  Absorption-free (also known as ``interaction-free'') measurement aims to
detect the presence of an opaque object using a test particle without that
particle being absorbed by the object. Here we consider semi-transparent
objects which have an amplitude $\alpha$ of transmitting a particle while
leaving the state of the object unchanged and an amplitude $\beta$ of absorbing
the particle. The task is to devise a protocol that can decide which of two
known transmission amplitudes is present while ensuring that no particle
interacts with the object. We show that the probabilities of being able to
achieve this are limited by an inequality. This inequality implies that
absorption free distinction between complete transparency and any partial
transparency is always possible with probabilities approaching 1, but that two
partial transparencies can only be distinguished with probabilities less than
1.
