problem in cross-spectra calculation

[HelloKaito]

Hi! I'm a new learner in wave related subjects. I'm confused about 'sar_slc/processing.py' line 776, cross-spectra is caculated by intensity(L2)*np.conj(intensity) , the question is why 'df' is multiplied?
looking to your reply.

[agrouaze]

Hello @HelloKaito ,
We plan to remove the cross spectra computation fro xsarsea to have the code available in this repo : https://github.com/umr-lops/xsar_slc . Regarding your question, it is not easy to answer if you don't quote the code itself.
The cross spectrum are computed from complex image modulation (i.e. after a Gaussian low pass filtering).

[HelloKaito]

Hello, @agrouaze ,
here's the code which is related with the computation of cross-spectra:

xsarsea/src/xsarsea/sar_slc/processing.py

Lines 773 to 776 in 719d82b

	for l1 in range(nlooks):
	for l2 in range(l1, nlooks):
	df = float(looks_spec[{'look': l2}][freq_azi_dim].spacing * looks_spec[{'look': l2}][freq_rg_dim].spacing)
	xspecs[str(l2 - l1) + 'tau'].append(looks_spec[{'look': l2}] * np.conj(looks_spec[{'look': l1}]) * df)

In sentinel-1 OSW algorithm (page 25),cross-spectra is computed by multiplying intensity image of two sub-looks, as illustrated in the equation below,

1.My 1st question is why a additional'df' is multiplied in the code above?

2.The 2nd question is does complex image modulation equivalent to image detrending mentioned in the OSW algorithm (showed in the image below)? They are alike in computation.

Thanks a lot for your reply!

[HelloKaito]

@agrouaze Please help me when you'are available. TUT

[agrouaze]

I can't answer your question but @lanougue (author of this part of the code) should be able to answer.

[HelloKaito]

Hello @lanougue,
Please give me a hand about the above question.