Abstract

The conditions for and formation of low-spatial-frequency beat patterns between superposed grid structures are studied. The application of moiré techniques for Fourier analysis of incoherently illuminated distributions is demonstrated. The different multiples of the fundamental spatial frequency of a grating are used to form distinguishable moiré patterns. Two particular applications are treated: increased sensitivity from fringe multiplication in a moiré display and examination of the element-profile shape of gratings. Moiré procedures with two, and with multiple, gratings are discussed. Indications of moiré pattern microstructures and moiré fringe profiles are indicated.

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  1. Lord Rayleigh, Phil. Mag. 47, 81, 193 (1874).
  2. J. Guild, The Interference Systems of Crossed Diffraction Gratings (Clarendon, Oxford, England, 1956).
  3. O. Bryngdahl, J. Opt. Soc. Am. 64, 1287 (1974).
  4. C. A. Sciammarella, Exp. Mech. 5, 154 (1965).
  5. G. L. Rogers, Proc. Phys. Soc. 73, 142 (1959).
  6. R. Lehmann and A. Wiemer, Feingerätetechnik 2, 199 (1953).
  7. O. Bryngdahl and A. W. Lohmann, J. Opt. Soc. Am. 58, 141 (1968); O. Bryngdahl, J. Opt. Soc. Am. 59, 142 (1969).
  8. D. Post, Appl. Opt. 6, 1938 (1967); Appl. Opt. 10, 901 (1971).
  9. J. M. Burch, in Progress in Optics, II, edited by E. Wolf (North—Holland, Amsterdam, 1963), p. 73.
  10. J. Ebbeni, Nouv. Rev. d'Opt. Appl. 1, 333 (1970).
  11. G. A. R. Foster, J. Text. Inst. 21, T18 (1930).
  12. M. Born, R. Fürth, and R. W. Pringle, Nature 156, 756 (1945).
  13. I. Leifer, G. L. Rogers, and N. W. F. Stephens, Opt. Acta 16, 535 (1969).
  14. K. Murata in Progress in Optics, V, edited by E. Wolf (North–Holland, Amsterdam, 1966), p. 201.
  15. L. Mertz, Transformations in Optics (Wiley, New York, 1965).
  16. R. H. Katyl, Appl. Opt. 11, 2278 (1972).

Born, M.

M. Born, R. Fürth, and R. W. Pringle, Nature 156, 756 (1945).

Bryngdahl, O.

O. Bryngdahl, J. Opt. Soc. Am. 64, 1287 (1974).

O. Bryngdahl and A. W. Lohmann, J. Opt. Soc. Am. 58, 141 (1968); O. Bryngdahl, J. Opt. Soc. Am. 59, 142 (1969).

Burch, J. M.

J. M. Burch, in Progress in Optics, II, edited by E. Wolf (North—Holland, Amsterdam, 1963), p. 73.

Ebbeni, J.

J. Ebbeni, Nouv. Rev. d'Opt. Appl. 1, 333 (1970).

Foster, G. A. R.

G. A. R. Foster, J. Text. Inst. 21, T18 (1930).

Fürth, R.

M. Born, R. Fürth, and R. W. Pringle, Nature 156, 756 (1945).

Guild, J.

J. Guild, The Interference Systems of Crossed Diffraction Gratings (Clarendon, Oxford, England, 1956).

Katyl, R. H.

R. H. Katyl, Appl. Opt. 11, 2278 (1972).

Lehmann, R.

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

Leifer, I.

I. Leifer, G. L. Rogers, and N. W. F. Stephens, Opt. Acta 16, 535 (1969).

Lohmann, A. W.

O. Bryngdahl and A. W. Lohmann, J. Opt. Soc. Am. 58, 141 (1968); O. Bryngdahl, J. Opt. Soc. Am. 59, 142 (1969).

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

Murata, K.

K. Murata in Progress in Optics, V, edited by E. Wolf (North–Holland, Amsterdam, 1966), p. 201.

Post, D.

D. Post, Appl. Opt. 6, 1938 (1967); Appl. Opt. 10, 901 (1971).

Pringle, R. W.

M. Born, R. Fürth, and R. W. Pringle, Nature 156, 756 (1945).

Rayleigh, Lord

Lord Rayleigh, Phil. Mag. 47, 81, 193 (1874).

Rogers, G. L.

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

I. Leifer, G. L. Rogers, and N. W. F. Stephens, Opt. Acta 16, 535 (1969).

Sciammarella, C. A.

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

Stephens, N. W. F.

I. Leifer, G. L. Rogers, and N. W. F. Stephens, Opt. Acta 16, 535 (1969).

Wiemer, A.

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

Other

Lord Rayleigh, Phil. Mag. 47, 81, 193 (1874).

J. Guild, The Interference Systems of Crossed Diffraction Gratings (Clarendon, Oxford, England, 1956).

O. Bryngdahl, J. Opt. Soc. Am. 64, 1287 (1974).

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

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

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

O. Bryngdahl and A. W. Lohmann, J. Opt. Soc. Am. 58, 141 (1968); O. Bryngdahl, J. Opt. Soc. Am. 59, 142 (1969).

D. Post, Appl. Opt. 6, 1938 (1967); Appl. Opt. 10, 901 (1971).

J. M. Burch, in Progress in Optics, II, edited by E. Wolf (North—Holland, Amsterdam, 1963), p. 73.

J. Ebbeni, Nouv. Rev. d'Opt. Appl. 1, 333 (1970).

G. A. R. Foster, J. Text. Inst. 21, T18 (1930).

M. Born, R. Fürth, and R. W. Pringle, Nature 156, 756 (1945).

I. Leifer, G. L. Rogers, and N. W. F. Stephens, Opt. Acta 16, 535 (1969).

K. Murata in Progress in Optics, V, edited by E. Wolf (North–Holland, Amsterdam, 1966), p. 201.

L. Mertz, Transformations in Optics (Wiley, New York, 1965).

R. H. Katyl, Appl. Opt. 11, 2278 (1972).

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