (1924).

1887 (1)

A. Righi, Nuovo Cimento 21, 203 (1887); Nuovo Cimento 22, 10 (1888).

1874 (1)

Lord Rayleigh, Philos. Mag. 47, 81 (1874); Philos. Mag. 47, 193 (1874).

Bahcevandžijev, S.

J. Moser, S. Bahčevandžijev, M. Janoska, and Lj. Janićijević, God. Zborn. PMF Skopje 15A, 113 (1964).

Conger, R. L.

R. L. Conger, L. T. Long, and J. A. Parks, Appl. Opt. 7, 623 (1968).

Datta, S. K.

S. K. Datta, Trans. Opt. Soc. 28, 214 (1926/27).

C. V. Raman and S. K. Datta, Trans. Opt. Soc. 27, 51 (1925/26).

Janicijevic, Lj.

J. Moser, S. Bahčevandžijev, M. Janoska, and Lj. Janićijević, God. Zborn. PMF Skopje 15A, 113 (1964).

Janoska, M.

J. Moser, S. Bahčevandžijev, M. Janoska, and Lj. Janićijević, God. Zborn. PMF Skopje 15A, 113 (1964).

Lehmann, R.

R. Lehmann and A. Wiener, Feingerätetechnik 2, 199 (1953).

Leifer, I.

I. Leifer, J. M. Walls, and H. N. Southworth, Opt. Acta 20, 33 (1973).

Lohmann, A. W.

A. W. Lohmann and D. P. Paris, Appl. Opt. 6, 1567 (1967).

A. W. Lohmann, Optik 18, 514 (1961).

Long, L. T.

R. L. Conger, L. T. Long, and J. A. Parks, Appl. Opt. 7, 623 (1968).

Moser, J.

J. Moser, S. Bahčevandžijev, M. Janoska, and Lj. Janićijević, God. Zborn. PMF Skopje 15A, 113 (1964).

Oster, G.

G. Oster, M. Wasserman, and C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).

Paris, D. P.

A. W. Lohmann and D. P. Paris, Appl. Opt. 6, 1567 (1967).

Parks, J. A.

R. L. Conger, L. T. Long, and J. A. Parks, Appl. Opt. 7, 623 (1968).

Pirard, A.

A. Pirard, Analyse des Contraintes, Mém. GAMAC 5, No. 2, 1 (1960).

Raman, C. V.

C. V. Raman and S. K. Datta, Trans. Opt. Soc. 27, 51 (1925/26).

Rayleigh, Lord

Lord Rayleigh, Philos. Mag. 47, 81 (1874); Philos. Mag. 47, 193 (1874).

Righi, A.

A. Righi, Nuovo Cimento 21, 203 (1887); Nuovo Cimento 22, 10 (1888).

Rogers, G. L.

G. L. Rogers, Proc. Phys. Soc. 73, 142 (1959).

Ronchi, V.

V. Ronchi, Attualita scientifiche, No. 37 (N. Zanichelli, Bologna, 1925), Ch. 9.

Sayce, L. A.

L. A. Sayce, Photogr. J. 80, 454 (1940).

Schuster, A.

A. Schuster, Philos. Mag. 48 (6), 609 (1924).

Sciammarella, C. A.

C. A. Sciammarella, Exp. Mech. 5, 154 (1965).

Southworth, H. N.

I. Leifer, J. M. Walls, and H. N. Southworth, Opt. Acta 20, 33 (1973).

Theocaris, P. S.

P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, Oxford, England, 1969); A. J. Durelli and V. J. Parks, Moiré Analysis of Strain (Prentice-Hall, Englewood Cliffs, N. J., 1970).

Walls, J. M.

I. Leifer, J. M. Walls, and H. N. Southworth, Opt. Acta 20, 33 (1973).

Wasserman, M.

G. Oster, M. Wasserman, and C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).

Wiener, A.

R. Lehmann and A. Wiener, Feingerätetechnik 2, 199 (1953).

Zwerling, C.

G. Oster, M. Wasserman, and C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).

Other (18)

Lord Rayleigh, Philos. Mag. 47, 81 (1874); Philos. Mag. 47, 193 (1874).

A. Righi, Nuovo Cimento 21, 203 (1887); Nuovo Cimento 22, 10 (1888).

A. Schuster, Philos. Mag. 48 (6), 609 (1924).

V. Ronchi, Attualita scientifiche, No. 37 (N. Zanichelli, Bologna, 1925), Ch. 9.

C. V. Raman and S. K. Datta, Trans. Opt. Soc. 27, 51 (1925/26).

S. K. Datta, Trans. Opt. Soc. 28, 214 (1926/27).

P. S. Theocaris, Moiré Fringes in Strain Analysis (Pergamon, Oxford, England, 1969); A. J. Durelli and V. J. Parks, Moiré Analysis of Strain (Prentice-Hall, Englewood Cliffs, N. J., 1970).

R. Lehmann and A. Wiener, Feingerätetechnik 2, 199 (1953).

A. Pirard, Analyse des Contraintes, Mém. GAMAC 5, No. 2, 1 (1960).

G. Oster, M. Wasserman, and C. Zwerling, J. Opt. Soc. Am. 54, 169 (1964).

G. L. Rogers, Proc. Phys. Soc. 73, 142 (1959).

A. W. Lohmann, Optik 18, 514 (1961).

C. A. Sciammarella, Exp. Mech. 5, 154 (1965).

A. W. Lohmann and D. P. Paris, Appl. Opt. 6, 1567 (1967).

I. Leifer, J. M. Walls, and H. N. Southworth, Opt. Acta 20, 33 (1973).

J. Moser, S. Bahčevandžijev, M. Janoska, and Lj. Janićijević, God. Zborn. PMF Skopje 15A, 113 (1964).

R. L. Conger, L. T. Long, and J. A. Parks, Appl. Opt. 7, 623 (1968).

L. A. Sayce, Photogr. J. 80, 454 (1940).

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