Digitized contours on map and interpolate contour line to create surface

I have digitized the contours on a map and I want to recreate the surface by interpolating (using IDW) using these contour line. When I generate contours (extract) to see how well they match with the input parameters (digitized contours they are quite off. I set the interpolation for IDW with a P of 20, if I use 2 then bulls eyes form on the raster.
I am not sure if I am using the right approach. should convert the lines to points? Use a different interpolation method etc?