Radiological Imaging by Harrison H Barrett; William Swindell

By Harrison H Barrett; William Swindell

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1 IMPULSE RESPONSE Nonlocal Behavior of Linear Systems It should be evident from the examples given above that the output of a system for some value of the independent variable u cannot in general be determined from the input at that one value of u. If u is the time t, then H)out(t) depends not only on Win evaluated at the current time, but also on ltt'in at previous times. No real system responds instantaneously to a stimulus; there is always a time delay. A similar situation occurs if u represents a spatial position.

Another popular image-forming element is the pinhole (Fig. 23). In this case the image can be either minified or magnified depending on the object location. This flexibility is the main advantage of the pinhole, since a large magnification is desired for imaging very small organs. magnified image light scinti Ilation crystal collimator srno 1/ radioactive organ Fig. 22 Magnifying collimator, often called a converging collimator, which can be used to increase the size of the image of a small organ.

Once again we subsume all questions of dimensionality and use the general variable u which can be one-, two-, or three-dimensional as required. In any case, K is the frequency variable conjugate to u. 'fin(K) = f~oo exp( - 2niKu)Win(U) du. 22) and similarly for wout{u). 'fin(K) dx. 23) We have now resolved an arbitrary input into a linear superposition of complex exponential functions. 16). 23) will pass through the system independently; this, in fact, is the definition of linearity. 16), with weighting factors ~n(K).

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