Digital Picture Processing, 2nd Edition

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 ...