Angular and spectral sensitivity of fly photoreceptors. I. Integrated facet lens and rhabdomere optics

Three optical components of a fly’s eye determine the angular sensitivity of the photoreceptors: the light diffracting facet lens, the wave-guiding rhabdomere and the light-absorbing visual pigment in the rhabdomere. How the integrated optical system of the fly eye shapes the angular sensitivity curves is quantitatively analyzed in five steps: (1) scalar diffraction theory for low Fresnel-number lenses is applied to four different facet lenses, with diameter 10, 20, 40, and 80 µm, respectively, assuming a constant F-number of 2.2; (2) optical waveguide theory is used to calculate waveguide modes propagating in circular cylindrical rhabdomeres with diameter 1.0, 2.0, and 4.0 µm, respectively; (3) the excitation of waveguide modes is studied with the tip of the waveguide positioned in the focal plane as well as outside this plane; (4) the light absorption from the various propagated modes by the visual pigment in the rhabdomere is calculated as a function of the angle of the incident light wave; and (5) the angular sensitivity of the photoreceptor is obtained by normalizing the total light absorption. Four wavelengths are considered: 300, 400, 500 and 600 nm. The analysis shows that the wavelength dependency of the lens diffraction is strongly compensated by that of the waveguide modes, an effect which is further enhanced by the decrease in light absorption when the mode number increases. The angular sensitivity of fly photoreceptors is robust to defocus and largely wavelength independent for all except very slender rhabdomeres