
402
8 Reconstruction
y
In order to express the reconstruction formula given by (91) in a form
that can be easily implemented on a computer we will first examine the
argument of the function h. The argument may be rewritten as
r cos(jS + y — φ) — D sin y = r cos(ß — φ) cos γ — [r sin(ß — φ) + D] sin γ
(92)
Let L be the distance from the source S to a point (x, y) [or (r, φ) in polar
coordinates] such as C in Fig. 26. Clearly, L is a function of three variables
r, φ, and ß. Also, let y' be the angle of the ray that passes through this point.
One can easily show that
L cos y' = D + r sin(/? — φ) and L sin y' = r cos(ß — φ) (93)
Fig. 26 This figure ...