Abstract

A linearly diffracted laser encoder that has high tolerance of head-to-scale misalignment and a high signal-to-noise ratio is described. The preservation of parallelism between the incident and the diffracted beams, which can be attributed to a built-in folded 1× telescope, allows for the high alignment tolerance. It can be shown that, by coupling this newly developed circular polarization interferometer configuration with grating scale geometry optimization, one can eliminate the problems associated with signal distortion that arise from various efficiencies of the p- and the s-polarized light beams and obtain a high signal-to-noise ratio. Both theoretical and experimental results are presented to confirm the improved results and performance.

© 2004 Optical Society of America

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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, S. R. Petterson, “A frequency domain method for the measurement of non-linearity in heterodyne interferometry,” Precis. Eng. 24, 41–49 (2000).
    [CrossRef]
  4. V. P. Drachev, S. V. Perminov, “Nonlinearity phase shift without cascaded second-order processes and third-order nonlinearity,” Appl. Phys. B 71, 193–196 (2000).
    [CrossRef]
  5. D. Lin, H. Jiang, C. Yin, “Analysis of nonlinearity in a high-resolution grating interferometer,” Opt. Laser Technol. 32, 95–99 (2000).
    [CrossRef]
  6. W. W. Chiang, C. K. Lee, “Wavefront reconstruction optics for use in disk drive position measurement system,” U.S. patent5,442,172 (15August1995).
  7. T. Nishimura, M. Tsukiji, S. Ishii, K. Ishizuka, Y. Kubota, “Optical type encoder,” U.S. patent5,000,542 (19March1991).
  8. L. Drain, The Laser Doppler Technique (Wiley, New York, 1980).
  9. F. Durst, A. Melling, J. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1981).
  10. R. Guenther, Modern Optics (Wiley, New York, New York, 1990).
  11. W. J. Wu, C. K. Lee, C. T. Hsieh, “On the signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys. Part 1 38, 1725–1729 (1999).
    [CrossRef]
  12. A. Cox, A System of Optical Design (Focal Press, New York, 1967).
  13. E. Hecht, Optics (Addison-Wesley, New York, 1998).
  14. H. Haus, Wave and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).
  15. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  16. L. Mickens, R. Coblentz, S. Montepio, LightTools User Guide (Optical Research Associates, Pasadena, Calif., 2000).
  17. Canon U.S.A., Model L-104 Laser Linear Encoder (Canon U.S.A., New York).
  18. E. G. Leowen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).
  19. K. G. Masreliez, “Position detection and method of measuring position,” U.S. patent5,104,225 (14April1992).
  20. E. N. Glytsis, T. K. Gaylord, “Rigorous three-dimensional coupled-wave diffraction analysis of single and cascaded anisotropic grating,” J. Opt. Soc. Am. A 4, 2061–2080 (1987).
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  21. R. Magnusson, T. K. Gaylord, “Equivalence of multiwave coupled-wave theory and modal theory of periodic-media diffraction,” J. Opt. Soc. Am. 68, 1777–1779 (1978).
    [CrossRef]
  22. M. G. Moharam, T. K. Gaylord, “Formulation for stable and efficient implementation of rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [CrossRef]
  23. D. Fluckiger, GSolver User’s Manual (Grating Solver Development Company, Allen, Tex., 1991).
  24. UDT Instruments, Electronic Autocollimators (UDT Instruments, Baltimore, Md.), http://www.udtinstruments.com .
  25. Hewlett-Packard Company, HP 5529A Dynamic Calibrator Measurements Reference Guide (Hewlett-Packard Company, Santa Clara, Calif., 1995).

2000 (3)

V. G. Badami, S. R. Petterson, “A frequency domain method for the measurement of non-linearity in heterodyne interferometry,” Precis. Eng. 24, 41–49 (2000).
[CrossRef]

V. P. Drachev, S. V. Perminov, “Nonlinearity phase shift without cascaded second-order processes and third-order nonlinearity,” Appl. Phys. B 71, 193–196 (2000).
[CrossRef]

D. Lin, H. Jiang, 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, C. T. Hsieh, “On the signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys. Part 1 38, 1725–1729 (1999).
[CrossRef]

1995 (1)

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]

1987 (1)

1978 (1)

Badami, V. G.

V. G. Badami, S. R. Petterson, “A frequency domain method for the measurement of non-linearity 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]

Chiang, W. W.

W. W. Chiang, C. K. Lee, “Wavefront reconstruction optics for use in disk drive position measurement system,” U.S. patent5,442,172 (15August1995).

Coblentz, R.

L. Mickens, R. Coblentz, S. Montepio, LightTools User Guide (Optical Research Associates, Pasadena, Calif., 2000).

Cox, A.

A. Cox, A System of Optical Design (Focal Press, New York, 1967).

Drachev, V. P.

V. P. Drachev, S. V. Perminov, “Nonlinearity phase shift without cascaded second-order processes and third-order nonlinearity,” Appl. Phys. B 71, 193–196 (2000).
[CrossRef]

Drain, L.

L. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

Durst, F.

F. Durst, A. Melling, J. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1981).

Fluckiger, D.

D. Fluckiger, GSolver User’s Manual (Grating Solver Development Company, Allen, Tex., 1991).

Gaylord, T. K.

Glytsis, E. N.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Guenther, R.

R. Guenther, Modern Optics (Wiley, New York, New York, 1990).

Haus, H.

H. Haus, Wave and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

Hecht, E.

E. Hecht, Optics (Addison-Wesley, New York, 1998).

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, C. T. Hsieh, “On the signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys. Part 1 38, 1725–1729 (1999).
[CrossRef]

Ishii, S.

T. Nishimura, M. Tsukiji, S. Ishii, K. Ishizuka, Y. Kubota, “Optical type encoder,” U.S. patent5,000,542 (19March1991).

Ishizuka, K.

T. Nishimura, M. Tsukiji, S. Ishii, K. Ishizuka, Y. Kubota, “Optical type encoder,” U.S. patent5,000,542 (19March1991).

Jiang, H.

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

Kubota, Y.

T. Nishimura, M. Tsukiji, S. Ishii, K. Ishizuka, Y. Kubota, “Optical type encoder,” U.S. patent5,000,542 (19March1991).

Lee, C. K.

W. J. Wu, C. K. Lee, C. T. Hsieh, “On the signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys. Part 1 38, 1725–1729 (1999).
[CrossRef]

W. W. Chiang, C. K. Lee, “Wavefront reconstruction optics for use in disk drive position measurement system,” U.S. patent5,442,172 (15August1995).

Leowen, E. G.

E. G. Leowen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Lin, D.

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

Magnusson, R.

Masreliez, K. G.

K. G. Masreliez, “Position detection and method of measuring position,” U.S. patent5,104,225 (14April1992).

Melling, A.

F. Durst, A. Melling, J. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1981).

Mickens, L.

L. Mickens, R. Coblentz, S. Montepio, LightTools User Guide (Optical Research Associates, Pasadena, Calif., 2000).

Moharam, M. G.

Montepio, S.

L. Mickens, R. Coblentz, S. Montepio, LightTools User Guide (Optical Research Associates, Pasadena, Calif., 2000).

Nishimura, T.

T. Nishimura, M. Tsukiji, S. Ishii, K. Ishizuka, Y. Kubota, “Optical type encoder,” U.S. patent5,000,542 (19March1991).

Perminov, S. V.

V. P. Drachev, S. V. Perminov, “Nonlinearity phase shift without cascaded second-order processes and third-order nonlinearity,” Appl. Phys. B 71, 193–196 (2000).
[CrossRef]

Petterson, S. R.

V. G. Badami, S. R. Petterson, “A frequency domain method for the measurement of non-linearity in heterodyne interferometry,” Precis. Eng. 24, 41–49 (2000).
[CrossRef]

Popov, E.

E. G. Leowen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

Tsukiji, M.

T. Nishimura, M. Tsukiji, S. Ishii, K. Ishizuka, Y. Kubota, “Optical type encoder,” U.S. patent5,000,542 (19March1991).

Whitelaw, J.

F. Durst, A. Melling, J. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1981).

Wu, W. J.

W. J. Wu, C. K. Lee, C. T. Hsieh, “On the 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, C. Yin, “Analysis of nonlinearity in a high-resolution grating interferometer,” Opt. Laser Technol. 32, 95–99 (2000).
[CrossRef]

Appl. Phys. B (1)

V. P. Drachev, S. V. Perminov, “Nonlinearity phase shift without cascaded second-order processes and third-order nonlinearity,” Appl. Phys. B 71, 193–196 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

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

W. J. Wu, C. K. Lee, C. T. Hsieh, “On the 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, 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, S. R. Petterson, “A frequency domain method for the measurement of non-linearity in heterodyne interferometry,” Precis. Eng. 24, 41–49 (2000).
[CrossRef]

Other (16)

W. W. Chiang, C. K. Lee, “Wavefront reconstruction optics for use in disk drive position measurement system,” U.S. patent5,442,172 (15August1995).

T. Nishimura, M. Tsukiji, S. Ishii, K. Ishizuka, Y. Kubota, “Optical type encoder,” U.S. patent5,000,542 (19March1991).

L. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

F. Durst, A. Melling, J. Whitelaw, Principles and Practice of Laser Doppler Anemometry (Academic, New York, 1981).

R. Guenther, Modern Optics (Wiley, New York, New York, 1990).

A. Cox, A System of Optical Design (Focal Press, New York, 1967).

E. Hecht, Optics (Addison-Wesley, New York, 1998).

H. Haus, Wave and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

L. Mickens, R. Coblentz, S. Montepio, LightTools User Guide (Optical Research Associates, Pasadena, Calif., 2000).

Canon U.S.A., Model L-104 Laser Linear Encoder (Canon U.S.A., New York).

E. G. Leowen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997).

K. G. Masreliez, “Position detection and method of measuring position,” U.S. patent5,104,225 (14April1992).

D. Fluckiger, GSolver User’s Manual (Grating Solver Development Company, Allen, Tex., 1991).

UDT Instruments, Electronic Autocollimators (UDT Instruments, Baltimore, Md.), http://www.udtinstruments.com .

Hewlett-Packard Company, HP 5529A Dynamic Calibrator Measurements Reference Guide (Hewlett-Packard Company, Santa Clara, Calif., 1995).

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Figures (13)

Fig. 1
Fig. 1

Configuration of the newly developed laser encoder system, DiLENS. The grating moves in the x direction.

Fig. 2
Fig. 2

Definition of fast-axis azimuth angle for Q1 and Q2. The positive Z axis starts from mirror M1 to grating G for Q1 and from M2 to grating G for Q2.

Fig. 3
Fig. 3

Folded 1× telescope configuration with h 0 and η0, which represent the height and the emitting angle, respectively, of the light beam diffracted from the grating.

Fig. 4
Fig. 4

Definition of runout for a moving grating scale.

Fig. 5
Fig. 5

Qualitative representation of misaligned beam spots for photodiodes under different runout conditions in which separation was found as a result of pitch only.

Fig. 6
Fig. 6

Spot location of photodiode for roll, pitch, and stand-off runout.

Fig. 7
Fig. 7

Experimental setup for measuring grating-scale runout and determining the alignment tolerance.

Fig. 8
Fig. 8

Diffraction efficiency of a grating scale at different incidence angles, where the simulated data and the experimental data agree well with each other: (a) measured TE efficiencies, (b) measured TM efficiencies.

Fig. 9
Fig. 9

Simulation of the optimization criterion [k p (θ)k p (0) + k s (θ)k s (0)]2 at various grating depths; the optimized depth was 190 nm.

Fig. 10
Fig. 10

Simulation of rate of variation in diffraction efficiency versus grating depth. The variation rate was minimum at a 190-nm grating depth.

Fig. 11
Fig. 11

Experimental results of repeatability tests in which 10 data sets (at 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 mm) were obtained. The repeatability represents the standard deviation of these 10 data sets; the average repeatability was 4.48 nm across 20 mm.

Fig. 12
Fig. 12

Experimental results of accuracy tests in which 10 data sets (at 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 mm) were obtained. The accuracy represents the root mean square of these 10 data sets; the average accuracy was 33.71 nm across 20 mm.

Fig. 13
Fig. 13

Comparison of displacement data measured by the DiLENS and by the HP 5529A interferometer.

Tables (3)

Tables Icon

Table 1 Destination of Light Beams Associated with Several Orientations of Quarter-Wave Plates Q1 and Q2 in Fig. 1

Tables Icon

Table 2 Destination of Light Beams Associated with Several Fast-Axis Azimuth Angles of a Quarter-Wave Plate for the Alternative Configuration

Tables Icon

Table 3 Alignment Tolerance of the DiLENS As Determined by Ray Tracing and the Experimental Setupa

Equations (25)

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

Δ w + 1 = 2 Δ w = u x × 4 π λ × sin   θ ,
Δ w - 1 = - 2 Δ w = - u x × 4 π λ × sin   θ ,
V 1 = - k p θ × k p 0 i k s θ × k s 0 exp i ω - 2 Δ ω t ,
V 2 = k p θ × k p 0 k s θ × k s 0 i exp i ω + 2 Δ ω t ,
U 1 = - bi a exp i ω - 2 Δ ω t ,
U 2 = a - bi exp i ω + 2 Δ ω t ,
a = 2 - 1 / 2 × k p θ × k p 0 + k s θ × k s 0 ,
b = 2 - 1 / 2 × k p θ × k p 0 - k s θ × k s 0 .
U 1 = 0 a exp i ω - 2 Δ ω t ,
U 2 = a 0 exp i ω + 2 Δ ω t .
W 1 = 2 - 1 / 2 a i 1 exp i ω - 2 Δ ω t ,
W 2 = 2 - 1 / 2 a 1 i exp i ω + 2 Δ ω t ,
I D 1 = 2 a 2 + 2 a 2 × cos 4 Δ ω × t ,
I D 2 = 2 a 2 - 2 a 2 × cos 4 Δ ω × t ,
I D 3 = 2 a 2 + 2 a 2 × sin 4 Δ ω × t ,
I D 4 = 2 a 2 - 2 a 2 × sin 4 Δ ω × t .
I P = 4 a 2 × cos 4 Δ ω × t ,
I Q = 4 a 2 × sin 4 Δ ω × t .
Φ =   d Φ =   4 Δ ω d t =   8 π λ   u x   sin   θ d t = 8 π λ   Δ X   sin   θ .
sin   θ = λ / d ,
Δ X = Φ × d 8 π .
1 - f - Δ Z 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 + Δ Z 0 1 h 0 η 0 = - h 0 - 2 Δ Z × η 0 η 0 .
u r x ,   y = u i - x ,   - y
u i x ,   y = A   exp j k x x + k y y .
u r x ,   y = A   exp - j k x x + k y y ,

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