  Remotely measuring subsurface water currents from imagery of the wave field
has become a much-used technique. We study the biases and errors in such
measurements due to spectral leakage, and suggest mitigating procedures.
Deviations between peak values in the three-dimensional wave spectrum and the
known dispersion relation in quiescent water are extracted and interpreted as
current-induced Doppler shifts, from which the sub-surface current is inferred.
The use of discrete Fourier transforms, however, introduces spectral leakage
between nearby frequency bins. Analysing synthetically generated wave data
adhering to realistic input spectra we show that although no current is in fact
present, spurious currents can be "measured" which can amount to a significant
fraction of the phase speed at the spectral peak. We analyse the effects of
data tapering, method of Doppler shift extraction, limited wavenumber and
frequency resolution, peakedness and angular width of the input spectrum, and
average misalignment between waves and Doppler shift velocity direction. The
narrower the input wave spectrum in frequency and/or direction, the greater the
biases become. The use of a window function reduces the severity in nearly all
cases, yet mitigates the effects of limited resolution more effectively in
space than in time. When a current is present the absolute biases remain
essentially unchanged, when waves and currents are roughly aligned tapering
much alleviates the concomitant biases, whereas in the case of a cross-current,
biases remain significant even for tapered data.
