The prediction of the sea echo Doppler spectrum of VHF and HF radio waves i
s important for the ocean wave remote sensing by VHF and HF radars. The aut
hors extended the theory of the sea echo Doppler spectrum. In previous theo
ries it is assumed that the scale of the illuminated area is much larger th
an the dominant wavelength. However, the effect of the finite illuminated a
rea may not be negligible. The authors considered the effect to predict sec
ond-order sea echo Doppler spectrum and extended previous theories. Further
more, the authors developed the numerical technique to compute radar cross
sections of the extended theory. As a result, the agreement between measure
d and predicted Doppler spectra is improved.