Skip to main content
Log in

Comparison of focal and afocal optics in insect eyes

  • Published:
Biological Cybernetics Aims and scope Submit manuscript

Abstract

Recent experiments suggest that an afocal lens system may occur in insect apposition eyes which are traditionally believed to contain focal systems. We present a theoretical analysis of lens-photoreceptor systems with focal and afocal optics. A simple parameterization of the systems is obtained and formulas are given for calculating receptor response to on-axis incident light and angular sensitivity. The simple parameterization and formulas allow the different lens photoreceptor systems to be compared: both systems may be similarily optimized for a given wavelength, but the focal lens may be marginally superior over a range of wavelengths. Possible refinements to the theory are discussed.

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

Access this article

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

  • Abramowitz M, Stegun IA (1972) Handbook of mathematical functions. Dover, New York

    Google Scholar 

  • Barrell KF, Pask C (1979a) Optical fibre excitation by lenses. Opt Acta 26:91–108

    Google Scholar 

  • Barrell KF, Pask C (1979b) Computation of Bessel functions of complex arguments using their zeros. Int J Comp Math 7B:65–72

    Google Scholar 

  • Born M, Wolf E (1970) Principles of optics. Pergamon Press, Oxford

    Google Scholar 

  • Horridge GA (1975) The compound eye and vision in insects. Clarendon Press, Oxford

    Google Scholar 

  • Kawakami S, Nishida S, Sumi M (1976) Transmission characteristics of a W-type optical fiber. Proc IEE 123:586–590

    Google Scholar 

  • Kirschfield K (1972) The visual system of Musca. In: Information processing in the visual system of arthropods. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Love JD, Hussey CD (1984) Variational approximations for higher-order modes of weakly-guiding fibres. Opt Quantum Electron 13:41–48

    Google Scholar 

  • Matic T (1983) Electrical inhibition in the retina of the butterfly Papilio. J Comp Physiol 152:169–182

    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 (submitted for publication)

  • 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 

  • Snyder AW (1969) Excitation and scattering of modes on a dielectric or optical fiber. IEEE Trans MTT-17:1138–1144

    Google Scholar 

  • Snyder AW, Pask C (1972) Light absorption in the bee photoreceptor. J Opt Soc Am 62:998–1008. See especially Appendix A. Modes for visual photoreceptors

    Google Scholar 

  • Welford WT (1962) Geometrical optics. North-Holland, Amsterdam

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pask, C., Garth, S.J. Comparison of focal and afocal optics in insect eyes. Biol. Cybern. 58, 337–344 (1988). https://doi.org/10.1007/BF00363943

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00363943

Keywords

Navigation