
8.2 The Fourier Slice Theorem
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where 7^ is the difference between the transit time through the material and
the transit time when the material is replaced by water. T
d
is positive if the
former transit time is longer than the latter. Note that we have expressed
the ray integral for 1 —
n(x
9
y)
rather than n(x, y). To ensure that in the
reconstructed image the background values are zero, one usually makes the
image for 1 — n(x, y). [For a point in water outside the material we have
n(x, y) = 1, so that 1 — n(x, y) = 0.]
The ray integral is valid provided in Fig. 8 the ultrasonic beam travels
along a straight line from A to B. In medical imagin ...