We propose schemes for measuring the joint quantum state of a two-mode
optical field using balanced homodyne detection, thereby generalizing
earlier single-mode schemes. We distinguish between two cases-the cas
e where the two modes are spatially separable and the case where they
are nonseparable. For each case we present a generalization of the dir
ect sampling method of state reconstruction and point out that its adv
antages over inverse Radon methods are even greater here than in the s
ingle-mode case. In the case of two modes that cannot be separated we
propose a scheme in which a single balanced homodyne detector is used
for data collection.