Abstract

Optical encoders are used in industrial and laboratory motion equipment to measure rotations and linear displacements. We introduce a design of an optical encoder based on a nondiffractive beam. We expect that the invariant profile and radial symmetry of the nondiffractive beam provide the design with remarkable tolerance to mechanical perturbations. We experimentally demonstrate that the proposed design generates a suitable output sinusoidal signal with low harmonic distortion. Moreover, we present a numerical model of the system based on the angular spectrum approximation whose predictions are in excellent agreement with the experimental results.

© 2008 Optical Society of America

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References

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  1. L. Wronkowski, “Diffraction model of an optoelectronic displacement measuring transducer,” Opt. Laser Technol. 27, 81-88 (1995).
    [CrossRef]
  2. D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
    [CrossRef]
  3. G. Swanson and E. Leith, “Analysis of the Lau effect and generalized grating imaging,” J. Opt. Soc. Am. A 2, 789-793(1985).
    [CrossRef]
  4. W. Huber and M. Allgauer, “Interferential linear and angular displacement apparatus having scanning and scale grating respectively greater than and less than the source wavelength,” U.S. patent 5,424,833 (13 June 1995).
  5. F. Perez-Quintian, A. Lutenberg, and M. A. Rebollo, “Linear displacement measurement with a grating and speckle pattern illumination,” Appl. Opt. 45, 4821-4825 (2006).
    [CrossRef] [PubMed]
  6. A. Lutenberg, F. Perez-Quintian, and M. A. Rebollo, “Study of a new design of an incremental optical encoder,” Proc. SPIE 6292, 629218 (2006),
    [CrossRef]
  7. J. E. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651-654 (1987).
    [CrossRef]
  8. B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
    [CrossRef]
  9. J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619(2003).
    [CrossRef]
  10. J. W Goodman, “The Fresnel approximation and the angular spectrum,” in Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 71-72.

2006 (2)

F. Perez-Quintian, A. Lutenberg, and M. A. Rebollo, “Linear displacement measurement with a grating and speckle pattern illumination,” Appl. Opt. 45, 4821-4825 (2006).
[CrossRef] [PubMed]

A. Lutenberg, F. Perez-Quintian, and M. A. Rebollo, “Study of a new design of an incremental optical encoder,” Proc. SPIE 6292, 629218 (2006),
[CrossRef]

2003 (1)

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619(2003).
[CrossRef]

2000 (1)

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

1999 (1)

B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
[CrossRef]

1996 (1)

J. W Goodman, “The Fresnel approximation and the angular spectrum,” in Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 71-72.

1995 (1)

L. Wronkowski, “Diffraction model of an optoelectronic displacement measuring transducer,” Opt. Laser Technol. 27, 81-88 (1995).
[CrossRef]

1987 (1)

1985 (1)

Allgauer, M.

W. Huber and M. Allgauer, “Interferential linear and angular displacement apparatus having scanning and scale grating respectively greater than and less than the source wavelength,” U.S. patent 5,424,833 (13 June 1995).

Alonso, J.

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Bernabeu, E.

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Crespo, D.

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Durnin, J. E.

Ferrari, J. A.

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619(2003).
[CrossRef]

Frins, E. M.

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619(2003).
[CrossRef]

Ganguly, A. K.

B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
[CrossRef]

Garbusi, E.

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619(2003).
[CrossRef]

Goodman, J. W

J. W Goodman, “The Fresnel approximation and the angular spectrum,” in Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 71-72.

Hafizi, B.

B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
[CrossRef]

Huber, W.

W. Huber and M. Allgauer, “Interferential linear and angular displacement apparatus having scanning and scale grating respectively greater than and less than the source wavelength,” U.S. patent 5,424,833 (13 June 1995).

Leith, E.

Lutenberg, A.

F. Perez-Quintian, A. Lutenberg, and M. A. Rebollo, “Linear displacement measurement with a grating and speckle pattern illumination,” Appl. Opt. 45, 4821-4825 (2006).
[CrossRef] [PubMed]

A. Lutenberg, F. Perez-Quintian, and M. A. Rebollo, “Study of a new design of an incremental optical encoder,” Proc. SPIE 6292, 629218 (2006),
[CrossRef]

Moore, C. I.

B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
[CrossRef]

Morlanes, T.

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Perez-Quintian, F.

A. Lutenberg, F. Perez-Quintian, and M. A. Rebollo, “Study of a new design of an incremental optical encoder,” Proc. SPIE 6292, 629218 (2006),
[CrossRef]

Perez-Quintian, F.

Rebollo, M. A.

F. Perez-Quintian, A. Lutenberg, and M. A. Rebollo, “Linear displacement measurement with a grating and speckle pattern illumination,” Appl. Opt. 45, 4821-4825 (2006).
[CrossRef] [PubMed]

A. Lutenberg, F. Perez-Quintian, and M. A. Rebollo, “Study of a new design of an incremental optical encoder,” Proc. SPIE 6292, 629218 (2006),
[CrossRef]

Sprangle, P.

B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
[CrossRef]

Swanson, G.

Ting, A.

B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
[CrossRef]

Wronkowski, L.

L. Wronkowski, “Diffraction model of an optoelectronic displacement measuring transducer,” Opt. Laser Technol. 27, 81-88 (1995).
[CrossRef]

Appl. Opt. (1)

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

Opt. Eng. (1)

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. 39, 817-824 (2000).
[CrossRef]

Opt. Laser Technol. (1)

L. Wronkowski, “Diffraction model of an optoelectronic displacement measuring transducer,” Opt. Laser Technol. 27, 81-88 (1995).
[CrossRef]

Phys. Rev. E (2)

B. Hafizi, A. K. Ganguly, A. Ting, C. I. Moore, and P. Sprangle, “Analysis of Gaussian beam and Bessel beam driven laser accelerators,” Phys. Rev. E 60, 4779-4792 (1999).
[CrossRef]

J. A. Ferrari, E. Garbusi, and E. M. Frins, “Generation of nondiffracting beams by spiral fields,” Phys. Rev. E 67, 036619(2003).
[CrossRef]

Proc. SPIE (1)

A. Lutenberg, F. Perez-Quintian, and M. A. Rebollo, “Study of a new design of an incremental optical encoder,” Proc. SPIE 6292, 629218 (2006),
[CrossRef]

Other (2)

J. W Goodman, “The Fresnel approximation and the angular spectrum,” in Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 71-72.

W. Huber and M. Allgauer, “Interferential linear and angular displacement apparatus having scanning and scale grating respectively greater than and less than the source wavelength,” U.S. patent 5,424,833 (13 June 1995).

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Figures (11)

Fig. 1
Fig. 1

Diagram of the slit-lens system.

Fig. 2
Fig. 2

Diagram of the proposed NDB optical encoder.

Fig. 3
Fig. 3

Spectrum of V ( w ) for a = 6 r o together with the spectrum T G ( w ) of the grating that minimizes the output signal harmonic distortion and maximizes its contrast.

Fig. 4
Fig. 4

Experimental NDB profiles and its numerical adjustment.

Fig. 5
Fig. 5

Experimental output signal s ( Δ x ) for a = 6.44 r o and f G = 0.768 / r o .

Fig. 6
Fig. 6

Experimental measurement of the light intensity distribution over the photodetector for Δ x = 25 μm .

Fig. 7
Fig. 7

Light intensity distribution over the photodetector for Δ x = 25 μm according to the ASM prediction.

Fig. 8
Fig. 8

Contrast of the output signal versus photodetector size a.

Fig. 9
Fig. 9

Spectrum of the output signal for a = 4.33 r o .

Fig. 10
Fig. 10

Spectrum of the output signal for a = 7.85 r o .

Fig. 11
Fig. 11

Mean value of the output signal versus the photo detector size.

Equations (10)

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I ( r , ϕ , z ) = | A ( z ) | 2 J 0 2 ( π d λ f r ) ,
t G ( x Δ x ) = 1 2 + n = 1 , 3 , 5 , .. + 2 n π sen [ 2 π n f G ( x Δ x ) ]
d ( x , y ) { 1 | x | , | y | a 2 0 otherwise .
s ( Δ x ) - + - + t G ( x Δ x ) J 0 2 ( x , y ) d ( x , y ) d x d y = - + t G ( x Δ x ) v ( x ) d x .
TF [ s ( Δ x ) ] = S ( ω ) T G ( ω ) V ( ω ) ,
p ( V ( ω ) ) = 1 2 V ( ω ) - V ( 3 ω ) V ( ω ) + 1 2 V ( ω ) - V ( 5 ω ) V ( ω ) ,
I ( x , y ) = A · J o 2 ( b ( x x o ) 2 + ( x y o ) 2 ) + C .
E ( x , y , Δ x ) TF 1 { TF [ t G ( x Δ x ) J 0 ( x , y ) ] H ( ω x , ω y ) } ,
H ( ω x , ω y ) = { exp [ j z λ ( 2 π ) 2 ( λ ω x ) 2 ( λ ω y ) 2 ] ω x 2 + ω y 2 < 2 π λ 0 otherwise .
s ( Δ x ) - + - + E ( x , y , Δ x ) 2 d ( x , y ) d x d y .

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