Considerable simplification occurs if the approximation, tan-1(y) = y, y in radians, can be used. Note that the p/a terms cancel. Thus, Cvi can be written:
If a = 1°, p = 0.1°, d = 0.2°, GKA = 3, then CVi = 0.598 vs. CV1 = 0.0983 for a single receptor. A contrast improvement ratio of R = 6.1 is noted.
It has been shown theoretically that, under certain conditions, synthetic aperture architecture using as few as two receptors from adjacent ommatidia can yield improved voltage contrast in the axon of the medullary interneuron that presumably drives a spiking output neuron whose function is to sense novel movement of small contrasting objects in the visual field. Note that the success of the synthetic aperture architecture in improving contrast depends on the overall light level making the retinula cell depolarization obey the logarithmic approximation Vr = A ln(Ie/B). The actual existence of such neural connections in arthropod OLs remains to be demonstrated.
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