Abstract

Inspired by the natural phenomenon of hyperacuity, redundant sampling in combination with the knowledge about the impulse response of the imaging system is used to extract highly accurate information using a low resolving artificial apposition compound eye. Thus the implementation of a precise position detection for simple objects like point sources and edges is described.

©2006 Optical Society of America

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References

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  1. J. Duparré, P. Dannberg, P. Schreiber, A. Bräuer, and A. Tünnermann, “Artificial apposition compound eye fabricated by micro-optics technology,” Appl. Opt. 43, 4303–4310 (2004).
    [Crossref] [PubMed]
  2. J. Duparré, P. Dannberg, P. Schreiber, A. Bräuer, and A. Tünnermann, “Thin compound-eye camera,” Appl. Opt. 44, 2949–2956 (2005).
    [Crossref] [PubMed]
  3. R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
    [Crossref]
  4. K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).
    [Crossref] [PubMed]
  5. M. J. Wilcox and D. C. Jr. Thelen, “A Retina with Parallel Input and Pulsed Output, Extracting High-Resolution Information,” IEEE Trans. Neural Net. 10, 574–583 (1999).
    [Crossref]
  6. S. B. Laughlin, “Form and function in retinal processing,” TINS 10, 478–483 (1987).
  7. J. S. Sanders and C. E. Halford, “Design and analysis of apposition compound eye optical sensors,” Opt. Eng. 34, 222–235 (1995).
    [Crossref]
  8. G. Westheimer, “Diffraction Theory and Visual Hyperacuity,” Am. J. Optom. Physiol. Opt. 53, 362–364 (1976).
    [Crossref] [PubMed]
  9. R. A. Young, “Bridging the gap between vision and commercial applications,” in Human Vision, Visual Processing and Digital Display VI, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE2411, 2–14 (1995).
    [Crossref]
  10. S. Viollet and N. Franceschini, “Visual servo system based on a biologically-inspired scanning sensor,” in Sensor Fusion and Decentralized Control in Robotic Systems II, G. T. McKee and P. S. Schenker, eds., Proc. SPIE3839, 144–155 (1999).
    [Crossref]
  11. K. Hoshino, F. Mura, and I. Shimoyama, “A one-chip scanning retina with an integrated microme-chanical scanning actuator,” J. Microelectromech. Syst. 10, 492–497 (2001).
    [Crossref]
  12. M. S. Currin, P. Schonbaum, C. E. Halford, and R. G. Driggers,“Musca domestica inspired machine vision system with hyperacuity,” Opt. Eng. 34, 607–611 (1995).
    [Crossref]
  13. D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
    [Crossref]
  14. K. G. Götz, “Die optischen Übertragungseigenschaften der Komplexaugen von Drosophila,” Kybernetik 2, 215–221 (1965).
    [Crossref] [PubMed]
  15. A. W. Snyder, “Acuity of compound eyes: Physical limitations and design,” J. Comp. Physiol. A 116, 161–182 (1977).
    [Crossref]
  16. J. Duparré, F. Wippermann, P. Dannberg, and A. Reimann, “Chirped arrays of refractive ellipsoidal microlenses for aberration correction under oblique incidence,” Opt. Express 13, 10539–10551 (2005).
    [Crossref] [PubMed]
  17. K. Kirschfeld and N. Franceschini, “Optische Eigenschaften der Ommatidien im Komplexauge von Musca,” Kybernetik 5, 47–52 (1968).
    [Crossref] [PubMed]

2005 (2)

2004 (1)

2003 (1)

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[Crossref]

2001 (1)

K. Hoshino, F. Mura, and I. Shimoyama, “A one-chip scanning retina with an integrated microme-chanical scanning actuator,” J. Microelectromech. Syst. 10, 492–497 (2001).
[Crossref]

1999 (1)

M. J. Wilcox and D. C. Jr. Thelen, “A Retina with Parallel Input and Pulsed Output, Extracting High-Resolution Information,” IEEE Trans. Neural Net. 10, 574–583 (1999).
[Crossref]

1995 (2)

M. S. Currin, P. Schonbaum, C. E. Halford, and R. G. Driggers,“Musca domestica inspired machine vision system with hyperacuity,” Opt. Eng. 34, 607–611 (1995).
[Crossref]

J. S. Sanders and C. E. Halford, “Design and analysis of apposition compound eye optical sensors,” Opt. Eng. 34, 222–235 (1995).
[Crossref]

1987 (1)

S. B. Laughlin, “Form and function in retinal processing,” TINS 10, 478–483 (1987).

1985 (1)

K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).
[Crossref] [PubMed]

1977 (1)

A. W. Snyder, “Acuity of compound eyes: Physical limitations and design,” J. Comp. Physiol. A 116, 161–182 (1977).
[Crossref]

1976 (1)

G. Westheimer, “Diffraction Theory and Visual Hyperacuity,” Am. J. Optom. Physiol. Opt. 53, 362–364 (1976).
[Crossref] [PubMed]

1968 (1)

K. Kirschfeld and N. Franceschini, “Optische Eigenschaften der Ommatidien im Komplexauge von Musca,” Kybernetik 5, 47–52 (1968).
[Crossref] [PubMed]

1965 (1)

K. G. Götz, “Die optischen Übertragungseigenschaften der Komplexaugen von Drosophila,” Kybernetik 2, 215–221 (1965).
[Crossref] [PubMed]

Barrett, S. F.

D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
[Crossref]

Bräuer, A.

Currin, M. S.

M. S. Currin, P. Schonbaum, C. E. Halford, and R. G. Driggers,“Musca domestica inspired machine vision system with hyperacuity,” Opt. Eng. 34, 607–611 (1995).
[Crossref]

Dannberg, P.

Driggers, R. G.

M. S. Currin, P. Schonbaum, C. E. Halford, and R. G. Driggers,“Musca domestica inspired machine vision system with hyperacuity,” Opt. Eng. 34, 607–611 (1995).
[Crossref]

Duparré, J.

Eisner, M.

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[Crossref]

Franceschini, N.

K. Kirschfeld and N. Franceschini, “Optische Eigenschaften der Ommatidien im Komplexauge von Musca,” Kybernetik 5, 47–52 (1968).
[Crossref] [PubMed]

S. Viollet and N. Franceschini, “Visual servo system based on a biologically-inspired scanning sensor,” in Sensor Fusion and Decentralized Control in Robotic Systems II, G. T. McKee and P. S. Schenker, eds., Proc. SPIE3839, 144–155 (1999).
[Crossref]

Götz, K. G.

K. G. Götz, “Die optischen Übertragungseigenschaften der Komplexaugen von Drosophila,” Kybernetik 2, 215–221 (1965).
[Crossref] [PubMed]

Halford, C. E.

J. S. Sanders and C. E. Halford, “Design and analysis of apposition compound eye optical sensors,” Opt. Eng. 34, 222–235 (1995).
[Crossref]

M. S. Currin, P. Schonbaum, C. E. Halford, and R. G. Driggers,“Musca domestica inspired machine vision system with hyperacuity,” Opt. Eng. 34, 607–611 (1995).
[Crossref]

Harman, W. M.

D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
[Crossref]

Hoshino, K.

K. Hoshino, F. Mura, and I. Shimoyama, “A one-chip scanning retina with an integrated microme-chanical scanning actuator,” J. Microelectromech. Syst. 10, 492–497 (2001).
[Crossref]

Jr. Thelen, D. C.

M. J. Wilcox and D. C. Jr. Thelen, “A Retina with Parallel Input and Pulsed Output, Extracting High-Resolution Information,” IEEE Trans. Neural Net. 10, 574–583 (1999).
[Crossref]

Kirschfeld, K.

K. Kirschfeld and N. Franceschini, “Optische Eigenschaften der Ommatidien im Komplexauge von Musca,” Kybernetik 5, 47–52 (1968).
[Crossref] [PubMed]

Laughlin, S. B.

S. B. Laughlin, “Form and function in retinal processing,” TINS 10, 478–483 (1987).

Mura, F.

K. Hoshino, F. Mura, and I. Shimoyama, “A one-chip scanning retina with an integrated microme-chanical scanning actuator,” J. Microelectromech. Syst. 10, 492–497 (2001).
[Crossref]

Nakayama, K.

K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).
[Crossref] [PubMed]

Reimann, A.

Riley, D. T.

D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
[Crossref]

Sanders, J. S.

J. S. Sanders and C. E. Halford, “Design and analysis of apposition compound eye optical sensors,” Opt. Eng. 34, 222–235 (1995).
[Crossref]

Schonbaum, P.

M. S. Currin, P. Schonbaum, C. E. Halford, and R. G. Driggers,“Musca domestica inspired machine vision system with hyperacuity,” Opt. Eng. 34, 607–611 (1995).
[Crossref]

Schreiber, P.

Shimoyama, I.

K. Hoshino, F. Mura, and I. Shimoyama, “A one-chip scanning retina with an integrated microme-chanical scanning actuator,” J. Microelectromech. Syst. 10, 492–497 (2001).
[Crossref]

Snyder, A. W.

A. W. Snyder, “Acuity of compound eyes: Physical limitations and design,” J. Comp. Physiol. A 116, 161–182 (1977).
[Crossref]

Tomberlin, E.

D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
[Crossref]

Tünnermann, A.

Viollet, S.

S. Viollet and N. Franceschini, “Visual servo system based on a biologically-inspired scanning sensor,” in Sensor Fusion and Decentralized Control in Robotic Systems II, G. T. McKee and P. S. Schenker, eds., Proc. SPIE3839, 144–155 (1999).
[Crossref]

Völkel, R.

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[Crossref]

Weible, K. J.

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[Crossref]

Westheimer, G.

G. Westheimer, “Diffraction Theory and Visual Hyperacuity,” Am. J. Optom. Physiol. Opt. 53, 362–364 (1976).
[Crossref] [PubMed]

Wilcox, M.

D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
[Crossref]

Wilcox, M. J.

M. J. Wilcox and D. C. Jr. Thelen, “A Retina with Parallel Input and Pulsed Output, Extracting High-Resolution Information,” IEEE Trans. Neural Net. 10, 574–583 (1999).
[Crossref]

Wippermann, F.

Wright, C. H. G.

D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
[Crossref]

Young, R. A.

R. A. Young, “Bridging the gap between vision and commercial applications,” in Human Vision, Visual Processing and Digital Display VI, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE2411, 2–14 (1995).
[Crossref]

Am. J. Optom. Physiol. Opt. (1)

G. Westheimer, “Diffraction Theory and Visual Hyperacuity,” Am. J. Optom. Physiol. Opt. 53, 362–364 (1976).
[Crossref] [PubMed]

Appl. Opt. (2)

IEEE Trans. Neural Net. (1)

M. J. Wilcox and D. C. Jr. Thelen, “A Retina with Parallel Input and Pulsed Output, Extracting High-Resolution Information,” IEEE Trans. Neural Net. 10, 574–583 (1999).
[Crossref]

J. Comp. Physiol. A (1)

A. W. Snyder, “Acuity of compound eyes: Physical limitations and design,” J. Comp. Physiol. A 116, 161–182 (1977).
[Crossref]

J. Microelectromech. Syst. (1)

K. Hoshino, F. Mura, and I. Shimoyama, “A one-chip scanning retina with an integrated microme-chanical scanning actuator,” J. Microelectromech. Syst. 10, 492–497 (2001).
[Crossref]

Kybernetik (2)

K. G. Götz, “Die optischen Übertragungseigenschaften der Komplexaugen von Drosophila,” Kybernetik 2, 215–221 (1965).
[Crossref] [PubMed]

K. Kirschfeld and N. Franceschini, “Optische Eigenschaften der Ommatidien im Komplexauge von Musca,” Kybernetik 5, 47–52 (1968).
[Crossref] [PubMed]

Microelectron. Eng. (1)

R. Völkel, M. Eisner, and K. J. Weible, “Miniaturized imaging systems,” Microelectron. Eng. 67–68, 461–472 (2003).
[Crossref]

Opt. Eng. (2)

J. S. Sanders and C. E. Halford, “Design and analysis of apposition compound eye optical sensors,” Opt. Eng. 34, 222–235 (1995).
[Crossref]

M. S. Currin, P. Schonbaum, C. E. Halford, and R. G. Driggers,“Musca domestica inspired machine vision system with hyperacuity,” Opt. Eng. 34, 607–611 (1995).
[Crossref]

Opt. Express (1)

TINS (1)

S. B. Laughlin, “Form and function in retinal processing,” TINS 10, 478–483 (1987).

Vision Res. (1)

K. Nakayama, “Biological image motion processing: a review,” Vision Res. 25, 625–660 (1985).
[Crossref] [PubMed]

Other (3)

R. A. Young, “Bridging the gap between vision and commercial applications,” in Human Vision, Visual Processing and Digital Display VI, B. E. Rogowitz and J. P. Allebach, eds., Proc. SPIE2411, 2–14 (1995).
[Crossref]

S. Viollet and N. Franceschini, “Visual servo system based on a biologically-inspired scanning sensor,” in Sensor Fusion and Decentralized Control in Robotic Systems II, G. T. McKee and P. S. Schenker, eds., Proc. SPIE3839, 144–155 (1999).
[Crossref]

D. T. Riley, W. M. Harman, E. Tomberlin, S. F. Barrett, M. Wilcox, and C. H. G. Wright, “Musca domestica inspired machine vision system with hyperacuity,” in Smart Structures and Materials 2005: Smart Sensor Technology and Measurement Systems, E. Udd and D. Inaudi, eds., Proc. SPIE5758, 304–320 (2005).
[Crossref]

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Figures (7)

Fig. 1.
Fig. 1. Schematic section of an artificial apposition compound eye with a system length L. Δϕ is the angle between two adjacent optical axes (sampling angle) and Δφ the acceptance angle which is a measure for the smallest resolvable feature size.

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Fig. 2.
Fig. 2. Origin of the angular sensitivity function (ASF) of one channel and its FWHM, the acceptance angle.

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Fig. 3.
Fig. 3. (a): Efficiency of intensity transfer for a point source at φp in three adjacent channels with overlapping FOVs. (b): Position of a point source within the projected image plane. For a given intensity the position lies on a circle with radius rk around the optical axis (•) of the k’th channel.

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Fig. 4.
Fig. 4. The difference of the normal distances of the edge to the optical axis of each channel (•) is given by the pitch difference Δ p and the orientation angle ϑK . Dashed box: The intensity in the image plane of one channel on a path normal to the edge.

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Fig. 5.
Fig. 5. Experimental setup for position detection with hyperacuity. A point source at infinity (a) or an edge (b) is used as object within the FOV of the artificial apposition compound eye (APCO). The edge is illuminated with homogenized white light from a RGB LED source. The illuminated pinholes on the backside of the artificial apposition compound eye are relayed onto a CCD. Rotating the ensemble of the artificial apposition compound eye, microscope objective (MO) and CCD camera simulates object movement.

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Fig. 6.
Fig. 6. (a): Example of measured angular distances Δϕm (blue dots) compared with reference values Δϕref (red line) for an artificial apposition compound eye with 64×64 channels imaging an edge. The difference of both gives the acuity δa of the measurement (black). The acceptance angle is Δϕ=0.9°. (b): Overlap of the high accuracy zones in three adjacent channels. The measured accuracies are shown in relation to the angular distance to the optical axis of one channel.

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Fig. 7.
Fig. 7. Measured maximum accuracy in degrees as a function of the signal-to-noise ratio (SNR).

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Tables (1)

Tables Icon

Table 1. Experimental results: Measured accuracies for different artificial compound eyes in relation to the acceptance angle that is corresponding to a resolu- tion of one line pair (LP). The pinhole diameters d are 2,3 and 4 µm.

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Equations (15)

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I ( x , y ) = ∫ − ∞ ∞ ∫ − ∞ ∞ R ( x − ξ , y − η ) · O ( ξ , η ) d ξ d η .
ASF ( φ ) ≈ exp [ − 4 · ln 2 · ( φ Δ φ ) 2 ] .
Δ φ = ( λ D ) 2 + ( d f ) 2 .
I k ( φ ) = c · ASF k ( φ P ) .
α x = I 1 ( φ 1 ) I 0 ( φ 0 ) ≈ exp [ − 4 ln ( 2 ) Δ φ 2 · ( φ 1 2 − φ 0 2 ) ] .
r 0 = x 0 2 + y 0 2
r 1 = x 1 2 + y 1 2 = ( x 0 − Δ p ) 2 + y 0 2 ,
φ = arctan ( r f ) ≈ r f .
α x ≈ exp { − s · [ Δ p 2 − 2 Δ p · x 0 ] } ,
s = 4 · ln ( 2 ) ( Δ φ · f ) 2 .
x 0 = ln ( α x ) 2 · s · Δ p + Δ p 2 .
I k ( r ) ≈ const · ∫ − ∞ ∞ R ( r − r k ) · Q 0 · Θ ( r k ) d r k + B .
I k ( r ) ≈ const · 1 2 π s [ er f ( s · r ) + 1 ] + B ,
er f ( x ) = 2 π · ∫ 0 x exp { − t 2 } d t .
r 0 = ± [ ln ( α ~ x ) 2 s · Δ p · cos ϑ k + Δ p · cos ϑ k 2 ] .

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