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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Duparre, P. Dannberg, P. Schreiber, A. Brauer and A. Tunnermann, "Artificial apposition compound eye fabricated by micro-optics technology," Appl. Opt. 43, 4303-4310 (2004).
    [CrossRef] [PubMed]
  2. J. Duparre, P. Dannberg, P. Schreiber, A. Brauer and A. Tunnermann, "Thin compound-eye camera," Appl. Opt. 44, 2949-2956 (2005).
    [CrossRef] [PubMed]
  3. R. Volkel, 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. SPIE 2411, 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. SPIE 3839, 144-155 (1999).
    [CrossRef]
  11. K. Hoshino, F. Mura and I. Shimoyama, "A one-chip scanning retina with an integrated micromechanical 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. SPIE 5758, 304-320 (2005).
    [CrossRef]
  14. K. G. Gotz, "Die optischen ¨Ubertragungseigenschaften 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. Duparre, 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. Volkel, 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 micromechanical 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. Gotz, "Die optischen ¨Ubertragungseigenschaften der Komplexaugen von Drosophila," Kybernetik 2, 215-221 (1965).
[CrossRef] [PubMed]

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]

Duparre, J.

Franceschini, N.

K. Kirschfeld and N. Franceschini, "Optische Eigenschaften der Ommatidien im Komplexauge von Musca," Kybernetik 5, 47-52 (1968).
[CrossRef] [PubMed]

Halford, C. E.

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]

Hoshino, K.

K. Hoshino, F. Mura and I. Shimoyama, "A one-chip scanning retina with an integrated micromechanical scanning actuator," J. Microelectromech. Syst. 10, 492-497 (2001).
[CrossRef]

Jr, 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 micromechanical 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.

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 micromechanical 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]

Westheimer, G.

G. Westheimer, "Diffraction Theory and Visual Hyperacuity," Am. J. Optom. Physiol. Opt. 53, 362-364 (1976).
[CrossRef] [PubMed]

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.

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 micromechanical scanning actuator," J. Microelectromech. Syst. 10, 492-497 (2001).
[CrossRef]

Kybernetik (2)

K. Kirschfeld and N. Franceschini, "Optische Eigenschaften der Ommatidien im Komplexauge von Musca," Kybernetik 5, 47-52 (1968).
[CrossRef] [PubMed]

K. G. Gotz, "Die optischen ¨Ubertragungseigenschaften der Komplexaugen von Drosophila," Kybernetik 2, 215-221 (1965).
[CrossRef] [PubMed]

Microelectron. Eng. (1)

R. Volkel, M. Eisner and K. J. Weible, "Miniaturized imaging systems," Microelectron. Eng. 67-68, 461-472 (2003).
[CrossRef]

Opt. Eng. (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]

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)

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. SPIE 5758, 304-320 (2005).
[CrossRef]

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. SPIE 2411, 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. SPIE 3839, 144-155 (1999).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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.

Fig. 2.
Fig. 2.

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

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.

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.

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.

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.

Fig. 7.
Fig. 7.

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

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.

Equations (15)

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

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 ] .

Metrics