Radon Transform--Cylinder

Let the two-dimensional cylinder function be defined by

(1)

Then the Radon transform is given by

(2)

where

(3)

is the delta function. Rewriting in polar coordinates then gives

(4)

(5)

with a phase shift. Then

Then use

(9)

which, with , becomes

(10)

Define

so the inner integral is

			(14)
			(15)

and the Radon transform becomes

			(16)
			(17)
		${2/(1+p^2)sqrt(R^2(1+p^2)-tau^2) for tau^2<R^2(1+p^2); 0 for tau^2>=R^2(1+p^2).$	(18)

Converting to using ,

which could have been derived more simply by

(22)

See also