Figure P57

5.8. Of interest is the motion sensitivity of a photoreceptor when a one-dimensional DSF, s(x) = exp[-x2/(2a2)], views a one-dimensional, spatial sinewave object given a small displacement, 8x. Mathematically this object can be written:

For algebraic ease, this sinewave can be written as a shifted cosine wave when Fourier transforming. Thus, F(u, 8x) = (Io/2)[2n 8(u) + 1/2 8(u + uo) + 1/2 8(u - uo]) exp[-ju(X/4 + 8x)]. Note that uo = 2n/X, where x = X is the spatial period of the sinewave. The right-hand exponential term shifts the cosine wave by 90° to make a -sinewave, and gives an additional displacement, 8x, required to give a contrast change. The contrast is defined here as C(8x) = AIe/Ie(0). Ie(0) is the effective absorbed light intensity with 8x = 0. AIe = Ie(0) - Ie(8x).

a. Use the Fourier transform approach to find an expression for Ie(0).

c. Use the expression for the contrast, C(8x), to calculate the 8x required to produce C(8x) = 0.01 as a function of the receptor DSF half-angle,

6m/2. Note that ct = 9m/2^ln(4) , let X = 5°. Consider 0.25 9 6m/2 9 2.5°. (Be careful to use proper angle dimensions, degrees or radians, when solving this problem.)

0 0

Peripheral Neuropathy Natural Treatment Options

This guide will help millions of people understand this condition so that they can take control of their lives and make informed decisions. The ebook covers information on a vast number of different types of neuropathy. In addition, it will be a useful resource for their families, caregivers, and health care providers.

Get My Free Ebook