Abstract

We reported on stereovisual localization of a labeled target versus three-dimensional (3D) position and orientation with a resolution of a few micrometers [Opt. Express 18, 24152 (2010) [CrossRef]  ]. A pseudo-periodic pattern (PPP) is fixed on the target, whose center is identified with subpixel accuracy in both stereo images. This subpixel position definition is fed into the geometrical model of the stereovision system and, thus, leads to subvoxel resolution in the 3D target positioning. This paper reports on improvements and specialization of the method for addressing the measurement of 3D translations: (a) The use of an encrypted PPP wider than the field of observation of the cameras has two beneficial effects. First, the allowed lateral target displacements are wider than the field of view of each camera, thus extending the workspace volume. Second, the 3D position is always derived from the same zone located at the center of the camera sensor chip. A simplified geometrical model is thus sufficient, and the effects of the lens distortions lead to a different kind of calibration issues. (b) By considering only translations, the pattern directions remain stationary in the recorded images. Two-dimensional Fourier transforms are then replaced by single dimension ones, thus reducing the computation time. (c) The choice of a higher magnification lens allows the achievement of submicrometer resolution in target position determination. This level of performance makes the method attractive in various automated applications requiring microstage position control and sensing. This approach may, for instance, fulfill the requirements for the coarse positioning of specimens in front of nanotechnology instruments that are equipped with their own high-accuracy but short-excursion-range translation stages.

© 2012 Optical Society of America

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References

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  1. H. S. Cho, Optomechatronics: Fusion of Optical and Mechatronic Engineering (CRC Press, 2006).
  2. N. A. Arias H., P. Sandoz, J. E. Meneses, M. A. Suarez, and T. Gharbi, “3D localization of a labeled target by means of a stereo vision configuration with subvoxel resolution,” Opt. Express 18, 24152–24162 (2010).
    [CrossRef]
  3. J. Y. Bouguet, “Camera calibration toolbox for MATLAB” (2008), http://www.vision.caltech.edu/bouguetj/calib_doc/ .
  4. P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
    [CrossRef]
  5. J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
    [CrossRef]
  6. Z. Galeano, A. July, P. Sandoz, E. Gaiffe, S. Launay, L. Robert, M. Jacquot, F. Hirchaud, J. L. Prétet, and C. Mougin, “Position-referenced microscopy for live cell culture monitoring,” Biomed. Opt. Express 2, 1307–1318 (2011).
    [CrossRef]
  7. S. W. Golomb, Shift Register Sequences (Holden-Day, 1967).
  8. P. Sandoz and M. Jacquot, “Lensless vision system for in-plane positioning of a patterned plate with subpixel resolution,” J. Opt Soc. Am. A 28, 2494–2500 (2011).
    [CrossRef]
  9. R. Kronland-Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Recogn. Artif. Intell. 1, 273–302 (1987).
    [CrossRef]
  10. R. J. Hansman, “Characteristics of instrumentation,” in The Measurement, Instrumentation, and Sensors Handbook, J. G. Webster, ed. (Springer-Verlag, 1999).
  11. B. Zhao and A. Asundi, “Microscopic grid methods—resolution and sensitivity,” Opt. Laser Eng. 36, 437–450 (2001).
    [CrossRef]

2011

P. Sandoz and M. Jacquot, “Lensless vision system for in-plane positioning of a patterned plate with subpixel resolution,” J. Opt Soc. Am. A 28, 2494–2500 (2011).
[CrossRef]

Z. Galeano, A. July, P. Sandoz, E. Gaiffe, S. Launay, L. Robert, M. Jacquot, F. Hirchaud, J. L. Prétet, and C. Mougin, “Position-referenced microscopy for live cell culture monitoring,” Biomed. Opt. Express 2, 1307–1318 (2011).
[CrossRef]

2010

N. A. Arias H., P. Sandoz, J. E. Meneses, M. A. Suarez, and T. Gharbi, “3D localization of a labeled target by means of a stereo vision configuration with subvoxel resolution,” Opt. Express 18, 24152–24162 (2010).
[CrossRef]

J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
[CrossRef]

2007

P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
[CrossRef]

2001

B. Zhao and A. Asundi, “Microscopic grid methods—resolution and sensitivity,” Opt. Laser Eng. 36, 437–450 (2001).
[CrossRef]

1987

R. Kronland-Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Recogn. Artif. Intell. 1, 273–302 (1987).
[CrossRef]

Arias H., N. A.

Asundi, A.

B. Zhao and A. Asundi, “Microscopic grid methods—resolution and sensitivity,” Opt. Laser Eng. 36, 437–450 (2001).
[CrossRef]

Cho, H. S.

H. S. Cho, Optomechatronics: Fusion of Optical and Mechatronic Engineering (CRC Press, 2006).

Froelhy, L.

P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
[CrossRef]

Gaiffe, E.

Z. Galeano, A. July, P. Sandoz, E. Gaiffe, S. Launay, L. Robert, M. Jacquot, F. Hirchaud, J. L. Prétet, and C. Mougin, “Position-referenced microscopy for live cell culture monitoring,” Biomed. Opt. Express 2, 1307–1318 (2011).
[CrossRef]

J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
[CrossRef]

Galeano, Z.

Galeano-Zea, J. A.

J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
[CrossRef]

Gharbi, T.

Golomb, S. W.

S. W. Golomb, Shift Register Sequences (Holden-Day, 1967).

Grossmann, A.

R. Kronland-Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Recogn. Artif. Intell. 1, 273–302 (1987).
[CrossRef]

Hansman, R. J.

R. J. Hansman, “Characteristics of instrumentation,” in The Measurement, Instrumentation, and Sensors Handbook, J. G. Webster, ed. (Springer-Verlag, 1999).

Hirchaud, F.

Jacquot, M.

Z. Galeano, A. July, P. Sandoz, E. Gaiffe, S. Launay, L. Robert, M. Jacquot, F. Hirchaud, J. L. Prétet, and C. Mougin, “Position-referenced microscopy for live cell culture monitoring,” Biomed. Opt. Express 2, 1307–1318 (2011).
[CrossRef]

P. Sandoz and M. Jacquot, “Lensless vision system for in-plane positioning of a patterned plate with subpixel resolution,” J. Opt Soc. Am. A 28, 2494–2500 (2011).
[CrossRef]

July, A.

Kronland-Martinet, R.

R. Kronland-Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Recogn. Artif. Intell. 1, 273–302 (1987).
[CrossRef]

Launay, S.

Meneses, J. E.

Morlet, J.

R. Kronland-Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Recogn. Artif. Intell. 1, 273–302 (1987).
[CrossRef]

Mougin, C.

Z. Galeano, A. July, P. Sandoz, E. Gaiffe, S. Launay, L. Robert, M. Jacquot, F. Hirchaud, J. L. Prétet, and C. Mougin, “Position-referenced microscopy for live cell culture monitoring,” Biomed. Opt. Express 2, 1307–1318 (2011).
[CrossRef]

J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
[CrossRef]

P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
[CrossRef]

Prétet, J. L.

Z. Galeano, A. July, P. Sandoz, E. Gaiffe, S. Launay, L. Robert, M. Jacquot, F. Hirchaud, J. L. Prétet, and C. Mougin, “Position-referenced microscopy for live cell culture monitoring,” Biomed. Opt. Express 2, 1307–1318 (2011).
[CrossRef]

J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
[CrossRef]

P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
[CrossRef]

Robert, L.

Sandoz, P.

Z. Galeano, A. July, P. Sandoz, E. Gaiffe, S. Launay, L. Robert, M. Jacquot, F. Hirchaud, J. L. Prétet, and C. Mougin, “Position-referenced microscopy for live cell culture monitoring,” Biomed. Opt. Express 2, 1307–1318 (2011).
[CrossRef]

P. Sandoz and M. Jacquot, “Lensless vision system for in-plane positioning of a patterned plate with subpixel resolution,” J. Opt Soc. Am. A 28, 2494–2500 (2011).
[CrossRef]

J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
[CrossRef]

N. A. Arias H., P. Sandoz, J. E. Meneses, M. A. Suarez, and T. Gharbi, “3D localization of a labeled target by means of a stereo vision configuration with subvoxel resolution,” Opt. Express 18, 24152–24162 (2010).
[CrossRef]

P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
[CrossRef]

Suarez, M. A.

Zeggari, R.

P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
[CrossRef]

Zhao, B.

B. Zhao and A. Asundi, “Microscopic grid methods—resolution and sensitivity,” Opt. Laser Eng. 36, 437–450 (2001).
[CrossRef]

Biomed. Opt. Express

Int. J. Optomech.

J. A. Galeano-Zea, P. Sandoz, E. Gaiffe, J. L. Prétet, and C. Mougin, “Pseudo-periodic encryption of extended 2-D surfaces for high accurate recovery of any random zone by vision,” Int. J. Optomech. 4, 65–82 (2010).
[CrossRef]

Int. J. Pattern Recogn. Artif. Intell.

R. Kronland-Martinet, J. Morlet, and A. Grossmann, “Analysis of sound patterns through wavelet transforms,” Int. J. Pattern Recogn. Artif. Intell. 1, 273–302 (1987).
[CrossRef]

J. Microsc.

P. Sandoz, R. Zeggari, L. Froelhy, J. L. Prétet, and C. Mougin, “Position referencing in optical microscopy thanks to sample holders with out-of-focus encoded patterns,” J. Microsc. 225, 293–303 (2007).
[CrossRef]

J. Opt Soc. Am. A

P. Sandoz and M. Jacquot, “Lensless vision system for in-plane positioning of a patterned plate with subpixel resolution,” J. Opt Soc. Am. A 28, 2494–2500 (2011).
[CrossRef]

Opt. Express

Opt. Laser Eng.

B. Zhao and A. Asundi, “Microscopic grid methods—resolution and sensitivity,” Opt. Laser Eng. 36, 437–450 (2001).
[CrossRef]

Other

H. S. Cho, Optomechatronics: Fusion of Optical and Mechatronic Engineering (CRC Press, 2006).

R. J. Hansman, “Characteristics of instrumentation,” in The Measurement, Instrumentation, and Sensors Handbook, J. G. Webster, ed. (Springer-Verlag, 1999).

J. Y. Bouguet, “Camera calibration toolbox for MATLAB” (2008), http://www.vision.caltech.edu/bouguetj/calib_doc/ .

S. W. Golomb, Shift Register Sequences (Holden-Day, 1967).

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Figures (12)

Fig. 1.
Fig. 1.

3 bits position encryption sequence. (a) Principle and (b) 2D pattern obtained.

Fig. 2.
Fig. 2.

Image processing steps: (a) horizontal band of the recorded image, (b) intensity profile obtained by summing along image columns, (c) spectral phase of (b), (d) modulus of (b), (e) binary signal locating the intensity extrema, (f) analog signal for the discrimination of absent and present stripes.

Fig. 3.
Fig. 3.

Effects of target translation on the measured position for each camera. A and B stand for the cameras; x and z stand for the unit vectors along the target displacement axes; θa and θb are the angles of the optical axes with respect to the z axis; a and b represent the vectors on which the target displacements are projected for cameras A and B, respectively; O and O represent the initial and final target positions, respectively; xa and xb are the pattern abscissa at its intersections with the optical axes of the two cameras; Δx and Δz represent the target displacement from O to O.

Fig. 4.
Fig. 4.

Variations in the measured positions xa and xb for cameras A and B, respectively, while the target was translated along the (a) Z and (b) X directions by 340 μm.

Fig. 5.
Fig. 5.

Variations in the measured positions ya and yb for cameras A and B, respectively, while the target was translated along the (a) Z and (b) X directions by 340 μm.

Fig. 6.
Fig. 6.

Variations in the measured positions (a) ya and yb and (b) xa and xb for cameras A and B, respectively, while the target was translated along the Y direction by 240 μm.

Fig. 7.
Fig. 7.

Reconstructed target translation along X versus (a) the position given by the PZT capacitive sensor and (b) deviation from a straight line (standard deviation: 0.037 μm).

Fig. 8.
Fig. 8.

Reconstructed target translation along Y versus (a) the position given by the PZT capacitive sensor and (b) deviation from a straight line (standard deviation: 0.045 μm).

Fig. 9.
Fig. 9.

Reconstructed target translation along Z (a) versus the position given by the PZT capacitive sensor and (b) deviation from a straight line (standard deviation: 0.033 μm).

Fig. 10.
Fig. 10.

Reconstruction of a 3D spiral-like translation applied to the PZT tranducer. Black: reconstructed position; red: position returned by the PZT capacitive sensor. (a) 3D view, (b) front view, (c) side view.

Fig. 11.
Fig. 11.

Same as Fig. 10 with a displacement range larger than the period of the PPP.

Fig. 12.
Fig. 12.

Reconstruction of an extended 3D translation (Δx=7mm, Δy=10mm, Δz=7mm).

Equations (8)

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

Φc=2kcπ+ϕc,
[ΔxaΔxb]=[1sinθa1sinθb]×[ΔxΔz],
[ΔxΔz]=0.5·[1sinθasinθbsinθa+sinθb02sinθa+sinθb]×[Δxa+ΔxbΔxaΔxb].
[ΔxaΔxb]=[sinθasinθb]×Δz.
Δxa=Δxb=Δx.
Δya=Δyb=Δy.
Δx=PPPxFoVxΔz·(sinθa+sinθb),
Δy=PPPyFoVy,

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