Abstract

The general properties of interference moiré fringes arising in the transmission of a light beam through a consisting of a reflection and a transmission diffraction grating are considered. The method of system measuring linear displacements, based upon this phenomenon, is applied to a ruling engine for controlling motion of a diffraction grating while it is being cut. These engines have been used to rule diffraction the gratings of very high quality in all respects.

© 1967 Optical Society of America

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References

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  1. F. M. Gerasimov, I. A. Teltevskii, S. N. Spizharskii, S. V. Nesmelov, Opt. Mekh. Promysh. No. 3, 47 (1957).
  2. F. M. Gerasimov, I. A. Teltevskii, S. V. Nesmelov, V. P. Sergeev, Opt. Mekh. Promysh. No. 12, 6 (1958).
  3. F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).
  4. F. M. Gerasimov, E. A. Yakovlev, I. A. Teltevskii, B. V. Koshelev, Opt. Mekh. Promysh. 1, 20 (1964).
  5. G. R. Harrison, G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
    [CrossRef]
  6. H. W. Babcock, Appl. Opt. 1, 415 (1962).
    [CrossRef]
  7. R. F. Jarrell, G. W. Stroke, Appl. Opt. 3, 1254 (1964).
    [CrossRef]
  8. W. R. Horsfield, Appl. Opt. 4, 189 (1965).
    [CrossRef]
  9. G. N. Rassudova, F. M. Gerasimov, Opt. i Spektroskopiya 14, 406, 559 (1963); Opt. Spectry. 14, 215, 295 (1963).
  10. J. Guild, The Interference Systems of Crossed Diffraction Gratings (Oxford University Press, New York, 1956).
  11. J. Guild, Diffraction Gratings as Measuring Scales (Oxford University Press, New York, 1960).
  12. G. N. Rassudovca, Opt. i Spektroskopiya 22, 142, 473, 614 (1967); Opt. Spectry. 22, 73, 255, 335 (1967).
  13. F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

1967 (1)

G. N. Rassudovca, Opt. i Spektroskopiya 22, 142, 473, 614 (1967); Opt. Spectry. 22, 73, 255, 335 (1967).

1965 (2)

F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

W. R. Horsfield, Appl. Opt. 4, 189 (1965).
[CrossRef]

1964 (2)

F. M. Gerasimov, E. A. Yakovlev, I. A. Teltevskii, B. V. Koshelev, Opt. Mekh. Promysh. 1, 20 (1964).

R. F. Jarrell, G. W. Stroke, Appl. Opt. 3, 1254 (1964).
[CrossRef]

1963 (1)

G. N. Rassudova, F. M. Gerasimov, Opt. i Spektroskopiya 14, 406, 559 (1963); Opt. Spectry. 14, 215, 295 (1963).

1962 (1)

1958 (2)

F. M. Gerasimov, I. A. Teltevskii, S. V. Nesmelov, V. P. Sergeev, Opt. Mekh. Promysh. No. 12, 6 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).

1957 (1)

F. M. Gerasimov, I. A. Teltevskii, S. N. Spizharskii, S. V. Nesmelov, Opt. Mekh. Promysh. No. 3, 47 (1957).

1955 (1)

Babcock, H. W.

Gerasimov, F. M.

F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

F. M. Gerasimov, E. A. Yakovlev, I. A. Teltevskii, B. V. Koshelev, Opt. Mekh. Promysh. 1, 20 (1964).

G. N. Rassudova, F. M. Gerasimov, Opt. i Spektroskopiya 14, 406, 559 (1963); Opt. Spectry. 14, 215, 295 (1963).

F. M. Gerasimov, I. A. Teltevskii, S. V. Nesmelov, V. P. Sergeev, Opt. Mekh. Promysh. No. 12, 6 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. N. Spizharskii, S. V. Nesmelov, Opt. Mekh. Promysh. No. 3, 47 (1957).

Guild, J.

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

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

Harrison, G. R.

Horsfield, W. R.

Jarrell, R. F.

R. F. Jarrell, G. W. Stroke, Appl. Opt. 3, 1254 (1964).
[CrossRef]

Koshelev, B. V.

F. M. Gerasimov, E. A. Yakovlev, I. A. Teltevskii, B. V. Koshelev, Opt. Mekh. Promysh. 1, 20 (1964).

Merichev, B. V.

F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

Naumov, S. S.

F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).

Nesmelov, S. V.

F. M. Gerasimov, I. A. Teltevskii, S. V. Nesmelov, V. P. Sergeev, Opt. Mekh. Promysh. No. 12, 6 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. N. Spizharskii, S. V. Nesmelov, Opt. Mekh. Promysh. No. 3, 47 (1957).

Rassudova, G. N.

G. N. Rassudova, F. M. Gerasimov, Opt. i Spektroskopiya 14, 406, 559 (1963); Opt. Spectry. 14, 215, 295 (1963).

Rassudovca, G. N.

G. N. Rassudovca, Opt. i Spektroskopiya 22, 142, 473, 614 (1967); Opt. Spectry. 22, 73, 255, 335 (1967).

Sergeev, V. P.

F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

F. M. Gerasimov, I. A. Teltevskii, S. V. Nesmelov, V. P. Sergeev, Opt. Mekh. Promysh. No. 12, 6 (1958).

Sergeev, V. V.

F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

Spizharskii, S. N.

F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. N. Spizharskii, S. V. Nesmelov, Opt. Mekh. Promysh. No. 3, 47 (1957).

Stroke, G. W.

R. F. Jarrell, G. W. Stroke, Appl. Opt. 3, 1254 (1964).
[CrossRef]

G. R. Harrison, G. W. Stroke, J. Opt. Soc. Am. 45, 112 (1955).
[CrossRef]

Teltevskii, I. A.

F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

F. M. Gerasimov, E. A. Yakovlev, I. A. Teltevskii, B. V. Koshelev, Opt. Mekh. Promysh. 1, 20 (1964).

F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. V. Nesmelov, V. P. Sergeev, Opt. Mekh. Promysh. No. 12, 6 (1958).

F. M. Gerasimov, I. A. Teltevskii, S. N. Spizharskii, S. V. Nesmelov, Opt. Mekh. Promysh. No. 3, 47 (1957).

Yakovlev, E. A.

F. M. Gerasimov, E. A. Yakovlev, I. A. Teltevskii, B. V. Koshelev, Opt. Mekh. Promysh. 1, 20 (1964).

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

Opt. i Spektroskopiya (4)

F. M. Gerasimov, I. A. Teltevskii, S. S. Naumov, S. N. Spizharskii, S. V. Nesmelov, Opt. i Spektroskopiya 4, 779 (1958).

G. N. Rassudova, F. M. Gerasimov, Opt. i Spektroskopiya 14, 406, 559 (1963); Opt. Spectry. 14, 215, 295 (1963).

G. N. Rassudovca, Opt. i Spektroskopiya 22, 142, 473, 614 (1967); Opt. Spectry. 22, 73, 255, 335 (1967).

F. M. Gerasimov, V. P. Sergeev, I. A. Teltevskii, V. V. Sergeev, B. V. Merichev, Opt. i Spektroskopiya 19, 270 (1965); Opt. Spectry. 19, 152 (1965).

Opt. Mekh. Promysh. (3)

F. M. Gerasimov, E. A. Yakovlev, I. A. Teltevskii, B. V. Koshelev, Opt. Mekh. Promysh. 1, 20 (1964).

F. M. Gerasimov, I. A. Teltevskii, S. N. Spizharskii, S. V. Nesmelov, Opt. Mekh. Promysh. No. 3, 47 (1957).

F. M. Gerasimov, I. A. Teltevskii, S. V. Nesmelov, V. P. Sergeev, Opt. Mekh. Promysh. No. 12, 6 (1958).

Other (2)

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

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

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Figures (3)

Fig. 1
Fig. 1

Diagram of the transmission of beams of different orders of diffraction through the system of transmission and reflection gratings: (a) general case; (b) general case, when the contrast of the fringes is independent of the distance between gratings, angular width of source, and wavelength interval (β1 = γ2, β2 = γ1, k1 = −k2).

Fig. 2
Fig. 2

Diagram of the interferometer of transmission and reflection gratings for observed moiré interference fringes in the resultant spectral first (a) and zeroth (b) orders: (1) light source; (2) entrance window; (3) mirror; (4) objective lens of collimator; (5) transmission grating; (6) reflection grating; (7) exit window; (8) photoelectric detector. Dashes indicate the path of the principal ray.

Fig. 3
Fig. 3

Principal configuration of the ruling machine: (1) ruling carriage; (2) grating blank; (3) screw; (4) worm gear; (5) tool carriage; (6) transmission and (7) reflection gratings of the counting system; (8) collimator; (9) photodetector; (10) electromagnetic clutch; (11) cam for operating electromagnetic clutch.

Equations (3)

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Δ Φ = Δ Φ 0 + ( 2 π t / λ ) ( cos β 1 + cos γ 1 - cos β 2 - cos γ 2 ) + [ 2 π ( k 1 - k 2 ) / d ] ( A 2 N 2 - A 1 N 1 ) ,
= d / ( k 1 - k 2 ) .
β 1 = γ 1             and β 2 = γ 2

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