Abstract

We introduce a new configuration for the optical head of a newly developed diffractive laser encoder system. This configuration has a high manufacturing tolerance and a high head-to-scale alignment tolerance, both of which can enhance the wider potential applicability of this newly designed laser encoder. The measurement principles of the encoder are discussed and detailed. We optimized the grating shape and analyzed the impact of the optical components and their arrangement on the measurement error. The head-to-scale alignment tolerance and the arrangement of components in the encoder were also determined. Finally, the measurement performance was evaluated and analyzed. Under nonenvironmentally controlled conditions, the measurement accuracy was found to be 37.3 nm with a standard deviation of 25.4  nm.

© 2007 Optical Society of America

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References

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  1. N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907-926 (1993).
    [CrossRef]
  2. S. Hosoe, "Highly precise and stable laser displacement measurement interferometer with differential optical passes in practical use," Nanotechnology 4, 81-85 (1993).
    [CrossRef]
  3. V. G. Badami and S. R. Patterson, "A frequency domain method for the measurement of nonlinearity in heterodyne interferometry," Precis. Eng. 24, 41-49 (2000).
    [CrossRef]
  4. D. Lin, H. Jiang, and C. Yin, "Analysis of nonlinearity in a high-resolution grating interferometer," Opt. Laser Technol. 32, 95-99 (2000).
    [CrossRef]
  5. K. G. Masreliez, "Position detection and method of measuring position," U.S. patent 5,104,225 (14 April 1992).
  6. F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, 1990).
  7. GSolver User Manual, http://www.gsolver.com.
  8. S. Ichikawa and H. O. Kawasaki, "Diffraction-type optical encoder with improved detection signal insensitivity to optical grating gap variations," U.S. patent 4,943,716 (24 July 1990).
  9. W.-J. Wu, C.-K. Lee, and C.-T. Hsieh, "Signal processing algorithms for Doppler effect based nanometer positioning systems," Jpn. J. Appl. Phys. Part 1 38, 1725-1729 (1999).
    [CrossRef]

2000 (2)

V. G. Badami and S. R. Patterson, "A frequency domain method for the measurement of nonlinearity in heterodyne interferometry," Precis. Eng. 24, 41-49 (2000).
[CrossRef]

D. Lin, H. Jiang, and C. Yin, "Analysis of nonlinearity in a high-resolution grating interferometer," Opt. Laser Technol. 32, 95-99 (2000).
[CrossRef]

1999 (1)

W.-J. Wu, C.-K. Lee, and C.-T. Hsieh, "Signal processing algorithms for Doppler effect based nanometer positioning systems," Jpn. J. Appl. Phys. Part 1 38, 1725-1729 (1999).
[CrossRef]

1993 (2)

N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

S. Hosoe, "Highly precise and stable laser displacement measurement interferometer with differential optical passes in practical use," Nanotechnology 4, 81-85 (1993).
[CrossRef]

Badami, V. G.

V. G. Badami and S. R. Patterson, "A frequency domain method for the measurement of nonlinearity in heterodyne interferometry," Precis. Eng. 24, 41-49 (2000).
[CrossRef]

Bobroff, N.

N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

Hosoe, S.

S. Hosoe, "Highly precise and stable laser displacement measurement interferometer with differential optical passes in practical use," Nanotechnology 4, 81-85 (1993).
[CrossRef]

Hsieh, C.-T.

W.-J. Wu, C.-K. Lee, and C.-T. Hsieh, "Signal processing algorithms for Doppler effect based nanometer positioning systems," Jpn. J. Appl. Phys. Part 1 38, 1725-1729 (1999).
[CrossRef]

Ichikawa, S.

S. Ichikawa and H. O. Kawasaki, "Diffraction-type optical encoder with improved detection signal insensitivity to optical grating gap variations," U.S. patent 4,943,716 (24 July 1990).

Jiang, H.

D. Lin, H. Jiang, and C. Yin, "Analysis of nonlinearity in a high-resolution grating interferometer," Opt. Laser Technol. 32, 95-99 (2000).
[CrossRef]

Kawasaki, H. O.

S. Ichikawa and H. O. Kawasaki, "Diffraction-type optical encoder with improved detection signal insensitivity to optical grating gap variations," U.S. patent 4,943,716 (24 July 1990).

Lee, C.-K.

W.-J. Wu, C.-K. Lee, and C.-T. Hsieh, "Signal processing algorithms for Doppler effect based nanometer positioning systems," Jpn. J. Appl. Phys. Part 1 38, 1725-1729 (1999).
[CrossRef]

Lin, D.

D. Lin, H. Jiang, and C. Yin, "Analysis of nonlinearity in a high-resolution grating interferometer," Opt. Laser Technol. 32, 95-99 (2000).
[CrossRef]

Masreliez, K. G.

K. G. Masreliez, "Position detection and method of measuring position," U.S. patent 5,104,225 (14 April 1992).

Patterson, S. R.

V. G. Badami and S. R. Patterson, "A frequency domain method for the measurement of nonlinearity in heterodyne interferometry," Precis. Eng. 24, 41-49 (2000).
[CrossRef]

Pedrotti, F. J.

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, 1990).

Pedrotti, L. S.

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, 1990).

Wu, W.-J.

W.-J. Wu, C.-K. Lee, and C.-T. Hsieh, "Signal processing algorithms for Doppler effect based nanometer positioning systems," Jpn. J. Appl. Phys. Part 1 38, 1725-1729 (1999).
[CrossRef]

Yin, C.

D. Lin, H. Jiang, and C. Yin, "Analysis of nonlinearity in a high-resolution grating interferometer," Opt. Laser Technol. 32, 95-99 (2000).
[CrossRef]

Jpn. J. Appl. Phys. Part 1 (1)

W.-J. Wu, C.-K. Lee, and C.-T. Hsieh, "Signal processing algorithms for Doppler effect based nanometer positioning systems," Jpn. J. Appl. Phys. Part 1 38, 1725-1729 (1999).
[CrossRef]

Meas. Sci. Technol. (1)

N. Bobroff, "Recent advances in displacement measuring interferometry," Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

Nanotechnology (1)

S. Hosoe, "Highly precise and stable laser displacement measurement interferometer with differential optical passes in practical use," Nanotechnology 4, 81-85 (1993).
[CrossRef]

Opt. Laser Technol. (1)

D. Lin, H. Jiang, and C. Yin, "Analysis of nonlinearity in a high-resolution grating interferometer," Opt. Laser Technol. 32, 95-99 (2000).
[CrossRef]

Precis. Eng. (1)

V. G. Badami and S. R. Patterson, "A frequency domain method for the measurement of nonlinearity in heterodyne interferometry," Precis. Eng. 24, 41-49 (2000).
[CrossRef]

Other (4)

K. G. Masreliez, "Position detection and method of measuring position," U.S. patent 5,104,225 (14 April 1992).

F. J. Pedrotti and L. S. Pedrotti, Introduction to Optics (Prentice-Hall, 1990).

GSolver User Manual, http://www.gsolver.com.

S. Ichikawa and H. O. Kawasaki, "Diffraction-type optical encoder with improved detection signal insensitivity to optical grating gap variations," U.S. patent 4,943,716 (24 July 1990).

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Figures (14)

Fig. 1
Fig. 1

DiLENS configuration.

Fig. 2
Fig. 2

Schematic of the splitter system.

Fig. 3
Fig. 3

Wave propagation near grating G; First diffraction path: lens L inclined incidence to grating G lens L mirror M2. Second diffraction path: mirror M2 lens L grating G lens L; the diffracted electric field along left path V 1 and the diffracted electric field along right path V 2 . (Note: θ is the angle of incidence for the first diffraction and is also the angle of diffraction for the second diffraction.)

Fig. 4
Fig. 4

Optimal grating depth ( 160   nm ) for the DiLENS as calculated with the GSolver.

Fig. 5
Fig. 5

Coordinate system defined for the optical analysis. X and Y are the global axes where x and y are the fast and slow axes for the quarter wave plate, respectively; α is the polarization transmission angle between x and X for polarizer P1; and β 1 , β 2 , and β 3 are the angles between x and X for quarter wave plates QW1, QW2, and QW3, respectively.

Fig. 6
Fig. 6

Electrical field components of the two optical arms projected on a coordinate system.

Fig. 7
Fig. 7

Optical path differences of two split optical arms from laser source LS to any photodetector under ideal conditions with a linear relationship.

Fig. 8
Fig. 8

Polarization misalignment definition of the PBS.

Fig. 9
Fig. 9

Mathematical analysis model for the runout between optical heads and encoder when the optical diffractive location is (a) in focus and (b) out of focus.

Fig. 10
Fig. 10

Experimental setup for determining head-to-scale alignment tolerances.

Fig. 11
Fig. 11

Experimental configuration for verification of the DiLENS.

Fig. 12
Fig. 12

Comparative verification of the DiLENS and the HP5529A when the encoder platform moves 1 μ m .

Fig. 13
Fig. 13

Comparative verification of the DiLENS and the HP5529A when the displacement of the encoder platform is 5 μm.

Fig. 14
Fig. 14

Verification of the DiLENS and the HP5529A when the displacement of the encoder platform is 5 mm at (a) a full path and (b) enlarged verification between 15.5 and 20 s.

Tables (1)

Tables Icon

Table 1 Comparison of Head-to-Scale Alignment Tolerances of the DiLENS

Equations (18)

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Δ ω + 1 = 2 Δ ω = ( 4 π / λ ) u X   sin   θ ,
Δ ω 1 = 2 Δ ω = ( 4 π / λ ) u X   sin   θ .
d Φ = ( 8 π / λ ) u X d t   sin   θ .
Φ = ( 8 π / λ ) Δ X   sin   θ .
Δ X = ( Φ d / 8 π ) .
V 1 = { k p ( θ ) k p ( 0 ) k s ( θ ) k s ( 0 ) i } ,
V 2 = { k p ( θ ) k p ( 0 ) k s ( θ ) k s ( 0 ) i } ,
tan   2 ψ = sin   2 α   sin   φ sin   2 α   sin   2 β 3   cos   φ cos   2 α   cos   2 β 3 .
tan   2 ψ = tan   β 1   cos   2 Δ 1   tan   φ .
tan 2 ψ = 2 [ A ˜ D ˜ sin ( Δ 3 φ ) B ˜ C ˜ sin ( Δ 3 + φ ) + C ˜ D ˜ sin Δ 3 A ˜ B ˜ sin Δ 3 ] B ˜ 2 + D ˜ 2 A ˜ 2 C ˜ 2 2 ( B ˜ D ˜ + A ˜ C ˜ ) cos φ ,
tan   2 ψ = sin   2 α   sin   φ ( cos 2 α sin   α ) cos   2 β 3 sin   2 α   sin   2 β 3   cos   φ ,
tan   2 ψ = 2 [ E ˜ H ˜   sin ( Δ 3 φ ) + F ˜ G ˜   sin ( Δ 3 + φ ) + E ˜ F ˜   sin   Δ 3 G ˜ H ˜   sin   Δ 3 ] F ˜ 2 + H ˜ 2 E ˜ 2 G ˜ 2 2 ( F ˜ H ˜ + E ˜ G ˜ ) cos   φ ,
tan   2 ψ = tan   φ   cos   Δ 3 .
ε ( Φ ) = tan 1 [ sin ( Φ + 2 ξ ) cos   Φ ] Φ .
I P = P ˜   sin ( 4 Δ ω t + Φ ˜ P ) ,
I Q = Q ˜   cos ( 4 Δ ω t + Φ ˜ Q ) ,
ε ( Φ ) = tan 1 [ sin ( Φ + 2 ξ + Φ 13 ) + sin ( Φ + 2 ξ + Φ 14 ) cos ( Φ + 2 ξ ) + cos ( Φ + 2 ξ + Φ 12 ) ] Φ ,
[ 1 f 0 1 ] [ 1 0 1 / f 1 ] [ 1 f 0 1 ] [ 1 0 0 1 ] [ 1 f 0 1 ] [ 1 0 1 / f 1 ] × [ 1 f 0 1 ] { h θ } = { h θ } .

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