Right (and that would be more efficient, I guess), but the Fourier transform of White Noise yields complex white noise with real and imaginary part such that th

Right (and that would be more efficient, I guess), but the Fourier transform of White Noise yields complex white noise with real and imaginary part such that their std deviation a and b obeys var_x = a^2 + b^2 (This follows from FFT being Unitary or Parveval's theorem), so each frequency component has sqrt(2)/2 times the (non-transformed) signal standard deviation. So simply generate two i.i.d. white noise fields with scaled variance (1/2). It's important to keep in mind when speaking of noise that we are referring to average values (or statistical values), e.g. although the power spectrum of white noise is on average flat, as we discussed it's really random (the expected amplitude spectrum in fact has average 0 anywhere, since it's also white noise!).