Info

d where Ib is the background intensity of illumination, and kj and Id are positive constants.

It is mathematically convenient to work in the spatial frequency domain to find the effective absorbed intensity, Ie, for various objects. That is, one takes the two-dimensional Fourier transforms of p(x, y) and s(x, y). u and v are spatial frequencies with the dimensions of radian/mm. Thus,

F{ko[p(x, y)**s(x, y)]} = k P(u, v) S(u, v) Real convolution theorem 5.2-4C

To find Ie, take the inverse Fourier transform of Equation 5.2.4C with x = y = 0. (x = y = 0 corresponds to the center of the coordinate system for the one retinula cell under study. It is tacitly assumed that because of axial symmetry, all retinula cells in a given ommatidium have the same DSF.) The effective intensity is found by le = F-1[koP(u,v)S(u, v)] = -ko2 f f P(u, v)S(u,v)dudv 5.2-5

Still further mathematical simplification occurs if it is assumed that s(x, y) is symmetrical and independent in x and y, i.e., s(x, y) ^ s(x) s(y), and s(x) = s(y). Now analysis can be carried out in one-dimensional with little loss of generality. Two models frequently used for one-dimensional DSFs are s(x) =--, n > 2 Hill function 5.2-6

Gaussian function

Was this article helpful?

0 0
Peripheral Neuropathy Natural Treatment Options

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


Post a comment