  The concept of measurement in classical scattering is interpreted as an
overlap of a particle packet with some area in phase space that describes the
detector. Considering that usually we record the passage of particles at some
point in space, a common detector is described e.g. for one-dimensional systems
as a narrow strip in phase space. We generalize this concept allowing this
strip to be transformed by some, possibly non-linear, canonical transformation,
introducing thus a canonically transformed detector. We show such detectors to
be useful in the context of the inverse scattering problem in situations where
recently discovered scattering echoes could not be seen without their help.
More relevant applications in quantum systems are suggested.
