If $f \in C_{c}^{\infty}\left(\mathbb{R}^{2}\right)$, the Radon transform of $f$ is the function $$R f(s, \omega):=\int_{-\infty}^{\infty} f\left(s \omega+t \omega^{\perp}\right) d t, \quad s \in \mathbb{R}, \omega \in S^{1} .$$

From the definition, Radon transform captures integral of functional along the line.

$R^{*}$ is the backprojection operator defined as $$R^{*}: C^{\infty}\left(\mathbb{R} \times S^{1}\right) \rightarrow C^{\infty}\left(\mathbb{R}^{2}\right), \quad R^{*} h(y)=\int_{S^{1}} h(y \cdot \omega, \omega) d \omega$$

Above is an adjoint of the Radon transform. I think it captures the integral of a function over the circle of radius $y\cdot \omega$ passing through the point $y$. Is this geometrical interpretation is correct?

Any help or hint will be greatly appreciated.