Let the 2-D cylinder function be defined by
|
(1) |
Then the Radon transform is given by
|
(2) |
where
|
(3) |
is the Delta Function.
|
|
|
|
|
(4) |
Now write
|
(5) |
with a phase shift. Then
Then use
|
(7) |
which, with , becomes
|
(8) |
Define
so the inner integral is
and the Radon transform becomes
Converting to using ,
which could have been derived more simply by
|
(16) |
© 1996-9 Eric W. Weisstein
1999-05-25