Adopting Equivalent Radar Cross Section (ERCS) as the Radiometric Measurement Quantity for SAR Images

May I answer with some questions?

• Which correction function should people use? (One way is described in the listed paper Reference Target Correction Based on Point Target SAR Simulation.). The procedure should certainly be the same so that different calibration teams arrive at compatible results, or not?

• Would you agree that we do not actually measure RCS? (phase and averaging play a role)

  Then how can we use reference targets whose RCS we know, but not the quantity value we are actually measuring?

Otherwise, I agree with your first point (an actual sphere has a frequency dependence), and it may be a good idea to reformulate this part of the proposal to avoid confusion with the aforementioned "theoretical sphere". Also, of course data should only be distributed calibrated, but the point here lies one step before: Different calibration bodies/teams using different but traceable references should arrive at the same calibration results, which is currently not ensured.

You have lost me with your statement about measuring rcs. The digital counts 'we measure' represent amplitude and phase of a radar echo. These counts can be related to various quantities related to the observed scene or target (e.g. rcs, sigma_0, polarimetric parameters) by means of data calibration. This process, if done properly, yields information related to the target only not the measuring system. In my experience this is a complicated job that required system knowledge and it is not something 'people' can do. ESA is in the Sentinel-1B commissioning phase and the above is demonstrated as we speak. The international commissioning team discovered many little details but gets in the end consistent results. I am not as pessimistic as you appears to be about the ability to resolve the calibration problem but indeed it needs a dedicated effort by experts. Perhaps a joined paper after the commissioning about the calibration process would be an idea.

Sorry for not being able to express myself any clearer... Let me respond foremost to your first remark because it is at the core of the discussion in this thread. You said:

The digital counts 'we measure' represent amplitude and phase of a radar echo. These counts can be related to various quantities related to the observed scene or target (e.g. rcs, sigma_0, polarimetric parameters) by means of data calibration."

I agree with the first sentence, but not the second. We do not actually measure RCS (or sigma_0 or similar quantities for distributed targets, which are simply RCS normalized by a reference area). This can be seen both from the principal equations (RCS vs. the SAR system equation, see attached image), but also by thinking about some examples:

• The calibration approach should work for any kind of SAR system, from low to high resolution. To take an extreme example: Consider an ultra wide band high-resolution SAR system with a relative bandwidth exceeding 100 % (airborne systems already exist). Now the RCS of any (distributed or point) target is in general frequency dependent. When we consider e.g. the backscatter of snow over a bandwidth of 10 GHz around a center frequency of 10 GHz, the backscatter varies by several dB (see exemplary plot on slide 6 in the ERCS CEOS presentation from 2015). Which RCS should be reported after calibration? In the SAR image, the spectral information is always reduced to a single value.

• Furthermore, this value actually depends on the SAR system as well. First, if we shift the center frequency, the measured "averaged" RCS (= ERCS) will change (again because of the general frequency dependence of the RCS). Second, if we modify our processor (mostly the type of apodization filter for improved side-lobe suppression), the measured "averaged" RCS (= ERCS) will change as well. This is all expected, but has not yet been considered for radiometric calibration.

• Besides the problem of "averaging" over frequency and angle, we also have the problem of phase. Our measurement result (after SAR processing) depends on the phase response (phase over frequency) of our target. Two targets with identical RCS (the phase response is not considered) may appear differently bright in a SAR image despite all calibration efforts, so we really do not measure RCS. Examples of targets with potentially identical RCSs but different phase responses are calibration transponders or moving targets, resulting in "smeared" impulse responses in the SAR image.

So to sum up, in SAR we have always measured something else than RCS (we call it ERCS), and there is no problem at all. The problem only starts to surface if we now tie our radiometric calibration targets to RCS, although our measurement quantity is not RCS. We need to agree on a way for going from RCS to ERCS so that radiometric calibrations give compatible results in all cases.

Dear Björn,
Our interesting discussion appears to go into a direction where the same message gets repeated in different wordings and I am afraid that it becomes a bit boring for the internet community at large.
I propose that we summarise our points of view and that the matter is further discussed in an appropriate forum such as CEOS.
It appears to me that we agree on the following:
What "we measure" with SAR is a complex response function involving amplitude and phase.
What we try to do is the characterise the measuring system (the SAR) in such a way that SAR processors can calibrate the response to produce calibrated products for the user community for example sigma_0 in the case of incoherent scattering by distributed targets. Ideally sigma_0 data products are independent of the SAR being used. In reality this goal cannot be reached due to target complexities such as partial coherence and wavelength dependence. However current SARs in orbit reach amazing calibration accuracies in the order of 0.1 dB. In terms of target phase response it is a similar story. By applying phase corrections very nice coherence values are achieved even with interferometry involving different sensors.
Where we may disagree is the use of the RCS concept. My position is the following:
Even before my time the RCS concept has been introduce to express a power ratio in terms of a surface measure (m squared). I found this concept in combination with the theoretical isotropic point target very useful particularly in addressing audiences without in-depth knowledge of EM theory and without a solid mathematical background.
However in the calibration business reference targets can only be an approximation of an ideal point target. Personally I am not a great fan of corner reflectors for radiometric calibration although they are great for phase calibration and achieving localisation accuracy.
In my opinion dedicated transponders are better for high accuracy but these devices have to be designed for a particular SAR and would obviously not work with all SARs. Their characteristics in terms of – amplitude & phase - angular response and frequency dependence have to be determined in detail to support amplitude and phase calibration. Transponder designs try to match the characteristics of a theoretical point target to simplify the corrections required within the operational angular and frequency range.
I agree with your statement that “we do not measure RCS” see above.
Where I disagree in the discussion is the way forward you propose to define an ERCS as a relation between the peak pixel intensity and the reference target. I may not interpret this properly but that is what your proposed definition says.
As you know we use for calibration purposes not the peak intensity but the integrated response of the reference target in the SAR image (scaled to sigma_0 or beta_0). I cannot help thinking that the proposal for an ERCS is a smoke screen that sweeps the full details of the SAR response (your equation) under the carpet. I believe that if “we do not measure RCS” we would not “measure your ERCS” either.
I found our public debate interesting and I am looking forward to the results of the discussion in the CEOS working group.

Thanks for your nice summary and your contribution to the discussion, Evert! It will help in reshaping the proposal. I am happy that we agree on the "we do not measure RCS" part though!

After a physical discussion between Björn and myself taking this discussion into account we drafted an updated proposal for which we opened a new thread:
https://www.loomio.org/d/vbESX9ud/updated-recommendation-adopting-equivalent-radar-cross-section-ercs-as-the-radiometric-measurement-quantity-for-sar-images