Homodyne Versus Heterodyne Detection Schemes

A distinction between homodyne and heterodyne detection must be made in optical scattering and diffraction experiments. Without careful treatment of the background, there is always the risk of mixed or unknown coherence conditions, and the diffusion coefficient determined from such data may be off by a factor of two. At least for the signal and background levels present in TDFRS, heterodyne detection is always superior to homodyne, especially since the heterodyne signal, contrary to the homodyne one, turns out to be very stable against perturbations and systematic errors. Even under nearly perfect homodyne conditions the tail of the decay curve is almost unavoidably heterodyne [34]. 

The intensity / as seen by the detector contains both homodyne and heterodyne contributions [34,38,39]  

Es is the electric field amplitude of the diffracted beam. Ec and Einc are the coherent and incoherent electric field amplitudes of the background intensity, respectively. 0 is the phase shift between the signal and the coherent background, and the phase of Ec is arbitrarily chosen to be zero. For convenience, the proportionality factor between E2 and / is set to unity. Sbom = E2 is the homodyne and Sbet = 2 ECES cos 0 the heterodyne signal. The total background is Jb=E2c + Efnc. 

The homodyne and heterodyne signals can be separated if two measurements with a phase shift of n between background and signal are combined according to 

In principle, the coherent background can be supplied as shown in Fig. 2a, where the reference beam is directed along the diffracted beam. The phase of the reference is directly controlled by means of a piezo-mounted mirror. 

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