Abstract

Two-grating measurement systems are routinely employed for high-resolution measurements of angular and linear displacement. Usually, these systems incorporate zero reference codes (ZRCs) to obtain a zero reference signal (ZRS), which is used as a stage-homing signal. This signal provides absolute information of the position to the otherwise relative information provided by the two-grating incremental subsystems. A zero reference signal is commonly obtained illuminating the superposition of two identical pseudorandom codes and registering the transmitted light by means of a photodiode. To increase the resolution of the system, a reduction of the grating period and the ZRC widths is required. Due to this reduction, the diffractive effects produce a widening of the ZRS and, in turn, a loss of the measuring accuracy. In this work, we propose a method to narrow the distorted signal obtained with a Lau-based encoder, reinstating the accuracy of the ZRS. The method consists of the inclusion of a correlation mask on the detector. A theoretical model to design the mask has been developed, and experimental results have been obtained that validate the proposed technique.

© 2009 Optical Society of America

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References

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  1. L. M. Sanchez-Brea and T. Morlanes, “Metrological errors in optical encoders,” Meas. Sci. Technol. 19, 1-8 (2008).
    [CrossRef]
  2. D. Crespo, J. Alonso, and E. Bernabeu, “Generalized grating imaging using an extended monochromatic light source,” J. Opt. Soc. Am. A 17, 1231-1240 (2000).
    [CrossRef]
  3. D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. (Bellingham) 39, 817-24 (2000).
    [CrossRef]
  4. L. M. Sanchez-Brea, J. Sáez-Landete, J. Alonso, and E. Bernabeu, “Invariant grating pseudoimaging using polychromatic light and a finite extension source,” Appl. Opt. 47, 1470-1477 (2008).
    [CrossRef] [PubMed]
  5. Y. Xiangyang and Y. Chunyong, “A new method for design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34-37 (1986).
    [CrossRef]
  6. Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571-1575 (1987).
    [CrossRef]
  7. Y. Li, “Optical valve using bar codes,” Optik (Stuttgart) 79, 67-74 (1988).
  8. J. Sáez-Landete, J. Alonso, and E. Bernabeu, “Design of zero reference codes by means of a global optimization method,” Opt. Express 13, 195-201 (2005).
    [CrossRef] [PubMed]
  9. J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Optimal design of optical reference signals using a genetic algorithm,” Opt. Lett. 30, 2724-2726 (2005).
    [CrossRef] [PubMed]
  10. J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Generation of optical reference signals robust to diffractive effects,” IEEE Photon. Technol. Lett. 19, 1133-1135 (2007).
    [CrossRef]
  11. E. E. Fenimore and T. M. Cannon, “Coded aperture imaging with uniformly redundant arrays,” Appl. Opt. 17, 337-347 (1978).
    [CrossRef] [PubMed]
  12. J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263-267 (1979).
    [CrossRef]
  13. L. Mertz, Transformations in Optics (Wiley, 1965).
  14. W. K. Pratt, Digital Image Processing (Wiley, 1991).

2008 (2)

2007 (1)

J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Generation of optical reference signals robust to diffractive effects,” IEEE Photon. Technol. Lett. 19, 1133-1135 (2007).
[CrossRef]

2005 (2)

2000 (2)

D. Crespo, J. Alonso, and E. Bernabeu, “Generalized grating imaging using an extended monochromatic light source,” J. Opt. Soc. Am. A 17, 1231-1240 (2000).
[CrossRef]

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. (Bellingham) 39, 817-24 (2000).
[CrossRef]

1988 (1)

Y. Li, “Optical valve using bar codes,” Optik (Stuttgart) 79, 67-74 (1988).

1987 (1)

Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571-1575 (1987).
[CrossRef]

1986 (1)

Y. Xiangyang and Y. Chunyong, “A new method for design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34-37 (1986).
[CrossRef]

1979 (1)

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263-267 (1979).
[CrossRef]

1978 (1)

Alonso, J.

Bernabeu, E.

Cannon, T. M.

Chunyong, Y.

Y. Xiangyang and Y. Chunyong, “A new method for design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34-37 (1986).
[CrossRef]

Crespo, D.

D. Crespo, J. Alonso, and E. Bernabeu, “Generalized grating imaging using an extended monochromatic light source,” J. Opt. Soc. Am. A 17, 1231-1240 (2000).
[CrossRef]

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. (Bellingham) 39, 817-24 (2000).
[CrossRef]

Fenimore, E. E.

Jahns, J.

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263-267 (1979).
[CrossRef]

Li, Y.

Y. Li, “Optical valve using bar codes,” Optik (Stuttgart) 79, 67-74 (1988).

Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571-1575 (1987).
[CrossRef]

Lohmann, A. W.

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263-267 (1979).
[CrossRef]

Mertz, L.

L. Mertz, Transformations in Optics (Wiley, 1965).

Morlanes, T.

L. M. Sanchez-Brea and T. Morlanes, “Metrological errors in optical encoders,” Meas. Sci. Technol. 19, 1-8 (2008).
[CrossRef]

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. (Bellingham) 39, 817-24 (2000).
[CrossRef]

Pratt, W. K.

W. K. Pratt, Digital Image Processing (Wiley, 1991).

Rosa-Zurera, M.

J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Generation of optical reference signals robust to diffractive effects,” IEEE Photon. Technol. Lett. 19, 1133-1135 (2007).
[CrossRef]

J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Optimal design of optical reference signals using a genetic algorithm,” Opt. Lett. 30, 2724-2726 (2005).
[CrossRef] [PubMed]

Sáez-Landete, J.

Salcedo-Sanz, S.

J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Generation of optical reference signals robust to diffractive effects,” IEEE Photon. Technol. Lett. 19, 1133-1135 (2007).
[CrossRef]

J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Optimal design of optical reference signals using a genetic algorithm,” Opt. Lett. 30, 2724-2726 (2005).
[CrossRef] [PubMed]

Sanchez-Brea, L. M.

Xiangyang, Y.

Y. Xiangyang and Y. Chunyong, “A new method for design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34-37 (1986).
[CrossRef]

Appl. Opt. (2)

IEEE Photon. Technol. Lett. (1)

J. Sáez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Alonso, and E. Bernabeu, “Generation of optical reference signals robust to diffractive effects,” IEEE Photon. Technol. Lett. 19, 1133-1135 (2007).
[CrossRef]

J. Mod. Opt. (1)

Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571-1575 (1987).
[CrossRef]

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

J. Phys. E (1)

Y. Xiangyang and Y. Chunyong, “A new method for design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34-37 (1986).
[CrossRef]

Meas. Sci. Technol. (1)

L. M. Sanchez-Brea and T. Morlanes, “Metrological errors in optical encoders,” Meas. Sci. Technol. 19, 1-8 (2008).
[CrossRef]

Opt. Commun. (1)

J. Jahns and A. W. Lohmann, “The Lau effect (a diffraction experiment with incoherent illumination),” Opt. Commun. 28, 263-267 (1979).
[CrossRef]

Opt. Eng. (Bellingham) (1)

D. Crespo, J. Alonso, T. Morlanes, and E. Bernabeu, “Optical encoder based on the Lau effect,” Opt. Eng. (Bellingham) 39, 817-24 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Optik (Stuttgart) (1)

Y. Li, “Optical valve using bar codes,” Optik (Stuttgart) 79, 67-74 (1988).

Other (2)

L. Mertz, Transformations in Optics (Wiley, 1965).

W. K. Pratt, Digital Image Processing (Wiley, 1991).

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Figures (6)

Fig. 1
Fig. 1

Lau configuration for the reference signals. The detection plane is placed at the focal plane of the lens where the mask of detection and the photodiodes are located.

Fig. 2
Fig. 2

Intensity profiles. The dashed trace is calculated propagating the field with the Fresnel approximation. The curve with circles is the autocorrelation, neglecting the distance between the codes (and therefore ignoring the diffraction). The continuous curve is the incident profile measured at the CCD.

Fig. 3
Fig. 3

Incident irradiance profile measured at the CCD (solid curve) and the lower and upper bounds (dashed and dashed–dotted curves) required.

Fig. 4
Fig. 4

Incident irradiance profile measured at the CCD (solid curve), the lower and upper bounds of the narrowed signal (dashed and dashed–dotted curves) and the narrowed signal obtained by means of the algorithm (filled circles).

Fig. 5
Fig. 5

Mask obtained by means of the algorithm. The superior region is associated with the positive detectivity and the inferior region corresponds to the negative detectivity.

Fig. 6
Fig. 6

Incident intensity profile measured by the CCD (solid curve), as well as the signal computed by means of the algorithm (dashed curve) and the experimental narrowed signal (open circles).

Equations (12)

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t ( x ) = j = 0 n 1 c j rect ( x j b b ) ,
I ( x ) = T ( x 0 ) T ̂ ( x 0 + z x f ) d x 0 = T ( x 0 ) T ̂ ( x 0 + u ) d x 0 = I ( f z u ) ,
T ̂ ( x + u ) = T ( x ) exp { i π λ z [ x ( x + u ) ] 2 } d x ,
I ( x ) = T ( x 0 + η ) T ̂ ( x 0 + z x f ) d x 0 = T ( x 0 ) T ̂ ( x 0 + u η ) d x 0 = I [ f z ( u η ) ] .
S ( η ) = K I ( x η ) D ( x ) d x ,
SL = S ( 0 ) S ( x 1 ) x 1 ,
R = S ( 0 ) S m S ( 0 ) ,
C = [ I n 0 0 0 0 ( 1 , m ) I n 0 0 0 I 1 0 0 0 I 1 0 0 I n 0 ( n + m 1 , 1 ) ] .
C = ( C T C ) 1 C T .
D = C S .
S = C D + e ( D ) ,
e ( S ) 2 = e ( S ) T e ( S ) = S T [ I C C ] S ,

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