Skip to main content
Log in

Butterfly optics exceed the theoretical limits of conventional apposition eyes

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Optical experiments on butterfly compound eyes show that they have angular sensitivities narrower than expected from conventional apposition eyes. This superior performance is explained by a theoretical model where the cone stalk is considered as a modecoupling device. In this model the Airy diffraction pattern of the corneal facet excites a combination of the two waveguide modes LP01 and LP02. When the two modes propagate through the cone stalk the power of LP02 is transferred to LP01 alone which is supported by the rhabdom. This mechanism produces a higher on-axis sensitivity and a narrower angular sensitivity than conventional apposition optics. Several predictions of the model were confirmed experimentally.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Born M, Wolf E (1965) Principles of optics. Pergamon Press, Oxford

    Google Scholar 

  • Franceschini N (1975) Sampling of the visual environment by the compound eye of the fly: fundamentals and applications. In: Snyder AW, Menzel R (eds) Photoreceptor optics. Springer, Berlin Heidelberg New York, pp 98–125

    Google Scholar 

  • Goodman JW (1968) Introduction to Fourier optics. McGraw-Hill, New York

    Google Scholar 

  • Hateren JH van (1984) Waveguide theory applied to optically measured angular sensitivities of fly photoreceptors. J Comp Physiol A 154:761–771

    Google Scholar 

  • Horowitz BR (1981) Theoretical considerations of the retinal receptor as a waveguide. In: Enoch JM, Tobey FL Jr (eds) Vertebrate photoreceptor optics. Springer, Berlin Heidelberg New York, pp 219–300

    Google Scholar 

  • Kuiper JW (1966) On the image formation in a single ommatidium of the compound eye in Diptera. In: Bernhard CG (ed) The functional organization of the compound eye. Pergamon Press, Oxford, pp 35–50

    Google Scholar 

  • Land MF, Osorio D, Nilsson D-E (1987) Ecological variation in the optical structure of butterfly eyes (in preparation)

  • Li Y, Wolf E (1984) Three-dimensional intensity distribution near the focus in systems of different Fresnel numbers. J Opt Soc Am A 1:801–808

    Google Scholar 

  • Lim TK, Garside BK, Marton JP (1979) An analysis of optical waveguide tapers. Appl Phys 18:53–62

    Google Scholar 

  • Nelson AR (1975) Coupling optical waveguides by tapers. Appl Opt 14:3012–3015

    Google Scholar 

  • Nilsson D-E, Land MF, Howard J (1984) Afocal apposition optics in butterfly eyes. Nature 312:561–563

    Google Scholar 

  • Nilsson D-E, Land MF, Howard J (1987) Optical characteristics of the butterfly eye. J Comp Physiol A (in press)

  • Pask C, Barrell KF (1980a) Photoreceptor optics I: Introduction to formalism and excitation in a lens-photoreceptor system. Biol Cybern 36:1–8

    Google Scholar 

  • Pask C, Barrell KF (1980b) Photoreceptor optics II: Application to angular sensitivity and other properties of a lensphotoreceptor system. Biol Cybern 36:9–18

    Google Scholar 

  • Smakman JGJ, Hateren JH van, Stavenga DG (1984) Angular sensitivity of blowfly photoreceptors: intracellular measurements and wave-optical predictions. J comp Physiol A 155:239–247

    Google Scholar 

  • Snyder AW (1970) Coupling of modes on a tapered dielectric cylinder. IEEE Trans Microwaves Theory Tech 18:383–392

    Google Scholar 

  • Snyder AW (1975) Photoreceptor optics-Theoretical principles. In: Snyder AW, Menzel R (eds) Photoreceptor optics. Springer, Berlin Heidelberg New York, pp 38–55

    Google Scholar 

  • Snyder AW (1977) Acuity of compound eyes: Physical limitations and design. J Comp Physiol A 116:161–182

    Google Scholar 

  • Snyder AW, Love DJ (1983) Optical waveguide theory. Chapman and Hall, London New York

    Google Scholar 

  • Snyder AW, Laughlin SB, Stavenga DG (1977) Information capacity of eyes. Vision Res 17:1163–1175

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

van Hateren, J.H., Nilsson, D.E. Butterfly optics exceed the theoretical limits of conventional apposition eyes. Biol. Cybern. 57, 159–168 (1987). https://doi.org/10.1007/BF00364148

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00364148

Keywords

Navigation