Abstract

A summary of the main known forms of moiré fringes for visual metrological applications is given. To observe and track displacements of a moving fringe in a conventional moiré system presents certain difficulties, as the individual fringes have no distinctive character. New types of moiré fringes were found and are discussed, where a recognizable unique fringe indicates an also unique position of a grating, displaced relative to its stationary counterpart.

© 1964 Optical Society of America

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References

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  1. E. Lau, K. Mütze, Wiss. Ann. 1, Jg. (1952), H. 1, P. 2.
  2. R. Lehmann, K. Mütze, H. Voigt, A. Wiemer, Feingeratetechnik 2, 153 (1953).
  3. R. Lehmann, A. Wiemer, Feingeratetechnik 2, 199 (1953).
  4. A. Wiemer, R. Lehmann, H. Voigt, Feingeratetechnik 3, 161 (1954).
  5. J. Guild, The Interference Systems of Crossed Diffraction Gratings (Clarendon Press, Oxford, 1956).
  6. J. M. Burch, “Photographic Production of Scales for Moiré Fringe Applications” in Optics in Metrology, edited by P. Mollet (Pergamon Press, Oxford, 1960), p. 361.
  7. J. M. Burch, “The Possibilities of Moiré-Fringe Interferometry”, Symposium on Interferometry (H. M. Stationery Office, London, 1960), p. 179.
  8. J. Guild, Diffraction Gratings as Measuring Scales (Oxford Univ. Press, New York, 1960).
  9. R. Pegis, private communication and pending patent.

1954 (1)

A. Wiemer, R. Lehmann, H. Voigt, Feingeratetechnik 3, 161 (1954).

1953 (2)

R. Lehmann, K. Mütze, H. Voigt, A. Wiemer, Feingeratetechnik 2, 153 (1953).

R. Lehmann, A. Wiemer, Feingeratetechnik 2, 199 (1953).

1952 (1)

E. Lau, K. Mütze, Wiss. Ann. 1, Jg. (1952), H. 1, P. 2.

Burch, J. M.

J. M. Burch, “Photographic Production of Scales for Moiré Fringe Applications” in Optics in Metrology, edited by P. Mollet (Pergamon Press, Oxford, 1960), p. 361.

J. M. Burch, “The Possibilities of Moiré-Fringe Interferometry”, Symposium on Interferometry (H. M. Stationery Office, London, 1960), p. 179.

Guild, J.

J. Guild, Diffraction Gratings as Measuring Scales (Oxford Univ. Press, New York, 1960).

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

Lau, E.

E. Lau, K. Mütze, Wiss. Ann. 1, Jg. (1952), H. 1, P. 2.

Lehmann, R.

A. Wiemer, R. Lehmann, H. Voigt, Feingeratetechnik 3, 161 (1954).

R. Lehmann, A. Wiemer, Feingeratetechnik 2, 199 (1953).

R. Lehmann, K. Mütze, H. Voigt, A. Wiemer, Feingeratetechnik 2, 153 (1953).

Mütze, K.

R. Lehmann, K. Mütze, H. Voigt, A. Wiemer, Feingeratetechnik 2, 153 (1953).

E. Lau, K. Mütze, Wiss. Ann. 1, Jg. (1952), H. 1, P. 2.

Pegis, R.

R. Pegis, private communication and pending patent.

Voigt, H.

A. Wiemer, R. Lehmann, H. Voigt, Feingeratetechnik 3, 161 (1954).

R. Lehmann, K. Mütze, H. Voigt, A. Wiemer, Feingeratetechnik 2, 153 (1953).

Wiemer, A.

A. Wiemer, R. Lehmann, H. Voigt, Feingeratetechnik 3, 161 (1954).

R. Lehmann, K. Mütze, H. Voigt, A. Wiemer, Feingeratetechnik 2, 153 (1953).

R. Lehmann, A. Wiemer, Feingeratetechnik 2, 199 (1953).

Feingeratetechnik (3)

R. Lehmann, K. Mütze, H. Voigt, A. Wiemer, Feingeratetechnik 2, 153 (1953).

R. Lehmann, A. Wiemer, Feingeratetechnik 2, 199 (1953).

A. Wiemer, R. Lehmann, H. Voigt, Feingeratetechnik 3, 161 (1954).

Wiss. Ann. (1)

E. Lau, K. Mütze, Wiss. Ann. 1, Jg. (1952), H. 1, P. 2.

Other (5)

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

J. M. Burch, “Photographic Production of Scales for Moiré Fringe Applications” in Optics in Metrology, edited by P. Mollet (Pergamon Press, Oxford, 1960), p. 361.

J. M. Burch, “The Possibilities of Moiré-Fringe Interferometry”, Symposium on Interferometry (H. M. Stationery Office, London, 1960), p. 179.

J. Guild, Diffraction Gratings as Measuring Scales (Oxford Univ. Press, New York, 1960).

R. Pegis, private communication and pending patent.

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Figures (13)

Fig. 1
Fig. 1

Moiré fringes generated by a crossed identical grating pair.

Fig. 2
Fig. 2

Moiré fringes generated by a parallel grating pair, with a small difference in their pitch (vernier-fringes).

Fig. 3
Fig. 3

Single grating with random spacing and pitch.

Fig. 4
Fig. 4

Identical grating pair with random spacing and pitch, crossed position; shows single (transparent) fringe. (Crossing angle exaggerated for better demonstration.)

Fig. 5
Fig. 5

Grating pair with random spacing and pitch; mutually negative copies, crossed position; shows single (opaque) fringe. (Small crossing angle.)

Fig. 6
Fig. 6

Single grating with gradually growing pitch.

Fig. 7
Fig. 7

Grating pair with gradually growing pitch, lined up parallel, and displaced from the position of identity (zero position). Passed fringes stay in field of view.

Fig. 8
Fig. 8

Grating pair with gradually growing pitch, crossed position. Unique fringe is vertical to bisector of crossing angle.

Fig. 9
Fig. 9

Position indicator using a grating pair shown on Fig. 8, along a regular (crossed) grating pair. Arrow-shaped unique fringe moves always together with adjoining fringe of the regular crossed system, having the same crossing angle of its lines.

Fig. 10
Fig. 10

(a) Another position indicator arrangement, where pitch size is gradually growing from opposing edges to center. (b) Same as (a), except pitch size is decreasing in the same manner. Unique fringe is straight in both cases.

Fig. 11
Fig. 11

Single grating with out-of-phase section.

Fig. 12
Fig. 12

Grating pair according to Fig. 11, mutually negative copies, crossed position. Unique fringe is straight, while all others form broken line.

Fig. 13
Fig. 13

Illuminating and viewing device.

Tables (1)

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Table I Relationship Between Accuracy, Range and Grating Pitch

Equations (4)

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W P θ ,
M 1 θ ,
W = P 1 · P 2 P 2 P 1 = P 1 · P 2 d ,
M = W P 1 = P 2 P 2 P 1 = P 1 + d d .

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