Abstract

A new type of translation–rotation encoder that makes use of two identical transparent dielectric gratings lighted in a -1-order Littrow mount is proposed. The correct choice of the wavelength-to-groove-spacing ratio produces only two transmitted beams, which interfere with the highest possible visibility in a large range of experimental conditions. Thus this mounting permits high-accuracy encoders to be produced by the use of cheap photoresist or plastic gratings and opens the way to industrial applications in high-precision mechanics, information processing, etc.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Heidenhain, M. Allgaüer, E. Spanner, “Measurement set-up,” German patentEP 92 11 0237.2 (17June1992).
  2. O. Parriaux, M. Nevière, E. Popov, “Dispositif optique de mesure d’un déplacement relatif entre deux éléments,” European patentEP 07 41 282 A2 (30April1996).
  3. C. R. Steinmetz, “Sub-micron position measurement and control on precision machine tools with laser interferometry,” Precision Eng. 22, 513–519 (1990).
  4. R. J. Hocken, H. P. Layer, “Lasers for dimensional measurement,” Ann. CIRP 28, 303–309 (1979).
  5. W. T. Estler, “High-accuracy displacement interferometry in air,” Appl. Opt. 24, 808–815 (1985).
    [CrossRef] [PubMed]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).
  7. J. L. Roumiguières, M. Nevière, “Process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits,” Japanese patent1,625,035 (29August1980); United States patent4,389,094 (21June1983); Canadian patent1,140,373 (1February1983).
  8. F. Montiel, M. Nevière, “Electromagnetic study of a photolithography set-up for periodic masks and application to non-periodic masks,” J. Opt. Soc. Am. A 13, 1429–1438 (1996).
    [CrossRef]
  9. A. Sentenac, D. Maystre, “Symmetry of the field transmitted by metallic grids,” J. Mod. Opt. 45, 785–797 (1998).
    [CrossRef]
  10. D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
    [CrossRef]
  11. R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

1998 (1)

A. Sentenac, D. Maystre, “Symmetry of the field transmitted by metallic grids,” J. Mod. Opt. 45, 785–797 (1998).
[CrossRef]

1996 (1)

1990 (1)

C. R. Steinmetz, “Sub-micron position measurement and control on precision machine tools with laser interferometry,” Precision Eng. 22, 513–519 (1990).

1985 (1)

1979 (1)

R. J. Hocken, H. P. Layer, “Lasers for dimensional measurement,” Ann. CIRP 28, 303–309 (1979).

Allgaüer, M.

J. Heidenhain, M. Allgaüer, E. Spanner, “Measurement set-up,” German patentEP 92 11 0237.2 (17June1992).

Bonnemasson, F.

R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Dauer, V.

R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

Estler, W. T.

Flamand, J.

R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

Grange, R.

R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

Heidenhain, J.

J. Heidenhain, M. Allgaüer, E. Spanner, “Measurement set-up,” German patentEP 92 11 0237.2 (17June1992).

Hocken, R. J.

R. J. Hocken, H. P. Layer, “Lasers for dimensional measurement,” Ann. CIRP 28, 303–309 (1979).

Layer, H. P.

R. J. Hocken, H. P. Layer, “Lasers for dimensional measurement,” Ann. CIRP 28, 303–309 (1979).

Maystre, D.

A. Sentenac, D. Maystre, “Symmetry of the field transmitted by metallic grids,” J. Mod. Opt. 45, 785–797 (1998).
[CrossRef]

D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
[CrossRef]

Montiel, F.

Nevière, M.

F. Montiel, M. Nevière, “Electromagnetic study of a photolithography set-up for periodic masks and application to non-periodic masks,” J. Opt. Soc. Am. A 13, 1429–1438 (1996).
[CrossRef]

O. Parriaux, M. Nevière, E. Popov, “Dispositif optique de mesure d’un déplacement relatif entre deux éléments,” European patentEP 07 41 282 A2 (30April1996).

R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

J. L. Roumiguières, M. Nevière, “Process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits,” Japanese patent1,625,035 (29August1980); United States patent4,389,094 (21June1983); Canadian patent1,140,373 (1February1983).

Parriaux, O.

O. Parriaux, M. Nevière, E. Popov, “Dispositif optique de mesure d’un déplacement relatif entre deux éléments,” European patentEP 07 41 282 A2 (30April1996).

Popov, E.

O. Parriaux, M. Nevière, E. Popov, “Dispositif optique de mesure d’un déplacement relatif entre deux éléments,” European patentEP 07 41 282 A2 (30April1996).

Roumiguières, J. L.

J. L. Roumiguières, M. Nevière, “Process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits,” Japanese patent1,625,035 (29August1980); United States patent4,389,094 (21June1983); Canadian patent1,140,373 (1February1983).

Saïsse, M.

R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

Sentenac, A.

A. Sentenac, D. Maystre, “Symmetry of the field transmitted by metallic grids,” J. Mod. Opt. 45, 785–797 (1998).
[CrossRef]

Spanner, E.

J. Heidenhain, M. Allgaüer, E. Spanner, “Measurement set-up,” German patentEP 92 11 0237.2 (17June1992).

Steinmetz, C. R.

C. R. Steinmetz, “Sub-micron position measurement and control on precision machine tools with laser interferometry,” Precision Eng. 22, 513–519 (1990).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

Ann. CIRP (1)

R. J. Hocken, H. P. Layer, “Lasers for dimensional measurement,” Ann. CIRP 28, 303–309 (1979).

Appl. Opt. (1)

J. Mod. Opt. (1)

A. Sentenac, D. Maystre, “Symmetry of the field transmitted by metallic grids,” J. Mod. Opt. 45, 785–797 (1998).
[CrossRef]

J. Opt. Soc. Am. A (1)

Precision Eng. (1)

C. R. Steinmetz, “Sub-micron position measurement and control on precision machine tools with laser interferometry,” Precision Eng. 22, 513–519 (1990).

Other (6)

D. Maystre, “Integral Methods,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 63–100.
[CrossRef]

R. Grange, V. Dauer, M. Saïsse, M. Nevière, J. Flamand, F. Bonnemasson, “6000 groove/mm holographic flight gratings for the high resolution Far Ultraviolet Spectroscopic Explorer: efficiency, resolution and stray-light measurements,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney, C. A. Palmer, eds., Proc. SPIE3450 (to be published).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1965).

J. L. Roumiguières, M. Nevière, “Process for casting on a support the faithful reproduction of a mask pierced with periodically distributed slits,” Japanese patent1,625,035 (29August1980); United States patent4,389,094 (21June1983); Canadian patent1,140,373 (1February1983).

J. Heidenhain, M. Allgaüer, E. Spanner, “Measurement set-up,” German patentEP 92 11 0237.2 (17June1992).

O. Parriaux, M. Nevière, E. Popov, “Dispositif optique de mesure d’un déplacement relatif entre deux éléments,” European patentEP 07 41 282 A2 (30April1996).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1
Fig. 1

Grating encoder basic mount.

Fig. 2
Fig. 2

Schematic representation of the encoder.

Fig. 3
Fig. 3

Photographs (actual size) of the interference pattern. (a) The gratings are placed to have a minimum in the center of the field; (b) starting from the position defined in (a), the upper grating is translated a d/2 distance along the Ox axis.

Fig. 4
Fig. 4

Measured intensity at the center of the interference pattern as a function of displacement x and of corresponding voltage V of the piezoelectric table.

Fig. 5
Fig. 5

View from the top of the lower mobile element on which two shifted identical gratings are engraved, a second grating is engraved with d/4 translation along the x axis, and there is a shift in the ruling direction large enough that the two rulings do not overlap.

Fig. 6
Fig. 6

Groove geometry of a dielectric lamellar grating.

Fig. 7
Fig. 7

Optimal groove depth and groove width of a dielectric lamellar grating to produce equal transmitted efficiencies.

Fig. 8
Fig. 8

Mounting for eliminating parasitic signals. Heavier lines represent the two gratings. Hatched areas are two detectors.

Fig. 9
Fig. 9

Schematic of gratings used to detect rotation motion.

Fig. 10
Fig. 10

Angular deviation of the (-1, 0) and (0, -1) beams owing to a tilt of the second grating.

Tables (1)

Tables Icon

Table 1 Comparison of the Interference Signals Produced by the Two Kinds of Interference Field for the Two Types of Grating

Equations (33)

Equations on this page are rendered with MathJax. Learn more.

φ=2πx/d,
sin θ=λ/2d,
2d/3<λ<2d.
Mx=D/2 sin θ,
T-1,0=T-1×T0, T-1,+1=T-1×T-1, T0,0=T0×T0, T0,-1=T0×T-1=T-1,0.
N=2|T0,-1|21+cos φ
V=NMax-NminNMax+Nmin,
|T0|2=|T-1|2.
N0,min=|T0,0|2+|T-1,+1|2-2|T0,0T-1,+1|, N0,Max=|T0,0|2+|T-1,+1|2+2|T0,0T-1,+1|.
V=2|T0,0T-1,+1||T0,0|2+|T-1,+1|2.
|T-1|2|T0|2=110,
N=2|T0,-1|21+cos2πx+d/4d=2|T0,-1|21-sin φ.
|T0,0|=|T-1,+1|.
T0,0=T0×T0,
T-1,+1=T-1×T+1.
T0,0=T02,
T-1,+1=T-12
T0=T-1.
Y/λ=8.399X/λ2-6.616X/λ+2.009,
X/λ0.40, X1;
Y/λ=1.039X/λ+0.423,
Y/λY1, 1.3.
Y/λ=8.679X/λ2-6.851X/λ2+2.113, Y/λ=0.974X/λ+0.514, Y/λ=8.120X/λ2-6.381X/λ+1.905, Y/λ=1.039X/λ+0.383, X/λ=0.40, Y/λ=1.30.
T0,0=T0T0, T-1,+1=T-1T+1-θ=T-1T-1=T0T0.
T-1,0=T-1T0=T0T0,
T0,-1=T0T-1=T0T0.
sin θL=λ/2d,
θ1=θL+α1
sin θ2=λd-sin θ1,  θ2>0.
α2=θL-θ2;
θ2=θL+α1-α2.
2 sinα1-α22=λI.
cos θ2dθ2=-cos θ1dθ1.

Metrics