Theory of the summation of scattered light in clear zone compound eyes

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Abstract
1. The clear zone between the cones and the receptors of dark-adapted nocturnal insects and crustaceans is considered as a region across which light entering the eye by many facets can sum upon the receptors beyond the clear zone. 2. In the model, light is admitted through each facet as a normal distribution. This amount of light spreads out from the cone tip as another normal distribution unrelated to the first except in total energy. The direction of arrival of a ray on the receptor is therefore minimally related to its direction of origin. 3. At the expense of acuity the geometry of summation across the clear zone increases the sensitivity of the eye in the ratio R21/R22 where R1 and R2 are the radii from the centre of the eye to the cone tips and to the receptor layer. 4. The existence of a clear zone permits a further increase in sensitivity in the dark-adapted state by allowing an increase in the acceptance angle of the facets and in cross-sectional area of the receptors, without prejudice to the acuity of the light-adapted eye. 5. In this model of the clear zone eye, a minimum of parameters and optical properties are assumed. An intensity at the receptor greater than that given by this ‘null hypothesis’ would then point to additional optical mechanisms.

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