  We experimentally study optical homodyne and heterodyne detections with a
same setup, which is flexible to manipulate the signal sideband modulation.
When the modulation only generate a single signal sideband, the light field
measurement by mixing the single sideband at $\omega_{0}+\Omega$ with a strong
local oscillator at the carrier frequency $\omega_{0}$ on a beam splitter
become balanced heterodyne detection. When two signal sidebands at
$\omega_{0}\pm\Omega$ are generated and the relative phase of the two sidebands
is locked, this measurement corresponds to optical balanced homodyne detection.
With this setup, we may confirm directly that the signal-to-noise ratio with
heterodyne detection is two-fold worse than that with homodyne detection. This
work will have important applications in quantum state measurement and quantum
information.
